Dispersion Relations, Power Laws, and Energy Loss for Waves in the Marginal Ice Zone

Analysis of field measurements of ocean surface wave activity in the marginal ice zone, from campaigns in the Arctic and Antarctic and over a range of different ice conditions, shows the wave attenuation rate with respect to distance has a power law dependence on the frequency with order between two and four. With this backdrop, the attenuation‐frequency power law dependencies given by three dispersion relation models are obtained under the assumptions of weak attenuation, negligible deviation of the wave number from the open water wave number, and thin ice. It is found that two of the models (both implemented in WAVEWATCH III®), predict attenuation rates that are far more sensitive to frequency than indicated by the measurements. An alternative method is proposed to derive dispersion relation models, based on energy loss mechanisms. The method is used to generate example models that predict power law dependencies that are comparable with the field measurements. Key Points An analysis of the measured wave attenuation shows a power law dependence on frequency with an exponent between two and four We show how to connect various dispersion equation models with a given power law, under the assumption of weak attenuation by a thin layer We show how energy loss mechanisms are connected to dispersion equations and power laws