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:

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

Evaporation unsaturated:

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} = \begin{cases} 0.0 & \text{if } d_{us} \text{ is } <= 0.0} \\ min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}})& \text{otherwise} \\ \end{cases} }

Evaporation saturated:

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

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

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

$E_{s}=max(0.0,min(E_{sp},h_{s}\cdot f_{gw},h_{r}\cdot f_{gw}$

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.

$w_{g}$ is the underground water level.

$d$ is the column height of the unsaturated zone.

$f_{t}$ 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.

$E_{w,t}$ is the evaporation rate of the weather at time t

$f_{0}$ 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.

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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