the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 May 2026
Lagged Responses of Seasonally Frozen Ground on the Qinghai-Tibet Plateau to Extreme Heat Events
Abstract. Extreme heat events can induce delayed responses in seasonally frozen ground (SFG) by altering soil heat storage and release processes, yet their lag characteristics and spatial variability remain poorly quantified. Here, we develop a distributed lag nonlinear model integrated with an explainable artificial intelligence framework (DLNM-XAI) to quantify the lagged responses of SFG to extreme heat events across the Qinghai-Tibet Plateau (QTP), based on in situ observations, multi-source remote sensing, and reanalysis datasets. Results show that extreme heat significantly modifies freeze–thaw dynamics. On average, each additional extreme heat day advances the thaw end date by 3.02 days, delays the freeze onset date by 1.52 days, and reduces maximum freezing depth by approximately 1.12 cm. The response of freezing depth exhibits a clear nonlinear lag pattern, with effects emerging within 5-10 days, peaking after approximately 15-20 days, and gradually weakening thereafter. Spatially, lagged responses also show pronounced spatial heterogeneity across the QTP. Regions with deeper snow cover, higher soil moisture, and stronger surface energy exchange generally exhibit longer lag durations. These factors, including extreme heat duration, snow depth, soil moisture, and surface energy fluxes, jointly regulate soil heat transfer and energy retention, thereby modulating the timing and persistence of SFG responses. Overall, this study provides a regional-scale characterization of the delayed thermal responses of SFG to extreme heat events and improves understanding of thermal memory and land-atmosphere interactions under short-term extreme climate forcing in cold regions.
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CC2: 'Comment on egusphere-2026-2202', Xiaofan Zhu, 02 Jun 2026
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CC3: 'Reply on CC2', Ting Zhang, 04 Jun 2026
Dear Referee,
Thank you very much for your careful reading of our manuscript and for providing detailed, constructive, and insightful comments. We sincerely appreciate your recognition of the scientific importance of this study, as well as your valuable suggestions regarding methodological design, model applicability, data validation, and interpretation of the results. We have carefully reviewed all comments and would like to briefly respond as follows.
We agree that the current graphical abstract can be further improved. Following your suggestion, we will redesign and optimize the graphical abstract to better illustrate the research motivation, analytical framework, and key findings. In addition, we acknowledge that some statements in the abstract may currently overemphasize the role of extreme heat in freeze–thaw dynamics. We agree that freeze–thaw processes are jointly controlled by multiple environmental factors (e.g., climate, hydrothermal conditions, vegetation, and snow cover), while extreme heat acts more as an important short-term disturbance factor. Accordingly, we will revise the relevant wording to improve scientific rigor and avoid overinterpretation.
Regarding the threshold depth described in Section 2.2.1, we sincerely thank the referee for identifying this issue. We confirm that the reported value of 5 m was a typographical error. The actual threshold depth used in this study was 3.5 m, which was also consistently adopted during freezing-depth estimation and validation. This will be corrected in the revised manuscript.
Regarding the selection of the maximum lag period (30 days) in Section 2.2.3, the current setting was based on previous lag-related studies and preliminary exploratory analyses. However, we agree with the referee that lag responses may vary across regions and event intensities. We therefore plan to conduct additional sensitivity experiments using different lag settings to further evaluate the robustness of the lag-response framework. We will also supplement additional details regarding model training, parameter settings, and validation procedures in the revised manuscript and appendices.
For the delineation of “high-frequency regions” in Figure 3, we appreciate this important comment. The current selection considered multiple aspects, including event frequency, event intensity, and consistency with the spatial distribution of seasonally frozen ground. We will provide clearer quantitative criteria and further strengthen the interpretation of regional differences with additional literature support.
Regarding the interpretation of the “thermal saturation mechanism” discussed in Section 4.2, we will further elaborate on the potential thermal processes involved and clarify why more prolonged extreme heat events may be associated with shorter lag durations. We also appreciate the referee’s insightful suggestion concerning possible threshold effects. We believe this is a highly meaningful direction for further investigation, and where feasible, we will explore additional analyses to evaluate and better characterize such potential threshold behavior.
We acknowledge that the current daily freezing-depth estimation still exhibits a noticeable positive bias and that its accuracy remains imperfect. In the revised manuscript, we will further investigate and discuss the spatial characteristics and potential sources of bias (e.g., topography, soil properties, vegetation, and environmental heterogeneity). In addition, we plan to conduct comparative experiments using alternative freezing-depth estimation approaches to systematically evaluate their performance and robustness. If additional experiments demonstrate substantial improvements in simulation accuracy and reliability, we are fully open to revising the current analytical framework and reconstructing the relevant analyses based on improved results. To further enhance methodological transparency and rigor, comparative results from different estimation approaches will also be summarized in the supplementary materials where appropriate.
Finally, we sincerely thank the referee for the valuable recommendation regarding additional station observations and the reliability of ERA5-Land data over the Qinghai–Tibet Plateau. We will further explore the incorporation of additional observations from the National Meteorological Data Center of the China Meteorological Administration to strengthen validation where feasible. We will also expand the discussion regarding the known seasonal and regional uncertainties of ERA5-Land reanalysis data over the Qinghai–Tibet Plateau and their potential implications for this study.We greatly appreciate these thoughtful comments, which will substantially improve the rigor and clarity of this work. We are currently working on corresponding revisions and additional analyses and will continue to engage in the discussion as progress is made.
Citation: https://doi.org/10.5194/egusphere-2026-2202-CC3
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CC3: 'Reply on CC2', Ting Zhang, 04 Jun 2026
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RC1: 'Comment on egusphere-2026-2202', Anonymous Referee #1, 16 Jun 2026
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CC4: 'Reply on RC1', Ting Zhang, 19 Jun 2026
Dear Referee,
Thank you very much for your careful review of our manuscript and for providing such detailed, thoughtful, and constructive comments. We sincerely appreciate the considerable time and effort you devoted to evaluating this work.
