Thermal modeling of three lakes within the continuous permafrost zone in Alaska using the LAKE 2.0 model

Clark, Jason A.; Jafarov, Elchin E.; Tape, Ken D.; Jones, Benjamin M.; Stepanenko, Victor

doi:https://doi.org/10.5194/gmd-15-7421-2022

Articles | Volume 15, issue 19

https://doi.org/10.5194/gmd-15-7421-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-15-7421-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 15, issue 19

Model evaluation paper

|

06 Oct 2022

Model evaluation paper |

| 06 Oct 2022

Thermal modeling of three lakes within the continuous permafrost zone in Alaska using the LAKE 2.0 model

Jason A. Clark, Elchin E. Jafarov, Ken D. Tape, Benjamin M. Jones, and Victor Stepanenko

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Final revised paper (published on 06 Oct 2022)
Preprint (discussion started on 28 Jan 2022)

Interactive discussion

Status: closed

RC1:
'Comment on gmd-2022-9', Anonymous Referee #1, 21 Feb 2022

This manuscript investigates the LAKE 2.0 model performance regarding the simulation of the seasonal cycle temperature in three Arctic lakes (Northern Alaska). Its relevance and main motivation is to improve the ability to model changes in Arctic lakes heat balance and the thermal effect over the permafrost, due to climate change. I think the topic is important for lake model´s development, numerical climate modeling and for limnology, as the number of modeling studies and available meteorological datasets for this region is quite scarce. The study showed that the LAKE model can be successfully considered for modeling the thermal regime of Arctic lakes. Additionally, a sensitivity analysis revealed that the model was not very sensible to the climate scenarios considered in this study. Results also show that snow depth and lake ice can have an important role in the heat storage by lakes. The manuscript is well written and easy to follow. I recommend the publication of this manuscript after the following comments are addressed.

Major comments:

I have some issues with the study. Firstly, I think that the model baseline simulations were not correctly validated. I can´t fully evaluate the model performance, and/or compare the model results with other model simulations (e.g. Guo et al., 2021, modeled Toolik lake) without a model evaluation metric such as: mean absolute error (MAE) or root mean square error (RMSE). Furthermore, I don´t understand how the model was calibrated. What function were you trying to minimize in order to optimize the model performance?

Secondly, why didn´t you show the lakes sediment temperature obtained with the model as a function of water temperature? This kind of data is quite relevant for other researchers.

Specific comments:

L25: I think that the word ”completes” is very strong.

L26-L29: This sentence is unclear to me. You say that the model “is not highly sensitive to the weather data perturbations”, and you conclude that “snow depth and lake ice strongly affect water temperatures during the frozen season”?

L31: I suggest the following change to this sentence: “Approximately forty percent…”

L70: Description of the model: I think that you need to improve the model description, namely, the multilayer snow and ice modules (Stepanenko and Lykossov, 2005; Stepanenko et al., 2011).

L85: LAKE model setup: Please describe the calibration procedure. Which parameters were calibrated in which ranges? Was calibration automatic? Please describe the parameters of the baseline simulation. The table 1 included in Stepanenko et al. (2016) is a very good example.

L94: Input data: Please describe all meteorological variables. How did you characterize the inflow water temperature to lake Toolik? Please describe the initial water temperature and sediments values, before and after the 10 years simulation.

L140: Please replace Wm^-1 with Wm^-2.

L150: Do you have lake water level values? Do you think that neglecting the lake water level may lead to errors in surface heat flux predictions?

L156: I suggest adding a new section, “Evaluation metrics” for the “new” evaluation metrics (e.g. RMSE). The Z-score equation can also be included here. You don’t need to apply the “new” metrics to the sensitivity analysis.

L169: “During the frozen season, the modeled temperatures underestimate cooling in the lake.” By how much?

L189-190: “For 2013 and 2014 the modeled shallow (0, 3 m) water temperature was overestimated while for 2015 and 2016 shallow water temperature was underestimated, though it tracked observed temperature.” By how much?

