Improving Deep Learning hydrological time series modeling using Gaussian Filter preprocessing

Hydrological time series modeling is an important task in water resources planning and management. However, time series may include noise, which can result in an inaccurate model. Therefore, removing noise from time series is valuable to obtain accurate predictions. The aims of this study are i) to develop and compare Long-Short Term Memory (LSTM) and Gated Recurring Units (GRU) Deep Learning (DL) models to predict hydrological time series and ii) to integrate a preprocessing method, Gaussian Filter (GF), to smooth out time series and couple it with DL to improve prediction accuracy. Moreover, the DL models are benchmarked against statistical time series models (e.g., Seasonal Autoregressive Integrated Moving Average (SARIMA)) to assess their added value for hydrological time series modeling. To establish predictive models, several monthly hydrological time series including water level (e.g., from the Great Lakes in North America, including Lakes Michigan, Ontario, and Erie (1918-2019)) and streamflow (e.g., gauging stations at Umfreville, along the English River, Ontario, Canada (1921-2019), Rapides Fryers, along the Richelieu River, Quebec, Canada (1937-2020) and near Lethbridge, along the Oldman River, Alberta, Canada (1957-2019)) were explored. For developing non-GF- and GF-DL models, time series were partitioned into training (70% of the data) and testing (the remaining 30% of the data) subsets and the time series’ past measurements up to 12 months (t-1, t-2, ..., t-12) were served to the DL models (LSTM and GRU) to predict the time series at time t. The structure of the DL models was tuned using Bayesian optimization. The SARIMA models (i.e., non-GF- and GF-SARIMA) were also implemented and tuned using pmdarima's auto-arima function. After calibrating the models, the testing step was implemented and the performance of the models was evaluated using statistical indicators including correlation coefficient, root mean square error, mean absolute error, the Nash-Sutcliffe efficiency coefficient, and Willmot’s index. The results of the developed DL models showed that the GRU outperforms the LSTM models. Moreover, both LSTM and GRU have superior performance when compared to the SARIMA models. It is observed that GF preprocessing significantly improves the accuracy of the developed DL and SARIMA models. It is concluded that coupling GF preprocessing with DL, due to capturing both linear and nonlinear features of the time series, represents a promising tool for obtaining accurate hydrological time series predictions.