MohidWiki - User contributions [en]

Module Basin

2011-03-09T13:00:50Z

Federico: /* Main Processes */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The processes made in the Module Basin can be summarized as following:

* Reading entering data and grid construction
* Atmospheric processes in order to obtain the water column from the precipitation
*Call of [[Module PorousMedia]] in order to obtain the infiltration rate
*Update of the water column
*Call of [[Module Runoff]]
*Redistribution of the fluxes into the water body
*Output of the different components of the water flux

==Evapotranspiration==
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-09T12:59:04Z

Federico: /* Main Processes */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The processes made in the Module Basin can be summarized as following:

* Reading entering data and grid construction
* Atmospheric processes in order to obtain the water column from the precipitation.
*Call of [[Module PorousMedia]] in order to obtain the infiltration rate
*Update of the water column
*Call of [[Module Runoff]]
*Redistribution of the fluxes into the water body
*Output of the different components of the water flux

==Evapotranspiration==
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-09T12:58:30Z

Federico: /* Main Processes */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The processes made in the Module Basin can be summarized as following:

* Reading entering data and grid construction
* Atmospheric processes in order to obtain the water column from the precipitation.
*Call of [[Module Porous Media]] in order to obtain the infiltration rate
*Update of the water column
*Call of [[Module Runoff]]
*Redistribution of the fluxes into the water body
*Output of the different components of the water flux

==Evapotranspiration==
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-09T12:30:53Z

Federico: /* Main Processes */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The processes made in the Module Basin can be summarized as following:

* Entering data reading and basin Geometry construction
* Atmospheric processes in order to obtain the water column from the precipitation
*Call of module Porous media in order to obtain the infiltration rate
*Update of the water column
*Call of Module Runoff
*The fluxes are directed to the river

==Evapotranspiration==
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-09T11:38:25Z

Federico: /* Main Processes */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The processes made in the Module Basin can be summarized as following:

The scheme followed in the module Basin is the following:
The module atmoshpere is called to obatin the water column from the pracipitation
update the water column
Porous media
Infiltration
update water column
Runoff
River

==Evapotranspiration==
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-09T11:38:10Z

Federico: /* Main Processes */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The processes made in the Module Basin can be summarized as following:

The scheme followed in the module Basin is the following:
The module atmoshpere is called to obatin the water column from the pracipitation
update the water column
Porous media
Infiltration
update water column
Runoff
River

====Evapotranspiration====
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-09T11:36:47Z

Federico: /* Evapotranspiration */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
The scheme followed in the module Basin is the following:
The module atmoshpere is called to obatin the water column from the pracipitation
update the water column
Porous media
Infiltration
update water column
Runoff
River

====Evapotranspiration====
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-08T19:58:19Z

Federico: /* Overview */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotranspiration, runoff and infiltration.

==Main Processes==
===Evapotranspiration===
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-08T19:57:39Z

Federico: /* Overview */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The final results of this module is the different water fluxes due to evapotrnspiration, runoff and infiltration.

==Main Processes==
===Evapotranspiration===
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module Basin

2011-03-08T18:33:44Z

Federico: /* Overview */

==Overview==
Module Basin is a connection among the different modules of Mohid-Land. Indeed it manages the entering data, namely the water column, that is updated after each call of each module. The aim of Module Basin is to obtained the different water fluxes due to evapotrnspiration, runoff and infiltration.

==Main Processes==
===Evapotranspiration===
Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

Potential evapotranspiration is calcuçtaed made in module Basin. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the [[Module PorousMedia]].

==Other Features==

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:35:34Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

'''Horizontal Direction X'''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot ComputeFace_{(i,j,k)}-Flux_{(i,j+1,k)}\cdot ComputeFace_{(i,j+1,k)}\cdot \Delta t) V_{cell}</math>

'''Horizontal Direction Y'''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot ComputeFace_{(i,j,k)}-FluxV_{(i+1,j,k)}\cdot ComputeFace_{(i+1,j,k)})\cdot \Delta t)\cdot V_{cell}</math>

'''Vertical Direction W'''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot ComputeFace_{(i,j,k})-FluxW_{(i,j,k+1)}\cdot ComputeFace_{(i,j,k+1}))\cdot \Delta t)\cdot V_{cell}</math>

'''Transpiration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Evaporation Flux'''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Infiltration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}\cdot(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|

|''<math>\theta</math>'' || is the water content (m 3/m 3)
|-
|''<math>V_{cell}</math>'' || is the cell volume (m 3)
|-
|''<math>Area_{cell}</math>'' || is the cell area (m 2)
|-
|''ComputeFace'' || is the computed face (dimensionless)
|-
|''<math>\Delta t</math>'' || is the time step (s)
|-
|''FluxX'' || is the flux in X direction (m 3/s)
|-
|''FluxV'' || is the flux in Y direction (m 3/s)
|-
|''FluxW'' || is the flux in W direction (m 3/s)
|-
|''TranspFlux'' || is the transpiration flux (m 3/s)
|-
|''EvapFlux'' || is the evaporation flux (m 3/s)
|-
|''UnsatK'' || is unsaturated conductivity (m /s)
|-
|''Imp'' || is the percentage of impermeable soil of the cell (dimensionless)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:34:28Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

