Please find my comments in the attached supplement.

General Comments

The paper uses machine learning to identify and extract flexural-gravity (FG) wave signals recorded on a small lake, and then uses these signals for an MCMC inversion of ice thickness, based on the dispersive nature of FG waves.

I have only passing knowledge of ML and thus cannot evaluate those portions of the paper. Details on the MCMC inversion were specified in another paper, which I did not track down, and so I also cannot evaluate the specifics of that. The core results of the ML clustering and MCMC inversion, as presented, do appear realistic. FG wave sources are back-located to the grounding lines of the lake ice and are likely icequakes. Lake ice thickens during the first two weeks of the study period, and stabilizes during the last two, consistent with stated (but not provided) temperature readings.

The manuscript has a marked lack of supporting ancillary data, specifically temperature and tidal observations. Despite this, the authors make a geophysical interpretation of their icequake as being thermally-driven, as opposed to tidally-driven. As outlined in the specific comments below, based on publicly-available temperature and tidal data, I disagree with this interpretation.

The manuscript mentions that it produces results that are in agreement with another study by the same group of authors (Serripierri et al., 2022). From a quick readthrough of that work, it appears that it uses the same methods, but with greater rigor and scope. It mentions a future publication (assumed to be the current manuscript) that will attempt to replicate their results using fewer stations and wave modes. In that context, the current work appears to be a companion paper, yet does not address the work done by Serripierri et al. (2022), or make any explicit statement of the differences between the two works. The current manuscript should make a clear statement on how it is substantially different from the prior work.

I believe the core results (ML extraction of events and MCMC inversion of FG waves) are sound, novel, and notable. However, I recommend revisions to address the points raised in the specific comments below. In particular, the lack of ancillary data and the related geophysical interpretation, and the implications for an assumption of an infinite-depth water column in a borderline shallow-water setting.

Specific Comments

Lines 11, 70, 92 : The authors state that they installed their seismic array on sea ice in Van Mijen fjord. Figure 1 shows that the field site is actually Vallunden Lake. While there is a short (100 m) channel connecting the lake to the fjord, the lake is geophysically distinct from the fjord. The authors do not provide any geologic context for the lake nor provide relevant references. The depth of Lake Vallunden is ~10 m (Marchenko et al. 2013), which is also not mentioned by the authors, but is an important consideration for their modeling (addressed further below).

Line 13 : “calibrated seismic sources”. The seismic sources, as described on line 221, appear to be more “estimated” than “calibrated.” Addressed further below.

Lines 18–19 : Citation needed. https://nsidc.org/arcticseaicenews/charctic-interactive-sea-ice-graph/ ?

Lines 31–33 : The densities of snow and ice are also a source of error for seismic measurements, so this statement is a little misleading in the context of putting forth seismology as an alternative to freeboard measurements. In my opinion, the greatest advantage of seismic methods vs satellite is orders of magnitude greater spatial and temporal resolutions, at the expense of spatial scale. The authors appear to agree with this, though not explicitly.

Line 35 : “The first seismic experiments on sea ice date back to the late 1950s…” Ewing and Crary (1934) on Saylor’s Lake and Crary (1954) on Fletcher’s Ice Island should not be overlooked.

Lines 122, 273–274, 283–284, Fig 5 caption : “Icequakes (in the 0–7 cluster family] are likely produced by thermomechanical forcing.” This interpretation is not substantiated by the data presented.

Hourly temperature data are not included in this manuscript, nor any of the references that I checked. Hourly temperatures recorded at Lufthavn, 50 km away, for March 2019 (https://meteostat.net/en/station/01008) do not show a diurnal cycle, consistent with a perpetually overcast Arctic coastal climate where temperatures are dominated by weather rather than solar heating. In the absence of locally recorded data, one could assume that Lake Vallunden has similar temperature trends. The noted 24-hour peak in icequake occurrence cannot be attributed to thermomechanical fracturing without an hourly-scale time domain correlation between temperature at Vallunden and icequake occurrence rates. Arguably, a spatiotemporal correlation would be most appropriate.

Fig. 3d does not show a consistent 24-hour recurrence pattern for the 0–7 cluster family. The deficit at 9 AM (local? UTC?) can be attributed to tides, as explained below.

Fig. 5 : In the absence of any collaborating geophysical data to the contrary, I would suspect that the n*24-hour peaks are binning-related artifacts.

