Calculation of Black Ice Thickness and Heat Fluxes inside the Ice and at the Water–Ice Boundary in a Boreal Lake

Round 1

Reviewer 1 Report

Please provide a picture or at least a sketch or schematic of the temperature chain setup in the field. 

Line 146-147: Normally, the temperature resolution was 0.003℃ without sign “±”.

Equation 1: Not very clear to understand the meaning of this equation, especially with the l_1­. I strongly suggest that authors add a graph to clarify the coordinate of thickness and distance l.

Font size in the all figures should be consistent with each other.

In fig. 4: why is there great difference between the q_w and averaged ?̅_? as the ?̅_? as just the averaged over 12 measurements. And the legend 1, 2 and 3 are so simple to be on the graph that did not make any sense. Also, I am curious that the negative flux responds a peak of the ?̅_? During Dec. 19-21 in 1995, why was that?

What do the A and B account for in the fig. 5?

I suspect the error analysis on the ice thickness only use an ice temperature chain without drilling hole measurements.

Please be more clear with the innovation of this study as the methods used in this paper are from previous research, and just the one temperature profile was be analyzed.

Section 4 discussion is more like conclusions for authors’ study, which needs to be discussed more deeply. 

Minor editing of English language required

Author Response

We are thankful to the Reviewer for the thorough consideration of our study and valuable suggestions. The point-to-point responses and the description of the corresponding changes in the ms are provided  in file.

Author Response File: Author Response.docx

Reviewer 2 Report

This study is pretty basic and simple. The heat fluxes within black ice and at the ice-water interface of one shallow boreal lake ice were investigated. The topic is not necessarily novel but understanding ice thermodynamics for one additional lake is not harmful either. The methodology applied in this study is well-known despite the fact that the data originated from a long time ago. This study offers new information to help better understand the underlying in-ice heat flux characteristics and black ice thermodynamics. For these reasons, I recommend acceptance of this manuscript to the Limnological Review after moderate revision to be carried out.

The abstract needs to be revised with more concrete results

Please add more information on the lake background. A geography map is needed.

There are equations in the introduction chapter which is usual, please present them in the method section.

Please provide more information on instrumentation. What kind of thermistor sensors were used? What was the accuracy? Have you done calibration? What are the snow conditions on lake ice?

Please add more information on comparison with other similar studies.

The conclusion needs to be reformulated.

Some other minor issues:

 L40: “When black ice is poured with water, the so…” Please explain what do you mean by doing this kind of experiment. How is linked with real world?

L245: How does ?w take its value when combining formula (3) and ?w to calculate the ice-water heat flux?

L256-259: “At the time of chain…of measurements.” duplicates L140-145

L264: “December to mid-March is shown in Figure 1” What happened after mid-March? Do you have air temperature time series? Why did all the sensors show the same 0 C temperature? Was ice melt or did sensors fail?

L331-332: “(3) heat fluxes from water to ice for the time interval between successive freezing of 331 sensors 0.32 m and 0.42 m” The authors got an ice-water heat flux of 10 to 40+ W/m². This value is too big to me. Please do the moving average (running mean) calculations.

L367: “Table 1”. Ice growth rate, ‘cm/day’ -> Harmonised as "mm/day"

 

The English quality is adequate.

Author Response

We are thankful to the Reviewer for the thorough consideration of our study and valuable suggestions. The point-to-point responses and the description of the corresponding changes in the ms are provided  in file

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

1.     Latitude and longitude should be on the left panel of the figure 1. It is not clear where the lake and land around the lake Vendyurskoe is on the right panel of the figure 1.

2.     Make the figure 2 good-looking.

3.     Put the variables q_w, q_ice, ?̅_? on the panel b of the figure7 instead of the 1, 2 and 3.

4.     In figure 8, x axis is “Time, hours”.

5.      In figure 3, legend of 1,2,3,4 is very unprofessional. It is better to write meaningful letters.

6.     Line 687: Is one of the factors temperature difference at the water-ice interface in the “two factors – water temperature and turbulence of the sub-ice layer……”?

Author Response

We are grateful to the reviewer for his careful reading of the manuscript and comments. We tried to take into account all the comments, except for the second, the essence of which is not clear to us. Responses to comments are provided below.

R.: 1.     Latitude and longitude should be on the left panel of the figure 1. It is not clear where the lake and land around the lake Vendyurskoe is on the right panel of the figure 1.

A.: Done

 

R.: 2.     Make the figure 2 good-looking.

A.: Figure 2 shows the position of the temperature sensors relative to the black ice surface. Layers of white ice and snow on top of black ice are also schematically shown. The figure shows the total ice thickness (x), the distance from the black ice surface to the bottom frozen sensor (l*) and the distance between the sensors (Dl). We don’t quite understand what exactly needs to be changed in Figure 2?

R.: 3.     Put the variables q_w, q_ice, ?̅_? on the panel b of the figure7 instead of the 1, 2 and 3.

A.: Done.

 

R.: 4.     In figure 8, x axis is “Time, hours”.

A.: Done.

R.: 5.      In figure 3, legend of 1,2,3,4 is very unprofessional. It is better to write meaningful letters.

A.: Done.

 

R.: 6.     Line 687: Is one of the factors temperature difference at the water-ice interface in the “two factors – water temperature and turbulence of the sub-ice layer……”?

A.: Ice temperature at the water-ice interface is 0°C, so temperature difference at the water-ice interface is numerically equal to the water temperature. However, we agree with the Reviewer: physically the definition “temperature difference at the water-ice interface” of the factor is more correct from the physical point of view. Therefore, we replaced “water temperature” by this new definition.

Author Response File: Author Response.docx

Reviewer 2 Report

I am satisfied with the revision of the manuscript and have no further major comments. I recommend this manuscript to be published in the  Limnological Review.

Congratulations.

Author Response

The authors are grateful to the Reviewer for his high assessment of the revised manuscript.

Author Response File: Author Response.docx