We are especially grateful for your recognition of the scientific importance of the research topic. At the same time, we fully understand your concerns regarding the study design, data processing, methodological transparency, model performance, and interpretation of physical mechanisms. Your comments have helped us recognize several shortcomings in the current version of the manuscript, particularly in terms of methodological descriptions, the organization of the results, and the clarity of the overall scientific narrative.
Regarding the freezing-depth estimation, we acknowledge that the current predictions still exhibit a noticeable positive bias, particularly the approximately 40 cm systematic bias highlighted by both you and Dr. Zhu. We fully agree that this issue deserves careful attention, as it may affect the credibility of the subsequent analyses. Although the current lag-response analysis primarily focuses on the temporal dynamics and lag characteristics of freezing-depth variations rather than the absolute magnitude of freezing depth itself, we agree that additional validation is necessary to further evaluate the robustness of the results.
We also recognize that the current manuscript does not provide sufficient detail regarding the freezing-depth prediction procedure, missing-value treatment, freezing-depth estimation methods, and related parameter settings (Section 2.2.1). If the current approach is retained, we will provide a substantially expanded description of the implementation of the “depth-corrected linear interpolation” and “controlled linear extrapolation” procedures, together with a more detailed explanation of the missing-data handling strategy and freezing-front identification process. In addition, the 5 m threshold mentioned in the manuscript was indeed a typographical error. The actual threshold used in this study was 3.5 m, and this will be corrected in the revised manuscript.
To address concerns regarding model performance, we plan to further investigate the spatial distribution of model bias and its potential causes, including topographic effects, soil properties, vegetation conditions, and environmental heterogeneity. We have already begun exploring alternative freezing-depth estimation schemes, including different soil-temperature profile interpolation approaches (e.g., piecewise linear interpolation and spline-based interpolation) and alternative freezing-front determination strategies. Preliminary results suggest that some alternatives can improve performance in certain regions; however, the overall improvement remains limited. Therefore, we are continuing to explore more accurate approaches for daily freezing-depth estimation. If subsequent experiments demonstrate substantial improvements in predictive accuracy and reduced systematic bias, we are fully willing to revise the current analytical framework and reconstruct the subsequent lag-response analyses based on improved estimates. Comparative results from different approaches will also be incorporated into the Supplementary Materials to enhance transparency and methodological rigor.
Regarding the LightGBM framework, we agree that the current manuscript does not sufficiently explain the relationship between the DLNM and LightGBM components, which may have contributed to confusion. In fact, the DLNM was employed to investigate lagged responses at the temporal scale by quantifying the relationship between extreme heat events and freezing-depth time series, thereby deriving lag-response characteristics for each pixel. In contrast, the LightGBM-SHAP analysis was designed to investigate the drivers of spatial variability in lag times. Its input variables include cumulative heat, vegetation conditions, soil properties, moisture conditions, and other environmental factors, while the objective is to explain spatial differences in lag duration rather than to model temporal sequences directly. We therefore believe that the use of LightGBM is appropriate for this spatial attribution task. Nevertheless, we acknowledge that the methodological description was not sufficiently clear and that the manuscript did not describe the evaluation of alternative machine-learning models. In the revised version, we will improve the methodological description, add a more detailed workflow diagram, and clearly explain how the continuous lag-response surfaces generated by the DLNM were transformed into the maximum lag-time metric used as the target variable in the LightGBM-SHAP analysis. We will also further evaluate the variable-selection strategy, including potential dependencies among sand, silt, and clay fractions, and clarify how snow-related processes and precipitation variables were handled.
Regarding the identification of extreme heat events, we appreciate your observation that the current description may be confusing. In this study, the 90th percentile (P90) threshold was used to identify extreme heat events and delineate the regions affected by such events. Subsequently, within those regions, daily freezing-depth estimates and extreme heat event time series were analyzed using the DLNM framework to quantify lagged responses. Because extreme heat intensity varies substantially among regions, the corresponding temperatures are not represented by a single fixed threshold but rather span a range of values. The “representative” temperatures shown in the manuscript (10°C, 15°C, 20°C, 25°C, and 30°C) were selected solely to facilitate visualization and interpretation of lag-response curves under different heat intensities and were not used as universal thresholds for event identification. We believe that your question regarding whether these representative temperatures are equally applicable across all regions of the Qinghai–Tibet Plateau is highly valuable and deserves further consideration. Given the substantial spatial variability in maximum temperatures across the Plateau, the current representation may be more reflective of lower-elevation regions. We will therefore further discuss this issue in the revised manuscript and evaluate the influence of regional climatic differences on lag-response characteristics.
We also greatly appreciate your comments regarding the organization of the Results section. We recognize that the current manuscript contains a large amount of information, which may obscure the central scientific questions and limit the depth of the discussion. In the revised version, we plan to reorganize the Results and Discussion sections, moving some supporting analyses to the Supplementary Materials while focusing the main text more directly on the following key scientific questions: (1) whether extreme heat events influence seasonally frozen ground processes; (2) whether such influences exhibit significant lagged responses; (3) how lag times vary spatially; (4) which environmental factors control this spatial variability; and (5) what physical mechanisms may explain these patterns. At the same time, we will reduce repetitive reporting of numerical results and strengthen the physical interpretation and scientific discussion of the findings.
Finally, we sincerely thank you for your valuable suggestions regarding the explanation of the proposed thermal saturation mechanism, the rationale for data selection, the harmonization of multiple datasets, the presentation of Table 2, and the interpretation of Figure 6. These comments have highlighted several important aspects of the manuscript that can be substantially improved. We will carefully revise the corresponding sections, provide additional methodological details and explanations, improve the presentation of figures and tables, clarify variable definitions and figure captions, and further enhance the scientific clarity and readability of the manuscript.
