Technical Note: GRACE-compatible filtering of water storage data sets via spatial autocorrelation analysis  

Ehsan Sharifi, Julian Haas, Eva Börgens, Henryk Dobslaw and Andreas Güntner  

This paper is accepted to subject a minor revision:

Rating on a 1 to 4 scale, 1 means excellent and 4 means poor score:

----------- Scientific significance ----------- SCORE: 2 (Good)

----------- Scientific quality ----------- SCORE: 2 (Good)

---------- Presentation quality ----------- SCORE: 2 (Good)

----------- Overall Rating ----------- SCORE: 2 (Good)

1.1. Recommendation

Minor Revision

1.2. Overview

This technical note explores methods to make Water Storage Compartments (WSCs) data compatible with Terrestrial Water Storage Anomaly (TWSA) data derived from GRACE satellite missions, specifically for isolating groundwater storage. Because GRACE data inherently have spatial smoothing and noise, other WSC datasets must be filtered similarly for accurate comparisons and subtractions. The study found that anisotropic decorrelation filters, like DDK, introduce artefacts in WSC data, suggesting that an isotropic Gaussian filter is more suitable. By analysing spatial autocorrelation and minimising differences between WSC and TWSA autocorrelation functions, an optimal Gaussian filter width of 250 km was identified for a combined WSC dataset to align with GRACE-based TWSA data characteristics.

This technical note is well written, and the overall quality of the manuscript is excellent. The research question is clearly defined and addressed in a scientifically sound manner. However, to enhance the scientific rigour of the work, I have a few specific comments regarding certain aspects of the study:

1.3 Minor comments

Abstract (line 20): Please include the RMSD results corresponding to the optimal filter width, as this will help emphasise the most significant findings for the reader.

Abstract: The time period of the data is not mentioned in the abstract. Please include it to provide readers with an immediate contextual understanding of the study.

Line 155: I would have appreciated more information regarding the choice of bilinear interpolation. Kindly consider including a specific reference and a clear justification for its use, particularly in relation to the data characteristics and the goals of the analysis.

Line 194: The manuscript mentions the time period as 2002 to 2023 in one instance, while the data preprocessing section refers to 2002 to 2020. Please ensure consistency throughout the manuscript regarding the time period to avoid confusion and maintain clarity.

Line 195: I would have liked to have more information on the spatial autocorrelation method employed in the study. It is not clearly described in the text, nor is a reference provided. Please consider elaborating on the approach used—such as whether it is based on Global Moran’s I or another technique—and include an appropriate citation to support the methodology.

Line 196: I would have liked to see equation numbers included throughout the manuscript, as currently the equations are only referred to in the text without numbering. Including equation numbers would improve clarity and allow for more precise referencing within the manuscript.

Line 242: For the sake of consistency, I would suggest using "RMSD" in Equation 4, as it aligns with the terminology used throughout the manuscript. This will help maintain uniformity and avoid potential confusion for the reader.

Line 250: I would have liked to see the Fig. 4 flowchart improved through a clearer colour scheme and more concise text to enhance readability and understanding.

Line 330: I would have liked to see the projection system specified for the global maps presented in Figure 8. Including this information would enhance the reproducibility and clarity of the spatial analysis.

Line 390: I would have liked to see proper basemap credits included in Figure 11. Acknowledging the source of the basemap is important for transparency and adherence to data usage guidelines.

I would recommend a thorough grammatical review of the manuscript, with particular attention to sentence structure and overall presentation. Enhancing linguistic clarity and coherence will significantly improve the readability and professional quality of the work. A few examples of:

(i)                      have been suggested change to “has been suggested” (line 56)

(ii)                    to change to “with” etc.. (line 70)

I would suggest including an abbreviation table at the end of the manuscript, as numerous technical terms and abbreviations are used throughout. This will enhance clarity and assist readers in understanding the content more easily.

In conclusion, I recommend that the study be accepted, subject to the minor corrections outlined above, to enhance its scientific rigour and clarity.

General comments:



This technical note entitled "GRACE-compatible filtering of water storage data sets via spatial autocorrelation analysis" addresses an important practical question in GRACE data processing: How to filter water storage component (WSC) datasets to make them compatible with GRACE-derived terrestrial water storage anomalies (TWSA)? While the topic is relevant and the approach is systematic, the note needs improvements in validation and methodological rigor before potential publication in HESS.



