A Two-Stage GMFAMM Approximation for Joint Bias Correction of NASA POWER Hydroclimatic Data: The ColClim Web...

We propose and empirically evaluate a two-stage approximation to a Generalized Multivariate Functional Additive Mixed Model (GMFAMM) for the joint bias correction of five NASA POWER reanalysis variables: minimum and maximum temperature (Tmin, Tmax), relative humidity (RH), solar radiation (Rad), and precipitation occurrence (Pbin). Our primary contribution is the first operational-scale evaluation of such a framework (≈200,000 station-day observations, two orders of magnitude beyond previous studies) together with its deployment in an open-access web application. A systematic grid of more than 200 marginal configurations is evaluated on a strict chronological 70/30 hold-out (training 2016-2022; testing 2023-2025) to identify the optimal marginal specification per variable. Against a correctly specified marginal baseline, station-level linear calibration combined with the marginal GAMM removes the bulk of the systematic bias (RMSE reductions of ≈80%, 82% and 30% for Tmin, Tmax and RH). A shared latent step, using the first principal component of the marginal residual matrix as a scalar proxy for Λ0(t), yields additional but conditional out-of-sample reductions (≈17% Tmax, 10% RH, 9% Rad; negligible for Tmin, with precipitation occurrence retained in the shared representation but its joint gain treated as exploratory); because it requires co-located donor observations, at ungauged locations the deployed pipeline applies the marginal correction only, whose spatial transfer is confirmed by leave-one-station-out cross-validation. The residual cross-correlation structure is consistent with, though not in itself proof of, Clausius-Clapeyron coupling. The trained artefacts are deployed in ColClim, an open-access R Shiny application that queries the NASA POWER API and the Open-Meteo forecast service for any location in Colombia and delivers historical bias-corrected series and short-range (1-16 day) forecasts.