4. Erosion Prediction - The Wind Erosion Equation (WEQ)


Using wind tunnels and field studies, the late Dr. W. S. Chepil and co-workers set out in the mid-1950's to develop the first wind erosion prediction equation which is now used by the Natural Resources Conservation Service (NRCS) and other action agencies throughout the country.

By 1954, Chepil and his coworkers began to publish results of their research in the form of wind erosion prediction equations. In 1959, Chepil released an equation:



E = quantity of erosion
I = soil cloddiness
R = residue
K = roughness
F = soil abradability
B = wind barrier
W = width of field
D = wind direction

Wind velocity at geographic locations was not addressed in this equation. In 1962, Chepils group released the equation:



A =percentage of soil fractions greater than 0.84millimeter.

Factors C, K, L, and V were the same as in the present equation although they were not handled the same. A C-factor map for the western half of the United States was also published in 1962.

In 1963, the current form of the equation:


was first released. In 1965, the concept of preponderance in assessing wind erosion forces was introduced.

In 1968, monthly climatic factors were published. These are no longer used by NRCS. Instead, NRCS adopted a proposal for computing soil erosion by periods using wind energy distribution. In 1981, the Wind Erosion Research Unit provided NRCS with data on the distribution of erosive wind energy for the United States and in 1982 provided updated annual C factors.

Although the present equation has significant limitations, it is the best tool currently available for making reasonable estimates of wind erosion. Currently, research and development of improved procedures for estimating wind erosion are underway.

The present Wind Erosion Equation is expressed as:



E =estimated average annual soil loss in tons per acre per year
=indicates relationships that are not straight-line mathematical calculations
I = soil erodibility index
K = soil surface roughness factor
C = climatic factor
L =the unsheltered distance
V =the vegetative cover factor

The I factor, expressed as the average annual soil loss in tons per acre per year from a field area, accounts for the inherent soil properties affecting erodibility. These properties include texture, organic matter, and calcium carbonate percentage. I is the potential annual wind erosion for a given soil under a given set of field conditions. The given set of field conditions for which I is referenced is that of an isolated, unsheltered, wide, bare, smooth, level, loose, and noncrusted soil surface, and at a location where the climatic factor (C) is equal to 100.

The K factor is a measure of the effect of ridges and cloddiness made by tillage and planting implements. It is expressed as a decimal from 0.1 to 1.0.

The C factor for any given locality characterizes climatic erosivity, specifically windspeed and surface soil moisture. This factor is expressed as a percentage of the C factor for Garden City, Kansas, which has a value of 100.

The L factor considers the unprotected distance along the prevailing erosive wind direction across the area to be evaluated and the preponderance of the prevailing erosive winds.

The V factor considers the kind, amount, and orientation of vegetation on the surface. The vegetative cover is expressed in pounds per acre of a flat small-grain residue equivalent.

Solving the equation involves five successive steps. Steps 1, 2 and 3 can be solved by multiplying the factor values. Determining the effects of L and V (steps 4 and 5) involves more complex functional relationships.

Step 1: E1 = I

Factor I is established for the specific soil. I may be increased for knolls less than 500 feet long facing into the prevailing wind, or decreased to account for surface soil crusting, and irrigation.

Step 2: E2 = IK

Factor K adjusts E1 for tillage-induced oriented roughness, Krd (ridges) and random roughness, Krr (cloddiness). The value of K is calculated by multiplying Krd times Krr. (K = Krd x Krr).

Step 3: E3 = IKC

Factor C adjusts E2 for the local climatic factor.

Step 4: E4 = IKCL

Factor L adjusts E3 for unsheltered distance.

Step 5: E5 = IKCLV

Factor V adjusts E4 for vegetative cover.

Limitations of the equation

When the unsheltered distance, L, is sufficiently long, the transport capacity of the wind for saltation and creep is reached. If the wind is moving all the soil it can carry across a given surface, the inflow into a downwind area of the field is equal to the outflow from that same area of the field, for saltation and creep. The net soil loss from this specific area of the field is then only the suspension component. This does not imply a reduced soil erosion problem because, theoretically, there is still the estimated amount of soil loss in creep, saltation, and suspension leaving the downwind edge of the field.

The equation does not account for snow cover or seasonal changes in soil erodibility. The equation does not estimate erosion from single storm events, and surface armoring by non-erodible gravel is not usually addressed in the I factor.


Alternative procedures for using the WEQ

The WEQ Critical Period Procedure is based on use of the Wind Erosion Equation as described by Woodruff and Siddoway in 1965. The conditions during the critical wind erosion period are used to derive the estimate of annual wind erosion.

The Critical Wind Erosion Period is described as the period of the year when the greatest amount of wind erosion can be expected to occur from a field under an identified management system. It is the period when vegetative cover, soil surface conditions, and expected erosive winds result in the greatest potential for wind erosion.
Erosion estimates developed using the critical period procedure are made using a single set of factor values (IKCL & V) in the equation to describe the critical wind erosion period conditions.
The critical period procedure is currently used for resource inventories. NRCS usually provides specific instructions on developing wind erosion estimates for resource inventories.

The WEQ Management Period Procedure was published by Bondy, Lyles, and Hayes in 1980. It solves the equation for situations where site conditions have significant variation during the year or planning period where the soil is exposed to soil erosion for short periods, and where crop damage is the foremost conservation concern, rather than the extent of soil loss. The management period procedure is described as being more responsive to changing conditions throughout the cropping year but is not considered more accurate than the critical period procedure.

Comparisons should not be made between the soil erosion predictions made by the management period procedure and the critical period procedure. In other words, where a conservation system has been determined to be acceptable by the management period procedure and placed in a conservation plan or the FOTG, then only the management period procedure will be used to determine if other conservation systems, planned or applied, provide equivalent treatment.

Adjustments to the WEQ soil erodibility factor, I, can be made for temporary conditions that include irrigation or crusts, but such adjustments are to be used only with the management period procedure. The use of monthly preponderance data to determine equivalent field width is also applicable only to the management period procedure.

States will use critical period or the management period procedure, within published guidelines, for conservation planning. The management period procedure will not be used for resource inventories unless specifically stated in instructions. Refer to individual program manuals for more specific instructions pertaining to the use of the Wind Erosion Equation.

In the late 1980s a computer version of WEQ was developed that allowed management period calculations. In 1997 Circular No 2 (amendment to the National Agronomy Manual) added an adjustment for irrigated fields, an adjustment for random roughness, and a way to interpolate the climate factors. Use of the management period procedure can be simplified through the use of worksheets on which information for each management period is documented. An acceptable WEQ calculator has been developed in Microsoft Excel, and is being adapted for use in many states. The most current worksheet version of the WEQ Management Period Procedure and be found at