# Ground evaporation formula (Water Overlay)

Conceptually, water can evaporate from the ground via crop, tree and plant foliage. This is called evapotranspiration. The amount a plant can evaporate depends on the saturation and ground water level, as well as the root structure. The factor by which roots can extract water from the ground is modeled using the Feddes trapezium.

Feddes trapezium indicating for what water levels and by what factor roots of a plant can extract water from the ground.

The amount a plant, crop or tree evaporates also depends on its growth season. Therefore, the species specific Water evaporation function value can be set as four seasonal values.

Last but not least, the calculated evapotranspiration factor is multiplied with the evaporation amount at time ${\displaystyle t}$, which is configured for a Weather.

The evaporated amount is first drawn from the unsaturated zone and then, when the expected amount is not yet reached, from the saturated zone.

## Formulas

This evaporation is calculated per cell. For all ground evaporation calculation, the ground water depth at time t is used.

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

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:

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

Seasonal transpiration factor:

${\displaystyle f_{ts,t}=(1.0-f_{se,t})\cdot f_{ts,c}+f_{se,t}\cdot f_{ts,n}}$

Max potential evaporation:

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

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:

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

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

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

Evaporation saturated zone:

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

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

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

where

${\displaystyle B_{c}}$ = the datum height of the surface of cell c, set by the elevation or a Terrain elevation prequel.
${\displaystyle w_{g,t}}$ = the ground water level (datum height) at time t.
${\displaystyle d_{gw,t}}$ = the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.
${\displaystyle f_{ts,c}}$ = the transpiration factor at current season c, of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present.
${\displaystyle f_{ts,n}}$ = the transpiration factor at coming season n, of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present.
${\displaystyle f_{se,t}}$ = Season fraction. Used for interpolating the transpiration factor.
${\displaystyle f_{ts,t}}$ = Can be supplied as four values; it is an interpolated value based on the current and next season.
${\displaystyle e_{w,t}}$ = the evaporation rate of the weather at time t.
${\displaystyle f_{o}}$ = 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.
${\displaystyle f_{s}}$ = 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.
${\displaystyle \Delta t}$ = the computational timestep in seconds.
${\displaystyle d_{b,c}}$ = 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.
${\displaystyle d_{s}}$ = the column height of the saturated zone covered by the roots.
${\displaystyle d_{r,n}}$ = the nth root depth value.
${\displaystyle h_{u}}$ = the amount of water in the unsaturated zone.
${\displaystyle E_{max}}$ = the potential max evaporation.
${\displaystyle E_{u}}$ = the evaporation in the unsaturated zone.
${\displaystyle E_{p,s}}$ = the potential evaporation in the saturated zone.
${\displaystyle f_{ws}}$ = The WATER_STORAGE_PERCENTAGE of the ground terrain type, used here as a fraction.
${\displaystyle E_{s}}$ = the evaporation in the saturated zone.
${\displaystyle E_{g}}$ = the total evaporation from the ground.

## Related

The following topics are related to this formula.

Formulas
Groundwater level formula (Water Overlay)
Models
Ground model (Water Overlay)
Evaporation model (Water Overlay)

## Notes

• The ground water level cannot be lowered further than the defined root depth by evapotranspiration.