Evaluation of Turbulent Flux Parameterizations over a Continental Glacier on the Tibetan Plateau

Xu, Yichan; Zhu, Meilin; Gao, Jing; Lin, Daijiao; Hui, Lei; Zhu, Fei; Zhao, Huabiao; Zhang, Fengying

doi:10.5194/egusphere-2025-4227

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https://doi.org/10.5194/egusphere-2025-4227

Preprints

15 Oct 2025

| 15 Oct 2025

Evaluation of Turbulent Flux Parameterizations over a Continental Glacier on the Tibetan Plateau

Yichan Xu, Meilin Zhu, Jing Gao, Daijiao Lin, Lei Hui, Fei Zhu, Huabiao Zhao, and Fengying Zhang

Abstract. A lack of observations of turbulent fluxes over continental glaciers limits our understanding of the mechanisms that control glacier variations and associated water resource changes across the Tibetan Plateau (TP). Here, we present the first comprehensive analysis of turbulent flux characteristics and a systematic evaluation of turbulent flux methods for a continental glacier on the TP, using eddy covariance observations from the Dunde Glacier (May–October, 2023). The Dunde Glacier persistently lost energy through latent heat flux (mean LE: −10.34 W m⁻²) and gained energy via sensible heat flux (mean H: 6.93 W m⁻²), with pronounced seasonal and diurnal variability. On the basis of these measured data, we tested five turbulent flux methods for the Dunde Glacier, including those derived from katabatic flow models, simplified Monin–Obukhov similarity theory without stability corrections, Monin–Obukhov similarity theory with stability corrections using two different bulk Richardson numbers, and the Monin–Obukhov similarity theory with universal stability functions. Among all schemes, the Monin–Obukhov similarity theory with universal stability functions achieved the highest accuracy for both H and LE at different timescales. We further evaluated the performance of these parameterizations in energy and mass balance modeling. Our results show that the recalibrated turbulent flux parameterizations are an effective approach for improving the accuracy of modelled glacier energy and mass balance, and that the Monin–Obukhov similarity theory with universal stability functions yielded the best simulation performance for modelled glacier mass balance. We also found that the Dunde Glacier experienced a sharp increase in H and reversal in LE during a humid heatwave event, shifting from a negative total turbulent flux under the mean climate condition to positive values during the extreme event. However, none of the turbulent flux methods fully captured the high values that occurred during the extreme weather and climate event, indicating that there is currently an underestimation of the contribution of turbulent fluxes to glacier melt energy. These findings advance our knowledge of turbulent fluxes for continental glaciers on the TP and provide important guidance for the improvement of glacier models.

Received: 29 Aug 2025 – Discussion started: 15 Oct 2025

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16 Oct 2026

Evaluation of turbulent flux parameterizations over a continental glacier on the Tibetan Plateau

Yichan Xu, Meilin Zhu, Jing Gao, Daijiao Lin, Lei Hui, Fei Zhu, Huabiao Zhao, and Fengying Zhang

The Cryosphere, 20, 6021–6044, https://doi.org/10.5194/tc-20-6021-2026,https://doi.org/10.5194/tc-20-6021-2026, 2026

Short summary

Yichan Xu, Meilin Zhu, Jing Gao, Daijiao Lin, Lei Hui, Fei Zhu, Huabiao Zhao, and Fengying Zhang

Interactive discussion

Status: closed

CC1:
'Comment on egusphere-2025-4227', Keqin Duan, 21 Oct 2025
This study presents the first comprehensive evaluation of turbulent flux parameterization schemes over a continental glacier on the Tibetan Plateau (TP), based on continuous eddy covariance (EC) observations collected at the Dunde Glacier from May to October 2023. The authors assess five representative turbulent flux schemes (C_kat, C_log, C_Rib1, C_Rib2, and C_M–O), analyze their performance across multiple temporal scales, and further evaluate their influence on glacier energy and mass balance simulations.
The topic is timely and significant, as turbulent fluxes are among the least constrained components of the surface energy balance on the TP, and direct EC observations over continental glaciers remain extremely rare. The manuscript is well structured, the data quality is high, and the results are clearly presented. The conclusions are supported by the analysis, and the discussion offers useful implications for improving glacier energy-balance modeling.
The paper provides valuable new insights into turbulent exchange processes over continental glaciers. I recommend mayor revisions before publication.
Specific Comments
Abstract：
Merely stating correlations is insufficient; are such correlations applicable across all glaciated regions? It is recommended that the authors explain with reference to the unique characteristics of the study area.

The abstract lacks a statement regarding the limitations of the study.

Why was the Dunde Glacier selected? In other words, what is the significance or importance of this glacier within the study region?

Introduction：
Although it already mentions “the first comprehensive analysis for a continental glacier,” it is suggested to emphasize the differences and scientific significance of this study compared with existing research on maritime and sub-continental glaciers, preferably in the last one or two sentences.

It is recommended to slightly shorten the review of previous studies (lines 64–91) and instead expand the final paragraph to highlight the study’s specific aims and hypotheses, ensuring a smooth logical transition into Section 2.

Minor language point: change “the important reasons of such difference are…” to “the main reason for such differences is…”.

