arXiv:2511.01528v1 [physics.ao-ph] 3 Nov 2025

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Wave Attenuation in Drifting Sea Ice: A Mechanistic Model for Observed Decay Profiles
Rhys Ransome †, Davide Proment1, Ian A. Renfrew and Alberto Alberello1
1School of Engineering, Mathematics and Physics, University of East Anglia, Norwich NR4 7TJ, UK 2School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK
(Received xx; revised xx; accepted xx)
Wave-sea ice interactions shape the transition zone between open ocean and pack ice in the polar regions. Most theoretical paradigms, implemented in coupled wave-sea ice models, predict exponential decay of the wave energy but recent observations deviate from this behaviour. Expanding on a framework based on wave energy dissipation due to icewater drag, we account for drifting sea ice to derive an improved model for wave energy attenuation. Analytical solutions replicate the observed non-exponential wave energy decay and the spatial evolution of the effective attenuation rate in Antarctic sea ice.
Key words: Sea ice; Surface gravity waves; wave-structure interactions.

are implemented in operational third generation spectral wave models (e.g. WaveWatchIII; Montiel et al. 2025) that are being coupled into global- and hemispheric-scale sea ice models. Most models predict a constant attenuation rate in homogeneous sea ice conditions and, consequently, exponential wave energy decay.
Overall, measurements conform reasonably well to the exponential attenuation paradigm and agree on the magnitude of the attenuation rate 𝛼, within the range (10-4 m-1 < 𝛼 < 10-5 m-1; Kohout et al. 2020; Montiel et al. 2022). However, recent satellite measurements of wave height in the Antarctic MIZ across seasons revealed an almost linear increase of the average attenuation rate with distance from the sea ice edge (up to ≈ 10×; Voermans et al. 2025) with individual transects showing sharp peaks in attenuation rate. Possible causes of deviation from the exponential profile were attributed to the misalignment between the transect and wave direction, and inhomogeneous sea ice conditions (sea ice concentration and thickness). Lacking a firm theoretical foundation, Voermans et al. (2025) propose an empirical wave attenuation formulation as an interim solution for implementation in wave models.
Amongst the various theoretical wave attenuation models, the ones that attribute wave energy dissipation to quadratic ice-water drag deviate from exponential decay in form. Icewater drag models capture the bulk of the energy loss when sea ice comprises floes with small diameter, relative to wavelength, in high concentration (Shen & Squire 1998; Kohout et al. 2011; Herman et al. 2019), this makes them well suited to the Antarctic MIZ. The attenuation rate due to drag is proportional to the square of the relative velocity between fluid orbital motion and sea ice (Herman et al. 2019). Assuming a stationary a semi-infinite sea ice domain, analytical, non-exponential, solutions for the amplitude profile have been obtained under slightly different approaches by Kohout et al. (2011), for the amplitude envelope, and Herman et al. (2019), for the phase-averaged amplitude. The former is a lower bound for the amplitude, i.e. higher bound for the attenuation rate.
Here, we develop an analytical framework for the attenuation of monochromatic waves due to drag, explicitly accounting for constant sea ice drift. We extend the previous works of Kohout et al. (2011) and Herman et al. (2019) where drift was neglected on the grounds that, in typical oceanic conditions, drift velocities are two orders of magnitude smaller than the wave group velocity. Despite its apparently negligible effect, we reveal distinctive consequences of including such drift, most notably the emergence of a location into the ice field where the wave amplitude vanishes and the attenuation rate becomes unbounded. We further demonstrate the capability of this enhanced model to reproduce recent observations of wave attenuation in the Antarctic MIZ.
2.		Mathematical Formulation and Analytical Solutions
The one-dimensional wave energy transport equation for energy density per unit surface area, 𝐸 (𝑥, 𝑡) , in sea ice-covered regions and excluding all other source terms is:

(2.1)