'''Horizontal Direction X'''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot ComputeFace_{i,j,k}-Flux_{(i,j+1,k)}\cdot ComputeFace_{i,j+1,k}\cdot \Delta t) V_{cell}</math>

'''Horizontal Direction Y'''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot ComputeFace_{i,j,k}-FluxV_{(i+1,j,k)}\cdot ComputeFace_{i+1,j,k})\cdot \Delta t)\cdot V_{cell}</math>

'''Vertical Direction W'''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot ComputeFace_{i,j,k}-FluxW_{(i,j,k+1)}\cdot ComputeFace_{i,j,k+1})\cdot \Delta t)\cdot V_{cell}</math>

'''Transpiration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Evaporation Flux'''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Infiltration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}\cdot(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|

|''<math>\theta</math>'' || is the water content (m 3/m 3)
|-
|''<math>V_{cell}</math>'' || is the cell volume (m 3)
|-
|''<math>Area_{cell}</math>'' || is the cell area (m 2)
|-
|''ComputeFace'' || is the computed face (dimensionless)
|-
|''<math>\Delta t</math>'' || is the time step (s)
|-
|''FluxX'' || is the flux in X direction (m 3/s)
|-
|''FluxV'' || is the flux in Y direction (m 3/s)
|-
|''FluxW'' || is the flux in W direction (m 3/s)
|-
|''TranspFlux'' || is the transpiration flux (m 3/s)
|-
|''EvapFlux'' || is the evaporation flux (m 3/s)
|-
|''UnsatK'' || is unsaturated conductivity (m /s)
|-
|''Imp'' || is the percentage of impermeable soil of the cell (dimensionless)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:28:51Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

'''Horizontal Direction X'''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

'''Horizontal Direction Y'''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot Area_{cell}-FluxV_{(i+1,j,k)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

'''Vertical Direction W'''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot Area_{cell}-FluxW_{(i,j,k+1)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

'''Transpiration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Evaporation Flux'''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Infiltration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|
|''<math>V_{cell}</math>'' || is the cell volume(m 3)
|-
|''<math>Area_{cell}</math>'' || is the cell area (m 2)
|-
|''<math>\Delta t</math>'' || is the time step (s)
|-
|''FluxX'' || is the flux in X direction (m 3/s)
|-
|''FluxV'' || is the flux in Y direction (m 3/s)
|-
|''FluxW'' || is the flux in W direction (m 3/s)
|-
|''TranspFlux'' || is the transpiration flux (m 3/s)
|-
|''EvapFlux'' || is the evaporation flux (m 3/s)
|-
|''UnsatK'' || is unsaturated conductivity (m /s)
|-
|''Imp'' || is the percentage of impermeable soil of the cell (dimensionless)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:12:43Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

'''Horizontal Direction X'''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

'''Horizontal Direction Y'''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot Area_{cell}-FluxV_{(i+1,j,k)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

'''Vertical Direction W'''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot Area_{cell}-FluxW_{(i,j,k+1)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

'''Transpiration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Evaporation Flux'''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

'''Infiltration Flux'''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:12:03Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

'''Horizontal Direction X'''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

''Horizontal Direction Y''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot Area_{cell}-FluxV_{(i+1,j,k)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Vertical Direction W''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot Area_{cell}-FluxW_{(i,j,k+1)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Transpiration Flux''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Evaporation Flux''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Infiltration Flux''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:11:48Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

'Horizontal Direction X'

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

''Horizontal Direction Y''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot Area_{cell}-FluxV_{(i+1,j,k)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Vertical Direction W''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot Area_{cell}-FluxW_{(i,j,k+1)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Transpiration Flux''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Evaporation Flux''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Infiltration Flux''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:11:18Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

''Horrizontal Direction X''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

''Horrizontal Direction Y''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot Area_{cell}-FluxV_{(i+1,j,k)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Vertical Direction W''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot Area_{cell}-FluxW_{(i,j,k+1)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Transpiration Flux''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Evaporation Flux''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Infiltration Flux''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:10:19Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

''Horrizontal Direction X''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

''Horrizontal Direction Y''

<math>\theta=(\theta\cdot V_{cell}+(FluxV_{(i,j,k)}\cdot Area_{cell}-FluxV_{(i+1,j,k)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Vertical Direction W''

