pith. sign in

arxiv: 2606.23833 · v1 · pith:TKNMS2MPnew · submitted 2026-06-22 · 💻 cs.LG

Reconstructing GRACE Terrestrial Water Storage with Spatio-Temporal Graph Neural Networks: An Application to South America

Lukas Arzoumanidis , Lara Johannsen , Klara Middendorf , Annette Eicker , Youness Dehbi This is my paper

Pith reviewed 2026-06-26 09:02 UTC · model grok-4.3

classification 💻 cs.LG
keywords terrestrial water storageGRACE reconstructiongraph neural networksERA5South Americahydrological modelingspatio-temporal modelingclimate variability
0
0 comments X

The pith

A graph neural network reconstructs GRACE terrestrial water storage back to 1940 from ERA5 data at basin correlations of 0.94.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that adapting a multi-variate time series graph neural network to satellite geodesy can learn the mapping from daily ERA5 meteorological forcing to monthly GRACE terrestrial water storage anomalies. This matters because the GRACE record begins only in 2002, limiting analyses of longer-term climate and human influences on the water cycle. The model encodes spatial dependencies through a hybrid adjacency matrix that blends geodesic proximity with lagged climatic correlations, yielding a grid-cell Pearson correlation of 0.69, a basin-mean correlation of 0.94, and near-zero bias. It matches the performance of leading reconstruction methods at basin scale while requiring only half to one-tenth as many predictors and reproduces the spatial patterns of the 2015/16 El Niño and 2020/21 La Niña events.

Core claim

The MTGNN architecture with a static hybrid adjacency matrix that combines geodesic proximity and lagged correlations of climatic time series reconstructs monthly GRACE-like TWSA from ERA5 precipitation, evapotranspiration and runoff, attaining a grid-cell Pearson correlation of 0.69, basin-mean correlation of 0.94 and near-zero bias while remaining statistically competitive with GTWS-MLrec, RM-REC and GRAiCE at basin scale despite using roughly half to a tenth of their predictors.

What carries the argument

Multi-variate time series graph neural network (MTGNN) equipped with a static hybrid adjacency matrix that merges geodesic proximity and lagged climatic correlations to capture local hydrological coupling and large-scale teleconnections.

If this is right

  • The reconstruction supplies an 80-year TWS record suitable for climate-scale studies of variability and human impacts.
  • All compared reconstruction methods share characteristic performance weaknesses in arid regions.
  • The model reproduces the spatial fingerprints of major ENSO events such as the 2015/16 El Niño and 2020/21 La Niña.
  • High basin-scale accuracy is maintained even when the number of meteorological predictors is reduced by a factor of two to ten.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same graph architecture could be retrained on global rather than South-American data to produce consistent long-term TWS fields worldwide.
  • The reduced predictor count may lower computational cost enough to support ensemble reconstructions under multiple climate scenarios.
  • Longer TWS series could be combined with other observational records to separate natural from anthropogenic contributions to storage trends.
  • The hybrid adjacency construction offers a template for incorporating additional geophysical constraints such as topography or soil properties.

Load-bearing premise

The statistical mapping learned between ERA5 forcing and GRACE TWS in the 2002-present overlap period continues to hold for the 1940-2001 period without major non-stationarities in the hydrological system.

What would settle it

A substantial drop in correlation or emergence of large bias when the trained model is tested against independent pre-2002 TWS estimates or against GRACE observations withheld from a later validation window.

Figures

Figures reproduced from arXiv: 2606.23833 by Annette Eicker, Klara Middendorf, Lara Johannsen, Lukas Arzoumanidis, Youness Dehbi.

