the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Nov 2024
Buoy measurements of strong waves in ice amplitude modulation: a signature of complex physics governing waves in ice attenuation
Abstract. The Marginal Ice Zone (MIZ) forms a critical transition region between the ocean and sea ice cover as it protects the close ice further in from the effect of the steepest and most energetic open ocean waves. As waves propagate through the MIZ, they get exponentially attenuated. Unfortunately, the associated attenuation coefficient is difficult to accurately estimate and model, and there are still large uncertainties around which attenuation mechanisms dominate depending on the conditions. This makes it challenging to predict waves in ice attenuation, as well as sea ice breakup and dynamics. Here, we report in-situ observations of strongly modulated waves-in-ice amplitude, with a modulation period of around 12 hours. We show that simple explanations, such as changes in the incoming open water waves, or the effect of tides and currents and bathymetry, cannot explain for the observed modulation. Therefore, the significant wave height modulation observed in the ice most likely comes from a modulation of the waves-in-ice attenuation coefficient. To explain this, we conjecture that one or several waves-in-ice attenuation mechanisms are periodically modulated and switched on and off in the area of interest. We gather evidence that sea ice convergence and divergence is likely the factor driving this change in the waves in ice attenuation mechanisms and attenuation coefficient, for example by modulating the intensity of floe-floe interaction mechanisms.
Status: open (until 26 Dec 2024)
-
RC1: 'Comment on egusphere-2024-2619', Anonymous Referee #1, 09 Dec 2024
reply
General comments:
This manuscript presents unique observations of ocean wave attenuation in sea ice, in which the attenuation is modulated on a 12-hour cycle. The increased attenuation coincides with sea convergence driven by tidal and/or inertial currents. The observations are clearly documented, including contextual information on sea ice and oceanographic conditions. The manuscript carefully presents and evaluates different hypotheses for the underlying mechanisms, before concluding [cautiously] that the increased attenuation arises from floe-floe interactions during ice convergence.
I find the analysis herein to be rigorous, and I am fully convinced that the observed changes in the waves are related to changes in the sea ice. That said, I have recommendations for major reorganization of the work and reframing of the results. I think the attenuation estimates should be the very first part of the results (and thereby more central to the paper). I think the wave-current analysis and “extra” hypotheses should be evaluated after the sea ice mechanism is evaluated, possibly as appendices or discussion material. It is important to retain this material and show that currents cannot explain the observed modulation, but in the present form the ‘reader-fatigue’ from this material undermines that impact of the attenuation results.
Once the attenuation estimates are more central in the paper, the results can be reframed to acknowledge that small changes in attenuation rate make big differences in wave observations over long propagation distances. Thus, the observed factor of 10 modulation in significant wave height (SWH) from 0.03 to 0.33 m arises from a mere factor of 2 modulation in the attenuation rate. In the context of prior waves-in-ice studies, this a very modest change in the attenuation rate. For example, Rogers et al 2016 (DOI:10.1002/2016JC012251) find similar changes that occur simply from differences in the shape and maturity of pancake ice floes. Other studies find that a factor of 2 change in the attenuation rate can occur between the compact edge of the marginal ice zone and the more diffuse interior (Hosekova et al 2020, DOI: 10.1029/2020JC016746). With this in mind, I disagree that with the interpretation that the convergence of the sea ice "switches on" a new mechanism related to floe-floe interactions (collisions, etc). Rather, I think that convergence of sea ice causes subtle changes in sea ice concentration and/or thickness (through volume conservation), and that causes an increase the attenuation rate. The increases might be reasonably well-described by existing parameterizations (Meylan et al, 2018, DOI: 10.1002/2018JC013776; Rogers et al 2018, NRL/MR/7320--18-9786). Those existing parameterizations have tuning parameters that are not tested here, so we cannot say whether new formulations are required.
Specific comments:
The introduction could be a bit more more careful not to overstate the ongoing buoy revolution. Certainly, more and more buoys are being developed and deployed (and this is great). Of the nine OMBs deployed for this study, only a few ended up in the analysis. We should humbly remember that works like Doble et 2006 (DOI: 10.3189/172756406781811303) deployed almost as many buoys 20 years ago, with similar capabilities.
Fig 2 shows clear the modulation of the wave spectra within the sea ice. The next logical step to compare with prior studies is to calculate the spectral attenuation rates (and then explore how this is modulated on the 12-hr cycle). In present form, that does not occur until page 31, and even then it is only a bulk attenuation rate. A spectral calculation might reveal more physics, including exploring the power laws described by Meylan et al 2018. If the goal of the paper is to show the cyclic convergence of sea ice changes wave attenuation, then please calculate the attenuation!