Minor grammatical and stylistic edits are needed (e.g., “Here we provide the first systematically analyze…” → “Here we provide the first systematic analysis…”).

Study Area and Data：
Figure 1 is informative, but panel (b) should include a scale bar, north arrows, which would help readers better understand the actual size and spatial extent of the Dunde Glacier.

The authors might briefly explain why the Dunde Glacier was selected—for example, its representativeness of mid-latitude continental glacier conditions, the logistical advantages for EC deployment, and its climatic relevance to the Qilian Mountains.

Please amend the elevation "5317 m" to the standard format "5,317 m".

Methods：
Section 3 is comprehensive but quite dense due to numerous equations. It is strongly suggested to include a summary table comparing the five schemes (C_kat, C_log, C_Rib1, C_Rib2, C_M–O) in terms of (a) stability correction, (b) iterative requirement, and (c) computational complexity. This would greatly enhance clarity and help readers grasp their physical and numerical distinctions.

Check the consistency of formula expressions — for example, ensure that the pressure variable symbols used in Equations (4), (11), and (16) and Table 2, as well as the air pressure notation in Section 4.1, remain consistent throughout the manuscript.

Results
In Sections 4.3.1 and 4.3.2, it is better to add a brief summary sentence at the end of each paragraph to highlight which method performs best overall for each flux (LE and H), and indicate which scheme performs best in different seasons.
Discussion
In Section 5.2, the authors should clearly specify the data required and their sources for the energy balance–snow and firn model used in this study, and indicate whether these details have been sufficiently provided in the Study Area and Data section. The model output variables should also be explicitly described.

In Section 5.3, Are the specific dates shown confirmed to represent extreme high temperature events? The authors should clearly describe the criteria used to identify extreme weather and climate events.

The heatwave analysis (Section 5.3) is one of the strengths of this paper. To further improve this section, it is recommended to include specific quantitative data to illustrate how the anomalous turbulent flux variations during the humid heatwave affected the glacier surface energy balance, thereby strengthening the comparison with non-extreme periods.
Citation: https://doi.org/10.5194/egusphere-2025-4227-CC1
- AC3: 'Reply on CC1', Zhu. Meilin, 25 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4227/egusphere-2025-4227-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4227-AC3
RC1:
'Comment on egusphere-2025-4227', Anonymous Referee #1, 21 Nov 2025
This study by Xu and others evaluates the suitability of five different turbulent flux models on a glacier on the Tibetan Plateau. This is done by comparing modeled and observed turbulent fluxes over a five-month period in 2023. In a next step, the turbulent flux models are included in a mass balance model to test sensitivity of the mass balance to the choice of turbulent flux model. The manuscript is well written, presents new data, and contains useful new insights in performance of different turbulent flux models on a glacier on the Tibetan Plateau. This information will be valuable e.g. for future applications of mass balance modelling in the area. In my opinion the manuscript needs major revisions though before it can be published. One concern I have is that the description of the methods is incomplete. For example, it remains entirely unclear how the calibration of the mass balance model with the different turbulent flux models was done. Furthermore, I think it is a missed opportunity that no attempt has been made to calibrate e.g. roughness lengths to improve agreement between modeled and observed turbulent fluxes. This would give useful insight in what parameter settings of the turbulent flux models are most suitable to use on this glacier (and possibly other glaciers on the Tibetan Plateau). The calibrated turbulent flux models could then be used in the mass balance model to assess mass balance sensitivity to the turbulent flux formulations. Maybe some of this was in fact done; if so, it just needs to be described more clearly. Detailed comments are given below.
Specific comments:
Missing parameter values & errors in equations:
Section 3: For many model-specific and physical constants (e.g. Ctub, Ctub2, Ls/f, Cp, Ch, CH etc) values are not specified in the manuscript (unless I missed it). Please add a table with all these parameters and their values, units and, where relevant, the source.

Equation 1: Division by pressure is missing. Please check that it is not missing in your code. See for example Radic et al. (2017). I think the corresponding equation in Oerlemans and Grisogono (2002) may also miss this.

Equation 2: The "0.622" should not be there and instead air density should be in the equation. Also here, see Radic et al. (2017), and please check that your code is correct.

Discrepancies between modeled and observed turbulent fluxes:
L139-140: "the roughness lengths are computed dynamically". Does this mean that roughness lengths are time-dependent? It is important to add a bit more information about how the roughness lengths are determined and add the relevant equations from Andreas (1987). The information is relevant in order to be able to judge whether some of the discrepancies between modeled and observed fluxes (Fig. 4) could result from this.

L308-309: "However, ... observed variability". It seems that the underestimation of variability of modelled turbulent fluxes applies over the whole period and for different turbulent flux models. Is this underestimation of temporal variability something that other studies also found (on other glaciers)? Could it be related to the calculation of the roughness lengths? How uncertain are the turbulent flux measurements themselves? Is it possible to assign a value to this uncertainty?

L336-341: "All five methods ... turbulent exchange." Since all methods seem to give roughly the same errors, I am inclined to think that it could also be related to the way roughness lengths are determined (since all methods depend on them). It could be worth looking into this further and check e.g. whether an alternative description (or calibration; see next point) of roughness lengths would strongly change the model results.

