Short Standing and Propagating Internal Waves in an Ice-Covered Shallow Lake

Round 1

Reviewer 1 Report

Short standing and propagating internal waves in an ice-covered shallow lake 

 

The authors provide a compelling data set  from an array of thermistor chains installed in Lake Vendyurskoe during two winters, from which they investigate under-ice internal gravity waves. The paper is well-written and the results are unique in their kind, reporting the presence of short standing and propagating internal gravity waves, and their properties, such as phase and group speed, and vertical modal structure. Indeed, the literature on short internal waves in these specific environments is limited and I think this paper does a relevant contribution. Results shown in Figure 2 are beautiful. I am providing suggestions to broaden the impact of the paper below.

 

Introduction.

I think the paper would benefit of broadening the citations in the introduction. In line 44, the authors mention vertical transport in ice-covered lakes controlled by convective motion that can also energise internal gravity waves. 

 

There is a number of relevant studies that could be cited here to stress this point. For instance:

 

Fine scale structure of convective mixed layer in ice-covered lake

Volkov et al. EFM 2019

 

Under-ice convection dynamics in a boreal lake

Bouffard et al. IW 2019

 

Structure and dynamics of convective mixing in Lake Onego under ice-covered conditions

Bogdanov et al. IW 2019

 

Line 48, Mixing:

 

Mechanical energy budget and mixing efficiency for a radiatively heated ice-covered waterbody

Ulloa et al. JFM 2018

 

Energetics of Radiatively Heated Ice‐Covered Lakes

Winters et al. GRL 2019

 

Line 57, Mixing and breaking :

Hydrodynamics of a periodically wind-forced small and narrow stratified basin: a large-eddy simulation experiment

Ulloa et al. EFM 2019

 

Line 89 Mechanisms to generate IW. Lateral gravity currents and convection can generate internal gravity waves in the stratified zone:

 

Differential heating drives downslope flows that accelerate mixed‐layer warming in ice‐covered waters

Ulloa et al. GRL 2019

 

Ice-covered Lake Onega: effects of radiation on convection and internal waves

Bouffard et al. Hydrobiology 2916

 

Results

Could the authors discuss about the nonlinear features that the internal wave field exhibits in Figure 6? 

 

Could the authors show power spectral density of temperature fluctuations to observe the range of frequencies that are energized?

 

Discussion

It would be interesting to have a brief discussion about the degenerative processes faced by basin-scale internal waves that could transfer energy to short internal waves.

 

Conclusions

What is driving the barotropic seiches?

Author Response

Dear Reviewer,

thank you very much for reviewing our study “Short standing and propagating internal waves in an ice-covered shallow lake” (manuscript water-2482713). We are thankful for the thorough consideration of our study and valuable suggestions. We have found your review helpful for promoting our study. Below, we provide the point-to-point responses to questions and remarks, and the description of the corresponding changes in the MS.

Reviewer: The authors provide a compelling data set from an array of thermistor chains installed in Lake Vendyurskoe during two winters, from which they investigate under-ice internal gravity waves. The paper is well-written and the results are unique in their kind, reporting the presence of short standing and propagating internal gravity waves, and their properties, such as phase and group speed, and vertical modal structure. Indeed, the literature on short internal waves in these specific environments is limited and I think this paper does a relevant contribution. Results shown in Figure 2 are beautiful. I am providing suggestions to broaden the impact of the paper below.

Authors: Thank you very much for your appreciation of our research.

Reviewer:

Introduction.

I think the paper would benefit of broadening the citations in the introduction. In line 44, the authors mention vertical transport in ice-covered lakes controlled by convective motion that can also energise internal gravity waves. 

There is a number of relevant studies that could be cited here to stress this point. For instance:

Fine scale structure of convective mixed layer in ice-covered lake

Volkov et al. EFM 2019

Under-ice convection dynamics in a boreal lake

Bouffard et al. IW 2019

Structure and dynamics of convective mixing in Lake Onego under ice-covered conditions

Bogdanov et al. IW 2019

Line 48, Mixing:

Mechanical energy budget and mixing efficiency for a radiatively heated ice-covered waterbody

Ulloa et al. JFM 2018

Energetics of Radiatively Heated Ice-Covered Lakes

Winters et al. GRL 2019

Line 57, Mixing and breaking:

Hydrodynamics of a periodically wind-forced small and narrow stratified basin: a large-eddy simulation experiment

Ulloa et al. EFM 2019

Line 89 Mechanisms to generate IW. Lateral gravity currents and convection can generate internal gravity waves in the stratified zone:

Differential heating drives downslope flows that accelerate mixed-layer warming in ice-covered waters

Ulloa et al. GRL 2019

Ice-covered Lake Onega: effects of radiation on convection and internal waves

Bouffard et al. Hydrobiology 2916

 

Authors: Thanks for the recommendations. We have expanded the review and added a number of publications concerning the hydrodynamics of ice-covered lakes.

