The Penman-Monteith equation combines components that account for energy needed to sustain evaporation, the strength of the mechanism required to remove the water vapor and aerodynamic and surface resistance terms. The Penman-Monteith equation is:

$\lambda E=\frac{\Delta*(H_{net}-G)+\rho_{air}*c_p*[e^o_z-e_z]/r_a}{\Delta+\gamma*(1+r_c/r_a)}$ 2:2.2.1

where $\lambda E$ is the latent heat flux density (MJ m$^{-2}$ d$^{-1}$), $E$ is the depth rate evaporation (mm d$^{-1}$), $\Delta$ is the slope of the saturation vapor pressure-temperature curve, $de/dT$ (kPa ˚C$^{-1}$), $H_{net}$ is the net radiation (MJ m$^{-2}$ d$^{-1}$), $G$ is the heat flux density to the ground (MJ m$^{-2}$ d$^{-1}$), $\rho_{air}$ is the air density (kg m$^{-3}$), $c_p$ is the specific heat at constant pressure (MJ kg$^{-1}$ ˚C$^{-1}$), is the saturation vapor pressure of air at height $z$ (kPa), $e_z$ is the water vapor pressure of air at height $z$ (kPa), $\gamma$ is the psychrometric constant (kPa ˚C$^{-1}$), $r_c$ is the plant canopy resistance (s m$^{-1}$), and $r_a$ is the diffusion resistance of the air layer (aerodynamic resistance) (s m$^{-1}$).

For well-watered plants under neutral atmospheric stability and assuming logarithmic wind profiles, the Penman-Monteith equation may be written (Jensen et al., 1990):

$\lambda E_t=\frac{\Delta*(H_{net}-G)+\gamma*K_1*(0.622*\gamma*\rho_{air}/P)*(e^o_z-e_z)/r_a}{\Delta+\gamma*(1+r_c/r_a)}$ 2:2.2.2

where $\lambda$ is the latent heat of vaporization (MJ kg$^{-1}$), $E_t$ is the maximum transpiration rate (mm d$^{-1}$), $K_1$ is a dimension coefficient needed to ensure the two terms in the numerator have the same units (for $u_z$ in m s$^{-1}$, $K_1$ = 8.64 x 104), and $P$ is the atmospheric pressure (kPa).

The calculation of net radiation, $H_{net}$, is reviewed in Chapter 1:1. The calculations for the latent heat of vaporization,$\lambda$, the slope of the saturation vapor pressure-temperature curve,$\Delta$, the psychrometric constant, $\gamma$, and the saturation and actual vapor pressure, $e^o_z$and $e_z$, are reviewed in Chapter 1:2. The remaining undefined terms are the soil heat flux, $G$, the combined term $K_1 0.622 \lambda\rho/P$, the aerodynamic resistance, $r_a$, and the canopy resistance, $r_c$.

Soil heat storage or release can be significant over a few hours, but is usually small from day to day because heat stored as the soil warms early in the day is lost when the soil cools late in the day or at night. Since the magnitude of daily soil heat flux over a 10- to 30-day period is small when the soil is under a crop cover, it can normally be ignored for most energy balance estimates. SWAT+ assumes the daily soil heat flux, $G$, is always equal to zero.

Evapotranspiration is a collective term that includes all processes by which water at the earth’s surface is converted to water vapor. It includes evaporation from the plant canopy, transpiration, sublimation and evaporation from the soil.

Evapotranspiration is the primary mechanism by which water is removed from a watershed. Roughly 62% of the precipitation that falls on the continents is evapotranspired. Evapotranspiration exceeds runoff in most river basins and on all continents except Antarctica (Dingman, 1994).

The difference between precipitation and evapotranspiration is the water available for human use and management. An accurate estimation of evapotranspiration is critical in the assessment of water resources and the impact of climate and land use change on those resources.