Figure 1
Figure 1. Figure 1: Model architecture of the adapted MTGNN (modi [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sequential train/validation/test split along the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Observed vs. predicted TWSA with scatter plots for [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Spatial difference between prediction and observa [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Residual (de-trended, de-seasonalized) TWSA of [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Deviations from the climatological monthly mean [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: MTGNN (orange line) vs. GTWS-MLrec (green line) [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 10
Figure 10. Figure 10: Taylor diagram of the reconstructions relative to [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: TWSA at the exemplary Amazon grid cell for each [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: Hybrid framework combining the data loss with a [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
read the original abstract

Terrestrial water storage (TWS) integrates snow, soil moisture, surface water, and groundwater and is a key indicator of how climate variability and human activity reshape the global water cycle. The GRACE and GRACE-FO satellite missions provide the only direct, globally consistent observations of TWS change, but their record only begins in 2002 which is too short for many climate-scale analyses. We present a deep learning application that reconstructs monthly GRACE-like TWS anomalies (TWSA) back to 1940 by learning the relationship between daily ERA5 meteorological forcing (precipitation, evapotranspiration, runoff) and monthly GRACE observations. In contrast to prior reconstruction approaches based on grid-cell-wise regression, CNNs, or LSTMs, we adapt a multi-variate time series graph neural network (MTGNN) architecture, which was originally developed for mobility and traffic forecasting on urban sensor networks to this satellite-geodesy task. Spatial dependencies are encoded in a static, interpretable hybrid adjacency matrix that combines geodesic proximity with lagged correlations of climatic time series, capturing both local hydrological coupling and large-scale teleconnections. The reconstruction achieves a grid-cell Pearson correlation of 0.69, a basin-mean correlation of 0.94, and a near-zero bias, and it reproduces the spatial fingerprints of the 2015/16 El Ni\~no and 2020/21 La Ni\~na events. A systematic comparison with established reconstruction approaches (GTWS-MLrec, RM-REC, GRAiCE) shows that the graph-based model is statistically competitive at basin scale, reaching a correlation within 0.025 of the best baseline while using only roughly half to a tenth of the predictors the other models require and revealing characteristic weaknesses in arid regions in all models. The complete implementation is publicly available at github.com/hcu-cml/MTGNN-TWS-Reconstruction-GRACE

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript adapts a multi-variate time series graph neural network (MTGNN) to reconstruct monthly GRACE-like terrestrial water storage anomalies (TWSA) over South America from daily ERA5 meteorological forcings (precipitation, evapotranspiration, runoff), using a static hybrid adjacency matrix that combines geodesic proximity and lagged climatic correlations. The model is trained on the 2002-present GRACE overlap and applied to produce a reconstruction back to 1940. Reported performance includes a grid-cell Pearson correlation of 0.69, basin-mean correlation of 0.94, near-zero bias, reproduction of 2015/16 El Niño and 2020/21 La Niña spatial fingerprints, and basin-scale competitiveness with GTWS-MLrec, RM-REC, and GRAiCE while using roughly half to one-tenth the predictors. The implementation is released publicly.

Significance. If the learned ERA5-to-TWSA mapping holds, the approach supplies a longer TWS record with substantially reduced predictor count and explicit public code, which is a clear strength for reproducibility. The basin-scale correlation and event reproduction are competitive, and the identification of shared weaknesses in arid regions across models is useful. Significance is limited by the absence of quantified uncertainty on the performance metrics and by the untested extrapolation assumption.

major comments (2)
  1. [Abstract] Abstract and comparison results: the statement that the model reaches a correlation 'within 0.025 of the best baseline' is presented without error bars, bootstrap intervals, or cross-validation statistics on the basin-scale metric, which is load-bearing for the competitiveness claim.
  2. [Reconstruction to 1940] Reconstruction to 1940 section: the central application of the trained MTGNN weights and hybrid adjacency to the 1940-2001 period rests on the assumption that P(TWSA | ERA5 forcings, graph) is stationary across the full interval, yet no regime-shift diagnostic, land-use proxy comparison, or pre-2002 validation is described.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below, proposing revisions where they strengthen the work without misrepresenting the results.

read point-by-point responses

  1. Referee: [Abstract] Abstract and comparison results: the statement that the model reaches a correlation 'within 0.025 of the best baseline' is presented without error bars, bootstrap intervals, or cross-validation statistics on the basin-scale metric, which is load-bearing for the competitiveness claim.

