Soil loss is one of the main causes of pauperization and alteration of agricultural soil properties. Various empirical models (e.g., USLE) are used to predict soil losses from climate variables which in general have to be derived from spatial interpolation of point measurements. Alternatively, Artificial Neural Networks may be used as a powerful option to obtain site-specific climate data from independent factors. This study aimed to develop an artificial neural network to estimate rainfall erosivity in the Ribeira Valley and Coastal region of the State of S？o Paulo. In the development of the Artificial Neural Networks the input variables were latitude, longitude, and annual rainfall and a mathematical equation of the activation function for use in the study area as the output variable. It was found among other things that the Artificial Neural Networks can be used in the interpolation of rainfall erosivity values for the Ribeira Valley and Coastal region of the State of S？o Paulo to a satisfactory degree of precision in the estimation of erosion. The equation performance has been demonstrated by comparison with the mathematical equation of the activation function adjusted to the specific conditions of the study area. 1. Introduction Erosion is considered one of the main causes of depauperation and alteration of soil properties and, consequently, of loss of agricultural soil. Mathematical models are used to quantify and/or predict such losses [1, 2]. One classical example is the universal soil loss equation (USLE), proposed by Wischmeier and Smith [3]. This equation predicts the average annual soil loss from agricultural land. The USLE is represented by the product of the following factors: (a) rainfall erosivity (R), (b) soil erodibility (K), (c) slope length (L), (d) slope percent (S), (e) soil use, handling, and coverage (C), and (f) conservative practices of soil support (P). The R factor is an index that expresses the rainfall erosivity, in other words, its erosive capacity [4]. Erosivity is defined as the rainfall potential for soil erosion and is exclusively a function of rainfall physical characteristics, including amount, intensity of fall, droplet size, terminal velocity, and kinetic energy. Some studies have been conducted to further detail research on this erosive agent and showed that the rainfall characteristics that provide the best correlations with soil losses are intensity of fall and kinetic energy [5]. Therefore, the estimation of erosivity values, which represents the rainfall potential for erosion, is essential for planning soil
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