<math>\theta=(\theta\cdot V_{cell}+(FluxW_{(i,j,k)}\cdot Area_{cell}-FluxW_{(i,j,k+1)}\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Transpiration Flux''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Evaporation Flux''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux_{(i,j,k)}\Delta t)\cdot V_{cell}</math>

''Infiltration Flux''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T20:07:03Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the water fluxes a balance on the water volume of each cell is apply in order to obtain the new water content <math>\theta</math>. The balance applied is the following:

''Horrizontal Direction X''

<math>\theta=(\theta\cdot V_{cell}+(FluxU_{(i,j,k)}\cdot Area_{cell}-Flux_{(i,j+1,k)}\cdot Area_{cell})\cdot \Delta t) V_{cell}</math>

''Horrizontal Direction Y''

<math>\theta=(\theta\cdot V_{cell}+(FluxV(i,j,k)\cdot Area_{cell}-FluxV(i+1,j,k)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Vertical Direction W''

<math>\theta=(\theta\cdot V_{cell}+(FluxW(i,j,k)\cdot Area_{cell}-FluxW(i,j,k+1)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

''Transpiration Flux''

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux(i,j,k)\Delta t)\cdot V_{cell}</math>

''Evaporation Flux''

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux(i,j,k)\Delta t)\cdot V_{cell}</math>

''Infiltration Flux''

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

The value of <math>\theta</math> so obtained is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T18:08:32Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the value of the velocity in each cell the evapotranspiration flux and the fluxes in the X,Y,Z direction are calculated. In particular are evaluated the volume associated to each flux in order to obtain a new value of <math>\theta</math>. This value is compared with one used in the volumes calculation and the iterative process stop when:

<math>\theta=(\theta\cdot V_{cell}+(FluxU(i,j,k)\cdot Area_{cell}-FluxV(i,j+1,k)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}+(FluxV(i,j,k)\cdot Area_{cell}-FluxV(i+1,j,k)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}+(FluxW(i,j,k)\cdot Area_{cell}-FluxW(i,j,k+1)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux(i,j,k)\Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux(i,j,k)\Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T18:05:00Z

Federico: /* Iteration Process */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the value of the velocity in each cell the evapotranspiration flux and the fluxes in the X,Y,Z direction are calculated. In particular are evaluated the volume associated to each flux in order to obtain a new value of <math>\theta</math>. This value is compared with one used in the volumes calculation and the iterative process stop when:

<math>\theta=(\theta\cdot V_{cell}+(FluxU(i,j,k)\cdot Area_{cell}-FluxV(i,j+1,k)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}+(FluxV(i,j,k)\cdot Area_{cell}-FluxV(i+1,j,k)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}+(FluxW(i,j,k)\cdot Area_{cell}-FluxW(i,j,k+1)\cdot Area_{cell})\cdot \Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}-(TranspFlux(i,j,k)\Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}-(EvapFlux(i,j,k)\Delta t)\cdot V_{cell}</math>

<math>\theta=(\theta\cdot V_{cell}-(UnsatK\cdot Area_{cell}(1-Imp) \Delta t)\cdot V_{cell}</math>

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T17:05:48Z

Federico: /* References */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the value of the velocity in each cell the evapotranspiration flux and the fluxes in the X,Y,Z direction are calculated. In particular are evaluated the volume associated to each flux in order to obtain a new value of <math>\theta</math>. This value is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and Martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module PorousMedia

2011-03-07T17:05:15Z

Federico: /* References */

==Overview==
Module Porous Media is based on the [[Finite Volume Method]] in order to take in account the non-linear behavior of the soil. This module allows the calculation of the water fluxes in a porous media; in particular the infiltration flow is obtained from the potential water column available for this process. The potential water column is given by the [[Module Basin]] as reported below:

<math>PIC=TF+IWC</math>

where:
:{|
| ''PIC'' || is the Potential Infiltration column (m)
|-
| ''TF'' || Throughfall is the percentage of the rain that reaches the soil (m)
|-
| ''IWC'' || is the Initial Water column (m)
|}

The infiltration flows is calculated by the Buckingham-Darcy equation (Jury et al,1991)

==Main Processes==
===Water flow===
Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that the forces of inertia are almost zero; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).

