Characterizing distributed hydrological model residual errors using a probabilistic long short-term memory network

Abstract

Errors in hydrological simulations have impacted their applications in flood prediction and water resources management. Properly characterizing the properties of errors such as heteroscedasticity and autocorrelation can provide improved hydrological predictions. Here, we present a probabilistic Long Short-Term Memory (LSTM) network for modeling hydrological residual errors. Three steps are undertaken to characterize uncertainty using the LSTM: (i) the network is trained with gradient optimization to obtain optimal predictions; (ii) the distribution of the errors for optimal predictions are estimated using a Bayesian Markov chain Monte Carlo (MCMC) algorithm; (iii) probabilistic predictions are made using the inferred error distribution and optimal predictions. We examine the model in the source of Yellow River, China over the period 1992–2015. A distributed hydrological model MIKE SHE is applied to simulate streamflows in the catchment. As benchmarks, we compare the results with a Bayesian linear regression model and a traditional probabilistic residual error model. Results show the probabilistic LSTM network reduces the heteroscedasticity and removes almost all autocorrelations in residual errors. Besides, compared with the other two methods, the proposed method produces more than 50% narrower uncertainty intervals with the best probability coverage. Our results highlight the potential ability of a deep learning approach integrated with a hydrological model to better characterize predictive uncertainty in hydrologic modeling.