L192: I can´t see the step-like dip in figures B1 and B2 can this fact be related with inflow water temperature?

L200: The datasets length (x values) shown in figures 3 and 4 is smaller than the datasets length shown in figures B1 and B2.

L210: “shallow depth water temperatures (1, 3, and 5 m 210 depth, -0.13 to 0.34)”. I can´t find the value -0.13 in Figure 5.

L246: “Modeled shallow water (1 m) temperature exceeded the observed temperatures” After the incorporation of inflows/outflows, the water temperature (1 m) in 2013 and 2014, still exceeds observed water temperatures. This kind of analysis would be easier with a model evaluation metric.

L270: I think that this entire section “Modeling Lake thermal effects in permafrost” must be in the introduction.

L286: “The “dips” of water temperature in LAKE model results for Toolik lake down to depths of 10 m prior to ice-off can be explained”. I can see the dip at 19 m (Figure 4, 2014-07).

L287: “can be explained by convective instability under the ice, where this instability can be caused by the under-ice penetration of solar radiation” As I said previously, I can´t see the “dips” in figures B1 and B2. Can this be related with the effect of lake inflow?

References:

Guo, M., Zhuang, Q., Yao, H., Golub, M., Leung, L. R., Pierson, D., and Tan, Z.: Validation and Sensitivity Analysis of a 1-D Lake Model Across Global Lakes, Journal of Geophysical Research: Atmospheres, 126, https://doi.org/10.1029/2020JD033417, 2021.

Stepanenko, V. M. and Lykossov, V. N.: Numerical modeling of heat and moisture transfer processes in a system lake–soil, Russ. Meteorol. Hydrol., 3, 95–104, 2005.

Stepanenko, V. M., Machul’skaya, E. E., Glagolev, M. V., and Lykossov, V. N.: Numerical modeling of methane emissions from lakes in the permafrost zone, Izvestiya, Atmos. Ocean. Phys., 47, 252–264, doi:10.1134/S0001433811020113, 2011.

Stepanenko, V., Mammarella, I., Ojala, A., Miettinen, H., Lykosov, V., and Vesala, T.: LAKE 2.0: a model for temperature, 490 methane, carbon dioxide and oxygen dynamics in lakes, Geoscientific Model Development, 9, 1977–2006, https://doi.org/10.5194/gmd-9-1977-2016, 2016.

Citation: https://doi.org/10.5194/gmd-2022-9-RC1
- AC4: 'Reply on RC1', Jason Clark, 29 Apr 2022
  
