Seasonal evolution of the Arctic sea ice thickness distribution

The Thorndike et al., (J. Geophys. Res. 80, 4501, 1975) theory of the ice thickness distribution, g(h), treats the dynamic and thermodynamic aggregate properties of the ice pack in a novel and physically self-consistent manner. Therefore, it has provided the conceptual basis of the treatment of sea-ice thickness categories in climate models. The approach, however, is not mathematically closed due to the treatment of mechanical deformation using the redistribution function ψ, the authors noting "The present theory suffers from a burdensome and arbitrary redistribution function ψ.''  Toppaladoddi and Wettlaufer (Phys. Rev. Lett. 115, 148501, 2015) showed how ψ can be written in terms of g(h), thereby solving the mathematical closure problem and writing the theory in terms of a Fokker-Planck equation, which they solved analytically to quantitatively reproduce the observed winter g(h). Here, we extend this approach to include open water by formulating a new boundary condition for their Fokker-Planck equation, which is then coupled to the observationally consistent sea-ice growth model of Semtner (J. Phys. Oceanogr. 6(3), 379, 1976) to study the seasonal evolution of g(h). We find that as the ice thins, g(h) transitions from a single- to a double-peaked distribution, which is in agreement with observations. To understand the cause of this transition, we construct a simpler description of the system using the equivalent Langevin equation formulation and solve the resulting stochastic ordinary differential equation numerically. Finally, we solve the Fokker-Planck equation for g(h) under different climatological conditions to study the evolution of the open-water fraction.