Interpolation methods for improving the RUSLE R-factor mapping in Brazil

Abstract

Methods for Revised Universal Soil Loss Equation (RUSLE) rainfall erosivity factor (R-factor) predictions have been useful for land use planning in agricultural areas related to soil erosion risk map assessment, which is crucial at the regional scale. Many studies have focused on the R-factor prediction in Brazil and have utilized ordinary kriging and other methods, especially inverse square distance weighted (ISDW) predictions. For large regions with sparse sample rain-gauge network and complex atmospheric systems, such as Brazil, regression-kriging method arises as one that can produce reliable and improved results. The objective of this study was to compare the performance of (1) ordinary kriging; (2) co-kriging taking altitude as spatially distributed covariate; (3) ISDW; (4) multivariate regression model for R-factor as function of latitude, longitude, and altitude; and (5) regression-kriging. Daily pluviometric data sets from 928 rain gauges were used, considering the Modified Fournier Index (MFI) methodology for estimating the mean annual R-factor values for each rain gauge. From these stations, 155 were extracted randomly and used exclusively for statistical comparison of the methods. Regression-kriging method has demonstrated higher performance than the others, with mean absolute error of 11% compared to 15.8%, 16.2%, 19%, and 19.5%, respectively, for co-kriging, ordinary kriging, regression model, and ISDW. In addition, Willmott's index D for regression-kriging was higher than 0.94 while for the others lower than 0.90, proving its greater prediction accuracy. Thus, regression-kriging method was the most reliable, producing the best practical map. With regard to other methods, co-kriging also produced acceptable results for developing R-factor maps for Brazil.