Retention Parameter

With SWAT+, users are allowed to select between two methods for calculating the retention parameter. The traditional method is to allow the retention parameter to vary with soil profile water content. An alternative added in SWAT+ allows the retention parameter to vary with accumulated plant evapotranspiration. Calculation of the daily CN value as a function of plant evapotranspiration was added because the soil moisture method was predicting too much runoff in shallow soils. By calculating daily CN as a function of plant evapotranspiration, the value is less dependent on soil storage and more dependent on antecedent climate.

When the retention parameter varies with soil profile water content, the following equation is used:

$S=S_{max}*(1-\frac{SW}{[SW+exp(w_1-w_2*SW)]})$ 2:1.1.6

where $S$ is the retention parameter for a given day (mm), $S_{max}$ is the maximum value the retention parameter can achieve on any given day (mm), $SW$ is the soil water content of the entire profile excluding the amount of water held in the profile at wilting point (mm H$_2$O), and $w_1$ and $w_2$ are shape coefficients. The maximum retention parameter value, $S_{max}$, is calculated by solving equation 2:1.1.2 using $CN_1$.

The shape coefficients are determined by solving equation 2:1.1.6 assuming that

1. the retention parameter for moisture condition I curve number corresponds to wilting point soil profile water content,

2. the retention parameter for moisture condition III curve number corresponds to field capacity soil profile water content, and

3. the soil has a curve number of 99 (S = 2.54) when completely saturated.

$w_1=ln[\frac{FC}{1-S_3*S_{max}^{-1}}-FC]+w_2*FC$ 2.1.1.7

$w_2=\frac{(ln[\frac{FC}{1-S_3*S_{max}^{-1}}-FC]-ln[\frac{SAT}{1-2.54*S_{max}^{-1}}-SAT])}{(SAT-FC)}$ 2.1.1.8

where $w_1$ is the first shape coefficient, $w_2$ is the second shape coefficient, $FC$ is the amount of water in the soil profile at field capacity (mm H$_2$O), $S_3$ is the retention parameter for the moisture condition III curve number, $S_{max}$ is the retention parameter for the moisture condition I curve number, $SAT$ is the amount of water in the soil profile when completely saturated (mm H$_2$O), and 2.54 is the retention parameter value for a curve number of 99.

When the retention parameter varies with plant evapotranspiration, the following equation is used to update the retention parameter at the end of every day:

$S=S_{prev}+E_o *exp(\frac{-cncoef*S_{prev}}{S_{max}})-R_{day}+Q_{surf}$ 2:1.1.9

where $S$ is the retention parameter for a given day (mm), $S_{prev}$ is the retention parameter for the previous day (mm), $E_o$ is the potential evapotranspiration for the day (mm d$^{-1}$), $cncoef$ is the weighting coefficient used to calculate the retention coefficient for daily curve number calculations dependent on plant evapotranspiration, $S_{max}$ is the maximum value the retention parameter can achieve on any given day (mm), Rday is the rainfall depth for the day (mm H$_2$O), and $Q_{surf}$ is the surface runoff (mm H$_2$O). The initial value of the retention parameter is defined as

$S=0.9*S_{max}$

When the top layer of the soil is frozen, the retention parameter is modified using the following equation:

$S_{frz}=S_{max}*[1-exp(-0.000862*S)]$ 2:1.1.10

where $S_{frz}$ is the retention parameter adjusted for frozen conditions (mm), $S_{max}$ is the maximum value the retention parameter can achieve on any given day (mm), and $S$ is the retention parameter for a given moisture content calculated with equation 2:1.1.6 (mm).

The daily curve number value adjusted for moisture content is calculated by rearranging equation 2:1.1.2 and inserting the retention parameter calculated for that moisture content:

$CN=\frac{25400}{(S+254)}$ 2:1.1.11

where $CN$ is the curve number on a given day and $S$ is the retention parameter calculated for the moisture content of the soil on that day.