Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

TL;DR

This paper models the seasonal and climate-forced changes in Arctic sea ice thickness distribution using a Fokker-Planck approach coupled with observational climatology, revealing the importance of mechanics in ice dynamics.

Contribution

It introduces a coupled Fokker-Planck and thermodynamic model to analyze Arctic sea ice thickness distribution under climate forcing, highlighting the role of mechanics in ice evolution.

Findings

g(h) spreads in winter and contracts in summer

Mean ice thickness decays exponentially with radiative forcing

Ice mechanics redistributes ice thickness more rapidly than thermodynamics alone

Abstract

We study the seasonal changes in the thickness distribution of Arctic sea ice, $g(h)$, under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for $g(h)$ (Toppaladoddi \& Wettlaufer \emph{Phys. Rev. Lett.} {\bf 115}, 148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman \& Wettlaufer (\emph{Proc. Natl. Acad. Sci. USA} {\bf 106}, pp. 28-32, 2009). We find that due to the combined effects of thermodynamics and mechanics, $g(h)$ spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok \& Cunningham, \emph{Phil. Trans. R. Soc. A} {\bf 373}, 20140157, 2015). Because $g(h)$ is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, $\Delta F_0$, increases. The mean ice thickness decays exponentially with $\Delta F_0$, but {\em much slower} than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice--far more rapidly than can thermal growth alone.