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 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.
Highlights
Arctic sea ice is one of the most sensitive components of the Earth’s climate system and serves as a bellwether for global scale climate change
Using concepts and methods from statistical physics we have transformed the theory of the sea ice thickness distribution, g(h), of Thorndike et al [14] into a solvable Fokker–Planck-like equation
The solution shows that the interaction of thermal and mechanical processes during the evolution of g(h) leads to the generation of multiple time scales, which in turn affect the evolution
Summary
Arctic sea ice is one of the most sensitive components of the Earth’s climate system and serves as a bellwether for global scale climate change. Where δ(h) is the source of open water, −2g(h) is the sink term for the ice that is used for ridging, and the convolution term represents the sum of all interactions that produce ice of thickness h While this approach overcame limitation 2 from the previous study, the nonlinear integro-differential equation could only be solved numerically. One could construct a theory that neglects the details of the collisions, but takes their net effect into account to study the geophysical-scale evolution of g(h) This line of reasoning led us to use an analogy with Brownian motion to interpret ψ [17]. We view the short length and time scales of individual mechanical processes (ridging and rafting) relative to the overall evolution of g(h, t) in direct analogy to the collisions of water molecules with a Brownian particle, and write ψ as ψ(h, t) =. We discuss the analytical and numerical solutions to Eq 11 with a particular focus on the climatological evolution of the thickness distribution
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