  We thank both reviewers for their effort and insightful comments. These are two of the more keen and constructive reviews that we have received. Reviewers identified several key issues: model validation and performance, model temporal resolution, model vertical resolution, sediment temperatures, and Toolik lake inflow data. We addressed these issues by adding model evaluation metrics, adding new appendices for model resolution sensitivity, correcting errors, and updating manuscript text to address comments. We provide detailed responses to these issues below. As the GMD interactive comments do not allow us to submit a revised manuscript at this stage, we have attached excerpts from our revised manuscript that should be viewed along with our responses.
  Major comments:
  Comment: “I have some issues with the study. Firstly, I think that the model baseline simulations were not correctly validated. I can´t fully evaluate the model performance, and/or compare the model results with other model simulations (e.g. Guo et al., 2021, modeled Toolik lake) without a model evaluation metric such as: mean absolute error (MAE) or root mean square error (RMSE). Furthermore, I don´t understand how the model was calibrated. What function were you trying to minimize in order to optimize the model performance?”
  Response: Thank you for your effort and insightful comments. We have updated the manuscript with model evaluation metrics (including MAE and RMSE) as requested. Model performance was similar to Guo et al. 2021, with RMSE ~2C. However, it should be noted Guo et al. 2021 simulated Toolik lake only for the thawed seasons of 1983-1988. The LAKE model was minimally calibrated for each lake, as described in Section 2.2, to initialize water and sediment temperatures. A standard set of model parameters were applied to all lakes to demonstrate the applicability of the LAKE model in simulating Arctic lakes (Table 1).
  Comment: “Secondly, why didn´t you show the lakes sediment temperature obtained with the model as a function of water temperature? This kind of data is quite relevant for other researchers.”
  Response: We have added results showing sediment temperatures and new figures for water temperature profiles in addition the figures already present showing water temperatures (Appendix C). As the focus of this paper was not directly on lake sediment temperatures we did not attempt to demonstrate sediment temperatures as a function of water temperatures.
  Specific comments:
  Comment: “L25: I think that the word ”completes” is very strong.”
  Response: We changed it to ‘is’.
  Comment: “L26-L29: This sentence is unclear to me. You say that the model “is not highly sensitive to the weather data perturbations”, and you conclude that “snow depth and lake ice strongly affect water temperatures during the frozen season”?”
  Response: We have updated the text to clarify our point. “The sensitivity analysis shows us that lake water temperature is not highly sensitive to small changes in air temperature or precipitation, while changes in shortwave radiation and large changes in precipitation produced larger effects. Snow depth and lake ice strongly affect water temperatures during the frozen season which dominates the annual thermal regime. These findings suggest that reductions in lake ice thickness and duration could lead to more heat storage by lakes and enhanced permafrost degradation.”
  
