Variations of ice thickness in a reservoir along Irtysh River: field measurement and regression analysis

Han, Chuntan; Kang, Chao; Zhao, Chengxian; Luo, Jianhua; Chen, Rensheng

doi:https://doi.org/10.5194/tc-2022-241

Preprints

https://doi.org/10.5194/tc-2022-241

Preprints

13 Feb 2023

| 13 Feb 2023

Status: this discussion paper is a preprint. It has been under review for the journal The Cryosphere (TC). The manuscript was not accepted for further review after discussion.

Variations of ice thickness in a reservoir along Irtysh River: field measurement and regression analysis

Chuntan Han, Chao Kang, Chengxian Zhao, Jianhua Luo, and Rensheng Chen

Abstract. This paper presents the analysis results of temperatures collected at three monitoring stations which were used to study ice freezing and thawing processes on a reservoir along Irtysh River. The measured temperatures were comprehensively analyzed and correlated with air temperature measured at a meteorological station. The results showed that air temperature was closely related to temperature at the ice surface, e.g., T₄₀, T₂₀ and T₀, and temperatures in ice almost increased linearly with depth. In addition, ice thicknesses were calculated based on measured temperatures along arrays of temperature and compared with that calculated using a simplified Stefan’s model. The results indicated that ice thickness varied spatially and temporally, and Stefan’s model overestimated the ice thicknesses with a maximum discrepancy of 12 cm. Moreover, the calculated ice thickness was correlated with temperatures, variations of temperature and accumulated freezing degree days (AFDD) based on Pearson correlation analysis, showing that ice thickness was proportional to AFDD with a coefficient of 0.89, and negatively correlated with T₀, T₋₃, and T_ice(c) with coefficients of −0.69, −0.73 and −0.62, respectively. Therefore, linear and non-linear models were proposed, which were validated using datasets from three stations in Russia and Finland, demonstrating that the linear model incorporating AFDD and T₀ can capture local ice freezing and thawing processes with a relatively minor discrepancy, and the results were consistent at different stations. The paper provides an approach to comprehensively study the ice formation process and a practical model to calculate local ice thickness.

Received: 01 Dec 2022 – Discussion started: 13 Feb 2023

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Chuntan Han, Chao Kang, Chengxian Zhao, Jianhua Luo, and Rensheng Chen

Status: closed

RC1:
'Comment on tc-2022-241', Anonymous Referee #1, 07 Mar 2023

The study conducted in situ observations of freezing and thawing processes in reservoir ice cover along the Irtysh River, identifying ice thickness and correlating it with air temperature using air-ice-water temperature chains from three monitoring stations. The simplified Stefan’s model is validated and a new approach to ice thickness simulation is proposed. The ice temperature profiles and air temperature curves described in the study have strengthened the understanding of air-ice interactions. The new method can serve areas where meteorological data is not abundant enough to simulate ice thickness by air temperature and surface temperature alone.
However, the descriptions of the experimental methods are not sufficiently clear, and numerous symbolic errors make it difficult to understand what the authors are trying to convey. Studies based on freezing and thawing processes, have largely focused on freezing degree days (AFDD), with few findings referring to thawing periods. For the geographical location of the study area, it is difficult to ignore the influence of solar radiation on the overall ice process. It is questionable whether T_air from a weather station 30 km away is representative of the air temperature conditions in the study area. The authors should clarify the subject of this study by examining the growing and melting periods separately and discussing the causes of model error in relation to the ice and water temperature data.
Intuitively, stefan's model ignores the effects of solar radiation, wind speed and many other factors, so it is inevitable that the simulation results are worse than the numerical model. However, the advantage of stefan's model is that it is possible to obtain ice thickness curves with a certain degree of accuracy with only air temperature data and statistical empirical parameters, which can be of great use in areas where abundant meteorological information is lacking. The great challenge exists during the melting period, as several studies point to the significant contribution of solar radiation absorbed by ice and under-ice water bodies to the decay of the ice cover. Ice temperatures that converge to 0°C as the ice cover decays interfere with the accuracy of discerning the ice-water interface using the temperature probe, which can be combined with the ice temperature profile and the water temperature profile under the ice to describe the cause of the error. It would be better to present the complete ice and water temperature field variation using ice and water temperature data from the three monitoring stations. I encourage authors to resubmit the manuscript with extensive revisions. Below are some specific comments aimed to provide guidance on the revision.

L11: “…temperature at the ice surface…” the generally defined surface temperature is monitored by an infrared temperature sensor, and is not measured by a temperature probe close to the ice surface. The temperature probe has a certain size and shifts position as the ice surface sublimates or melts.
L12: “…temperatures in ice almost increased linearly with depth.” the increase in ice temperature with depth is only characteristic of the growth phase.
L20: “…can capture local ice freezing and thawing processes…” please add some description of the applicability of the thawing period to the manuscript.
L29-30: “Factors affecting ice thickness include air temperature, flow velocity/fluctuating rate of water level, chemical components in the water, water depth, water area, etc.” the most important point, solar radiation, is not presented. Solar radiation is a key factor influencing ice processes. At high latitudes, solar radiation mostly acts in spring. At mid-latitudes, solar radiation influences the ice process throughout the winter. (e.g Huang et al. 2022; Leppäranta et al. 2010; Winters et al. 2019)
L35-36: remove “The maximum depth can reach up to 4 to 10 m below the ice surface.”
L57-58: “In practice, the degree day model proposed by Stefan was commonly used” additional information on the advantages of the freezing degree-day model, e.g. fewer input parameters and the ability to simulate ice thickness profiles within a certain error range even in areas where only air temperature records are available.
L81-82: “…temperatures were measured using three…” -> “…air/ice/water temperatures”
L87: “…one of the reservoirs along…” please add information about the study area, including but not limited to latitude, longitude, area, and water depth.
L93-94: “M1 was installed…” complementing the water depth conditions at each observation point, this determines whether there are differences in the hydrothermal environment under the ice, which in turn affects the control of the ice-water heat flux to the ice bottom.
L95: “…two of them were above the water surface…” are radiation shields taken into account when measuring T₂₀ and T₄₀? If there is no radiation shield, the solar radiation heating the temperature probe during daytime measurements will cause the measured temperature to be higher than the air temperature at the same altitude, resulting in errors.
L100: Figure 2. The 1.5 m identified by T_air in figure 2(c) is the elevation information at the weather station and is not equal to the 1.5 m elevation at the measurement point.
L106: “…includes temperatures at M1, M2 and M3…” -> “includes air/ice/water temperatures…”
L108: “Temperature-sensing resistance…” I would like to know what the diameter of the temperature probe is. This affects the absolute nature of the temperature corresponding to the monitoring depth.
L119: “…accuracy of ±0.5°C over the range…” is the accuracy (0.5°C) not sufficient to identify the exact ice bottom. During the growth period of the ice cover, the ice temperature near the ice-water interface is usually slightly below 0°C and the water temperature is no higher than 0.5°C.
L124-125: “For calculating ice thickness based on measured data, the ice water surface was identified at the change of temperature from that below zero degrees to a value that is above zero degrees.” it is important to note that it is the location of the ice bottom that is identified not the thickness of the ice. When the surface sublimates or melts, the surface and the bottom together determine the ice thickness and not just the bottom.
L134: Equation (1) is displayed incomplete.
L141, L159: “h is ice thickness (cm)”; “I_m is maximum ice thickness (mm)” units need to be uniform.
L157: “β_F” -> “β_T”
L158: “…ATDD is the accumulated thawing degree days (°C d)…” please describe in detail how the ATDD is calculated.
L174: “Variation of ice thickness in a day ....” how does the 3 cm error ensure that the daily variation of ice thickness is accurate? Can the daily ice thickness change rate be guaranteed above 3 cm?
L179: “…were -12°C, 0°C, -16°C ....” 0°C？
L181: “The temperatures at M2 were always higher than that measured at M1.” The manuscript should be precise as to whether "temperatures" refers to air, ice or water temperatures？
L186: “There are two reasons contributing…” Considering that the air temperature data comes from 30 km away, it is normal that there are differences between that and the T₄₀.
L188: “The first reason was the presence of the snow can reduce heat loss below and at water/ice surface.” please label the periods when the snow cover was present and the thickness in Figure 3.
L192: “The instrument shelter limited the direct solar radiation” the air temperature measurements from 30 km away must be equipped with radiation shield, otherwise the results observed during the day would be wrong. The difference between T₄₀, T₂₀, etc., and T_air can therefore be considered separately for daytime and dark conditions, and a significant change in the value of T_air would indicate that the absence of radiation shields at the M1, M2 and M3 sites is responsible for the error (the measured temperature is higher than the true value). However, the larger reason is due to the spatial distance between the air temperature data and the observation sites.
L195: “However, a significant difference exists between T_air and the temperature close to the ice surface.” I do not think the differences are significant, please add references. It is possible that the differences in the text are due to the distance of the weather stations and it cannot be said that there is a significant difference between the air temperature at the study site and the temperature close to the ice.
L213: Figure 3. please use more obvious colors to distinguish M1, M2 and M3.
L219-220: “…T_air and T³, and T_air and T³ are approximately 0.73 and 0.53, respectively.” ?
L223: “…the north side of the deck, where solar radiation has…” apart from the effect of solar radiation is there also a heat transfer effect from the deck? Because M1 and M2 are closer to the deck, they may also be thermally influenced by the building.
L234: “It is well known that ice temperature was below zero degrees.” ice temperature should be below or equal to 0°C. Ice temperatures tending towards 0°C during the melting period are common.
L235: “However, temperature gradient in the ice was rarely investigated.” a large number of studies have reported on ice temperature gradients.
L235-236: “change of the temperature along the vertical profile in the ice.” the manuscript studies the growth and melting of the ice cover, so the ice temperature profile should also reflect features from these two periods.
L238-239: “The average temperature was normalized by subtracting the average ice temperature at the beginning of every day.” since the authors have complete ice temperature data, please present a complete ice temperature profile for the ice-covered period. This way the development of the ice bottom is also clearly visible. (e.g Huang et al. 2019)
L274-275: “However, the high intensity of the temperature sensor may interrupt the measurement results to a certain extent.” what do you mean?
L289-291: “The estimated maximum ice thickness was 60 cm observed on March 11, 2022, indicating discrepancies of 5 cm and 31 days in terms of thickness and time, respectively.” although the maximum ice thickness is close, the error in the dates is too large. Perhaps a better result would be calculated using T₄₀.
L300: Figure 7. Why does it show the ice thickness changing from less than 5 cm back to more than 10 cm between 10 March and 31 March? Figure 3 does not show significant negative air temperature conditions.
L303-305: “At the begging of the freezing process, the variation of ice thickness was up to 24 cm at the monitoring station M1. However, the variation of ice thickness dropped to approximately 6 cm before the decaying process.” what do you mean?
L310-311: “A small variation in ice thickness and short duration for changing ice thickness were attributed to the duration of solar radiation.” it is important to clarify whether the conclusions obtained are truly based on the process of the thermal action of solar radiation on the ice cover, or the radiant heating temperature probe has produced a data error.
L318: Figure 8. The results of the dramatic changes in ice thickness over the course of a day are incredible. 1 cm melt at the ice bottom corresponds to the ice-water heat flux of about 35 W m^-2. I prefer to think that this is an effect of sensor error. When solar radiation penetrates into the ice during the day, the ice temperature, which is already close to the ice-water interface, is slightly below 0°C. It is quite possible that a value above 0°C could be measured and be mistaken for water.
L329-331: “Although using AFDD can only obtain the average daily ice thickness, it still provides valuable information in understanding the freezing and decaying process.” AFDD can only provide information on the growth of ice cover, not on decay.
L352: “…below the ice surface, T₀ was adopted…” please ensure that T₀ is always located at the gas-ice interface.
L362: Table 1. Table 1 only considers AFDD and does not include ATDD? “T40” -> “T₄₀”.
L371: Figure 10. The coordinates of the Y-axis should be in (cm), not (mm).
L372: “…were included in Table 2.” the four models should be substituted into the Figure 7 for simulation. I only see the error of the ice thickness, and I do not know the error of the date. Accurate modeling of ice processes and estimated maximum ice thickness are two study purposes.
L387: “…model 3 (LM-3)…” how is T₀ obtained in S1,S2 and S3?
L407-408: “Air temperature in this study overall was close to the monitoring stations.” this is not evident from Figure 3.
L410: “…considered that T_air was equal to T_air, which…” ?
L435-437: “The lowest temperature was noticed before sunrise and the highest temperature was before sunset. In addition, the temperature in ice almost increases linearly with depth.” this needs to be illustrated by presenting the daily temperature field, not just by virtue of the typical date.
L441-443: “The variation of ice thickness occurred in the afternoon and when the ice became thicker, ice thickness varied in a comparatively small range.” the results for ice thickness variation over the course of one day lack credibility.
L452-454: “The paper provides an approach to study the ice freezing and thawing processes comprehensively and a practical model to calculate ice thickness with air temperature and temperature at the ice surface incorporated.” The study essentially focuses on the growing phase of the ice cover and a new method is constructed in conjunction with AFDD. But no feasible method is proposed for the melt period.

