= Solution
It is important to distinguish loss of forward-going <surface-gravity-wave energy> from conversion of mechanical <energy> into <heat>. <Scattering attenuation by ice floes> redirects energy; it can attenuate a coherent transmitted wave without dissipating the total energy.
For fixed floe geometry, increasing frequency usually increases attenuation over the relevant swell range: shorter <wavelengths> respond more strongly to the contrast between water and the <elastic plate>, and to repeated floe edges. Long <surface gravity waves> have weak curvature and often penetrate much farther. This is a trend over a specified frequency range, not a theorem excluding resonances.
The diameter dependence is governed by $d/\lambda$. An <ice floe> much smaller than the <wavelength> moves nearly with the water and scatters weakly. Scattering becomes appreciable when floe size is comparable with the <wavelength>, and interference between its two edges can give maxima and minima. At fixed ice concentration, larger <ice floes> also mean fewer edges per unit propagation distance, roughly proportional to $p/d$. Consequently the attenuation coefficient need not increase monotonically with diameter: the single-floe reflection and the number of encounters must both be considered. Thickness increases areal inertia as $\rho_i h$ and <bending stiffness> as $h^3$, generally increasing wave mismatch and reflection, although detailed frequency-dependent resonances again prevent a universal monotonic law.
When $d\ll\lambda$, particularly for <frazil ice> and <pancake ice>, weak individual scattering leaves other processes dominant. Relative crystal and water motion causes <viscous dissipation>; an aggregate layer can behave as a viscous or viscoelastic material, and <pancake ice> collisions, rubbing and overwash remove energy. Their importance depends on concentration and wave amplitude.
For a uniform continuous sheet with horizontal dimensions much greater than the <wavelength>, there are no repeated floe edges in its interior. A perfectly elastic sheet over inviscid water supports undamped <flexural-gravity waves>, so internal scattering is not an explanation of decay there. Real attenuation can instead arise from internal ice anelasticity or <viscoelasticity>, a dissipative sub-ice <viscous boundary layer>, turbulence, cracks and brine-related processes. \b[Small-floe mixtures and continuous sheets require dissipation models beyond the isolated-floe scattering picture.]
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