    Authors: We agree that uncertainty quantification would better support the basin-scale competitiveness claim. In the revised manuscript we will add bootstrap confidence intervals (resampling over basins and years) to the reported basin-mean correlations, allowing readers to assess whether the 0.025 difference is statistically distinguishable from zero. revision: yes

  2. Referee: [Reconstruction to 1940] Reconstruction to 1940 section: the central application of the trained MTGNN weights and hybrid adjacency to the 1940-2001 period rests on the assumption that P(TWSA | ERA5 forcings, graph) is stationary across the full interval, yet no regime-shift diagnostic, land-use proxy comparison, or pre-2002 validation is described.

    Authors: The referee correctly notes the stationarity assumption required for the 1940–2001 extrapolation. Direct pre-2002 validation against GRACE is impossible. We will add (i) a regime-shift analysis on the ERA5 forcing distributions (e.g., Kolmogorov–Smirnov tests on precipitation and evapotranspiration across 1940–2001 vs. 2002–present) and (ii) an expanded discussion of the assumption’s limitations, including the lack of land-use change proxies. These additions will be included in the revised text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper trains an MTGNN on the 2002-present overlap between external ERA5 meteorological forcings and GRACE TWSA observations, then applies the learned mapping to pre-2002 ERA5 data. Reported metrics (grid-cell correlation 0.69, basin-mean 0.94) are measured against held-out GRACE data inside the overlap period and do not reduce to fitted parameters by construction. The hybrid adjacency matrix and MTGNN architecture are adapted from external traffic-forecasting literature with no load-bearing self-citations. The stationarity assumption for extrapolation is a correctness risk but is not a circularity issue per the evaluation rules.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Central claim rests on the learned mapping from ERA5 forcing to TWS generalizing outside the training window and on the hybrid adjacency matrix adequately capturing both local and teleconnected hydrological dependencies.

free parameters (1)
  • MTGNN hyperparameters and weights
    All neural-network parameters are fitted to the GRACE-ERA5 overlap data.
axioms (1)
  • domain assumption The relationship between daily ERA5 meteorological variables and monthly TWS anomalies is stationary across 1940-present.
    Required for the extrapolation step described in the abstract.

pith-pipeline@v0.9.1-grok · 5907 in / 1244 out tokens · 24175 ms · 2026-06-26T09:02:34.271910+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 31 canonical work pages

  1. [1]

    Lukas Arzoumanidis, Julius Knechtel, Jan-Henrik Haunert, and Youness Dehbi

  2. [2]

    doi:10.1080/15230406.2025.2468304

    Semantic Segmentation of Historical Maps Using Self-Constructing Graph Convolutional Networks.Cartography and Geographic Information Science53, 2 (2026), 177–187. doi:10.1080/15230406.2025.2468304

    work page doi:10.1080/15230406.2025.2468304 2026

  3. [3]

    Akarsh Asoka and Vimal Mishra. 2020. Anthropogenic and Climate Contributions on the Changes in Terrestrial Water Storage in India.Journal of Geophysical Research: Atmospheres125, 10 (2020), 1–21. doi:10.1029/2020JD032470

    work page doi:10.1029/2020jd032470 2020

  4. [4]

    Jules J. Berman. 2016. Chapter 4 - Understanding Your Data. InData Simplification. Morgan Kaufmann, Boston, 135–187. doi:10.1016/B978-0-12-803781-2.00004-7

    work page doi:10.1016/b978-0-12-803781-2.00004-7 2016

  5. [5]

    Bucker, Ernest Pokropek, Willa Potosnak, Salomey Osei, and Björn Lütjens

    Salva Rühling Cachay, Emma Erickson, Arthur Fender C. Bucker, Ernest Pokropek, Willa Potosnak, Salomey Osei, and Björn Lütjens. 2020. Graph Neural Networks for Improved El Niño Forecasting. InTackling Climate Change with Machine Learning Workshop at NeurIPS 2020. https://www.climatechange.ai/papers/ neurips2020/86