References
Huang, W., Zhang, J., Leppäranta, M., Li, Z., Cheng, B., Lin, Z., 2019. Thermal structure and water-ice heat transfer in a shallow ice-covered thermokarst lake in central Qinghai-Tibet Plateau. J. Hydrol. 578, 124122.
Huang, W., Zhao, W., Zhang, C., Leppäranta, M., Li, Z., Li, R., Lin, Z., 2022. Sunlight penetration dominates the thermal regime and energetics of a shallow ice-covered lake in an arid climate. The Cryosphere. 16, 1793–1806.
Leppäranta, M., Terzhevik, A., Shirasawa, K., 2010. Solar radiation and ice melting in Lake Vendyurskoe, Russian Karelia. Hydrol. Res. 41(1), 50–62.
Winters, K. B., Ulloa, H. N., Wüest, A., & Bouffard, D. (2019). Energetics of Radiatively Heated Ice-Covered Lakes. Geophysical Research Letters, 46(15), 8913-8925.

Citation: https://doi.org/10.5194/tc-2022-241-RC1
- AC1:
  'Reply on RC1', Chao Kang, 30 Mar 2023
  The study conducted in situ observations of freezing and thawing processes in reservoir ice cover along the Irtysh River, identifying ice thickness and correlating it with air temperature using air-ice-water temperature chains from three monitoring stations. The simplified Stefan’s model is validated and a new approach to ice thickness simulation is proposed. The ice temperature profiles and air temperature curves described in the study have strengthened the understanding of air-ice interactions. The new method can serve areas where meteorological data is not abundant enough to simulate ice thickness by air temperature and surface temperature alone.
  
  Response: We really appreciate the time you spent on reviewing our manuscript and provided a such comprehensive summary. Our specific responses to these noted comments are provided in a point-by-point reply given below. A detailed response will be provided along with revised manuscript.
  However, the descriptions of the experimental methods are not sufficiently clear, and numerous symbolic errors make it difficult to understand what the authors are trying to convey. Studies based on freezing and thawing processes, have largely focused on freezing degree days (AFDD), with few findings referring to thawing periods. For the geographical location of the study area, it is difficult to ignore the influence of solar radiation on the overall ice process. It is questionable whether Tair from a weather station 30 km away is representative of the air temperature conditions in the study area. The authors should clarify the subject of this study by examining the growing and melting periods separately and discussing the causes of model error in relation to the ice and water temperature data.
  
  Response: Thank you for the comments. We are going to enrich the information of field instrument and methods of collecting data. In addition, symbols in the manuscript will be checked throughout the manuscript.
  Thanks for your constructive comments. Yes, we agree with you that freezing and thawing processes should be discussed in detail which will included in the revised the manuscript.
  Regarding solar radiation, we have collected the information of solar radiation along with the variation of ice thickness in the study area in 2023, which we can be used to investigate the incoming shortwave, longwave and net all-wave radiation (R_net) on ice process.
  We will explore the correlation between ice and water temperatures and model error.
  Intuitively, stefan's model ignores the effects of solar radiation, wind speed and many other factors, so it is inevitable that the simulation results are worse than the numerical model. However, the advantage of stefan's model is that it is possible to obtain ice thickness curves with a certain degree of accuracy with only air temperature data and statistical empirical parameters, which can be of great use in areas where abundant meteorological information is lacking. The great challenge exists during the melting period, as several studies point to the significant contribution of solar radiation absorbed by ice and under-ice water bodies to the decay of the ice cover. Ice temperatures that converge to 0°C as the ice cover decays interfere with the accuracy of discerning the ice-water interface using the temperature probe, which can be combined with the ice temperature profile and the water temperature profile under the ice to describe the cause of the error. It would be better to present the complete ice and water temperature field variation using ice and water temperature data from the three monitoring stations. I encourage authors to resubmit the manuscript with extensive revisions. Below are some specific comments aimed to provide guidance on the revision.
  
  Response: We agree with you Stefan’s model can be used to calculate ice thickness of areas where abundant meteorological information is lacking. However, as you also mentioned, many factors were ignored in the Stefan’s model and ice thickness varies temporally and spatially, which means that Stefan’s model cannot capture the change of ice thickness based on limited ice temperature information. The main idea of this manuscript is to come up with a new model that can be comparatively accurately calculate the ice thickness based on the temperature of ice thickness and regional meteorological information. We still admit Stefan’s model is useful. However, including ice surface temperature along with air temperature can capture the variation of ice thickness based on the proposed model which can be of help in reservoir management.
  In addition, measuring ice surface temperature is more economical and practical than utilizing temperature chains in the field. It means that under the same proposed budget, we can collect more useful information of the dynamic characteristics of ice thickness.
  L11: “…temperature at the ice surface…” the generally defined surface temperature is monitored by an infrared temperature sensor, and is not measured by a temperature probe close to the ice surface. The temperature probe has a certain size and shifts position as the ice surface sublimates or melts.
  
  Response: We have used both infrared temperature sensor and conventional temperature sensors from 2022 to 2023 which will be used to compare based on your comments. Additionally, we installed sensors after ice was formed in 2022 instead of prior to freezing, which can be used to study the effect of ice melt on the vertical location of sensors. From the observed data from 2021 to 2022, the ice surface temperature was always below zero degrees in freezing process. The melting of ice may have some impact on the vertical location of sensors in thawing process.
  L12: “…temperatures in ice almost increased linearly with depth.” the increase in ice temperature with depth is only characteristic of the growth phase.
  
  Response: we will clarify it in the revised manuscript.
  L20: “…can capture local ice freezing and thawing processes…” please add some description of the applicability of the thawing period to the manuscript.
  
  Response: we will add the process of thawing period interpretation in the revised manuscript.
  L29-30: “Factors affecting ice thickness include air temperature, flow velocity/fluctuating rate of water level, chemical components in the water, water depth, water area, etc.” the most important point, solar radiation, is not presented. Solar radiation is a key factor influencing ice processes. At high latitudes, solar radiation mostly acts in spring. At mid-latitudes, solar radiation influences the ice process throughout the winter. (e.g Huang et al. 2022; Leppäranta et al. 2010; Winters et al. 2019)
  
  Response: we have measured the incoming shortwave (SW↓), longwave (LW↓) and net all-wave radiation (R_net) in the study area this year and will analyze the correlation between net all-wave radiation (R_net) and ice thickness in the revised manuscript.
  L35-36: remove “The maximum depth can reach up to 4 to 10 m below the ice surface.”
  
  Response: Thank you for your detailed reminder. We can delete it in the revised manuscript.
  L57-58: “In practice, the degree day model proposed by Stefan was commonly used” additional information on the advantages of the freezing degree-day model, e.g., fewer input parameters and the ability to simulate ice thickness profiles within a certain error range even in areas where only air temperature records are available.
  
  Response: Thank you for your input. We can include it in the revised manuscript.
  L81-82: “…temperatures were measured using three…” -> “…air/ice/water temperatures”
  
  Response: Thank you for your detailed reminder. We will revise it in the revised manuscript.
  L87: “…one of the reservoirs along…” please add information about the study area, including but not limited to latitude, longitude, area, and water depth.
  
  Response: We will include more information of study area in the revised manuscript.
  L93-94: “M1 was installed…” complementing the water depth conditions at each observation point, this determines whether there are differences in the hydrothermal environment under the ice, which in turn affects the control of the ice-water heat flux to the ice bottom.
  
  Response: Thank you all. We will supplement the information in the revised manuscript.
  L95: “…two of them were above the water surface…” are radiation shields taken into account when measuring T20 and T40? If there is no radiation shield, the solar radiation heating the temperature probe during daytime measurements will cause the measured temperature to be higher than the air temperature at the same altitude, resulting in errors.
  
  Response: We have collected the temperatures of radiation shields and that in the sensors above the ice surface. They are proportional to each other. We will show it in the official response and can discuss it in the revised manuscript.
  L100: Figure 2. The 1.5 m identified by Tair in figure 2(c) is the elevation information at the weather station and is not equal to the 1.5 m elevation at the measurement point.
  
  Response: You are correct. Since the closest metrological station was 30 km away from the lake, it is not proper to label the elevation difference. We will change it in the revised manuscript.
  L106: “…includes temperatures at M1, M2 and M3…” -> “includes air/ice/water temperatures…”
  
  Response: Thank you. We can revise it in the revised manuscript.
  L108: “Temperature-sensing resistance…” I would like to know what the diameter of the temperature probe is. This affects the absolute nature of the temperature corresponding to the monitoring depth.
  
  Response: We used sensors of thermistor mounted in a cable rather than a probe. The thermistor cables were assembled at the State Key Laboratory of Frozen Soil Engineering (SKLFSE), Lanzhou, China. a Fluke meter (accuracy of 0.05%, model: 289, Fluke Corporation, Everett, WA) was used to calibrate the initial resistance value of these thermistors. The temperature sensitivity of these thermistors is ±0.05°C. For continuous observation, ice temperatures were initially measured for electrical resistivity by using a datalogger (CR6, Campell Scientific Inc., Logan, UT) and then were converted into temperature values, and the ice temperatures were automatically collected in a half hour time step. Details of the sensors will be supplemented in the revised manuscript.
  L119: “…accuracy of ±0.5°C over the range…” is the accuracy (0.5°C) not sufficient to identify the exact ice bottom. During the growth period of the ice cover, the ice temperature near the ice-water interface is usually slightly below 0°C and the water temperature is no higher than 0.5°C.
  
  Response: This is a typo. The resolution is 0.05°C. Additionally, we drilled one hole to identify the ice thickness and compared with what we calculated based on temperature sensors.
  L124-125: “For calculating ice thickness based on measured data, the ice water surface was identified at the change of temperature from that below zero degrees to a value that is above zero degrees.” it is important to note that it is the location of the ice bottom that is identified not the thickness of the ice. When the surface sublimates or melts, the surface and the bottom together determine the ice thickness and not just the bottom.
  
  Response: We agree with you. For the freezing period, the surface temperature was always below zero degree as no thawing process was involved. For thawing period, we will elaborate it in the revised manuscript.
  L134: Equation (1) is displayed incomplete.
  
  Response: We can revise it in the revised manuscript.
  L141, L159: “h is ice thickness (cm)”; “Im is maximum ice thickness (mm)” units need to be uniform.
  
  Response: Thank you for your detailed reminder. We will revise it and check it throughout the manuscript.
  L157: “βF” -> “βT”
  
  Response: Thank you. We can revise it in the revised manuscript.
  L158: “…ATDD is the accumulated thawing degree days (°C d)…” please describe in detail how the ATDD is calculated.
  
  Response: We can include detailed information in revised manuscript.
  L174: “Variation of ice thickness in a day ....” how does the 3 cm error ensure that the daily variation of ice thickness is accurate? Can the daily ice thickness change rate be guaranteed above 3 cm?
  
  Response: Thank you for your careful reminder. Considering the size and manufacturing process of the thermistor sensor, the thermistor sensor with too dense arrangement will affect each other. After comprehensive consideration, we set the measurement interval of 3cm for the thermistor sensor.
  L179: “…were -12°C, 0°C, -16°C ....” 0°C？
  
  Response: We will check the data and revise the manuscript.
  L181: “The temperatures at M2 were always higher than that measured at M1.” The manuscript should be precise as to whether "temperatures" refers to air, ice or water temperatures？
  
  Response: We can clarify the terminology in the revised manuscript.
  L186: “There are two reasons contributing…” Considering that the air temperature data comes from 30 km away, it is normal that there are differences between that and the T40.
  
  Response: We can try to include T40 for analysis as well.
  L188: “The first reason was the presence of the snow can reduce heat loss below and at water/ice surface.” please label the periods when the snow cover was present and the thickness in Figure 3.
  
  Response: We can include T40 for correlation analysis. Additionally, radiation information was collected from 2022 to 2023 which will be considered to be included for comparison. We will supplement the snow depth on the frozen reservoir.
  L192: “The instrument shelter limited the direct solar radiation” the air temperature measurements from 30 km away must be equipped with radiation shield, otherwise the results observed during the day would be wrong. The difference between T40, T20, etc., and Tair can therefore be considered separately for daytime and dark conditions, and a significant change in the value of Tair would indicate that the absence of radiation shields at the M1, M2 and M3 sites is responsible for the error (the measured temperature is higher than the true value). However, the larger reason is due to the spatial distance between the air temperature data and the observation sites.
  
  Response: We can include T40 for correlation analysis. Additionally, radiation information was collected from 2022 to 2023 will be considered to be included for comparison.
  L195: “However, a significant difference exists between Tair and the temperature close to the ice surface.” I do not think the differences are significant, please add references. It is possible that the differences in the text are due to the distance of the weather stations and it cannot be said that there is a significant difference between the air temperature at the study site and the temperature close to the ice.
  
  Response: We can include T40 for correlation analysis.
  L213: Figure 3. please use more obvious colors to distinguish M1, M2 and M3.
  
  Response: We can revise the figure in the revised manuscript.
  L219-220: “…Tair and T3, and Tair and T3 are approximately 0.73 and 0.53, respectively.” ?
  
  Response: We will correct the typos.
  L223: “…the north side of the deck, where solar radiation has…” apart from the effect of solar radiation is there also a heat transfer effect from the deck? Because M1 and M2 are closer to the deck, they may also be thermally influenced by the building.
  
  Response: We can explore reason further.
  L234: “It is well known that ice temperature was below zero degrees.” ice temperature should be below or equal to 0°C. Ice temperatures tending towards 0°C during the melting period are common.
  
