Theory of the sea ice thickness distribution

• Main Authors: Toppaladoddi, Srikanth, Wettlaufer, J. S.
• Format: Text
• Language: unknown
• Published: arXiv 2015
• Subjects: Atmospheric and Oceanic Physics physics.ao-ph; FOS Physical sciences; ice pack; Sea ice
• Online Access: https://dx.doi.org/10.48550/arxiv.1507.05198; https://arxiv.org/abs/1507.05198

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. : 3 pages, 2 figures