<math>J=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} \right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1 \right )\,\,\,\,(1.1)\\ </math>

where:
:{|
|''J'' || is the water velocity at the cell interface (m/s)
|-
| ''H'' || is the hydraulic head (m)
|-
| ''θ'' || is the water content (m3/m3)
|-
| ''K''|| is the hydraulic conductivity (m/s)
|}

In particular the hydraulic head is given by the formula:

<math>H=h+p+z\,\,\,\,(1.2)</math>

where:
:{|
|-
| ''h'' || is the hydraulic head (m)
|-
| ''p'' || is hydrostatic pressure (m)
|-
| ''z''|| is the topography (m)
|-
|}

The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two layers:

*Saturated soil <math>\Longrightarrow</math> The soil pores are filled by water

*Unsaturated one <math>\Longrightarrow</math> The soil pores are filled by water and air

In the first case the equation of Buckingham Darcy is simplified to the Darcy law and the parameter associated for its resolution are connected with the saturated layer. On the other hand for the resolution of the equation (1.1) a description of the characteristics of the the unsaturated layer is needed.

==Vadose Zone==

Many vadose flow and transport studies require description if unsaturated soil hydraulic proprieties over a wide range of pressure head. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

===Water content===

Water content is the quantity of water contained in the soil (called '''soil moisture'''). It is given as a volumetric basis and it is defined mathematically as:

:<math>\theta = \frac{V_w}{V_T}\hspace{5cm}(1.3) </math>

:<math>V_T = V_s + V_v = V_s + V_w + V_a\hspace{1.6cm}(1.4)</math>

where:
:{|
| ''<math>\theta</math>'' || is water content (m 3/m 3)
|-
|''<math>V_w</math> '' || is the volume of water (m s3)
|-
| ''<math>V_T</math>'' || is the total volume (m 3)
|-
| ''<math>V_s</math>'' || is the soil volume (m 3)
|-
| ''<math>V_a</math>'' || is the air space (m 3)
|}

Once determined the aquifer level ('''water table''') the water content is associated at each cells by the following criteria:
:{|
*If the cell is located above the water table <math>\theta=\theta_{s}</math>
|-
*If the cell is located over the water table <math>\theta=\theta_{ns}</math>
|}

where:
:{|
| ''<math>\theta=\theta_{s}</math>'' || is the water content in the saturated soil (m3/m3)
|-
| ''<math>\theta=\theta_{ns}</math>'' || is the water content in the non saturated soil (m3/m3)
|-
|}

The water content in the non saturated soil can be associated with observed data, if these are not available it is imposed by default the water content equal to the [[Field Capacity]]. In order to calculate this parameter by the equation (1.7) the evaluation of the suction head is needed :

:<math> h=-DWZ\cdot 0.5\hspace{2cm}for\,\, the\,\, cells\,\, immediately\,\, above\,\, the\,\, water\,\, table \hspace{5cm} (1.5)</math>

:<math>h=-(-DZZ-h)\hspace{1.5cm}for\,\, the\,\, other\,\, cells\hspace{9.75cm} (1.6) </math>

[[Image:Figure05.jpg|thumb|center|300px|Figure 1: Suction Head Calculation]]

As shown in the picture the suction head is calculated in order to maintain the same total head (H=z+p+h) in the cells in agreement with the field capacity definition.

===Water retention===
The model use for characterizing the shape of water retention curves is the van Genuchten model:

:<math>\theta(h) = \theta_r + \frac{\theta_s - \theta_r}{\left[ 1+(\alpha |h|)^n \right]^{1-1/n}}\hspace{0.5cm}\Longrightarrow\hspace{0.5cm}h(\theta)=\left |\frac{(S_{E}^{-1/n}-1)^{1/n}}{\alpha} \right |\hspace{3cm}(1.7)</math>

:<math>S_{E}=\frac{\theta-\theta_{r}}{\theta_{s}-\theta_{r}}\hspace{11cm}(1.8)</math>

where:
:{|
|''<math>\theta(h)</math>'' || is the the water retention curve (m 3/m 3)
|-
| ''<math>\theta_s</math>'' || is the saturated water content (m 3/m 3)
|-
| ''<math>\theta_r</math>'' || is the residual water content (m 3/m 3)
|-
| ''h''|| is the suction head (m)
|-
| ''<math>\alpha</math>'' || is related to the inverse of the air entry (m -1)
|-
| ''n''|| is a measure of the pore-size distribution n>1 (dimensionless)
|-
| ''<math>S_{E}</math>''|| is the effective saturation (dimensionless)
|}

===Saturated and Unsaturated Conductivity===

The saturated conductivity is given depending on the type of soil; instead the unsaturated conductivity is obtained from the suction head by the Maulem model:

<math>K(\theta)=K_{s}\cdot Se^{L}\cdot (1-(1-Se^{1/m})^{m})^{2}</math>

where:
:{|
|''<math>K(\theta)</math>'' || is the unsaturated conductivity (m/s)
|-
| ''<math>K_{s}</math>'' || is the saturated conductivity(m/s)
|-
| ''L'' || empirical pore-connectivity (m)
|-
| ''m''|| m=1-1/n(dimensionless)
|}

==Evapotranspiration==

Some water may disappear from the soil because of the evaporation and transpiration processes, which become a sink in soil water profile. These two processes, currently named Evapotranspiration may be modeled using the Penmann Monteith equation.