𝜕𝐸	𝜕𝐸
+ 𝑐	= 𝑆	= 𝑆 + 𝑆	, 𝜕𝑡	𝑔 𝜕𝑥 ice sd exp , where 𝑐𝑔 denotes the group velocity and, similarly to Kohout et al. (2011), the effect of the ice (𝑆ice) is explicitly expressed as a linear superposition of all the mechanisms with constant decay, that lead to exponential attenuation (𝑆exp), and the ones due to ocean-ice skin drag drag (𝑆sd). Here, in agreement with most wave-in-ice parametrisations in WaveWatchIII (Montiel et al. 2025), we assume the open water dispersion relation between angular frequency 𝜔 and wave-number 𝑘 to hold in sea ice.
The transport equation in terms of wave amplitude 𝑎 (𝑥, 𝑡) , using 𝐸 ∝ 𝜌𝑔𝑎2 where 𝜌 is
water density and 𝑔 acceleration due to gravity, becomes:
𝜕𝑎	𝜕𝑎
𝑎	+ 𝑎 𝑐	= 𝑠	= 𝑠	+ 𝑠 ,	(2.2)
𝜕𝑡	𝑔 𝜕𝑥 ice exp	sd,
where 𝑠 = 𝑆/𝜌𝑔. In agreement with previous work (e.g. Kohout et al. 2011; Herman et al. 2019), in ice covered regions we define the exponential source term as
𝑠exp = -𝑐 𝑔 𝛼exp 𝑎 ,	(2.3)
where 𝛼exp is the constant attenuation rate for all other contributing non skin-drag mechanisms. Its inclusion provides flexibility for future operational model implementations.
In ice covered regions, for a monochromatic wave, the rate of change of energy per unit area due to skin drag is proportional to |𝑢 orb - 𝑣|3 (Shen & Squire 1998), where 𝑢orb = 𝑈 sin (𝜙) is the wave orbital velocity at the ice-water interface, here evaluated at the free surface under the hypothesis of thin sea ice, and 𝑣 is the ice drift velocity. The magnitude of the orbital velocity is 𝑈 = 𝑎Ω, where Ω = 𝑔 𝑘 /𝜔, and 𝜙 is time-dependent phase. Phase averaging, we obtain:
𝐶𝑑 1	2𝜋
𝑠sd = -	|𝑎Ω sin(𝜙) - 𝑣|3 𝑑𝜙,	(2.4) 𝑔 2𝜋 0
with 𝐶𝑑 the drag coefficient, assumed constant in homogeneous sea ice conditions.
We consider a thin semi-infinite homogenised sea ice layer drifting at a constant velocity 𝑣 and arbitrarily set a frame of reference moving at 𝑣, i.e. 𝑥ˆ = 𝑥 - 𝑣𝑡, with 𝑥ˆ the distance from the edge of the sea ice. Taking the steady state system in the moving frame with a constant wave forcing at the ice edge 𝑎 (0) = 𝑎0, the one-dimensional wave energy transport equation Eq. 2.2 in the ice region (𝑥ˆ ⩾ 0) reduces to:

with

𝑑𝑎
𝑑 𝑥ˆ

= -𝛼 𝑎 -

2 𝜋 Γ
𝑎 0

|𝑎Ω sin ( 𝜙) - 𝑣|3 𝑑𝜙 ,

𝐶𝑑	𝑐𝑔
Γ =	, and 𝛼 =	𝛼 ,
Γ= 2𝜋𝑔(𝑐𝑔-𝑣) , and 𝛼= 𝑐𝑔-𝑣𝛼exp,

(2.5)
(2.6)