 

Results

Reviewer: Could the authors discuss about the nonlinear features that the internal wave field exhibits in Figure 6? 

 

Authors: Indeed, Figure 6 (Figure 7 in new version of MS) presents the pattern which may be considered as nonlinear IW, which propagate away from the source.

We also agree that IW nonlinear features are very important issue, especially considering the problem of IW damping, breaking and dissipation. One of the ways of damping, as pointed out in [Shimizu and Imberger, 2008] is connected with wave steepening and the conversion to internal surges and solitary waves. The corresponding mechanisms are rather complicated and thoroughly studied in a number of papers ([Vlasenko et al., 2003; Boegman et al,m 2003…]). But all these issues are beyond the scope of our article, so we did not discuss the shape of wave trains in the paper. Besides, we had not enough experimental facilities and settings, which would allow tracing of trains paths.

 

 

Reviewer: Could the authors show power spectral density of temperature fluctuations to observe the range of frequencies that are energized?

 

Authors: We added Figure 2_new which illustrates the range of frequencies that are energized.

 

 

Discussion

Reviewer: It would be interesting to have a brief discussion about the degenerative processes faced by basin-scale internal waves that could transfer energy to short internal waves.

 

Authors: Unfortunately, we did not find published works on this topic. Basin-scale internal waves in ice-covered lake were studied in [Kirilin et al. 2009], but the authors did not provide data on the possible generation of short internal waves by these basin-scale internal waves. We expanded the Introduction section to mention study [Kirilin et al. 2009]. According to our data, we analyzed only short internal waves. We suggest a resonant mechanism of generation of short internal waves, which results from interaction of barotropic seiches with undulating bottom. This mechanism is similar to tidal conversion in the oceans, and its detailed study is presented in our previous paper [Volkov et al., 2020].

Kirillin, G.; Engelhardt, C.; Golosov S.; Hintze, T. Basin scale internal waves in the bottom boundary layer of ice-covered Lake Müggelsee, Germany. Aquatic Ecology, 2009, 43, 641–651, https://doi.org/10.1007/s10452-009-9274-3

Volkov, S. Yu.; Bogdanov, S. R.,; Zdorovennov, R. E.; Palshin, N. I.; Zdorovennova, G. E.; Efremova, T. V.; Gavrilenko, G. G.; Terzhevik, A. Yu. Resonance Generation of Short Internal Waves by the Barotropic Seiches in an Ice-Covered Shallow Lake. Phys. Oceanogr., 2020, 27(4), 407-422.

Conclusions

Reviewer: What is driving the barotropic seiches?

Authors: We suggest that the barotropic seiches excitation is the result of atmospheric forcing, with following energy path: air pressure disturbances -- wind forcing -- ice cover oscillations – currents in the water. We have expanded the text of the introduction and added references to two papers discussing this mechanism of seiche generation in an ice-covered lake:

Malm J., Terzhevik A., Bengtsson L., Boyarinov P., Glinsky A., Palshin N., Petrov M. Temperature and Hydrodynamics in Lake Vendurskoe during Winter 1995/1996 / Department of Water Resources Engineering, Institute of Technology. University of Lund, 1997. №. 3213. 203 p.

Petrov, M. P.; Terzhevik, A. Yu.; Zdorovennov, R. E.; Zdorovennova, G. E. Motion of Water in an Ice-Covered Shallow Lake. Water Resources, 2007, 34(2), 113-122. DOI: 10.1134/S0097807807020017

We have added a fragment to the text about the reasons for the appearance of seiches in an ice-covered lake

Author Response File: Author Response.docx

Reviewer 2 Report

The study concerns short-term changes in the temperature of the water column in a small and shallow lake located in Karelia. The work is very well documented and the collected research material is impressive. However, I have a few critical remarks and questions about this study: What is new in the presented work in relation to previous research? How can these changes in water temperature translate into the thickness of the ice in the tank or the formation of so-called star patterns? Why is the discussion and introduction so perfunctory?

Why the authors refer to such a small number of other studies (the number of citations is only 32 papers). One could refer, for example, to the study: Choiński, A.; Ptak, M. Variation in the Ice Cover Thickness on Lake Samołęskie as a Result of Underground Water Supply. Limnol. Rev. 2012, 12, 133-138. https://doi.org/10.2478/v10194-012-0053-5

 

and others. Why is there no reference to the location of the research facility among the keywords?

