Erosion is the wearing down of a landscape over time. It includes the detachment, transport, and deposition of soil particles by the erosive forces of raindrops and surface flow of water.

A land area contains rills and channels. Raindrop impact can detach soil particles on unprotected land surfaces between rills and initiate transport of these particles to the rills. From the small rills, the particles move to larger rills, then into ephemeral channels and then into continuously flowing rivers. Entrainment and deposition of particles can occur at any point along the path. When erosion occurs without human influence, it is called geologic erosion. Accelerated erosion occurs when human activity increases the rate of erosion.

Erosion is a matter of concern to watershed and natural resource managers. Two of the main reasons reservoirs are built are water supply and flood control. Erosion upstream of a reservoir deposits sediment in the bottom of the reservoir which lowers the reservoir’s water-holding capacity and consequently its usefulness for both of these purposes. The soil surface is the part of the soil profile highest in organic matter and nutrients. Organic matter forms complexes with soil particles so that erosion of the soil particles will also remove nutrients. Excessive erosion can deplete soil reserves of nitrogen and phosphorus needed by plants to grow and extreme erosion can degrade the soil to the point that it is unable to support plant life. If erosion is severe and widespread enough, the water balance of a watershed can be altered—remember that most water is lost from a watershed via evapotranspiration.

Erosion caused by rainfall and runoff is computed with the Modified Universal Soil Loss Equation (MUSLE) (Williams, 1975). MUSLE is a modified version of the Universal Soil Loss Equation (USLE) developed by Wischmeier and Smith (1965, 1978).

USLE predicts average annual gross erosion as a function of rainfall energy. In MUSLE, the rainfall energy factor is replaced with a runoff factor. This improves the sediment yield prediction, eliminates the need for delivery ratios, and allows the equation to be applied to individual storm events. Sediment yield prediction is improved because runoff is a function of antecedent moisture condition as well as rainfall energy. Delivery ratios (the sediment yield at any point along the channel divided by the source erosion above that point) are required by the USLE because the rainfall factor represents energy used in detachment only. Delivery ratios are not needed with MUSLE because the runoff factor represents energy used in detaching and transporting sediment.

Some soils erode more easily than others even when all other factors are the same. This difference is termed soil erodibility and is caused by the properties of the soil itself. Wischmeier and Smith (1978) define the soil erodibility factor as the soil loss rate per erosion index unit for a specified soil as measured on a unit plot. A unit plot is 22.1-m (72.6-ft) long, with a uniform length-wise slope of 9-percent, in continuous fallow, tilled up and down the slope. Continuous fallow is defined as land that has been tilled and kept free of vegetation for more than 2 years. The units for the USLE soil erodibility factor in MUSLE are numerically equivalent to the traditional English units of 0.01 (ton acre hr)/(acre ft-ton inch).

Wischmeier and Smith (1978) noted that a soil type usually becomes less erodible with decrease in silt fraction, regardless of whether the corresponding increase is in the sand fraction or clay fraction.

Direct measurement of the erodibility factor is time consuming and costly. Wischmeier et al. (1971) developed a general equation to calculate the soil erodibility factor when the silt and very fine sand content makes up less than 70% of the soil particle size distribution.

$K_{USLE}=\frac{0.00021*M^{1.14}*(12-OM)+3.25*(c_{soilstr}-2)+2.5*(c_{perm}-3)}{100}$ 4:1.1.2

where $K_{USLE}$ is the soil erodibility factor, $M$ is the particle-size parameter, $OM$ is the percent organic matter (%), $c_{soilstr}$ is the soil structure code used in soil classification, and $c_{perm}$ is the profile permeability class.

The particle-size parameter, $M$, is calculated

$M=(m_{silt}+m_{vfs})*(100-m_c)$ 4:1.1.3

where $m_{silt}$ is the percent $silt$ content (0.002-0.05 mm diameter particles), $m_{vfs}$ is the percent very fine sand content (0.05-0.10 mm diameter particles), and $m_c$ is the percent clay content (< 0.002 mm diameter particles).

The percent organic matter content, $OM$, of a layer can be calculated:

$OM=1.72*orgC$ 4:1.1.4

where $orgC$ is the percent organic carbon content of the layer (%).

Soil structure refers to the aggregation of primary soil particles into compound particles which are separated from adjoining aggregates by surfaces of weakness. An individual natural soil aggregate is called a ped. Field description of soil structure notes the shape and arrangement of peds, the size of peds, and the distinctness and durability of visible peds. USDA Soil Survey terminology for structure consists of separate sets of terms defining each of these three qualities. Shape and arrangement of peds are designated as type of soil structure; size of peds as class; and degree of distinctness as grade.

