Estimating
Soil Erosion Using RUSLE (Revised Universal Soil Loss Equation) Using ArcView
Bernie Engel
This document describes the use of the ArcView GIS tool to estimate soil erosion using RUSLE (Revised Universal Soil Loss Equation). Calculations that are required will be done using capabilities available within the spatial analyst extension. In this example, we will start with a DEM (digital elevation model) and grid themes for the USLE K and USLE C factors. Note that USLE K can be obtained by adding the K factor as an attibute to a soil theme's table. The C factor can be obtained from tables or using the RUSLE program given information about land use and management. A land use theme can be used to add the C factors as an attirbute field.
The LS factor can be estimated from the DEM. The technique described here for computing LS requires a flow accumulation theme. Flow accumulation can be computed from a DEM using the hydrologic extension or other watershed delineation techniques. Flow accumulation is used to estimate slope length in this example. The slope length can be estimated in other ways too such as assuming it is a constant, creating a map and assigning slope length values, etc. The slope length is often difficult to estimate due to insufficient detail in commonly available DEMs (such as 1:24000 USGS DEMs). Thus, the technique described here for estimating the slope length and LS value are necessary.
First we will compute slope steepness using the DEM. Before beginning the analysis, check the Analysis Properties to make sure the extent and gird cell size are acceptable. The grid cell size should be set to the grid cell size of the DEM for this analysis. Make the DEM active, select the Surface pull down menu as shown below and select the Derive Slope option.
The slope that was derived is shown below. The slope units are degrees. Note that this is only true if the units are consistent (e.g. if UTM coordinates are used, elevation values should be in meters).
The technique for estimating the RUSLE LS factor that will be used here was proposed by Moore and Burch (1986a and 1986b). They derived an equation for estimating LS based on flow accumulation and slope steepness. The equation is:
LS = (Flow Accumulation * Cell Size/22.13)^0.4 * (sin slope/0.0896)^1.3
Where Flow Accumulation is a grid theme of flow accumulation expressed as number of grid cells (readily derived from watershed delineation processing steps) and Cell Size is the length of a cell side
Flow accumulation was estimated using a watershed delineation tool and slope steepness was estimated in the previous step.
Since RUSLE is only suitable for estimating erosion due to interrill and rill processes, there is an upper bound on the slope length that should be used. To enforce an upper bound using the above approach, we will need to modify the flow accumulation map. For the example here, assume there is an upper bound of 150 meters. Since the grid cell width is 10 meters, this translates to an accumulation of approximately 15 grid cells. The steps below demonstrate how to modify the flow accumulation theme so that the maximum flow accumulation is 15. Note: your grid cell size may be different and thus the maximum number of grid cells may be different.
Use the map calculator as shown below to create a theme that contains 0 if the flow accumulation is less than or equal to 15 and a 1 if flow accumulation is greater than 15.
Next multiply the newly created theme by 15. This will result in a new theme with a 15 in all grid cells that had a flow accumulation greater than 15.
Create a theme using map calculator that contains a 1 in areas in which the flow accumulation is less than or equal to 15 (note this is not shown in any of the figures). Then using map calculator, multiply this theme by the original flow accumulation theme as shown below.
Grid cells with a flow accumulation value of 0 (these are where flow initiates) should be set to 1 so that the slope length for these cells is not 0. Use a process similar to that above to identify these cells and create a map with a value of 1 for these areas.
Now add the three themes that contain flow accumulation data from the previous steps. This should result in a new theme (flow accumulation) that has a maximum flow accumulation value of 15. Note the figure below shows only 2 of the themes being added together.
Use map calculator to compute the LS factor as shown below. The equation for computing LS using flow accumulation was given earlier. Note that the slope must be converted to radians from degrees by multiplying the slope by 3.14 (pi) and dividing by 180.
The LS map is shown below. Check the values in the theme to make sure the calculation was performed correctly.
The map calculator can be used to estimate RUSLE soil erosion for every grid cell in the area of interest using map calculator as shown below. Note that in this example, the R factor was assumed to be a constant and has a value of 180. The P factor is assumed to be 1 here.
The RUSLE soil erosion estimate for the area is shown below. Note that the units in this example would be tons/acre/year. Average erosion can be computed from the theme using techniques that have been seen previously (note the result is non-integer so will need to be converted to an integer representation before the table can be opened).
References
Moore, I. and G. Burch. 1986a. Physical basis of the length-slope factor in the universal soil loss equation. Soil Science Society of America Journal 50:1294-1298.
Moore` I. and G. Burch. 1986b. Modeling erosion and deposition: topographic effects. TRANS of ASAE 29(6):1624-1630,1640.