    2020

  6. [6]

    Jianli Chen, Anny Cazenave, Christoph Dahle, William Llovel, Isabelle Panet, Julia Pfeffer, and Lorena Moreira. 2022. Applications and Challenges of GRACE and GRACE Follow-On Satellite Gravimetry.Surveys in Geophysics43, 1 (2022), 305–345. doi:10.1007/s10712-021-09685-x

    work page doi:10.1007/s10712-021-09685-x 2022

  7. [7]

    Tapley, and John C

    Minkang Cheng, Byron D. Tapley, and John C. Ries. 2013. Deceleration in the Earth’s Oblateness.Journal of Geophysical Research: Solid Earth118, 2 (2013), 740–747. doi:10.1002/jgrb.50058

    work page doi:10.1002/jgrb.50058 2013

  8. [8]

    Gabriel Jonas da Silva Duarte, Tamara Arruda Pereira, Erik Jhones Fernandes Nascimento, Diego Parente Paiva Mesquita, and Amauri Holanda de Souza Jr. 2021. How Do Loss Functions Impact the Performance of Graph Neural Networks?. InCongresso Brasileiro de Inteligência Computacional (CBIC 2021). doi:10.21528/ CBIC2021-161

    2021

  9. [9]

    Annette Eicker, Laura Jensen, Viviana Wöhnke, Henryk Dobslaw, Andreas Kvas, Torsten Mayer-Gürr, and Robert Dill. 2020. Daily GRACE Satellite Data Evaluate Short-term Hydro-meteorological Fluxes from Global Atmospheric Reanalyses. Scientific Reports10, 1 (2020), 4504. doi:10.1038/s41598-020-61166-0

    work page doi:10.1038/s41598-020-61166-0 2020

  10. [10]

    2020.CCI Sea Level Budget Closure: Product Validation and Intercomparison Report (PVIR)

    European Space Agency. 2020.CCI Sea Level Budget Closure: Product Validation and Intercomparison Report (PVIR). Technical Report D4.7 v1.1. Climate Change Initiative. https://climate.esa.int/documents/192/ESA_SLBC_cci_D4.7_v1.1.pdf

    2020

  11. [11]

    Gentner, Junyang Gou, Mohammad J

    Luis Q. Gentner, Junyang Gou, Mohammad J. Tourian, Lara Börger, Nico Sneeuw, and Benedikt Soja. 2026. DeepRec: Global Terrestrial Water Storage Recon- struction Since 1941 Using Spatiotemporal-Aware Deep Learning Model.Jour- nal of Geophysical Research: Machine Learning and Computation3, 1 (2026). doi:10.1029/2025JH000889

    work page doi:10.1029/2025jh000889 2026

  12. [12]

    Jinyun Guo, Dapeng Mu, Xin Liu, Haoming Yan, and Honglei Dai. 2014. Equiv- alent Water Height Extracted from GRACE Gravity Field Model with Robust Independent Component Analysis.Acta Geophysica62, 4 (01 Aug 2014), 953–972. doi:10.2478/s11600-014-0210-0

    work page doi:10.2478/s11600-014-0210-0 2014

  13. [13]

    Yi Guo, Naichen Xing, Fuping Gan, Baikun Yan, and Juan Bai. 2023. Evaluating the Hydrological Components Contributions to Terrestrial Water Storage Changes in Inner Mongolia with Multiple Datasets.Sensors23, 14 (2023). doi:10.3390/ s23146452

    2023

  14. [14]

    Hans Hersbach, Bill Bell, Paul Berrisford, Giovanni Biavati, András Horányi, Joaquín Muñoz Sabater, Julien Nicolas, Carole Peubey, Raluca Radu, Iryna Rozum, Dinand Schepers, Adrian Simmons, Cornel Soci, Dick Dee, and Jean-Noël Thépaut

  15. [15]

    Copernicus Cli- mate Change Service (C3S) Climate Data Store (CDS)