Figure 5: Given the weaker intra-day variability of in particular the latent heat flux, maybe the roughness length for the latent heat flux is off? I think it could have been an interesting strategy to try to find optimum values for (constant) roughness lengths by trying to minimize the differences between modelled and observed turbulent fluxes. Have you considered doing this?

Mass balance modelling strategy:
Section 5.2: I can see why the authors want to run a mass balance model with the different turbulent flux schemes as it may give insight in sensitivity of the mass balance to the turbulent flux descriptions. However, in its current form I do not think the mass balance modelling experiment is of very much use. To me it would have made more sense to first calibrate the individual turbulent flux models against the observed turbulent flux data (by optimizing e.g. roughness lengths). In a next step these calibrated turbulent flux models could then be used in the mass balance model and the resulting mass balance from the runs with different turbulent flux schemes can be compared. There may be (like now) some biases between modeled and observed mass balance, but at least such an experiment will give robust insight in the sensitivity of the mass balance to using different turbulent flux models. If the above approach is what was already done by the authors, then it is just a matter of describing it more clearly.

Selecting a best turbulent flux model:
L327: "indicating the best accuracy among the tested methods". I think it should rather be emphasized that the performance of the five methods is very similar. Given uncertainty in the observations, and these small differences, it is not possible to argue (with statistical significance) that one method is better than the others based on these results.

L425: "the best performance". It is only marginally better than the other models. So statistically speaking the performance is not significantly different across the models.

L549-552: "Among the five schemes ... variability.". Again, this is a rather bold statement based on the presented results. There are clear benefits for using the simpler (easier to implement and quicker to run) models too, especially if their performance is similar to the MO model.

Minor comments / technical corrections:
L30: "a negative total ... climate condition". Replace with "the commonly observed negative total turbulent heat flux".

L32: "extreme weather and climate event". Replace with "extreme event".

L47: "frequencies ... events". Replace with "frequency and intensity of extreme weather events".

L48: Not only enhanced turbulent fluxes are responsible for increased glacier mass loss but also e.g. increased incoming LW radiation. Please reformulate.

L63: "climatic mechanisms". Please note that climate refers to much longer timescales than considered here. Maybe use "weather patterns" or similar instead.

L64: "has become" --> "is".

L65: "are" --> "have been".

L68: "intensive" --> "expensive".

L76-80: "Taking the ... 2006-2011". This comparison requires a bit more info to be useful. E.g. what methods were used (modelling or observations)? How large were uncertainties in the two studies? Could the different periods considered explain the differences?

L88: "... on the TP.". Add "has previously been done".

L90-92: "These uncertainties hinder ... between glaciers and climate.". This becomes a bit repetitive now. I suggest to remove it here.

L93: "systematically analyze" --> "systematic analysis".

L98: "the model robustness" --> "performance of the turbulent flux models".

Section 2: I suppose surface temperature is estimated from the observed outgoing longwave radiation. This should be described somewhere. Was an emissivity of 1 assumed?

L119: "using" --> "using a".

L190: "pressure Ps". Please note that air pressure was already defined as "P" in L165.

L201: Please note that the 𝛜 constant is the same as the "0.622" that is used in several equations (e.g. Eqs (1) and (3)).

Sect. 4.1: Please make sure that italic font is used for variables.

L224-242: This is a lot of text about the temperature time-series, which are also shown in a figure and do not contain too many surprising features. I suggest to shorten this.

L243-268: Also this can be shortened. Essentially, everything mentioned here is also visible in Figure 2 so just a short summary would work.

Figure 2: Units on the y-axes should be in brackets. Additionally, please use the same variable names as in the main text.

Figure 2: You could consider adding a panel with Ta-Ts (the temperature deficit), which is an important parameter for the turbulent fluxes and their direction. Furthermore, albedo could be shown. It is discussed in connection to the extreme event in July 2023.

L286 (for example): With an observation period starting in May and finishing in October it maybe is better to not refer to "spring" and "autumn" but rather the months in question, e.g. "May-Jun" or "Sep-Oct".

L287-288: "with June having the lowest monthly average". I suppose that coincides with the period with the lowest temperature deficit at the surface(?). If so, that could be mentioned here.

L291: "through turbulent heat exchange". So sublimation / evaporation are large. Related question, do you find penitentes on the glacier surface? If so, it could be worth highlighting in the introduction as it is a visible confirmation of the significance of sublimation and evaporation.

Figure 3: Please add the type of flux in the y-axis labels.

Figure 3: Since there are data gaps I suppose some filtering of the data was done. Unless I missed it, I do not think this is currently described. If so, please add this.

Figure 4: Since the modeled data are unique in every graph, I suggest to plot these lines on top of the lines with the measured values. Currently it is the other way around.

L462-463: "while CMB estimates ... -304.19 mm.". It is not surprising that there are biases as the mass balance model (EBFM), with standard values for model parameters, is not optimized for this region/glacier. Besides turbulent flux parameters, e.g. correct albedo parameters are at least equally important for the simulated mass balance. This should be acknowledged.

Figure 7: Why not zoom in only the heat wave period? The rest of the timeseries are also shown elsewhere, so no need to include them again here.

