A stochastic dynamical model of Arctic sea ice

Abstract

he noise forcing underlying the variability in the Arctic ice cover has a wide range of principally unknown origins. For this reason, we analyze the analytical and numerical solutions of a stochastic Arctic sea ice model with both additive and multiplicative noise over a wide range of external heat-fluxes, ?F0, corresponding to greenhouse gas forcing. The stochastic variability influences the nature of the deterministic steady state solutions corresponding to perennial, seasonal ice and ice free states. Thus, the results are particularly relevant for the interpretation of the state of the system as the ice cover thins with ?F0, allowing a thorough examination of the differing effects of additive versus multiplicative noise. In the perennial ice regime, the principal stochastic moments are calculated and compared with those determined from a stochastic perturbation theory described previously. As ?F0 increases, we examine in detail the competing contributions to the variability of the destabilizing sea ice-albedo-feedback and the stabilizing long-wave radiative loss. At the end of summer the variability of the stochastic paths shows a clear maximum, which is due to the combination of the increasing influence of the albedo-feedback and an associated ?memory effect?, in which fluctuations accumulate from early spring to late summer. This is counterbalanced by the stabilization of the ice cover due to the longwave loss of energy from the ice surface, which is enhanced during winter, thereby focusing the stochastic paths and decreasing the variability. Finally, we discuss common examples in stochastic dynamics with multiplicative noise wherein the choice of the stochastic calculus (Itô or Stratonovich) is not necessarily determinable a-priori from observations alone, which is why we treat both calculi on equal footing herein.