  Response: Thank you. We will revise the statement accordingly.
  L235: “However, temperature gradient in the ice was rarely investigated.” a large number of studies have reported on ice temperature gradients.
  
  Response: Thank you. This is an imprecise expression; we will revise it further and include more references.
  L235-236: “change of the temperature along the vertical profile in the ice.” the manuscript studies the growth and melting of the ice cover, so the ice temperature profile should also reflect features from these two periods.
  
  Response: Thank you. We will include it in the revised manuscript.
  L238-239: “The average temperature was normalized by subtracting the average ice temperature at the beginning of every day.” since the authors have complete ice temperature data, please present a complete ice temperature profile for the ice-covered period. This way the development of the ice bottom is also clearly visible. (e.g Huang et al. 2019)
  
  Response: Thank you. We will present it as you suggested in the revised manuscript.
  L274-275: “However, the high intensity of the temperature sensor may interrupt the measurement results to a certain extent.” what do you mean?
  
  Response: We can clarify it in the revised manuscript.
  L289-291: “The estimated maximum ice thickness was 60 cm observed on March 11, 2022, indicating discrepancies of 5 cm and 31 days in terms of thickness and time, respectively.” although the maximum ice thickness is close, the error in the dates is too large. Perhaps a better result would be calculated using T40.
  
  Response: Thank you. We will try it in the revised manuscript.
  L300: Figure 7. Why does it show the ice thickness changing from less than 5 cm back to more than 10 cm between 10 March and 31 March? Figure 3 does not show significant negative air temperature conditions.
  
  Response: This is a good catch. Thank you. We will check it and correct it in the revised manuscript.
  L303-305: “At the begging of the freezing process, the variation of ice thickness was up to 24 cm at the monitoring station M1. However, the variation of ice thickness dropped to approximately 6 cm before the decaying process.” what do you mean?
  
  Response: We can clarify it in the revised manuscript.
  L310-311: “A small variation in ice thickness and short duration for changing ice thickness were attributed to the duration of solar radiation.” it is important to clarify whether the conclusions obtained are truly based on the process of the thermal action of solar radiation on the ice cover, or the radiant heating temperature probe has produced a data error.
  
  Response: We will clarify in the revised manuscript. Additionally, we can use the data of 2023 to validate it.
  L318: Figure 8. The results of the dramatic changes in ice thickness over the course of a day are incredible. 1 cm melt at the ice bottom corresponds to the ice-water heat flux of about 35 W m-2. I prefer to think that this is an effect of sensor error. When solar radiation penetrates into the ice during the day, the ice temperature, which is already close to the ice-water interface, is slightly below 0°C. It is quite possible that a value above 0°C could be measured and be mistaken for water.
  
  Response: We will check the raw data thoroughly to ensure the accuracy of the presented information.
  L329-331: “Although using AFDD can only obtain the average daily ice thickness, it still provides valuable information in understanding the freezing and decaying process.” AFDD can only provide information on the growth of ice cover, not on decay.
  
  Response: We can clarify it in the revised manuscript.
  L352: “…below the ice surface, T0 was adopted…” please ensure that T0 is always located at the gas-ice interface.
  
  Response: We will include the details in the revised manuscript.
  L362: Table 1. Table 1 only considers AFDD and does not include ATDD? “T40” -> “T40”.
  
  Response: We can include ATDD in the revised manuscript.
  L371: Figure 10. The coordinates of the Y-axis should be in (cm), not (mm).
  
  Response: We will correct in the revised manuscript.
  L372: “…were included in Table 2.” the four models should be substituted into the Figure 7 for simulation. I only see the error of the ice thickness, and I do not know the error of the date. Accurate modeling of ice processes and estimated maximum ice thickness are two study purposes.
  
  Response: We can plot ice process in the revised manuscript.
  L387: “…model 3 (LM-3)…” how is T0 obtained in S1,S2 and S3?
  
  Response: We can elaborate it in the revised manuscript.
  L407-408: “Air temperature in this study overall was close to the monitoring stations.” this is not evident from Figure 3.
  
  Response: We can elaborate it in the revised manuscript by considering the location of metrological station.
  L410: “…considered that Tair was equal to Tair, which…” ?
  
  Response: Thank you for pointing this out. We will revise in the revised manuscript.
  L435-437: “The lowest temperature was noticed before sunrise and the highest temperature was before sunset. In addition, the temperature in ice almost increases linearly with depth.” this needs to be illustrated by presenting the daily temperature field, not just by virtue of the typical date.
  
  Response: We can elaborate it in the revised manuscript.
  L441-443: “The variation of ice thickness occurred in the afternoon and when the ice became thicker, ice thickness varied in a comparatively small range.” the results for ice thickness variation over the course of one day lack credibility.
  
  Response: We can include the temperature variation of several days.
  L452-454: “The paper provides an approach to study the ice freezing and thawing processes comprehensively and a practical model to calculate ice thickness with air temperature and temperature at the ice surface incorporated.” The study essentially focuses on the growing phase of the ice cover and a new method is constructed in conjunction with AFDD. But no feasible method is proposed for the melt period.
  
  Response: Thawing process will be included in the revised manuscript.
  
  Citation: https://doi.org/10.5194/tc-2022-241-AC1
RC2:
'Comment on tc-2022-241', Anonymous Referee #2, 12 Mar 2023

I cannot recommend this manuscript for publication. Moreover, I request the authors to withdraw this text from “TC Discussions” and will consult with the TC editorial on the possible ways to do this in a fast and painless way. Here are my concerns in short: (i) the authors collected an interesting dataset but they were not able to present any consistent analysis of the observations; (ii) the authors tried to propose a statistical model “superior” to the Stefan (1890) model but their approach is far below the current state of knowledge on this subject, uses vague statistics, lacks generality, and does not add any novelty; (iii) the most important: for testing their model, the authors use data from Lake Kilpisjärvi and refer to the paper of Aslamov et al. (2021). Not a single piece of the Kilpisjärvi data was published by Aslamov et al. (2021). These data have not been made available for the public at all. Eventually, I found online some graphics based on raw unprocessed data from Kilpisjärvi, which was used for real-time tracking of the values registered by the ice station during its operation. These graphical data do not contain actual numerical values, did not undergo quality check, and were never supposed to be used by any researchers. After contacting Dr. I. Aslamov I can declare with all my responsibility that no permission from the data owners was given on public use of the Kilpisjärvi data. The ms has to be withdrawn with no possibility of public access to it.
Specific comments:
Introduction.
The introduction lacks focus. The overview of relevant previous studies is incomplete and partially irrelevant. Many statements lack the necessary references (L.51-52, “the most commonly used tool was SWIP..”; L71-72 “few of [studies] investigated the correlation between To and Tair…”, among others). Other statements use superfluous or irrelevant citations (e.g. at Line 53, the study of Aslamov et al. did not require any reference point at the lake bed. It is also unclear why such a reference point is needed when measuring the ice thickness is in question. Formulations are uncertain, like at L35 “The maximum depth can reach..” the maximum depth of what?
Study site and methodology
The descriptions of the study area and the field setup are inconsequential, with information on the temperature measurements configuration mixed between Sections 2.1 and 2.2, and some information on methods scattered over the Results section. Some essential information, like the height of the air temperature measurements, is missing.The description of the Stefan model is lengthy and erroneous (Eq. 1 is a mess, units in Eq. 4 are inconsistent, Eq. 5 misses the square root). Important background on the model assumptions about relationship between the air temperature and the ice temperature is not provided. The role of snow is not discussed. I refer the authors to the seminal book of Zubov(1945, Arctic Ice. English translation: 1963 US Navy Electronics Laboratory.) and the review of Leppäranta (1993, A review of analytical models of sea‐ice growth. Atmosphere-Ocean 31(1), 123-138) for a detailed discussion on the fundamentals of Stefan's problem. Awkward formulations hinder understanding of the text: L86 “Irtysh River Basin is a tributary..” L92 “three arrays of temperature were installed…” are just a few examples.
Results
The description of the measurement results is hard to follow: information on the height of air temperature measurements appears first in the middle of results (L187) and then repeated once more at L189. Effect of snow is mentioned but no information on snow cover is provided and no treatment of this effect is suggested in the following analysis. A lot of attention is paid to “temperature differences” but it is hardly possible to figure out which differences are meant here (cf. the paragraph L195-204 and the sentence at L205-206). The graphs in Fig. 4 are not informative and overloaded with data points. In general, results on the ice temperatures should be presented in a more concise and coherent way to be of any value.
Section 3.3, which is dedicated to variability of the ice thickness and the validity of Stefan's law for its prediction, has several major flaws. As stated earlier in Methods, the authors are aware of the fact that Stefan’s formula derivation is based on ice surface temperatures, and substituting them with air temperatures requires additional assumptions/adjustments. The ice surface temperatures are available from measurements, but the authors ignore them in calculations completely, using the daily mean air temperatures instead - why? Additional model calculations with daily min/max air temperatures have little if any sense with regard to the physics of ice growth and melt. The reported daily variations in ice thickness of up to 24 cm are questionable and cannot be presented without further details on their derivation and possible sources of this extremely strong variability, which is, I believe, a result of data misinterpretation. According to Fig. 8, the ice thickness on 01 Mar decreased by 18 cm within 6 hours and then grew back by ~15 cm within 4 hours. It means, the ice experienced first a heat supply of ~2500 W/m^2 and a heat loss of the same order of magnitude afterwards. Unless the heat flux amplitude of 5000 W/m^2 within less than a day is supported by any realistic explanation, the results read like nonsense.
Discussion
Any discussion, which could put the study in the context of the current knowledge, or could outline the novelty and applicability of results on wider scales, is simply absent. The matrix of correlation coefficients does not belong to discussion and is non-informative. The regression analysis (Table 1) is not supported by any reasonable considerations and looks senseless: if it is well known that h_ice depends on the square root of AFDD (Eq. 7), why a linear dependence h_ice = a*AFDD is explored (model Linear-2)? For me, it is a demonstration of complete authors’ incompetence in the problem. An addition of temperatures, which already enter the AFDD, as independent variables to other linear models, makes little sense as well.
I am surprised, how such a loosely developed pseudo-scientific piece of work landed in the “TC Discussions” without being carefully read before by (i) an experienced scientific supervisor of the study (ii) a couple of experts familiar with the subject, and (iii) an associate editor, who is expected to read some excerpts from the manuscript before approving it for the review.

Citation: https://doi.org/10.5194/tc-2022-241-RC2
- AC2:
  'Reply on RC2', Chao Kang, 31 Mar 2023
  I cannot recommend this manuscript for publication. Moreover, I request the authors to withdraw this text from “TC Discussions” and will consult with the TC editorial on the possible ways to do this in a fast and painless way. Here are my concerns in short: (i) the authors collected an interesting dataset but they were not able to present any consistent analysis of the observations; (ii) the authors tried to propose a statistical model “superior” to the Stefan (1890) model but their approach is far below the current state of knowledge on this subject, uses vague statistics, lacks generality, and does not add any novelty; (iii) the most important: for testing their model, the authors use data from Lake Kilpisjärvi and refer to the paper of Aslamov et al. (2021). Not a single piece of the Kilpisjärvi data was published by Aslamov et al. (2021). These data have not been made available for the public at all. Eventually, I found online some graphics based on raw unprocessed data from Kilpisjärvi, which was used for real-time tracking of the values registered by the ice station during its operation. These graphical data do not contain actual numerical values, did not undergo quality check, and were never supposed to be used by any researchers. After contacting Dr. I. Aslamov I can declare with all my responsibility that no permission from the data owners was given on public use of the Kilpisjärvi data. The ms has to be withdrawn with no possibility of public access to it.
  
  Response: Thank you for your evaluation of the current state of our manuscript. We really appreciate the time and effort you have spent to share your insightful comments. Please see our brief responses below.
  (i) the authors collected an interesting dataset but they were not able to present any consistent analysis of the observations;
  Response: we will follow your constructive comments to revise the structure and include thawing process in the revised manuscript as well. Additionally, ice thickness measured from 2023 will be used to evaluate the proposed model as well.
  (ii) the authors tried to propose a statistical model “superior” to the Stefan (1890) model but their approach is far below the current state of knowledge on this subject, uses vague statistics, lacks generality, and does not add any novelty;
  Response: We agree with you that the information from metrological station can provide a reference value to estimate the average ice thickness. However, the variation of ice thickness was neglected. It is also understood that ice thickness cannot be measured instantaneously due to limited access and cost of installing apparatus/temperature sensors. Therefore, a practical approach to calculate ice thickness is required. The proposed model has a capacity to capture the variation of ice thickness based on ice surface temperature.
  The highlights of this model were having Pearson analysis and machine learning technique involved in ice thickness identification and regression analysis.
  The flow of the manuscript was (1) identifying the thickness based on temperature sensors; (2) find the parameters that are more related to ice thickness based on calculated Pearson coefficients; (3) using machine learning method, three linear and one non-linear models were proposed by including different parameters which were also practical to be measured.
  Therefore, we are confident that our research was innovative and the logic behind the statistic was clear. However, we appreciate your comments and comments from both editor and the first reviewer.
  (iii) the most important: for testing their model, the authors use data from Lake Kilpisjärvi and refer to the paper of Aslamov et al. (2021). ….. The ms has to be withdrawn with no possibility of public access to it.
  Response: Thank you for helping us contact Dr. I. Aslamov. Honestly, we have contacted Dr. I. Aslamov and ask for permission of using processed data in the analysis. Unfortunately, we haven’t heard back from Dr. I. Aslamov before we planned to use raw data from https://hlserver.lin.irk.ru/shs/icemon/. We admit the citation format was not appropriate which can be revised in the revised manuscript.
  An alternative approach is to use new dataset we collected in 2023, which can be used in the model verification and included in Figure 10 of the revised manuscript.
  Specific comments:
  Introduction.
  The introduction lacks focus. The overview of relevant previous studies is incomplete and partially irrelevant. Many statements lack the necessary references (L.51-52, “the most commonly used tool was SWIP..”; L71-72 “few of [studies] investigated the correlation between To and Tair…”, among others). Other statements use superfluous or irrelevant citations (e.g. at Line 53, the study of Aslamov et al. did not require any reference point at the lake bed. It is also unclear why such a reference point is needed when measuring the ice thickness is in question. Formulations are uncertain, like at L35 “The maximum depth can reach..” the maximum depth of what?
  