L506-507: "Such positive LE values ... maritime glaciers.". I agree, but also in the high Arctic where surface temperatures are typically much lower than air temperatures due to less incoming solar radiation.

L509: "18.53". Please be consistent in the use of significant digits (e.g. I recommend to use "18.5" here).

L512: "surface albedo decreased". I suppose the surface was already ice-covered at the start of the heat wave(?). If so, I do not see how the albedo dropped further during the heatwave. It would by the way be nice to see albedo time-series in the manuscript, e.g. in Fig. 2.

L526: "warrant further investigation". I am not sure what is the cause either, but since the even the sign is off, I suppose it in some way must be related to the humidity gradient (which in turn depends on the temperature gradient).

L528-531: "All calculated values ... to glacier melting.". This applies to the uncalibrated turbulent flux models. It would be great to see if that still applies after calibrating the turbulent heat fluxes (e.g. by tuning the roughness lengths).

L535-536: "to increasingly ... increased H. ". It could be worth emphasizing that it is primarily that the surface temperature cannot exceed 0 ^oC that causes positive LE and higher H during such extreme events.
Citation: https://doi.org/10.5194/egusphere-2025-4227-RC1
- AC1: 'Reply on RC1', Zhu. Meilin, 21 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4227/egusphere-2025-4227-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4227-AC1
RC2:
'Comment on egusphere-2025-4227', Cole Lord-May, 26 Nov 2025

See attached comments.

Citation: https://doi.org/10.5194/egusphere-2025-4227-RC2
- AC2: 'Reply on RC2', Zhu. Meilin, 21 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4227/egusphere-2025-4227-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4227-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (13 Apr 2026) by Valentina Radic

AR by Zhu. Meilin on behalf of the Authors (15 Apr 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (25 Apr 2026) by Valentina Radic

RR by Anonymous Referee #1 (12 Jun 2026)

Suggestions for revision or reasons for rejection

I have now reviewed the revised manuscript by Xu et al. I thank the reviewers for their efforts to revise the manuscript. Most of my major concerns regarding the methods are now resolved. I do have some remaining comments though, primarily about the presentation, which are detailed below.

Specific comments:

Calibration of turbulent flux models:
The new strategy to calibrate roughness lengths or similar in the turbulent flux models against observations is an improvement. It is clear how a best value for z_0m was found, but it is not described how the constants in the C_kat and C_log methods were calibrated. What range of values was tested? And what measure (RMSE, bias, R) was used to select a best value? Please add this information in Sect. 3.2.

Results with and without calibration:
It could be made more clear at the start of Sect. 4.3 that all results in that section are based on the calibrated turbulent fluxes. Furthermore, it is unclear what Table 3 is showing. It is not cited in the text and it contains different values than the similar Table 4. Maybe Table 3 simply needs to be removed (?).

Figure 5: I am not sure whether this new figure is an improvement. It remains very hard to see how well the observed temporal variations are captured by the different turbulent flux models. It might help to use smaller symbols for every measurement, and to horizontally stretch the panels over the full-page width (rather than half).

Equation (16): If I am correct z_0m and z_0q are the same, so please select one term for those.

Equation (23): Similarly, z_0e should probably be z_0q(?).

Equation (22): z_1 is not defined.

Table 2: C_p should be with small p. Furthermore, C_h is listed twice. One occurrence should probably be C_H.

Section 3.3:
It remains unclear with what (standard) parameter settings the mass balance model was run or what version of the model was used. Please include a reference. This is important for reproducibility of the presented results.

Section 5.2:
• The results of the mass balance modelling are currently presented in the Discussion chapter. Please reorganize this, so that mass balance modelling results go to Sect. 4 and the discussion of the results remains in Sect. 5.
• It remains a mystery why only three (out of seven) of the turbulent flux methods were included in the mass balance modelling, and why these three were selected. Please indicate this.
• The cumulative mass balance observations and surface height measurements are currently not described (unless I missed it). This information should be included in Chapter 2. The analysis in Sect. 5.2 for example depends on what density was used to convert cumulative surface height change observations to CMB estimates.

Figure 7:
• The lines are too thick, which makes that there is a lot of overlap between them.
• Are the fluxes daily mean values? This information should be included in the caption.
• For comparison purposes it would be helpful to have the same y-axis range per row. This is currently not the case for the fluxes and surface temperature.
• It is confusing that the green line is showing something else than observations in the uppermost panels. Please choose another colour in the uppermost panels for clarity.
• It could be discussed in the text that the smaller surface height variability in the modelled timeseries (lowermost panels in Fig. 7) is a result of the lack of a seasonal snow compaction model in the used version of EBFM. Instead of simulating quick densification of low-density snow directly after a snowfall event, EBFM directly sets a much higher “fresh snow density” and simulates compaction as if it is firn. The newer versions of EBFM (https://github.com/EBFMorg/EBFM) also contain a seasonal snow compaction model.

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ED: Publish subject to revisions (further review by editor and referees) (09 Jul 2026) by Valentina Radic

AR by Zhu. Meilin on behalf of the Authors (09 Aug 2026) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (06 Sep 2026) by Valentina Radic

Dear Authors,

Thank you for your careful revision of the manuscript and for addressing the reviewer’s comments. The manuscript has improved substantially through the review process, and I consider the scientific content suitable for publication in The Cryosphere. Before I can accept the manuscript, however, I would like you to address a few remaining points concerning the interpretation and presentation of the results. These are minor revisions and, in most cases, should require clarification or modification of the text rather than additional analyses.