The work to show that currents and other non-ice mechanisms are insufficient to explain observations is very thorough, but it is almost a distraction. It's pretty clear from buoy 200913 that there is not modulation near the ice edge. So it’s not the incident wave field that is changing. In particular, the historic/statical open-water wave analysis would be better placed in an appendix.
Bottom of p 27: the statement that the CICE model used as input to the wave-current-ice ("WCI") model results reproduces the "time dynamics of the sea ice cover" is not supported in a quantitative way. Does CICE reproduce the convergence and divergence calculated from the buoys (Figure 3)? More broadly, the tone of this section is “well, the WCI model does not show the modulation, so a new mechanism must be needed”. My alternate interpretation is that the WCI model has ice damping parameters that could be tuned for convergence of sea ice (increasing concentration, thickness, or both). Figure 5 shows that sea ice concentration is very high at buoy 19648, but it is not 100%. Convergence could cause it to increase.
Bottom of p29: the literature is pretty clear that ice floes do not follow the waves in "synchronization" but rather they slide down-slope on the face of the waves and have 'added mass' that introduces phase changes. Thus, they definitely collide. See Shen et al 1987 (DOI: 10.1029/JC092iC07p07085) and also Herman et al (JGR, 2018). Also the Smith and Thomson 2020 stereo work (already cited in the intro).
Technical corrections:
The lack of line numbers in the PDF is frustrating.
The usage of a hyphenated ‘waves-in-ice’ or simply ‘waves in ice’ is not very consistent. I suggest the convention of hyphenation when the phrase is used as an adjective (e.g., “waves-in-ice physics are estimated”) and no hyphen when used as a noun (e.g., “waves in ice are measured…”)
Top of p3: it is the *gradients* in wave radiation stress that transfer momentum to the ice and water. Without gradients, the radiation stress is simply an ongoing flux of momentum (but no transfer).
Top p3: another recent fetch study is Brenner and Horvat (2024): https://doi.org/10.1029/2024JC021629
P 11: The inclusion of possible temperature modulation (and associated changes in sea ice rheology) is a good point, but evaluating with ERA5 seems like a poor match to the task. ERA5 would probably only show temperature changes if it also had modulation sea ice, which it does not. Surely the CICE model employed herein has temperatures?
Citation: https://doi.org/10.5194/egusphere-2024-2619-RC1 -
RC2: 'Comment on egusphere-2024-2619', Anonymous Referee #2, 20 Dec 2024
reply
The manuscript describes a detailed analysis of an observed wave event in the Arctic MIZ via wave buoy measurements that exhibits a large amplitude modulation over a period of 3 days in the Spring of 2021. The 12-hour modulation period strongly points towards an effect of currents/tides. A wide range of datasets are then used to test this hypothesis. The main finding is that currents and tides alone cannot fully explain the magnitude of the observed modulation and that processes related wave-ice interactions are likely the main cause of this effect. In particular, a periodic switch between ice drift convergent and divergent regimes, which leads to stronger vs weaker ice-induced wave attenuation, respectively, is most likely what explains the modulation. A discussion of the physical mechanisms that can cause wave attenuation in ice-covered seas leads the authors to conclude that an on-off switch of floe-floe interactions, e.g. inelastic collisions and hydrodynamic pumping, could explain these alternating wave attenuation regimes.
Overall, the manuscript is reasonably well written and most conclusions are well supported by evidence. Discussions of limitations and uncertainty are also well incorporated. My main criticism relates to the style of writing, which is (i) quite informal in places and (ii) not efficient, with a lot of repetitions and general lack of conciseness. This makes the paper unnecessarily long in my opinion, which in turn deteriorates the reading experience. Therefore, I strongly suggest that the many authors of this paper have a critical look at the writing and attempt to be more concise in presenting their arguments. This is the main reason why I recommend major revisions. More details and suggestions are provided in my comments below.
Main comments:
- p2: I find the list of references given for the different sources of wave attenuation by sea ice and sea ice breakup to be somewhat biased and missing key papers, especially from key contributors like Squire, Meylan, Bennetts, Montiel, etc. Some suggestions: Mosig et al (2015) for viscoelasticity; Kohout and Meylan (2008), Montiel et al (2016), Pitt and Bennetts (2024) for scattering; Montiel and Squire (2017), Mokus and Montiel (2022) for breakup. In addition, I fail to see the distinction between diffraction and scattering in this context. The paper by Zhao and Shen develops a diffusion approximation from a scattering model in a specific regime and is not really representative of the research on wave scattering in the MIZ.
