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.

$d_{g w, t} = B_{c} - w_{g, t}$

Feddes oxygen stress factor:

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

Feddes saturated zone root update factor:

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

Seasonal transpiration factor: $f_{t s} = (1.0 - f_{s e}) \cdot f_{t s, c} + f_{s e} * f_{t s, n}$

Max potential evaporation:

$E_{m a x} = f_{t s} \cdot e_{w, t} \cdot f_{o}$

Evaporation unsaturated:

$E_{u} = {\begin{cases} 0.0 & if d_{g w, t} is \leq 0.0 \\ m i n (E_{m a x}, h_{u} \cdot \frac{d_{r, 1}}{d_{g w, t}}) & otherwise \end{cases}$

Potential evaporation saturated:

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

$d_{r} = m a x (0.0, w_{g, t} - (B_{c} - d_{r, 1}))$

$E_{p, s} = (E_{m a x} - E_{u}) \cdot f_{s}$

Evaporation saturated zone:

$E_{s} = m a x (0.0, m i n (E_{p, s}, d_{s} \cdot f_{w s}, d_{r} \cdot f_{w s}))$

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_{g w, t}

= the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.

s_{c}

= Current season. Used for interpolating the transpiration factor.

s_{n}

= Next season. Used for interpolating the transpiration factor.

f_{s e}

= Season fraction. Used for interpolating the transpiration factor.

f_{t s}

= the transpiration factor of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present. 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.

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

d_{r, n}

= the nth root depth value.

h_{u}

= the amount of water in the unsaturated zone.

E_{m a x}

= the potential max evaporation

E_{u}

= the evaporation in the unsaturated zone

E_{p, s}

= the potential evaporation in the saturated zone

f_{w s}

= The WATER_STORAGE_PERCENTAGE of the ground terrain type, used here as a fraction.

E_{s}

= the evaporation in the saturated zone

E_{g}

= the total evaporation from the ground.

Ground evaporation formula (Water Overlay)

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Ground evaporation formula (Water Overlay)

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