Once again, we sincerely appreciate your thoughtful and insightful comments. We are currently conducting additional analyses and supplementary experiments and will systematically revise the manuscript in response to the concerns raised by you and the other reviewers. As this work progresses, we would be pleased to continue engaging in the discussion and to provide updates where appropriate.
With best regards,
Ting Zhang
Citation: https://doi.org/10.5194/egusphere-2026-2202-CC4 -
AC1: 'Reply on RC2', Tingbin Zhang, 23 Oct 2026
Dear Reviewer,
We sincerely thank you for your careful evaluation of our manuscript and for identifying several important methodological and statistical issues. We appreciate your recognition of the scientific relevance of this study, the conceptual framework, and the substantial effort involved in the research. At the same time, we fully understand your central concern that the current manuscript does not provide sufficient statistical evidence and methodological detail for readers to independently assess the main quantitative findings.
After carefully considering your comments, we recognize that several of the issues you have raised cannot be adequately addressed through textual clarification alone. In particular, the uncertainty associated with freezing-depth estimation, the spatial representativeness of the validation data, and the potential confounding effects of long-term warming trends and temporal autocorrelation require further investigation. We will undertake additional analyses, reconsider the existing analytical framework where necessary, reassess the principal findings, and revise our conclusions in accordance with the results.
Our point-by-point responses are provided below.
Reviewer comment 1: The manuscript does not report p-values, confidence intervals, R² values, or standard errors, yet the word “significantly” is used several times.
Response:
We agree with this comment. The current manuscript does not report statistical uncertainty systematically or adequately, and some statements in the Results section therefore lack sufficient statistical support. In the subsequent revision, we will strengthen the reporting of statistical evidence by providing effect estimates, 95% confidence intervals, standard errors, p-values, and appropriate goodness-of-fit metrics where applicable.
For analyses of temporal trends, we will explicitly describe the statistical methods employed, the corresponding null hypotheses, and the approaches used to account for temporal dependence. We will also examine potential multiple-comparison issues in the spatial analyses to avoid interpreting isolated statistically significant results as robust regional patterns. Statements involving statistical significance that are not adequately supported by the analyses will be revised or removed.
Reviewer comment 2: The validation of the interpolated freezing depth yields a systematic bias of 39.79 cm and an RMSE of 54.01 cm, whereas the principal signal reported is only approximately 1.12 cm per extreme heat day. The authors nevertheless describe the error as “a consistent offset rather than random fluctuations” and conclude that the product is “sufficiently reliable.”
Response:
Thank you for raising this important concern. We acknowledge that using the relatively high correlation coefficient as evidence that the estimated freezing depths are sufficiently accurate was not adequately justified. The substantial bias and RMSE in the existing validation results require us to reassess whether the reported response magnitude can be distinguished reliably from the uncertainty associated with freezing-depth reconstruction.
We previously interpreted the estimation errors primarily as a consistent systematic offset. However, we recognize that this interpretation was not supported by a sufficiently detailed analysis of the error structure. We will investigate whether the errors are approximately constant or instead vary systematically with environmental conditions and freezing depth. Unless the additional analyses provide adequate evidence for the former interpretation, we will not retain this claim in the revised manuscript.
We also recognize that focusing on temporal changes and lagged responses, rather than absolute freezing-depth values alone, does not eliminate the potential influence of absolute estimation errors on subsequent analyses. We will therefore investigate alternative approaches to estimating daily freezing depth, including nonlinear interpolation and, where supported by the available soil-temperature profiles, machine-learning-based approaches. Any alternative method will be evaluated using appropriate and consistent validation criteria rather than being assumed to be more accurate simply because it is more complex.
To address the concern that the estimation errors substantially exceed the reported response magnitude, we plan to conduct three additional analyses.
First, we will investigate the structure of the validation errors, including their variation with geographic location, season, and freezing depth. This analysis will help determine whether the systematic bias is approximately constant or varies with environmental conditions and the magnitude of freezing depth.
Second, we will compare alternative methods for estimating freezing-front depth from soil-temperature profiles, including piecewise linear interpolation and, where the available profile data permit, appropriate nonlinear interpolation or freezing-front identification methods. All methods will be evaluated using consistent validation criteria, including bias, mean absolute error (MAE), root mean square error (RMSE), and correlation coefficients. We will not regard a method as superior solely because it yields a higher correlation coefficient.
Third, we will examine the sensitivity of the principal lagged-response characteristics to the method used to estimate freezing depth. Specifically, we plan to repeat the core DLNM analyses using freezing-depth series derived from different estimation methods. Where scientifically appropriate, we will also compare results based on the original freezing-depth series, temporal anomalies or changes, and estimates subjected to an appropriate bias-correction procedure.
These analyses will help determine whether the reported lagged-response patterns are robust to uncertainty in freezing-depth estimation. If different reasonable estimation methods produce substantial changes in the magnitude or direction of the estimated effects, we will revise the corresponding quantitative conclusions. If the available data do not support reliable estimation of a response of this small magnitude, we will explicitly acknowledge this limitation and will no longer present the reported reduction of approximately 1.12 cm per additional extreme heat day as a quantitatively robust finding.
Reviewer comment 3: The validation sample does not cover the region where the bias is expected to be largest. Stations are concentrated in the eastern and southeastern low-elevation areas, whereas the estimated freezing depths exceed 200 cm in the central and northwestern plateau.
