A deep learning modeling framework with uncertainty quantification for inflow-outflow predictions for cascade reservoirs

Accurate prediction of reservoir inflows and outflows and their uncertainties is essential for managing water resources and establishing early-warning systems. However, this can be a formidable challenge due to numerous uncertainties, particularly in cascade reservoir systems. To seamlessly quantify aleatoric (data-caused) and epistemic (model network–caused) uncertainties simultaneously in a single framework, we estimated the posterior distribution of parameters in a Bayesian neural network while measuring prediction variance to reflect the noise in data. By randomly discarding certain units within the network, the estimated posterior distribution can be combined with a new loss function. This sophisticated deep learning framework for a long short-term memory network has also included advanced supporting approaches, such as input variable selection, data transformation, and hyperparameter optimization. The model trained in this study was applied to two cascade reservoir systems with four reservoirs in Vietnam, providing uncertainty estimates from two distinct sources. Comparing three global reservoir operation schemes, we found that the proposed model achieved superior performance in all cases, and uncertainty in the forecasts was due primarily to data noise, rather than uncertainty in the model itself. Preprocessing data using a wavelet transform can reduce noise that the model cannot classify on its own, resulting in improved performance, particular with longer lead times. The satisfactory performance of the prediction results confirms that the framework can effectively assess the uncertainty of hydrologic predictions using deep learning.