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Arctic permafrost coastlines are retreating faster as climate warming intensifies. Accurate modelling of the thermomechanical process is hindered by a lack of direct measurement of heat flux or heat transfer coefficients ([[EQUATION]]) at the water-permafrost interface. This study presents the first, direct laboratory measurements of wave-induced convective heat transfer coefficients. In twelve wave-flume experiments, artificial permafrost samples were exposed to air, still water, and irregular waves (0.02 - 0.04 m height; 0.8 - 1.2 s period). Embedded resistance temperature detectors tracked temperature changes at high spatial and temporal resolution, allowing for precise heat flux and heat transfer coefficient calculations. Under wave action, thaw-front advanced rapidly into the permafrost blocks at about 160 - 350 mmh-1 compared to 3.24 mmh-1 in air and 50.14 mmh-1 in still water. Similarly, heat transfer coefficient ranged from 459-1210 Wm-2K-1 in wave tests, significantly exceeding those for still water (~165 Wm-2K-1) and air exposure (~4.4 Wm-2K-1) tests. Heat flux correlated most strongly with wave height; higher ice content slowed thawing but did not evidently affect [[EQUATION]] magnitude. A novel empirical model was developed linking [[EQUATION]] to surf similarity and dimensionless wave height and period. The model achieved strong predictive performance (R2 = 0.89, RMSE = 81.1 Wm-2K-1) offering a practical alternative to existing analytical formulations that required parameter tuning. These results provide essential parameters for coastal permafrost erosion models and demonstrate the critical role of waves in heat delivery to permafrost coastlines improving forecasting capabilities for Arctic coastal management.
heat transfer coefficient ranged from 459-1210 Wm-2K-1 in wave tests, significantly exceeding those for still water (~165 Wm-2K-1) and air exposure (~4.4 Wm-2K-1) tests.
large controlled contrasts support the direction and reported range, although single runs do not establish reproducibility
[The novel empirical model] provides a practical, experimentally validated tool for specifying hw in coastal permafrost erosion models, eliminating the reliance on parameter tuning required by previous analytical approaches.
in-sample fitting without independent validation or varied geometry does not establish predictive utility across coastal conditions
the Kobayashi (1986) approach for approximating the heat transfer coefficient was validated and improved through empirical calibration by which the aK constant was found to be more accurate at 0.15
calibration against the same experimental means identifies a laboratory-specific constant rather than independently validating the approach
higher ice content slowed thawing but did not evidently affect hw magnitude.
one comparison with different frozen densities cannot establish independence from ice content despite the appropriately hedged wording
Under wave action, thaw-front advanced rapidly into the permafrost blocks at about 160–350 mmh−1 compared to 3.24 mmh−1 in air and 50.14 mmh−1 in still water.
the reported laboratory comparisons support faster thaw under waves, with unreplicated conditions limiting reproducibility
Derived from the full evaluation — not a separate score.
Strengths
The wave tests provide apparent heat-transfer coefficients of approximately 459–1210 Wm−2 K−1 across varied heights and periods, supplying empirical constraints for coastal-permafrost models.
↳ Introduction; Section 4.3; Fig. 6
Air and still-water exposures provide reference conditions, while wave gauges and embedded temperature sensors connect imposed forcing to the energy-balance estimates.
↳ Sections 3.1–3.3; Table 1; Eqs. 10–11
The Discussion compares the measured range with analytical, fluvial and earlier wave-flume estimates, and identifies salinity and hydrodynamic scaling as barriers to field extrapolation.
↳ Section 5
Limitations
The tests were not repeated, and the basis of the standard-deviation bars and effective fitting n is not clearly stated. Within-run variation cannot establish between-run reproducibility.
↳ Section 4.3; Figs. 6–7; Section 5
The empirical model and calibrated analytical constant are evaluated against the same experimental data used to fit them. This supports preliminary calibration, not independent predictive validation.
↳ Abstract; Section 4.3; Section 6(iii–iv)
The reported dimensionless-period range does not match the stated toe-depth definition. Slope and depth were also fixed, leaving their interpreted effects untested and insufficiently qualified.
↳ Sections 3.1–3.4; Section 4.3, Eq. 18 and parameter range; Section 5
The controlled comparisons and systematic wave matrix establish a useful laboratory measurement contribution. Lack of repeated runs and an unclear effective n constrain the precision and reproducibility of the quantitative calibration. The model's reported fit does not justify calling it independently validated, and fixed slope and depth prevent testing their separate effects. The positive dimensionless-period exponent is not itself contradictory because the other predictor also depends on period, but the mismatch in depth normalization remains unresolved.
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Sound3.1
Confidence mediumThe systematic wave-height and period experiments provide apparent heat-transfer coefficients for a documented uncertainty in coastal-permafrost models. The advance remains meaningful without accepting the unqualified first-measurement framing or treating the fitted parameterization as validated.
Measured hydrodynamics, temperature instrumentation, and air and still-water comparisons support the measurement core. Single runs, unclear effective n, in-sample fitting, and unresolved depth normalization limit confidence in quantitative calibration.
The progression from energy balance to experiments and results is traceable. Validation and tuning-elimination language nevertheless communicates greater predictive certainty than the fitting design establishes.
The paper compares its coefficients with analytical, fluvial and earlier wave-flume estimates and discusses several environmental limitations. It does not acknowledge that fixed slope and depth prevent experimental testing of their separate effects in the proposed parameterization.
Caveats4 of 4 checks
The empirical model's depth normalization is unresolved, and its validation language exceeds the in-sample evidence. The positive exponent on dimensionless period alone does not establish a contradiction because the other predictor also depends on period.
No research-conduct concern is established. Competing interests are disclosed as absent and experimental wave and temperature data are stated to be available through a persistent repository identifier.
Flags: 2 declared / 5 total
63 references in manuscript 56 of 58 checkable references found in an index 5 are books, websites or datasets — counted, but not index-checkable
No retraction notice found in Retraction Watch.
Sources: Crossref (incl. Retraction Watch) ✓
Where this paper’s evidence sits on the path from initial observation to real-world use.
The work supplies a laboratory-scale parameterization rather than a field-tested forecasting input. Independent model and field validation remain necessary before routine application.
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