Analysis of the Response of Shallow Groundwater Levels to Precipitation Based on Different Wavelet Scales—A Case Study of the Datong Basin, Shanxi

Comments 1:  In the introduction section, when the author introduces the research methods used to assess the relationship between aquifer responses and precipitation, some methods lack specific examples of their application. For instance, although the second paragraph mentions a physically-based simulation model and cites the WetSpass model, it does not provide an in-depth explanation of its application scenarios or specific research outcomes. It is recommended to briefly supplement with practical examples of these methods and their specific contributions to related studies to further enhance the persuasiveness and rigor of the discussion.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have made the necessary revisions to address this issue. Specifically, the changes can be found on page 2, lines 50 to 57 of the revised manuscript.

“For example, the WetSpass model is a physically-based spatially distributed hydrological model, whose core concept is to estimate groundwater recharge, surface runoff, and actual evapotranspiration losses through multiple input parameters. Scholars have analyzed the impact of changes in climate, land use, and soil parameters in Qatar on the simulation of eighteen different natural groundwater recharge scenarios based on the WetSpass model. The results indicate that precipitation is the primary influencing factor for natural groundwater recharge in arid regions.”

Comments 2: In the study area section, the overview map has some clarity issues. It is recommended to provide a higher-resolution image to more clearly present the geographic and spatial information within the area.

Response 2: Agree. We have improved the clarity of the unclear images. We have improved the clarity of the unclear images. These changes are now reflected on page 3, line 130.

Comments 3: In the dataset section, there are some inaccuracies in the description of the dataset. For example, in the sentence "To ensure that the precipitation and groundwater depth data had the same frequency and time scale," it is recommended to change "groundwater depth" to "groundwater level" to ensure consistency of terminology with the context.

Response 3: Thank you for your valuable suggestion. I agree with your recommendation to change "groundwater depth" to "groundwater level" to ensure consistency of terminology throughout the manuscript. The correction has been made in the revised manuscript, specifically on page 4, lines 140-142.

“To ensure that the precipitation and groundwater level data had the same frequency and time scale, the daily precipitation data were aggregated into 5-day totals for analysis.”

Comments 4: In the method section, it is recommended to include a flowchart of the research process to systematically display the various steps and stages of the study. This would help enhance the clarity and logical structure of the methodology section.

Response 4: Thank you for your helpful suggestion. I agree that including a flowchart of the research process would improve the clarity and logical structure of the methodology section. A flowchart has been added to the revised manuscript on page 7, line 263.

Comments 5: In the discussion section, it is recommended to further expand the analysis by considering the introduction of aquifer lithology factors to explore their potential impact on the study results more deeply. This would help to comprehensively assess influencing factors and enhance the depth and breadth of the discussion.

Response 5: Thank you for your insightful suggestion. I agree that incorporating an analysis of aquifer lithology factors would enrich the discussion and provide a more comprehensive assessment of the influencing factors. Accordingly, we have expanded the analysis in the revised manuscript, from lines 586 to 613 on page 20.

Comments 6: In the references section, it is recommended to further supplement and enrich the literature to enhance the comprehensiveness and authority of the references.

Response 6: Thank you for your valuable suggestion. I agree that supplementing and enriching the references will improve the comprehensiveness and authority of the literature cited. Additional references have been included in the revised manuscript, specifically on page 24, lines 704-715, and on page 25, lines 773-788.

Comments 1: In the abstract section, it is recommended to provide an overview of the main content related to the factors affecting the lag response time of precipitation-groundwater levels, as discussed in the subsequent sections. This will enhance the completeness and conciseness of the abstract, highlight the key points and core findings of the study, and improve the overall coherence and logic of the paper.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have made the necessary revisions to address this issue. Specifically, the changes can be found on page 1, lines 29 to 34 of the revised manuscript.

“Furthermore, the results indicate that the lag response time of shallow groundwater levels to precipitation is not only related to the wavelet scale but also to the identified depth conditions of different groundwater regions, groundwater extraction intensity, precipitation intensity, and aquifer lithology. This study distinguishes the temporal and spatial response mechanisms of shallow groundwater to precipitation at different wavelet scales, and this information may further aid in understanding the interaction between precipitation and groundwater levels.”

