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.

$d_{gw,t}=B_{c}-w_{g,t}$

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:

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

Potential evaporation saturated:

$d_{s}=w_{g,t}-(B_{c}-d_{b,c})$

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

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

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:

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

where

$B_{c}$ = the datum height of the surface of cell c, set by the elevation or a Terrain elevation prequel.

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

$d_{gw,t}$ = the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.

$f_{t}$ = the transpiration factor of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present.

$e_{w,t}$ = the evaporation rate of the weather at time t

$f_{o}$ = the calculated feddes oxygen stress factor, calculated using the 3rd and 4th root depths and the feddes trapezium interpolation model and the ground water depth.

$f_{s}$ = the calculated 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.

$d_{b,c}$ = The ground bottom distance of the cell c, defined by a Bottom distance prequel or a general GROUND_BOTTOM_DISTANCE_M of the Water Overlay.

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

$d_{r,n}$ = the nth root depth value.

$h_{u}$ = the amount of water in the unsaturated zone.

$E_{max}$ = the potential max evaporation

$E_{u}$ = the evaporation in the unsaturated zone

$E_{p,s}$ = the potential evaporation in the saturated zone

$E_{s}$ = the evaporation in the saturated zone

$E_{g}$ = the total evaporation from the underground.

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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