A model of a stochastically driven ice sheet with planetary wave feedback

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Abstract
The growth and decay of continental ice sheets forms a key problem in dynamical climatology. Apart from knowledge about their behaviour for given external conditions, like the distribution of incoming solar energy, it is desirable to know something about their variability due to forcing with a stochastic character. This paper presents a simple model of ice-sheet variability in which the interaction between ice sheet and atmosphere is taken into account in a crude way. The model is formulated by a linear second-order differential equation describing the evolution of the ice-sheet size, and is stochastically forced by white noise representing year-to-year weather fluctuations. The results, statistics of ice-sheet size variability, are very sensitive to the model parameters prescribing the ice sheet-atmosphere interaction. For realistic values of those parameters, the standard deviation of the ice-sheet size (in north-south direction) is in the 10–500 km range for a large ice sheet, thus leaving much uncertainty. The main conclusion of the analysis is that stochastic forcing of ice sheets is important only if strong positive feedback between ice sheets and atmosphere exists. DOI: 10.1111/j.2153-3490.1979.tb00928.x