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

Once total potential evapotranspiration is determined, actual evaporation must be calculated. SWAT+ first evaporates any rainfall intercepted by the plant canopy. Next, SWAT+ calculates the maximum amount of transpiration and the maximum amount of sublimation/soil evaporation using an approach similar to that of Richtie (1972). The actual amount of sublimation and evaporation from the soil is then calculated. If snow is present in the HRU, sublimation will occur. Only when no snow is present will evaporation from the soil take place.

If the Penman-Monteith equation is selected as the potential evapotranspiration method, transpiration is also calculated with the equations summarized in Section 2:2.2.1. For the other potential evapotranspiration methods, transpiration is calculated as:

$E_t=\frac{E'_o*LAI}{3.0}$ $0 \le LAI \le 3.0$ 2:2.3.5

$E_t=E'_o$ $LAI>3.0$ 2:2.3.6

where $E_t$ is the maximum transpiration 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 $LAI$ is the leaf area index. The value for transpiration calculated by equations 2:2.3.5 and 2:2.3.6 is the amount of transpiration that will occur on a given day when the plant is growing under ideal conditions. The actual amount of transpiration may be less than this due to lack of available water in the soil profile. Calculation of actual plant water uptake and transpiration is reviewed in Chapters 5:2 and 5:3.

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.

Evapotranspiration (ET) is estimated as the sum of plant transpiration and evaporation rates. SWAT+ inherits the SWAT model simulating potential evapotranspiration (PET) rates using the Priestley-Taylor method (Priestley and Taylor, 1972), the Penman-Monteith method (Monteith, 1965), or the Hargreaves method (Hargreaves and Samani, 1985). The estimated daily PET serves as the maximum daily actual ET amount. Thus, daily ET is assumed to be the same as PET if the sum of transpiration (EP) and soil evaporation (ES) is higher than PET. In this case, the soil evaporation rate is adjusted as ES = PET – EP. In rice paddies and wetlands where standing water exists, daily ET is calculated as the sum of EP and EVP, which can exceed the calculated daily PET. However, shades of mature rice straws can limit water evaporation (Choi et al., 2017; Sakaguchi et al., 2014b).

2:2.3.22

2:2.3.23

where is the evaporation of standing water, LAI is the dimensionless leaf area index, and PET is the potential evapotranspiration.

The SWAT soil evaporation equation substitutes Equation 2:2.3.23 if standing water is entirely depleted by transmission losses.

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

Any free water present in the canopy is readily available for removal by evapotranspiration. The amount of actual evapotranspiration contributed by intercepted rainfall is especially significant in forests where in some instances evaporation of intercepted rainfall is greater than transpiration.

SWAT+ removes as much water as possible from canopy storage when calculating actual evaporation. If potential evapotranspiration, $E_o$, is less than the amount of free water held in the canopy, $R_{INT}$, then

$E_a=E_{can}=E_o$ 2:2.3.1

$R_{INT(f)}=R_{INT(i)}-E_{can}$ 2:2.3.2

where $E_a$ is the actual amount of evapotranspiration occurring in the watershed on a given day (mm H$_2$O), $E_{can}$ is the amount of evaporation from free water in the canopy on a given day (mm H$_2$O), $E_o$ is the potential evapotranspiration on a given day (mm H$_2$O), $R_{INT(i)}$ is the initial amount of free water held in the canopy on a given day (mm H$_2$O), and $R_{INT(f)}$ is the final amount of free water held in the canopy on a given day (mm H$_2$O). If potential evapotranspiration, $E_o$, is greater than the amount of free water held in the canopy, $R_{INT}$, then

$E_{can}=R_{INT(i)}$ 2:2.3.3

$R_{INT(f)}=0$ 2:2.3.4

Once any free water in the canopy has been evaporated, the remaining evaporative water demand$(E'_o=E_o-E_{can})$is partitioned between the vegetation and snow/soil.

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 , $E'_o$,$E'_s\rightarrow\frac{E_s}{1+cov_{sol}}$ .