    ERA5 Hourly Data on Single Levels from 1940 to Present. Copernicus Cli- mate Change Service (C3S) Climate Data Store (CDS). doi:10.24381/cds.adbb2d47

    work page doi:10.24381/cds.adbb2d47 1940

  16. [16]

    Hans Hersbach, Bill Bell, Paul Berrisford, Shoji Hirahara, András Horányi, Joaquín Muñoz-Sabater, Julien Nicolas, Carole Peubey, Raluca Radu, Dinand Schepers, Adrian Simmons, Cornel Soci, Saleh Abdalla, Xavier Abellan, Gianpaolo Bal- samo, Peter Bechtold, Gionata Biavati, Jean Bidlot, Massimo Bonavita, Giovanna De Chiara, Per Dahlgren, Dick Dee, Michail D...

    work page doi:10.1002/qj.3803 2020

  17. [17]

    Ruixi Huang, Yin Long, and Tehseen Zia. 2025. A Physical-Enhanced Spatio- Temporal Graph Convolutional Network for River Flow Prediction.Applied Sciences15, 16 (2025). doi:10.3390/app15169054

    work page doi:10.3390/app15169054 2025

  18. [18]

    Vincent Humphrey and Lukas Gudmundsson. 2019. GRACE-REC: A Reconstruc- tion of Climate-driven Water Storage Changes over the Last Century.Earth System Science Data11, 3 (2019), 1153–1170. doi:10.5194/essd-11-1153-2019

    work page doi:10.5194/essd-11-1153-2019 2019

  19. [19]

    Laura Jensen, Annette Eicker, Henryk Dobslaw, and Roland Pail. 2020. Emerging Changes in Terrestrial Water Storage Variability as a Target for Future Satellite Gravity Missions.Remote Sensing12, 23 (2020). doi:10.3390/rs12233898

    work page doi:10.3390/rs12233898 2020

  20. [20]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. 2015. Adam: A Method for Stochastic Op- timization. In3rd International Conference on Learning Representations (ICLR). https://arxiv.org/abs/1412.6980

    Pith/arXiv arXiv 2015

  21. [21]

    Nikolas Kirschstein and Yixuan Sun. 2024. The merit of river network topology for neural flood forecasting. InProceedings of the 41st International Conference on Machine Learning(Vienna, Austria)(ICML’24). Article 990, 13 pages

    2024

  22. [22]

    Enrico Kurtenbach, Annette Eicker, Torsten Mayer-Gürr, Matthias Holschneider, Hayn Hayn, Marcel Fuhrmann, and Jürgen Kusche. 2012. Improved daily GRACE gravity field solutions using a Kalman smoother.Journal of Geodynamics59–60 (2012), 39–48. doi:10.1016/j.jog.2012.02.006

    work page doi:10.1016/j.jog.2012.02.006 2012

  23. [23]

    Landerer, Frank M

    Felix W. Landerer, Frank M. Flechtner, Himanshu Save, Frank H. Webb, Tamara Bandikova, William I. Bertiger, Srinivas V. Bettadpur, Sung Hun Byun, Christoph Dahle, Henryk Dobslaw, Eugene Fahnestock, Nate Harvey, Zhigui Kang, Gerhard L. H. Kruizinga, Bryant D. Loomis, Christopher McCullough, Michael Murböck, Peter Nagel, Meegyeong Paik, Nadege Pie, Steve Po...

    work page doi:10.1029/2020gl088306 2020

  24. [24]

    Fupeng Li, Jürgen Kusche, Nengfang Chao, Zhengtao Wang, and Anno Löcher

  25. [25]

    doi:10.1029/2021GL093492

    Long-Term (1979-Present) Total Water Storage Anomalies Over the Global Land Derived by Reconstructing GRACE Data.Geophysical Research Letters48, 8 (2021), 1–10. doi:10.1029/2021GL093492

    work page doi:10.1029/2021gl093492 1979

  26. [26]