  Comment: “L31: I suggest the following change to this sentence: “Approximately forty percent…””
  Response: We have made this change.
  Comment: “L70: Description of the model: I think that you need to improve the model description, namely, the multilayer snow and ice modules (Stepanenko and Lykossov, 2005; Stepanenko et al., 2011).”
  Response: We have elaborated on this section to include a description of the snow and ice modules, including references.
  Comment: “L85: LAKE model setup: Please describe the calibration procedure. Which parameters were calibrated in which ranges? Was calibration automatic? Please describe the parameters of the baseline simulation. The table 1 included in Stepanenko et al. (2016) is a very good example.”
  Response: Our calibration procedure simply involved the initialization of the soil and water temperature values as described in the Section 2.2. No other parameters were calibrated. The parameters of the baseline scenarios have been added as Table 1.
  Comment: “L94: Input data: Please describe all meteorological variables. How did you characterize the inflow water temperature to lake Toolik? Please describe the initial water temperature and sediments values, before and after the 10 years simulation.”
  Response: We have added text to section 2.3 describing all met variables. Inflow water temperature was measured daily with discharge. Water temperature is included in the inflow input file. Discharge and temperature are described in section 2.7. Initial water temperature was taken from observed water temperature data. Initial and calibrated sediment temperatures are now reported in Table 1.
  Comment: “L140: Please replace Wm^-1 with Wm^-2.”
  Response: Thanks, we made this change.
  Comment: “L150: Do you have lake water level values? Do you think that neglecting the lake water level may lead to errors in surface heat flux predictions?”
  Response: Interesting point. We do not have observations of lake water level values. The water level change may affect surface fluxes via the thickness of the mixed (or active) layer of a lake, the latter is a layer which total heat capacity interacts with the atmosphere. If not limited by lake depth, the typical summertime ML thickness in mid- and high latitudes is 3-5 m (see e.g. simulated/observed temperature profiles in LakeMIP papers). Thus, there are two situations with respect to the lake level effects on ML depth and thus the surface fluxes. First, the lake is shallower than 3-5 m, then the ML is a lake depth. In this case, the water level may affect fluxes, if it varies significantly retaining the depth below 3-5 m. In the case where the lake depth much exceeds 3-5 m (Toolik lake), the level variations do not change ML depth and thus the fluxes.
  Comment: “L156: I suggest adding a new section, “Evaluation metrics” for the “new” evaluation metrics (e.g. RMSE). The Z-score equation can also be included here. You don’t need to apply the “new” metrics to the sensitivity analysis.”
  Response: We have added this section, now section 2.8.
  Comment: “L169: “During the frozen season, the modeled temperatures underestimate cooling in the lake.” By how much?”
  Response: We have added Table 2 which shows model error (MAE, RMSE, Bias) for the entire time series, and split by frozen and thawed season. For this particular sentence the error for Atqasuk over the frozen period was 5.8 (RMSE).
  Comment: “L189-190: “For 2013 and 2014 the modeled shallow (0, 3 m) water temperature was overestimated while for 2015 and 2016 shallow water temperature was underestimated, though it tracked observed temperature.” By how much?”
  Response: We have added Table 2 which shows model error (MAE, RMSE, Bias) for the entire time series, and split by frozen and thawed season. The Toolik model simulations have been updated based on corrected discharge data. This sentence and interpretation of the Toolik water temperatures have been changed. Thawed and frozen season errors are presented in Table 2.
  Comment: “L192: I can´t see the step-like dip in figures B1 and B2 can this fact be related with inflow water temperature?”
  Response: We thank the keen reviewer who caught this error. We were able to trace the ‘dips’ to a formatting error in the inflow data file. This has been corrected. All Toolik simulations have been repeated and figures updated (Section 3.3). The ‘dips’ were an artifact of the erroneous inflow data and are no longer present (Figs. 3 & 4).
  Comment: “L200: The datasets length (x values) shown in figures 3 and 4 is smaller than the datasets length shown in figures B1 and B2.”
  Response: These have been corrected to show the same length of data.
  Comment: “L210: “shallow depth water temperatures (1, 3, and 5 m 210 depth, -0.13 to 0.34)”. I can´t find the value -0.13 in Figure 5.”
  Response: This was an error. The text has been updated to reflect the data in the figure. Please note this figure and data have been updated to reflect the new simulations for Fox Den (now hourly) and Toolik (with corrected inflow data)(Fig. 5).
  Comment: “L246: “Modeled shallow water (1 m) temperature exceeded the observed temperatures” After the incorporation of inflows/outflows, the water temperature (1 m) in 2013 and 2014, still exceeds observed water temperatures. This kind of analysis would be easier with a model evaluation metric.”
  Response: Error metrics have been added and are included in Table 2, B1, & B2 for this sentence.
  Comment: “L270: I think that this entire section “Modeling Lake thermal effects in permafrost” must be in the introduction.”
  Response: We have moved this section to the Introduction.
  Comment: “L286: “The “dips” of water temperature in LAKE model results for Toolik lake down to depths of 10 m prior to ice-off can be explained”. I can see the dip at 19 m (Figure 4, 2014-07).”
  Response: We thank the keen reviewer who caught this error. We were able to trace the ‘dips’ to a formatting error in the inflow data file. This has been corrected. All Toolik simulations have been repeated and figures updated (Section 3.3). The ‘dips’ were an artifact of the erroneous inflow data and are no longer present (Figs. 3 & 4).
  Comment: “L287: “can be explained by convective instability under the ice, where this instability can be caused by the under-ice penetration of solar radiation” As I said previously, I can´t see the “dips” in figures B1 and B2. Can this be related with the effect of lake inflow?”
  Response: We thank the keen reviewer who caught this error. We were able to trace the ‘dips’ to a formatting error in the inflow data file. This has been corrected. All Toolik simulations have been repeated and figures updated (Section 3.3). The ‘dips’ were an artifact of the erroneous inflow data and are no longer present (Figs. 3 & 4).
  