being the attenuation, therefore remaining exponential in the moving frame.
2.1.		Solving the Amplitude Profile
Equation 2.5 represents a challenging nonlinear ordinary differential equation. Also note that a polynomial solution in 𝑎 for the integral of the skin drag (Eq. 2.4) exists only for |𝑣| ⩾ 𝑎Ω. In effort to enable closed form analytical solutions for Eq. 2.5, we consider an asymptotic expression for the skin drag in the regime |𝑣| ≪ 𝑎Ω, then extended into the region |𝑣| < 𝑎Ω, therefore obtaining:
𝐼=∫2𝜋|𝑎Ωsin(𝜙)-𝑣|3𝑑𝜙(≈83(𝑎Ω)3+12𝑎Ω𝑣2,	if|𝑣|<𝑎Ω;	(2.7)
0	= 3𝜋(𝑎Ω)2|𝑣| + 2𝜋|𝑣|3, if |𝑣| ⩾ 𝑎Ω.
Note that, in oceanic conditions, 𝑐𝑔 is two orders of magnitude lager than the wind and current induced drift, i.e. O(10) m/s versus O(0.1) m/s, therefore |𝑣| ≪ 𝑐𝑔 implying that, as the results of Eq. 2.7 are strictly positive, the amplitude 𝑎 monotonically decreases in Eq. 2.5. For 𝑎0Ω > |𝑣 |, we define 𝑥ˆ∗ to be the location into the ice domain such that 𝑎 (𝑥ˆ∗)Ω = |𝑣 |. Therefore, the condition | 𝑣 | ≶ 𝑎Ω corresponds to 𝑥ˆ ≶ 𝑥ˆ∗ in the physical domain. In contrast, for 𝑎0Ω ⩽ |𝑣|, one obtains 𝑥ˆ∗ = 0.

(2.8)

Solving Eq. 2.5 with the integral approximation Eq. 2.7, the amplitude solutions are written in piecewise form as:
𝑎 (𝑥ˆ) ≈ 𝑎𝐴(𝑥ˆ) 1{𝑥ˆ<𝑥ˆ∗} + 𝑎𝐵 (𝑥ˆ) 1{𝑥ˆ⩾𝑥ˆ∗}, where the piecewise solution components result in:

𝑎𝐴(𝑥) =

3√Δ
16ΓΩ3

tan -

Δ
𝑥ˆ + arctan 2

16ΓΩ3 𝑎0 + 3𝛼	3𝛼

32ΓΩ3𝑎0 - ^16𝛼ΓΩ3 𝑎0 + 3𝛼2𝑥ˆ

3√Δ

16ΓΩ3,

𝛿 > 1,

32ΓΩ3 + ^32ΓΩ3𝑎0 + 6𝛼 𝑥ˆ	,
𝑟-(𝑎0 - 𝑟+) exp 8Γ3Ω3 (𝑟- - 𝑟+)𝑥ˆ

- 𝑟+(𝑎0 - 𝑟-)

𝛿 = 1,

(2.9)

(𝑎0 - 𝑟+) exp 8Γ3Ω3 (𝑟

- 𝑟+)𝑥ˆ - (𝑎0 - 𝑟-)

𝛿 < 1,

𝑎𝐵(𝑥ˆ) = 𝑒-(6𝜋Ω2|𝑣|Γ+2𝛼)(𝑥ˆ-𝑥ˆ∗)	𝑣2
Ω2	3𝜋Ω2|𝑣|Γ + 𝛼	3𝜋Ω2|𝑣|Γ + 𝛼

2𝜋|𝑣|3Γ

2𝜋|𝑣|3Γ

(2.10)

Here Δ ≡ 𝛼2 (𝛿2 - 1), 𝑟± ≡ -3(𝛼 ± -Δ)/( 16ΓΩ3), and

𝛿 =

8√2ΓΩ2|𝑣|
𝛼

(2.11)

which controls the roots of the quadratic polynomial in 𝑎 affecting the solution in the 𝑥ˆ < 𝑥ˆ∗ region. Note that the physical interpretation of 𝛿 will be discussed in §2.2.
The solution has a few interesting features. It is nonlinear, i.e. drag effects and other mechanisms cannot be added as linear superposition. The solutions for 𝑥ˆ < 𝑥ˆ∗ in Eq. 2.9 differs in form but possess similar qualitative behaviour, where we note that 𝑥ˆ∗ depends on 𝛿. For a wave with initial orbital velocity magnitude 𝑈0 < | 𝑣 | we obtain a single branched solution, i.e. 𝑎𝐵 .
A distinctive consequence of such solution is the existence of an extinction location

(2.12)