The soil-structure codes for equation 4:1.1.2 are defined by the type and class of soil structure present in the layer. There are four primary types of structure:

-Platy, with particles arranged around a plane, generally horizontal

-Prismlike, with particles arranged around a verticle line and bounded by relatively flat vertical surfaces

-Blocklike or polyhedral, with particles arranged around a point and bounded by flat or rounded surfaces which are casts of the molds formed by the faces of surrounding peds

-Spheroidal or polyhedral, with particles arranged around a point and bounded by curved or very irregular surfaces that are not accomodated to the adjoining aggregates

Each of the last three types has two subtypes:

-Prismlike Prismatic: without rounded upper ends Columnar: with rounded caps

-Blocklike Angular Blocky: bounded by planes intersecting at relatively sharp angles Subangular Blocky: having mixed rounded and plane faces with vertices mostly rounded

-Spheroidal Granular: relatively non-porous Crumb: very porous

1. very fine granular

2.fine granular

3.medium or coarse granular

4.blocky, platy, prismlike or massive

1.rapid (> 150 mm/hr)

2.moderate to rapid (50-150 mm/hr)

3.moderate (15-50 mm/hr)

4.slow to moderate (5-15 mm/hr)

5.slow (1-5 mm/hr)

6.very slow (< 1 mm/hr)

Williams (1995) proposed an alternative equation:

In large subbasins with a time of concentration greater than 1 day, only a portion of the surface runoff will reach the main channel on the day it is generated. SWAT+ incorporates a surface runoff storage feature to lag a portion of the surface runoff release to the main channel. Sediment in the surface runoff is lagged as well.

Once the sediment load in surface runoff is calculated, the amount of sediment released to the main channel is calculated:

$sed=(sed'+sed_{stor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:1.4.1

where $sed$ is the amount of sediment discharged to the main channel on a given day (metric tons), $sed'$ is the amount of sediment load generated in the HRU on a given day (metric tons), $sed_{stor,i-1}$ is the sediment stored or lagged from the previous day (metric tons), $surlag$ is the surface runoff lag coefficient, and $t_{conc}$ is the time of concentration for the HRU (hrs).

The expression $(1-exp[\frac{-surlag}{t_{conc}}])$ in equation 4:1.4.1 represents the fraction of the total available sediment that will be allowed to enter the reach on any one day.

Figure 4:1-1 plots values for this expression at different values for $surlag$ and $t_{conc}$.

Table 4:1-7: SWAT+ input variables that pertain to sediment lag calculations.

The topographic factor, $LS_{USLE}$, is the expected ratio of soil loss per unit area from a field slope to that from a 22.1-m length of uniform 9 percent slope under otherwise identical conditions. The topographic factor is calculated:

$LS_{USLE}=(\frac{L_{hill}}{22.1})^m*(65.41*sin^2(\alpha_{hill})+4.56*sin\alpha_{hill}+0.065)$ 4:1.1.12

where $L_{hill}$ is the slope length ($m$), $m$ is the exponential term, and $\alpha_{hill}$ is the angle of the slope. The exponential term, $m$, is calculated:

$m=0.6*(1-exp[-35.835*slp])$ 4:1.1.13

where $slp$ is the slope of the HRU expressed as rise over run (m/m). The relationship between $\alpha_{hill}$ and $slp$ is:

$slp=tan\alpha_{hill}$ 4:1.1.14

The modified universal soil loss equation (Williams, 1995) is:

4:1.1.1

where is the sediment yield on a given day (metric tons), is the surface runoff volume (mm HO/ha), is the peak runoff rate (m/s), is the area of the HRU (ha), is the USLE soil erodibility factor (0.013 metric ton m hr/(m-metric ton cm)), is the USLE cover and management factor, is the USLE support practice factor, is the USLE topographic factor and is the coarse fragment factor. Surface runoff and peak rate calculations are reviewed in Chapter 2:1. The USLE factors are discussed in the following sections.

The erosive power of rain and runoff will be less when snow cover is present than when there is no snow cover. During periods when snow is present in an HRU, SWAT+ modifies the sediment yield using the following relationship:

$sed=\frac{sed'}{exp[\frac{3*SNO}{25.4}]}$ 4:1.3.1

where $sed$ is the sediment yield on a given day (metric tons), $sed'$ is the sediment yield calculated with MUSLE (metric tons), and $SNO$ is the water content of the snow cover (mm H$_2$O).