<math> \overset{\text{Energy flux rate}}{\lambda_v E=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a }{\Delta + \gamma \left ( 1 + g_a / g_s \right)}}~ \iff ~ \overset{\text{Volume flux rate}}{ET_o=\frac{\Delta R_n + \rho_a c_p \left( \delta q \right) g_a } { \left( \Delta + \gamma \left ( 1 + g_a / g_s \right) \right) \lambda_v }}
</math>

:''λ''v = Latent heat of vaporization. Energy required per unit mass of water vaporized. (J/g)
:''L''v = Volumetric latent heat of vaporization. Energy required per water volume vaporized. (''L''v = 2453 MJ m-3)

:''E'' = Mass water evapotranspiration rate (g s-1 m-2)
:''ET''o = Water volume evapotranspired (m3 s-1 m-2)

:Δ = Rate of change of saturation specific humidity with air temperature. (Pa K-1)
:''R''n = Net irradiance (W m-2), the external source of energy flux
:''c''p = Specific heat capacity of air (J kg-1 K-1)
:''ρ''a = dry air density (kg m-3)
:δ''e'' = vapor pressure deficit, or specific humidity (Pa)
:''g''a = Hydraulic conductivity of air, atmospheric conductance (m s-1)
:''g''s = Conductivity of stoma, surface conductance (m s-1)
:''γ'' = Psychrometric constant (''γ'' ≈ 66 Pa K-1)

All of these calculations about potential evapotranspiration are made in module Basin in MohiLand model. However, not all of the potential water that can be evaporated or transpirated will be in fact removed from the soil. The water that will really leave the soil through these processes is calculated in the Porous Media module.
In Figure below it can be seen that the actual transpiration and evaporation are calculated in Porous Media module of MohidLand. The actual evaporation, which happens only at the soil surface, is calculated based on a pressure head limit imposed by the user. It allows the model to not evaporate any surface water, even if it is available, when the soil is very far way from the saturation point.

[[Image:evapotranspiration fluxogram.jpg|thumb|center|400px|Evapotranspiration fluxogram in Mohid Land model]]

==Iteration Process==

Once obtained the value of the velocity in each cell the evapotranspiration flux and the fluxes in the X,Y,Z direction are calculated. In particular are evaluated the volume associated to each flux in order to obtain a new value of <math>\theta</math>. This value is compared with one used in the volumes calculation and the iterative process stop when:

<math>(\theta^{'})-(\theta^{new})<\,\, Tolerance\hspace{3cm} (1.9) </math>

where:

:{|
|''<math>\theta^{'}</math>'' || is the water content of the previous iteration (m 3/m 3)
|}

If the equation (1.9) is not satisfy the temporal step is divided in half and the new value of <math>\theta</math> is used for solving the equation (1.7) for restarting the calculation process. The iteration process is stoped when the tolerance desired is reached.

[[Image:Figure06.jpg|thumb|center|300px|Figure 2: Time step reduction]]

==Other Features==
===How to Generate Info needed in Porous Media===
====SoilMap====
Model needs to know soil ID in each cell and layer to pick hydraulic properties from that type of soil.

Options:
* Constant value
* Soil Grid. One possible option is to associate with soil shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the soil shape file and iii) the corespondence between soil codes and soil ID defined in data file.

Soil ID must be defined in [[Module_FillMatrix|Module FillMatrix]] standards for each soil horizon defined (grid example):
<beginhorizon>
KLB : 1
KUB : 10

<beginproperty>
NAME : SoilID
DEFAULTVALUE : 1
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\SoilID200m.dat
<endproperty>

<beginproperty>
<endproperty>
..
<endhorizon>

'''Remarks'''

All the soil ID's appearing in the soil grid(s) must be defined in the PorousMedia data file in terms of hydraulic properties:
<beginsoiltype>
ID : 1
THETA_S : 0.3859
THETA_R : 0.0476
N_FIT : 1.39
SAT_K : 3.5556e-6
ALPHA : 2.75
L_FIT : 0.50
THETA_CV_MIN : 0.2844
THETA_CV_MAX : 0.3791
<endsoiltype>

<beginsoiltype>
ID : 2
...
<endsoiltype>
...

====Soil Bottom====
The soil depth must be known by the model. This is computed by the model from terrain altitude (topography) and soil bottom altitude. As so, a soil bottom grid is needed.

Options:
* Grid File.
Soil depth (and soil bottom altitude, the effective grid needed) can be defined with a constant depth or estimated from slope [[HOW TO SoilBottom LINK]].