8	5	4√2
𝑥	= 𝑥 ∗ +	log +	, 𝑥end = 𝑥 + 3√2𝜋𝛼𝛿 + 8 log 2 + 𝜋𝛿	, such that 𝑎𝐵 (𝑥ˆ = 𝑥ˆend) = 0. The extinction location is unique to dissipation due to drift induced skin drag and defines the extent of the wave affected region. It moves closer to the sea ice edge for increasing 𝐶𝐷 coefficient and 𝛼 (see solution in red, for 𝑣 = 0.05 m/s and 𝛼 = 7 × 10-6 m/s [𝛿 = 3.4], vs in blue, for 𝑣 = 0.05 m/s and 𝛼 = 0 [𝛿 = ∞], in Fig. 1a), while its dependence on drift is not trivial. Such extinction locations are not present in the solutions of Kohout et al. (2011) and Herman et al. (2019), shown dashed green and orange respectively, for which 𝛼 = 0 and 𝑣 = 0.
In the special case of no drift, i.e. 𝑣 = 0, the solution reduces to:

𝑎 (𝑥) =

(2.13)

3𝑎0𝛼𝑒-𝛼𝑥ˆ
3𝛼 + 8𝑎0ΓΩ3 - 8𝑎0ΓΩ3𝑒-𝛼𝑥ˆ .
Taking 𝐶𝐷 = 0, i.e. no drag, we recover the exponential attenuation at a rate 𝛼 whereas for 𝛼 → 0 the solution converges to the one of Herman et al. (2019). Therefore, Eq. 2.13 is an extension Herman et al. (2019) that accounts for additional mechanisms. As a result, our solution predicts lower amplitudes compared to Herman et al. (2019), see Fig. 1a.
Fig. 1a showcases the effect of drift. The attenuation is stronger when drift is present, see

Figure 1: Sample amplitude (a) and corresponding attenuation (b) profiles according to our model and formulations by Kohout et al. (2011) and Herman et al. (2019). Dashed lines denote 𝑥∗. Amplitude is normalised by the initial amplitude and distance by 𝑥end for 𝛼 = 0. Attenuation rate is normalised by 𝛼.

solution in red vs in purple (𝑣 = 0 m/s and 𝛼 = 7 × 10-6). The increased attenuation due to other mechanisms also manifests when drift is present, see solutions in blue vs in red.
2.2.		Predicting the Attenuation Rate
To allow better comparison with results as they appear in the literature, we compute the effective attenuation rate in the moving frame in the ice covered region defined as

(2.14)

if 𝑥ˆ < 𝑥ˆ∗ ;
if 𝑥ˆ ⩾ 𝑥ˆ ∗ .

(2.15)