  Citation: https://doi.org/10.5194/gmd-2022-9-AC4
CEC1:
'Comment on gmd-2022-9', Juan Antonio Añel, 01 Mar 2022

Dear authors,

After checking your manuscript, it has come to our attention that it does not comply with our Code and Data Policy.

https://www.geoscientific-model-development.net/policies/code_and_data_policy.html

First of all, for the data and processing scripts, you point to two papers where it is impossible to get them unless after contact with the authors. However, we can not accept embargoes such as registration or previous contact with the authors. Therefore, to continue with the review process of your manuscript, you must publish your code in one of the appropriate repositories listed in our policy. We understand that some files used in your study can be large (e.g., full output from models). In such cases, instead of storing the complete files, you should at least keep the variables or final fields computed and used in your work.

Also, we can not accept Parallel.ru as a suitable repository. Again, it is not listed in our policy and does not comply with our long-term archival requirements, not removal and persistent digital identifier. Therefore, deposit in a repository covered by our guidelines a copy of the version of the LAKE model used here.

Also, I have not seen a license listed in the LAKE repository. If you do not include a license, the code continues to be your property and can not be used by others, despite any statement on being free to use. Therefore, when uploading the model's code to the repository, you could want to choose a free software/open-source (FLOSS) license. We recommend the GPLv3. You only need to include the file 'https://www.gnu.org/licenses/gpl-3.0.txt' as LICENSE.txt with your code. Also, you can choose other options that Zenodo provides: GPLv2, Apache License, MIT License, etc.

In this way, you must reply to this comment with the link to the new repository used in your manuscript, with its DOI. Also, you must include in a potential reviewed version of your manuscript the modified 'Code and Data Availability' section and the DOI of the code.

Please, reply as soon as possible to this comment with the link for it so that it is available for the peer-review process, as it should be.
Regards,
Juan A. Añel

Geosci. Model Dev. Exec. Editor

Citation: https://doi.org/10.5194/gmd-2022-9-CEC1
- AC1:
  'Reply on CEC1', Jason Clark, 02 Mar 2022
  
  We thank you for our time in handling our manuscript. We believe both of the repositories we used for model data and processing scripts do not require login, accounts, or author contact to download the data. All model input, configuration, forcing data, preprocessing and post processing scripts are included in these repositories.
  Repo: https://data.ess-dive.lbl.gov/view/doi:10.15485/1808368
  DOI: 10.15485/1808368
  Download: https://data.ess-dive.lbl.gov/catalog/d1/mn/v2/packages/application%2Fbagit-097/ess-dive-5d5ce1351b06e44-20210714T193925670
  Repo: https://doi.org/10.5281/zenodo.5593754
  DOI:10.5281/zenodo.5593754
  Download: https://zenodo.org/record/6323700/files/xisphias/LAKE2.0_processing-scripts-v4.zip?download=1
  We have added the relevant model output files to the github/zenodo repository.
  We are working on archiving the LAKE 2.0 model on github/zenodo and will post an update when it is completed. We will also post an updated manuscript version to reflect the new model repository.
  
  Citation: https://doi.org/10.5194/gmd-2022-9-AC1
  - CEC2: 'Reply on AC1', Juan Antonio Añel, 03 Mar 2022
    
    Dear authors,
    Many thanks for replying so quickly. Please, note that the servers at the LBL are not acceptable repositories. Therefore, please, copy any data you link in them, and it is not included in the Zenodo repositories to the Zenodo repositories.
    Regards,
    Juan A. Añel
    
    Geosci. Model Dev. Exec. Editor
    
    Citation: https://doi.org/10.5194/gmd-2022-9-CEC2
    
    AC2: 'Reply on CEC2', Jason Clark, 03 Mar 2022
    
    We are unclear as to why ESS-DIVE is an unsuitable repository. We have been in contact with the support team at ESS-DIVE and they believe it meets the journal requirements. The ESS-DIVE is public data repository funded by the U.S. Department of Energy. This repository replaced the former CDIAC archive and meets all the repository criteria required by ESSD (https://www.earth-system-science-data.net/for_authors/repository_criteria.html). ESS-DIVE issues digital object identifiers (persistent identifiers), provides free, open, and anonmyous access to its data, offers the CC0 and CCby4 data licences, and has a data preservation plan to provide long term availability. Please note that our dataset has a DOI and is available publicly with a CCBy4 license on ESS-DIVE.
    
