Chained Linear Model of Coregionalization Gaussian Process for Hydrological Forecasting

Effective management of water resources is crucial for the optimal operation of public water supply services. Despite streamflow forecasting is essential due to the complexity of hydrological dynamics, the traditional linear autoregressive models inadequately capture these temporal dependencies. Forecasting based on recurrent neural network architectures, such as Long Short-Term Memory (LSTM), lack the ability to quantify uncertainty. This study presents a hydrological forecasting approach based on Gaussian Processes (GPs) by modeling likelihood parameters through transformations of a latent linear model of corregionalization. This allows for flexible, non-Gaussian predictive distributions while employing a hybrid optimization strategy that combines the Adam optimizer with Natural Gradient updates to enhance parameter estimation. Validation on daily streamflow data from 23 Colombian reservoirs demonstrates that the proposed model significantly improves predictive accuracy and stability over conventional GP models, particularly adapting data noise across input space.