The USLE cover and management factor, CUSLE, is defined as the ratio of soil loss from land cropped under specified conditions to the corresponding loss from clean-tilled, continuous fallow (Wischmeier and Smith, 1978). The plant canopy affects erosion by reducing the effective rainfall energy of intercepted raindrops. Water drops falling from the canopy may regain appreciable velocity but it will be less than the terminal velocity of free-falling raindrops. The average fall height of drops from the canopy and the density of the canopy will determine the reduction in rainfall energy expended at the soil surface. A given percentage of residue on the soil surface is more effective that the same percentage of canopy cover. Residue intercepts falling raindrops so near the surface that drops regain no fall velocity. Residue also obstructs runoff flow, reducing its velocity and transport capacity.

Because plant cover varies during the growth cycle of the plant, SWAT+ updates $C_{USLE}$ daily using the equation:

$C_{USLE}=exp([ln(0.8)-ln(C_{USLE,mn})]*exp\lfloor-0.00115*rsd_{surf}\rfloor+ln[C_{USLE,mn}])$

4:1.1.10

where $C_{USLE,mn}$ is the minimum value for the cover and management factor for the land cover, and $rsd_{surf}$ is the amount of residue on the soil surface (kg/ha).

The minimum $C$ factor can be estimated from a known average annual $C$ factor using the following equation (Arnold and Williams, 1995):

$C_{USLE,mn}=1.463ln[C_{USLE,aa}]+0.1034$ 4:1.1.11

where $C_{USLE,mn}$ is the minimum $C$ factor for the land cover and $C_{USLE,aa}$ is the average annual $C$ factor for the land cover.

For comparative purposes, SWAT+ prints out sediment loadings calculated with USLE. These values are not used by the model, they are for comparison only. The universal soil loss equation (Williams, 1995) is:

$sed=1.292*EI_{USLE}*K_{USLE}*C_{USLE}*P_{USLE}*LS_{USLE}*CFRG$ 4:1.2.1

where $sed$ is the sediment yield on a given day (metric tons/ha), $EI_{USLE}$ is the rainfall erosion index (0.017 m-metric ton cm/(m$^2$ hr)), $K_{USLE}$ is the USLE soil erodibility factor (0.013 metric ton m$^2$ hr/(m$^3$-metric ton cm)), $C_{USLE}$ is the USLE cover and management factor, $P_{USLE}$ is the USLE support practice factor, $L_{USLE}$ is the USLE topographic factor and $CFRG$ is the coarse fragment factor. The factors other than $EI_{USLE}$ are discussed in the preceding sections.

The value of $EI_{USLE}$ for a given rainstorm is the product, total storm energy times the maximum 30 minute intensity. The storm energy indicates the volume of rainfall and runoff while the 30 minute intensity indicates the prolonged peak rates of detachment and runoff.

$EI_{USLE}=E_{storm}*I_{30}$ 4:1.2.2

where $EI_{USLE}$ is the rainfall erosion index (0.017 m-metric ton cm/(m$^2$ hr)), $E_{storm}$ is the total storm energy (0.0017 m-metric ton/m$^2$), and $I_{30}$ is the maximum 30-minute intensity (mm/hr).

The energy of a rainstorm is a function of the amount of rain and of all the storm’s component intensities. Because rainfall is provided to the model in daily totals, an assumption must be made about variation in rainfall intensity. The rainfall intensity variation with time is assumed to be exponentially distributed:

$i_t=i_{mx}*exp(-\frac{t}{k_i})$ 4:1.2.3

where $i_t$ is the rainfall intensity at time $t$ (mm/hr), $i_{mx}$ is the maximum rainfall intensity (mm/hr), $t$ is the time (hr), and $k_i$ is the decay constant for rainfall intensity (hr).

The USLE energy equation is

$E_{storm}=\Delta R_{day}*(12.1+8.9*log_{10}[\frac{\Delta R_{day}}{\Delta t}])$ 4:1.2.4

where $\Delta R_{day}$ is the amount of rainfall during the time interval (mm H$_2$O), and $\Delta t$ is the time interval (hr). This equation may be expressed analytically as:

$E_{storm}=12.1\int_0^{\infty}i_t dt+8.9\int_0^{\infty} i_t log_{10} i_tdt$ 4:1.2.5

Combining equation 4:1.2.5 and 4:1.2.3 and integrating gives the equation for estimating daily rainfall energy:

$E_{storm}=\frac{R_{day}}{1000}*(12.1+8.9*(log_{10}[i_{mx}]-0.434))$ 4:1.2.6

where $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O), and $i_{mx}$ is the maximum rainfall intensity (mm/hr). To compute the maximum rainfall intensity, $i_{mx}$, equation 4:1.2.3 is integrated to give