Response:
We acknowledge that the spatial representativeness of the validation data is an important limitation of the current study. As described in the manuscript, the available freezing-depth observations are concentrated primarily in the eastern and southeastern Qinghai–Tibet Plateau, while observations from the central and northwestern regions are comparatively sparse. Consequently, the existing validation results cannot independently establish that the estimates are equally reliable in regions where substantially greater freezing depths are reported.
To address this issue, we plan to distinguish more explicitly between the spatial coverage of the available observations and the spatial coverage of the gridded estimates. Where the available station information and observations permit, we will conduct stratified validation according to elevation, geographic region, and observed or estimated freezing-depth range to examine estimation errors under different environmental conditions.
We will also examine station-level validation residuals and, where the data permit, employ leave-one-station-out validation to assess the dependence of the estimation method on individual stations and its performance at stations excluded from the corresponding model fitting.
Nevertheless, statistical resampling of the existing stations cannot substitute for independent observations in regions where validation data are lacking. We will therefore avoid extrapolating validation results from the eastern and southeastern plateau to the entire Qinghai–Tibet Plateau without sufficient supporting evidence. If independent observations or suitable reference data for the central and northwestern regions cannot be obtained, we will explicitly acknowledge the greater uncertainty in these areas and reassess the applicability of plateau-wide quantitative conclusions that depend on absolute freezing-depth estimates.
Reviewer comment 4: The extreme heat threshold is defined inconsistently: the 90th percentile is computed from daily mean temperature but applied to daily maximum temperature in Section 2.2.2.
Response:
Thank you for identifying this inconsistency. We have examined the original analysis code and found that the analysis was designed to use daily maximum temperature, rather than daily mean temperature, to define extreme heat events.
Specifically, using 1981–2010 as the climatological baseline period, we calculate the 90th-percentile threshold (P90) from daily maximum temperature using a 31-day moving calendar window comprising the target calendar day and the 15 days before and after it. During the study period of 2000–2024, an extreme heat event is identified when daily maximum temperature exceeds the corresponding calendar-day P90 threshold for at least three consecutive days. Exceedance sequences lasting fewer than three days are excluded from the event definition, and daily extreme-heat labels are generated accordingly.
We will correct the corresponding description in the manuscript to ensure that the temperature variable, percentile threshold, and event-identification criteria are described consistently. We will also verify that the event data used in the subsequent analyses were generated using this definition and examine the handling of leap days and missing dates in the event-identification procedure.
Reviewer comment 5: The dominant confound—the 2000–2024 warming trend—is not addressed anywhere, and neither is the strong autocorrelation of daily freezing depth.
Response:
We agree that the long-term warming trend and temporal autocorrelation require more explicit and rigorous treatment.
During the study period, extreme heat events may exhibit temporal trends, while freezing depth and related freeze–thaw indicators also exhibit seasonal cycles and interannual variability. If these temporal structures are not adequately accounted for, the estimated lagged associations may partly reflect shared long-term trends, seasonal cycles, or the persistence of the freezing-depth series itself, rather than the response to individual extreme heat events alone.
To address this concern, we plan to reassess the DLNM results under several complementary model specifications. We will explicitly control for long-term temporal trends and seasonal variation using appropriate smooth functions of time and seasonal terms, and compare these results with analyses based on detrended series or anomaly series. We will also examine the temporal autocorrelation structure of the freezing-depth series and the model residuals. Where supported by the data and model structure, we will consider appropriate autoregressive error structures or block-bootstrap methods to estimate uncertainty while accounting for temporal dependence.
In addition, we will compare the exposure–lag–response relationships across different scientifically reasonable specifications of the long-term trend, approaches to handling temporal autocorrelation, and maximum lag windows. These sensitivity analyses will help determine whether the principal lagged-response characteristics depend strongly on particular modelling assumptions.
We will revise the interpretation of the findings in accordance with the results of these analyses, including modifying or withdrawing conclusions that are not robust to reasonable alternative specifications.
Reviewer comment 6: The abstract and Section 4.2 reach physically contradictory conclusions regarding the sign of the soil-moisture and surface-flux controls on lag duration.
Response:
Thank you for identifying this inconsistency. We agree that the descriptions in the Abstract, Results, Discussion, and Conclusions must be internally consistent. More importantly, these interpretations must be grounded in the actual statistical results rather than based on an assumed physical mechanism.
In the subsequent revision, we will systematically examine the relevant model outputs, figures, SHAP values, and their interpretations in the text. Specifically, we will recheck the direction, units, and data-processing procedures of the environmental variables and clearly distinguish statistical associations between these variables and predicted lag duration from the physical mechanisms that may link them to soil heat-transfer processes.
For soil moisture, latent heat flux, and sensible heat flux, we will examine whether the directions of their associations remain consistent across alternative model specifications. We will also investigate whether nonlinear relationships or interactions among variables contribute to the apparent inconsistencies.
If the conflicting interpretations cannot be resolved through these checks and additional analyses, we will revise or remove the corresponding mechanistic explanations rather than present unsupported interpretations as established findings. We will also ensure that SHAP-based associations are not interpreted as evidence of causation.
Closing remarks
We sincerely thank you again for your detailed and constructive comments. Your review has helped us recognize that the central challenge facing the current study is not simply insufficient presentation of the results, but the need to demonstrate that the estimated lagged responses are statistically supported, spatially applicable, and robust to alternative data-processing methods and modelling assumptions.
We are committed to undertaking the additional analyses outlined above, including comparisons of alternative freezing-depth estimation methods, spatially stratified validation, assessments of the effects of long-term trends and temporal autocorrelation, and a reassessment of the relationships between environmental factors and lag duration. Based on the results, we will determine which findings can be retained, which require more qualified interpretations, and which should be revised or removed.
We also recognize that these additional analyses may require substantial effort and may lead to changes in some of the principal quantitative conclusions. We are grateful for the opportunity to strengthen the study and will work to ensure that the conclusions presented in the subsequent revision are adequately supported by evidence and can be independently evaluated by readers.
