Once the maximum amount of sublimation/soil evaporation for the day is calculated, SWAT+ will first remove water from the snow pack to meet the evaporative demand. If the water content of the snow pack is greater than the maximum sublimation/soil evaporation demand, then

$E_{sub}=E'_s$ 2:2.3.10

$SNO_{(f)}=SNO_{(i)}-E'_s$ 2:2.3.11

$E''_s=0.$ 2:2.3.12

where $E_{sub}$ is the amount of sublimation on a given day (mm H$_2$O),$E'_s$ is the maximum sublimation/soil evaporation adjusted for plant water use on a given day (mm H$_2$O), $SNO_{(i)}$ is the amount of water in the snow pack on a given day prior to accounting for sublimation (mm H$_2$O), $SNO_{(f)}$ is the amount of water in the snow pack on a given day after accounting for sublimation (mm H$_2$O), and $E''_s$is the maximum soil water evaporation on a given day (mm H$_2$O). If the water content of the snow pack is less than the maximum sublimation/soil evaporation demand, then

$E_{sub}=SNO_{(i)}$ 2:2.3.13

$SNO_{(f)}=0.$ 2:2.3.14

$E''_s=E'_s-E_{sub}$ 2:2.3.15

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:

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

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), 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.

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 2:2.3.17 to allow the user to modify the depth distribution used to meet the soil evaporative demand. The modified equation is:

$E_{soil,ly}=E_{soil,zl}-E_{soil,zu}*esco$ 2:2.3.18

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 shown in Figure 2:2-1.

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 $SW_{ly}<FC_{ly}$ 2:2.3.19

$E'_{soil,ly}=E_{soil,ly}$ when $SW_{ly} \ge FC_{ly}$ 2:2.3.20

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).

$E''_{soil,ly}=min(E'_{soil,ly} 0.8*(SW_{ly}-WP_{ly}))$ 2:2.3.21

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.

The amount of sublimation and soil evaporation will be impacted by the degree of shading. The maximum amount of sublimation/soil evaporation on a given day is calculated as:

$E_s=E'_o*cov_{sol}$ 2:2.3.7

where $E_s$ is the maximum sublimation/soil evaporation on a given day (mm H$_2$O), $E'_o$ is the potential evapotranspiration adjusted for evaporation of free water in the canopy (mm H$_2$O), and $cov_{sol}$ is the soil cover index. The soil cover index is calculated

$cov_{sol}=exp(-5.0*10^{-5}*CV)$ 2:2.3.8

where $CV$ is the aboveground biomass and residue (kg ha$^{-1}$). If the snow water content is greater than 0.5 mm H$_2$O, the soil cover index is set to 0.5.

The maximum amount of sublimation/soil evaporation is reduced during periods of high plant water use with the relationship:

$E'_s=min[E_s,\frac{E_s*E'_o}{E_s+E_t}]$ 2:2.3.9

where $E'_s$is the maximum sublimation/soil evaporation adjusted for plant water use on a given day (mm H$_2$O), $E_s$ is the maximum sublimation/soil evaporation on a given day (mm H$_2$O), $E'_o$is the potential evapotranspiration adjusted for evaporation of free water in the canopy (mm H$_2$O), and $E_t$ is the transpiration on a given day (mm H$_2$O). When $E_t$ is low $E'_s \rightarrow E_s$. However, as $E_t$ approaches , $E'_o$,$E'_s\rightarrow\frac{E_s}{1+cov_{sol}}$ .