Theory of the sea ice thickness distribution

TL;DR

This paper applies statistical physics to derive a Fokker-Planck type equation for sea ice thickness distribution, providing a theoretical framework that aligns with observational data and elucidates the roles of thermodynamics and mechanics.

Contribution

It transforms the sea ice thickness evolution equation into a conservation law and derives a steady-state solution with a Langevin equation, offering a new theoretical approach.

Findings

Steady-state distribution matches observational fits.

For small h, both thermodynamics and mechanics influence g(h).

For large h, mechanics dominates g(h).

Abstract

We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution $g(h)$ due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is $g(h) = {\cal N}(q) h^q \mathrm{e}^{-~ h/H}$, where $q$ and $H$ are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for $h \ll 1$, $g(h)$ is controlled by both thermodynamics and mechanics, whereas for $h \gg 1$ only mechanics controls $g(h)$. Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness $h$, from which we predict the observed $g(h)$. The genericity of our approach provides a framework for studying the geophysical scale structure of the ice pack using methods of broad relevance in statistical mechanics.