Author Response

Dear Reviewer,

thank you very much for reviewing our study “Short standing and propagating internal waves in an ice-covered shallow lake” (manuscript water-2482713). We are thankful for the thorough consideration of our study and valuable suggestions. We have found your review helpful for promoting our study. Below, we provide the point-to-point responses to questions and remarks, and the description of the corresponding changes in the MS.

Reviewer: The study concerns short-term changes in the temperature of the water column in a small and shallow lake located in Karelia. The work is very well documented and the collected research material is impressive. However, I have a few critical remarks and questions about this study:

What is new in the presented work in relation to previous research?

Authors: Our previous studies, the results of which were published in [Palshin et al., 2018 and Volkov et al., 2020] were based on measurements on two TR-chains located at a fairly large distance from each other - on the order of several hundred meters. In this work, the measurement methodology was changed. We placed TR-chains at a short distance from each other - from 50 to 100 m in 2014 and 4 m in 2016. In this work, data from these TR-chains were analyzed for the first time. The close location of TR-chains helped us to more accurately determine the length of internal waves. The group and phase velocities of propagating waves in an ice-covered lake are estimated for the first time. For the first time, the length of the propagating wave is estimated by joint analysis of TR-chains located at a short distance (4 m).

Reviewer: How can these changes in water temperature translate into the thickness of the ice in the tank or the formation of so-called star patterns? 

Authors: we have added a fragment of text to the Discussion section, where we discuss the possibility of the influence of internal waves on the ice thickness.

Reviewer: Why is the discussion and introduction so perfunctory? Why the authors refer to such a small number of other studies (the number of citations is only 32 papers). One could refer, for example, to the study: Choiński, A.; Ptak, M. Variation in the Ice Cover Thickness on Lake Samołęskie as a Result of Underground Water Supply. Limnol. Rev. 2012, 12, 133-138. https://doi.org/10.2478/v10194-012-0053-5 and others.

Authors: We included some additional topics and references to the discussion in order to present the results in a wider context.

Reviewer: Why is there no reference to the location of the research facility among the keywords?

Authors: Done. We added “temperate zone” to keywords

Author Response File: Author Response.docx

Reviewer 3 Report

This paper focus on the internal waves (IWs) in an ice-covered shallow lake, and presents the estimates of these IW parameters based on data obtained in the winter months of 2014 and 2016 in a small boreal ice-covered lake. Having analyzed horizontally spaced thermistor chain data, the author managed to detect the presence of short standing and propagating IWs, and to estimate their length (from several meters to several tens of meters), and phase and group velocities (from several mm/s to several tens of mm/s). By analyze ΔT in the water column, make conclusion: IW generation events were characterized by a high degree of spatial localization; IW energy was unevenly distributed through the water column. This paper research on the intensity of vertical heat and mass transfer topics, have done a good job on reveal the presence of standing and propagating short IWs in an ice-covered lake; detection of propagating short IWs and specific features of their generation and propagation; assessment of the key parameters of IWs. But there is some confusion about some content in the article. The questions are as follows and are needed to consider to modify them in new version.

Q1: It was shown that IW generation events were characterized by a high degree of spatial localization, and the IW energy was unevenly distributed through the water column. Is this conclusion too concise to describe the core work of this paper?

Q2: Keywords: “small lake and ice-covered period” replaced by “ice-covered shallow lake” will be better?

Q3: The formula in P3 is the first formula in this article but the formula for p4 is (1).

Q4: Typically, ΔT oscillations at different depths occurred in counterphase during a long time period (5-10 hours). Which data or figures in the article are used to make the above conclusions? and give a detailed description.

Q5: The paper presents an analysis of the structure of the temperature field in a small ice-covered boreal lake. A special feature of the 2014 and 2016 winter measurements consisted in the use of several horizontally spaced TR-chains. The main goal was to detect short IWs and estimate their parameters. The Figure 2, Figure 3 and the corresponding description describes the characteristics of ΔT, but seems do not be connected to the main goal or further clarification is lacking?

Q6: The dynamics of temperature fluctuations in near-bottom layers (at 5.5 m depth) on all four TR-chains in 2016 is shown in Figure 8a. At a first glance, the signals seem to be correlated for 3 out of 4 TR-chains. However, a more detailed analysis of the ΔT series at a higher time resolution shows that the signals are not identical for different TR-chains (Figure 8b). As a reader feel Figure 8b seems have the same conclusion: the signals seem to be correlated for 3 out of 4 TR-chains? so please describe the differences in detail.

