Technical note: Using long short-term memory models to fill data gaps in hydrological monitoring networks

Abstract

Quantifying the spatiotemporal dynamics in subsurface hydrological flows over a long time window usually employs a network of monitoring wells. However, such observations are often spatially sparse with potential temporal gaps due to poor quality or instrument failure. In this study, we explore the ability of recurrent neural networks to fill gaps in a spatially distributed time-series dataset. We use a well network that monitors the dynamic and heterogeneous hydrologic exchanges between the Columbia River and its adjacent groundwater aquifer at the U.S. Department of Energy's Hanford site. This 10-year-long dataset contains hourly temperature, specific conductance, and groundwater table elevation measurements from 42 wells with gaps of various lengths. We employ a long short-term memory (LSTM) model to capture the temporal variations in the observed system behaviors needed for gap filling. The performance of the LSTM-based gap-filling method was evaluated against a traditional autoregressive integrated moving average (ARIMA) method in terms of error statistics and accuracy in capturing the temporal patterns of river corridor wells with various dynamics signatures. Our study demonstrates that the ARIMA models yield better average error statistics, although they tend to have larger errors during time windows with abrupt changes or high-frequency (daily and subdaily) variations. The LSTM-based models excel in capturing both high-frequency and low-frequency (monthly and seasonal) dynamics. However, the inclusion of high-frequency fluctuations may also lead to overly dynamic predictions in time windows that lack such fluctuations. The LSTM can take advantage of the spatial information from neighboring wells to improve the gap-filling accuracy, especially for long gaps in system states that vary at subdaily scales. While LSTM models require substantial training data and have limited extrapolation power beyond the conditions represented in the training data, they afford great flexibility to account for the spatial correlations, temporal correlations, and nonlinearity in data without a priori assumptions. Thus, LSTMs provide effective alternatives to fill in data gaps in spatially distributed time-series observations characterized by multiple dominant frequencies of variability, which are essential for advancing our understanding of dynamic complex systems.