1 𝑑𝑎	Γ
𝛼	≡ -	= 𝛼 +	𝐼 .
e.
𝑎 𝑑𝑥	𝑎2
Using the integral estimation (Eq. 2.7) we obtain:
8	3	12Ω𝑣2Γ
≈ 𝛼 + 𝑎 Ω Γ +	,
𝛼eff(𝑥ˆ) =𝛼+3𝜋Ω2|𝑣|Γ+2𝜋𝑎|𝑣2|3Γ,
Note that, by extending asymptotic solution of 𝐼 for |𝑣| < 𝑎Ω to |𝑣| = 𝑎Ω, the decay rate inherits a jump discontinuity at 𝑥ˆ∗, shown in Fig. 1b, with the suitability of the integral approximation justified by discontinuity magnitude being only 7%. The nonlinearity between skin drag and other exponential decay mechanisms leads to the lower bound
𝛼eff ⩾ 𝛼+ 8√2ΓΩ2|𝑣| = 𝛼(1 + 𝛿) , (2.16)
with the global minimum located in the region 𝑥ˆ < 𝑥ˆ∗ if 𝑎0Ω ⩾ 3 2|𝑣 |/2, whereas for lower orbital velocity at the sea ice edge the attenuation monotonically increases. This result allows for a physical interpretation of the dimensionless parameter 𝛿: for 𝛿 > 1 wave attenuation is dominated by drift induced skin drag and for 𝛿 < 1 all other mechanisms dominate.
For drifting sea ice, the attenuation rate grows unbounded in the neighbourhood of the extinction location (see solutions in red and blue in Fig. 1b), i.e. 𝛼eff (𝑥ˆ) ∼ [ 2 (𝑥end - 𝑥ˆ)] -1, therefore the extinction location affects the magnitude of the attenuation rate in this region. When drift is absent, 𝑥ˆ∗ → ∞ and the solution for 𝑥ˆ < 𝑥ˆ∗ applies to the entire domain. Skin drag dominates attenuation close to the sea ice edge whereas other processes dominate deeper into the sea ice, where we retrieve the classical exponential attenuation, i.e. 𝛼eff → 𝛼 for 𝑥ˆ → ∞ (see solution in purple in Fig. 1b; the grey dashed line denotes 𝛼eff = 𝛼).
3.		Comparisons to Antarctic Measurements
In this section comparisons are made with measured amplitudes and derived attenuations in the Antarctic sea ice (Brouwer et al. 2022; Voermans et al. 2025). The data comprises quality controlled ICESat-2 satellite transects of wave height (total and across frequency components corresponding to periods 𝑇 = 9, 12, 15, 18 s) across the MIZ throughout 2019. Note that transects seldom start at the ice edge and, in computing attenuation rates, transects are assumed to align with the wave direction (Voermans et al. 2025). Drift is not measured by ICESat-2.
To compare data to model results, which are derived for a monochromatic wave, we attribute all energy to the most energetic frequency component measured over the transect, normalising amplitude and attenuation rate by the first available measurement from the ice edge, 𝑎 1𝑉 and 𝛼𝑉1 respectively. The ice edge is taken to coincide be the start of each transect.
Drift and drag are used as fitting parameters, within the range of available Antarctic sea ice observations, i.e. 𝑣 = O(10-1) m/s and 𝐶𝑑 = O(10-2), together with 𝛼. The drift is assumed to be constant along the transect, justified by slow spatial variation over 10–100 km in Antarctic sea ice (Holland & Kwok 2012). The water density is set 𝜌 = 1025 kg/m3 and deep water dispersion relation used, namely Ω = 𝜔.
3.1.		Individual Transects
The two transects reported in Voermans et al. (2025) are analysed in detail. Transect I, taken on 26 December 2019 at 85◦W, 69◦S, is 61.5 km long and waves have peak period 15 s. Transect II, taken on 24 May 2019 at 88◦W, 68◦ S, is longer (𝑥MIZ = 137.5 km) and waves have a shorter peak period (𝑇 =12 s).
For Transect I the parameters 𝑣 = 0.26 m/s, 𝐶𝑑 = 6.0 × 10-3 and 𝛼 = 5.0 × 10-6 provide good qualitative and quantitative agreement in terms of amplitude decay (see Fig. 2a). Similar performances are achieved by the the non-drifting model, i.e. 𝑣 = 0, and the exponential decay. However, the model with drift outperforms the others reproducing the observed increase in effective attenuation rate along the transect (between 𝑥ˆ/𝑥MIZ ≈ 0.2 and 0.6; see Fig. 2b). Note that for the chosen parameters, drift is stronger than the orbital velocity throughout the transect (|𝑣|/𝑈0 ≈ 1.2), i.e. only the branch 𝑥 > 𝑥ˆ∗ of Eq. 2.15 is used. Remarkably, the model predicts an extinction location consistent with the observed wave-affected sea ice extend, i.e. at 𝑥/𝑥MIZ ≈ 1.
For Transect II the parameters 𝑣 = 0.49 m/s, 𝐶𝑑 = 2.8 × 10-3 and 𝛼 = 1.0 × 10-7 qualitatively reproduce the measured mild amplitude decay up to 𝑥ˆ/𝑥MIZ < 0.6 followed by a sharp decline (see Fig. 2c). Other models, i.e. the exponential and non-drifting model, fail to capture the sharp decline deeper into the sea ice. The predictive performance of the drifting model is clearly highlighted by the attenuation rate, shown in Fig. 2d, where steady attenuation rate near the ice edge followed by rapid growth for 𝑥/𝑥MIZ > 0.6 are well captured qualitatively and quantitatively. A jump discontinuity appears at 𝑥/𝑥MIZ ≈ 0.1, consistent with the choice of 𝑣 resulting in |𝑣|/𝑈0 ≈ 0.9 and the presence of 𝑥ˆ∗ within the domain. Unlike our formulation, all other models predict either a decreasing attenuation rate (no drift model) or constant attenuation (exponential model), as shown in Fig. 2d.
In summary, Transect I and II showcase two different regimes, in Transect I drag attenuation is weak (𝛿 = 0.6) whereas in Transect II it is the dominant mechanism (𝛿 = 8.0). Therefore, as expected, in Transect I deviations from exponential attenuation are weaker than in Transect II however, also in Transect II, inclusion of exponential attenuation through 𝛼 provides significantly better predictions. When drag dominates, the extinction location 𝑥end occurs earlier and the spike in attenuation is more prominent.