Sincerely,
The Authors
Citation: https://doi.org/10.5194/egusphere-2026-2202-AC1
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AC1: 'Reply on RC2', Tingbin Zhang, 23 Oct 2026
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AC2: 'Reply on RC1', Tingbin Zhang, 23 Oct 2026
Dear Reviewer,
Thank you very much for your careful review of our manuscript and for providing such detailed, thoughtful, and constructive comments. We sincerely appreciate the considerable time and effort you devoted to evaluating this work.
We are especially grateful for your recognition of the scientific importance of the research topic. At the same time, we fully understand your concerns regarding the study design, data processing, methodological transparency, model performance, and interpretation of physical mechanisms. Your comments have helped us recognize several shortcomings in the current version of the manuscript, particularly in terms of methodological descriptions, the organization of the results, and the clarity of the overall scientific narrative.
Regarding the freezing-depth estimation, we acknowledge that the current predictions still exhibit a noticeable positive bias, particularly the approximately 40 cm systematic bias highlighted by both you and Dr. Zhu. We fully agree that this issue deserves careful attention, as it may affect the credibility of the subsequent analyses. Although the current lag-response analysis primarily focuses on the temporal dynamics and lag characteristics of freezing-depth variations rather than the absolute magnitude of freezing depth itself, we agree that additional validation is necessary to further evaluate the robustness of the results.
We also recognize that the current manuscript does not provide sufficient detail regarding the freezing-depth prediction procedure, missing-value treatment, freezing-depth estimation methods, and related parameter settings (Section 2.2.1). If the current approach is retained, we will provide a substantially expanded description of the implementation of the “depth-corrected linear interpolation” and “controlled linear extrapolation” procedures, together with a more detailed explanation of the missing-data handling strategy and freezing-front identification process. In addition, the 5 m threshold mentioned in the manuscript was indeed a typographical error. The actual threshold used in this study was 3.5 m, and this will be corrected in the revised manuscript.
To address concerns regarding model performance, we plan to further investigate the spatial distribution of model bias and its potential causes, including topographic effects, soil properties, vegetation conditions, and environmental heterogeneity. We have already begun exploring alternative freezing-depth estimation schemes, including different soil-temperature profile interpolation approaches (e.g., piecewise linear interpolation and spline-based interpolation) and alternative freezing-front determination strategies. Preliminary results suggest that some alternatives can improve performance in certain regions; however, the overall improvement remains limited. Therefore, we are continuing to explore more accurate approaches for daily freezing-depth estimation. If subsequent experiments demonstrate substantial improvements in predictive accuracy and reduced systematic bias, we are fully willing to revise the current analytical framework and reconstruct the subsequent lag-response analyses based on improved estimates. Comparative results from different approaches will also be incorporated into the Supplementary Materials to enhance transparency and methodological rigor.
Regarding the LightGBM framework, we agree that the current manuscript does not sufficiently explain the relationship between the DLNM and LightGBM components, which may have contributed to confusion. In fact, the DLNM was employed to investigate lagged responses at the temporal scale by quantifying the relationship between extreme heat events and freezing-depth time series, thereby deriving lag-response characteristics for each pixel. In contrast, the LightGBM-SHAP analysis was designed to investigate the drivers of spatial variability in lag times. Its input variables include cumulative heat, vegetation conditions, soil properties, moisture conditions, and other environmental factors, while the objective is to explain spatial differences in lag duration rather than to model temporal sequences directly. We therefore believe that the use of LightGBM is appropriate for this spatial attribution task. Nevertheless, we acknowledge that the methodological description was not sufficiently clear and that the manuscript did not describe the evaluation of alternative machine-learning models. In the revised version, we will improve the methodological description, add a more detailed workflow diagram, and clearly explain how the continuous lag-response surfaces generated by the DLNM were transformed into the maximum lag-time metric used as the target variable in the LightGBM-SHAP analysis. We will also further evaluate the variable-selection strategy, including potential dependencies among sand, silt, and clay fractions, and clarify how snow-related processes and precipitation variables were handled.
Regarding the identification of extreme heat events, we appreciate your observation that the current description may be confusing. In this study, the 90th percentile (P90) threshold was used to identify extreme heat events and delineate the regions affected by such events. Subsequently, within those regions, daily freezing-depth estimates and extreme heat event time series were analyzed using the DLNM framework to quantify lagged responses. Because extreme heat intensity varies substantially among regions, the corresponding temperatures are not represented by a single fixed threshold but rather span a range of values. The “representative” temperatures shown in the manuscript (10°C, 15°C, 20°C, 25°C, and 30°C) were selected solely to facilitate visualization and interpretation of lag-response curves under different heat intensities and were not used as universal thresholds for event identification. We believe that your question regarding whether these representative temperatures are equally applicable across all regions of the Qinghai–Tibet Plateau is highly valuable and deserves further consideration. Given the substantial spatial variability in maximum temperatures across the Plateau, the current representation may be more reflective of lower-elevation regions. We will therefore further discuss this issue in the revised manuscript and evaluate the influence of regional climatic differences on lag-response characteristics.
We also greatly appreciate your comments regarding the organization of the Results section. We recognize that the current manuscript contains a large amount of information, which may obscure the central scientific questions and limit the depth of the discussion. In the revised version, we plan to reorganize the Results and Discussion sections, moving some supporting analyses to the Supplementary Materials while focusing the main text more directly on the following key scientific questions: (1) whether extreme heat events influence seasonally frozen ground processes; (2) whether such influences exhibit significant lagged responses; (3) how lag times vary spatially; (4) which environmental factors control this spatial variability; and (5) what physical mechanisms may explain these patterns. At the same time, we will reduce repetitive reporting of numerical results and strengthen the physical interpretation and scientific discussion of the findings.