Q7: Internal waves, especially basin-scale ones, often represent the most vigorous flows in stratified lakes, being the driving force for horizontal and vertical mixing. This paper obtains a lot of temperature data through TR-chain, analyzes its characteristics and evaluates the key parameters of IWs. Is it necessary to explain how IWs causes the above temperature characteristics to further confirm the accuracy of IWs revealed in this paper?

N/A

Author Response

Dear Reviewer,

thank you very much for reviewing our study “Short standing and propagating internal waves in an ice-covered shallow lake” (manuscript water-2482713). We are thankful for the thorough consideration of our study and valuable suggestions. We have found your review helpful for promoting our study. Below, we provide the point-to-point responses to questions and remarks, and the description of the corresponding changes in the MS.

Reviewer: This paper focus on the internal waves (IWs) in an ice-covered shallow lake, and presents the estimates of these IW parameters based on data obtained in the winter months of 2014 and 2016 in a small boreal ice-covered lake. Having analyzed horizontally spaced thermistor chain data, the author managed to detect the presence of short standing and propagating IWs, and to estimate their length (from several meters to several tens of meters), and phase and group velocities (from several mm/s to several tens of mm/s). By analyze ΔT in the water column, make conclusion: IW generation events were characterized by a high degree of spatial localization; IW energy was unevenly distributed through the water column. This paper research on the intensity of vertical heat and mass transfer topics, have done a good job on reveal the presence of standing and propagating short IWs in an ice-covered lake; detection of propagating short IWs and specific features of their generation and propagation; assessment of the key parameters of IWs.

Authors: Thank you for appreciating our research.

Reviewer: But there is some confusion about some content in the article. The questions are as follows and are needed to consider to modify them in new version.

Q1: It was shown that IW generation events were characterized by a high degree of spatial localization, and the IW energy was unevenly distributed through the water column. Is this conclusion too concise to describe the core work of this paper?

Authors: We are not sure, that we understood the question correctly. Indeed, the uneven distribution of IW energy through the water column is one of the results of the paper, but not the only one. Our previous studies, the results of which were published in (Palshin et al., 2018 and Volkov et al., 2020) were based on measurements on two TR-chains located at a fairly large distance from each other - on the order of several hundred meters. In this work, the measurement methodology was changed. We placed TR-chains at a short distance from each other - from 50 to 100 m in 2014 and 4 m in 2016. In this work, data from these TR-chains were analyzed for the first time. The close location of TR-chains helped us to more accurately determine the length of internal waves. The group and phase velocities of propagating waves in an ice-covered lake are estimated for the first time. For the first time, the length of the propagating wave is estimated by joint analysis of TR-chains located at a short distance (4 m).

Reviewer: Q2: Keywords: “small lake and ice-covered period” replaced by “ice-covered shallow lake” will be better?

Authors: We agree: the “shallow ice-covered lake” is more appropriate as key word; lake shallowness (against the smallness) here is more correct as far as the applicability of the results is concerned.

Reviewer: Q3: The formula in P3 is the first formula in this article but the formula for p4 is (1).

Authors: We moved the formula in P3 to the text.

Reviewer: Q4: Typically, ΔT oscillations at different depths occurred in counterphase during a long time period (5-10 hours). Which data or figures in the article are used to make the above conclusions? and give a detailed description.

Authors: Indeed, by analyzing the temperature series for each chain separately, we found that temperature oscillations were rather complicated, but during long time periods at some depths occurred in counter phase. The corresponding curves for depths 3 m and 5 m at station 1 on January 30, 2016 are presented on the Figure below. This Figure format is the same, as for Figures 5_new and Figure 6_new, which present the counterphase nature of oscillations for some sensors at different chains. In turn, Figure 3_new presents the temperature dynamics for individual chains, but for all depths; we regard this way of presentation as more illustrative for individual chain.

Reviewer: Q5: The paper presents an analysis of the structure of the temperature field in a small ice-covered boreal lake. A special feature of the 2014 and 2016 winter measurements consisted in the use of several horizontally spaced TR-chains. The main goal was to detect short IWs and estimate their parameters. The Figure 2, Figure 3 and the corresponding description describes the characteristics of ΔT, but seems do not be connected to the main goal or further clarification is lacking?

Authors: We split the data analysis by two parts. Namely, the data were first processed for each TR-chain separately. The main results of this first stage of analysis include the revealing of:

• Highly heterogeneity of temperature oscillations amplitudes in depths; layering of the water column.
• Long episodes with counterphase oscillations at different depths.