1. Calibration and evaluation using the same EC observations
In Sect. 3.2 (approximately lines 267–282), the empirical parameters of the CkatC_{\mathrm{kat}} and Clog⁡C_{\log} methods are recalibrated against the quality-controlled 30-min EC observations, while the other methods are also observation-constrained through the EC-derived representative roughness length. These observation-constrained configurations are subsequently evaluated against the EC observations in Sect. 4.3. While I think this is a reasonable approach for assessing and constraining the parameterizations for the Dunde Glacier, the distinction between calibration/observation constraint and independent validation should be made clearer.
Please clarify explicitly that the performance statistics presented for these configurations are not based on an independent validation dataset. Correspondingly, please check the manuscript for statements implying independent validation or overly general conclusions about model performance (e.g. statements that a particular method “performs better” or that the schemes show “good performance”) and qualify these where necessary. I do not think that an additional split-sample analysis is required at this stage; rather, the limitations of evaluating the schemes using the same observational record used to constrain them should be transparently acknowledged.

2. Interpretation of the observation-constrained cumulative mass balance
I appreciate the substantial clarification made regarding the cumulative mass-balance analysis in Sect. 4.4. The use of the term “observation-constrained reference CMB” is appropriate. However, this reference is still a model-derived quantity: EC fluxes are prescribed where available, while gaps are filled using the recalibrated CRib2C_{\mathrm{Rib2}} configuration. The independent stake measurement provides useful support, but it covers a somewhat different period from the model simulation.
Please make sure that this distinction remains clear throughout the Results, Discussion, figure captions, and Conclusions, and that the reference CMB is not inadvertently described as an observed mass balance. I would also suggest briefly acknowledging the partial dependence between this reference simulation and the recalibrated CRib2C_{\mathrm{Rib2}} parameterization when interpreting the comparative CMB results. Again, I do not request additional analysis here; this is primarily an issue of transparency in the interpretation.

3. Statement concerning turbulent fluxes during the humid heatwave
The Abstract currently states that the inability of the schemes to reproduce LE during the humid heatwave indicates “an underestimation of the contribution of turbulent fluxes to glacier melt energy” (approximately lines 36–38). I do not think that this conclusion follows directly from the presented results. During the event, most schemes substantially overestimate the magnitude of negative LE relative to the observations and fail to reproduce the occasional reversal of LE, whereas the representation of H is considerably better.
The results therefore clearly demonstrate difficulties in representing latent heat exchange under extreme warm and humid conditions, but they do not necessarily demonstrate a general underestimation of the total turbulent contribution to melt energy. Please revise this statement in the Abstract, and any equivalent statements elsewhere, so that the conclusion more directly reflects the results. For example, the emphasis could be placed on the inability of the existing parameterizations to accurately represent LE, particularly its weakening and occasional sign reversal, during the humid heatwave.

4. “Mean climate state” and “multi-year averages” in Sect. 5.3
At the beginning of Sect. 5.3 (approximately lines 744–748), the manuscript states that optimization improves simulations under the “mean climate state (e.g., multi-year averages of TaT_a and precipitation).” This appears inconsistent with the analysis presented here, which is based on observations collected during May–October 2023.
Please revise this wording. I think the intended contrast is between the performance during the broader observation period / non-extreme conditions and performance during the specific humid heatwave event, rather than between a multi-year mean climate and an extreme event.

5. Strength of the conclusion regarding glacier-type dependence of aerodynamic roughness length
The Abstract and Conclusions state that the analysis reveals a “clear glacier type dependence” or that glacier type “exerts a pronounced influence” on aerodynamic roughness length. The comparison is interesting and worth retaining, but these formulations seem somewhat stronger than can be supported by the available observations, particularly given the limited number of long-term EC datasets for continental glaciers—a limitation that the manuscript itself appropriately acknowledges.
Please consider moderating this conclusion throughout the manuscript. For example, the results could be described as showing that the available observations indicate a broader and generally lower range of aerodynamic roughness lengths for continental glaciers than for maritime glaciers, or as providing evidence for possible systematic differences between glacier types. This would preserve the interesting result without implying that glacier type itself has been established as the controlling cause.

Once these points have been addressed and the corresponding wording has been checked for consistency throughout the manuscript, I expect that the paper should be suitable for acceptance.