- I think section 3 is too long and redundant. I understand the authors want to cover their bases, but I think the analysis done in section 3.2 is sufficient to demonstrate that wave-current interactions alone is not enough to explain the observed modulation. Sections 3.1 and 3.3 add very little to the paper in my opinion. My advice would be to focus on the results of section 3.2 and briefly mention that other lines of evidence though ray tracing analysis and altimeter data in open water support the conclusions. Maybe 3.1 and 3.3 could be included as a supplement or appendix if the authors think they are important. In it's current form, I don't see the added value of having them in the main text.
- In section 4, I think the discussion of all physical processes that could explain the observed modulation is not that convincing. Sea ice convergence/divergence will change ice concentration locally, but many processes are likely to damp waves more in tightly pack ice compared to loose ice, including scattering (due to array effects), turbulence and yes also floe-floe interactions. I think this section does not need to be that long, as what it mostly says is that waves are attenuated more in tighter ice packs.
- I think the discussion of the paper is missing an analysis of what is causing convergence/divergence regime shift in the ice drift. I imagine this currents and tides, but I don't think the point has been made sufficiently clear. This means that currents and tides are responsible indirectly, i.e. through their effect on the ice, on the observed modulation. If that's indeed the case, why is this not a more common feature observed in other datasets? Have the authors looked at other students showing SWH time series to see if a similar modulation is seen?
Other comments:
- p3, last sentence: This sentence is hard to read and could be worded better.
- Fig 1: It is not clear which of the buoys on the left panel are selected for the SWH data shown on the right panel. Do the colours of the tracks and curves match? If so, why is there no black dot on the orange track?
- p7: "As visible there ..." -> that is not obvious to me. How can we make out the MIZ in this image and where are the BOIs at the time of the image?
- Fig 4: It is clear which tracks correspond to the BOIs. Also I count more than 9 tracks, even though it was mentioned earlier that 9 buoys were deployed.
- p8: The discussion of Fig 5 should probably guide the reader towards the conclusion made. It is not clear at all to me that ice floes around the BOIs have similar size to the wavelength. Are dark patches open water? If so, in panel (d) it seems to be the other way around.
- Fig 5: annotations on each panel are too small.
- p11: The wave attenuation model used by Yu et al (2022) is not a common choice. Could this choice be better explained? The empirical model was obtained by fitting data obtained in the Southern Ocean Autumn, likely with a lot of pancake ice, so probably very different ice conditions compared to the Arctic Spring.
- Eqs (7), (8), (9): mathematical notations are quite poor in all these equations. Usually successive letters in italic denotes the product of the quantities denoted by the corresponding letters, so for instance $SWH$ actually means S*W*H. Grouping letters together to denote a single quantities is usually done by using roman font type.
- p27, penultimate sentence: This statement assumes that the ice-induced wave attenuation model used captures properly the dependence on thickness and concentration. I don't think this has been verified.
- p28, second paragraph: I don't understand why refraction, reflection and diffusion are used instead of the more general term "scattering". Also, overwash should be mentioned as a dissipative process, noting that it doesn't fit into the categories listed. Further, scattering does not just depend on floe geometry. There are also array effects (multiple scattering), so the response (including attenuation) will change if floes are loosely or tightly packed, as could be expected in a divergent or convergent ice drift regime, respectively. Therefore, I'm not sure scattering should be dismissed so easily.
- p28, 3rd paragraph: Viscoelasticity is interesting as it has been used to explain attenuation in homogeneous ice cover as well as highly inhomogeneous ice covers. In the latter case, viscoelasticity is of course not the process that causes attenuation, but a convenient effective model for wave damping by sea ice. It the present case, where the ice field seems to be broken up into floes, i.e. non homogeneous, I agree viscoelasticity is likely to not be the dominant physics explaining wave attenuation. I don't think changes in Young's modulus or temperature is the main argument against viscoelasticity.
- p28/29: I think the discussion on collision based on reviews from a different paper is out of place. I'm sorry to hear the authors had a difficult reviewing experience in the past, but I don't think the present manuscript is the place to settle scores. Collision studies have been conducted, at least in the lab, so why not just refer to those, e.g. Bennetts and Williams (2015).
Citation: https://doi.org/10.5194/egusphere-2024-2619-RC2
Viewed
Since the preprint corresponding to this journal article was posted outside of Copernicus Publications, the preprint-related metrics are limited to HTML views.
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 91 | 0 | 0 | 91 | 0 | 0 |
- HTML: 91
- PDF: 0
- XML: 0
- Total: 91
- BibTeX: 0
- EndNote: 0
Viewed (geographical distribution)
Since the preprint corresponding to this journal article was posted outside of Copernicus Publications, the preprint-related metrics are limited to HTML views.
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1