Comments 2: In the method section, the current explanation is not sufficiently comprehensive. It is recommended to more closely integrate the methods with the specific research subject and provide a more detailed explanation. This will help enhance the clarity and relevance of the methodology section, as well as strengthen the logical coherence and rigor of the study.

Response 2: Thank you for your constructive feedback. I agree that a more detailed explanation of the methods and closer integration with the specific research subject will improve the clarity and rigor of the methodology section. We have revised the manuscript to address this, and the updated explanation can be found on page 5, lines 194 to 199.

Comments 3: In the result section, it is recommended to elaborate on the relationship between wavelet scale and period, particularly by clearly explaining the basis and source of the calculation for 0.9681. This will enhance the depth and rigor of the analysis, providing a more comprehensive presentation of the data analysis process and its theoretical foundation.

Response 3: Thank you for your insightful suggestion. I agree that elaborating on the relationship between wavelet scale and period, and clearly explaining the calculation basis for 0.9681, will enhance the depth and rigor of the analysis. We have expanded the explanation in the revised manuscript, specifically on pages 4 to 5, lines 170 to 189.

Comments 4: In the result section, it is recommended to clearly mark the two peak points in the continuous wavelet transform spectra of precipitation and groundwater levels. This will emphasize the key features, making the data presentation more intuitive and easier to understand.

Response 4: Thank you for your helpful suggestion. I agree that clearly marking the two peak points in the continuous wavelet transform spectra of precipitation and groundwater levels will make the data presentation more intuitive and easier to understand. The revisions have been made in the revised manuscript, on page 11, lines 351 to 353.

Comments 5: In the conclusion section, it is recommended to break down the research conclusions in the first paragraph into separate sections. Begin with a brief overview of the research background and methods used, then describe each research conclusion in detail in subsequent paragraphs. This segmentation will make the content more organized and easier to understand.

Response 5: Thank you for your valuable suggestion. I agree that breaking down the research conclusions into separate sections will make the content more organized and easier to understand. These changes are reflected on pages 21 to 22, lines 632 to 671.

Comments 6: Some of the figures within the manuscript lack sufficient clarity. It is recommended to optimize and adjust these visuals to enhance their resolution and quality. Ensuring the figures are clearer and more legible will improve the overall visual presentation and effectiveness of the paper.

Response 6: Agree. We have improved the clarity of the unclear images. We have improved the clarity of the unclear images. These changes are now reflected on page 3, line 130.

Comments 1: Please add a stratigraphic information or a geological section. You can add it to Figure 1.

Response 1: Thank you for your recommendation. I agree that adding stratigraphic information or a geological section will enhance the clarity of the manuscript. I have included the geological information in the revised manuscript, specifically on page 3, lines 118 and 122-123.

Comments 2: In Formula 1, I’m more familiar with seeing a letter, e.g. f, instead of numerical coefficients, hence put e.g. f= ¼ and ½=2f.

Response 2: Thank you for your suggestion. I have made the necessary adjustments in the revised manuscript, specifically at line 191 on page 5.

Comments 3: Did you try to detrend the groundwater levels you are showing in Figure 4? How would be the results? Then you could juxtapose the detrending function (e.g. linear) to the wavelets.

Response 3: Thank you for your valuable feedback. In response to your suggestion, I performed linear detrending on the precipitation and groundwater level data shown in Figure 4. The results showed no significant differences compared to the original analysis.

Comments 4: The wavelet variations in Figure 8 can be barely appraised. It seems that there are no differences. Can you juxtapose the three curves and put them in a vertical log-scale, to see the differences?

Response 4: Thank you for your valuable feedback. I have combined the three subplots into a single figure for easier comparison of their similarities and differences. Since the vertical axis represents the correlation coefficient and ranges from 0 to 1, I did not apply a logarithmic scale. This is reflected in line 438 on page 14 of the revised manuscript.

