# A statistical atmosphere model

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## Abstract

For simple analysis of stochastic climate models the ocean is often forced with a statistical atmosphere model. The atmosphere model mimics the observed statistics of the atmospheric forcing, e.g. the heat fluxes and the wind stress. This study serves as the beginning of the development of such a global statistical atmosphere model. The starting point of the development is a Monte-Carlo-like model written by Dietmar Dommenget, which is coupled to an one-dimensional model of the upper ocean. An important question in this context is how good the existing model simulates the atmospheric forcing. For that purpose the probability distribution functions of the net heat flux and the wind stress (respectively the surface fricion velocity u* ) derived from observations and a coupled run of the GCM ECHAM5 with the above mentioned ocean model are examined. The results are compared to the output of the statistical atmosphere model. The spatial and temporal patterns of the statistical moments mean, standard deviation, skewness and kurtosis are considered particularly. The investigation of the moments shows considerable differences between the model data and the observations. Especially the wind speed and thereby the friction velocity of the observations differs from that calculated by ECHAM5. The distributions of the friction velocity simulated by the statistical model deviate from both the observations and the ECHAM5 model data. By performing sensitivity studies it is shown that the deviations between the probability distribution functions have a non-negligible influence on the evolution of the sea surface temperature. The results of this analysis lead to possible modifcations of the statistical atmosphere model. Two different atmosphere models including these modifcations are presented. Another approach for the development of a statistical model, the usage of spatial correlation patterns is elucidated. Because of the enormous number of EOF modes needed to reach 90 percent of explained variance, even in the coupled EOF analysis between u* and the netflux, it is refrained from developing a statistical atmosphere based on these EOF modes. Finally an atmosphere model based on the bulk formulas is formulated as a result of a cross spectral analysis, which indicates an underrepresentation of the low-frequency variability in the SST time series caused by the direct forcing of the ocean with the surface fluxes. The SST time series simulated by this model exhibit a much higher coherency with the SST of the ECHAM5 model run.

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