  Response: Thank you for your good suggestion. In the Introduction Section, we summarized the monitoring method since measuring ice thickness is an important component of this study. Different approaches used in investigating ice formation process was introduced.
  We did not describe it clearly in the original manuscript, and we will accurately include more reference to support our statement. Additionally, as you suggested, we will focus on ice thickness measurement and calculation in the revised manuscript.
  Study site and methodology
  The descriptions of the study area and the field setup are inconsequential, with information on the temperature measurements configuration mixed between Sections 2.1 and 2.2, and some information on methods scattered over the Results section. Some essential information, like the height of the air temperature measurements, is missing. The description of the Stefan model is lengthy and erroneous (Eq. 1 is a mess, units in Eq. 4 are inconsistent, Eq. 5 misses the square root). Important background on the model assumptions about relationship between the air temperature and the ice temperature is not provided. The role of snow is not discussed. I refer the authors to the seminal book of Zubov(1945, Arctic Ice. English translation: 1963 US Navy Electronics Laboratory.) and the review of Leppäranta (1993, A review of analytical models of sea‐ice growth. Atmosphere-Ocean 31(1), 123-138) for a detailed discussion on the fundamentals of Stefan's problem. Awkward formulations hinder understanding of the text: L86 “Irtysh River Basin is a tributary..” L92 “three arrays of temperature were installed…” are just a few examples.
  
  Response: Thank you for this helpful comment and your recommended key literatures.
  We retrieved the seminal book of arctic ice (1963) by N. N. Zubov and a review of analytical models of sea‐ice growth (1993) by Matti Leppäranta. We will revise Section 2.1 and 2.2 in the revised manuscript to make sure the information for study area and measurement is accurately described. The information, e.g., air temperature measurement, will be supplemented as well.
  Thank you for helping us check the equation. We will correct the equations. Additionally, we will review the suggested books, and provide descriptions of assumptions in formula derivation. We will also carefully check the entire section again to ensure the consistency and accuracy of the statements.
  Results
  The description of the measurement results is hard to follow: information on the height of air temperature measurements appears first in the middle of results (L187) and then repeated once more at L189. Effect of snow is mentioned but no information on snow cover is provided and no treatment of this effect is suggested in the following analysis. A lot of attention is paid to “temperature differences” but it is hardly possible to figure out which differences are meant here (cf. the paragraph L195-204 and the sentence at L205-206). The graphs in Fig. 4 are not informative and overloaded with data points. In general, results on the ice temperatures should be presented in a more concise and coherent way to be of any value.
  
  Response: Thanks for the reminder. It has been corrected in the revised manuscript.
  We will read throughout the manuscript to remove any repeated description and make sure the revised manuscript is concise.
  The role of snow will be discussed in model description section as you suggested. In addition, continuous snow information in 2023 will be presented in the official response for further discussion.
  We discussed the difference of temperature from metrological station and temperature close to ice surface, i.e., T40 and T20. We can revise the statement to avoid unexpected confusion.
  Figure 4 shows the correlation between temperatures from metrological station and measured average temperature at three monitoring stations. We can try to revise Figure 4 to provide an informative graph.
  Section 3.3, which is dedicated to variability of the ice thickness and the validity of Stefan's law for its prediction, has several major flaws. As stated earlier in Methods, the authors are aware of the fact that Stefan’s formula derivation is based on ice surface temperatures, and substituting them with air temperatures requires additional assumptions/adjustments. The ice surface temperatures are available from measurements, but the authors ignore them in calculations completely, using the daily mean air temperatures instead - why? Additional model calculations with daily min/max air temperatures have little if any sense with regard to the physics of ice growth and melt. The reported daily variations in ice thickness of up to 24 cm are questionable and cannot be presented without further details on their derivation and possible sources of this extremely strong variability, which is, I believe, a result of data misinterpretation. According to Fig. 8, the ice thickness on 01 Mar decreased by 18 cm within 6 hours and then grew back by ~15 cm within 4 hours. It means, the ice experienced first a heat supply of ~2500 W/m^2 and a heat loss of the same order of magnitude afterwards. Unless the heat flux amplitude of 5000 W/m^2 within less than a day is supported by any realistic explanation, the results read like nonsense.
  
  Response: Thank you for your detailed reminder.
  As you mentioned, air temperatures instead of ice surface temperature was generally used to calculate AFDD. Therefore, we firstly use air temperature in the calculation for comparison purpose. However, ice surface temperature was adopted in Table 1 for further analysis. We can ice surface temperature to calculate AFDD for comparison in Figure 7.
  We will explore the possible error in the revised manuscript based on the raw data. In addition, solar radiation was measured at the same locations in 2023 which will be presented in the official response along with the revised manuscript, if possible, for further discussion.
  Discussion
  Any discussion, which could put the study in the context of the current knowledge, or could outline the novelty and applicability of results on wider scales, is simply absent. The matrix of correlation coefficients does not belong to discussion and is non-informative. The regression analysis (Table 1) is not supported by any reasonable considerations and looks senseless: if it is well known that h_ice depends on the square root of AFDD (Eq. 7), why a linear dependence h_ice = a*AFDD is explored (model Linear-2)? For me, it is a demonstration of complete authors’ incompetence in the problem. An addition of temperatures, which already enter the AFDD, as independent variables to other linear models, makes little sense as well.
  
  Response: In Section 3, we investigated the variation of ice temperature (Section 3.1), ice thickness (Section 3.2) during freezing and thawing process in details. Discussion section is focused on exploring the analyzing the potential relationship between ice thickness with temperatures and extending the proposed models on wider scale as you mentioned. In doing so, we think the flow of the manuscript is clear and easier for readers to follow.
  Selection of variables in Table 1 was based on the regression analysis in Section 4.1 and practical consideration, e.g., how difficult of collecting the corresponding information, dependence of variables, etc. For instance, three variables were chosen for Linear-1 model, which represent air temperature, temperature close to ice surface (T40), ice temperature at ice surface (T0) and AFDD showing temperature in the past.
  Yes, h-ice is correlated with the square root of AFDD. We have compared the calculated ice thickness using the square root of AFDD/ATDD in Figure 7. We will provide a detailed explanation in the revised manuscript.
  The purpose of regression analysis in Section 4.2 is to provide a model that can be used to calculate ice thicknesses that vary temporally and spatially. Therefore, we include T40, T0, etc., in the proposed models. Instead of using the square root of AFDD, AFDD was directly used. However, we can include the square root of AFDD in Table 1 for comparison.
  Again, AFDD can provide regional information while T0 and T40 can offer information regarding local temperature which varies in a day as well as at different stations.
  I am surprised, how such a loosely developed pseudo-scientific piece of work landed in the “TC Discussions” without being carefully read before by (i) an experienced scientific supervisor of the study (ii) a couple of experts familiar with the subject, and (iii) an associate editor, who is expected to read some excerpts from the manuscript before approving it for the review.
  
  Response: We would like to extend our sincerest thanks for your thoughtful review of our manuscript. Your feedback has been immensely helpful in refining our ideas and strengthening our arguments.
  Your comments have challenged us to think more deeply about our research and to consider new avenues of inquiry. We are grateful for the opportunity to learn from your expertise.
  We would also like to provide a revised manuscript for reconsideration of TC. Please leave us a comment for further discussion of the initial submission or comment on our revised manuscript, if any. Thank you very much.
  
  Citation: https://doi.org/10.5194/tc-2022-241-AC2
CC1:
'Comment on tc-2022-241', Ilya Aslamov, 04 Apr 2023
The article presents data on the processes of freezing and thawing of the ice cover of the reservoir on the Irtysh River. Authors tried to analyze obtained data using correlation between various parameters and proposed several model variants. Undoubtedly a lot of work has been done, but the meaning of many operations is highly questionable.
The first question that arises is: what do the authors measure at all? The maximum distance between the stations is only 30 meters, and between M1 and M2 - about 10 meters. At the same time, we see significant differences in temperatures at stations. Unfortunately there is no detailed description of the construction of the measuring system, but judging by the photo in figure 2a, the sensors go down into the ice in a black tube. Therefore, I think, authors do not measure the actual temperature, but how well they have placed the station, and where it is better or worse heated by solar radiation. Judging by Figure 3, panel a2, the air temperature (T₊₄₀) at station M2 was almost all winter positive? At the same time, 10 meters away, it was already 10-15 degrees cooler. What the nonsense... This is already enough to not take the obtained data seriously.

The description of the measurement system is very vague and jumbled.

It is not clear: Was the Fluke meter used only for calibration or is it included in each station?

Page 5, Line 110: "The principle of the thermometer was to measure the variation of electrical resistance of water". The electrical resistance of water? Are you sure?

It is not clear whether DS18B20 sensors were used only at station M3, or at all stations?

How did you match the DS18B20 1-wire sensors to the SDI-12 datalogger input?

Have you calibrated the DS18B20 sensors?

Why was it necessary to give a detailed conclusion of the well-known Stephan's formula? This is a scientific article, not a student review. In addition, the conclusion of the formula contains typos / inconsistencies.

What is the physical sense to calculate Stephan's formula on minimum and maximum daily temperatures (Fig. 7)?

It is very strange that the results of ice thickness calculations by Stefan's formula do not reflect the dynamics of ice thickness obtained from the thermosensors in ice (Fig. 7). It seems the problem lies in the determination of the initial moment of AFDD integrating. The authors apparently confused the water reservoir with a puddle and assumed that the ice will freeze on the first day after the average daily temperature drops below zero. Obviously, this is not true, and the date of freezing highly depends on the size of the water reservoir, its depth and wind activity. It is also confusing that the rate of ice growth according to Stefan's model is less than the real data (Fig. 7), although it should be the other way around. Apparently, there is an error in the calculations. And the larger ice thickness, obtained by Stefan's formula, were achieved not due to a higher growth rate, but to longer integration time.

There is also confusion in the article about the definition of AFDD. Based on formula 7 and the text in the description, we can conclude that AFDD is accumulated freezing degree days (°C d). Why then the models proposed by the authors (Table 1) use not the root of AFDD (as the authors themselves proved at the beginning of the article when deriving Stephan's formula), but a linear relationship? It does not make physical sense.

If you measure temperature of the ice surface or near it in the ice (T₀ or T_-3cm), so you should calculate the ice thickness using Stefan's formula based on them. The result will be much better than using an obscure combination of AFDD, T0 and other temperatures that are already implicit in T_-3cm (Table 1). The same applies to the calculation of the Pearson coefficient (Fig. 9). If you calculate the correlation not with T₄₀, T₀, T_-3, but with AFDD on their basis, you will get a much stronger correlation than with AFDD based on the air temperature at the weather station.

The stations were installed on a river reservoir, and there may probably under-ice currents. Currents significantly influence ice cover growth, and it would be useful to give at least approximate information about the average velocities of under-ice currents measured by conventional tracers. The authors also measured the temperatures of the under-ice water, but did not present any results. The water temperature under the ice affects the heat flux at its lower boundary and, therefore, its growth rate. Also, authors ignored in their analysis the solar radiation and snow cover (only general phrases instead of quantitative analysis), which have a great influence on ice formation and decay.

The discussion in full earnest of diurnal variations in ice thickness up to 20 centimeters or more (Fig. 8) is without any physical basis. It is impossible under the given conditions. The variations are due to an error in their determination. By the way, the algorithm how exactly the ice thickness is calculated from the temperature data was not presented in manuscript.

To verify their models, authors use data from lakes Kilpisjärvi (2018) and Baikal (2017), citing the work of Aslamov et al. (2021). While that paper only published data for Lake Baikal in 2014. Obviously, the raw data were taken from https://hlserver.lin.irk.ru/shs/icemon/ . According to the Disclaimer (under "info" button), using of the data from this site is possible only with the permission of the Limnological Institute SB RAS. As the primary data owner, I did not receive any requests from the authors on using of Kilpisjärvi and Baikal data in their study.

There are many typos and inconsistencies in the manuscript that make it difficult to understand.

