From conventional machine learning to Transformers: multi-model hindcasting of GRACE terrestrial water storage anomalies (TWSA) with multi-source validation

GRACE and GRACE-FO satellite missions offer an observation-based perspective on terrestrial water storage anomalies (TWSA), which is valuable for assessing climate variability and human influence on large-scale water resources. In practice, however, the short duration of the GRACE record and its coarse spatial resolution make it difficult to build long, spatially consistent storage information that are needed to study basin-scale responses to hydrologic extremes such as droughts and floods. To address this limitation, we develop a multi-model hindcasting framework that reconstructs monthly GRACE TWSA from hydro-climatic predictors and evaluates both predictive performance and hydrologic plausibility using independent evidence related to extremes.

We compare four models representing three methodological families: (i) tree-based machine learning (Extreme Gradient Boosting and Extra Trees Regressor), (ii) spatio-temporal deep learning (Convolutional LSTM), and (iii) an efficient Transformer architecture for long-sequence forecasting (Informer). All models are trained and tested over the observational GRACE period (2002–2025) using strict time-block splits, and then applied to hindcast historical monthly TWSA. Predictor co-variables include precipitation, evapotranspiration, temperature, soil moisture, and land data assimilation–based storage components from GLDAS products (Noah and CLSM), enabling the models to learn storage persistence and hydro-climatic controls beyond what can be inferred from GRACE alone. The performance of the models is assessed using standard error and agreement metrics (RMSE and correlation) as well as hydrologically oriented measures (Nash–Sutcliffe Efficiency and Kling–Gupta Efficiency), with additional diagnostics targeting the representation of seasonal and inter-annual variability.

Transformer model shows the best performance on testing periods with R² of 0.81, CC of 0.89, NSE of 0.86 and KGE of 0.88, and RMSE of 61.3 mm, while ETR showed the least R² of 0.713, CC of 0.76, NSE of 0.68 and KGE of 0.73. To move beyond statistical agreement with GRACE, we evaluate physical reliability through multi-source validation across all major sub-basins of Türkiye using (1) groundwater table observations and (2) independent flood information, including a flood potential indicator and mapped flood extents where available. All model families capture key groundwater storage variability, while Informer generally provides the highest predictive skill and better preserves persistence and the seasonal cycle than ConvLSTM and the tabular learners. Periods of elevated reconstructed storage are consistently associated with historical record of higher flood potential, while the lower extremes of TWSA record identifying historical droughts, supporting the hydrologic realism of the hindcast products. At the same time, the tree-based models—particularly XGBoost—remain attractive due to their low computational cost and, their stronger ability to reproduce observed flood-extent spatial patterns in some basins while maintaining extreme behavior comparable to transformer architecture.

Overall, the inter-comparison highlights practical trade-offs among accuracy, robustness to extremes, and computational efficiency, and provides guidance for scalable GRACE TWSA hindcasting on cloud platforms. The validation approach is transferable and supports the use of reconstructed storage fields for drought–flood assessment and basin-scale water resources analysis.