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United States Department of Agriculture

Agricultural Research Service

Revised Universal Soil Loss Equation 2 - How RUSLE2 Computes Rill and Interrill Erosion
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How RUSLE2 Computes Rill and Interrill Erosion

Uses Conservation of Mass Principle

RUSLE2uses the conservation of mass principle to compute estimates of rill and interrill erosion. This principle can be illustrated by considering a segment of the overland-flow path.

If rill erosion occurs within the segment, the amount of sediment leaving the segment (sediment load) = the amount of segment that enters the segment from upslope + the amount of sediment produced by interrill erosion within the segment + the sediment detached within the segment by rill erosion. If deposition occurs within the segment, the sediment load leaving the segment = the sediment load that enters the segment from upslope + the amount of sediment produced by interrill erosion within the segment - the sediment deposited within the segment. If net detachment occurs by both rill and interrill erosion, the sediment load increases along the slope, which is typical for uniform, convex, and mildly concave slopes. If net deposition occurs, the sediment load decreases along the slope in the depositional area, which is typical of strongly concave slopes. In contrast to the USLE and most applications of RUSLE1, RUSLE2 can be applied to concave and complex slopes where deposition occurs. Thus, RUSLE2 can compute sediment yield from hillslopes where deposition occurs.

Detachment or Transport Limiting Principle

The other basic computational principle is that RUSLE2 computes detachment by flow when the transport capacity of the runoff exceeds the sediment load in the flow. Conversely, RUSLE2 computes deposition when the sediment load is greater than transport capacity. The principle is like a bucket. A bucket can’t carry more than its capacity.

Computing Net Detachment

RUSLE2 computes net detachment each day using a variation of the familiar USLE factors:

a = r k l S c p [1]

where: a = net detachment (mass/unit area), r = erosivity factor, k = soil erodibility factor, l = slope length factor, S = slope steepness factor, c = cover-management factor, and p = supporting practices factor. The lower case symbols represent daily values. Upper case symbols used in the USLE and RUSLE1 represent annual values. Each factor, except the slope steepness factor S, in equation 1 changes as environmental conditions change daily and as cover-management conditions changes with specific events, like a soil-disturbing operation. Although the values used for each factor are daily values, they represent long-term average conditions for that day.

The key element in this equation is the product of rk, which produces a daily sediment production estimate for unit-plot conditions. The variables r and k have units so that the product rk has absolute unitsof mass/area. The other variables in equation 1 adjust the unit-plot sediment production value to reflect differences between unit-plot conditions and site-specific field conditions. The factors l, S, c, and p are ratiosof sediment production from the given field condition to unit-plot conditions and do not have units.

Computing Deposition

Deposition is computed with the equation:

D = (Vf/q) (Tc –g ) [2]

where: D = deposition rate (mass/unit area), Vf = fall velocity of the sediment, q = runoff rate, Tc = transport capacity of the runoff, and g = sediment load (mass/ unit width). RUSLE2 divides the sediment load into five sediment classes (primary clay, silt, and sand, small aggregates, large aggregates) that vary in size and density. The distribution of the sediment load among these classes depends on soil texture and the amount of upslope deposition. When RUSLE2 computes deposition, it computes how deposition enriches the sediment load in fine particles. The sand and large aggregate particles are deposited first while the clay, silt, and small aggregate particles travel further downstream before being deposited. Whereas detachment is a nonselective process, deposition is a highly selective process.

Mathematical Integration of Equations

Solving erosion equations involves a mathematical integration process. RUSLE2 uses a complete integration procedure while both the USLE and RUSLE1 use approximations. RUSLE2 multiplies daily factor values and adds those values to compute annual erosion. In contrast, the USLE and RUSLE1 first integrate the individual factors and then multiplies those values to compute annual erosion. The USLE and RUSLE1 approximations, which are less accurate than the RUSLE2 computations, can account for a difference of up to 20% difference in erosion estimates between RUSLE2 and the USLE or RUSLE1.

The approximations used in the USLE and RUSLE1 were required so that those equations could be implemented in a “paper” version. Although RUSLE2 can compute values for the familiar annual K, L, C, and P factors, those factors are not used in RUSLE2 and are not typically displayed in the RUSLE2 output.

Factors Used in Erosion Equations in RUSLE2

r factor: Annual erosivity R is the sum of the daily r values. The R factor represents the erosivity of the climate at a particular location. An average annual value of R is determined from historical weather records using erosivity values determined for individual storms. The erosivity of an individual storm is computed as the product of the storm's total energy, which is closely related to storm amount, and the storm's maximum 30-minute intensity. Erosivity range from less than 8 (US customary units) in the western US to about 700 for New Orleans. All other factors being the same, soil loss is 100 times greater at New Orleans, Louisiana than at Las Vegas, Nevada. (RUSLE2 can also work in metric units as well as US customary units.)

The required erosivity information has been placed in the RUSLE2 database for individual U.S. counties in the eastern US where erosivity does not vary spatially over the county and by precipitation zone and specific locations in counties in the western US where erosivity varies spatially because of elevation or other effects. A similar organization of the climate data can be used for RUSLE2 applications outside of the U.S.

k factor: In RUSLE2, the upper case K represents the base soil erodibility as determined using the soil erodibility nomograph. The lower case k represents the soil erodibility factor value on a given day during the year. RUSLE2 computes temporal values of soil erodibility as a function of temperature and precipitation. The K factor is an empirical measure of soil erodibility as affected by intrinsic soil properties. Erosion measurements based on unit-plot conditions were used to experimentally determine the values for K used to derive the soil erodibility nomograph.

