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the Creative Commons Attribution 4.0 License.
| 27 May 2025
A Review of Current Best Practices and Future Directions in Assimilating GRACE/-FO Terrestrial Water Storage Data into Numerical Models
Abstract. Water cycle reanalyses, generated by integrating observations into hydrological and land surface models, provide long-term and consistent estimates of key water cycle components. Reanalyses are essential to understand hydrological variability, extreme events such as droughts and floods, and to improve water resource management. Over the past two decades, the assimilation of terrestrial water storage anomaly data from the GRACE and GRACE Follow-On (GRACE/-FO) missions has significantly enhanced these reanalyses, as GRACE/-FO observations uniquely constrain total water storage variability across all terrestrial compartments. Incorporating GRACE/-FO data has led to major advances in representing trends in key hydrological variables, climate-driven changes in the water cycle, and anthropogenic influences such as irrigation-induced groundwater depletion – factors often poorly captured in models. However, challenges remain, particularly in resolving mismatches in spatial and temporal resolution between GRACE/-FO observations and high-resolution models, and there is no consensus yet on the optimal approach for assimilating GRACE/-FO data. In light of the upcoming launches of next-generation gravity missions and the development of increasingly sophisticated Earth system modeling frameworks, it is an opportune time to compile the recommendations of GRACE/-FO data assimilation studies to date, in an attempt to converge to best practices. This review synthesizes past achievements, critically examines unresolved challenges, and explores future directions for advancing water cycle reanalyses using satellite gravimetry observations through improved assimilation strategies, machine learning, and near-real-time intake of satellite data.
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Status: open (until 10 Oct 2025)
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RC1: 'Comment on egusphere-2025-2058', Anonymous Referee #1, 30 Aug 2025
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This paper reviews data assimilation techniques and applications that combine GRACE water storage data with hydrological modeling to improve estimation of water storages and fluxes. The paper is of interest to the HESS readership and generally informative and well written. Overall, I enjoyed reading the paper, but I think there is room for increasing impact and accessibility of the work. My comments are detailed below.
1. Contribution of the paper: the introduction asserts that "a thorough synthesis of existing studies is not yet available" (line 119). There have been previous review papers on GRACE data assimilation, so this statement needs clarification and the specific contribution of this review paper needs to be articulated better.
2. Structure of the paper: the paper could benefit from a more systematic structure. For example, the authors could start by introducing the three main components of a GRACE DA system (observation model and errors, hydrological model and errors, DA algorithm and setup) and then systematically present previous work, best practices, open problems, and future directions for those three components. I mention these three components, because that is what the conclusions section ("synthesis" section 7) uses. The other sections of the paper do not really follow this pattern (or at least less obviously so). A more consistent structure could help readability and coherence.
3. It's interesting that a paper on data assimilation manages to avoid any mathematical equations. On the one hand, this makes the material readable, but on the other hand it can also make things less precise/concrete. For example, section 3.5 introduces "innovations" and "increments" without defining these in an equation. The meaning of these terms is described on lines 458-460, but for readers not familiar with data assimilation the connection between them may remain a bit vague without an equation. Do the authors think this is a problem?
4. Observation errors:
4a. The use of grid scaling factors to restore some of the signal in GRACE data is mentioned on lines 180-181: is any advancement or alternative approach needed here since these scaling factors are derived from hydrological models and therefore contaminated by various errors (as also acknowledged on lines 224-225)?
4b. Line 240: why are the relationships nonlinear? It would help to specify which variables we are talking about here. For example, the relations between fine-scaled storages and fluxes (precipitation, ET...) and large-scale storage are actually linear, since both the water balance and spatial averaging are linear operations.
4c. Line 259, "DA methods take care of the horizontal and vertical downscaling by design": what if the modeling domain does not fully cover all GRACE 'grid' cells that overlap with the modeling domain?
4d. Line 281-282, "the trend of the GRACE/-FO observations is kept to correct missing trends in the model". To what extent is the trend in GRACE observations also subject to error (e.g. different GRACE products showing different trends)?
4e. Line 393, "uniform and uncorrelated errors": I suppose "uniform" means "spatially uniform"? Would be good to also specify which probability distribution is used for the random errors, e.g. Gaussian.
4f. Section 3.3: this section discusses how random errors in GRACE observations are modeled, separate from systematic errors (bias) discussed in section 2.5. However, how the two are modeled (noise and bias) is linked, i.e. a modeling choice in one affects the other, so I wonder why the two are discussed separately.
5. Forecast errors:
5a. More thorough and critical review could be useful here. For example, a table that summarizes how forecast errors are computed in different GRACE DA studies (e.g. which variables are perturbed, by how much, and how; whether there is accounting for spatial/temporal correlation in forcing...). This can lead to identifying gaps and give pointers for future studies. Section 5.3 does identify some open issues with forecast errors, but it's not clear how these should be tackled. E.g. how can the suggestions in section 6.1 help with the issue of bias due to nonlinearity mentioned in section 5.3?
5b. It seems generating the forecast ensemble is mostly done offline, e.g. the authors mention sensitivity analysis. Are there opportunities for calibrating forecast uncertainties as part of the DA system, i.e. in an automated fashion?
6. DA algorithm and setup:
6a. The paper would benefit from more clearly discussing the relation between the intended goal of the DA application and how DA is implemented. The first sentence of the abstract suggests that the main goal here is reanalysis, i.e. create consistent historical datasets of water storage and fluxes that incorporate information from GRACE. However, it seems most of the paper discusses studies and implementations that are more related to operational DA (for use in e.g. early drought warning systems), as evidenced by the focus on filtering implementations (or smoothing implementations that only look at the last month) where DA is used to update initial storages for the next forecast. For reanalysis purposes it seems more appropriate to use smoothing implementations that make use of the entire historical record. Do the authors agree with this? If so, it would be helpful to include papers that use smoothing (not just last month) to assimilate GRACE data.
6b. Likewise, when the aim is in generating consistent estimates of the various water storages and fluxes, it is interesting that the paper reports (line 669) that most DA studies violate the water balance (which clearly introduces inconsistency in the estimates). I guess this relates to which variables are being updated by the DA system. Most DA studies cited in the paper only update the storages, but there are various studies that use Kalman filtering and smoothing techniques to update other variables of the water balance as well with the aim of maintaining a closing water balance.
6c. Line 357, "the EnKF and EnKS are optimal and unbiased only when assuming Gaussian errors": these algorithms are 'optimal' when you assume the errors are Gaussian or when that assumption is correct?
7. Abstract: would benefit from a rewrite, as it currently reads more like an introduction and does not contain concrete information on the findings ("best practices and future directions" as promised by the title of the paper).
8. Conclusions: several open issues identified in the text don't find their way into the conclusions.
9. Edits: (line 30) at the other hand --> on the other hand, (line 381) weighing --> weighting, (line 247) GARCE --> GRACE.
Citation: https://doi.org/10.5194/egusphere-2025-2058-RC1
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