The U.S. Natural Resource Conservation Service (NRCS) classifies soils into four hydrologic groups based on infiltration characteristics of the soils. NRCS Soil Survey Staff (1996) defines a hydrologic group as a group of soils having similar runoff potential under similar storm and cover conditions. Soil properties that influence runoff potential are those that impact the minimum rate of infiltration for a bare soil after prolonged wetting and when not frozen.

These properties are depth to seasonally high water table, saturated hydraulic conductivity, and depth to a very slowly permeable layer.

Soil may be placed in one of four groups, A, B, C, and D, or three dual classes, A/D, B/D, and C/D.

Definitions of the classes are:

A: (Low runoff potential). The soils have a high infiltration rate even when thoroughly wetted. They chiefly consist of deep, well drained to excessively drained sands or gravels. They have a high rate of water transmission.

B: The soils have a moderate infiltration rate when thoroughly wetted. They chiefly are moderately deep to deep, moderately well-drained to well-drained soils that have moderately fine to moderately coarse textures. They have a moderate rate of water transmission.

C: The soils have a slow infiltration rate when thoroughly wetted. They chiefly have a layer that impedes downward movement of water or have moderately fine to fine texture. They have a slow rate of water transmission.

D: (High runoff potential). The soils have a very slow infiltration rate when thoroughly wetted. They chiefly consist of clay soils that have a high swelling potential, soils that have a permanent water table, soils that have a claypan or clay layer at or near the surface, and shallow soils over nearly impervious material. They have a very slow rate of water transmission.

Dual hydrologic groups are given for certain wet soils that can be adequately drained. The first letter applies to the drained condition, the second to the undrained. Only soils that are rated D in their natural condition are assigned to dual classes.

The SCS runoff equation is an empirical model that came into common use in the 1950s. It was the product of more than 20 years of studies involving rainfall-runoff relationships from small rural watersheds across the U.S. The model was developed to provide a consistent basis for estimating the amounts of runoff under varying land use and soil types (Rallison and Miller, 1981).

The SCS curve number equation is (SCS, 1972):

$Q_{surf}=\frac{(R_{day}-I_a)^2}{(R_{day}-I_a+S)}$ 2:1.1.1

where $Q_{surf}$ is the accumulated runoff or rainfall excess (mm H$_2$O), $R_{day}$ is the rainfall depth for the day (mm H$_2$O), $I_a$ is the initial abstractions which includes surface storage, interception and infiltration prior to runoff (mm H$_2$O), and $S$ is the retention parameter (mm H$_2$O). The retention parameter varies spatially due to changes in soils, land use, management and slope and temporally due to changes in soil water content. The retention parameter is defined as:

2:1.1.2

where is the curve number for the day. The initial abstractions, , is commonly approximated as and equation 2:1.1.1 becomes

2:1.1.3

Runoff will only occur when . A graphical solution of equation 2:1.1.3 for different curve number values is presented in Figure 2:1-1.

The moisture condition II curve numbers provided in the tables are assumed to be appropriate for 5% slopes. Williams (1995) developed an equation to adjust the curve number to a different slope:

$CN_{2s}=\frac{(CN_3-CN_2)}{3}*[1-2*exp(-13.86*slp)]+CN_2$ 2:1.1.12

where $CN_{2s}$ is the moisture condition II curve number adjusted for slope, $CN_3$ is the moisture condition III curve number for the default 5% slope, $CN_2$ is the moisture condition II curve number for the default 5% slope, and $slp$ is the average fraction slope of the subbasin. SWAT+ does not adjust curve numbers for slope. If the user wishes to adjust the curve numbers for slope effects, the adjustment must be done prior to entering the curve numbers in the management input file.

Table 2:1-1: SWAT+ input variables that pertain to surface runoff calculated with the SCS curve number method.

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 are shape coefficients. The maximum retention parameter value, , is calculated by solving equation 2:1.1.2 using .

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.

2.1.1.7

2.1.1.8

where is the first shape coefficient, is the second shape coefficient, is the amount of water in the soil profile at field capacity (mm HO), is the retention parameter for the moisture condition III curve number, is the retention parameter for the moisture condition I curve number, is the amount of water in the soil profile when completely saturated (mm HO), 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:

2:1.1.9

where is the retention parameter for a given day (mm), is the retention parameter for the previous day (mm), is the potential evapotranspiration for the day (mm d), is the weighting coefficient used to calculate the retention coefficient for daily curve number calculations dependent on plant evapotranspiration, is the maximum value the retention parameter can achieve on any given day (mm), Rday is the rainfall depth for the day (mm HO), and is the surface runoff (mm HO). The initial value of the retention parameter is defined as

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

2:1.1.10

where is the retention parameter adjusted for frozen conditions (mm), is the maximum value the retention parameter can achieve on any given day (mm), and 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:

2:1.1.11

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

The SCS curve number is a function of the soil’s permeability, land use and antecedent soil water conditions. Typical curve numbers for moisture condition II are listed in tables 2:1-1, 2:1-2 and 2:1-3 for various land covers and soil types (SCS Engineering Division, 1986). These values are appropriate for a 5% slope.

Table 2:1-1: Runoff curve numbers for cultivated agricultural lands (from SCS Engineering Division, 1986)

Table 2:1-2: Runoff curve numbers for other agricultural lands (from SCS Engineering Division, 1986)

Table 2:1-3: Runoff curve numbers for urban areas (from SCS Engineering Division, 1986)

SCS defines three antecedent moisture conditions: I—dry (wilting point), II—average moisture, and III—wet (field capacity). The moisture condition I curve number is the lowest value the daily curve number can assume in dry conditions. The curve numbers for moisture conditions I and III are calculated with the equations:

2:1.1.4

2:1.1.5

where is the moisture condition I curve number, is the moisture condition II curve number, and is the moisture condition III curve number.