Summarizing the above, I cannot recommend the manuscript for publication.
Citation: https://doi.org/10.5194/tc-2022-241-CC1
EC1: 'Comment on tc-2022-241 by the handing editor', Bin Cheng, 08 Apr 2023

Dear Authors,
As you have seen already, we received comments from two reviewers and one reader Ilya Aslamov whom you claimed that you have asked for data but you admitted that you didn't receive any reply. As I stated in my initial decision: "Not many ice works have been published in this part of nature. For this reason, I see the potential of this study", However, both reviewers have pointed out serious problems and fundamental questions about this work that all well beyond a major revision of this study. At this stage, I can't give any positive decision on your manuscript but rejection. Meanwhile, I encourage authors to check carefully comments from both reviewers and reader Ilya Aslamov. If the authors want to go forward with this study, the entire procedure needs to be reconsidered/redesigned. Finally, I urge authors to pay particular attention to handling properly on the scientific ethical matter. In your case, how to acquire and handling of other's data. This is very important.
Best regards,
Bin Cheng

Citation: https://doi.org/10.5194/tc-2022-241-EC1

Status: closed

RC1:
'Comment on tc-2022-241', Anonymous Referee #1, 07 Mar 2023

The study conducted in situ observations of freezing and thawing processes in reservoir ice cover along the Irtysh River, identifying ice thickness and correlating it with air temperature using air-ice-water temperature chains from three monitoring stations. The simplified Stefan’s model is validated and a new approach to ice thickness simulation is proposed. The ice temperature profiles and air temperature curves described in the study have strengthened the understanding of air-ice interactions. The new method can serve areas where meteorological data is not abundant enough to simulate ice thickness by air temperature and surface temperature alone.
However, the descriptions of the experimental methods are not sufficiently clear, and numerous symbolic errors make it difficult to understand what the authors are trying to convey. Studies based on freezing and thawing processes, have largely focused on freezing degree days (AFDD), with few findings referring to thawing periods. For the geographical location of the study area, it is difficult to ignore the influence of solar radiation on the overall ice process. It is questionable whether T_air from a weather station 30 km away is representative of the air temperature conditions in the study area. The authors should clarify the subject of this study by examining the growing and melting periods separately and discussing the causes of model error in relation to the ice and water temperature data.
Intuitively, stefan's model ignores the effects of solar radiation, wind speed and many other factors, so it is inevitable that the simulation results are worse than the numerical model. However, the advantage of stefan's model is that it is possible to obtain ice thickness curves with a certain degree of accuracy with only air temperature data and statistical empirical parameters, which can be of great use in areas where abundant meteorological information is lacking. The great challenge exists during the melting period, as several studies point to the significant contribution of solar radiation absorbed by ice and under-ice water bodies to the decay of the ice cover. Ice temperatures that converge to 0°C as the ice cover decays interfere with the accuracy of discerning the ice-water interface using the temperature probe, which can be combined with the ice temperature profile and the water temperature profile under the ice to describe the cause of the error. It would be better to present the complete ice and water temperature field variation using ice and water temperature data from the three monitoring stations. I encourage authors to resubmit the manuscript with extensive revisions. Below are some specific comments aimed to provide guidance on the revision.

L11: “…temperature at the ice surface…” the generally defined surface temperature is monitored by an infrared temperature sensor, and is not measured by a temperature probe close to the ice surface. The temperature probe has a certain size and shifts position as the ice surface sublimates or melts.
L12: “…temperatures in ice almost increased linearly with depth.” the increase in ice temperature with depth is only characteristic of the growth phase.
L20: “…can capture local ice freezing and thawing processes…” please add some description of the applicability of the thawing period to the manuscript.
L29-30: “Factors affecting ice thickness include air temperature, flow velocity/fluctuating rate of water level, chemical components in the water, water depth, water area, etc.” the most important point, solar radiation, is not presented. Solar radiation is a key factor influencing ice processes. At high latitudes, solar radiation mostly acts in spring. At mid-latitudes, solar radiation influences the ice process throughout the winter. (e.g Huang et al. 2022; Leppäranta et al. 2010; Winters et al. 2019)
L35-36: remove “The maximum depth can reach up to 4 to 10 m below the ice surface.”
L57-58: “In practice, the degree day model proposed by Stefan was commonly used” additional information on the advantages of the freezing degree-day model, e.g. fewer input parameters and the ability to simulate ice thickness profiles within a certain error range even in areas where only air temperature records are available.
L81-82: “…temperatures were measured using three…” -> “…air/ice/water temperatures”
L87: “…one of the reservoirs along…” please add information about the study area, including but not limited to latitude, longitude, area, and water depth.
L93-94: “M1 was installed…” complementing the water depth conditions at each observation point, this determines whether there are differences in the hydrothermal environment under the ice, which in turn affects the control of the ice-water heat flux to the ice bottom.
L95: “…two of them were above the water surface…” are radiation shields taken into account when measuring T₂₀ and T₄₀? If there is no radiation shield, the solar radiation heating the temperature probe during daytime measurements will cause the measured temperature to be higher than the air temperature at the same altitude, resulting in errors.
L100: Figure 2. The 1.5 m identified by T_air in figure 2(c) is the elevation information at the weather station and is not equal to the 1.5 m elevation at the measurement point.
L106: “…includes temperatures at M1, M2 and M3…” -> “includes air/ice/water temperatures…”
L108: “Temperature-sensing resistance…” I would like to know what the diameter of the temperature probe is. This affects the absolute nature of the temperature corresponding to the monitoring depth.
L119: “…accuracy of ±0.5°C over the range…” is the accuracy (0.5°C) not sufficient to identify the exact ice bottom. During the growth period of the ice cover, the ice temperature near the ice-water interface is usually slightly below 0°C and the water temperature is no higher than 0.5°C.
L124-125: “For calculating ice thickness based on measured data, the ice water surface was identified at the change of temperature from that below zero degrees to a value that is above zero degrees.” it is important to note that it is the location of the ice bottom that is identified not the thickness of the ice. When the surface sublimates or melts, the surface and the bottom together determine the ice thickness and not just the bottom.
L134: Equation (1) is displayed incomplete.
L141, L159: “h is ice thickness (cm)”; “I_m is maximum ice thickness (mm)” units need to be uniform.
L157: “β_F” -> “β_T”
L158: “…ATDD is the accumulated thawing degree days (°C d)…” please describe in detail how the ATDD is calculated.
L174: “Variation of ice thickness in a day ....” how does the 3 cm error ensure that the daily variation of ice thickness is accurate? Can the daily ice thickness change rate be guaranteed above 3 cm?
L179: “…were -12°C, 0°C, -16°C ....” 0°C？
L181: “The temperatures at M2 were always higher than that measured at M1.” The manuscript should be precise as to whether "temperatures" refers to air, ice or water temperatures？
L186: “There are two reasons contributing…” Considering that the air temperature data comes from 30 km away, it is normal that there are differences between that and the T₄₀.
L188: “The first reason was the presence of the snow can reduce heat loss below and at water/ice surface.” please label the periods when the snow cover was present and the thickness in Figure 3.
L192: “The instrument shelter limited the direct solar radiation” the air temperature measurements from 30 km away must be equipped with radiation shield, otherwise the results observed during the day would be wrong. The difference between T₄₀, T₂₀, etc., and T_air can therefore be considered separately for daytime and dark conditions, and a significant change in the value of T_air would indicate that the absence of radiation shields at the M1, M2 and M3 sites is responsible for the error (the measured temperature is higher than the true value). However, the larger reason is due to the spatial distance between the air temperature data and the observation sites.
L195: “However, a significant difference exists between T_air and the temperature close to the ice surface.” I do not think the differences are significant, please add references. It is possible that the differences in the text are due to the distance of the weather stations and it cannot be said that there is a significant difference between the air temperature at the study site and the temperature close to the ice.
L213: Figure 3. please use more obvious colors to distinguish M1, M2 and M3.
L219-220: “…T_air and T³, and T_air and T³ are approximately 0.73 and 0.53, respectively.” ?
L223: “…the north side of the deck, where solar radiation has…” apart from the effect of solar radiation is there also a heat transfer effect from the deck? Because M1 and M2 are closer to the deck, they may also be thermally influenced by the building.
L234: “It is well known that ice temperature was below zero degrees.” ice temperature should be below or equal to 0°C. Ice temperatures tending towards 0°C during the melting period are common.
L235: “However, temperature gradient in the ice was rarely investigated.” a large number of studies have reported on ice temperature gradients.
L235-236: “change of the temperature along the vertical profile in the ice.” the manuscript studies the growth and melting of the ice cover, so the ice temperature profile should also reflect features from these two periods.
L238-239: “The average temperature was normalized by subtracting the average ice temperature at the beginning of every day.” since the authors have complete ice temperature data, please present a complete ice temperature profile for the ice-covered period. This way the development of the ice bottom is also clearly visible. (e.g Huang et al. 2019)
L274-275: “However, the high intensity of the temperature sensor may interrupt the measurement results to a certain extent.” what do you mean?
L289-291: “The estimated maximum ice thickness was 60 cm observed on March 11, 2022, indicating discrepancies of 5 cm and 31 days in terms of thickness and time, respectively.” although the maximum ice thickness is close, the error in the dates is too large. Perhaps a better result would be calculated using T₄₀.
L300: Figure 7. Why does it show the ice thickness changing from less than 5 cm back to more than 10 cm between 10 March and 31 March? Figure 3 does not show significant negative air temperature conditions.
L303-305: “At the begging of the freezing process, the variation of ice thickness was up to 24 cm at the monitoring station M1. However, the variation of ice thickness dropped to approximately 6 cm before the decaying process.” what do you mean?
L310-311: “A small variation in ice thickness and short duration for changing ice thickness were attributed to the duration of solar radiation.” it is important to clarify whether the conclusions obtained are truly based on the process of the thermal action of solar radiation on the ice cover, or the radiant heating temperature probe has produced a data error.
L318: Figure 8. The results of the dramatic changes in ice thickness over the course of a day are incredible. 1 cm melt at the ice bottom corresponds to the ice-water heat flux of about 35 W m^-2. I prefer to think that this is an effect of sensor error. When solar radiation penetrates into the ice during the day, the ice temperature, which is already close to the ice-water interface, is slightly below 0°C. It is quite possible that a value above 0°C could be measured and be mistaken for water.
L329-331: “Although using AFDD can only obtain the average daily ice thickness, it still provides valuable information in understanding the freezing and decaying process.” AFDD can only provide information on the growth of ice cover, not on decay.
L352: “…below the ice surface, T₀ was adopted…” please ensure that T₀ is always located at the gas-ice interface.
L362: Table 1. Table 1 only considers AFDD and does not include ATDD? “T40” -> “T₄₀”.
L371: Figure 10. The coordinates of the Y-axis should be in (cm), not (mm).
L372: “…were included in Table 2.” the four models should be substituted into the Figure 7 for simulation. I only see the error of the ice thickness, and I do not know the error of the date. Accurate modeling of ice processes and estimated maximum ice thickness are two study purposes.
L387: “…model 3 (LM-3)…” how is T₀ obtained in S1,S2 and S3?
L407-408: “Air temperature in this study overall was close to the monitoring stations.” this is not evident from Figure 3.
L410: “…considered that T_air was equal to T_air, which…” ?
L435-437: “The lowest temperature was noticed before sunrise and the highest temperature was before sunset. In addition, the temperature in ice almost increases linearly with depth.” this needs to be illustrated by presenting the daily temperature field, not just by virtue of the typical date.
L441-443: “The variation of ice thickness occurred in the afternoon and when the ice became thicker, ice thickness varied in a comparatively small range.” the results for ice thickness variation over the course of one day lack credibility.
L452-454: “The paper provides an approach to study the ice freezing and thawing processes comprehensively and a practical model to calculate ice thickness with air temperature and temperature at the ice surface incorporated.” The study essentially focuses on the growing phase of the ice cover and a new method is constructed in conjunction with AFDD. But no feasible method is proposed for the melt period.

References
Huang, W., Zhang, J., Leppäranta, M., Li, Z., Cheng, B., Lin, Z., 2019. Thermal structure and water-ice heat transfer in a shallow ice-covered thermokarst lake in central Qinghai-Tibet Plateau. J. Hydrol. 578, 124122.
Huang, W., Zhao, W., Zhang, C., Leppäranta, M., Li, Z., Li, R., Lin, Z., 2022. Sunlight penetration dominates the thermal regime and energetics of a shallow ice-covered lake in an arid climate. The Cryosphere. 16, 1793–1806.
Leppäranta, M., Terzhevik, A., Shirasawa, K., 2010. Solar radiation and ice melting in Lake Vendyurskoe, Russian Karelia. Hydrol. Res. 41(1), 50–62.
Winters, K. B., Ulloa, H. N., Wüest, A., & Bouffard, D. (2019). Energetics of Radiatively Heated Ice-Covered Lakes. Geophysical Research Letters, 46(15), 8913-8925.

Citation: https://doi.org/10.5194/tc-2022-241-RC1
- AC1:
  'Reply on RC1', Chao Kang, 30 Mar 2023
  The study conducted in situ observations of freezing and thawing processes in reservoir ice cover along the Irtysh River, identifying ice thickness and correlating it with air temperature using air-ice-water temperature chains from three monitoring stations. The simplified Stefan’s model is validated and a new approach to ice thickness simulation is proposed. The ice temperature profiles and air temperature curves described in the study have strengthened the understanding of air-ice interactions. The new method can serve areas where meteorological data is not abundant enough to simulate ice thickness by air temperature and surface temperature alone.
  
