Combined climate-mode regimes and South American precipitation anomalies: statistical inference and interpretable machine learning

South America experiences recurrent precipitation variability and hydroclimatic anomalies, yet two questions remain unresolved: whether joint climate-mode states add information beyond individual-mode effects and how predictably their associated regional anomalies can be recovered out of sample. This study assesses precipitation anomalies across the Amazon Region (AR), Northeast Brazil (NB), and southern Brazil and the La Plata basin (SL) using Global Precipitation Climatology Centre (GPCC) Full Data Daily precipitation for 1982–2020. Individual phases of the El Niño–Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Southern Annular Mode/Antarctic Oscillation (SAM/AAO), and Tropical North Atlantic/Tropical South Atlantic (TNA/TSA) are compared with pairwise combined regimes using block-bootstrap confidence intervals and false-discovery-rate (FDR) correction; continuous seasonal-year regressions separate main effects from interaction terms. Random Forest and XGBoost are evaluated through climate-year-grouped out-of-fold (OOF) validation, mode ablation, and OOF SHapley Additive exPlanations (SHAP). Five of 18 ENSO regional phase–season composites are FDR-significant, compared with two of 54 secondary-mode composites. Selected combined regimes reach approximately − 35% in NB and − 30% to + 25% in SL, but none of the 18 continuous interaction coefficients remains significant after FDR correction. Overall OOF R² is positive in AR (0.210–0.233); during December–February (DJF), it reaches 0.257–0.293, compared with 0.006–0.159 during September–November (SON). Overall R² is − 0.037 to − 0.121 in NB and − 0.002 to − 0.036 in SL. The two frameworks distinguish conditional climate-state responses from formal non-additivity and quantify the regional and seasonal limits of climate-index-based predictability.