Ground evaporation formula (Water Overlay)

Ground evaporation is calculated per cell.

For all ground 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:

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

Seasonal transpiration factor:

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

Max potential evaporation:

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

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:

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

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_{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.

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.

f_{se}

= Season fraction. Used for interpolating the transpiration factor.

f_{ts,t}

= Can be supplied as four values; it is an interpolated value based on the current and next season.

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.