Ground evaporation formula (Water Overlay)

Underground evaporation is calculated per cell.

For all underground evaporation calculation, the ground water depth at time t is used.

$d_{gw,t}=b_{s}-w_{g,t}$

Feddes oxygen stress factor:

$f_{o}={\begin{cases}1.0&{\text{if }}d_{gw,t}{\text{ is }}\geq d_{r,3}\\{\frac {d_{gw,t}-d_{r,4}}{d_{r,3}-d_{r,4}}}&{\text{if }}d_{gw,t}{\text{ is }}\geq d_{r,4}\\0.0&{\text{otherwise}}\end{cases}}$

Feddes saturated zone root update factor:

$f_{s}={\begin{cases}0.0&{\text{if }}d_{gw,t}{\text{ is }}\geq d_{r,1}\\1.0-{\frac {d_{gw,t}-d_{r,2}}{d_{r,1}-d_{r,2}}}&{\text{if }}d_{gw,t}{\text{ is }}\geq d_{r,2}\\1.0&{\text{otherwise}}\end{cases}}$

Max potential evaporation:

$E_{max}=f_{t}\cdot E_{w,t}\cdot f_{o}$

Evaporation unsaturated:

$E_{u}={\begin{cases}0.0&{\text{if }}d_{gw,t}{\text{ is }}\geq 0.0\\min(E_{max},h_{u}\cdot {\frac {d_{r,1}}{d_{gw,t}}})&{\text{otherwise}}\\\end{cases}}$

Potential evaporation saturated:

$d_{s}=w_{g,t}-(b_{s}-d_{gb})$

$d_{r}=max(0.0,w_{g,t}-(b_{s}-d_{r,1}))$

$E_{p,s}=(E_{max}-E_{u})\cdot f_{s}$

Evaporation saturated zone:

$E_{s}=max(0.0,min(E_{p,s},d_{s}\cdot f_{gw},d_{r}\cdot f_{gw}))$

Evaporation total is the sum of evaporation in the saturated and unsaturated zone:

$E=E_{u}+E_{s}$

where

$b_{s}$ is the datum height of the surface.

$w_{g,t}$ is the ground water level (datum height) at time t.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_{gw,t}} is the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_t} is the transpiration factor of the buildings (plants) on the surface, or the surface terrain's

[Terrain_water_evaporation_factor_(Water_Overlay)|transpiration factor]] if none present.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{w,t}} is the evaporation rate of the weather at time t

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_o} is the feddes oxygen stress factor, calculated using the 3rd and 4th root depths and the feddes trapezium interpolation model and the ground water depth.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_s} is the feddes saturated zone root update factor, calculated using the 1st and 2nd root depths and the feddes trapezium interpolation model and the ground water depth.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_{r,n}} is the nth root depth value.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{max}} is the potential max evaporation

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{u}} is the evaporation in the unsaturated zone

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{p,s}} is the potential evaporation in the saturated zone

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{s}} is the evaporation in the saturated zone

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_{gb}} is the ground bottom distance

$d_{s}$ is the column height of the saturated zone covered by the roots

Related

The following topics are related to this formula.

Formulas

Groundwater level formula

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Underground model

Evaporation model

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