Major issues:



1.    Lines 15-17: The claim that DDK filters “introduced striping artefacts” needs quantitative support. Show correlation coefficients or other metrics demonstrating the inappropriateness.

2.    Lines 167-188: The DDK filter implementation description is unclear. How exactly were the WSC data converted to spherical harmonics? What degree/order was used? Please, add such details that are crucial for reproducibility.

3.    Lines 189-210: The de-trending and de-seasonalization approach (Lines 159-161) may remove important signal characteristics. The text justifies this as eliminating "long-distance correlations...not of interest" but this seems arbitrary. Seasonal signals are fundamental to water storage dynamics, and their removal may bias the autocorrelation analysis.

4.    Lines 195-210: The autocorrelation calculation (Equation 2) appears computationally expensive and may be sensitive to data gaps. Specifically, GRACE TWSA data contains missing values and temporal gaps (e.g., during the gap between GRACE and GRACE-FO missions, instrument failures, or data quality flags), yet the text does not address how these gaps affect the reference autocorrelation function calculation. Additionally, individual WSC datasets may have their own spatial or temporal gaps. The text should clarify: (1) How are missing values handled when computing correlations between grid cell pairs? (2) Are months with insufficient data coverage excluded from the analysis? (3) How sensitive is the optimal filter width determination to the presence of data gaps? (4) Given that the method aims to match WSC autocorrelation to GRACE autocorrelation, how do gaps in the GRACE reference data affect the reliability of the “target” autocorrelation function itself? Without proper gap handling procedures, the computed autocorrelation functions may be biased, potentially leading to suboptimal filter width selection. (5) What about grid cells with “insufficient” neighbors?

5.    Lines 213-225: The Weibull model fitting approach needs more justification. Why was this model chosen over simpler exponential decay (I guess the difference would be the shape parameter). What are the goodness-of-fit statistics?

6.    A proper validation of the proposed approach is required. The study demonstrates that filtered WSCs match GRACE autocorrelation functions, but it doesn't validate whether this actually improves groundwater storage anomaly (GWSA) estimates. Does the 250 km filter width actually produce more accurate GWSA compared to other approaches? How do the filtered WSCs compare against independent observations? What is the impact on signal preservation versus noise reduction?

7.    Lines 159, 275-280: The 0.5° resolution analysis may be too coarse to capture important small-scale spatial patterns, and although the text acknowledges this limitation (Lines 275-280), it doesn't adequately address it.

8.    Lines 336-340: The optimal 250 km filter width is presented as definitive, but Table 2 shows the RMSD minimum is quite broad (200-300 km range), and the sensitivity analysis seems insufficient.



Minor issues:



1.    Line 27: "TWS is a fundamental component" - this statement is too strong. Consider "TWS is an important component."

2.    Lines 40-45: The review of GRACE applications is superficial. Please provide a more comprehensive review of the studies that applied a filter to WSC components. For example, Ferreira et al. (2024, doi: 10.1016/j.ejrh.2024.102046) did this through spherical harmonic analysis and synthesis.

3.    Lines 154-164: The harmonization procedure needs more detail. Bilinear interpolation may introduce artifacts; was this tested?

4.    Line 125: Equation (2) is missing the number.

5.    Line 240: Equation (4) is missing the number, and consider using RMSD instead of RMSE for consistency throughout the text.

6.    Consider improving Figure 4.

7.    Lines 365-385: For a technical note format, the computational efficiency discussion is appropriate and adds practical value. However, this section could be strengthened by providing more quantitative details. The study demonstrates that preprocessing at 0.5° resolution yields identical results to filtering at higher resolution, and that filtering the combined 4WSC dataset once is equivalent to filtering each WSC individually, both valuable practical insights. To enhance this section, consider adding: (1) quantitative timing comparisons between the different approaches, (2) memory usage considerations for large datasets, (3) specific computational cost savings (e.g., "reduces processing time by X%"), and (4) clearer recommendations for different use cases (e.g., when computational resources are limited vs. when maximum precision is needed). These additions would make the computational guidance even more actionable for researchers implementing this filtering approach.

8.    Consider adding an interpretation of what the autocorrelation patterns mean physically