Wischmeier and Smith's Empirical Soil Loss Model (USLE)

After 20 years of erosion trials on plots in at least 10 states in the USA, a large amount of data was waiting to be processed. In 1958, Wischmeier, a statistician with the Soil Conservation Service, was put in charge of analysing and collating over 10000 annual records of- erosion on plots and small catchments at 46 stations on the Great Plains. Wischmeier and Smith's aim (1960 and 1978) was to establish an empirical model for predicting erosion on a cultivated field so that erosion control specialists could choose the kind of measures needed in order to keep erosion within acceptable limits given the climate, slope and production factors.

ANALYSIS OF THE PRINCIPLES OF THE EQUATION

Erosion is seen as a multiplier of rainfall erosivity (the R factor, which equals the potential energy); this multiplies the resistance of the environment, which comprises K (soil erodibility), SL (the topographical factor), C (plant cover and farming techniques) and P (erosion control practices). Since it is a multiplier, if one factor tends toward zero, erosion will tend toward zero.

This erosion prediction equation is composed of five sub-equations:

E = R × K × SL × C × P

1. First, R, the rainfall erosivity index, equals E, the kinetic energy of rainfall, multiplied by I30 (maximum intensity of rain in 30 minutes expressed in cm per hour). This index corresponds to the potential erosion risk in a given region where sheet erosion appears on a bare plot with a 9% slope.

2. Soil erodibility, K, depends on the organic matter and texture of the soil, its permeability and profile structure. It varies from 70/100 for the most fragile soil to 1/100 for the most stable soil. It is measured on bare reference plots 22.2 m long on 9% slopes, tilled in the direction of the slope and having received no organic matter for three years.

3. SL, the topographical factor, depends on both the length and gradient of the slope. It varies from 0.1 to 5 in the most frequent farming contexts in West Africa, and may reach 20 in mountainous areas.

4. C, the plant cover factor, is a simple relation between erosion on bare soil and erosion observed under a cropping system. The C factor combines plant cover, its production level and the associated cropping techniques. It varies from 1 on bare soil to 1/1000 under forest, 1/100 under grasslands and cover plants, and 1 to 9/10 under root and tuber crops.

5. Finally, P is a factor that takes account of specific erosion control practices such as contour tilling or mounding, or contour ridging. It varies from 1 on bare soil with no erosion control to about 1/10 with tied ridging on a gentle slope.

Each of these factors will be studied in detail in the following paragraphs. In practice, in order to work out the production systems and erosion control measures to be set up in a given region the first step is to determine the risk of erosion from rainfall, then the degree of erodibility. A series of trials then follow to determine a factor C on the basis of desired rotations, farming techniques and erosion control practices; finally, the length and gradient are calculated for the slope to be obtained through erosion control structures in order to reduce land loss to a tolerable level (1-12 t/ha/yr). It is thus a practical model for an engineer with few data to use as a less empirical basis for finding rational solutions to practical problems.

INTRINSIC LIMITATIONS OF THE USLE MODEL

1. The model applies only to sheet erosion since the source of energy is rain; so it never applies to linear or mass erosion.

2. The type of countryside: the model has been tested and verified in peneplain and hilly country with 1-20% slopes, and excludes young mountains, especially slopes steeper than 40%, where runoff is a greater source of energy than rain and where there are significant mass movements of earth.

3. The type of rainfall: the relations between kinetic energy and rainfall intensity generally used in this model apply only to the American Great Plains, and not to mountainous regions although different sub-models can be developed for the index of rainfall erosivity, R.

4. The model applies only for average data over 20 years and is not valid for individual storms. A MUSLE model has been developed for estimating the sediment load produced by each storm, which takes into account not rainfall erosivity but the volume of runoff (Williams 1975).

5. Lastly, a major limitation of the model is that it neglects certain interactions between factors in order to distinguish more easily the individual effect of each. For example, it does not take into account the effect on erosion of slope combined with plant cover, nor the effect of soil type on the effect of slope.

CALCULATING THE R INDEX OF RAINFALL AGGRESSIVENESS
(cf. Wischmeier and Smith 1978)

For each rainfall, define the periods of uniform intensity.

Each intensity has a corresponding kinetic energy, according to the equation:

E = 210 + 89 log10I

E = kinetic energy of rainfall expressed in metric tonnes × m/ha/cm of rainfall.

 Intensity cm/in 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0 121 148 163 175 184 191 197 202 206 1 210 214 217 220 223 226 228 231 233 235 2 237 239 241 242 244 246 247 249 250 251 3 253 254 255 256 258 259 260 261 262 263 4 264 265 266 267 268 268 269 270 271 272 5 273 273 274 275 275 276 277 278 278 279 6 280 280 281 281 282 283 283 284 284 285 7 286 286 287 287 288 288 289

The value 289 can be applied to all intensities above 76 mm/in.

Construct a table as follows:

 Shower Date Total rainfall mm Duration in minutes Rainfall of equal intensity Partial intensity mm/in Unit energy per cm see table Total E I30 mm/in 19.7.67 30.5 10 5.0 30 253 33 5.5 10.0 210 32 12.5 23.4 242 23.0 177 7.5 2.5 157 30.5 6622,5 23.0

Cumulative values of R per month/season/year.

To rainfall energy must be added the energy from snow, irrigation and/or runoff.

Although the annual R index is not directly linked to annual rainfall, in West Africa Roose has shown that the mean annual R over 10 years = mean annual rainfall × a

a = • 0.5 in most cases ± 0.05

• 0.6 near the sea (< 40 km)
• 0.3 to 0.2 in tropical mountain areas
• 0.1 in Mediterranean mountain areas

At present this empirical model is being used as a practical guide for engineers and is still being developed in several countries. However, it does not always satisfy scientists who are looking for physical models based on the primary erosion processes and also hope to identify the processes occurring in isolated rainstorms instead of average values collected over 20 years. One must avoid trying to derive more from the model than the initial hypotheses permit - and, above all, more than the authors actually incorporated in their empirical model. In Zimbabwe a model valid for the region - SLEMSA - has been developed (Elwell 1981). Other models are based on Wischmeier's equation, such as EPIC (Williams 1982) or on physical processes, such as the RILL AND INTER-RILL MODEL or EUROSEL, the new European model for predicting erosion. It should be noted that at present only the USLE model is widely used in many countries. A good ten years must pass before other models can be used on a daily basis in the field. Moreover, it is not certain that such physical models will be more effective than the best locally adapted versions of present empirical models (Renard et al. 1991) - a point confirmed at the Merida Seminar in Venezuela (May 1993).