An idealised stochastic model of sea ice thickness dynamics

Observations of sea ice thickness distributions typically display an exponential decrease (or ‘tail’) in the frequency of ice above the limit of thermodynamic growth. Any sea ice which is more than approximately 2 m thick is formed by redistribution processes involving the damaging and ridging of ice, and modelling the dynamic evolution of the thickness distribution of sea ice requires that these processes be adequately represented. In this work, an idealised zero-dimensional model of the redistribution process and the evolution of the thickness distribution is presented, with the aim of determining the processes responsible for the ubiquity of the exponential tail of the distribution. The model is stochastic in nature, and redistribution events occur with probabilities which are dependent on their energetic magnitudes. Unlike many existing models, no detailed ice rheology is included. The model is able to produce qualitatively realistic thickness distributions and thickness distribution dynamics. Sensitivity analysis of the model demonstrates a robust response to the exact form of the energetic dependence of redistribution. However, the qualitative features of the simulated populations are strongly affected by the description of the manner in which redistribution events transfer ice between thickness categories. The construction and behaviour of the sea ice model is compared to a family of equations known as Smoluchowski Coagulation Models which feature similar dynamics and are known to produce exponentially distributed populations. We conclude that the exponential tail of the thickness distribution arises due to the nature of the redistribution process, rather than because of any detailed features of rheological properties of the ice, or any spatial aspect of the redistribution process.