Spatial and temporal prediction and uncertainty of soil loss using the revised universal soil loss equation: a case study of the rainfall–runoff erosivity R factor

Soil loss is commonly predicted using the revised universal soil loss equation consisting of rainfall–runoff erosivity, soil erodibility, slope steepness and length, cover management, and support practice factors. Because of the multiple factors, their interactions, and spatial and temporal variability, soil erosion varies considerably over space and time. For these reasons, modeling soil loss is very complicated. Decision-makers need local and regional estimates of soil loss as well as their corresponding uncertainties. Neglecting the local and detailed information may lead to improper decision-making. This paper demonstrates a strategy based on a sample data set and a geostatistical method called sequential Gaussian simulation to derive local estimates and their uncertainties for the input factors of a soil erosion system. This strategy models the spatial and temporal variability of the factors and derives their estimates and variances at any unknown location and time. This strategy was applied to a case study at which the rainfall–runoff erosivity R factor was spatially and temporally estimated using a data set of rainfall. The results showed that the correlation between the observations and estimates by the strategy ranged from 0.89 to 0.97, and most of the mean estimates fell into their confidence intervals at a probability of 95%. Comparing the estimates of the R factor using a traditional isoerodent map to the observed values suggested that the R factor might have increased and a new map may be needed. The method developed in this study may also be useful for modeling other complex ecological systems.