Self-organizing map (SOM) and geographic information system (GIS) models were used to investigate the nonlinear relationships associated with geochemical weathering processes at local (~100 km²) and regional (~50,000 km²) scales. The data set consisted of 1) 22 B-horizon soil variables: P, C, pH, Al, total acidity, Ca, Mg, K, total cation exchange capacity, sum of exchangeable bases, base saturation, Cu, Zn, Fe, B, S, Mn, gammaspectrometry (total count, potassium, thorium, and uranium) and magnetic susceptibility measures; and 2) six topographic variables: elevation, slope, aspect, hydrological accumulated flux, horizontal curvature and vertical curvature. It is characterized at 304 locations from a quasi-regular grid spaced about 24 km across the state of Paraná. This data base was split into two subsets: one for analysis and modeling (274 samples) and the other for validation (30 samples) purposes. The self-organizing map and clustering methods were used to identify and classify the relations among solid-phase chemical element concentrations and GIS derived topographic models. The correlation between elevation and k-means clusters related the relative position inside hydrologic macro basins, which was interpreted as an expression of the weathering process reaching a steady-state condition at the regional scale. Locally, the chemical element concentrations were related to the vertical curvature representing concave–convex hillslope features, where concave hillslopes with convergent flux tends to be a reducing environment and convex hillslopes with divergent flux, oxidizing environments. Stochastic cross validation demonstrated that the SOM produced unbiased classifications and quantified the relative amount of uncertainty in predictions. This work strengthens the hypothesis that, at B-horizon steady-state conditions, the terrain morphometry were linked with the soil geochemical weathering in a two-way dependent process: the topographic relief was a factor on environmental geochemistry while chemical weathering was for terrain feature delineation.