A Generalized Multivariate Functional Additive Mixed Model for Joint Bias Correction of Hydroclimatic Satellite Data and Its Implementation in the ColClim Web Application

We propose a Generalized Multivariate Functional Additive Mixed Model (GMFAMM) for the simultaneous bias correction of five hydroclimatic variables derived from the NASA POWER satellite product: minimum temperature (Tmin), maximum temperature (Tmax), relative humidity (HR), solar radiation (Rad), and precipitation occurrence (Pbin). The GMFAMM extends the univariate functional framework by incorporating a shared latent Gaussian process Λ0i(t) that captures cross-variable thermodynamic dependence. A systematic experimental grid of more than 200 model configurations across four distributional families (Gaussian, Gamma, Poisson, Binomial), two effect structures (linear and smooth P-splines), and four nested covariate sets is evaluated on a strict chronological 70/30 hold-out – seven training years (2016–2022) and three hold-out years (2023–2025) – to identify the optimal marginal specification for each variable. The value of joint modelling is quantified through a two-stage cross-residual approximation to the GMFAMM shared latent process, which constitutes a conservative lower bound on the gains achievable by the full simultaneous model: out-of-sample RMSE is reduced by 53% for Tmin, 38% for Tmax, and 51% for relative humidity relative to the independent GAMM baseline. These gains are physically interpretable through the Clausius-Clapeyron thermodynamic coupling documented in the residual cross-correlation analysis. The trained model artefacts are deployed in ColClim, an open-access R Shiny web application that queries the NASA POWER API and the Open-Meteo forecast service for any user-selected location in Colombia, applies the GMFAMM correction pipeline, and delivers both historical bias-corrected time series and short-range (1–16 day) forecasts across the five variables.