Multivariate models for annual rainfall erosivity in Brazil

• GIS-regression models to estimate climatic variables were studied for Brazil.
• Erosivity models (MRM-EI30) having as input geographical coordinates were reliable.
• Models make possible EI30 estimate for any location in Brazil with good precision.
• MRM-EI30 models can support soil water management practices in Brazil.
• We updated the Brazil EI30 map on the basis of MRM-EI30 coupled in GIS tools.

Water erosion has been considered as the most important worldwide environmental problem, being especially caused by intense rainfall events. The potential of rain to generate soil erosion is known as rainfall erosivity and its estimation is fundamental for the understanding of climatic vulnerability of a given region. This work aims to develop models for estimating mean annual rainfall erosivity for Brazilian regions based on multiple linear regression, using latitude, longitude and altitude as predictors for the models. Equations for rainfall erosivity estimations as function of the Modified Fournier Index (MFI) were acquired from 54 Brazilian pluviographic stations (termed as “Main Stations” in this work) to generate the database for this study. These equations were applied to estimate mean annual rainfall erosivity for 773 different rain gauges taking into account historical series with at least 15 consecutive years of daily precipitation and considering the similarity of the Precipitation Concentration Index (PCI). These rain gauges contain only pluviometric records, thus allowing the rainfall erosivity calculation in function of MFI in accordance with the order of PCI. The goodness-of-fit of each model was evaluated taking into account the adjusted coefficient of determination and the significance level of each variable. Moreover, the mean absolute error, bias of estimation, and the residual probability distribution were evaluated for other 155 rain gauges which were used exclusively for validation. All the adjusted multivariate models presented acceptable values for the statistical coefficients, being possible to estimate the mean annual rainfall erosivity for any location in Brazil using only its geographical coordinates and altitude. An annual rainfall erosivity map was created for Brazil based on the multivariate models and ordinary kriging map for residuals derived from the models (regression-kriging technique). It can be concluded that this map resulted in a spatial distribution of EI30 better than the former map and, in addition, it can be considered an important update related to the rainfall erosivity study in Brazil since more representative data sets were used.