Integrating Regressive and Probabilistic Streamflow Forecasting via a Hybrid Hydrological Forecasting System: Application to the Paraíba do Sul River Basin

This study introduces the Hybrid Hydrological Forecast System (HHFS), a dual-stage, data-driven framework for monthly streamflow forecasting at the Santa Branca outlet in the upper Paraíba do Sul River Basin, Brazil. The system combines two nonlinear regressors, Multi-Layer Perceptron (MLP) and extreme Gradient Boosting (XGB), calibrated through a structured four-step evolutionary procedure in GA1 (hydrological weighting, dual-regime Ridge fusion, rolling bias correction, and monthly mean–variance adjustment) and a hydro-adaptive probabilistic optimization in GA2. SHAP-based analysis provides physical interpretability of the learned relations. The regressive stage (GA1) generates a bias-corrected and climatologically consistent central forecast. After the full four-step optimization, GA1 achieves robust generalization skill during the independent test period (2020–2023), yielding NSE = 0.77 ± 0.05, KGE = 0.85 ± 0.05, R2 = 0.77 ± 0.05, and RMSE = 20.2 ± 3.1 m3 s−1, representing a major improvement over raw MLP/XGB outputs (NSE ≈ 0.5). Time-series, scatter, and seasonal diagnostics confirm accurate reproduction of wet- and dry-season dynamics, absence of low-frequency drift, and preservation of seasonal variance. The probabilistic stage (GA2) constructs a hydro-adaptive prediction interval whose width (max-min streamflow) and asymmetry evolve with seasonal hydrological regimes. The optimized configuration achieves comparative coverage COV = 0.86 ± 0.00, hit rate p = 0.96 ± 0.04, and relative width r = 2.40 ± 0.15, correctly expanding uncertainty during wet-season peaks and contracting during dry-season recessions. SHAP analysis reveals a coherent predictor hierarchy dominated by streamflow persistence, precipitation structure, temperature extremes, and evapotranspiration, jointly explaining most of the predictive variance. By combining regressive precision, probabilistic realism, and interpretability within a unified evolutionary architecture, the HHFS provides a transparent, physically grounded, and operationally robust tool for reservoir management, drought monitoring, and hydro-climatic early-warning systems in data-limited regions.