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A method to describe unresolved processes in meteorological models byphysically based stochastic processes (SP) is proposed by the example of anenergy budget model (EBM). Contrary to the common approach using additive whitenoise, a suitable variable within the model is chosen to be represented by aSP. Spectral analysis of ice core time series shows a red noise character ofthe underlying fluctuations. Fitting Ornstein Uhlenbeck processes to theobserved spectrum defines the parameters for the stochastic dynamic model(SDM). Numerical simulations for different sets of ice core data lead to threesets of strongly differing systems. Pathwise, statistical and spectral analysisof these models show the importance of carefully choosing suitable stochasticterms in order to get a physically meaningful SDM.

A Stochastic Energy Budget Model Using Physically Based Red Noise