    Tourian, Nico Sneeuw, and Johannes Riegger

    Christof Lorenz, Harald Kunstmann, Balaji Devaraju, Mohammad J. Tourian, Nico Sneeuw, and Johannes Riegger. 2014. Large-Scale Runoff from Landmasses: A Global Assessment of the Closure of the Hydrological and Atmospheric Water Balances.Journal of Hydrometeorology15, 6 (2014), 2111–2139. doi:10.1175/JHM- D-13-0157.1

    work page doi:10.1175/jhm- 2014

  27. [27]

    Kuang Luo, Jingshang Zhao, Yingping Wang, Jiayao Li, Junjie Wen, Jiong Liang, Henry Soekmadji, and Shaolin Liao. 2025. Physics-Informed Neural Networks for PDE Problems: A Comprehensive Review.Artificial Intelligence Review58, 10 (2025), 323. doi:10.1007/s10462-025-11322-7

    work page doi:10.1007/s10462-025-11322-7 2025

  28. [28]

    Torsten Mayer-Gürr, Saniya Behzadpour, Annette Eicker, Matthias Ellmer, Beate Koch, Sandro Krauss, Christian Pock, Daniel Rieser, Sebastian Strasser, Barbara Süsser-Rechberger, Norbert Zehentner, and Andreas Kvas. 2021. GROOPS: A Software Toolkit for Gravity Field Recovery and GNSS Processing.Computers & Geosciences155 (2021), 104864. doi:10.1016/j.cageo....

    work page doi:10.1016/j.cageo.2021.104864 2021

  29. [29]

    Torsten Mayer-Gürr, Saniya Behzadpur, Matthias Ellmer, Andreas Kvas, Beate Klinger, Sebastian Strasser, and Norbert Zehentner. 2018. ITSG-Grace2018 – Monthly, Daily and Static Gravity Field Solutions from GRACE. doi:10.5880/ ICGEM.2018.003

    2018

  30. [30]

    Irene Palazzoli, Serena Ceola, and Pierre Gentine. 2025. GRAiCE: reconstructing terrestrial water storage anomalies with recurrent neural networks.Scientific Data12, 1 (2025), 146. doi:10.1038/s41597-025-04403-3

    work page doi:10.1038/s41597-025-04403-3 2025

  31. [31]

    Nijia Qian, Guobin Chang, Pavel Ditmar, Jingxiang Gao, and Zhengqiang Wei

  32. [32]

    doi:10.3390/rs14122810

    Sparse DDK: A Data-Driven Decorrelation Filter for GRACE Level-2 Products.Remote Sensing14, 12 (2022). doi:10.3390/rs14122810

    work page doi:10.3390/rs14122810 2022

  33. [33]

    Zuzana Reitermanová. 2010. Data Splitting. InWDS’10 Proceedings of Contributed Papers: Part I – Mathematics and Computer Sciences. 31–36

    2010

  34. [34]

    Silva, Didier A

    Filipi N. Silva, Didier A. Vega-Oliveros, Xiaoran Yan, Alessandro Flammini, Filippo Menczer, Filippo Radicchi, Ben Kravitz, and Santo Fortunato. 2021. Detecting Climate Teleconnections With Granger Causality.Geophysical Research Letters 48, 18 (2021). doi:10.1029/2021GL094707

    work page doi:10.1029/2021gl094707 2021

  35. [35]

    Dalwinder Singh and Birmohan Singh. 2022. Feature wise normalization: An effective way of normalizing data.Pattern Recognition122 (2022), 108307. doi:10. 1016/j.patcog.2021.108307

    arXiv 2022

  36. [36]

    Sun, Peishi Jiang, Maruti K

    Alexander Y. Sun, Peishi Jiang, Maruti K. Mudunuru, and Xingyuan Chen. 2021. Explore Spatio-Temporal Learning of Large Sample Hydrology Using Graph Neu- ral Networks.Water Resources Research57, 12 (2021). doi:10.1029/2021WR030394

    work page doi:10.1029/2021wr030394 2021

  37. [37]

