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

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 and Wettlaufer in Phys Rev Lett 115(14):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 and Wettlaufer (Proc Natl Acad Sci USA 106:28–32, 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 and Cunningham in Philos Trans R Soc A 373(2045):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 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.