$R_{day}=i_{mx}*k_i$ 4:1.2.7

and

$R_t=R_{day}*(1-exp[-\frac{t}{k_i}])$ 4:1.2.8

where $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O), $i_{mx}$ is the maximum rainfall intensity (mm/hr), $k_i$ is the decay constant for rainfall intensity (hr), $R_t$ is the amount of rain falling during a time interval (mm H$_2$O), and $t$ is the time interval (hr). The maximum half-hour rainfall for the precipitation event is known:

$R_{0.5}=\alpha_{0.5}*R_{day}$ 4:1.2.9

where $R_{0.5}$ is the maximum half-hour rainfall (mm H$_2$O), $\alpha_{0.5}$ is the maximum half-hour rainfall expressed as a fraction of daily rainfall, and $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O). Calculation of $\alpha_{0.5}$ is reviewed in Chapter 1:2 and Chapter 1:3. Substituting equation 4:1.2.9 and 4:1.2.7 into 4:1.2.8 and solving for the maximum intensity gives:

$i_{mx}=-2*R_{day}*1n(1-\alpha_{0.5})$ 4:1.2.10

where $i_{mx}$ is the maximum rainfall intensity (mm/hr), $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O), and $\alpha_{0.5}$ is the maximum half-hour rainfall expressed as a fraction of daily rainfall.

The maximum 30 minute intensity is calculated:

$I_{30}=2*\alpha_{0.5}*R_{day}$ 4:1.2.11

where $I_{30}$ is the maximum 30-minute intensity (mm/hr), $\alpha_{0.5}$ is the maximum half-hour rainfall expressed as a fraction of daily rainfall, and $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O).

Table 4:1-6: SWAT+ input variables that pertain to USLE sediment yield.

The support practice factor, $P_{USLE}$, is defined as the ratio of soil loss with a specific support practice to the corresponding loss with up-and-down slope culture. Support practices include contour tillage, stripcropping on the contour, and terrace systems. Stabilized waterways for the disposal of excess rainfall are a necessary part of each of these practices.

Contour tillage and planting provides almost complete protection against erosion from storms of low to moderate intensity, but little or no protection against occasional severe storms that cause extensive breakovers of contoured rows. Contouring is most effective on slopes of 3 to 8 percent. Values for $P_{USLE}$ and slope-length limits for contour support practices are given in Table 4:1-2.

Stripcropping is a practice in which contoured strips of sod are alternated with equal-width strips of row crop or small grain. Recommended values for contour stripcropping are given in Table 4:1-3.

Terraces are a series of horizontal ridges made in a hillside. There are several types of terraces. Broadbase terraces are constructed on gently sloping land and the channel and ridge are cropped the same as the interterrace area. The steep backslope terrace, where the backslope is in sod, is most common on steeper land. Impoundment terraces are terraces with underground outlets.

Terraces divide the slope of the hill into segments equal to the horizontal terrace interval. With terracing, the slope length is the terrace interval. For broadbase terraces, the horizontal terrace interval is the distance from the center of the ridge to the center of the channel for the terrace below. The horizontal terrace interval for steep backslope terraces is the distance from the point where cultivation begins at the base of the ridge to the base of the frontslope of the terrace below.

Values for $P_{USLE}$ for contour farming terraced fields are listed in Table 4:1-4. These values apply to broadbase, steep backslope and level terraces. Keep in mind that the values given in Table 4:1-4 do not account for all erosion control benefits of terraces. The shorter slope-length used in the calculation of the length-slope factor will produce additional reduction.

The coarse fragment factor is calculated:

$CFRG=exp(-0.053*rock)$ 4:1.1.15

where rock is the percent rock in the first soil layer (%).

Table 4:1-5: SWAT input variables that pertain to sediment yield.

SWAT+ allows the lateral and groundwater flow to contribute sediment to the main channel. The amount of sediment contributed by lateral and groundwater flow is calculated:

$sed_{lat}=\frac{(Q_{lat}+Q_{gw})*area_{hru}*conc_{sed}}{1000}$ 4:1.5.1

where $sed_{lat}$ is the sediment loading in lateral and groundwater flow (metric tons), $Q_{lat}$ is the lateral flow for a given day (mm H$_2$O), $Q_{gw}$ is the groundwater flow for a given day (mm H$_2$O), $area_{hru}$ is the area of the HRU (km$^2$), and $conc_{sed}$ is the concentration of sediment in lateral and groundwater flow (mg/L).

Table 4:1-8: SWAT+ input variables that pertain to sediment lag calculations.