  Response: We really appreciate the time you spent on reviewing our manuscript and provided a such comprehensive summary. Our specific responses to these noted comments are provided in a point-by-point reply given below. A detailed response will be provided along with revised manuscript.
  However, the descriptions of the experimental methods are not sufficiently clear, and numerous symbolic errors make it difficult to understand what the authors are trying to convey. Studies based on freezing and thawing processes, have largely focused on freezing degree days (AFDD), with few findings referring to thawing periods. For the geographical location of the study area, it is difficult to ignore the influence of solar radiation on the overall ice process. It is questionable whether Tair from a weather station 30 km away is representative of the air temperature conditions in the study area. The authors should clarify the subject of this study by examining the growing and melting periods separately and discussing the causes of model error in relation to the ice and water temperature data.
  
  Response: Thank you for the comments. We are going to enrich the information of field instrument and methods of collecting data. In addition, symbols in the manuscript will be checked throughout the manuscript.
  Thanks for your constructive comments. Yes, we agree with you that freezing and thawing processes should be discussed in detail which will included in the revised the manuscript.
  Regarding solar radiation, we have collected the information of solar radiation along with the variation of ice thickness in the study area in 2023, which we can be used to investigate the incoming shortwave, longwave and net all-wave radiation (R_net) on ice process.
  We will explore the correlation between ice and water temperatures and model error.
  Intuitively, stefan's model ignores the effects of solar radiation, wind speed and many other factors, so it is inevitable that the simulation results are worse than the numerical model. However, the advantage of stefan's model is that it is possible to obtain ice thickness curves with a certain degree of accuracy with only air temperature data and statistical empirical parameters, which can be of great use in areas where abundant meteorological information is lacking. The great challenge exists during the melting period, as several studies point to the significant contribution of solar radiation absorbed by ice and under-ice water bodies to the decay of the ice cover. Ice temperatures that converge to 0°C as the ice cover decays interfere with the accuracy of discerning the ice-water interface using the temperature probe, which can be combined with the ice temperature profile and the water temperature profile under the ice to describe the cause of the error. It would be better to present the complete ice and water temperature field variation using ice and water temperature data from the three monitoring stations. I encourage authors to resubmit the manuscript with extensive revisions. Below are some specific comments aimed to provide guidance on the revision.
  
  Response: We agree with you Stefan’s model can be used to calculate ice thickness of areas where abundant meteorological information is lacking. However, as you also mentioned, many factors were ignored in the Stefan’s model and ice thickness varies temporally and spatially, which means that Stefan’s model cannot capture the change of ice thickness based on limited ice temperature information. The main idea of this manuscript is to come up with a new model that can be comparatively accurately calculate the ice thickness based on the temperature of ice thickness and regional meteorological information. We still admit Stefan’s model is useful. However, including ice surface temperature along with air temperature can capture the variation of ice thickness based on the proposed model which can be of help in reservoir management.
  In addition, measuring ice surface temperature is more economical and practical than utilizing temperature chains in the field. It means that under the same proposed budget, we can collect more useful information of the dynamic characteristics of ice thickness.
  L11: “…temperature at the ice surface…” the generally defined surface temperature is monitored by an infrared temperature sensor, and is not measured by a temperature probe close to the ice surface. The temperature probe has a certain size and shifts position as the ice surface sublimates or melts.
  
  Response: We have used both infrared temperature sensor and conventional temperature sensors from 2022 to 2023 which will be used to compare based on your comments. Additionally, we installed sensors after ice was formed in 2022 instead of prior to freezing, which can be used to study the effect of ice melt on the vertical location of sensors. From the observed data from 2021 to 2022, the ice surface temperature was always below zero degrees in freezing process. The melting of ice may have some impact on the vertical location of sensors in thawing process.
  L12: “…temperatures in ice almost increased linearly with depth.” the increase in ice temperature with depth is only characteristic of the growth phase.
  
  Response: we will clarify it in the revised manuscript.
  L20: “…can capture local ice freezing and thawing processes…” please add some description of the applicability of the thawing period to the manuscript.
  
  Response: we will add the process of thawing period interpretation in the revised manuscript.
  L29-30: “Factors affecting ice thickness include air temperature, flow velocity/fluctuating rate of water level, chemical components in the water, water depth, water area, etc.” the most important point, solar radiation, is not presented. Solar radiation is a key factor influencing ice processes. At high latitudes, solar radiation mostly acts in spring. At mid-latitudes, solar radiation influences the ice process throughout the winter. (e.g Huang et al. 2022; Leppäranta et al. 2010; Winters et al. 2019)
  
  Response: we have measured the incoming shortwave (SW↓), longwave (LW↓) and net all-wave radiation (R_net) in the study area this year and will analyze the correlation between net all-wave radiation (R_net) and ice thickness in the revised manuscript.
  L35-36: remove “The maximum depth can reach up to 4 to 10 m below the ice surface.”
  
  Response: Thank you for your detailed reminder. We can delete it in the revised manuscript.
  L57-58: “In practice, the degree day model proposed by Stefan was commonly used” additional information on the advantages of the freezing degree-day model, e.g., fewer input parameters and the ability to simulate ice thickness profiles within a certain error range even in areas where only air temperature records are available.
  
  Response: Thank you for your input. We can include it in the revised manuscript.
  L81-82: “…temperatures were measured using three…” -> “…air/ice/water temperatures”
  
  Response: Thank you for your detailed reminder. We will revise it in the revised manuscript.
  L87: “…one of the reservoirs along…” please add information about the study area, including but not limited to latitude, longitude, area, and water depth.
  
  Response: We will include more information of study area in the revised manuscript.
  L93-94: “M1 was installed…” complementing the water depth conditions at each observation point, this determines whether there are differences in the hydrothermal environment under the ice, which in turn affects the control of the ice-water heat flux to the ice bottom.
  
  Response: Thank you all. We will supplement the information in the revised manuscript.
  L95: “…two of them were above the water surface…” are radiation shields taken into account when measuring T20 and T40? If there is no radiation shield, the solar radiation heating the temperature probe during daytime measurements will cause the measured temperature to be higher than the air temperature at the same altitude, resulting in errors.
  
  Response: We have collected the temperatures of radiation shields and that in the sensors above the ice surface. They are proportional to each other. We will show it in the official response and can discuss it in the revised manuscript.
  L100: Figure 2. The 1.5 m identified by Tair in figure 2(c) is the elevation information at the weather station and is not equal to the 1.5 m elevation at the measurement point.
  
  Response: You are correct. Since the closest metrological station was 30 km away from the lake, it is not proper to label the elevation difference. We will change it in the revised manuscript.
  L106: “…includes temperatures at M1, M2 and M3…” -> “includes air/ice/water temperatures…”
  
  Response: Thank you. We can revise it in the revised manuscript.
  L108: “Temperature-sensing resistance…” I would like to know what the diameter of the temperature probe is. This affects the absolute nature of the temperature corresponding to the monitoring depth.
  
  Response: We used sensors of thermistor mounted in a cable rather than a probe. The thermistor cables were assembled at the State Key Laboratory of Frozen Soil Engineering (SKLFSE), Lanzhou, China. a Fluke meter (accuracy of 0.05%, model: 289, Fluke Corporation, Everett, WA) was used to calibrate the initial resistance value of these thermistors. The temperature sensitivity of these thermistors is ±0.05°C. For continuous observation, ice temperatures were initially measured for electrical resistivity by using a datalogger (CR6, Campell Scientific Inc., Logan, UT) and then were converted into temperature values, and the ice temperatures were automatically collected in a half hour time step. Details of the sensors will be supplemented in the revised manuscript.
  L119: “…accuracy of ±0.5°C over the range…” is the accuracy (0.5°C) not sufficient to identify the exact ice bottom. During the growth period of the ice cover, the ice temperature near the ice-water interface is usually slightly below 0°C and the water temperature is no higher than 0.5°C.
  
  Response: This is a typo. The resolution is 0.05°C. Additionally, we drilled one hole to identify the ice thickness and compared with what we calculated based on temperature sensors.
  L124-125: “For calculating ice thickness based on measured data, the ice water surface was identified at the change of temperature from that below zero degrees to a value that is above zero degrees.” it is important to note that it is the location of the ice bottom that is identified not the thickness of the ice. When the surface sublimates or melts, the surface and the bottom together determine the ice thickness and not just the bottom.
  
  Response: We agree with you. For the freezing period, the surface temperature was always below zero degree as no thawing process was involved. For thawing period, we will elaborate it in the revised manuscript.
  L134: Equation (1) is displayed incomplete.
  
  Response: We can revise it in the revised manuscript.
  L141, L159: “h is ice thickness (cm)”; “Im is maximum ice thickness (mm)” units need to be uniform.
  
  Response: Thank you for your detailed reminder. We will revise it and check it throughout the manuscript.
  L157: “βF” -> “βT”
  
  Response: Thank you. We can revise it in the revised manuscript.
  L158: “…ATDD is the accumulated thawing degree days (°C d)…” please describe in detail how the ATDD is calculated.
  
  Response: We can include detailed information in revised manuscript.
  L174: “Variation of ice thickness in a day ....” how does the 3 cm error ensure that the daily variation of ice thickness is accurate? Can the daily ice thickness change rate be guaranteed above 3 cm?
  
  Response: Thank you for your careful reminder. Considering the size and manufacturing process of the thermistor sensor, the thermistor sensor with too dense arrangement will affect each other. After comprehensive consideration, we set the measurement interval of 3cm for the thermistor sensor.
  L179: “…were -12°C, 0°C, -16°C ....” 0°C？
  
  Response: We will check the data and revise the manuscript.
  L181: “The temperatures at M2 were always higher than that measured at M1.” The manuscript should be precise as to whether "temperatures" refers to air, ice or water temperatures？
  
  Response: We can clarify the terminology in the revised manuscript.
  L186: “There are two reasons contributing…” Considering that the air temperature data comes from 30 km away, it is normal that there are differences between that and the T40.
  
  Response: We can try to include T40 for analysis as well.
  L188: “The first reason was the presence of the snow can reduce heat loss below and at water/ice surface.” please label the periods when the snow cover was present and the thickness in Figure 3.
  
  Response: We can include T40 for correlation analysis. Additionally, radiation information was collected from 2022 to 2023 which will be considered to be included for comparison. We will supplement the snow depth on the frozen reservoir.
  L192: “The instrument shelter limited the direct solar radiation” the air temperature measurements from 30 km away must be equipped with radiation shield, otherwise the results observed during the day would be wrong. The difference between T40, T20, etc., and Tair can therefore be considered separately for daytime and dark conditions, and a significant change in the value of Tair would indicate that the absence of radiation shields at the M1, M2 and M3 sites is responsible for the error (the measured temperature is higher than the true value). However, the larger reason is due to the spatial distance between the air temperature data and the observation sites.
  
  Response: We can include T40 for correlation analysis. Additionally, radiation information was collected from 2022 to 2023 will be considered to be included for comparison.
  L195: “However, a significant difference exists between Tair and the temperature close to the ice surface.” I do not think the differences are significant, please add references. It is possible that the differences in the text are due to the distance of the weather stations and it cannot be said that there is a significant difference between the air temperature at the study site and the temperature close to the ice.
  
  Response: We can include T40 for correlation analysis.
  L213: Figure 3. please use more obvious colors to distinguish M1, M2 and M3.
  
  Response: We can revise the figure in the revised manuscript.
  L219-220: “…Tair and T3, and Tair and T3 are approximately 0.73 and 0.53, respectively.” ?
  
  Response: We will correct the typos.
  L223: “…the north side of the deck, where solar radiation has…” apart from the effect of solar radiation is there also a heat transfer effect from the deck? Because M1 and M2 are closer to the deck, they may also be thermally influenced by the building.
  
  Response: We can explore reason further.
  L234: “It is well known that ice temperature was below zero degrees.” ice temperature should be below or equal to 0°C. Ice temperatures tending towards 0°C during the melting period are common.
  
  Response: Thank you. We will revise the statement accordingly.
  L235: “However, temperature gradient in the ice was rarely investigated.” a large number of studies have reported on ice temperature gradients.
  
  Response: Thank you. This is an imprecise expression; we will revise it further and include more references.
  L235-236: “change of the temperature along the vertical profile in the ice.” the manuscript studies the growth and melting of the ice cover, so the ice temperature profile should also reflect features from these two periods.
  
  Response: Thank you. We will include it in the revised manuscript.
  L238-239: “The average temperature was normalized by subtracting the average ice temperature at the beginning of every day.” since the authors have complete ice temperature data, please present a complete ice temperature profile for the ice-covered period. This way the development of the ice bottom is also clearly visible. (e.g Huang et al. 2019)
  
  Response: Thank you. We will present it as you suggested in the revised manuscript.
  L274-275: “However, the high intensity of the temperature sensor may interrupt the measurement results to a certain extent.” what do you mean?
  
  Response: We can clarify it in the revised manuscript.
  L289-291: “The estimated maximum ice thickness was 60 cm observed on March 11, 2022, indicating discrepancies of 5 cm and 31 days in terms of thickness and time, respectively.” although the maximum ice thickness is close, the error in the dates is too large. Perhaps a better result would be calculated using T40.
  
