# 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.

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

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

$d_{s}=w_{g,t}-(b_{s}-d_{gb})$ $d_{r}=max(0.0,w_{g,t}-(b_{s}-d_{r,1}))$ $E_{p,s}=(E_{max}-E_{u})\cdot f_{s}$ 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:

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

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