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 preprint is currently under review for the journal TC.

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

Chuntan Han et al.

Status: open (until 10 Apr 2023)

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

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.

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Citation: https://doi.org/10.5194/tc-2022-241-RC1
RC2: 'Comment on tc-2022-241', Anonymous Referee #2, 12 Mar 2023 reply

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.

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Citation: https://doi.org/10.5194/tc-2022-241-RC2

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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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