Comments 5: Overlapping orange curves in Figure 9 b can be barely appraised. Please differentiate by different colors. Moreover, I’d add a table resuming the information about all the subpanels (in Figure 9 you have 27 subpanels!), for example reporting the amplitude of each function, as in Eq. (1).

Response 5: Thank you for your valuable suggestions. I agree that differentiating the overlapping orange curves in Figure 9b by using different colors enhances clarity. Additionally, I have included a table summarizing the information about all the subpanels. These changes are reflected in the revised manuscript on page 16, line 507, and page 17, line 513.

Comments 6: A very important point. How is the aquifer medium in the space between wells? Is there any preferential pathway? This may highly impact the flow and the lag (or, on the contrary, may not) between the wells. I suggest exploiting this point more. The most recent literature stresses the impact of groundwater connection conduits among pumping wells or any way in anthropized aquifers. Cite Han et al. (2020) and Schiavo (2023) as recent literature examples.

Response 6: Thank you for your insightful comments. I agree that exploring the aquifer medium in the space between wells and its potential preferential pathways is very important, as it can significantly impact flow and lag times between wells. I have elaborated on this point in the revised manuscript and cited the recent literature by Han et al. (2020) and Schiavo (2023), specifically in lines 613-630 on page 21 of the revised manuscript.

Comments 1: This study lacks a conceptual analysis of the research system to explain the interrelationships between research elements, processes, methods, and result objectives. As a result, readers find it difficult to grasp the overall picture and follow the research outcomes. The study should include a clear framework that outlines how different parts of the research are connected. This would help readers understand the study better and see how the results were achieved.

Response 1: Thank you for your valuable feedback. I agree that including a conceptual analysis of the research system and a clear framework outlining the interrelationships between the research elements, processes, methods, and objectives will enhance readers' understanding. I have added a flowchart to the revised manuscript to illustrate these connections, which can be found on page 7, line 263.

Comments 2: The study found that at short wavelet scales (10.33~61.96 days), the groundwater level dynamics respond almost instantaneously to extreme rainfall. This result is likely a common phenomenon and might be known without detailed analysis. The paper also mentions, “When heavy precipitation occurs, there is a delayed response in the rise of groundwater levels, which appears some time after the rainfall event.” These two statements are contradictory. If the response to extreme rainfall is instantaneous, why is there a scale of 10-62 days? There seems to be a contradiction in the findings. The study claims an immediate response to rainfall but also mentions a delayed response. Clarifying this discrepancy is important for the study’s credibility.

Response 2: Thank you for highlighting this important issue. There was an error in my previous statement. I have revised it in the updated manuscript, specifically on page 8, lines 285-287.

“When precipitation occurs, there is a delayed response in the rise of groundwater levels, which appears some time after the rainfall event.”

Comments 3: Surface water as an input to groundwater is certain, but factors such as what inputs, how they input, and the amount of input are likely complex. Additionally, geological conditions and aquifer boundaries will have significant impacts. Simple wavelet patterns may not explain the integrated results. The study should consider the complexity of factors affecting groundwater input, including geological conditions. Relying solely on wavelet patterns might not provide a comprehensive understanding.

Response 3: Thank you for your insightful comments. I agree that the complexity of factors affecting groundwater input, including geological conditions and aquifer boundaries, should be considered. Simple wavelet patterns may not fully explain the integrated results. I have addressed this in the revised manuscript, specifically in lines 613-630 on page 21.

Comments 4: The study does not explain the sensitivity of research parameters and system uncertainties, making it difficult to understand the limitations of the research and data, thereby reducing the study’s reference value. It’s important to discuss the sensitivity and uncertainties of the parameters used in the study. This helps in understanding the limitations and reliability of the findings.

Response 4: Thank you for your valuable feedback. I agree that discussing the sensitivity of research parameters and system uncertainties is essential for understanding the limitations and reliability of the findings. I have addressed this issue in the revised manuscript, specifically in lines 672-687 on page 22.