Deep Learning for Isotope Hydrology: The Application of Long Short-Term Memory to Estimate High Temporal Resolution of the Stable Isotope Concentrations in Stream and Groundwater

Recent advances in laser spectroscopy has made it feasible to measure stable isotopes of water in high temporal resolution (i.e., sub-daily). High-resolution data allow the identification of fine-scale, short-term transport and mixing processes that are not detectable at coarser resolutions. Despite such advantages, operational routine and long-term sampling of stream and groundwater sources in high temporal resolution is still far from being common. Methods that can be used to interpolate infrequently measured data at multiple sampling sites would be an important step forward. This study investigates the application of a Long Short-Term Memory (LSTM) deep learning model to predict complex and non-linear high-resolution (3 h) isotope concentrations of multiple stream and groundwater sources under different landuse and hillslope positions in the Schwingbach Environmental Observatory (SEO), Germany. The main objective of this study is to explore the prediction performance of an LSTM that is trained on multiple sites, with a set of explanatory data that are more straightforward and less expensive to measure compared to the stable isotopes of water. The explanatory data consist of meteorological data, catchment wetness conditions, and natural tracers (i.e., water temperature, pH and electrical conductivity). We analyse the model's sensitivity to different input data and sequence lengths. To ensure an efficient model performance, a Bayesian optimization approach is employed to optimize the hyperparameters of the LSTM. Our main finding is that the LSTM allows for predicting stable isotopes of stream and groundwater by using only short-term sequence (6 h) of measured water temperature, pH and electrical conductivity. The best performing LSTM achieved, on average of all sampling sites, an RMSE of 0.7 parts per thousand, MAE of 0.4 parts per thousand, R-2 of 0.9 and NSE of 0.7. The LSTM can be utilized to predict and interpolate the continuous isotope concentration time series either for data gap filling or in case where no continuous data acquisition is feasible. This is very valuable in practice because measurements of these tracers are still much cheaper than stable isotopes of water and can be continuously conducted with relatively minor maintenance.

Automated summary

Recent advances in laser spectroscopy have made it possible to measure stable isotopes of water in high temporal resolution. This study explores the application of a Long Short-Term Memory (LSTM) deep learning model to predict complex and non-linear high-resolution isotope concentrations in multiple stream and groundwater sources. The LSTM achieved an average RMSE of 0.7 parts per thousand and can be used for data interpolation or gap filling.