Speaker: Srikanth Toppaladoddi
Title: Brownian Motion, Polar Oceans, and the Statistical Physics of Climate
Abstract:
In this talk, I will show how tools from statistical physics can be used to study the Earth’s climate. The specific problem addressed is the geophysical-scale evolution of Arctic sea ice. Using an analogy with Brownian motion, the original evolution equation for the sea ice thickness distribution function, g(h), by Thorndike et al. (J. Geophys. Res. 80(33), 4501(1975)) is transformed to a Fokker-Planck-like equation. The steady solution for wintertime is g(h) = N(q, H) * h^q * exp(-h/H), where q and H are expressible in terms of moments over the transition probabilities between thickness categories. This solution exhibits the functional form used in observational fits and shows that for h << 1, g(h) is controlled by both thermodynamics and mechanics, whereas for h >> 1 only mechanics controls g(h). Furthermore, seasonality is introduced by using the Eisenman-Wettlaufer (Proc. Natl. Acad. Sci. USA 106, 28 (2009)) and Semtner (J. Phys. Oceanogr. 6, 379 (1976)) models for the thermal growth of sea ice. The time-dependent problem is studied by numerically integrating the Fokker-Planck equation. The results obtained from these numerical integrations and their comparison with submarine and satellite observations of ice thickness will also be discussed.