/xxx/MxxIMZIZ

x/xxx/M/xxIMZMI

Figure 2: Amplitude (left) and corresponding attenuation profiles (right) for Transect A (top) and B (bottom). Measurements (red dots) are shown against model predictions.
Distance is normalised with respect to the wave-affected sea ice extent 𝑥MIZ and amplitude/attenuation with respect to the measurement closest to the sea ice edge as reported in Voermans et al. (2025).

3.2.		Averaged Attenuation
Voermans et al. (2025) report average attenuation profiles across seasons and sectors of the Antarctic MIZ. To reproduce the observed variability, we drive our model, i.e. Eq. 2.15, with 𝑁0 = 3 × 105 random realisations with Gaussian distributed drift velocity (with mean 𝜇𝑣 and standard deviation 𝜎𝑣), constant throughout the transect. The simulations replicate the variability of drift around Antarctica (Kwok et al. 2017). The attenuation rate is computed for the wave component 𝑇 = 12 s (angular frequency Ω = 0.52 s-1 and wavelength 𝜆 = 225 m) and we set the wave amplitude at the sea ice edge to 𝑎0 = 1m. The other parameters are 𝐶𝑑 = 0.02 and 𝛼 = 7.0 × 10-6 m-1, to match the averaged measured attenuation rate at the sea ice edge. For the comparison, only 𝑎 ⩾ 0.05m are averaged, in analogy with the methodology used by Voermans et al. (2025) to exclude data with high uncertainty.
For drift 𝜇𝑣 = 0.22 m/s ( 𝜇 𝑣 /𝑈0 = 0.42) and variance 𝜎𝑣 = 0.03 m/s (Fig. 3a) the attenuation only slightly increases up to 𝑥 /𝜆 ≈ 550, consistent with the fact that simulations are in weak drag regime (𝛿 = 0.42). From 𝑥 /𝜆 ≈ 550 to 𝑥 /𝜆 ≈ 700 the increase in more noticeable, up to ≈ 3 times the attenuation rate at the sea ice edge, in qualitative agreement with simulations for Transect A (cf. Fig. 2b), before stabilising farther in the sea ice domain. The spread of individual profiles, shaded in grey, also grows when attenuation rate increases. Note that the increase in attenuation corresponds to a reduction in available measurements of amplitude over threshold (shown in red) and, similarly, individual amplitude profiles reaching the extinction location (distribution shaded in blue).
With the same average drift (𝜇𝑣 = 0.22 m/s) but lower variability (from 𝜎𝑣 = 0.03 m/s to 𝜎𝑣 = 0.01 m/s; Fig. 3b) the same qualitative behaviour is observed. The increase in attenuation is sharper, i.e. it starts deeper in the sea ice (at ≈ 650 wavelengths) and reaches higher values (𝛼eff ≈ 5.5 × 10-4 vs 𝛼eff ≈ 3.5 × 10-4).
The increase in drift (𝜇𝑣 = 0.29 m/s, 𝜇 𝑣 /𝑈0 = 0.55 and 𝜎𝑣 = 0.03 m/s; Fig. 3c), results in higher 𝛿 = 0.55, still in weak drag regime, and moves the increase in attenuation rate

Fig2ure 3: Ave0r.0aged 0a.2ttenua0.t4ionxr/ates (in black; for negative velocity in green) and interq0uartile range (shaded in grey). On the right axis, number of measurements (in red) and distribution of1 the extinction location (shaded in b4lxu/e; not to s5cale). Insets show the drift velocity distribution.