Finally, we sincerely thank you for your valuable suggestions regarding the explanation of the proposed thermal saturation mechanism, the rationale for data selection, the harmonization of multiple datasets, the presentation of Table 2, and the interpretation of Figure 6. These comments have highlighted several important aspects of the manuscript that can be substantially improved. We will carefully revise the corresponding sections, provide additional methodological details and explanations, improve the presentation of figures and tables, clarify variable definitions and figure captions, and further enhance the scientific clarity and readability of the manuscript.
Once again, we sincerely appreciate your thoughtful and insightful comments. We are currently conducting additional analyses and supplementary experiments and will systematically revise the manuscript in response to the concerns raised by you and the other reviewers. As this work progresses, we would be pleased to continue engaging in the discussion and to provide updates where appropriate.
With best regards,
The Authors
Citation: https://doi.org/10.5194/egusphere-2026-2202-AC2
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CC4: 'Reply on RC1', Ting Zhang, 19 Jun 2026
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RC2: 'Comment on egusphere-2026-2202', Anonymous Referee #2, 01 Oct 2026
This manuscript examines the lagged response of seasonally frozen ground (SFG) to extreme heat events across the Qinghai–Tibet Plateau (QTP) using a combined Distributed Lag Non-linear Model and eXplainable Artificial Intelligence (DLNM-XAI) framework. The topic is scientifically relevant and timely. Previous work has largely focused on multi-year trends in freeze–thaw dynamics, on borehole-scale observations at a handful of sites, or on physically based models that neglect latent heat and soil-moisture coupling. The present study attempts to provide a gridded, event-scale quantification of lagged responses and to attribute their spatial heterogeneity to snow cover, soil moisture and surface energy fluxes. The conceptual framing is sound, the figures are well prepared, and the amount of work involved is substantial.
Nevertheless, the current version contains several methodological and statistical shortcomings that are serious enough to undermine the principal quantitative conclusions:
1. The manuscript contains no p-values, confidence intervals, R² values or standard errors anywhere, yet the word "significantly" is used several times;
2. The validation of the interpolated freezing depth yields a systematic bias of 39.79 cm and an RMSE of 54.01 cm, whereas the principal signal reported (1.12 cm per extreme heat day) is only ~2% of that RMSE. The authors nonetheless describe the error as "a consistent offset rather than random fluctuations" and conclude that the product is "sufficiently reliable";
3. The validation sample does not cover the region where the bias is expected to be largest. Stations are concentrated in the eastern and southeastern low-elevation areas, i.e. in shallow-freezing terrain, whereas the reported freezing depths exceed 200 cm in the central and northwestern plateau;
4. The extreme heat threshold is defined inconsistently — the 90th percentile is computed from daily mean temperature but applied to daily maximum temperature (Section 2.2.2);
5. The dominant confound — the 2000–2024 warming trend — is not addressed anywhere, and neither is the strong autocorrelation of daily freezing depth;
6. The abstract and Section 4.2 reach physically contradictory conclusions regarding the sign of the soil-moisture and surface-flux controls on lag duration;
In my view the manuscript is not yet in a state where the main findings can be independently verified. Substantial re-analysis and a reconstruction of the argument are required.
Citation: https://doi.org/10.5194/egusphere-2026-2202-RC2 -
AC1: 'Reply on RC2', Tingbin Zhang, 23 Oct 2026
Dear Reviewer,
We sincerely thank you for your careful evaluation of our manuscript and for identifying several important methodological and statistical issues. We appreciate your recognition of the scientific relevance of this study, the conceptual framework, and the substantial effort involved in the research. At the same time, we fully understand your central concern that the current manuscript does not provide sufficient statistical evidence and methodological detail for readers to independently assess the main quantitative findings.
After carefully considering your comments, we recognize that several of the issues you have raised cannot be adequately addressed through textual clarification alone. In particular, the uncertainty associated with freezing-depth estimation, the spatial representativeness of the validation data, and the potential confounding effects of long-term warming trends and temporal autocorrelation require further investigation. We will undertake additional analyses, reconsider the existing analytical framework where necessary, reassess the principal findings, and revise our conclusions in accordance with the results.
Our point-by-point responses are provided below.
Reviewer comment 1: The manuscript does not report p-values, confidence intervals, R² values, or standard errors, yet the word “significantly” is used several times.
Response:
We agree with this comment. The current manuscript does not report statistical uncertainty systematically or adequately, and some statements in the Results section therefore lack sufficient statistical support. In the subsequent revision, we will strengthen the reporting of statistical evidence by providing effect estimates, 95% confidence intervals, standard errors, p-values, and appropriate goodness-of-fit metrics where applicable.
For analyses of temporal trends, we will explicitly describe the statistical methods employed, the corresponding null hypotheses, and the approaches used to account for temporal dependence. We will also examine potential multiple-comparison issues in the spatial analyses to avoid interpreting isolated statistically significant results as robust regional patterns. Statements involving statistical significance that are not adequately supported by the analyses will be revised or removed.
Reviewer comment 2: The validation of the interpolated freezing depth yields a systematic bias of 39.79 cm and an RMSE of 54.01 cm, whereas the principal signal reported is only approximately 1.12 cm per extreme heat day. The authors nevertheless describe the error as “a consistent offset rather than random fluctuations” and conclude that the product is “sufficiently reliable.”
Response:
Thank you for raising this important concern. We acknowledge that using the relatively high correlation coefficient as evidence that the estimated freezing depths are sufficiently accurate was not adequately justified. The substantial bias and RMSE in the existing validation results require us to reassess whether the reported response magnitude can be distinguished reliably from the uncertainty associated with freezing-depth reconstruction.
