By now, you may have noticed that environmental scientists like maths. You can find equations for almost anything – including the rate of soil loss.
Soil erosion and degradation can be influenced by the natural environment, as well as human activities. Fortunately, all of these details are found in a simple multiplication called the Universal Soil Loss Equation.
Ready to give it a go yourself? There's nothing to lose … except soil!
USLE: Meaning
Let’s begin with a definition of the USLE.
The Universal Soil Loss Equation (USLE) is a mathematical model used to predict the long-term average annual rate of soil erosion.
Environmental scientists can use the USLE to estimate soil erosion rates. This can help them assess the effectiveness of soil conservation programmes.
It is important that we use soil erosion control as a preventative measure to protect the planet and its inhabitants from things such as water pollution, protecting habitats and safeguarding properties.
History of the USLE
The USLE technology was the culmination of decades of soil erosion research. It was first published as a complete technology in 1965 in the USDA Agriculture Handbook 282, then updated in 1978.
The Revised Universal Soil Loss Equation (RUSLE) is a computerised version of the USLE. It was released for public use in 1992. RUSLE uses the same formula as USLE, but with improvements in estimation of the factors affecting soil.
USLE Formula
As formulas go, the USLE is relatively simple.
A = R × K × LS × C × P
Where:
A = long-term average annual soil loss (measured in tonnes per hectare per year)
R = rainfall and runoff factor by geographical location
K = soil erodibility factor
LS = slope length-gradient factor
C = crop and management factor
P = support practice factor
The R and K factors of an area cannot be altered, but it is possible to reduce soil loss by constructing terraces, changing crops, or modifying agricultural practices.
USLE: R Factor
We learned earlier that the R factor represents the erosion potential, based on the rainfall and runoff by geographic location.
Runoff is the flow of water on the ground when it cannot rapidly infiltrate the soil.
The greater the rainfall duration and intensity, the higher the erosion potential.
Fig. 1 – Soil erosion after a period of heavy rainfall in Sudeley, Gloucestershire. Source: Wikimedia Commons
Western regions of the UK tend to have a greater erosion potential due to the higher levels of precipitation.
R Factor Equation
R = E x I30 ÷ 100
Where:
USLE: K Factor
The K factor is the soil erodibility factor. It's a measure of the susceptibility of the soil particles to detachment and transport by rainfall and runoff. The K factor is primarily influenced by soil texture, but it can also be impacted by structure, organic matter, and permeability.
Sand has the lowest K factor of just 0.04 tonnes per hectare. The soil type with the highest K factor (0.96) is very fine sand, closely followed by silt loam (0.85).
USLE: LS Factor
The LS factor represents soil loss dependent on slope steepness and length. The steeper and longer the slope, the greater the risk of soil erosion.
The LS factor is usually obtained from a pre-determined table.
If you're a maths whizz, you might be interested to know the calculation used to generate the LS value:
LS = [0.065 + 0.0456 (slope) + 0.006541 (slope)2](slope length ÷ constant)NN
Where:
- slope = slope steepness (%)
- slope length = length of slope (m)
- constant = 22.1
- NN = dependent on slope (see table below)
| Slope | < 1 | ≤ Slope < 3 | 3 ≤ Slope < 5 | ≥ 5 |
NN | 0.2 | 0.3 | 0.4 | 0.5 |
USLE: C Factor Table
The C factor combines soil loss from a specific crop and soil loss from a specific land management technique.
| Crop Type | Factor |
| Grain corn | 0.40 |
| Silage corn / beans / canola | 0.50 |
| Cereals | 0.35 |
| Seasonal horticultural crops | 0.50 |
| Fruit trees | 0.10 |
| Hay and pasture | 0.02 |
| Tillage Method | Factor |
| Autumn plough | 1.0 |
| Spring plough | 0.9 |
| Mulch tillage | 0.6 |
| Ridge tillage | 0.35 |
| Zone tillage | 0.25 |
| No-till | 0.25 |
The two factors are multiplied together to find C.
USLE: P Factor
The P factor represents how an agricultural support practice will affect soil loss.
| Agricultural Practice | Description | P Factor |
| Up and down slope | Growing crops vertically up and down a slope, rather than horizontally across. | 1.0 |
| Cross slope | Growing crops perpendicular to the angle of the slope. | 0.75 |
| Contour farming | Growing crops along lines of consistent elevation. | 0.50 |
| Strip cropping (cross slope) | Growing different crops in strips perpendicular to the angle of the slope. | 0.37 |
| Strip cropping (contour) | Growing different crops in lines of consistent elevation. | 0.25 |
Fig. 2 – Building terraces allows farmers to use strip cropping strategies. Source: Wikimedia Commons
USLE: Worked Example
Now that we've looked at the factors affecting soil loss, let's work out an example together.
Environmental scientists have been trying to conserve soil in two different locations.
Site A is located in a hilly, wet part of western UK.
Site B is located in a drier, flatter part of eastern UK.
Which soil conservation project has been more effective?
| Factor | Site A | Site B |
| Rainfall and Runoff Factor (R) | High rainfall | 1200 | Lower rainfall | 500 |
| Soil Erodibility Factor (K) | Loam | 0.67 | Fine sandy loam | 0.40 |
| Slope (LS) | Long, steep slope | 3.99 | Relatively flat landscape | 0.54 |
| Crop Type (C) | Apple trees | 0.10 | Wheat | 0.35 |
| Tillage Method (C) | No till | 0.25 | Spring plough | 0.9 |
| Agricultural Practice (P) | Contour farming | 0.5 | Cross slope | 0.75 |
Erosion Rate in Site A = 1200 × 0.67 × 3.99 × (0.10 × 0.25) × 0.5
Erosion Rate in Site A = 1200 × 0.67 × 3.99 × 0.025 × 0.5
Erosion Rate in Site A = 40.10
Erosion Rate in Site B = 500 × 0.40 × 0.54 x (0.35 × 0.9) × 0.75
Erosion Rate in Site B = 500 × 0.40 × 0.54 × 0.315 × 0.75
Erosion Rate in Site B = 25.52
Site B has a smaller annual average soil loss, so this conservation programme has been more effective.
Site A has minimised soil loss through crop type, tillage method, and agricultural practice. Unfortunately, these changes haven't been able to compensate for the naturally high precipitation and steep slopes of the area.
I hope that this article has clarified the Universal Soil Loss Equation (USLE) for you. Remember that it's a mathematical model used to predict the long-term average annual rate of soil erosion. The equation incorporates rainfall and runoff, soil erodibility, slope, crop type, tillage method, and agricultural practice.
USLE - Key takeaways
- The Universal Soil Loss Equation (USLE) is a mathematical model used to predict the long-term average annual rate of soil erosion.
- The equation is A = R × K × LS × C × P.
- A is the long-term average annual soil loss (measured in tonnes per hectare per year).
- R is the erosion potential, dependent on the rainfall and runoff of the region.
- K is the soil erodibility factor, primarily dependent on soil texture.
- LS is the steepness and length of the slope.
- C is the crop type and tillage method.
- P is the agricultural support practice.
1. Agricultural Research Service, USLE History, National Soil Erosion Research Laboratory: West Lafayette, IN, 2016
2. Gabor Mezosi, Estimation of the Changes in the Rainfall Erosivity in Hungary, Journal of Environmental Geography, 2016
3. Qiang Dai, Estimation of rainfall erosivity based on WRF-derived raindrop size distributions, Hydrology and Earth System Science, 2020
4. Robert P. Stone, Universal Soil Loss Equation (USLE), Kings Printer for Ontario, 2016
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