closer to the sea ice edge, from 𝑥 /𝜆 ≈ 450 to 𝑥 /𝜆 ≈ 550. A slightly higher attenuation is also achieved compared to the previous cases, up to 𝛼eff ≈ 6 × 10-4, after which decreases slightly. The number of observations decreases sharply due to individual transects reaching their extinction location (cf. Fig. 1b), and only less than 0.1% remain after 800 wavelengths, also explaining the larger variance in effective attenuation.
In Fig. 3 the mean attenuation rates for negative mean velocity are also reported in dashed green line. The direction of the drift has only marginal effect on the effective attenuation profile, i.e. the growth of attenuation rate is deeper into the sea ice (by ≈ 10 wavelengths) but does not affect its magnitude. This is expected for oceanic conditions, as 𝛼 ≈ 𝛼exp and Γ ≈ 𝐶𝑑/(𝑔𝑐𝑔2𝜋), hence the dependence of direction of the drift is negligible for operational purposes.
Fig. 3c is remarkably similar to the measured averaged attenuation in Voermans et al. (2025), i.e. a linear increase followed by slight decline, also matching the range of observed attenuation rates. Unlike in the measurements, in the model all individual transects are available from the edge but the decrease of available observations in Voermans et al. (2025) deeper into the sea ice is also captured. It can be argued that the presence of drift limits the extent of the wave-affected area, and its extent in our model (≈ 185 km; Fig. 3d) is consistent to the one in observations (Brouwer et al. 2022) and model simulations (Day et al. 2024).
4.		Conclusions
We derived a mechanistic model for wave attenuation that accounts for both phenomenological exponential attenuation mechanisms and dissipation due to drag at the ocean-sea ice interface, as well as the effect of sea ice drift, therefore combining and extending previous models (cf. Shen & Squire 1998; Kohout et al. 2011; Herman et al. 2019). We identified the parameter 𝛿 which governs attenuation dominated by drift-induced drag mechanisms (𝛿 > 1) and exponential mechanisms (𝛿 < 1) . Analytical solutions reveal that in drag dominated regime, the amplitude eventually dies-off, unlike prediction based on exponential attenuation, and the attenuation profile spikes close to the extinction location.
The model agrees qualitatively and quantitatively well with pan-Antarctic measurements of attenuation rate recently reported by Voermans et al. (2025) when sea ice is allowed to drift slowly (𝜇𝑣 /𝑈0 = 0.55), even for small 𝛿, i.e. 𝛿 = 0.55. In particular, drift is responsible for the increase in wave attenuation rate deeper into the sea ice and, to a certain extent, regulates the extent of the wave-affected sea ice in quantitative agreement to observations (Brouwer et al. 2022) and model simulations (Day et al. 2024).
The quantitative agreement against individual transects is reasonable with limitations. Differences with the measured data can be attributed to experimental uncertainty, e.g. negative attenuation rates and misalignment with wave direction, and current model assumptions, i.e. no interaction between wave components, no presence of other forcing mechanisms, heterogeneous drift along the transect and changes in ice type and morphology.
Ultimately the model provides a solid theoretical foundation to better interpret observations of wave attenuation in drifting sea ice as found around Antarctica, and prompts for new measurements for further validation. Moreover, while only drag has been studied explicitly, the approach can be extended to better specify other wave attenuation mechanisms for integration in coupled wave-sea ice models.
Acknowledgements. This work was supported by the Natural Environment Research Council and the ARIES Doctoral Training Partnership [grant number NE/S007334/1]. RR and AA acknowledge funding from Royal Society (IEC\R3\243016). This work was stimulated by discussions during the “Maths of Sea Ice” meeting, made possible by the Isaac Newton Institute for Mathematical Sciences. DP is supported by EPSRC Grant No. EP/Y021118/1 and by the ExtreMe Matter Institute EMMI at the GSI Helmholtzzentrum fuer Schwerionenphysik, Darmstadt, Germany.
Declaration of interests. The authors report no conflict of interest.
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