DISCUSSION

The distribution of water losses and gains across Brazil follows climatic domains (Cherlet et al. , 2018) and is consistently supported by the Budyko framework. The Amazon and Pampa biomes presented both losing and gaining water conditions without a clear tendency for each condition due to the low density of catchments with observed hydrometeorological monitoring data in these biomes (Figure 3). It reveals the heterogeneous distribution of gauged catchments among the Brazilian regions and biomes (ANA, 2019) and the lack of basic observed data systematically collected over time and space (Marengo, 2006). Especially in the Amazon biome, the sparse monitoring network is due to the difficulty in access for local operations.
Most arid catchments located in the Caatinga and Cerrado biomes presented effective areas smaller than half of their topographic boundaries, indicating a losing water condition (dark red circles in Figure 4). We observed that these catchments have higher evaporative and aridity indices when all catchments were plotted on the classic Budyko framework (Figure 4a), i.e., the framework which considers the topographic area. In fact, topographic catchments with a strong deviation from their effective areas (Aefftopo or Aefftopo) were closer to theoretical water and energy limits. Catchments that are close or exceed these limits support the hypothesis of inter-catchment connectivity (e.g., groundwater fluxes) (Bouaziz et al. , 2018). Therefore, considering a closed water balance in those Brazilian catchments with larger deviation possibly increases uncertainty in hydrological studies, leading to inconsistent results.
The effective area represents the subsurface fluxes and processes (Figure 4b) by estimating possible gains or losses from the relationship between Q and P-ET. The effective catchment area provided a better fit of catchments in the adjusted Budyko framework as expected. Nonetheless, the arid catchments with effective areas smaller than half of their topographic areas were outside the Budyko range (dark red circles, Figure 4b). This scenario suggests other hydrological processes not captured by the use of the effective area. Those arid catchments are located along the northeast coast of Brazil (Caatinga and Atlantic Forest biomes) and share particular characteristics that influence the surface and subsurface hydrological processes. They have a complex network of reservoirs (Nascimento & Neto, 2017; ANA, 2021), which alters the local water cycle by reducing flow downstream and increasing ET losses. In the ECI estimation, this disturbance exacerbates the deviation of the effective area from its corresponding topographic area. Consequently, even small deviations can represent a large offset between streamflow change and aridity, primarily in arid regions (Berghuijs, Gnann, &Woods, 2020). The hydrological disturbances caused by a series of reservoirs may violate the hypothesis of Budyko about the climate aridity control over the precipitation partitioning. Furthermore, considering heavy hydrological disturbances in approaches that investigate catchments effective areas and inter-catchment connectivity.
Inadequate measures of P, ET, and Q can also be considered as sources of uncertainty not only in the Budyko framework but also in the ECI estimation. We made use of the best database available in order to make our findings reliable, but there are still some uncertainties such as low density of precipitation monitoring stations, mathematical limitations to represent the ET processes, and possible non-representative rating curves for discharge estimations. Despite the uncertainties associated with the ECI estimate, we achieved a better adjustment of the catchments using the effective area within the Budyko framework (Figure 4b). Therefore, we can assume that these uncertainties in the ECI estimates are lower than those associated with studies using the topographic area. Nonetheless, hydrological disturbances should be carefully investigated. Overall, the Budyko framework corroborates the water losing and gaining conditions assumed from ECI as an alternative to comply with the assumptions of a closed water balance.

The ECI most influencing attributes

The climatic and physiographic attributes found in the Brazilian biomes support the effective area indices found and contribute to a better country-scale understanding of hydrological processes and inter-catchment connectivity. Liu et al. (2020) significantly contributed to understanding how physiographic factors and some catchment location aspects could explain the deviation between topographic and effective areas at a global scale. Our study takes further steps towards downscaling their global study and investigating other factors that, in turn, were relevant influencing the variability of ECI in Brazil. Furthermore, we bring some practical implications of our findings to water resources management in Brazil.
The strong negative correlation between the aridity index and ECI found in the semiarid region is closely related to its hydrological characteristic of intermittent rivers and ephemeral streams. This region is characterized by shallow soils formed on crystalline bedrock with a minimum contribution of baseflow from deeper groundwater to the surface flow. Moreover, the semiarid has great spatiotemporal variability of precipitation, with a mean annual amount of less than 600 mm (Silva, Santos, and Santos, 2018; Toledo & Alcantara, 2019). The effective precipitation (P-ET) is larger than the surface runoff in losing water catchments (negative ECI) and therefore contributes to the subsurface flow, which may not return as baseflow in the same draining catchment (Figure 6). The absence of rainfall precipitation in most part of the year limits the ET losses, which corroborates the correlation between aridity and the losing water condition (negative ECI) in the semiarid when combined with intermittent flow.