The plant canopy can significantly affect infiltration, surface runoff and evapotranspiration. As rain falls, canopy interception reduces the erosive energy of droplets and traps a portion of the rainfall within the canopy. The influence the canopy exerts on these processes is a function of the density of plant cover and the morphology of the plant species.

When calculating surface runoff, the SCS curve number method lumps canopy interception in the term for initial abstractions. This variable also includes surface storage and infiltration prior to runoff and is estimated as 20% of the retention parameter value for a given day (see Chapter 2:1). When the Green and Ampt infiltration equation is used to calculate surface runoff and infiltration, the interception of rainfall by the canopy must be calculated separately.

SWAT+ allows the maximum amount of water that can be held in canopy storage to vary from day to day as a function of the leaf area index:

$can_{day}=can_{mx}*\frac{LAI}{LAI_{mx}}$ 2:2.1.1

where $can_{day}$ is the maximum amount of water that can be trapped in the canopy on a given day (mm H$_2$O), $can_{mx}$ is the maximum amount of water that can be trapped in the canopy when the canopy is fully developed (mm H$_2$O), $LAI$ is the leaf area index for a given day, and $LAI_{mx}$ is the maximum leaf area index for the plant.

When precipitation falls on any given day, the canopy storage is filled before any water is allowed to reach the ground:

$R_{INT(f)}=R_{INT(i)}+R'_{day}$ and $R_{day}=0$

when $R'_{day} \le can_{day} - R_{INT(i)}$ 2:2.1.2

$R_{INT(f)}=can_{day}$ and $R_{day}=R'_{day}-(can_{day}-R_{INT(i)})$

when $R'_{day}>can_{day}-R_{INT(i)}$ 2:2.1.3

where $R_{INT(i)}$ is the initial amount of free water held in the canopy on a given day (mm H$_2$O), $R_{INT(f)}$ is the final amount of free water held in the canopy on a given day (mm H$_2$O), is the amount of precipitation on a given day before canopy interception is removed (mm H$_2$O), $R_{day}$ is the amount of precipitation on a given day that reaches the soil surface (mm H2O), and $can_{day}$ is the maximum amount of water that can be trapped in the canopy on a given day (mm H$_2$O).

Table 2:2-1: SWAT+ input variables used in canopy storage calculations.

Priestley and Taylor (1972) developed a simplified version of the combination equation for use when surface areas are wet. The aerodynamic component was removed and the energy component was multiplied by a coefficient, = 1.28, when the general surroundings are wet or under humid conditions

2:2.2.23

where is the latent heat of vaporization (MJ kg), is the potential evapotranspiration (mm d), is a coefficient, is the slope of the saturation vapor pressure-temperature curve, (kPa ˚C), is the psychrometric constant (kPa ˚C), is the net radiation (MJ m d), and is the heat flux density to the ground (MJ m d).

The Priestley-Taylor equation provides potential evapotranspiration estimates for low advective conditions. In semiarid or arid areas where the advection component of the energy balance is significant, the Priestley-Taylor equation will underestimate potential evapotranspiration.

The Hargreaves method was originally derived from eight years of cool-season Alta fescue grass lysimeter data from Davis, California (Hargreaves, 1975). Several improvements were made to the original equation (Hargreaves and Samani, 1982 and 1985) and the form used in SWAT+ was published in 1985 (Hargreaves et al., 1985):

2:2.2.24

where is the latent heat of vaporization (MJ kg), is the potential evapotranspiration (mm d), is the extraterrestrial radiation (MJ m d), is the maximum air temperature for a given day (°C), is the minimum air temperature for a given day (°C), and is the mean air temperature for a given day (°C).

Studies in canopy resistance have shown that the canopy resistance for a well-watered reference crop can be estimated by dividing the minimum surface resistance for a single leaf by one-half of the canopy leaf area index (Jensen et. al, 1990):

2:2.2.8

where is the canopy resistance (s m), is the minimum effective stomatal resistance of a single leaf (s m), and is the leaf area index of the canopy.

