Investigating the variability of the Arctic sea ice thickness in response to a stochastic thermodynamic atmospheric forcing

The natural low frequency variability of the sea-ice thickness in the Arctic is investigated based on a 10 000 years simulation with a one-dimensional thermodynamic sea-ice model forced by random perturbations of the air surface temperature and solar radiation. The simulation results suggest that atmospheric random perturbations are integrated by the sea-ice. Moreover those perturbations occurring at the onset of ice melting force the largest ice thickness anomalies, which are successively amplified in summer by the albedo feedback and damped in winter by the feedback of the heat conduction through the ice. They also result in a global shift of the melting season which, in the mean annual cycle, leads to earlier melting as compared to the mean climatological cycle. The power spectrum of the ice anomalies suggests that the thickness of the perennial ice should vary preferentially on a time scale of approximately 20 years. The shape of the spectrum is consistent with that of a first order Markov process in which the characteristic time scale of the ice fluctuations would be the relaxation time scale associated with the linear feedback. The equivalent Markov model is constructed by linearizing the ice growth rate anomaly equations and allows us to derive an analytical expression of the feedback and of the forcing of the anomalies. The characteristic time scale depends explicitly on those model parameters involved in the atmosphere-ice interaction but also on the mean seasonal characteristics of the forcing and of the ice thickness.