Define the grid just generated, in the porous media data file with:
BOTTOM_FILE : ..\..\GeneralData\PorousMedia\BottomLevel.dat

====Water Level====
Options:
*Grid File.
The water table altitude represents the initial altitude of the water table.
It is recommended to do a spin-up run to estabilize water level and then do a continuous simulation starting with the final water table achieved.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginwaterlevel>
NAME : waterlevel
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 0
FILENAME : ..\..\GeneralData\PorousMedia\WaterLevel0.50.dat
<endwaterlevel>

====Impermeability====
Impermeability values (0 - completely permeable, 1 - impermeable) must be provided.

Options:
* Constant Value.
* Grid File. One possible option is to associate with land use shape file. In this case can use MOHID GIS going to menu [Tools]->[Shape to Grid Data] and provide: i) the grid (model grid), ii) the land use shape file and iii) the corespondence between land use codes and Impermeability values.
Use the following blocks with [[Module_FillMatrix|Module FillMatrix]] standards:
<beginimpermeablefraction>
NAME : impermeablefraction
INITIALIZATION_METHOD : ASCII_FILE
DEFAULTVALUE : 0
REMAIN_CONSTANT : 1
FILENAME : ..\..\GeneralData\PorousMedia\AreaImpermeavel.dat
<endimpermeablefraction>

==Outputs==

==References ==
*Jury,W.A.,Gardner,W.R.,Gardner,W.H., 1991,Soil Physics
*Van Genuchten, M.T., A closed form equation for predicting the hydraulic conductivity of unsaturated soils
*Wu,J.,Zhang, R., Gui,S.,1999, Modelling soil water movement with water uptake by roots, Plant and soil 215: 7-17
*Marcel G.Schaap and martinus Th. van Genuchten, A modified Maulem van Genuchten Formulation for Improved Description of Hydraulic Conductivity
Near Saturation, 16 December 2005

==Data File ==

===Keywords===
Keywords read in the Data File

Keyword : Data Type Default !Comment

BOTTOM_FILE : char - !Path to Bottom Topography File
START_WITH_FIELD : logical 1 !Sets Theta initial Field Capacity
CONTINUOUS : logical 0 !Continues from previous run
STOP_ON_WRONG_DATE : logical 1 !Stops if previous run end is different from actual
!Start
OUTPUT_TIME : sec. sec. sec. - !Output Time
TIME_SERIE_LOCATION : char - !Path to File which defines Time Series
CONTINUOUS_OUTPUT_FILE : logical 1 !Writes "famous" iter.log
CONDUTIVITYFACE : integer 1 !Way to interpolate conducivity face
!1 - Average, 2 - Maximum, 3 - Minimum, 4 - Weigthed
HORIZONTAL_K_FACTOR : real 1.0 !Factor for Horizontal Conductivity = Kh / Kv
CUT_OFF_THETA_LOW : real 1e-6 !Disables calculation when Theta is near ThetaR
CUT_OFF_THETA_HIGH : real 1e-15 !Set Theta = ThetaS when Theta > ThetaS - CUT_OFF_THETA_HIGH
MIN_ITER : integer 2 !Number of iterations below which the DT is increased
MAX_ITER : integer 3 !Number of iterations above which the DT is decreased
LIMIT_ITER : integer 50 !Number of iterations of a time step (for restart)
THETA_TOLERANCE : real 0.001 !Converge Parameter
INCREASE_DT : real 1.25 !Increase of DT when iter < MIN_ITER
DECREASE_DT : real 0.70 !Decrease of DT when iter > MAX_ITER

<beginproperty>
NAME : Theta / waterlevel

see Module FillMatrix for more options

<endproperty>

===Sample===

Some keywords of the PorousMedia input file:

<beginsoiltype>
*Saturated water content
THETA_S : 0.55

*residual water content
THETA_R : 0.1

*N of Van Genuchten: 1.5(clay) to 4.5 (sandy)
N_FIT : 1.15

*Saturated hydraulic conductivity
SAT_K : 1.39e-8

*alpha of Van Genuchten: 0.005 (clay) - 0.035 (sandy)
ALPHA : 0.02

*L of Mualem - Van Genuchten (mostly 0.5)
L_FIT : 0.50
<endsoiltype>

[[Category:MOHID Land]]

Module Runoff

2011-03-07T16:09:01Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula (1.3) are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages
*http://www.hkh-friend.net.np/rhdc/training/lectures/HEGGEN/Tc_3.pdf

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:08:43Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula (1.3) are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages
*[http://www.hkh-friend.net.np/rhdc/training/lectures/HEGGEN/Tc_3.pdf]

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:07:22Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula (1.3) are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages
*[[http://www.hkh-friend.net.np/rhdc/training/lectures/HEGGEN/Tc_3.pdf]]

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:05:42Z

Federico: /* Calculated Flows */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula (1.3) are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:05:19Z

Federico: /* Overview */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:05:04Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:04:53Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* Hubert Chanson|Chanson, H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:04:38Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
* [[Hubert Chanson|Chanson]], H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:04:24Z

Federico: /* How To Generate Manning Coefficients */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

== Outputs==

== References ==
*Brown, Rebecca (2006). "Size of the Moon," ''Scientific American'', 51(78).
*Miller, Edward (2005). ''The Sun''. Academic Press.

