Laboratory Investigations of Iceberg Melting under Wave Conditions in Sea Water

Round 1

Reviewer 1 Report (Previous Reviewer 2)

This study conducted the laboratory experiments on the melting of icebergs in sea water under calm and rough conditions. The author using experimental data calculated the horizontal dimensions of icebergs, latent heat fluxes, conductive heat fluxes inside model icebergs, and turbulent heat fluxes in water as a function of time. And discovered the influence of surface waves and water mixing on melt rates and found significant reduction in melt rates due to the lateral protection of the iceberg model by a plastic barrier. This research result has certain significance for the evaluation and prediction of iceberg melting. Followings suggestions still need to be improved:

 As shown in Figure 8, the changes of iceberg shapes with time, does the iceberg shapes obtained from time Lapse camera consider the refraction of light in the water body. The author needs to provide an explanation for the accuracy of their shooting dimensions

Author Response

Thank you for the review.

We have added the following clarification regarding the use of time laps images in lines 484-487:

Time lapse images were used to reveal the shape changes and particular form appearance. For measurement of height keeping in mind the refraction of light in the water body, we made corrections by measuring initial and final parameters of samples on the table/air.

Reviewer 2 Report (Previous Reviewer 3)

Not being a specialist in glaciology, I appreciate all the more the rigor of the approach adopted by the authors as well as the extent of the work carried out.

I think this article will be of interest to the readership of jmse as well as other climate and environment-oriented journals, because it provides a serious documentary basis on the melting of icebergs in the context of climate change.

Author Response

Thank you for the review. 

Reviewer 3 Report (New Reviewer)

Eight laboratory experiments were carried out in this study, analyzing the melting of icebergs in sea water under calm and rough conditions. The authors discovered the influence of surface waves and water mixing on melt rates and found a significant reduction in melt rates due to the lateral protection of the iceberg model by a plastic barrier. This provides a useful reference for more simulation and research on iceberg melting in the Arctic and Antarctic. However, there are different points of the paper that require some explanation from the authors, and I do have some feedback that can be used to improve the paper:

1. The abstract needs to add some information about why the research is being done and what it means to do the research.

2. What is the purpose of the first half of the introduction about describing the icebergs in the Barents Sea? Is there any relationship with the design of the laboratory simulation in this study?

3. Lines 60-61, “Therefore, we assume that bending failure is a relatively rare phenomenon in the Bar-60 ents Sea.” What is the relationship between this viewpoint of the study and the experimental simulation?

4. Lines 104-110, how are these numbers determined? For example, 3.5m, 30cm, 33.5 ppt, 32cm, 15cm, 24cm.

5. Table 3 can be shown more intuitively in the form of a Figure.

6. The conclusion lacks prospects for this study.

Author Response

Thank you for the review. The following changed were made in the paper according to the reviewer's comments

1. The abstract needs to add some information about why the research is being done and what it means to do the research.

The following lines were added in the abstract

Lines 8-9: Changes in the mass of icebergs due to deterioration processes affect the drift of icebergs and should be taken into account when assessing the iceberg risks in the areas of offshore development

Lines 22-24: Based on the experimental data obtained, the ratio of the rates of lateral and bottom melting of icebergs and lateral melting of icebergs under wave conditions was parametrized depending on the wave frequency.

2. What is the purpose of the first half of the introduction about describing the icebergs in the Barents Sea? Is there any relationship with the design of the laboratory simulation in this study?

In the introduction we describe different physical phenomena leading to the deterioration of icebergs. In our study we focus on the study of deterioration of relatively small icebergs in the Barents Sea caused by the melting. The sizes of icebergs in the Barents Sea are given in Lines 32-35. In Lines 101-104 of the Introduction we added:

This paper describes the results of laboratory experiments on the melting of model icebergs floating in sea water under rough conditions. In accordance with geometrical similarity, the sizes of model icebergs and wave frequencies correspond to the sizes of icebergs and the frequencies of swell and wind waves in the Barents Sea.

Another task of the paper is to study the bottom melting of icebergs. Formula derived by Weeks and Campbell [23] determines melting rate proportional to the difference of the iceberg velocity v_1 and water velocity v_w. We write in Lines 75-79: The use of this formula runs into problems when the iceberg drifts with surrounding water. In this case v_w is determined by the movement of melt water in the boundary layer and must be found from the solution of the boundary layer problem. The rocking of icebergs caused by waves also affects the movement of water relative to the surface of icebergs.   

3. Lines 60-61, “Therefore, we assume that bending failure is a relatively rare phenomenon in the Bar-60 ents Sea.”What is the relationship between this viewpoint of the study and the experimental simulation?

In Section. 3 Scaling we clarify in Lines 215-219:

We assume that the scaling factor changes in the range . This corresponds to the vertical dimensions of icebergs in full scale from 12 m to 60 m with a vertical height of a model iceberg of 15 cm. Accordingly, the radii of icebergs in full scale vary in the range from 10 m to 50 m, when the radius of a model iceberg is 12 cm. Full-scale dimensions correspond to typical sizes of icebergs in the Barents Sea  

and in Lines 246-250:

Figure 4 shows the full-scale periods and amplitudes of waves calculated with model wave periods measured in the experiments versus the geometrical scaling factor (Table 1). Full-scale periods varying from 4 s to 15 s correspond to periods of wind waves and swell. Full-scale amplitudes are within the typical values of swell and wind waves amplitudes in the Barents Sea [15].

