Application of Ensemble LSTM Transfer Learning for Water Table Depth Prediction and Uncertainty Assessment in Data-Scarce Regions

Global change poses significant challenges to water resource management. Water Table Depth (WTD) is a critical variable linking subsurface dynamics with land surface processes. Local observations support WTD monitoring; however, observations are sparse and unevenly distributed. Transfer learning applications are a solution for WTD monitoring; however, prediction quality assessment is challenging in locations without observations. Consequently, a generalized, scalable, and transferable WTD monitoring framework with a prediction quality assessment tool is essential for such locations.

This contribution explores a method to estimate prediction quality for transfer learning applications from observed grid cells to target locations without observations. Specifically, we implement an ensemble approach with 100 Long Short-Term Memory (LSTM) networks to predict WTD. By leveraging the ensemble spread, we develop spread-skill relationships (which measure the ability of the ensemble uncertainty to predict accuracy) to assess prediction quality in target locations.

We use the Terrestrial Systems Modelling Platform Ground to Atmosphere (TSMP-G2A) dataset from 2001 to 2020, and spatially split it into training and transfer sets. Each ensemble LSTM member was trained on a spatial subset of the training set from 2001 to 2015, randomly sampled based on geographic location. We also evaluated the local prediction performance on the training grid cells over the testing period from 2016 to 2020. The transfer learning performance was assessed on the transfer set, with the same testing period but different locations from the training set. The spread-skill relationships were explored between ensemble spread and performance metrics on the transfer set.

Results indicate good generalization and transfer abilities. Additionally, expanding the spatial size of each ensemble member’s training subset from 100 to 400 grid cells leads to a global improvement in transfer prediction accuracy by 11.52% and 17.42% in RMSE and Pearson correlation, respectively. The spread-skill relationships show a strong correlation between ensemble spread (ensemble variance and interquartile range) and both RMSE and absolute mean bias, demonstrating a potential effective estimation of prediction quality for certain performance metrics without the need for observations. In contrast, the ensemble spread exhibits a weak relationship with Pearson correlation.

The study highlights the potential of transfer learning to improve hydrological modeling and provides an assessment tool for prediction quality, particularly in regions lacking observations. These findings demonstrate the feasibility of scalable data-driven groundwater prediction and suggest that future research could extend this framework to evaluate its transferability and performance at the global scale.