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:02:21Z

Federico: /* Notes */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

The sun is pretty big,<ref>Miller 2005, p. 1.</ref> but the moon is not so big.<ref>Brown 2006, p. 2.</ref> The sun is also quite hot.<ref>Miller 2005, p. 3.</ref>

== Outputs==

== References ==
*Brown, Rebecca (2006). "Size of the Moon," ''Scientific American'', 51(78).
*Miller, Edward (2005). ''The Sun''. Academic Press.

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T16:01:34Z

Federico: /* Outputs */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

The sun is pretty big,<ref>Miller 2005, p. 1.</ref> but the moon is not so big.<ref>Brown 2006, p. 2.</ref> The sun is also quite hot.<ref>Miller 2005, p. 3.</ref>

== Notes ==
{{Reflist}}

== References ==
*Brown, Rebecca (2006). "Size of the Moon," ''Scientific American'', 51(78).
*Miller, Edward (2005). ''The Sun''. Academic Press.

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Template:Reflist

2011-03-07T16:01:23Z

Federico: New page: <ref>Miller 2005, p. 1.</ref>

[[<ref>Miller 2005, p. 1.</ref>]]

Help:Contents

2011-03-07T16:00:55Z

Federico: New page: Link title

[[Link title]]

Module Runoff

2011-03-07T15:59:45Z

Federico: /* General */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T15:57:44Z

Federico: /* Manning Equation */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation <ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> :

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References==
<references/>
===General===
* [[Hubert Chanson|Chanson]], H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)
* Walkowiak, D. (Ed.) ''Open Channel Flow Measurement Handbook'' (2006) Teledyne ISCO, 6th ed., ISBN 0962275735.

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T15:56:12Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References==
<references/>
===General===
* [[Hubert Chanson|Chanson]], H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)
* Walkowiak, D. (Ed.) ''Open Channel Flow Measurement Handbook'' (2006) Teledyne ISCO, 6th ed., ISBN 0962275735.

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T15:54:40Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References==
<references/>

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T15:21:24Z

Federico: /* Overview */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation <ref name="Miller2005p23" />.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References==
{{Reflist|refs=
<ref name="Miller2005p23">Miller, Edward.''The Sun''. Academic Press, 2005, p. 23.</ref>
<ref name="Miller2005p34">Miller, Edward.''The Sun''. Academic Press, 2005, p. 34.</ref>
<ref name="Brown2006">Brown, Rebecca. "Size of the Moon," ''Scientific American,'' 51(78):46</ref>
}}

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T15:20:41Z

Federico: /* References */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References==
{{Reflist|refs=
<ref name="Miller2005p23">Miller, Edward.''The Sun''. Academic Press, 2005, p. 23.</ref>
<ref name="Miller2005p34">Miller, Edward.''The Sun''. Academic Press, 2005, p. 34.</ref>
<ref name="Brown2006">Brown, Rebecca. "Size of the Moon," ''Scientific American,'' 51(78):46</ref>
}}

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:45:39Z

Federico: /* Calculated Flows */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|upright=2.0|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|upright=2|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|upright=2|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:43:06Z

Federico: /* Slope */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.4cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:42:33Z

Federico: /* Slope */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.5cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5.1cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5.1cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.5cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:41:52Z

Federico: /* Manning Equation */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5.7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.4cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.5cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:41:30Z

Federico: /* Manning Equation */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {6cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.4cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.5cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:41:07Z

Federico: /* Manning Equation */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {5cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.4cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.5cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:40:24Z

Federico: /* Manning Equation */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {7cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.4cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.5cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]

Module Runoff

2011-03-07T14:36:41Z

Federico: /* Manning Equation */

==Overview==
Module Runoff allows the calculation of the overland surface runoff over a regular structured grid as function of the water column and terrain slope. The water column, namely the water located above the terrain, is given by the [[Module Basin]] where the precipitation is converting into a water column considering the losses due to the evapotranspiration and the infiltration processes. In particular the overland flow is evaluated by the Manning’s equation.