We previously interpreted the estimation errors primarily as a consistent systematic offset. However, we recognize that this interpretation was not supported by a sufficiently detailed analysis of the error structure. We will investigate whether the errors are approximately constant or instead vary systematically with environmental conditions and freezing depth. Unless the additional analyses provide adequate evidence for the former interpretation, we will not retain this claim in the revised manuscript.
We also recognize that focusing on temporal changes and lagged responses, rather than absolute freezing-depth values alone, does not eliminate the potential influence of absolute estimation errors on subsequent analyses. We will therefore investigate alternative approaches to estimating daily freezing depth, including nonlinear interpolation and, where supported by the available soil-temperature profiles, machine-learning-based approaches. Any alternative method will be evaluated using appropriate and consistent validation criteria rather than being assumed to be more accurate simply because it is more complex.
To address the concern that the estimation errors substantially exceed the reported response magnitude, we plan to conduct three additional analyses.
First, we will investigate the structure of the validation errors, including their variation with geographic location, season, and freezing depth. This analysis will help determine whether the systematic bias is approximately constant or varies with environmental conditions and the magnitude of freezing depth.
Second, we will compare alternative methods for estimating freezing-front depth from soil-temperature profiles, including piecewise linear interpolation and, where the available profile data permit, appropriate nonlinear interpolation or freezing-front identification methods. All methods will be evaluated using consistent validation criteria, including bias, mean absolute error (MAE), root mean square error (RMSE), and correlation coefficients. We will not regard a method as superior solely because it yields a higher correlation coefficient.
Third, we will examine the sensitivity of the principal lagged-response characteristics to the method used to estimate freezing depth. Specifically, we plan to repeat the core DLNM analyses using freezing-depth series derived from different estimation methods. Where scientifically appropriate, we will also compare results based on the original freezing-depth series, temporal anomalies or changes, and estimates subjected to an appropriate bias-correction procedure.
These analyses will help determine whether the reported lagged-response patterns are robust to uncertainty in freezing-depth estimation. If different reasonable estimation methods produce substantial changes in the magnitude or direction of the estimated effects, we will revise the corresponding quantitative conclusions. If the available data do not support reliable estimation of a response of this small magnitude, we will explicitly acknowledge this limitation and will no longer present the reported reduction of approximately 1.12 cm per additional extreme heat day as a quantitatively robust finding.
Reviewer comment 3: The validation sample does not cover the region where the bias is expected to be largest. Stations are concentrated in the eastern and southeastern low-elevation areas, whereas the estimated freezing depths exceed 200 cm in the central and northwestern plateau.
Response:
We acknowledge that the spatial representativeness of the validation data is an important limitation of the current study. As described in the manuscript, the available freezing-depth observations are concentrated primarily in the eastern and southeastern Qinghai–Tibet Plateau, while observations from the central and northwestern regions are comparatively sparse. Consequently, the existing validation results cannot independently establish that the estimates are equally reliable in regions where substantially greater freezing depths are reported.
To address this issue, we plan to distinguish more explicitly between the spatial coverage of the available observations and the spatial coverage of the gridded estimates. Where the available station information and observations permit, we will conduct stratified validation according to elevation, geographic region, and observed or estimated freezing-depth range to examine estimation errors under different environmental conditions.
We will also examine station-level validation residuals and, where the data permit, employ leave-one-station-out validation to assess the dependence of the estimation method on individual stations and its performance at stations excluded from the corresponding model fitting.
Nevertheless, statistical resampling of the existing stations cannot substitute for independent observations in regions where validation data are lacking. We will therefore avoid extrapolating validation results from the eastern and southeastern plateau to the entire Qinghai–Tibet Plateau without sufficient supporting evidence. If independent observations or suitable reference data for the central and northwestern regions cannot be obtained, we will explicitly acknowledge the greater uncertainty in these areas and reassess the applicability of plateau-wide quantitative conclusions that depend on absolute freezing-depth estimates.
Reviewer comment 4: The extreme heat threshold is defined inconsistently: the 90th percentile is computed from daily mean temperature but applied to daily maximum temperature in Section 2.2.2.
Response:
Thank you for identifying this inconsistency. We have examined the original analysis code and found that the analysis was designed to use daily maximum temperature, rather than daily mean temperature, to define extreme heat events.
Specifically, using 1981–2010 as the climatological baseline period, we calculate the 90th-percentile threshold (P90) from daily maximum temperature using a 31-day moving calendar window comprising the target calendar day and the 15 days before and after it. During the study period of 2000–2024, an extreme heat event is identified when daily maximum temperature exceeds the corresponding calendar-day P90 threshold for at least three consecutive days. Exceedance sequences lasting fewer than three days are excluded from the event definition, and daily extreme-heat labels are generated accordingly.
We will correct the corresponding description in the manuscript to ensure that the temperature variable, percentile threshold, and event-identification criteria are described consistently. We will also verify that the event data used in the subsequent analyses were generated using this definition and examine the handling of leap days and missing dates in the event-identification procedure.
Reviewer comment 5: The dominant confound—the 2000–2024 warming trend—is not addressed anywhere, and neither is the strong autocorrelation of daily freezing depth.
Response:
We agree that the long-term warming trend and temporal autocorrelation require more explicit and rigorous treatment.
During the study period, extreme heat events may exhibit temporal trends, while freezing depth and related freeze–thaw indicators also exhibit seasonal cycles and interannual variability. If these temporal structures are not adequately accounted for, the estimated lagged associations may partly reflect shared long-term trends, seasonal cycles, or the persistence of the freezing-depth series itself, rather than the response to individual extreme heat events alone.