As mentioned in the text, these both features are typical for standing internal waves and may serve as the markers of IWs presence and instrument of IWs detecting. Moreover, the relatively small period of temperature oscillations (~ 27 min.) indirectly indicates that these waves are short, as compared to the basin-scale ones.

On the other hand, the alone chain as instrument is not quite appropriate for estimates of IWs parameter, especially wavelength; some horizontally separated chains are necessary. These data were used in the second part of the analysis.

Reviewer: Q6: The dynamics of temperature fluctuations in near-bottom layers (at 5.5 m depth) on all four TR-chains in 2016 is shown in Figure 8a. At a first glance, the signals seem to be correlated for 3 out of 4 TR-chains. However, a more detailed analysis of the ΔT series at a higher time resolution shows that the signals are not identical for different TR-chains (Figure 8b). As a reader feel Figure 8b seems have the same conclusion: the signals seem to be correlated for 3 out of 4 TR-chains? so please describe the differences in detail.

Authors: For both panels the signals are correlated as far as diurnal dynamics is concerned. But the disturbances which generate IWs have much shorter time intervals. For such intervals the correlation is practically absent; at least the largest surges on different chains, which are presumably responsible for IWs generation, are observed at different time moments. To make effect more visual, we shortened the time interval on Figure 9b_new.

Reviewer: Q7: Internal waves, especially basin-scale ones, often represent the most vigorous flows in stratified lakes, being the driving force for horizontal and vertical mixing. This paper obtains a lot of temperature data through TR-chain, analyzes its characteristics and evaluates the key parameters of IWs. Is it necessary to explain how IWs causes the above temperature characteristics to further confirm the accuracy of IWs revealed in this paper?

Authors: Internal waves are characterized by very significant displacements of liquid particles along the vertical, and the indicator of these displacements in a stratified medium is the temperature variations revealed by us over time.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

thank you very much for reviewing our study “Short standing and propagating internal waves in an ice-covered shallow lake” (manuscript water-2482713). We are thankful for the thorough consideration of our study and valuable suggestions. We have found your review helpful for promoting our study. Below, we provide the point-to-point responses to questions and remarks, and the description of the corresponding changes in the MS.

Reviewer:

The paper presents a study on standing and propagating internal waves in ice covered lakes and their relevance to heat transfer mechanisms and energy distribution through the water column. The study is based on filed measurements, and their thorough analysis, taken from a relatively small boreal lake. The measurements period spans the winter months of two years, namely 2014 and 2016. The paper is well written and within the scope of the issue. The analysis and discussion are thorough, and the conclusions are in general supported by the data.

Authors: Thank you very much for your appreciation of our research.

Reviewer: A few more comments on the natural frequencies of the ice-covered basin could have been included in the analysis. In the case of standing waves, the location of nodes is of major importance, since these locations are associated with increased horizontal velocities (see e.g. Alexander B. Rabinovich, Seiches and Harbor Oscillations, Handbook of Coastal and Ocean Engineering (edited by Y.C. Kim), World Scientific Publ., Singapoure, 2009). Stations placed at such locations could therefore lead to measurements indicative of these increased velocities during seiche formation. There exist in the literature models and solution methodologies (semi-analytical, Finite Elements) for the determination of eigenfrequencies and eigenmodes of ice-covered basins, e.g. Sturova, I.V., 2007. Effect of ice cover on oscillations of fluid in a closed basin. Izv. Atmos. Ocean. Phys. 43 (1), 112–118. Papathanasiou, T.; Belibassakis, K. A nonconforming hydroelastic triangle for ice shelf modal analysis. Journal of Fluids and Structures 2019, 91, 102741.  Have the authors considered such an analysis for the specific basin in order to locate the nodal lines for different layouts of the ice-cover? In particular, it has been shown in [Papathanasiou, T.; Belibassakis, K. Resonances of enclosed shallow water basins with slender floating elastic bodies, Journal of Fluids and Structures 2018, 82, 538–558.] that the presence of the ice-cover, although not significantly altering the eigenfrequencies, can influence the eigenmodes and therefore the location of the nodes and anti-nodes of the basin.

Authors: We are grateful to the Reviewer for providing valuable references and we added a discussion of this important issue - the choice of measurement points in the presence of seiches in the lake. In our study, when choosing measurement points, we did not rely on a preliminary analysis of the position of the bonds and antinodes of the barotropic seiche, but in future studies we will fill this gap.

Reviewer: Final proof reading of the manuscript to correct some typos, although they are very minor, e.g. In reference 4, ‘Dynamics of mixed bottom boundary layers’

Authors: Thank you. Fixed.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The work has been supplemented (including literature) and corrected and can be published in the current version.