the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Dec 2025
Observations of high-frequency spectral peaks from in-situ waves in ice data: evidence for nonlinear waves in ice triad interactions?
Abstract. The propagation of waves through the marginal ice zone (MIZ) and deeper into pack ice is a key phenomenon that influences the breakup and drift of sea ice. Waves in ice propagation can be characterized by the associated dispersion relation, which describes both the speed and wavelength of the waves and their attenuation. When waves in ice propagate through a solid, non-cracked, thick enough sea ice cover, significant flexural elastic effects can be present in the dispersion relation. This results in a dispersion relation that opens up for 3-wave interactions, also known as wave triads.
Here, we report the observation of high-frequency spectral peaks in the power spectral density of waves in ice spectra. We show, in two timeseries datasets, that the presence of these high-frequency peaks is accompanied by high values for the spectral bicoherence. This is a signature that the high-frequency peak is phase-locked with frequency components in the main spectral energy peak, and a necessary condition for nonlinear coupling to take place. Moreover, we show for a timeseries dataset that includes several closely located sensors that the dispersion relation recovered from a cross-spectrum analysis is compatible with the possible existence of wave triads at the same frequencies for which the bicoherence peak is observed. In addition to these observations in timeseries datasets, we show that similar high-frequency peaks are observed from additional, independent datasets of waves in ice power spectrum densities transmitted over iridium from autonomous buoys.
These results suggest that nonlinear energy transfers between wave in ice spectral components are likely to occur in some waves and sea ice conditions. This may enable redistribution of energy from weakly damped low-frequency waves to more strongly attenuated higher-frequency spectral components, which can contribute to energy dissipation in the ice. However, more data are needed to offer definite conclusions about the practical importance of this effect in real-world conditions. We suggest several in-situ measurements, numerical investigations, and laboratory experiments to further investigate these phenomena.
Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-4748', valentin resseguier, 04 Feb 2026
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RC2: 'Comment on egusphere-2025-4748', Anonymous Referee #2, 17 Mar 2026
Review of manuscript “Observations of high-frequency spectral
peaks from in-situ waves in ice data: evidence for nonlinear
waves in ice triad interactions?” by Rabault et al.The manuscript analyzes several sets of observations of waves in
the Arctic, notes the occurrence of secondary high frequency
peaks in the power density spectrum and investigates their
relationship to 3-wave nonlinear interactions.To follow TC review criteria:
Originality (novelty: does the manuscript represent substantial
progress beyond current scientific understanding (new insight,
concepts, methods, or data?). Good.I cannot judge whether the study represents "substantial
progress" in unerstanding wave dynamics in the cold regions. The
concept of hierarchichal nonlienar wave interactions is quite old
(mid 20th century) and rather well understood in the context of
the non-frozen ocean. It is natural to ask this question in the
frozen ocean environment.Scientific quality (rigour; purpose clearly articulated, adequate
methodology, compellingly underpinned by the evidence presented;
methods and techniques valid and suitable? discussion appropriate
and balanced way). Fair.1. The goal of the analysis is not clearly formulated. If the
question is whether there is evidence of 3-wave interactions, in
my opinion, for the data set that has some bicoherence analysis,
the bicoherence maps give a clear answer "yes". They exhibit is a
typical 3-wave phase coupling of the peak - second harmonic kind
embedded in an overall linear wave field. The other data sets
show perhaps similar peaks and it is tempting to call these
nonlinear interactions (the 3-4 peaks in figs 8-9 are
intriguing). But without a phase coupling measure, these could
just be independent wave fields. However, the authors seem to be
looking for more, i.e, resonant 3-wave interactions. in other
words, an exact match of frequencies and wavenumbers (eqs. 3).
Resonances are always of interest because in the long time limit
the effect of non-resonant interactions vanishes. But the long
time limit is an abstraction; unless waves are propagating on an
infinite homogeneous ocean, every interaction has its scales of
transience. Analyzing 3-wave interaction based on the resonant
model begs the question: what are the scales on inhomogeneity
relevant to waves in icy waters? I could not find much discussion
about this question. Wave periods (spectral peaks) shown vary
from 6 s to more that 15 s (figs 1 and 9). Are the conditions
homogeneous for large enough spatial scales to justify
resonances? Strong enough disspation is enough to detune
resonances.2. Data description is inadequate. This is supposed to be an
analysis ow wave fields that propagate in a very peculiar
environment. Where where these measurements taken? Please give
maps, locations of instruments, type of instruments. using
cross-spectra and phase lags to estimate wavenmbers might be fine
where wave numbers are well defined (homogeneous conditions), but
its, a crude estimate otherwise. The spectral, cross-spectral,
and bispectral analysis are superficial: no information about
error estimates, bandwitdhs etc. the authors seem intrigued by
the bicoherence “blob”. We they expecting delta function phase
correlations?3. The discussion of the effect of the interactions suggests an
underlying “energy cascade” idea, e.g., “These may be a signature
of the energy that is being "stolen" from the main peak and
transferred into the high-frequency peak by the triad
interactions.” This kind of description makes sense in the
infinite, homogeneous, non-dissipative ocean, that has a well
defined inertial range. Is there such a thing here? if there is,
where is the evidence?Significance (impact - contribution to substantial scientific
understanding; new practical applications of broad relevance?)
Fair.Please see above; Concepts are old and misapplied. Might be
relevant, but the manuscript does not make this point clearly.Presentation quality (results and conclusions clear, concise, and
well-structured; number and quality of figures/tables,
appropriate use of English language) Fair. (see above)Citation: https://doi.org/10.5194/egusphere-2025-4748-RC2
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- 1
The authors analyze experimental data of sea-ice waves in order to diagnose the possible existence of triad interactions. After preprocessing, analyses are based on cross-spectra, bicoherence, and triad diagrams.
The paper is interesting, although it seems a bit lengthy to me. The signal processing analysis is rigorous and instructive. From my background, I cannot evaluate the experimental side nor the possible impact on the community interested in waves in ice.
I would recommend publication after some revisions:
Typo