An improved long short-term memory network for streamflow forecasting in the upper Yangtze River

Characterized by essential complexity, dynamism, and dynamics, streamflow forecasting presents a great challenge to hydrologists. Long short-term memory (LSTM) streamflow forecast model has received a lot of attention in recent years due to its powerful non-linear modeling ability. But probabilistic streamflow forecasting has rarely been addressed by the LSTM approach. In this study, a probabilistic Long Short-Term Memory network coupled with the Gaussian process (GP) is proposed to deal with the probabilistic daily streamflow forecasting. Moreover, considering that changing mean and variance over time exist in the daily streamflow time series, the heteroscedastic Gaussian process regression is adopted to produce a varying prediction interval. The proposed method encapsulates the inductive biases of the LSTM recurrent network and retains the non-parametric, probabilistic property of Gaussian processes. The performance of the proposed model is investigated by predicting the daily streamflow time series collected from the upper Yangtze River and its tributaries. Artificial neuron network, generalized linear model, heteroscedastic GP, and regular LSTM models are also developed for comparison. Results indicated that the performance of the proposed model is satisfying. It improves prediction accuracy as well as provides an adaptive prediction interval, which is of great significance for water resources management and planning.