Best regards,
Valentina Radic

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AR by Zhu. Meilin on behalf of the Authors (13 Sep 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (30 Sep 2026) by Valentina Radic

AR by Zhu. Meilin on behalf of the Authors (30 Sep 2026)

Post-review adjustments

AA – Author's adjustment | EA – Editor approval

AA by Zhu. Meilin on behalf of the Authors (14 Oct 2026) Author's adjustment Manuscript

EA: Adjustments approved (14 Oct 2026) by Valentina Radic

Interactive discussion

Status: closed

CC1:
'Comment on egusphere-2025-4227', Keqin Duan, 21 Oct 2025
This study presents the first comprehensive evaluation of turbulent flux parameterization schemes over a continental glacier on the Tibetan Plateau (TP), based on continuous eddy covariance (EC) observations collected at the Dunde Glacier from May to October 2023. The authors assess five representative turbulent flux schemes (C_kat, C_log, C_Rib1, C_Rib2, and C_M–O), analyze their performance across multiple temporal scales, and further evaluate their influence on glacier energy and mass balance simulations.
The topic is timely and significant, as turbulent fluxes are among the least constrained components of the surface energy balance on the TP, and direct EC observations over continental glaciers remain extremely rare. The manuscript is well structured, the data quality is high, and the results are clearly presented. The conclusions are supported by the analysis, and the discussion offers useful implications for improving glacier energy-balance modeling.
The paper provides valuable new insights into turbulent exchange processes over continental glaciers. I recommend mayor revisions before publication.
Specific Comments
Abstract：
Merely stating correlations is insufficient; are such correlations applicable across all glaciated regions? It is recommended that the authors explain with reference to the unique characteristics of the study area.

The abstract lacks a statement regarding the limitations of the study.

Why was the Dunde Glacier selected? In other words, what is the significance or importance of this glacier within the study region?

Introduction：
Although it already mentions “the first comprehensive analysis for a continental glacier,” it is suggested to emphasize the differences and scientific significance of this study compared with existing research on maritime and sub-continental glaciers, preferably in the last one or two sentences.

It is recommended to slightly shorten the review of previous studies (lines 64–91) and instead expand the final paragraph to highlight the study’s specific aims and hypotheses, ensuring a smooth logical transition into Section 2.

Minor language point: change “the important reasons of such difference are…” to “the main reason for such differences is…”.

Minor grammatical and stylistic edits are needed (e.g., “Here we provide the first systematically analyze…” → “Here we provide the first systematic analysis…”).

Study Area and Data：
Figure 1 is informative, but panel (b) should include a scale bar, north arrows, which would help readers better understand the actual size and spatial extent of the Dunde Glacier.

The authors might briefly explain why the Dunde Glacier was selected—for example, its representativeness of mid-latitude continental glacier conditions, the logistical advantages for EC deployment, and its climatic relevance to the Qilian Mountains.

Please amend the elevation "5317 m" to the standard format "5,317 m".

Methods：
Section 3 is comprehensive but quite dense due to numerous equations. It is strongly suggested to include a summary table comparing the five schemes (C_kat, C_log, C_Rib1, C_Rib2, C_M–O) in terms of (a) stability correction, (b) iterative requirement, and (c) computational complexity. This would greatly enhance clarity and help readers grasp their physical and numerical distinctions.

Check the consistency of formula expressions — for example, ensure that the pressure variable symbols used in Equations (4), (11), and (16) and Table 2, as well as the air pressure notation in Section 4.1, remain consistent throughout the manuscript.

Results
In Sections 4.3.1 and 4.3.2, it is better to add a brief summary sentence at the end of each paragraph to highlight which method performs best overall for each flux (LE and H), and indicate which scheme performs best in different seasons.
Discussion
In Section 5.2, the authors should clearly specify the data required and their sources for the energy balance–snow and firn model used in this study, and indicate whether these details have been sufficiently provided in the Study Area and Data section. The model output variables should also be explicitly described.

In Section 5.3, Are the specific dates shown confirmed to represent extreme high temperature events? The authors should clearly describe the criteria used to identify extreme weather and climate events.

The heatwave analysis (Section 5.3) is one of the strengths of this paper. To further improve this section, it is recommended to include specific quantitative data to illustrate how the anomalous turbulent flux variations during the humid heatwave affected the glacier surface energy balance, thereby strengthening the comparison with non-extreme periods.
Citation: https://doi.org/10.5194/egusphere-2025-4227-CC1
- AC3: 'Reply on CC1', Zhu. Meilin, 25 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4227/egusphere-2025-4227-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4227-AC3
RC1:
'Comment on egusphere-2025-4227', Anonymous Referee #1, 21 Nov 2025
This study by Xu and others evaluates the suitability of five different turbulent flux models on a glacier on the Tibetan Plateau. This is done by comparing modeled and observed turbulent fluxes over a five-month period in 2023. In a next step, the turbulent flux models are included in a mass balance model to test sensitivity of the mass balance to the choice of turbulent flux model. The manuscript is well written, presents new data, and contains useful new insights in performance of different turbulent flux models on a glacier on the Tibetan Plateau. This information will be valuable e.g. for future applications of mass balance modelling in the area. In my opinion the manuscript needs major revisions though before it can be published. One concern I have is that the description of the methods is incomplete. For example, it remains entirely unclear how the calibration of the mass balance model with the different turbulent flux models was done. Furthermore, I think it is a missed opportunity that no attempt has been made to calibrate e.g. roughness lengths to improve agreement between modeled and observed turbulent fluxes. This would give useful insight in what parameter settings of the turbulent flux models are most suitable to use on this glacier (and possibly other glaciers on the Tibetan Plateau). The calibrated turbulent flux models could then be used in the mass balance model to assess mass balance sensitivity to the turbulent flux formulations. Maybe some of this was in fact done; if so, it just needs to be described more clearly. Detailed comments are given below.
Specific comments:
Missing parameter values & errors in equations:
Section 3: For many model-specific and physical constants (e.g. Ctub, Ctub2, Ls/f, Cp, Ch, CH etc) values are not specified in the manuscript (unless I missed it). Please add a table with all these parameters and their values, units and, where relevant, the source.

