Satellite-Based Daily Precipitation Bias Correction in a Tropical Mountainous Region Using Functional Generalized Additive Mixed Models: A Case Study in Valle del Cauca, Colombia

Accurate correction of daily satellite-derived precipitation estimates in data-scarce tropical regions remains a critical challenge for climate monitoring, agriculture, and public health. Satellite products such as CHIRPS offer broad spatial coverage but exhibit systematic biases relative to ground-based observations particularly in complex terrain under bimodal tropical regimes influenced by ENSO. We propose a Functional Generalised Additive Mixed Model (FGAMM) that corrects CHIRPS-derived precipitation estimates by treating the annual accumulated precipitation curve as a functional response and the satellite accumulation curve as a functional covariate, while incorporating station-level random effects and the Southern Oscillation Index. This functional formulation targets the systematic, slowly varying bias between satellite and ground-station accumulation, the quantity most relevant for water-balance applications such as reservoir management and agricultural planning rather than day-to-day storm nowcasting. Applied to 62 IDEAM stations in the Valle del Cauca department of Colombia (2012–2020), the FGAMM achieves a mean cross-validation RMSE of 0.68 mm/day (95% bootstrap CI: 0.61–0.75), a substantially lower error than linear regression, SVM, and Random Forest within this dataset, where the gap is statistically significant across all competing methods. This magnitude of advantage is not reproduced when applying the same fitting-and-differencing pipeline, via a simplified concurrent approximation, to an independent national-network dataset; we discuss the methodological factors that likely contribute to this discrepancy—including an inherent smoothness asymmetry between the penalised-spline FGAMM fit and the unconstrained benchmark models, and differences in validation design between the two checks—in the Discussion, and treat the true size of the FGAMM’s advantage as an open question pending a fully controlled comparison. Corrected estimates are currently restricted to the calibrated station locations; because CHIRPS provides near-global daily coverage from 1981 to the present, we discuss how the same modelling approach could in principle be applied to other tropical or subtropical regions with a sparse reference station network, including areas of Latin America, sub-Saharan Africa, and South Asia where station density is similarly limited.