Fig. 6 indicates that the icequakes in the 0–7 cluster family were overwhelmingly back-located to the lake ice grounding zones. This is more suggestive of tidally forced fracture (e.g., Cole, 2020). One would expect thermomechanical fracturing to occur uniformly distributed throughout the interior of the lake ice. An argument could be made for solar heating of exposed geology at the shorelines, but would require in situ temperature and solar radiance data to validate.

Lines 122­–123, 273–274 : “[S]emidiurnal tide reaches 10-20 cm, so it is likely that tides have less effect than changes in temperature….” The opposite interpretation is suggested by the data presented.

The stated tidal range is 0.1–0.2 m, potentially 30–40% of the 0.45–0.6 m inverted ice thicknesses presented in Fig. 6. Given the steep bathymetry suggested by Marchenko et al. (2021), this seems to be a substantial tidal deflection relative to the ice thicknesses.

Fig. 3c shows calendar day occurrences for icequakes. The authors note that “The icequakes have calendar occurrences every day of the deployment, but are more frequent between February 27th and March 13th, and then between March 21^st and March 25^th” (lines 118–119). Spring tides occurred on Mar 6 and Mar 21, 2019, and a neap tide on Mar 13.

Hourly tidal data from Nylesund, 157 km away, shows tidal heights that are visually well-correlated with the icequake occurrence plots in Fig 3c. (http://uhslc.soest.hawaii.edu/data/csv/fast/hourly/h823.csv) The decreased occurrence rates in the latter half of March 2019 may be due to the thickening (and, presumably, strengthening) of the lake ice (Fig. 6b).

The roughly uniform occurrence of icequakes throughout the summed days shown in Fig 3d for cluster family 0–7 could be explained by the hourly precession of high tides throughout the month. Tidal minimums during the Mar 13 neap tide occurred at 0800–0900 UTC, coincident with the 9AM (local? UTC?) decrease in icequakes noted on line 120.

Lines 150–154 : Forward modeling uses the flexural-gravity wave dispersion relation from Stein et al. (1998). This equation assumes an infinite depth water column. Vallunden Lake has a depth of no more than 10 m (Marchenko et al. 2013). Ewing and Crary (1934) provide a formulation for FG waves in shallow water. Based on a comparison of the two dispersion relations, the Stein formulation diverges from the shallow water case for frequency-thickness products less than 1 Hz m. The current study uses icequakes in the 1–50 Hz range, with a peak at 8 Hz (presumably; the authors do not explicitly state the frequency band for their inversions). Their results are likely not significantly impacted by the assumption of infinite depth. However, the regime change—and their avoidance of it—should nonetheless be acknowledged, especially given that they do acknowledge the high frequency regime change for frequency-thickness > 1000 Hz m.

Lines 208–209, 296–298 : The authors state that their method could be adapted for near real time monitoring of ice thickness. What actual time scales are envisioned for a data product? Hourly? Daily?

Line 221 : The jumps are stated to be 1 m. How was this guaranteed? Was the jumpee stepping off a 1 m platform? Was the impact onto un-groomed snow & ice, or onto a strike plate? A standing jump does not have sufficient repeatability to be classified as a “calibrated source.”

Line 260 : The authors mention expanding further work to include longer period ice waves, to the order of 0.1 Hz m. Such waves would absolutely interact with the lake bottom and thus necessitate the Ewing and Crary (1934) or similar formulation.

References

Cole, Hank M. Tidally Induced Seismicity at the Grounded Margins of the Ross Ice Shelf, Antarctica. Diss. Colorado State University, 2020.

Crary, A. P. "Seismic studies on Fletcher's ice island, T‐3." Eos, Transactions American Geophysical Union 35.2 (1954): 293-300.

Ewing, Maurice, and A. P. Crary. "Propagation of elastic waves in ice. Part II." Physics 5.7 (1934): 181-184.

Marchenko, A. V., and E. G. Morozov. "Asymmetric tide in Lake Vallunden (Spitsbergen)." Nonlinear Processes in Geophysics 20.6 (2013): 935-944.

Marchenko, A. V., et al. "Ice thickening caused by freezing of tidal jet." Russian Journal of Earth Sciences 21.2 (2021): 5.

Technical Comments

Due to the revisions recommended, this is section is withheld. In general, the grammar and organization are clear and concise.