==Main Processes==
===Manning Equation===

The overland surface runoff is calculated at the interface of the grid cells and it is obtained by applying the Manning's equation:

:<math>Q=\frac{1}{n}\cdot A\cdot R_{h}^{2/3}\cdot s^{1/2}\hspace {3cm}(1.1)</math>

where:
:{|
| ''Q'' || is the overland flow (m3/s)
|-
| ''A'' || is the area of the cross-section (m2)
|-
| ''n'' || is the Manning coefficient (s/m1/3)
|-
| ''Rh''|| is the hydraulic radius (m)
|-
| ''S'' || is the slope of the water surface (m/m)
|}

In order to apply the Manning's equation each grid cell is considered as an open channel as shown in the scheme below.

[[Image:Figure00.jpg|thumb|center|upright=8.0|Figure 1: Cell scheme]]

where:
:{|
| ''h'' || is the water column (m)
|-
| ''w'' || is the cell width (m)
|}

===Hydraulics radius===

The hydraulic radius is evaluated by the formula:

:<math>\[R_{h}=\frac{w\cdot h}{w+2\cdot h}\hspace {6.8cm}(1.2)</math>

In according with the Figure 1 the width is 'much' grater than the water column (w>>h) and the hydraulic radius can be considered only Rh=h. Therefore the Manning's equation can be simplified as:

:<math>\[Q=\frac{1}{n}\cdot w\cdot h^{5/3}\cdot s^{1/2}\hspace {5.8cm}(1.3)</math>

===Slope===

The slope (s) is calculated by the difference of the water levels at the extremities of the considered cell:

:<math>\[H(i,j)=\h(i,j)+T(i,j)\hspace {5.4cm}(1.4)</math>

where:
:{|
|-
|''H'' || is the water level (m)
|-
| ''h(i,j)'' || is the water column (m)
|-
| ''T(i,j)'' || is the Topography (m)
|-
| ''j'' || is X direction
|-
| ''i'' || is Y direction
|}

:<math>\[s_{x}=\frac{H(i,j-1)-H(i,j)}{DZX}\hspace {5cm}(1.5)</math>

where:
:{|
|-
|''sx'' || is the slope in the X direction (m)
|-
| ''H(i,j-1)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZX'' || is width of the cell in the X direction (m)
|}

:<math>\[s_{y}=\frac{H(i-1,j)-H(i,j)}{DZY}\hspace {5cm}(1.6)</math>

where:
:{|
|''sy'' || is the slope in the Y direction (m)
|-
| ''H(i-1,j)'' || is the water column at the left face of the cell (m)
|-
| ''H(i,j)'' || is the water column at the right face of the cell (m)
|-
| ''DZY'' || is width of the cell in the X direction (m)
|}

In order to take in account the limitation given by the Manning's equation (1.1)[it tends to overestimate the flow velocity when solpe > 0.04] , the slope value obtained by the formulas (1.5) and (1.6) it is subsequently adjusted by the following function:

:<math>s= 0.05247 + 0.06363 \cdot s - 0.182\cdot e^{(-62.38\cdot s)}\hspace {2.5cm}(1.7)</math>

where:
:{|
|''s'' || is the slope (m)
|}

===Manning cofficient===

The Manning coefficient is derived from the land use map. Indeed by using a GIS program it is possible to associate at each cell a land use class in order to obtain by the support of an abacus a Manning coefficent value.

===Calculated Flows===

The flows obtained by the formula [3] are diveded into flows in X direction and Y direction according with the Figure 2.

[[Image:Figure02.jpg|thumb|center|250px|250px|Figure 2:Flow directions]]

In the eventuality presence of a river in the basin analyzed it is possible to obtain two different configurations:

:{|
* Flow to the river when the water level of the river is lower that soil one
|-

|-
[[Image:Figure03.jpg|thumb|center|1000px|500px|Figure 3: Flow to the river]]
|-
|-
* Flow from the river when the water level is higher than the soil one
|-
|-
[[Image:Figure04.jpg|thumb|center|500px|500px|Figure 4: Flow from the river]]

|}

==Other Features==
===How To Generate Manning Coefficients===
Manning coefficients must be provided in runoff data file.

Options:
* Use a constant value
* Define a Manning's grid: One possible option is to associate Manning with land use classes (shape file). In this case can use MOHID GIS going to menu [Tools] <math>\Longrightarrow </math> [Shape to Grid Data] and provide:
:{|
|(i) the grid (model grid)
|-
|ii) the land use shape file
|-
| iii) the corespondence between land use codes and Manning
|}
Use Manning inicialization with [[Module_FillMatrix|Module FillMatrix]] standards in the block:
<BeginOverLandCoefficient>
FILE_IN_TIME : NONE
INITIALIZATION_METHOD : ASCII_FILE
REMAIN_CONSTANT : 1
DEFAULTVALUE : 0.08
FILENAME : ..\..\GeneralData\Runoff\Mannings200m_v2.dat
<EndOverLandCoefficient>

==Outputs==

==References ==

==Data File ==

===Keywords===

===Sample===

[[Category: MOHID Land]]