# Underground evaporation formula (Water Overlay)

Underground evaporation is calculated per cell.

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

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

Feddes oxygen stress factor:

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

Feddes saturated zone root update factor:

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

Max potential evaporation:

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

Evaporation unsaturated:

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

Potential evaporation saturated:

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

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

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

Evaporation saturated zone:

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

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

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

where

${\displaystyle b_{s}}$ is the datum height of the surface.
${\displaystyle w_{g,t}}$ is the ground water level (datum height) at time t.
${\displaystyle d_{gw,t}}$ is the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.
${\displaystyle f_{t}}$ is the transpiration factor of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present.
${\displaystyle e_{w,t}}$ is the evaporation rate of the weather at time t
${\displaystyle f_{o}}$ is 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.
${\displaystyle f_{s}}$ is 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.
${\displaystyle d_{r,n}}$ is the nth root depth value.
${\displaystyle h_{u}}$ is the amount of water in the unsaturated zone.
${\displaystyle E_{max}}$ is the potential max evaporation
${\displaystyle E_{u}}$ is the evaporation in the unsaturated zone
${\displaystyle E_{p,s}}$ is the potential evaporation in the saturated zone
${\displaystyle E_{s}}$ is the evaporation in the saturated zone
${\displaystyle E_{g}}$ is the total evaporation from the underground.
${\displaystyle d_{gb}}$ is the ground bottom distance
${\displaystyle d_{s}}$ 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
Models
Underground model
Evaporation model