    Citation: https://doi.org/10.5194/gmd-2022-9-AC2
    
    CEC3: 'Reply on AC2', Juan Antonio Añel, 03 Mar 2022
    
    Dear authors,
    Many thanks for the information and apologies for the misunderstanding about ESS-DIVE. Yes, we can accept it. We receive many papers with data stored directly on LBL servers or similar (PNNL, NCAR, etc.), which are not suitable, and I did not realize that it was one of the services covered by FairSharing.org.
    Regards.
    Juan A. Añel
    Geosci. Model Dev. Exec. Editor
    
    Citation: https://doi.org/10.5194/gmd-2022-9-CEC3
  - AC3: 'Reply on AC1', Jason Clark, 15 Mar 2022
    
    We have published the LAKE model on zenodo (https://doi.org/10.5281/zenodo.6353237). We will update the references in the manuscript and submit a revised version with reviewer revisions soon.
    
    Citation: https://doi.org/10.5194/gmd-2022-9-AC3
RC2:
'Comment on gmd-2022-9', Anonymous Referee #2, 11 Mar 2022

Modeling of lake thermodynamics in polar regions is a highly relevant topic with regard to the response of the Arctic permafrost to the global change. The model LAKE has been intensively applied in recent studies on lake dynamics and air-lake interaction. Therefore, a study on the LAKE model abilities to simulate thermal properties of lakes in the permafrost zone falls into the scope of the GMD and is of interest for its readership. Comparison of the model performance for three Arctic lakes of different morphometry provides a necessary background for future analysis of the atmosphere-lake-permafrost interaction. Herewith, the study is a valuable contribution to modeling of lakes as components of the climate system. The methods, presentation of results, and discussion are generally adequate to the problem statement, however contain some gaps, related, in particular, to the effects of the spatial and temporal resolution on the modeling results and to the simulation of the water-sediment interaction as a crucial aspect of lake modeling in the permafrost zone. I recommend extending the study with relevant details providing the reader with a necessary overview of the model performance beyond the sensitivity to variations in the input forcing, which is currently the major focus of the manuscript.

As it was pointed out by the previous reviewer, the model validation is presented in a rather qualitative way, and some numerical scores of the model performance, like bias, absolute error, RMSE etc., will be useful here.

The temporal resolution of the model input was different for three different lakes: 1 day for one of them and 1 hour for the two others. It is unclear how the diurnal cycle of the atmospheric forcing and radiation was treated in the model. Were the daily data interpolated on sub-diurnal scales? If yes, how the interpolation was performed? How does the neglect of the sub-daily variations in the input data affect the model output? The question could be answered by comparison of model runs with daily and hourly inputs for the lakes where sub-diurnal data on forcing are available.

The vertical resolution for both water column and sediment was set to 1 meter and did not vary between lakes. What were the criteria for the choice of the resolution? One can assume that for the vertical diffusion rates within the sediment of 10^{-6} m^2 s^{-1}, the vertical resolution of 1 m will capture the processes with typical time scales of >10 days. Is it sufficient? How many vertical grid points did Fox Den have, whose depth is 1.5 m? Can you perform sensitivity runs demonstrating the effect of the vertical resolution on the model output?

L316, Section 5.4 The details on the sediment layer modeling results are crucial for discussion on the model applicability to permafrost lakes. The information is missing in the ms. How did the soil temperatures under the lake bottom vary during the modeling period? What are the values of the bottom heat flux and how do they depend on the model configuration, initial and boundary conditions?

Some minor remarks:

“It is a large lake (2,732,050 m2 )...” why 2 km^2 area is large for a lake?

“ 30 cm and 250 cm” better use meters here for consistency.

