Why soil erosion models over-predict small soil losses and under-predict large soil losses

Evaluation of various soil erosion models with large data sets have consistently shown that these models tend to over-predict soil erosion for small measured values, and under-predict soil erosion for larger measured values. This trend appears to be consistent regardless of whether the soil erosion value of interest is for individual storms, annual totals, or average annual soil losses, and regardless of whether the model is empirical or physically based. The hypothesis presented herein is that this phenomenon is not necessarily associated with bias in model predictions as a function of treatment, but rather with limitations in representing the random component of the measured data within treatments (i.e., between replicates) with a deterministic model. A simple example is presented, showing how even a `perfect' deterministic soil erosion model exhibits bias relative to small and large measured erosion rates. The concept is further tested and verified on a set of 3007 measured soil erosion data pairs from storms on natural rainfall and run-off plots using the best possible, unbiased, real-world model, i.e., the physical model represented by replicated plots. The results of this study indicate that the commonly observed bias, in erosion prediction models relative to over-prediction of small and under-prediction of large measured erosion rates on individual data points, is normal and expected if the model is accurately predicting erosion rates as a function of environmental conditions, i.e., treatments.