Comparison of scenario reduction approaches for reservoir inflow timeseries generated by a Bayesian Neural Network

Abstract

Dealing with uncertainty in predicted inflows presents a major challenge in optimal reservoir flood control. Scenario-based stochastic control approaches address this by generating multiple inflow time series from probabilistic models, each representing a possible future with associated likelihoods. However, using too many scenarios increases computational complexity, while too few may compromise representativeness. Although the two critical steps of scenario generation and reduction have been extensively explored in other fields, their application to reservoir inflow dynamics remains limited. This study develops and applies a probabilistic data-driven model, specifically, a Bayesian Neural Network (BNN), for scenario generation. While the model exhibits limitations in predicting peak inflows due to data scarcity, it effectively captures temporal dependencies in inflow time series and achieves high short-term accuracy, as measured by the Nash–Sutcliffe Efficiency Coefficient (NSE) and Root Mean Squared Error (RMSE), though performance declines over longer horizons. For scenario reduction, four distance measures widely used in other domains, i.e., the Manhattan, Euclidean, Wasserstein, and energy distances, are evaluated. Experimental results show that the energy distance best preserves the statistical properties of the full scenario set, followed by the Manhattan and Euclidean distances. However, in terms of retaining extreme inflow scenarios, which are critical for flood control, the Manhattan and Euclidean distances outperform others based on a custom index measuring the envelope size of the original scenario set using the l1-norm. In terms of computational efficiency of scenario reduction approaches, the energy distance is the most expensive (quadratic in m, the number of reduced scenarios), while the Wasserstein scales linearly. In the examples used, reduced sets are shown to adequately capture extremes when the number of scenarios m≥30. Considering the trade-off between preserving extremes and computational cost, the Manhattan and Euclidean distances with m=30 are recommended as a practical choice for reservoir inflow scenario reduction.