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:

$f_o=\{\begin{array}{ll}1.0& \text{if }{d}_{gw,t}\text{ is }\ge d_{r,3}\\ \frac{d_{gw,t}-d_{r,4}}{d_{r,3}-d_{r,4}}& \text{if }{d}_{gw,t}\text{ is }\ge d_{r,4}\\ 0.0& \text{otherwise}\end{array}$

Feddes saturated zone root update factor:

$f_s=\{\begin{array}{ll}0.0& \text{if }{d}_{gw,t}\text{ is }\ge d_{r,1}\\ 1.0-\frac{d_{gw,t}-d_{r,2}}{d_{r,1}-d_{r,2}}& \text{if }{d}_{gw,t}\text{ is }\ge d_{r,2}\\ 1.0& \text{otherwise}\end{array}$

Max potential evaporation:

$E_{max}=f_t\cdot e_{w,t}\cdot f_o$

Evaporation unsaturated:

$E_u=\{\begin{array}{ll}0.0& \text{if }{d}_{gw,t}\text{ is }\le 0.0\\ min(E_{max},h_u\cdot \frac{d_{r,1}}{d_{gw,t}})& \text{otherwise}\\ \end{array}$

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.

$d_{r,n}$ = 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.

$d_{b,c}$ = 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

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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