In Fox Den the model calculated up to 1.0 m thick ice cover in a 1.5 m deep lake. Was the water volume/depth adjusted during the ice-covered period? Was 1 m vertical resolution sufficient for simulation?

L286: “The “dips” of water temperature in the LAKE model results for Toolik lake…” How did the vertical model resolution affect the representation of free convection? The 1 m resolution seems to be crude for the typical values of the convective layer entrainment rates of < 1 m/day (e.g. Kirillin et al. 2012).

Citation: https://doi.org/10.5194/gmd-2022-9-RC2
- AC5: 'Reply on RC2', Jason Clark, 29 Apr 2022
  
  We thank both reviewers for their effort and insightful comments. These are two of the more keen and constructive reviews that we have received. Reviewers identified several key issues: model validation and performance, model temporal resolution, model vertical resolution, sediment temperatures, and Toolik lake inflow data. We addressed these issues by adding model evaluation metrics, adding new appendices for model resolution sensitivity, correcting errors, and updating manuscript text to address comments. We provide detailed responses to these issues below. As the GMD interactive comments do not allow us to submit a revised manuscript at this stage, we have attached excerpts from our revised manuscript that should be viewed along with our responses.
  Comment: “Modeling of lake thermodynamics in polar regions is a highly relevant topic with regard to the response of the Arctic permafrost to the global change. The model LAKE has been intensively applied in recent studies on lake dynamics and air-lake interaction. Therefore, a study on the LAKE model abilities to simulate thermal properties of lakes in the permafrost zone falls into the scope of the GMD and is of interest for its readership. Comparison of the model performance for three Arctic lakes of different morphometry provides a necessary background for future analysis of the atmosphere-lake-permafrost interaction. Herewith, the study is a valuable contribution to modeling of lakes as components of the climate system. The methods, presentation of results, and discussion are generally adequate to the problem statement, however contain some gaps, related, in particular, to the effects of the spatial and temporal resolution on the modeling results and to the simulation of the water-sediment interaction as a crucial aspect of lake modeling in the permafrost zone. I recommend extending the study with relevant details providing the reader with a necessary overview of the model performance beyond the sensitivity to variations in the input forcing, which is currently the major focus of the manuscript.”
  Response: Thank you for your comments. We have added several new sections to the manuscript and to the Appendix that we believe add more detail and aid in understanding the spatial resolution an temporal resolution on modeling results as well as results of the water-sediment interaction.
  Comment: “As it was pointed out by the previous reviewer, the model validation is presented in a rather qualitative way, and some numerical scores of the model performance, like bias, absolute error, RMSE etc., will be useful here.”
  Response: We have updated the manuscript with model evaluation metrics (including MAE and RMSE) as requested. Please see Table 2 and the Appendix.
  Comment: “The temporal resolution of the model input was different for three different lakes: 1 day for one of them and 1 hour for the two others. It is unclear how the diurnal cycle of the atmospheric forcing and radiation was treated in the model. Were the daily data interpolated on sub-diurnal scales? If yes, how the interpolation was performed? How does the neglect of the sub-daily variations in the input data affect the model output? The question could be answered by comparison of model runs with daily and hourly inputs for the lakes where sub-diurnal data on forcing are available.”
  Response: We have updated the simulations to use the same temporal resolution (1 hour) for all lakes. Additionally we have added a section to the Appendix that shows the effect of temporal resolution on model performance (Appendix F). Daily data are linearly interpolated to finer temporal scales within LAKE.
  Comment: “The vertical resolution for both water column and sediment was set to 1 meter and did not vary between lakes. What were the criteria for the choice of the resolution? One can assume that for the vertical diffusion rates within the sediment of 10^{-6} m^2 s^{-1}, the vertical resolution of 1 m will capture the processes with typical time scales of >10 days. Is it sufficient? How many vertical grid points did Fox Den have, whose depth is 1.5 m? Can you perform sensitivity runs demonstrating the effect of the vertical resolution on the model output?”
