Collision integrals, sea ice thickness distribution and Arctic climatology

Abstract:

We first describe how the original theory of the sea-ice thickness distribution, g(h), due to Thorndike et al., J. Geophys. Res. 80 4501 (1975) can be written in a closed form as a Fokker-Planck like equation by treating their redistribution function, ψ(h), in the framework of a collision integral in statistical mechanics. We then extend the new theory (Toppaladoddi and Wettlaufer, Phys. Rev. Lett. 115 148501, 2015) for g(h) to include open water by formulating a new boundary condition that accounts for the true norm. The Fokker-Planck equation, together with the new boundary condition, is then coupled to a modified version of the observationally consistent sea-ice growth model of Eisenman and Wettlaufer (Proc. Natl. Acad. Sci. USA 106, 28 2009) to study the climatological evolution of g(h). We find that g(h) transitions from a single- to a double-peaked distribution in the melt season, which is in qualitative agreement with recent satellite observations. To understand the cause of this transition, we construct a simpler description of the system using the equivalent Langevin formulation and solve the resulting stochastic ordinary differential equation numerically. Further, we solve the Fokker-Planck equation for g(h) for different climatological conditions to study the effects on the open-water fraction.