Universal Soil Loss Equation (USLE)

Between 1930 and the mid-1950s the United States ran thousands of erosion plots — small bounded strips of field, each with a collection trough at the bottom, each cropped and tilled in a known way, each weighed after every storm. Walter Wischmeier and Dwight Smith took more than ten thousand plot-years of that data and, in USDA Agriculture Handbook 537 (1978), reduced it to six multiplied factors. RUSLE, in Handbook 703 (1997), kept the same six and rebuilt the sub-factors underneath them. Both handbooks are US government publications and both are in the public domain, which is why the equation is on every continent: it was free, and nothing better came along.

The factors are a climate term, a soil term, two geometry terms and two management terms. $R$ is rainfall erosivity — not rainfall depth, but the sum over a year of each storm's energy multiplied by its maximum thirty-minute intensity, because it is the hard short bursts that detach soil. $K$ is the soil's own erodibility, measured on a standard bare fallow plot 22.13 m long at 9 % slope. $L$ and $S$ scale that unit plot to your slope's actual length and steepness. $C$ is the cover and management factor, running from 1.0 for continuously bare tilled fallow down to a thousandth of that under undisturbed forest — it is by far the largest lever a farmer holds. $P$ is the support practice factor, the credit for contouring, strip cropping and terracing.

Now the three things this equation does not do, every one of which is asked of it routinely. It does not predict a single storm. It was fitted to long-run averages, the scatter around it for individual events is enormous, and a number for one August thunderstorm is not a weak answer but a category error. It does not do gully erosion, streambank erosion, tillage translocation, landslides or wind — only the sheet and rill erosion that happens on the face of the slope. And most importantly it does not estimate sediment delivery to a watercourse. Soil that leaves the top of a slope very largely does not reach a stream: it stops in a footslope, a fence line, a grassed margin, a ditch, a depression. The delivered fraction is commonly a tenth to a half of $A$ and depends on the whole path between the field and the water. Quoting a USLE result as a sediment load into a river is the single most common misuse of the equation, and it usually overstates the load by a large factor.

The factors are regionally calibrated and they do not travel. $R$ is derived from decades of recording-rain-gauge data and is published as isoerodent maps by national agencies; a value from Iowa means nothing in Alberta and less in Kenya. $K$ comes from the soil survey for your soil series. $C$ comes from regional tables built for regional rotations. This site takes all three as inputs and names the source rather than reproducing a table, because the tables belong to the agencies that measured them and because a table used outside its region is worse than no table at all.

Finally, the unit trap, which is the USLE cousin of the API C-factor problem. $R$ and $K$ each come in two incompatible flavours. The SI set of Handbook 703 has $R$ in MJ·mm/(ha·h·yr) and $K$ in t·ha·h/(ha·MJ·mm), and their product with the dimensionless factors gives $A$ in tonnes per hectare per year. The older US customary set gives $A$ in tons per acre per year. To convert, multiply a US customary $R$ by 17.02 and a US customary $K$ by 0.1317. This page uses the SI set, which is why it can hand you the answer in either t/ha or ton/ac — the conversion at the end is a units conversion and is always safe. Mixing an American $R$ with a metric $K$, on the other hand, is wrong by more than a factor of ten, and the answer will not look obviously silly.