The K factor is a measure of soil erodibility under the standard unit-plot condition. Land use, such as that involving plant roots and incorporation of organic material into the soil affects, soil erodibility, but such effects are considered in the cover-management c factor. The K factor represents the combination of detachability of the soil, runoff potential of the soil, and the transportability of the sediment eroded from the soil.

The main soil properties affecting K are soil texture, including the amount of very fine sand in addition to the usual sand, silt, and clay percentage used to describe soil texture; organic matter; structure; and runoff potential as related to permeability of the soil profile. In general terms, high clay soils have low K values because theses soils are resistant to detachment. High sand soils have low K values because these soils have high infiltration rates and reduced runoff, and sediment eroded from these soils is not easily transported. Silt loam soils have moderate to high K values because soil particles are moderate to easily detached, infiltration is moderate to low producing moderate to high runoff, and the sediment is moderate to easily transported. Silt soils have the highest K values because these soils readily crust producing high runoff. Also, soil particles from silt soils are easily detached, and the sediment is easily transported.

This mixture of effects illustrates that K is empirical. It is not a soil property but is defined by RUSLE definitions. The definition for K, and for all RUSLE factors as well, must be carefully observed to achieve accurate results. For example, using K to account for reduced soil loss from incorporation of manure is not proper and produces incorrect results.

lS factor: The l and S factors jointly represent the effect of slope length, steepness, and shape on sediment production. The lowercase ‘l’ in RUSLE2 represents how the slope length factor varies daily as cover-management conditions vary. The upper case L represents an annual value that has been weighted based on the distribution of erosivity during the year. The S factor does not vary during the year in RUSLE2.

RUSLE2 represents the total of rill and interrill erosion. Rill erosion increases in a downslope direction because runoff, which is the primary erosive agent for rill erosion, increases in a downslope direction. In contrast, interrill does not vary with location on the slope because it is primarily caused by raindrop impact. Therefore, the slope length factor “l” is greater for those conditions where rill erosion is greater relative to interrill erosion.

Erosion increases with slope steepness. RUSLE2 makes no differentiation between rill and interrill erosion in the S factor that computes the effect of slope steepness on soil loss. The science for the effect of slope steepness on the rill-interrill erosion ratio did not seem sufficient to adjust the S factor in RUSLE2.

Slope shape is the spatial variation of steepness along the slope. Steepness at a position on the hillslope greatly affects erosion. Erosion is greatest for convex slopes that are steep near the end of the slope length where runoff is greatest. Erosion is least for concave slopes where the upper end of the slope is steep and runoff is least. Deposition occurs on concave slopes where transport capacity of the runoff is significantly reduced as the slope flattens. Sediment yield from these slopes is less than the amount of sediment produced by erosion.

c factor: The c factor accounts for the effects of cover-management. The lower case c in RUSLE2 refers to the cover-management factor for each day. The upper case C refers to an average annual C factor value where the individual daily c factor values have been weighted by the distribution of erosivity during the year.

Daily c factor values are computed using the subfactor method. RUSLE2 uses subfactors for canopy (cover above but not in contact with the soil surface), ground cover (cover directly in contact with the soil surface), surface roughness, time since last mechanical soil disturbance, amount and distribution of live and dead roots in the soil, organic material that has been incorporated into the soil, ridge height, and antecedent soil moisture, which is only used in the Northwest Wheat and Range Region (NWRR). These variable change through the year as plants grow and senesce, the soil is disturbed, materials are added to the soil surface, and vegetative or other organic materials are removed or incorporated into the soil.

RUSLE2 computes the decay of organic material and the amount of standing stubble that falls each day based on properties of the material and daily precipitation and temperature at the location. RUSLE2 computes loss of surface roughness and ridge height based on daily precipitation amount and interrill erosion. RUSLE2 computes how a mechanical soil disturbance buries surface materials and distributes buried materials and dead roots in the soil.

RUSLE2 does not model vegetative growth. Instead, RUSLE2 makes its erosion computations based on a description of the vegetation. The user provides a description of the vegetation by making selections from the RUSLE2 database. These descriptions are stored in the RUSLE2 database and are selected by making a menu choice. Key values such as production level and crop yield can be changed to represent local conditions.

p factor: The lower case p refers to a daily value of the support practices factor. The upper case P is an average annual value determined from the individual daily p values weighted by the erosivity distribution or by taking the ratio of soil loss with the practice to soil loss without the practice. The effect of ridging (contouring) is taken into account by how ridge height, row grade, and runoff affect detachment and transport of sediment. The effect of barriers like vegetative strips is taken into account by how these features reduce transport capacity by slowing the runoff (e.g., vegetative retardance) and cause deposition. The effect of runoff interceptors (diversions, terraces) is taken into account by how these practices reduce slope length and cause deposition in the channels created by these interceptors. The effect of small impoundments is taken into account by how these practices deposit sediment. Deposition that occurs on concave slopes is taken into account by solving the conservation of mass equation along the flow path.

T c transport capacity: Transport capacity is computed as a function of runoff rate, slope steepness, and hydraulic resistance. RUSLE2 uses the 10 yr-24 hr precipitation amount and the NRCS curve number method to compute runoff. RUSLE2 computes how runoff potential changes daily as a function of cover-management conditions. RUSLE2 computes daily hydraulic roughness from the soil surface roughness, live ground cover, ground cover provided by crop residue and mulch, and vegetative retardance.

Last Modified: 4/21/2010