  Comment: “L316, Section 5.4 The details on the sediment layer modeling results are crucial for discussion on the model applicability to permafrost lakes. The information is missing in the ms. How did the soil temperatures under the lake bottom vary during the modeling period? What are the values of the bottom heat flux and how do they depend on the model configuration, initial and boundary conditions?”
  Response: We have added new figures and a new section in the results to show the sediment temperatures and heat flux during simulations (Appendix C). Soil temperatures responded differently in each lake. In general, shallow sediment showed warming in the thaw period and deeper sediments remained constant over the simulation period.
  Some minor remarks:
  Comment: “ “It is a large lake (2,732,050 m2 )...” why 2 km^2 area is large for a lake?”
  Response: It is large relative to our study lakes. We have updated the text reflect this comparison.
  Comment: “ “ 30 cm and 250 cm” better use meters here for consistency.”
  Response: We have made this change.
  Comment: “In Fox Den the model calculated up to 1.0 m thick ice cover in a 1.5 m deep lake. Was the water volume/depth adjusted during the ice-covered period? Was 1 m vertical resolution sufficient for simulation?”
  Response: All frozen water (which formed the ice layer) is subtracted from the lake water volume. The water depth is adjusted accordingly. As to resolution, the grid spacing in water and ice is automatically adjusted in the model to keep the predefined number of numerical layers in each physical layer. In the manuscript you reviewed, we misstated the vertical resolution used for the simulations (Table 1). We have corrected these errors. For Fox Den the vertical resolution was 0.0375m which we believe was sufficient for simulation.
  Comment: “L286: “The “dips” of water temperature in the LAKE model results for Toolik lake…” How did the vertical model resolution affect the representation of free convection? The 1 m resolution seems to be crude for the typical values of the convective layer entrainment rates of < 1 m/day (e.g. Kirillin et al. 2012).”
  Response: The statement of 1m resolution was incorrect. We have corrected the text to reflect the vertical resolution used in each Lake (Table 1). For Toolik the resolution was 0.65m. We have added an appendix to look at the effects of increasing model water vertical resolution. Using 1m, 0.5m, and 0.25m vertical resolutions we found minimal effects on lake water temperatures and model performance. Kirillin et al. 2012 report rates of 0.5 m per day increasing to several meters per day in deep lakes. We simulated lakes with vertical resolutions of 0.0635m, 0.0375m, and 0.65m (for Atqasuk, Fox Den, and Toolik respectively) and tested vertical resolutions down to 0.25m for Toolik and 0.025m for Atqasuk (Appendix D). We did not see evidence that the vertical resolutions used in the manuscript was too coarse.
  
  Citation: https://doi.org/10.5194/gmd-2022-9-AC5

Peer review completion

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

AR by Jason Clark on behalf of the Authors (29 Apr 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (03 May 2022) by Jinkyu Hong

RR by Anonymous Referee #1 (11 May 2022)

RR by Anonymous Referee #3 (18 Jul 2022)

ED: Reconsider after major revisions (21 Jul 2022) by Jinkyu Hong

AR by Jason Clark on behalf of the Authors (04 Aug 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (05 Aug 2022) by Jinkyu Hong

AR by Jason Clark on behalf of the Authors (18 Aug 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (26 Aug 2022) by Jinkyu Hong

AR by Jason Clark on behalf of the Authors (28 Aug 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (31 Aug 2022) by Jinkyu Hong

AR by Jason Clark on behalf of the Authors (07 Sep 2022) Author's response Manuscript

Short summary

Lakes in the Arctic are important reservoirs of heat. Under climate warming scenarios, we expect Arctic lakes to warm the surrounding frozen ground. We simulate water temperatures in three Arctic lakes in northern Alaska over several years. Our results show that snow depth and lake ice strongly affect water temperatures during the frozen season and that more heat storage by lakes would enhance thawing of frozen ground.