The distribution of stomates on a plant leaf will vary between species. Typically, stomates are distributed unequally on the top and bottom of plant leaves. Plants with stomates located on only one side are classified as hypostomatous while plants with an equal number of stomates on both sides of the leaf are termed amphistomatous. The effective leaf stomatal resistance is determined by considering the stomatal resistance of the top (adaxial) and bottom (abaxial) sides to be connected in parallel (Rosenburg, et al., 1983). When there are unequal numbers of stomates on the top and bottom, the effective stomatal resistance is calculated:

2:2.2.9

where is the minimum effective stomatal resistance of a single leaf (s m), is the minimum adaxial stomatal leaf resistance (s m), and is the minimum abaxial stomatal leaf resistance (s m). For amphistomatous leaves, the effective stomatal resistance is:

2:2.2.10

For hypostomatous leaves the effective stomatal resistance is:

2:2.2.11

Leaf conductance is defined as the inverse of the leaf resistance:

2:2.2.12

where is the maximum effective leaf conductance (m s). When the canopy resistance is expressed as a function of leaf conductance instead of leaf resistance, equation 2:2.2.8 becomes:

2:2.2.13

where is the canopy resistance (s m), is the maximum conductance of a single leaf (m s), and is the leaf area index of the canopy.

For climate change simulations, the canopy resistance term can be modified to reflect the impact of change in CO concentration on leaf conductance. The influence of increasing CO concentrations on leaf conductance was reviewed by Morison (1987). Morison found that at CO concentrations between 330 and 660 ppmv, a doubling in CO concentration resulted in a 40% reduction in leaf conductance. Within the specified range, the reduction in conductance is linear (Morison and Gifford, 1983). Easterling et al. (1992) proposed the following modification to the leaf conductance term for simulating carbon dioxide concentration effects on evapotranspiration:

2:2.2.14

where is the leaf conductance modified to reflect CO effects (m s) and CO is the concentration of carbon dioxide in the atmosphere (ppmv).

Incorporating this modification into equation 2:2.2.8 gives

When calculating actual evapotranspiration, the canopy resistance term is modified to reflect the impact of high vapor pressure deficit on leaf conductance (Stockle et al, 1992). For a plant species, a threshold vapor pressure deficit is defined at which the plant’s leaf conductance begins to drop in response to the vapor pressure deficit. The adjusted leaf conductance is calculated:

Users are now able to read in measured or estimated potential evapotranspiration (PET) values from an external data source for each climate station. This process is explained below.

First, each hydrological response unit (HRU) needs to be associated with a specific climate station. The variable (iob), which is initialized with hru(j)%obj_no is the index corresponding to the object number for the current HRU and links it to the climate data.

iob = hru(j)%obj_no

where iob: This variable holds the object number of the HRU, which is crucial for linking the HRU to its corresponding weather data.

Next, the iwst variable is used to obtain the weather station index associated with the current HRU by accessing ob(iob)%wst. This effectively retrieves the identifier for the climate station that provides the PET data.

iwst = ob(iob)%wst

where iwst: This retrieves the specific weather station identifier associated with the HRU from the array of objects.

Finally, the measured or estimated PET values for the specified weather station are then accessed using wst(iwst)%weat%pet. Here, weat refers to a weather data structure that holds various weather-related parameters, including the PET. The specific PET value is retrieved and assigned to the variable .

= wst(iwst)%weat%pet

where : This variable is then assigned the PET value from the weather data structure, allowing the subroutine to utilize pre-existing climate data instead of calculating PET through other methods.

This method relies on the availability of PET data for the specific climate stations associated with each HRU. The PET values must be formatted and stored correctly in the data structures used by the model to ensure proper retrieval. The PET data should be organized in a hierarchical structure that reflects the relationship between HRUs, climate stations, and the specific weather data. The weather data structure (weat) must include a field for PET. Each weather station entry in the main weather data array should be indexed in a way that relates it to the HRUs. For instance, if you have an array of weather stations (wst), each HRU might reference its corresponding weather station via an index (iwst).