  Response: Thank you. We will try it in the revised manuscript.
  L300: Figure 7. Why does it show the ice thickness changing from less than 5 cm back to more than 10 cm between 10 March and 31 March? Figure 3 does not show significant negative air temperature conditions.
  
  Response: This is a good catch. Thank you. We will check it and correct it in the revised manuscript.
  L303-305: “At the begging of the freezing process, the variation of ice thickness was up to 24 cm at the monitoring station M1. However, the variation of ice thickness dropped to approximately 6 cm before the decaying process.” what do you mean?
  
  Response: We can clarify it in the revised manuscript.
  L310-311: “A small variation in ice thickness and short duration for changing ice thickness were attributed to the duration of solar radiation.” it is important to clarify whether the conclusions obtained are truly based on the process of the thermal action of solar radiation on the ice cover, or the radiant heating temperature probe has produced a data error.
  
  Response: We will clarify in the revised manuscript. Additionally, we can use the data of 2023 to validate it.
  L318: Figure 8. The results of the dramatic changes in ice thickness over the course of a day are incredible. 1 cm melt at the ice bottom corresponds to the ice-water heat flux of about 35 W m-2. I prefer to think that this is an effect of sensor error. When solar radiation penetrates into the ice during the day, the ice temperature, which is already close to the ice-water interface, is slightly below 0°C. It is quite possible that a value above 0°C could be measured and be mistaken for water.
  
  Response: We will check the raw data thoroughly to ensure the accuracy of the presented information.
  L329-331: “Although using AFDD can only obtain the average daily ice thickness, it still provides valuable information in understanding the freezing and decaying process.” AFDD can only provide information on the growth of ice cover, not on decay.
  
  Response: We can clarify it in the revised manuscript.
  L352: “…below the ice surface, T0 was adopted…” please ensure that T0 is always located at the gas-ice interface.
  
  Response: We will include the details in the revised manuscript.
  L362: Table 1. Table 1 only considers AFDD and does not include ATDD? “T40” -> “T40”.
  
  Response: We can include ATDD in the revised manuscript.
  L371: Figure 10. The coordinates of the Y-axis should be in (cm), not (mm).
  
  Response: We will correct in the revised manuscript.
  L372: “…were included in Table 2.” the four models should be substituted into the Figure 7 for simulation. I only see the error of the ice thickness, and I do not know the error of the date. Accurate modeling of ice processes and estimated maximum ice thickness are two study purposes.
  
  Response: We can plot ice process in the revised manuscript.
  L387: “…model 3 (LM-3)…” how is T0 obtained in S1,S2 and S3?
  
  Response: We can elaborate it in the revised manuscript.
  L407-408: “Air temperature in this study overall was close to the monitoring stations.” this is not evident from Figure 3.
  
  Response: We can elaborate it in the revised manuscript by considering the location of metrological station.
  L410: “…considered that Tair was equal to Tair, which…” ?
  
  Response: Thank you for pointing this out. We will revise in the revised manuscript.
  L435-437: “The lowest temperature was noticed before sunrise and the highest temperature was before sunset. In addition, the temperature in ice almost increases linearly with depth.” this needs to be illustrated by presenting the daily temperature field, not just by virtue of the typical date.
  
  Response: We can elaborate it in the revised manuscript.
  L441-443: “The variation of ice thickness occurred in the afternoon and when the ice became thicker, ice thickness varied in a comparatively small range.” the results for ice thickness variation over the course of one day lack credibility.
  
  Response: We can include the temperature variation of several days.
  L452-454: “The paper provides an approach to study the ice freezing and thawing processes comprehensively and a practical model to calculate ice thickness with air temperature and temperature at the ice surface incorporated.” The study essentially focuses on the growing phase of the ice cover and a new method is constructed in conjunction with AFDD. But no feasible method is proposed for the melt period.
  
  Response: Thawing process will be included in the revised manuscript.
  
  Citation: https://doi.org/10.5194/tc-2022-241-AC1
RC2:
'Comment on tc-2022-241', Anonymous Referee #2, 12 Mar 2023

I cannot recommend this manuscript for publication. Moreover, I request the authors to withdraw this text from “TC Discussions” and will consult with the TC editorial on the possible ways to do this in a fast and painless way. Here are my concerns in short: (i) the authors collected an interesting dataset but they were not able to present any consistent analysis of the observations; (ii) the authors tried to propose a statistical model “superior” to the Stefan (1890) model but their approach is far below the current state of knowledge on this subject, uses vague statistics, lacks generality, and does not add any novelty; (iii) the most important: for testing their model, the authors use data from Lake Kilpisjärvi and refer to the paper of Aslamov et al. (2021). Not a single piece of the Kilpisjärvi data was published by Aslamov et al. (2021). These data have not been made available for the public at all. Eventually, I found online some graphics based on raw unprocessed data from Kilpisjärvi, which was used for real-time tracking of the values registered by the ice station during its operation. These graphical data do not contain actual numerical values, did not undergo quality check, and were never supposed to be used by any researchers. After contacting Dr. I. Aslamov I can declare with all my responsibility that no permission from the data owners was given on public use of the Kilpisjärvi data. The ms has to be withdrawn with no possibility of public access to it.
Specific comments:
Introduction.
The introduction lacks focus. The overview of relevant previous studies is incomplete and partially irrelevant. Many statements lack the necessary references (L.51-52, “the most commonly used tool was SWIP..”; L71-72 “few of [studies] investigated the correlation between To and Tair…”, among others). Other statements use superfluous or irrelevant citations (e.g. at Line 53, the study of Aslamov et al. did not require any reference point at the lake bed. It is also unclear why such a reference point is needed when measuring the ice thickness is in question. Formulations are uncertain, like at L35 “The maximum depth can reach..” the maximum depth of what?
Study site and methodology
The descriptions of the study area and the field setup are inconsequential, with information on the temperature measurements configuration mixed between Sections 2.1 and 2.2, and some information on methods scattered over the Results section. Some essential information, like the height of the air temperature measurements, is missing.The description of the Stefan model is lengthy and erroneous (Eq. 1 is a mess, units in Eq. 4 are inconsistent, Eq. 5 misses the square root). Important background on the model assumptions about relationship between the air temperature and the ice temperature is not provided. The role of snow is not discussed. I refer the authors to the seminal book of Zubov(1945, Arctic Ice. English translation: 1963 US Navy Electronics Laboratory.) and the review of Leppäranta (1993, A review of analytical models of sea‐ice growth. Atmosphere-Ocean 31(1), 123-138) for a detailed discussion on the fundamentals of Stefan's problem. Awkward formulations hinder understanding of the text: L86 “Irtysh River Basin is a tributary..” L92 “three arrays of temperature were installed…” are just a few examples.
Results
The description of the measurement results is hard to follow: information on the height of air temperature measurements appears first in the middle of results (L187) and then repeated once more at L189. Effect of snow is mentioned but no information on snow cover is provided and no treatment of this effect is suggested in the following analysis. A lot of attention is paid to “temperature differences” but it is hardly possible to figure out which differences are meant here (cf. the paragraph L195-204 and the sentence at L205-206). The graphs in Fig. 4 are not informative and overloaded with data points. In general, results on the ice temperatures should be presented in a more concise and coherent way to be of any value.
Section 3.3, which is dedicated to variability of the ice thickness and the validity of Stefan's law for its prediction, has several major flaws. As stated earlier in Methods, the authors are aware of the fact that Stefan’s formula derivation is based on ice surface temperatures, and substituting them with air temperatures requires additional assumptions/adjustments. The ice surface temperatures are available from measurements, but the authors ignore them in calculations completely, using the daily mean air temperatures instead - why? Additional model calculations with daily min/max air temperatures have little if any sense with regard to the physics of ice growth and melt. The reported daily variations in ice thickness of up to 24 cm are questionable and cannot be presented without further details on their derivation and possible sources of this extremely strong variability, which is, I believe, a result of data misinterpretation. According to Fig. 8, the ice thickness on 01 Mar decreased by 18 cm within 6 hours and then grew back by ~15 cm within 4 hours. It means, the ice experienced first a heat supply of ~2500 W/m^2 and a heat loss of the same order of magnitude afterwards. Unless the heat flux amplitude of 5000 W/m^2 within less than a day is supported by any realistic explanation, the results read like nonsense.
Discussion
Any discussion, which could put the study in the context of the current knowledge, or could outline the novelty and applicability of results on wider scales, is simply absent. The matrix of correlation coefficients does not belong to discussion and is non-informative. The regression analysis (Table 1) is not supported by any reasonable considerations and looks senseless: if it is well known that h_ice depends on the square root of AFDD (Eq. 7), why a linear dependence h_ice = a*AFDD is explored (model Linear-2)? For me, it is a demonstration of complete authors’ incompetence in the problem. An addition of temperatures, which already enter the AFDD, as independent variables to other linear models, makes little sense as well.
I am surprised, how such a loosely developed pseudo-scientific piece of work landed in the “TC Discussions” without being carefully read before by (i) an experienced scientific supervisor of the study (ii) a couple of experts familiar with the subject, and (iii) an associate editor, who is expected to read some excerpts from the manuscript before approving it for the review.

Citation: https://doi.org/10.5194/tc-2022-241-RC2
- AC2:
  'Reply on RC2', Chao Kang, 31 Mar 2023
  I cannot recommend this manuscript for publication. Moreover, I request the authors to withdraw this text from “TC Discussions” and will consult with the TC editorial on the possible ways to do this in a fast and painless way. Here are my concerns in short: (i) the authors collected an interesting dataset but they were not able to present any consistent analysis of the observations; (ii) the authors tried to propose a statistical model “superior” to the Stefan (1890) model but their approach is far below the current state of knowledge on this subject, uses vague statistics, lacks generality, and does not add any novelty; (iii) the most important: for testing their model, the authors use data from Lake Kilpisjärvi and refer to the paper of Aslamov et al. (2021). Not a single piece of the Kilpisjärvi data was published by Aslamov et al. (2021). These data have not been made available for the public at all. Eventually, I found online some graphics based on raw unprocessed data from Kilpisjärvi, which was used for real-time tracking of the values registered by the ice station during its operation. These graphical data do not contain actual numerical values, did not undergo quality check, and were never supposed to be used by any researchers. After contacting Dr. I. Aslamov I can declare with all my responsibility that no permission from the data owners was given on public use of the Kilpisjärvi data. The ms has to be withdrawn with no possibility of public access to it.
  
  Response: Thank you for your evaluation of the current state of our manuscript. We really appreciate the time and effort you have spent to share your insightful comments. Please see our brief responses below.
  (i) the authors collected an interesting dataset but they were not able to present any consistent analysis of the observations;
  Response: we will follow your constructive comments to revise the structure and include thawing process in the revised manuscript as well. Additionally, ice thickness measured from 2023 will be used to evaluate the proposed model as well.
  (ii) the authors tried to propose a statistical model “superior” to the Stefan (1890) model but their approach is far below the current state of knowledge on this subject, uses vague statistics, lacks generality, and does not add any novelty;
  Response: We agree with you that the information from metrological station can provide a reference value to estimate the average ice thickness. However, the variation of ice thickness was neglected. It is also understood that ice thickness cannot be measured instantaneously due to limited access and cost of installing apparatus/temperature sensors. Therefore, a practical approach to calculate ice thickness is required. The proposed model has a capacity to capture the variation of ice thickness based on ice surface temperature.
  The highlights of this model were having Pearson analysis and machine learning technique involved in ice thickness identification and regression analysis.
  The flow of the manuscript was (1) identifying the thickness based on temperature sensors; (2) find the parameters that are more related to ice thickness based on calculated Pearson coefficients; (3) using machine learning method, three linear and one non-linear models were proposed by including different parameters which were also practical to be measured.
  Therefore, we are confident that our research was innovative and the logic behind the statistic was clear. However, we appreciate your comments and comments from both editor and the first reviewer.
  (iii) the most important: for testing their model, the authors use data from Lake Kilpisjärvi and refer to the paper of Aslamov et al. (2021). ….. The ms has to be withdrawn with no possibility of public access to it.
  Response: Thank you for helping us contact Dr. I. Aslamov. Honestly, we have contacted Dr. I. Aslamov and ask for permission of using processed data in the analysis. Unfortunately, we haven’t heard back from Dr. I. Aslamov before we planned to use raw data from https://hlserver.lin.irk.ru/shs/icemon/. We admit the citation format was not appropriate which can be revised in the revised manuscript.
  An alternative approach is to use new dataset we collected in 2023, which can be used in the model verification and included in Figure 10 of the revised manuscript.
  Specific comments:
  Introduction.
  The introduction lacks focus. The overview of relevant previous studies is incomplete and partially irrelevant. Many statements lack the necessary references (L.51-52, “the most commonly used tool was SWIP..”; L71-72 “few of [studies] investigated the correlation between To and Tair…”, among others). Other statements use superfluous or irrelevant citations (e.g. at Line 53, the study of Aslamov et al. did not require any reference point at the lake bed. It is also unclear why such a reference point is needed when measuring the ice thickness is in question. Formulations are uncertain, like at L35 “The maximum depth can reach..” the maximum depth of what?
  
