Evaporation from soil surface

The maximum amount of evaporation from the soil surface equals the maximum evaporation from a shaded soil surface, $ES_{max} [mm]$, which is computed as:

\[ES_{max} = ES0 \cdot e^{(\frac{- \kappa_{gb} \cdot LAI} {\Delta t})}\]

where $ES0$ is the potential evaporation rate from bare soil surface $[\frac{mm}{day}]$. The actual evaporation from the soil mainly depends on the amount of soil moisture near the soil surface: evaporation decreases as the topsoil is drying. In the model this is simulated using a reduction factor which is a function of the number of days since the last rain storm (Stroosnijder, 1987, 1982):

\[ES_a = ES_{max } \cdot (\sqrt{D_{slr}} - \sqrt{D_{slr} - 1} )\]

The variable $D_{slr}$ represents the number of days since the last rain event. Its value increases over time: if the amount of water that is available for infiltration ($W_{av}$) is below a critical threshold, $D_{slr}$ increases by an amount of $\Delta t [days]$ for each time step. $D_{slr}$ is reset to 1 if the critical amount of water is exceeded. In the LISFLOOD settings file this critical amount is currently expressed as an intensity $[\frac{mm}{day}]$. This is because the equation was originally designed for a daily time step only. Because the current implementation will likely lead to DSLR being reset too frequently, the exact formulation may change in future versions (e.g. by keeping track of the accumulated available water of the last 24 hours).

The actual soil evaporation is always the smallest value out of the result of the equation above and the available amount of moisture in the soil, i.e.:

\[ES_a = \min (ES_a,w_1 - w_{res1})\]

where $w_1 [mm]$ is the amount of moisture in the upper soil layer and $w_{res1} [mm]$ is the residual amount of soil moisture . Like transpiration, direct evaporation from the soil is set to zero if the soil is frozen (i.e. when the frost index $F$ is above the crtitical threshold value).

The actual soil evaporation is extracted from the superficial soil layer ($ES_{a,1a}$) and, subsequently, from the upper soil layer ($ES_{a,1b}$):
$ES_{a,1a} = \min ([w_{1a} - w_{res1a}] , ES_a)$
$ES_{a,1b} = \max ([ES_a-ES_{a,1a}], 0)$

The amount of moisture in the superficial and upper soil layers is then updated as follows:
$w_{1a} = w_{1a} - ES_{a,1a}$
$w_{1b} = w_{1b} - ES_{a,1b}$
$w_1 = w_{1a} + w_{1b}$