Hydrologic multi-model ensemble predictions using variational Bayesian deep learning

Abstract

Multi-model ensembles enable assessment of model structural uncertainty across multiple disciplines. Bayesian Model Averaging (BMA) is one of the most popular ensemble averaging approaches in hydrology but its predictions are easily impacted by the type of ensemble members selected. Here, we propose a regression-based ensemble approach, namely a Variational Bayesian Long Short-Term Memory network (VB-LSTM) to address this issue. In this approach, a state-of-the-art variational inference (VI) algorithm that is faster and more scalable than Bayesian Markov chain Monte Carlo (MCMC) is employed to approximate the posterior distributions of thousands of parameters in the LSTM networks. To interpret the behavior of deep learning methods, the Permutation Feature Importance (PFI) algorithm is introduced to understand the degree to which VB-LSTM relies on each ensemble member. Twenty conceptual hydrological models are considered to evaluate BMA and VB-LSTM in four catchments from China. Four scenarios with different ensemble members are established to investigate the impacts of ensemble members on model results. Our results show that compared with BMA, VB-LSTM improves deterministic and probabilistic predictions by approximately 10%–30% in terms of Mean Absolute Error (MAE), Sharpness and Continous Ranked Probability Score (CRPS). In addition, the VB-LSTM predictions are more robust and less impacted by the selection of ensemble members. Furthermore, our study encourages the use of Bayesian deep learning in hydrology as an alternative to other approaches tackling model structural uncertainty.