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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Status: open (until 17 Jul 2026)
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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
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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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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.