Catchments better fitted the Budyko curve when considering the effective area (the adjusted Budyko Framework, Figure 4b). Moreover, we noted a different behavior of those catchments regarding the long-term evaporative index (P-Q)/P. Catchments that gain water are closer to the upper water limit while catchments that lose water are mostly concentrated below the Fu curve by comparing the classic and adjusted framework. The increase in the evaporative index of catchments with larger effective areas reflects the correction of Q (i.e., the difference between P and Q increases as Q is corrected by an effective area larger than the topographic area). Conversely, lower evaporative indices were observed in catchments that lose water as P-Q decreases. Furthermore, three catchments that gain water exceeded the energy limit probably due to errors in the ET estimation. These catchments are geographically close to each other and both belong to a mountainous region. Most catchments that deviated from the Budyko curve range are those which lose water. These deviations may be attributed to the framework limitations regarding the assumption of a closed water balance and the climate aridity control of catchment hydrological processes (e.g., the long-term partitioning of precipitation into streamflow (Budyko, 1951) and evapotranspiration).

Identifying Influencing Attributes

From the subsequent PCA phase, three attributes — distance to coast, baseflow index, and the Strahler order — were excluded from the Random Forest analysis. Most catchments studied are more densely distributed along the Brazilian coast (Figure 3) and share similar branching complexity. Thus, those attributes may not contribute to the variance of the entire dataset (Supplement S2). Based on the RFA, the aridity index was the most influencing factor and negatively correlated with ECI (Pearson coefficient of -0.6 and p-value < 0.05). The global study of Liu et al. (2020) (Figure 5a) also showed a strong correlation between the ECI and the aridity index. Most catchments with effective areas smaller than half of their topographic areas are located in the aridest biomes: the Cerrado and Caatinga. On the contrary, larger effective areas were mostly found in the Amazon and Atlantic Forest biomes, which are characterized by lower aridity indices.