| 23 Jun 2026
Hierarchical Graph Networks for Seasonal Forecasts of Terrestrial Water Storage Anomalies
Abstract. Fresh water availability is critical for ecosystems, agriculture, industry, and human communities. Anticipating drought conditions benefits from forecasting changes in terrestrial water storage (TWS), the total water stored on land across all compartments, including groundwater, rivers, glaciers, and soil moisture. While individual compartments, such as groundwater, are difficult to observe directly at large scales, TWS integrates their combined changes and can be measured globally through satellite gravimetry. Since 2002, the GRACE and GRACE Follow-On (GRACE-FO) missions have delivered monthly, global estimates of terrestrial water storage anomalies (TWSA), deviations from a long-term mean, making TWSA the most accessible large-scale indicator of hydrological change. Predicting TWSA is nonetheless challenging as it reflects processes operating at vastly different temporal and spatial scales. We present HiGNN-LSTM, a hierarchical graph neural network that represents the Earth across two spatial scales, coupled with an LSTM module to forecast global TWSA for up to six months ahead. As a proof of concept, we show that the hierarchical graph neural network can automatically generate meaningful input features for TWSA forecasting from ERA5 climate variables, without requiring manual predictor selection or lag-correlation analysis. Trained on a GRACE-like reconstruction of TWSA extending from 1979 to 2020, the model substantially reduces the one-month-lead RMSE relative to a seasonal climatology baseline (1.83 cm vs 3.70 cm) and consistently outperforms a ConvLSTM across the full six-month horizon. Skill over climatology shrinks at longer leads and is lost by six months, indicating that most of the gain concentrates at short leads. Evaluation against GRACE- and GRACE-FO-derived TWSA highlights the difficulty of transferring a model trained on reconstructed TWSA to satellite-derived observations.
I appreciate the substantial technical effort involved in developing and implementing this global hierarchical graph model. However, I have more fundamental concerns about the study's hydrological framing. The manuscript is primarily organized around a machine-learning architecture and then applies that architecture to TWSA, but it does not yet demonstrate that the resulting framework addresses a clearly formulated hydrological question. In particular, the central interpretation that the graph learns useful hydrological teleconnections is not supported by the current experiments. At present, the manuscript demonstrates that the proposed network can reproduce a reconstructed TWSA product more clearly than it demonstrates a new hydrological understanding or a useful advance in seasonal hydrological prediction. I therefore consider major revision necessary, and I am uncertain whether the required changes can be achieved without a substantial redesign of the study.
1) The current interpretability analysis does not yet establish which hydrological information the model has learned. The attribution analysis only shows that the output is sensitive to the GNN latent features, but it does not identify where the predictive information comes from. TWSA is primarily controlled by local water-balance processes and storage memory, and remote climate connections may provide additional information in specific regions and seasons. I suggest adding process-oriented attribution experiments and determining whether the learned remote connections correspond to known hydroclimatic relationships.
2) The practical hydrological value of forecasting total TWSA over a six-month horizon needs to be clarified. A technically accurate prediction of this integrated signal does not necessarily translate into useful forecasts of drought, groundwater deficit, reservoir conditions, or other hydrological impacts. I suggest that the authors define the intended hydrological application and evaluate metrics relevant to that application.
3) More importantly, because the seasonal cycle is retained in the target and the month of the year is explicitly provided as an input, the reported RMSE and correlation can be strongly influenced by the model’s ability to reproduce seasonality. For seasonal hydrological prediction, skill in the anomaly component is usually more informative than skill in the full signal. I recommend evaluating deseasonalized TWSA anomalies directly. The results should be reported separately for each lead time and basin.
4) The relationship between the predictor data and the reconstructed TWSA target requires a more careful discussion. The Li et al. (2021) reconstruction was itself produced using climatic and hydrological predictors and machine-learning methods, but the present model uses ERA5 climatic and hydrological variables to predict that reconstruction. Good performance on the reconstructed product may partly reflect HiGNN-LSTM's ability to reproduce relationships already built into that product. Ideally, the author may wish to repeat the analysis with more than one reconstruction product or provide a stronger observation-based evaluation.
5) Right now, it seems every ocean cluster is connected to every basin. I cannot immediately understand this strong structural assumption of universal ocean-to-basin connectivity. I suggest testing graph variants without ocean nodes, with only local basin connections, and with river-network connections. Otherwise, I don't think improved performance can be interpreted as evidence that the model has identified physically meaningful teleconnections.
Specific comments:
L24: However, these effects are not explicitly represented in the model inputs or graph structure, and their treatment in the reconstructed TWSA target remains unclear. The authors should clarify the extent to which the reconstruction preserves signals of human interventions. They should also discuss how detrending may remove persistent anthropogenic storage changes and how this affects transferability to GRACE observations and performance in strongly managed basins.
L60: Please specify which parts are hydrologically informed. The basin aggregation might be hydrologically motivated, but the nearest-neighbor and universal ocean-to-basin connections appear primarily geometric. Not sure of the value of basin aggregation here.
L69: For a hydrology journal, the manuscript should formulate one or more hydrological hypotheses in addition to this architectural objective. Otherwise, I have to say this manuscript is more suitable for a general Earth data science journal.
L82: Please explain why remote relationships are expected to contribute materially to TWSA prediction relative to local storage memory and local water-balance inputs with literature.
L92: Please specify the basin-selection procedure used to obtain the basin nodes. How are grid cells that intersect multiple basins treated?
L97: Connecting each basin to its geographically nearest neighbors does not necessarily represent hydrological interaction. Please explain how information transfer between hydrologically unrelated neighboring basins should be interpreted.
L133: Because the Li et al. (2021) reconstruction uses climatic and hydrological predictors, please compare its predictor set with the variables used in this study.
L145: Removing linear trends changes the scientific target. Please explain which hydrological signals are removed by detrending; some regions may be affected by long-term groundwater depletion or glacier mass loss.
L161: The CSR mascon product is just distributed on a 0.25-degree grid, but this grid spacing does not represent its independent spatial resolution. Please make sure this sentence is precise.
Section 4.1: Aggregating attribution values over all nodes removes the spatial and temporal information that is most relevant to the graph hypothesis. Please provide basin-specific examples and show how attribution changes across input months and lead times.
L191: All four latent dimensions having nonzero attribution by themselves does not demonstrate that they contain distinct or useful information. A latent-dimension removal experiment would provide more direct evidence.
L261: I cannot understand here. Predicting the full signal may be harder in absolute RMSE terms, but the strong seasonal cycle can make correlation and normalized skill easier to obtain. The comparison should use common anomaly-based metrics.
L290: The poor performance in anomaly-dominated basins may also reflect human water management, groundwater abstraction, snow processes, or reconstruction errors. The discussion currently focuses mainly on seasonality and graph connectivity.
L306: The experiments show that the full model outperforms ConvLSTM and an embedder-only variant, but they do not identify the learned connections as teleconnections.