Equation 1: Division by pressure is missing. Please check that it is not missing in your code. See for example Radic et al. (2017). I think the corresponding equation in Oerlemans and Grisogono (2002) may also miss this.

Equation 2: The "0.622" should not be there and instead air density should be in the equation. Also here, see Radic et al. (2017), and please check that your code is correct.

Discrepancies between modeled and observed turbulent fluxes:
L139-140: "the roughness lengths are computed dynamically". Does this mean that roughness lengths are time-dependent? It is important to add a bit more information about how the roughness lengths are determined and add the relevant equations from Andreas (1987). The information is relevant in order to be able to judge whether some of the discrepancies between modeled and observed fluxes (Fig. 4) could result from this.

L308-309: "However, ... observed variability". It seems that the underestimation of variability of modelled turbulent fluxes applies over the whole period and for different turbulent flux models. Is this underestimation of temporal variability something that other studies also found (on other glaciers)? Could it be related to the calculation of the roughness lengths? How uncertain are the turbulent flux measurements themselves? Is it possible to assign a value to this uncertainty?

L336-341: "All five methods ... turbulent exchange." Since all methods seem to give roughly the same errors, I am inclined to think that it could also be related to the way roughness lengths are determined (since all methods depend on them). It could be worth looking into this further and check e.g. whether an alternative description (or calibration; see next point) of roughness lengths would strongly change the model results.

Figure 5: Given the weaker intra-day variability of in particular the latent heat flux, maybe the roughness length for the latent heat flux is off? I think it could have been an interesting strategy to try to find optimum values for (constant) roughness lengths by trying to minimize the differences between modelled and observed turbulent fluxes. Have you considered doing this?

Mass balance modelling strategy:
Section 5.2: I can see why the authors want to run a mass balance model with the different turbulent flux schemes as it may give insight in sensitivity of the mass balance to the turbulent flux descriptions. However, in its current form I do not think the mass balance modelling experiment is of very much use. To me it would have made more sense to first calibrate the individual turbulent flux models against the observed turbulent flux data (by optimizing e.g. roughness lengths). In a next step these calibrated turbulent flux models could then be used in the mass balance model and the resulting mass balance from the runs with different turbulent flux schemes can be compared. There may be (like now) some biases between modeled and observed mass balance, but at least such an experiment will give robust insight in the sensitivity of the mass balance to using different turbulent flux models. If the above approach is what was already done by the authors, then it is just a matter of describing it more clearly.

Selecting a best turbulent flux model:
L327: "indicating the best accuracy among the tested methods". I think it should rather be emphasized that the performance of the five methods is very similar. Given uncertainty in the observations, and these small differences, it is not possible to argue (with statistical significance) that one method is better than the others based on these results.

L425: "the best performance". It is only marginally better than the other models. So statistically speaking the performance is not significantly different across the models.

L549-552: "Among the five schemes ... variability.". Again, this is a rather bold statement based on the presented results. There are clear benefits for using the simpler (easier to implement and quicker to run) models too, especially if their performance is similar to the MO model.

Minor comments / technical corrections:
L30: "a negative total ... climate condition". Replace with "the commonly observed negative total turbulent heat flux".

L32: "extreme weather and climate event". Replace with "extreme event".

L47: "frequencies ... events". Replace with "frequency and intensity of extreme weather events".

L48: Not only enhanced turbulent fluxes are responsible for increased glacier mass loss but also e.g. increased incoming LW radiation. Please reformulate.

L63: "climatic mechanisms". Please note that climate refers to much longer timescales than considered here. Maybe use "weather patterns" or similar instead.

L64: "has become" --> "is".

L65: "are" --> "have been".

L68: "intensive" --> "expensive".

L76-80: "Taking the ... 2006-2011". This comparison requires a bit more info to be useful. E.g. what methods were used (modelling or observations)? How large were uncertainties in the two studies? Could the different periods considered explain the differences?

L88: "... on the TP.". Add "has previously been done".

L90-92: "These uncertainties hinder ... between glaciers and climate.". This becomes a bit repetitive now. I suggest to remove it here.

L93: "systematically analyze" --> "systematic analysis".

L98: "the model robustness" --> "performance of the turbulent flux models".

Section 2: I suppose surface temperature is estimated from the observed outgoing longwave radiation. This should be described somewhere. Was an emissivity of 1 assumed?

L119: "using" --> "using a".

L190: "pressure Ps". Please note that air pressure was already defined as "P" in L165.

L201: Please note that the 𝛜 constant is the same as the "0.622" that is used in several equations (e.g. Eqs (1) and (3)).

Sect. 4.1: Please make sure that italic font is used for variables.

L224-242: This is a lot of text about the temperature time-series, which are also shown in a figure and do not contain too many surprising features. I suggest to shorten this.

L243-268: Also this can be shortened. Essentially, everything mentioned here is also visible in Figure 2 so just a short summary would work.

Figure 2: Units on the y-axes should be in brackets. Additionally, please use the same variable names as in the main text.