  Response: Thank you for your good suggestion. In the Introduction Section, we summarized the monitoring method since measuring ice thickness is an important component of this study. Different approaches used in investigating ice formation process was introduced.
  We did not describe it clearly in the original manuscript, and we will accurately include more reference to support our statement. Additionally, as you suggested, we will focus on ice thickness measurement and calculation in the revised manuscript.
  Study site and methodology
  The descriptions of the study area and the field setup are inconsequential, with information on the temperature measurements configuration mixed between Sections 2.1 and 2.2, and some information on methods scattered over the Results section. Some essential information, like the height of the air temperature measurements, is missing. The description of the Stefan model is lengthy and erroneous (Eq. 1 is a mess, units in Eq. 4 are inconsistent, Eq. 5 misses the square root). Important background on the model assumptions about relationship between the air temperature and the ice temperature is not provided. The role of snow is not discussed. I refer the authors to the seminal book of Zubov(1945, Arctic Ice. English translation: 1963 US Navy Electronics Laboratory.) and the review of Leppäranta (1993, A review of analytical models of sea‐ice growth. Atmosphere-Ocean 31(1), 123-138) for a detailed discussion on the fundamentals of Stefan's problem. Awkward formulations hinder understanding of the text: L86 “Irtysh River Basin is a tributary..” L92 “three arrays of temperature were installed…” are just a few examples.
  
  Response: Thank you for this helpful comment and your recommended key literatures.
  We retrieved the seminal book of arctic ice (1963) by N. N. Zubov and a review of analytical models of sea‐ice growth (1993) by Matti Leppäranta. We will revise Section 2.1 and 2.2 in the revised manuscript to make sure the information for study area and measurement is accurately described. The information, e.g., air temperature measurement, will be supplemented as well.
  Thank you for helping us check the equation. We will correct the equations. Additionally, we will review the suggested books, and provide descriptions of assumptions in formula derivation. We will also carefully check the entire section again to ensure the consistency and accuracy of the statements.
  Results
  The description of the measurement results is hard to follow: information on the height of air temperature measurements appears first in the middle of results (L187) and then repeated once more at L189. Effect of snow is mentioned but no information on snow cover is provided and no treatment of this effect is suggested in the following analysis. A lot of attention is paid to “temperature differences” but it is hardly possible to figure out which differences are meant here (cf. the paragraph L195-204 and the sentence at L205-206). The graphs in Fig. 4 are not informative and overloaded with data points. In general, results on the ice temperatures should be presented in a more concise and coherent way to be of any value.
  
  Response: Thanks for the reminder. It has been corrected in the revised manuscript.
  We will read throughout the manuscript to remove any repeated description and make sure the revised manuscript is concise.
  The role of snow will be discussed in model description section as you suggested. In addition, continuous snow information in 2023 will be presented in the official response for further discussion.
  We discussed the difference of temperature from metrological station and temperature close to ice surface, i.e., T40 and T20. We can revise the statement to avoid unexpected confusion.
  Figure 4 shows the correlation between temperatures from metrological station and measured average temperature at three monitoring stations. We can try to revise Figure 4 to provide an informative graph.
  Section 3.3, which is dedicated to variability of the ice thickness and the validity of Stefan's law for its prediction, has several major flaws. As stated earlier in Methods, the authors are aware of the fact that Stefan’s formula derivation is based on ice surface temperatures, and substituting them with air temperatures requires additional assumptions/adjustments. The ice surface temperatures are available from measurements, but the authors ignore them in calculations completely, using the daily mean air temperatures instead - why? Additional model calculations with daily min/max air temperatures have little if any sense with regard to the physics of ice growth and melt. The reported daily variations in ice thickness of up to 24 cm are questionable and cannot be presented without further details on their derivation and possible sources of this extremely strong variability, which is, I believe, a result of data misinterpretation. According to Fig. 8, the ice thickness on 01 Mar decreased by 18 cm within 6 hours and then grew back by ~15 cm within 4 hours. It means, the ice experienced first a heat supply of ~2500 W/m^2 and a heat loss of the same order of magnitude afterwards. Unless the heat flux amplitude of 5000 W/m^2 within less than a day is supported by any realistic explanation, the results read like nonsense.
  
  Response: Thank you for your detailed reminder.
  As you mentioned, air temperatures instead of ice surface temperature was generally used to calculate AFDD. Therefore, we firstly use air temperature in the calculation for comparison purpose. However, ice surface temperature was adopted in Table 1 for further analysis. We can ice surface temperature to calculate AFDD for comparison in Figure 7.
  We will explore the possible error in the revised manuscript based on the raw data. In addition, solar radiation was measured at the same locations in 2023 which will be presented in the official response along with the revised manuscript, if possible, for further discussion.
  Discussion
  Any discussion, which could put the study in the context of the current knowledge, or could outline the novelty and applicability of results on wider scales, is simply absent. The matrix of correlation coefficients does not belong to discussion and is non-informative. The regression analysis (Table 1) is not supported by any reasonable considerations and looks senseless: if it is well known that h_ice depends on the square root of AFDD (Eq. 7), why a linear dependence h_ice = a*AFDD is explored (model Linear-2)? For me, it is a demonstration of complete authors’ incompetence in the problem. An addition of temperatures, which already enter the AFDD, as independent variables to other linear models, makes little sense as well.
  
  Response: In Section 3, we investigated the variation of ice temperature (Section 3.1), ice thickness (Section 3.2) during freezing and thawing process in details. Discussion section is focused on exploring the analyzing the potential relationship between ice thickness with temperatures and extending the proposed models on wider scale as you mentioned. In doing so, we think the flow of the manuscript is clear and easier for readers to follow.
  Selection of variables in Table 1 was based on the regression analysis in Section 4.1 and practical consideration, e.g., how difficult of collecting the corresponding information, dependence of variables, etc. For instance, three variables were chosen for Linear-1 model, which represent air temperature, temperature close to ice surface (T40), ice temperature at ice surface (T0) and AFDD showing temperature in the past.
  Yes, h-ice is correlated with the square root of AFDD. We have compared the calculated ice thickness using the square root of AFDD/ATDD in Figure 7. We will provide a detailed explanation in the revised manuscript.
  The purpose of regression analysis in Section 4.2 is to provide a model that can be used to calculate ice thicknesses that vary temporally and spatially. Therefore, we include T40, T0, etc., in the proposed models. Instead of using the square root of AFDD, AFDD was directly used. However, we can include the square root of AFDD in Table 1 for comparison.
  Again, AFDD can provide regional information while T0 and T40 can offer information regarding local temperature which varies in a day as well as at different stations.
  I am surprised, how such a loosely developed pseudo-scientific piece of work landed in the “TC Discussions” without being carefully read before by (i) an experienced scientific supervisor of the study (ii) a couple of experts familiar with the subject, and (iii) an associate editor, who is expected to read some excerpts from the manuscript before approving it for the review.
  
  Response: We would like to extend our sincerest thanks for your thoughtful review of our manuscript. Your feedback has been immensely helpful in refining our ideas and strengthening our arguments.
  Your comments have challenged us to think more deeply about our research and to consider new avenues of inquiry. We are grateful for the opportunity to learn from your expertise.
  We would also like to provide a revised manuscript for reconsideration of TC. Please leave us a comment for further discussion of the initial submission or comment on our revised manuscript, if any. Thank you very much.
  
  Citation: https://doi.org/10.5194/tc-2022-241-AC2
CC1:
'Comment on tc-2022-241', Ilya Aslamov, 04 Apr 2023
The article presents data on the processes of freezing and thawing of the ice cover of the reservoir on the Irtysh River. Authors tried to analyze obtained data using correlation between various parameters and proposed several model variants. Undoubtedly a lot of work has been done, but the meaning of many operations is highly questionable.
The first question that arises is: what do the authors measure at all? The maximum distance between the stations is only 30 meters, and between M1 and M2 - about 10 meters. At the same time, we see significant differences in temperatures at stations. Unfortunately there is no detailed description of the construction of the measuring system, but judging by the photo in figure 2a, the sensors go down into the ice in a black tube. Therefore, I think, authors do not measure the actual temperature, but how well they have placed the station, and where it is better or worse heated by solar radiation. Judging by Figure 3, panel a2, the air temperature (T₊₄₀) at station M2 was almost all winter positive? At the same time, 10 meters away, it was already 10-15 degrees cooler. What the nonsense... This is already enough to not take the obtained data seriously.

The description of the measurement system is very vague and jumbled.

It is not clear: Was the Fluke meter used only for calibration or is it included in each station?

Page 5, Line 110: "The principle of the thermometer was to measure the variation of electrical resistance of water". The electrical resistance of water? Are you sure?

It is not clear whether DS18B20 sensors were used only at station M3, or at all stations?

How did you match the DS18B20 1-wire sensors to the SDI-12 datalogger input?

Have you calibrated the DS18B20 sensors?

Why was it necessary to give a detailed conclusion of the well-known Stephan's formula? This is a scientific article, not a student review. In addition, the conclusion of the formula contains typos / inconsistencies.

What is the physical sense to calculate Stephan's formula on minimum and maximum daily temperatures (Fig. 7)?

It is very strange that the results of ice thickness calculations by Stefan's formula do not reflect the dynamics of ice thickness obtained from the thermosensors in ice (Fig. 7). It seems the problem lies in the determination of the initial moment of AFDD integrating. The authors apparently confused the water reservoir with a puddle and assumed that the ice will freeze on the first day after the average daily temperature drops below zero. Obviously, this is not true, and the date of freezing highly depends on the size of the water reservoir, its depth and wind activity. It is also confusing that the rate of ice growth according to Stefan's model is less than the real data (Fig. 7), although it should be the other way around. Apparently, there is an error in the calculations. And the larger ice thickness, obtained by Stefan's formula, were achieved not due to a higher growth rate, but to longer integration time.

There is also confusion in the article about the definition of AFDD. Based on formula 7 and the text in the description, we can conclude that AFDD is accumulated freezing degree days (°C d). Why then the models proposed by the authors (Table 1) use not the root of AFDD (as the authors themselves proved at the beginning of the article when deriving Stephan's formula), but a linear relationship? It does not make physical sense.

If you measure temperature of the ice surface or near it in the ice (T₀ or T_-3cm), so you should calculate the ice thickness using Stefan's formula based on them. The result will be much better than using an obscure combination of AFDD, T0 and other temperatures that are already implicit in T_-3cm (Table 1). The same applies to the calculation of the Pearson coefficient (Fig. 9). If you calculate the correlation not with T₄₀, T₀, T_-3, but with AFDD on their basis, you will get a much stronger correlation than with AFDD based on the air temperature at the weather station.

The stations were installed on a river reservoir, and there may probably under-ice currents. Currents significantly influence ice cover growth, and it would be useful to give at least approximate information about the average velocities of under-ice currents measured by conventional tracers. The authors also measured the temperatures of the under-ice water, but did not present any results. The water temperature under the ice affects the heat flux at its lower boundary and, therefore, its growth rate. Also, authors ignored in their analysis the solar radiation and snow cover (only general phrases instead of quantitative analysis), which have a great influence on ice formation and decay.

The discussion in full earnest of diurnal variations in ice thickness up to 20 centimeters or more (Fig. 8) is without any physical basis. It is impossible under the given conditions. The variations are due to an error in their determination. By the way, the algorithm how exactly the ice thickness is calculated from the temperature data was not presented in manuscript.

To verify their models, authors use data from lakes Kilpisjärvi (2018) and Baikal (2017), citing the work of Aslamov et al. (2021). While that paper only published data for Lake Baikal in 2014. Obviously, the raw data were taken from https://hlserver.lin.irk.ru/shs/icemon/ . According to the Disclaimer (under "info" button), using of the data from this site is possible only with the permission of the Limnological Institute SB RAS. As the primary data owner, I did not receive any requests from the authors on using of Kilpisjärvi and Baikal data in their study.

There are many typos and inconsistencies in the manuscript that make it difficult to understand.

Summarizing the above, I cannot recommend the manuscript for publication.
Citation: https://doi.org/10.5194/tc-2022-241-CC1
EC1: 'Comment on tc-2022-241 by the handing editor', Bin Cheng, 08 Apr 2023

Dear Authors,
As you have seen already, we received comments from two reviewers and one reader Ilya Aslamov whom you claimed that you have asked for data but you admitted that you didn't receive any reply. As I stated in my initial decision: "Not many ice works have been published in this part of nature. For this reason, I see the potential of this study", However, both reviewers have pointed out serious problems and fundamental questions about this work that all well beyond a major revision of this study. At this stage, I can't give any positive decision on your manuscript but rejection. Meanwhile, I encourage authors to check carefully comments from both reviewers and reader Ilya Aslamov. If the authors want to go forward with this study, the entire procedure needs to be reconsidered/redesigned. Finally, I urge authors to pay particular attention to handling properly on the scientific ethical matter. In your case, how to acquire and handling of other's data. This is very important.
Best regards,
Bin Cheng

Citation: https://doi.org/10.5194/tc-2022-241-EC1

Chuntan Han, Chao Kang, Chengxian Zhao, Jianhua Luo, and Rensheng Chen

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Short summary

This paper presents analysis results of temperatures collected at three monitoring stations on a reservoir along Irtysh River. Temperatures close to ice surface were analyzed and correlated with air temperature. Ice thickness was correlated with temperatures, variations of temperature and AFDD. Regression models were proposed and compared using the dataset in this study which was then validated using data from stations in Russia and Finland.


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