Uncertainty-Aware and Non-Negative Hydrological Forecasting Using Gamma-Likelihood Chained Gaussian Processes for Sustainability-Oriented Water Management

Suitable forecasting of streamflow plays a fundamental role in the sustainable management of water resources. This is especially important in regions with high hydroclimatic variability, such as Colombia. Reliable predictions of water availability are essential to support decision-making on water allocation, risk mitigation, and the long-term resilience of supply systems, including urban aqueduct services. However, traditional deterministic models often require extensive parameterization. They may lack flexibility. Data-driven approaches such as Long Short-Term Memory networks typically fail to provide meaningful uncertainty quantification. In this work, we introduce the Chained Correlated Gaussian Process. This is a scalable probabilistic framework for jointly forecasting multiple hydrological time series. The proposed model represents likelihood parameters through latent Gaussian Processes. This enables the use of non-Gaussian likelihoods to enforce physical constraints on the outputs. In particular, a Gamma likelihood is integrated into a Linear Model of Coregionalization. This approach captures interdependencies among multiple time series while ensuring non-negativity. To achieve computational scalability, we employ a variational inference framework with shared inducing points. This reduces computational complexity from cubic to linear with respect to the number of observations. Additionally, a hybrid optimization strategy is adopted. It combines Adam and Natural Gradient methods to improve numerical stability and avoid poor local optima. The proposed methodology is validated using twelve years of daily observations from 23 reservoirs in Colombia. These reservoirs serve as proxies for water availability dynamics within interconnected resource systems. Experimental results demonstrate that the ChdGP framework consistently outperforms baseline models across multiple forecasting horizons. The Gamma-likelihood configuration shows superior performance. It provides physically consistent predictions, improves uncertainty quantification, and effectively captures asymmetric behaviors and extreme hydrological events. Performance evaluation based on the Negative Log Predictive Density metric confirms the robustness of the proposed approach under non-Gaussian conditions. The results highlight the potential of the proposed framework as a reliable tool for probabilistic forecasting and risk-aware decision-making in sustainable water resource management. It offers a flexible, scalable methodology for modeling complex hydrological systems under uncertainty.