The PET data could be read from various file formats, such as:

• CSV/TSV Files: Easy to parse and read using Fortran I/O operations.

• Binary Files: More efficient for large datasets.

• Database Formats: Can be accessed via specific libraries or APIs.

This approach allows the model to use real observed data, which can improve accuracy and reliability. By integrating measured data, the model can account for local variations in climatic conditions that might not be captured by theoretical methods. By incorporating this functionality, the model enhances its capability to simulate real-world conditions, making it a valuable tool for hydrological studies and water resource management.

Table 2:2-2: SWAT+ input variables used in potential evapotranspiration calculations summarized in this section.

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

For wind speed in m s$^{-1}$, Jensen et al. (1990) provided the following relationship to calculate $K_1 0.622\lambda\rho/P$:

$K_1 *0.622*\lambda*\rho/P=1710-6.85*\overline T_{av}$ 2:2.2.19

where $^{\overline T_{av}}$is the mean air temperature for the day (˚C).

To calculate potential evapotranspiration, the Penman-Monteith equation must be solved for a reference crop. SWAT+ uses alfalfa at a height of 40 cm with a minimum leaf resistance of 100 s m$^{-1}$ for the reference crop. Using this canopy height, the equation for aerodynamic resistance (2:2.2.3) simplifies to:

$r_a=\frac{114.}{u_z}$ 2:2.2.20

The equation for canopy resistance requires the leaf area index. The leaf area index for the reference crop is estimated using an equation developed by Allen et al. (1989) to calculate $LAI$ as a function of canopy height. For nonclipped grass and alfalfa greater than 3 cm in height:

$LAI=1.5*ln(h_c)-1.4$ 2:2.2.21

where $LAI$ is the leaf area index and $h_c$ is the canopy height (cm). For alfalfa with a 40 cm canopy height, the leaf area index is 4.1. Using this value, the equation for canopy resistance simplifies to:

$r_c=49/(1.4-0.4*\frac{CO_2}{330})$ 2:2.2.22

The most accurate estimates of evapotranspiration with the Penman-Monteith equation are made when evapotranspiration is calculated on an hourly basis and summed to obtain the daily values. Mean daily parameter values have been shown to provide reliable estimates of daily evapotranspiration values and this is the approach used in SWAT+. However, the user should be aware that calculating evapotranspiration with the Penman-Monteith equation using mean daily values can potentially lead to significant errors. These errors result from diurnal distributions of wind speed, humidity, and net radiation that in combination create conditions which the daily averages do not replicate.

The aerodynamic resistance to sensible heat and vapor transfer, $r_a$, is calculated:

$r_a=\frac{ln[(z_w-d)/z_{om}]ln\lfloor(z_p-d)/z_{ov}\rfloor}{k^2u_z}$ 2:2.2.3

where $z_w$ is the height of the wind speed measurement (cm), $z_p$ is the height of the humidity (psychrometer) and temperature measurements (cm), $d$ is the zero plane displacement of the wind profile (cm), $z_{om}$ is the roughness length for momentum transfer (cm), $z_{ov}$ is the roughness length for vapor transfer (cm), $k$ is the von Kármán constant, and $u_z$ is the wind speed at height $z_w$ (m s$^{-1}$).

The von Kármán constant is considered to be a universal constant in turbulent flow. Its value has been calculated to be near 0.4 with a range of 0.36 to 0.43 (Jensen et al., 1990). A value of 0.41 is used by SWAT+ for the von Kármán constant.

Brutsaert (1975) determined that the surface roughness parameter, $z_o$, is related to the mean height ($h_c$) of the plant canopy by the relationship $h_c/z_o$ = $3e$ or 8.15 where e is the natural log base. Based on this relationship, the roughness length for momentum transfer is estimated as:

$z_{om} = h_c/8.15 =0.123*h_c$ $h_c \le 200cm$ 2:2.2.4

$z_{om}= 0.058*(h_c)^{1.19}$ $h_c>200cm$ 2:2.2.5

where mean height of the plant canopy ($h_c$) is reported in centimeters.

