Evaluation of transfer learning in hydrological forecasting using ensemble LSTM models: a statistical approach to uncertainty and accuracy

Global change poses significant challenges to water resource management. Water Table Depth (WTD) is a critical variable linking subsurface dynamics to land-surface processes; however, real-world observations remain sparse. Transfer learning can support WTD monitoring, but assessing prediction quality in locations without observations is challenging. This contribution explores a method using an assessment tool to estimate prediction quality in such locations. We implement an ensemble of 100 Long Short-Term Memory (LSTM) networks to predict WTD using the physically-based Terrestrial Systems Modeling Platform Groundwater to Atmosphere (TSMP-G2A) simulation dataset, spatially split into training and transfer subsets. The training subset is temporally split into training and testing time periods, while the transfer subset evaluates transferability to unseen locations within the TSMP-G2A dataset during the testing period. Each ensemble LSTM member was trained on a spatial sample of the training subset, randomly sampled based on geographic location. By leveraging the ensemble spread, we develop spread-skill relationships to assess prediction quality in the transfer subset. Results indicate good generalization and transfer abilities on the TSMP-G2A dataset within the study domain. Additionally, expanding each ensemble member's training subset from 100 to 400 grid cells improves global transfer prediction accuracy by 11.52 and 17.42% in root mean square error (RMSE) and Pearson correlation, respectively. The spread-skill relationships show a strong correlation between ensemble spread and both RMSE and absolute mean bias, suggesting that spread can effectively estimate prediction quality for these metrics without observations, whereas the relationship with Pearson correlation is weak. This study highlights transfer learning's potential to improve hydrological modeling and provides an assessment tool for prediction quality in regions lacking observations. Future research could extend this framework to evaluate its global-scale transferability and validate it against real-world observational data.