4. Lines 104-110, how are these numbers determined? For example, 3.5m, 30cm, 33.5 ppt, 32cm, 15cm, 24cm.

Dimensions of the ice tank are technical characteristics of the equipment used in the experiments.  We added in Section 6. Discussion:

The equipment used in the experiments imposed a number of restrictions on the range of studied dependencies and phenomena. The experiments were carried out in a narrow wave tank, the dimensions of which corresponded to the size of cold laboratory at UNIS.

Dimensions of model icebergs where chosen according to the geometrical scaling of icebergs in the Barents Sea.

5. Table 3 can be shown more intuitively in the form of a Figure.

Dependencies of iceberg masses and height on time were added in Fig. 10.

6. The conclusion lacks prospects for this study.

Description of prospects for the study was added to Section 6. Discussion in Lines 827-838:

The equipment used in the experiments imposed a number of restrictions on the range of studied dependencies and phenomena. The experiments were carried out in a narrow wave tank, the dimensions of which corresponded to the size of cold laboratory at UNIS. Technical difficulties associated with the design of the wavemaker did not allow generating waves of small amplitudes. The walls of the tank influenced the interaction of waves with icebergs. The small size of icebergs imposed restrictions on the wave amplitudes, since as the wave amplitudes increased, water splashed onto the surface of the icebergs, significantly changing the rate of ice melting. At the same time, the range and quality of the research carried out can be improved through more detailed control of the iceberg shape using 3D laser scanning and photogrammetry, measurement of iceberg accelerations, visualization of the movement of melt water in the boundary layer, and more accurate measurement of wave amplitudes.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The melting process of iceberg is very important to determine the thermo, even dynamics of iceberg under nature conditions. In this study, the melting characteristics of iceberg were investigated with several physical experiments. During the experiments, iceberg masses, water temperatures, and ice temperatures were measured. Water velocities near model icebergs were also measured well. Based on the physical experimental data, the effects of surface waves and turbulence on the melting rate were investigated.

Some comments and suggestions are listed below for consideration.

1. In the tittle of this manuscript, the influence of wave can be mentioned.

2. In the physical experiments, the cylinder shaped iceberg model was adopted. In fact, the iceberg shape is irregular under nature conditions. Meanwhile, the melting process of real iceberg is quite complex. Please discuss the limitation of this model test for iceberg melting.

3. In Eq.(7), the melting rate and heat fluxes of iceberg are assumed as uniform for the lateral and bottom surfaces. But after melting, the shape of iceberg model becomes irregular. Does this equation can be suitable to calculate the melting rate?

Reviewer 2 Report

This study conducted the laboratory experiments on the melting of model icebergs floating in seawater in calm conditions and in wave conditions. The author is using the experimental data calculated the horizontal dimensions, the latent heat fluxes, the conductive heat fluxes inside the model icebergs and the turbulent heat fluxes in the water versus time. However, due to shortcomings in the experimental design, the results and conclusions need to be further validated. The authors could do much better job on analyzing and presenting the data before publishing. Followings suggestions still need to be improved:

1. In lines 126-127, ‘The accuracy and resolution of temperature measurements with FBG sensors are respectively 0.4°C and 0.08°C’. The accuracy of the sensors used is too low, which will result in inaccurate measurement of temperature changes inside the ice.

2. The mass of ice is measured by volume, and its accuracy needs to be provided.

3. Inaccurate measurement of ice temperature and volume will lead to meaningless analysis of parameters such as heat flux and melting rate.

4. The performance of the images listed in the article is not ideal, such as in Figures 13, 14, 18, 19.

Reviewer 3 Report

Dear Editor, dear Authors

The paper concerns laboratory experiments on iceberg melting in seawater with temperatures varying in calm and wave conditions.

But this purely metrological study, although carried out with great rigor, is insufficient to justify its publication in the Journal of Marine Science and Engineering for the following reasons:

1)      Laboratory experiments do not include bubble release effect.

2)      Laboratory results should be scaled to ice walls and iceberg length.

3)      The study should show what is new in understanding and estimating the melting of icebergs in real conditions after extrapolation of laboratory results. In order not to remain purely academic, the study should provide new elements to overcome the difficulties of moving from the laboratory scale to the real scale, which is limited by the free convection of sea water in the vicinity of the iceberg and by stratification.

In a nutshell, what quantifiable contribution does the study bring compared to what was established a good forty years ago?

I think that significant work remains to be done to interest a wide readership before resubmitting the manuscript.

Minor recommendations:

Line 170: the reference [33] relative to the added mass coefficient is not sufficient. Could you explain in one sentence what is the meaning of ?

Line 197: were higher than the natural frequency

Figure 4: clarify how  is in relation to .

Line 246: Is  the effective surface?

What is  in (7)?

Line 281: 2.22 Wm −1 °C −1 or 2.22 W/m °C, replace C by °C wherever it is needed.

Comments for author File: Comments.pdf