To address this concern, we plan to reassess the DLNM results under several complementary model specifications. We will explicitly control for long-term temporal trends and seasonal variation using appropriate smooth functions of time and seasonal terms, and compare these results with analyses based on detrended series or anomaly series. We will also examine the temporal autocorrelation structure of the freezing-depth series and the model residuals. Where supported by the data and model structure, we will consider appropriate autoregressive error structures or block-bootstrap methods to estimate uncertainty while accounting for temporal dependence.
In addition, we will compare the exposure–lag–response relationships across different scientifically reasonable specifications of the long-term trend, approaches to handling temporal autocorrelation, and maximum lag windows. These sensitivity analyses will help determine whether the principal lagged-response characteristics depend strongly on particular modelling assumptions.
We will revise the interpretation of the findings in accordance with the results of these analyses, including modifying or withdrawing conclusions that are not robust to reasonable alternative specifications.
Reviewer comment 6: The abstract and Section 4.2 reach physically contradictory conclusions regarding the sign of the soil-moisture and surface-flux controls on lag duration.
Response:
Thank you for identifying this inconsistency. We agree that the descriptions in the Abstract, Results, Discussion, and Conclusions must be internally consistent. More importantly, these interpretations must be grounded in the actual statistical results rather than based on an assumed physical mechanism.
In the subsequent revision, we will systematically examine the relevant model outputs, figures, SHAP values, and their interpretations in the text. Specifically, we will recheck the direction, units, and data-processing procedures of the environmental variables and clearly distinguish statistical associations between these variables and predicted lag duration from the physical mechanisms that may link them to soil heat-transfer processes.
For soil moisture, latent heat flux, and sensible heat flux, we will examine whether the directions of their associations remain consistent across alternative model specifications. We will also investigate whether nonlinear relationships or interactions among variables contribute to the apparent inconsistencies.
If the conflicting interpretations cannot be resolved through these checks and additional analyses, we will revise or remove the corresponding mechanistic explanations rather than present unsupported interpretations as established findings. We will also ensure that SHAP-based associations are not interpreted as evidence of causation.
Closing remarks
We sincerely thank you again for your detailed and constructive comments. Your review has helped us recognize that the central challenge facing the current study is not simply insufficient presentation of the results, but the need to demonstrate that the estimated lagged responses are statistically supported, spatially applicable, and robust to alternative data-processing methods and modelling assumptions.
We are committed to undertaking the additional analyses outlined above, including comparisons of alternative freezing-depth estimation methods, spatially stratified validation, assessments of the effects of long-term trends and temporal autocorrelation, and a reassessment of the relationships between environmental factors and lag duration. Based on the results, we will determine which findings can be retained, which require more qualified interpretations, and which should be revised or removed.
We also recognize that these additional analyses may require substantial effort and may lead to changes in some of the principal quantitative conclusions. We are grateful for the opportunity to strengthen the study and will work to ensure that the conclusions presented in the subsequent revision are adequately supported by evidence and can be independently evaluated by readers.
Sincerely,
The Authors
Citation: https://doi.org/10.5194/egusphere-2026-2202-AC1
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AC1: 'Reply on RC2', Tingbin Zhang, 23 Oct 2026
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This study focuses on the lagged responses of seasonally frozen ground to extreme heat events over the Qinghai–Tibet Plateau and proposes a DLNM‑XAI integrated framework to reveal the non-linear, lagged response characteristics and spatial heterogeneity of frozen ground to extreme heat events. The topic has significant scientific importance. However, several issues remain in terms of methodological details, data validation, model applicability, and interpretation of results. I recommend major revision before publication.
The specific comments and suggestions are as follows:
The current graphical abstract appears to be a simple assembly of relevant figures, making it repetitive. I suggest the authors redraw the graphical abstract to help readers better understand the research rationale and the key findings.
In the abstract, the authors state: “Results show that extreme heat significantly modifies freeze–thaw dynamics.” Freeze–thaw cycles are the result of multiple factors including climate, soil hydro-thermal condition, vegetation, and snow cover. Extreme heat events are likely only a disturbance factor rather than a dominant control on freeze–thaw cycles.
In section 2.2.1, how did the authors define 5 m as the threshold depth? The annual maximum freezing depth of seasonally frozen ground on the Qinghai–Tibet Plateau is mostly in the range of 2–3 m.
In section 2.2.3, “L is the maximum lag (set to 30 days in this study)”. Why was 30 days chosen? The lag time likely varies greatly under different regions and different intensities of extreme heat events. I recommend adding sensitivity experiments with different lag values. Additionally, please provide more details on model training and validation.
In Figure 3, what is the basis for delineating the “high-frequency regions”? I note there appear to be areas with even higher frequency than the selected regions. Moreover, why are extreme heat events more significant in these regions? Please cite relevant literature to support the explanation.
In section 4.2, the authors state that “lag time exhibits a negative relationship with the duration of extreme heat events” and explain this in terms of a “thermal saturation mechanism”, but the specific physical processes of this mechanism are not described. Why would a greater number of hot days shorten the lag time? Is there a threshold effect?
According to Figure A1, the predicted values are generally overestimated, with a bias of about 40 cm, indicating poor simulation. What is the spatial pattern of this bias? Is it related to topography, soil type, vegetation, or other factors? Such a large positive bias would significantly affect the reliability of lag-time estimation. In fact, many methods exist for estimating maximum freezing depth; I suggest the authors compare and adopt a method with higher simulation accuracy.
The station data used in this study are relatively sparse and unevenly distributed. I recommend that the authors use the station meteorological observation data from the National Meteorological Data Center of the China Meteorological Administration. The number of stations in the seasonally frozen ground region of the Qinghai–Tibet Plateau is likely no less than 50, and these stations provide soil temperature observations at depths from 0 to 320 cm, which would be very helpful for this study. Furthermore, the reliability of ERA5-Land reanalysis data over the Qinghai–Tibet Plateau exhibits notable seasonal and regional differences; the authors should add a discussion of this issue.