    Yu Sun, Pavel Ditmar, and Riccardo Riva. 2017. Statistically optimal estimation of degree-1 and C20 coefficients based on GRACE data and an ocean bottom pressure model.Geophysical Journal International210, 3 (2017), 1305–1322. doi:10.1093/gji/ggx241

    work page doi:10.1093/gji/ggx241 2017

  38. [38]

    B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber. 2004. The gravity recovery and climate experiment: Mission overview and early results.Geophysical Research Letters31, 9 (2004). doi:10.1029/2004GL019920

    work page doi:10.1029/2004gl019920 2004

  39. [39]

    Tapley, Michael M

    Byron D. Tapley, Michael M. Watkins, Frank Flechtner, Christoph Reigber, Srini- vas Bettadpur, Matthew Rodell, Ingo Sasgen, James S. Famiglietti, Felix W. Lan- derer, Don P. Chambers, John T. Reager, Alex S. Gardner, Himanshu Save, Erik R. Ivins, Sean C. Swenson, Carmen Boening, Christoph Dahle, David N. Wiese, Henryk Dobslaw, Mark E. Tamisiea, and Isabel...

    work page doi:10.1038/s41558-019-0456-2 2019

  40. [40]

    Isaac Ronald Ward, Jack Joyner, Casey Lickfold, Yulan Guo, and Mohammed Bennamoun. 2022. A Practical Tutorial on Graph Neural Networks.ACM Comput. Surv.54, 10s (2022), 35 pages. doi:10.1145/3503043

    work page doi:10.1145/3503043 2022

  41. [41]

    Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Philip S. Yu. 2021. A Comprehensive Survey on Graph Neural Networks.IEEE Transactions on Neural Networks and Learning Systems32, 1 (2021), 4–24. doi:10. 1109/TNNLS.2020.2978386

    arXiv 2021

  42. [42]

    Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, Xiaojun Chang, and Chengqi Zhang. 2020. Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. InProceedings of the 26th ACM SIGKDD International Conference acronym ’XX, June 03–05, 2018, Woodstock, NY Arzoumanidis et al. Conference on Knowledge Discovery & Data Mining(Virtua...

    work page doi:10.1145/3394486.3403118 2020

  43. [43]

    Slater, Abdou Khouakhi, Le Yu, Pan Liu, Fupeng Li, Yadu Pokhrel, and Pierre Gentine

    Jiabo Yin, Louise J. Slater, Abdou Khouakhi, Le Yu, Pan Liu, Fupeng Li, Yadu Pokhrel, and Pierre Gentine. 2023. GTWS-MLrec: global terrestrial water storage reconstruction by machine learning from 1940 to present.Earth System Science Data15, 12 (2023), 5597–5615. doi:10.5194/essd-15-5597-2023

    work page doi:10.5194/essd-15-5597-2023 2023

  44. [44]

    Qianheng Zhang, Dev Paul, Michelle Miller, Alfonso Morales, and Song Gao. 2025. Scalable Inter-County Food Flow Prediction Using Graph Neural Networks. In Proceedings of the 33rd ACM International Conference on Advances in Geographic Information Systems(The Graduate Hotel Minneapolis, Minneapolis, MN, USA) (SIGSPATIAL ’25). Association for Computing Machi...

    work page doi:10.1145/3748636.3764168 2025

  45. [45]

    Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun. 2020. Graph neural networks: A review of methods and applications.AI Open1 (2020), 57–81. doi:10.1016/j. aiopen.2021.01.001

    work page doi:10.1016/j 2020

  46. [46]

    2002.Learning from Labeled and Unlabeled Data with Label Propagation

    Xiaojin Zhu and Zoubin Ghahramani. 2002.Learning from Labeled and Unlabeled Data with Label Propagation. Technical Report CMU-CALD-02-107. Carnegie Mellon University, School of Computer Science. https://mlg.eng.cam.ac.uk/ zoubin/papers/CMU-CALD-02-107.pdf

    2002