A deep learning approach based on Bayesian optimization for prediction of stable isotope concentrations in stream and groundwater

High temporal resolution (i.e., sub-daily) stable isotope concentrations of multiple stream and groundwater sources reveal small-scale, rapid transport and mixing processes that are not discernible at coarser resolution. However, long-term, routine sampling of multiple water sources at high temporal resolution is far from widespread. In recent years, the rise of deep learning offers the opportunity to further improve the prediction accuracy of infrequently measured data owing to its capability to efficiently abstract interrelationship patterns in complex and non-linear systems. In this research, we explore the potential of a Long Short-Term Memory (LSTM) deep learning model to predict high-resolution (3 h) isotope concentrations of multiple stream and groundwater sources in the Schwingbach Environmental Observatory (SEO), Germany. The key objective of this study is to examine the predictive performance of the LSTM that is simultaneously trained on multiple sites with a set of explanatory data that are more convenient and less expensive to collect in comparison to the stable water isotopes. The explanatory data comprise meteorological data, soil moisture, and natural tracers (i.e., water temperature, pH, and electrical conductivity). A sensitivity analysis is applied to investigate the model performance under different input data and sequence lengths. A Bayesian optimization algorithm is employed to optimize the hyperparameters of the LSTM to ensure an efficient model performance. The main outcome of our study shows that the LSTM enables the prediction of stable isotopes in streams and groundwater by using only a short sequence (6 hours) of recorded water temperature, pH, and electrical conductivity. The best performing LSTM reached on average an RMSE of 0.7‰, MAE of 0.4‰, R² of 0.9, and NSE of 0.7. The proposed model can be used to predict continuous time series of stable water isotope concentrations, either for gap filling or in cases when continuous data collection is not possible. This is very worthwhile in practice since measurements of tracers used in our LSTM are still much cheaper than those of stable water isotopes and can be carried out continuously with relatively low associated maintenance. In future research, the pre-trained LSTM should be applied through transfer learning to other catchments at which the length and resolution of available data are not sufficient to build a standalone model.