A probabilistic integration of LSTM and Gaussian process regression for uncertainty-aware reservoir water level predictions

Abstract

ABSTRACT Reservoir-level forecasting, while being crucial for optimal operation, is challenged by complex physical processes and changing climate conditions. Machine learning approaches offer deterministic predictions but often neglect system physics and uncertainty. This article presents a probabilistic data-driven approach combining long short-term memory (LSTM) and Gaussian process regression (GPR) to provide both point forecasts and uncertainty estimates. The hybrid model leverages LSTM’s fitting capabilities with GPR’s robust Bayesian frameworks for uncertainty estimation in non-linear problems, offering accurate predictions without extensive high-fidelity modelling, and avoiding frequent training and parameter optimization. Evaluation with real reservoir data from India shows the model’s superiority over the vanilla LSTM for both univariate and multivariate scenarios. The proposed model achieved a Nash-Sutcliffe efficiency of 0.97 to 0.98, a mean biased error of −0.5634 to −1.0314 for 10-day forecasts, and a continuous ranked probability score of 5.80 and 1.87 for the Bhakra and Pong reservoirs, respectively.