Response to Reviewers’ Comments

We are grateful to the anonymous reviewers for their detailed, insightful, and constructive comments and questions that have been used to improve the quality of our manuscript. We thank the editor for inviting us to respond to reviewers’ comments and revise the manuscript.

# Response to Reviewer 1 Comments

- L. 42: 'SM' is undefined.

Response : SM means soil moisture. We suggest to write «’soil moisture’ in the highlights section, and introduce the abbreviation later in the the main text, line 137.

- L. 162: The title of Section 2 is inaccurate. This section also includes a model description.

Response : We suggest to rename the section to « Study area, Datasets and Models ».

- L. 186 (Figure 1): I think that Figure 2 should be merged with Figure 1. The unknown satellite image in Figure 1 should be replaced by the land cover map in Figure 2.

Response : In the revised manuscript, Figures 1 and 2 will be merged, and the satellite image will be replaced by the land cover map to improve clarity and relevance.

- L. 187 (section 2.2): Neither Section 2.2.1 nor Section 2.2.2 provides a description of a dataset. I suggest replacing the title of Section 2.2 with 'Data and Models'. A short introduction to Section 2.2 should mention which atmospheric forcing data are used to perform the model simulations, rather than including this important information in the model description sections. The titles of sections 2.2.1 and 2.2.2 should also make it clear that these sections deal with models.

- L. 223: CORDEX was not defined before.

- L. 238: CRUNCEP was not defined before.

Response : We suggest to rename section 2.2 “Datasets and Models” and to add a short introductory paragraph to clearly describe the atmospheric forcing datasets used. CORDEX and CRUNCEP will be fully defined at first mention.

- L. 248: Only papers by Dorigo et al. are cited here. Dorigo et al. did not take these measurements. Please cite the papers describing the data and the sites here.

Response : The Dorigo paper references the ISMN network and we believe it is correct here.

- L. 397: In the description of Eq. 4, you should indicate that theta_wt and theta_fc correspond to wilting point and field capacity, respectively. What you call "wt" has been called SWI (Soil Westness Index) during the last 3 decades. It seems that Tian et al. did not use the standard term 'SWI'. Could you switch to using the term SWI and cite a paper that uses this concept? It should be mentioned that the main purpose of SWI is to highlight the drought signal rather than mapping soil texture-driven volumetric soil moisture. Drought maps can only be produced using SWI.

Response : In the revised manuscript, we plan to explicitly define wilting point and field capacity and adopt the standard terminology Soil Wetness Index (SWI) as you indicated. We will also cite foundational literature using this concept and clarify that SWI is primarily intended for drought characterization rather than absolute volumetric soil moisture mapping.

- L. 414: 'The episodic and seasonal variations': these should be clearly defined, as should the method used to obtain them.

Response : We agree. clear definitions of episodic and seasonal variability, along with the methods used to derive them, will be added to the Methods section.

- L. 425: The results and discussion sections should be separate. The current organisation of the paper is unclear.

Response :

We thank the reviewer for this comment and for raising the issue of manuscript structure. After internal discussion among the co-authors, we would like to clarify that the current structure was chosen intentionally. Given that the manuscript already includes a dedicated Conclusions and Implications section, we consider that a fully separated Results and Discussion structure is not strictly necessary for this study. In our view, the close coupling between results and their interpretation is essential for the methodological and regional analyses presented, and an integrated Results–Discussion approach is commonly used in similar hydrological and geophysical studies. That said, we agree as a team that parts of the manuscript would benefit from clearer organization. In the revised version, we will improve the structure by more clearly distinguishing descriptive results from interpretative statements within each subsection and by relocating broader synthesis, cross-regional comparisons, and implications to the Conclusions and Implications section. We believe this approach preserves the scientific coherence of the study while addressing the reviewer’s concern regarding clarity. We are open to further restructuring if recommended by the editor.

- L. 432: The methods used to produce these time series should be clearly presented in the 'Methods' section.