The roughness length for momentum transfer includes the effects of bluff-body forces. These forces have no impact on heat and vapor transfer, and the roughness length for vapor transfer is only a fraction of that for momentum transfer. To estimate the roughness length for vapor transfer, Stricker and Brutsaert (1978) recommended using:

$z_{ov} =0.1*z_{om}$ 2:2.2.6

The displacement height for a plant can be estimated using the following relationship (Monteith, 1981; Plate, 1971):

$d=2/3*h_c$ 2:2.2.7

The height of the wind speed measurement, $z_w$, and the height of the humidity (psychrometer) and temperature measurements, $z_p$, are always assumed to be 170 cm.

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.

Potential evapotranspiration (PET) was a concept originally introduced by Thornthwaite (1948) as part of a climate classification scheme. He defined PET is the rate at which evapotranspiration would occur from a large area uniformly covered with growing vegetation that has access to an unlimited supply of soil water and that was not exposed to advection or heat storage effects. Because the evapotranspiration rate is strongly influenced by a number of vegetative surface characteristics, Penman (1956) redefined PET as “the amount of water transpired ... by a short green crop, completely shading the ground, of uniform height and never short of water”. Penman used grass as his reference crop, but later researchers (Jensen, et al., 1990) have suggested that alfalfa at a height of 30 to 50 cm may be a more appropriate choice.

Numerous methods have been developed to estimate PET. Three of these methods have been incorporated into SWAT+: the Penman-Monteith method (Monteith, 1965; Allen, 1986; Allen et al., 1989), the Priestley-Taylor method (Priestley and Taylor, 1972) and the Hargreaves method (Hargreaves et al., 1985). The model will also read in daily PET values if the user prefers to apply a different potential evapotranspiration method.

The three PET methods included in SWAT+ vary in the amount of required inputs. The Penman-Monteith method requires solar radiation, air temperature, relative humidity and wind speed. The Priestley-Taylor method requires solar radiation, air temperature and relative humidity. The Hargreaves method requires air temperature only.

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).

$EVP_t=0.6*(1-\frac {LAI}{4.0})*PET, \; if LAI≤4.0$ 2:2.3.22

$EVP_t = 0, \; if LAI>4.0$ 2:2.3.23

where $EVP_t$ 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..

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:

2:2.3.7

where is the maximum sublimation/soil evaporation on a given day (mm HO), is the potential evapotranspiration adjusted for evaporation of free water in the canopy (mm HO), and is the soil cover index. The soil cover index is calculated

2:2.3.8

where is the aboveground biomass and residue (kg ha). If the snow water content is greater than 0.5 mm HO, 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:

2:2.3.9

where is the maximum sublimation/soil evaporation adjusted for plant water use on a given day (mm HO), is the maximum sublimation/soil evaporation on a given day (mm HO), is the potential evapotranspiration adjusted for evaporation of free water in the canopy (mm HO), and is the transpiration on a given day (mm HO). When is low . However, as approaches , , .

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, , is less than the amount of free water held in the canopy, , then

2:2.3.1

2:2.3.2

where is the actual amount of evapotranspiration occurring in the watershed on a given day (mm HO), is the amount of evaporation from free water in the canopy on a given day (mm HO), is the potential evapotranspiration on a given day (mm HO), is the initial amount of free water held in the canopy on a given day (mm HO), and is the final amount of free water held in the canopy on a given day (mm HO). If potential evapotranspiration, , is greater than the amount of free water held in the canopy, , then

2:2.3.3

2:2.3.4

Once any free water in the canopy has been evaporated, the remaining evaporative water demandis partitioned between the vegetation and snow/soil.