Multivariate Models for Annual Rainfall Erosivity in Brazil

Abstract

Water erosion has been considered as the most important environmental problem worldwide; as a result of this, some mathematical tools have been applied to estimate soil erosion rates for supporting soil water management practices. In order to predict spatial variability of soil erosion in agricultural lands, some models like USLE and RUSLE have been applied. Both models have some physical elements related to the erosion process; however, the rainfall erosivity is the most important parameter to estimate soil erosion. Maps have been developed in several countries on the basis of spatial interpolations for providing representative annual rainfall erosivity values for application of such models. However, this kind of product has limitations, especially when one wishes to determine rainfall erosivity for a specific point on the map. This work aims to generate multivariate models for estimating annual rainfall erosivity for Brazilian regions based on a backward multiple linear regression technique. Geographical coordinates (latitude, longitude and altitude) are the input variables for the models application. Data from 42 Brazilian pluviometric stations (termed as Main Stations), in which a good relationship between monthly rainfall erosivity and Fourniers index was observed, were acquired to generate the database for the various multivariate models. In addition to these main stations, data from another 773 rain gauge stations with at least 20year-duration series of daily precipitation were obtained, thus allowing calculation of the respective Fourniers index. Afterwards, the Thiessen Polygon method was employed to determine the influence area of each Main Station. This way, it was possible to group the rain gauges under influence of a given Main Station, and therefore, make it possible to estimate the monthly and annual rainfall erosivity. The backward procedure was applied by considering a basic model in which the most significant variables were selected, according to Student t test, for each Brazilian region. The model precision was evaluated taking into account the adjusted coefficient of determination and significance level of parameter estimation by each variable, and in addition by analyzing if the residual had a Gaussian distribution. Moreover, the mean absolute error and bias of estimation were evaluated for approximately 20% of the data base. All the adjusted models presented acceptable values for statistical coefficients, especially if one looks at the models developed for precipitation estimation with a similar procedure. This method makes it possible to estimate annual rainfall erosivity for any location in Brazilian territory using only its geographical coordinates and elevation. As a final result, we developed a new Brazilian annual rainfall erosivity map based on the adjusted models using spatial GIS tools for generating an input data base for models, using 500-m-resolution cells.