  A theoretical model is used to study water waves propagating into and through
a region containing thin floating ice, for ice covers transitioning from
consolidated (large floe sizes) to fully broken (small floe sizes). The degree
of breaking is simulated by a mean floe length. It is shown that there are
deterministic limits for consolidated and fully broken ice covers where the
wave fields do not depend on the particular realisation of the ice cover for a
given mean floe length. The consolidated ice limit is consistent with classic
flexural-gravity wave theory, and the fully broken limit is well modelled by
Bloch waves in a periodic ice cover. In the transition between the limits, the
wave field depends on the ice cover realisation, as multiple wave scattering is
a dominant process. The effects of the ice cover on the wave field are
quantified using a wavelength, attenuation rate, and a transferred amplitude
measuring the amplitude drop at the ice edge. It is shown that as the ice cover
breaks up (mean floe size gets smaller), the wavelength and amplitude drop
decreases (transferred amplitude increases) and the attenuation rate increases.
The results provide a new interpretation of field observations.

Fluid Dynamics;Atmospheric and Oceanic Physics