Figure 2: You could consider adding a panel with Ta-Ts (the temperature deficit), which is an important parameter for the turbulent fluxes and their direction. Furthermore, albedo could be shown. It is discussed in connection to the extreme event in July 2023.

L286 (for example): With an observation period starting in May and finishing in October it maybe is better to not refer to "spring" and "autumn" but rather the months in question, e.g. "May-Jun" or "Sep-Oct".

L287-288: "with June having the lowest monthly average". I suppose that coincides with the period with the lowest temperature deficit at the surface(?). If so, that could be mentioned here.

L291: "through turbulent heat exchange". So sublimation / evaporation are large. Related question, do you find penitentes on the glacier surface? If so, it could be worth highlighting in the introduction as it is a visible confirmation of the significance of sublimation and evaporation.

Figure 3: Please add the type of flux in the y-axis labels.

Figure 3: Since there are data gaps I suppose some filtering of the data was done. Unless I missed it, I do not think this is currently described. If so, please add this.

Figure 4: Since the modeled data are unique in every graph, I suggest to plot these lines on top of the lines with the measured values. Currently it is the other way around.

L462-463: "while CMB estimates ... -304.19 mm.". It is not surprising that there are biases as the mass balance model (EBFM), with standard values for model parameters, is not optimized for this region/glacier. Besides turbulent flux parameters, e.g. correct albedo parameters are at least equally important for the simulated mass balance. This should be acknowledged.

Figure 7: Why not zoom in only the heat wave period? The rest of the timeseries are also shown elsewhere, so no need to include them again here.

L506-507: "Such positive LE values ... maritime glaciers.". I agree, but also in the high Arctic where surface temperatures are typically much lower than air temperatures due to less incoming solar radiation.

L509: "18.53". Please be consistent in the use of significant digits (e.g. I recommend to use "18.5" here).

L512: "surface albedo decreased". I suppose the surface was already ice-covered at the start of the heat wave(?). If so, I do not see how the albedo dropped further during the heatwave. It would by the way be nice to see albedo time-series in the manuscript, e.g. in Fig. 2.

L526: "warrant further investigation". I am not sure what is the cause either, but since the even the sign is off, I suppose it in some way must be related to the humidity gradient (which in turn depends on the temperature gradient).

L528-531: "All calculated values ... to glacier melting.". This applies to the uncalibrated turbulent flux models. It would be great to see if that still applies after calibrating the turbulent heat fluxes (e.g. by tuning the roughness lengths).

L535-536: "to increasingly ... increased H. ". It could be worth emphasizing that it is primarily that the surface temperature cannot exceed 0 ^oC that causes positive LE and higher H during such extreme events.
Citation: https://doi.org/10.5194/egusphere-2025-4227-RC1
- AC1: 'Reply on RC1', Zhu. Meilin, 21 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4227/egusphere-2025-4227-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4227-AC1
RC2:
'Comment on egusphere-2025-4227', Cole Lord-May, 26 Nov 2025

See attached comments.

Citation: https://doi.org/10.5194/egusphere-2025-4227-RC2
- AC2: 'Reply on RC2', Zhu. Meilin, 21 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4227/egusphere-2025-4227-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-4227-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (13 Apr 2026) by Valentina Radic

AR by Zhu. Meilin on behalf of the Authors (15 Apr 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (25 Apr 2026) by Valentina Radic

RR by Anonymous Referee #1 (12 Jun 2026)

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ED: Publish subject to revisions (further review by editor and referees) (09 Jul 2026) by Valentina Radic

AR by Zhu. Meilin on behalf of the Authors (09 Aug 2026) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (06 Sep 2026) by Valentina Radic

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AR by Zhu. Meilin on behalf of the Authors (13 Sep 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (30 Sep 2026) by Valentina Radic

AR by Zhu. Meilin on behalf of the Authors (30 Sep 2026)

Post-review adjustments

AA – Author's adjustment | EA – Editor approval

AA by Zhu. Meilin on behalf of the Authors (14 Oct 2026) Author's adjustment Manuscript

EA: Adjustments approved (14 Oct 2026) by Valentina Radic

Journal article(s) based on this preprint

16 Oct 2026

Evaluation of turbulent flux parameterizations over a continental glacier on the Tibetan Plateau

Yichan Xu, Meilin Zhu, Jing Gao, Daijiao Lin, Lei Hui, Fei Zhu, Huabiao Zhao, and Fengying Zhang

The Cryosphere, 20, 6021–6044, https://doi.org/10.5194/tc-20-6021-2026,https://doi.org/10.5194/tc-20-6021-2026, 2026

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Yichan Xu, Meilin Zhu, Jing Gao, Daijiao Lin, Lei Hui, Fei Zhu, Huabiao Zhao, and Fengying Zhang

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Glaciers on the Tibetan Plateau are losing mass, yet their turbulent heat exchange with the atmosphere remains uncertain. Using direct observations from the Dunde Glacier (May–October 2023), we analyzed turbulent flux variations at the glacier surface and evaluated five turbulent flux methods. We also showed that during a humid heatwave, turbulent heat input rose sharply and accelerated melt, highlighting the need to improve models under extreme conditions.


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