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:

$sed=11.8*(Q_{surf}*q_{peak}*area_{hru})^{0.56}*K_{USLE}*C_{USLE}*P_{USLE}*LS_{USLE}*CFRG$

4:1.1.1

where $sed$ is the sediment yield on a given day (metric tons), $Q_{surf}$ is the surface runoff volume (mm H$_2$O/ha), $q_{peak}$ is the peak runoff rate (m$^3$/s), $area_{hru}$ is the area of the HRU (ha), $K_{USLE}$ 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. Surface runoff and peak rate calculations are reviewed in Chapter 2:1. The USLE factors are discussed in the following sections.

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

The size criteria for the class will vary by type of structure and are summarized in Table 4:1-1. The codes assigned to $c_{soilstr}$ are:

1. very fine granular

2.fine granular

3.medium or coarse granular

4.blocky, platy, prismlike or massive

Permeability is defined as the capacity of the soil to transmit water and air through the most restricted horizon (layer) when moist. The profile permeability classes are based on the lowest saturated hydraulic conductivity in the profile. The codes assigned to $c_{perm}$ are:

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:

$K_{USLE}=f_{csand}*f_{cl-si}*f_{orgc}*f_{hisand}$ 4:1.1.5

where $f_{csand}$ is a factor that gives low soil erodibility factors for soils with high coarse-sand contents and high values for soils with little sand, $f_{cl-si}$ is a factor that gives low soil erodibility factors for soils with high clay to silt ratios, $f_{orgc}$ is a factor that reduces soil erodibility for soils with high organic carbon content, and $f_{hisand}$ is a factor that reduces soil erodibility for soils with extremely high sand contents. The factors are calculated:

$f_{csand}=(0.2+0.3*exp[-0.256*m_s*(1-\frac{m_{silt}}{100})])$ 4:1.1.6

$f_{cl-si}=(\frac{m_{silt}}{m_c+m_{silt}})^{0.3}$ 4:1.1.7

$f_{orgc}=(1-\frac{0.25*orgC}{orgC+exp[3.72-2.95*orgC]})$ 4:1.1.8

$f_{hisand}=(1-\frac{0.7*(1-\frac{m_s}{100})}{(1-\frac{m_s}{100})+exp[-5.51+22.9*(1-\frac{m_s}{100})]})$ 4:1.1.9

where $m_s$ is the percent sand content (0.05-2.00 mm diameter particles), $m_{silt}$ is the percent $silt$ content (0.002-0.05 mm diameter particles), $m_c$ is the percent clay content (< 0.002 mm diameter particles), and $orgC$ is the percent organic carbon content of the layer (%).

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.

The support practice factor, , 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 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.

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 daily using the equation:

4:1.1.10

where is the minimum value for the cover and management factor for the land cover, and is the amount of residue on the soil surface (kg/ha).

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

4:1.1.11

where is the minimum factor for the land cover and is the average annual factor for the land cover.