Soil Water Evaporation

When an evaporation demand for soil water exists, SWAT+ must first partition the evaporative demand between the different layers. The depth distribution used to determine the maximum amount of water allowed to be evaporated is:

$E_{soil,z}=E''_s*\frac{z}{z+exp(2.374-0.00713*z)}$ 2:2.3.16

where $E_{soil,z}$ is the evaporative demand at depth $z$ (mm H$_2$O), $E''_s$ is the maximum soil water evaporation on a given day (mm H$_2$O), and $z$ is the depth below the surface. The coefficients in this equation were selected so that 50% of the evaporative demand is extracted from the top 10 mm of soil and 95% of the evaporative demand is extracted from the top 100 mm of soil.

The amount of evaporative demand for a soil layer is determined by taking the difference between the evaporative demands calculated at the upper and lower boundaries of the soil layer:

$E_{soil,ly}=E_{soil,zl}-E_{soil,zu}$ 2:2.3.16

where $E_{soil,ly}$ is the evaporative demand for layer $ly$ (mm H$_2$O), $E_{soil,zl}$ is the evaporative demand at the lower boundary of the soil layer (mm H$_2$O), and $E_{soil,zu}$ is the evaporative demand at the upper boundary of the soil layer (mm H$_2$O).

Figure 2:2-1 graphs the depth distribution of the evaporative demand for a soil that has been partitioned into 1 mm layers assuming a total soil evaporation demand of 100 mm.

Figure 2:2-1: Soil evaporative demand distribution with depth.

As mentioned previously, the depth distribution assumes 50% of the evaporative demand is met by soil water stored in the top 10 mm of the soil profile. With our example of a 100 mm total evaporative demand, 50 mm of water is 50%. This is a demand that the top layer cannot satisfy.

SWAT+ does not allow a different layer to compensate for the inability of another layer to meet its evaporative demand. The evaporative demand not met by a soil layer results in a reduction in actual evapotranspiration for the HRU.

A coefficient has been incorporated into equation 2:2.3.16 to allow the user to modify the depth distribution used to meet the soil evaporative demand. The modified equation is:

$E_{soil,ly}=E_{soil,zl}-E_{soil,zu}*esco$ 2:2.3.17

where $E_{soil,ly}$ is the evaporative demand for layer $ly$ (mm H$_2$O), $E_{soil,zl}$ is the evaporative demand at the lower boundary of the soil layer (mm H$_2$O), $E_{soil,zu}$ is the evaporative demand at the upper boundary of the soil layer (mm H$_2$O), and $esco$ is the soil evaporation compensation coefficient. Solutions to this equation for different values of $esco$ are graphed in Figure 7-2. The plot for $esco=1.0$ is that shown in Figure 2:2-1.

Figure 2:2-2: Soil evaporative demand distribution with depth

As the value for $esco$ is reduced, the model is able to extract more of the evaporative demand from lower levels.

When the water content of a soil layer is below field capacity, the evaporative demand for the layer is reduced according to the following equations:

$E'_{soil,ly}=E_{soil,ly}*exp(\frac{2.5*(SW_{ly}-FC_{ly})}{FC_{ly}-WP_{ly}})$when $SW_{ly}<FC_{ly}$ 2:2.3.18

$E'_{soil,ly}=E_{soil,ly}$ when $SW_{ly} \ge FC_{ly}$ 2:2.3.19

where $E'_{soil,ly}$ is the evaporative demand for layer $ly$ adjusted for water content (mm H$_2$O), $E_{soil,ly}$ is the evaporative demand for layer $ly$ (mm H$_2$O), $SW_{ly}$ is the soil water content of layer $ly$ (mm H$_2$O), $FC_{ly}$ is the water content of layer ly at field capacity (mm H$_2$O), and $WP_{ly}$ is the water content of layer $ly$ at wilting point (mm H$_2$O).

In addition to limiting the amount of water removed by evaporation in dry conditions, SWAT+ defines a maximum value of water that can be removed at any time. This maximum value is 80% of the plant available water on a given day where the plant available water is defined as the total water content of the soil layer minus the water content of the soil layer at wilting point (-1.5 MPa).

$E''_{soil,ly}=min(E'_{soil,ly} 0.8*(SW_{ly}-WP_{ly}))$ 2:2.3.20

where $E''_{soil,ly}$is the amount of water removed from layer $ly$ by evaporation (mm H$_2$O), $E'_{soil,ly}$is the evaporative demand for layer $ly$ adjusted for water content (mm H$_2$O), $SW_{ly}$ is the soil water content of layer $ly$ (mm H$_2$O), and $WP_{ly}$ is the water content of layer $ly$ at wilting point (mm H$_2$O).

Table 2:2-3: SWAT+ input variables used in soil evaporation calculations.

Variable Name	Definition	File Name
ESCO	$esco$: soil evaporation compensation coefficient	.bsn,.hru