Statistical Mechanical Theory of the Thickness Distribution of Arctic Sea Ice

We extend the theory of sea-ice thickness distribution [Toppaladoddi and Wettlaufer, Phys. Rev. Lett. 115, 148501 (2015)], g(h), to include open water by formulating a new boundary condition for the Fokker-Planck equation for g(h). 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 evolution of g(h). We find that g(h) transitions from a single- to a double-peaked distribution in spring, which is in qualitative agreement with recent 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. Furthermore, we explore the effects of different climatological conditions on the formation of open water.