A deep learning approach for spatio-temporal prediction of stable water isotopes in soil moisture

Water flows and related mixing dynamics in the unsaturated zone are difficult to measure directly, so stable water isotope tracers have been used successfully to quantify flux and storage dynamics and to constrain process-based hydrological models as proxy data. In this study, a data-driven model based on deep learning was adapted to interpolate and extrapolate spatio-temporal isotope signals of δ¹⁸O and δ²H in soil water in three dimensions. Further, this was also used to help quantify evapotranspiration and groundwater recharge processes in the unsaturated zone. To consider both spatial and temporal dependencies of water isotope signals in the model design, the output space was decomposed into temporal basis functions and spatial coefficients using singular value decomposition. Then, temporal functions and spatial coefficients were predicted separately by specialized deep learning models in interdependencies among target data, such as the LSTM model and convolutional neural network. Finally, the predictions by the models were integrated and analyzed post-hoc using XAI tools.

Such an integrated framework has the potential to improve understanding of model behavior based on features (e.g., climate, hydrological component) connected to either temporal or spatial information. Furthermore, the model can serve as a surrogate model for process-based hydrological models, improving the use of process-based models as learning tools.