Response : We agree with the reviewer. In the revised manuscript, the methods used to produce these time series will be clearly described in the Methods section.

- L. 437: The quality of Fig. 3 could be improved. Could each year on the x-axis be clearly identified? Indicating months is not useful. The caption is incomplete.

Response : We suggest to address all figure and table issues, including correcting captions, ensuring consistent symbols, correcting table titles, and fixing figure numbering inconsistencies.

- L. 442-444: Why have you suddenly moved from Africa to the Tibetan Plateau? This is confusing. Move this part to a discussion section.

Response : This part is already in the joint results and discussion section.

- L. 444-448: Move to a discussion section.

- L. 464-466: This sentence should be moved to the Methods section or to the Discussion section.

Response : The content in lines 464-466 is already in the joint results and discussion section.

- P. 22, Table 2: Use the correct symbols as defined in the main text. 'Corr' should be replaced by 'R', 'RMSE' by 'RMSE', and so on. To improve readability, use fewer digits. For example, replace 0.894 with 0.89.

Response : We agree. The correct symbols will be used to define Corr and others metrics.

- P. 22, Table 3: Table 3 cannot have the same title as Table 2.

Response : We thank the reviewer for pointing out. This will be corrected.

- L. 491: The Sahel region should be labelled on either Fig. 5 or Fig. 1.

Response : The Sahelian region is already defined and described in Section 2.1 (Study area) but we can add an explicit label of this region to Fig. 1 in the revised manuscript.

- L. 497-506: This part should be moved to a discussion section.

Response : As discussed above, the manuscript follows an integrated Results–Discussion structure agreed upon by the co-authors. The content in Lines 497–506 is therefore intentionally included there, but we will clarify the distinction between results and interpretation to improve readability.

- L. 513-523: This part should be moved to a discussion section.

Response : As discussed above, the content in Lines 513–523 is therefore intentionally included in the Results and Discussion section.

- L. 531: "these models": is ESA CCI a model?

Response : This is a mistake. It will be corrected.

- L. 534-554: This part should be moved to a discussion section.

Response : The content in Lines 534–554 is included in the Results and Discussion section.

- L. 555: Section 4.3 should be moved to a discussion section.

Response : The content in Line 555 is included in the Results and Discussion section.

- l. 608: The conclusion section is far too long. Some parts could be moved to a discussion section. This section should focus on the main take-home messages and possible areas for further research.

Response : We agree that the Conclusions section is currently pretty long. After discussion among the co-authors, we suggest to substantially shorten this section rather than modify the overall manuscript structure. In particular, the part at the beginning of the Conclusions section, which largely repeats results, will be drastically reduced (Lines 609–642), allowing the section to focus more clearly on key take-home messages and future research directions.

# Response to Reviewer 2 Comments

 We thank Reviewer 2 for the positive evaluation of the study’s relevance and for the insightful suggestions to strengthen the methodological and interpretative aspects of the manuscript.

This study offers a valuable integration of GRACE/-FO-based water storage anomalies with land surface and hydrological model soil moisture products to estimate root-zone soil moisture. The fusion of these data sources is a significant contribution to understanding soil moisture dynamics. However, the methodological novelty, in comparison to previous GRACE assimilation or analytical approaches, is not fully explained. The paper would benefit from a clearer explanation of how the adopted analytical solution extends beyond existing methods, and what specific improvements in accuracy or process representation have been achieved by this approach.

Response: We thank the reviewer for highlighting this important point. In the revised manuscript, we will more clearly articulate the methodological novelty by explicitly contrasting our analytical solution with previous GRACE assimilation and analytical approaches. 

While the results are well presented, they remain largely descriptive. The discussion could be expanded to explore the physical reasons behind the observed differences between products, particularly in relation to regional hydro-climatic conditions. Interpreting how these differences manifest in the context of the West African climate would significantly enhance the scientific insight and generalizability of the conclusions.

Response: We thank the reviewer for pointing out this. in the joint results and discussion section, we will provide a deeper interpretation of the observed differences between products, linking them to regional hydro-climatic conditions in West Africa, including precipitation regimes, soil properties, and vegetation dynamics.

The workflow is logically structured, but certain analytical steps, particularly the parameterization of the Richards equation, require deeper justification. A more thorough explanation of why specific parameter values were chosen would add robustness to the methodology. Additionally, a stronger uncertainty analysis is needed to make the validation results more convincing. The current approach could benefit from more detailed discussion of the limitations and sources of uncertainty, especially in relation to data assimilation.

Response: The revised Data and Methods section will include a clearer justification of parameter choices used in the Richards equation, along with discussion of their physical meaning and sensitivity.

The use of the GRACE/-FO-based global assimilation model GLWS2.0, which is based on WaterGAP, is an interesting aspect of the study. However, the paper lacks sufficient details on how GRACE data, which includes various components like groundwater, soil moisture, and vegetation weight, is assimilated into the model. It would be helpful to know how the integration of these different components improves soil moisture predictions specifically. For example, how do variations in groundwater levels influence soil moisture estimates? Are these variations significant enough to warrant inclusion in the model?

Response: We thank the reviewer for this comment. A full description of the data set is in the Gerdener et al 2023 paper, which we cite here. We suggest to remove the sentence in lines 218-219 and add a few lines on how the assimilation works. In response to the reviewer’s question, we point out that WaterGAP and GLWS do take groundwater variations into account, of course depending on the quality of the require data sets. GLWS and its predecessor data sets have been validated against groundwater and soil moisture data in the past, but not for West Africa.

The application of the analytical solution to Richards’ equation, as proposed by Sadeghi et al. (2020), is an interesting approach, but the assumptions underlying the Gardner model need to be more thoroughly examined. This model assumes homogeneous soil and neglects plant water uptake, which may not align with the assumptions of the WaterGAP model. The paper does not sufficiently address whether these assumptions are compatible or if they introduce contradictions. A more detailed discussion of the theoretical framework, particularly how the assumptions in both models align or diverge, would strengthen the overall argument.

Response : We agree and we suggest to add a more detailed theoretical discussion addressing the assumptions of the Gardner model and their consistency (and limitations) relative to the WaterGAP framework.  

While the results are presented in detail, there is a need for deeper analysis of the underlying processes that lead to the observed patterns in the data. For instance, how do soil moisture and flux relationships differ across various depths, and how do these differences relate to regional hydro-climatic variability? Expanding this part of the discussion would help connect the empirical findings with broader environmental processes.

Response : We agree with the reviewer that this would be a very useful analysis, but we fear this would change the character of the paper significantly. The relationships between soil moisture and flux across various depths could be analyzed purel from data, but the data are sparse as we describe here. Or they could be analysed from the CLM simulations, but again this is not in the focus of this paper.

Minor Comments:

    • The paper would benefit from a clearer structure in terms of presenting the key innovations of the study. It is important to ensure that the reader can easily identify how this work advances current understanding, particularly in relation to model improvements and new methodological contributions. 

Response : We thank the reviewer for this helpful suggestion.  We will add a short framing paragraph at the beginning of the Introduction (around Line 49) summarizing the importance of soil moisture, the sparsity of in situ networks, the surface limitation of remote sensing products, and the strong dependence of root-zone soil moisture estimates on model assumptions, thereby emphasizing the need for validation. In addition, we will condense the beginning of the Conclusions section into a short synthesis of no more than three sentences (e.g. starting with “We find that…”), replacing the current repetitive content and clearly summarizing the main findings relative to initial expectations.

    • Additional references to recent work in the field of soil moisture modeling and data assimilation, especially focusing on studies that use GRACE data, would provide more context and help justify the novel aspects of this study. 

Response : We agree. We suggest to add some references of recent assimilation works and suggest also to include them in the discussion.

Once again, we thank both reviewers for their valuable comments, which will significantly improve the quality and clarity of the manuscript.