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Idealized low-order spectral models based on quasi-geostrophy have been proposed by Charney, Egger, and others for a qualitative explanation of quasi-stationary flow patterns in the troposphere, such as blocking highs. To test these concepts, we consider spectral, quasi-geostrophic, barotropic models of a slightly higher, but still relatively low resolution (28 and 68 degrees of freedom). The models are treated as regression models, the predictors being the individual components of the prognostic vorticity equation, namely the beta, advection, orography, friction and forcing terms. A 10-year record of observed north-hemispheric geopotential data is used as data basis for the statistical regression analysis. The regression model may be interpreted as a truncated model in which the individual terms have been modified by (a) projecting the truncation and other systematic model errors onto the terms retained in the simplified system, and (b) keeping in the retained terms only the contributions which are correlated with the observed change in the atmospheric state. The model is applied in the inverse mode as a diagnostic tool to determine which processes are most important for the evolution of the system, and how much of the observed large-scale variance of the atmosphere can be explained by such a low-order system. Despite the strong spectral truncation, the model is found to explain a reasonable percentage of the observed variance (of the order of 30%, or 0.55 correlation, for 68 components). However, it was not possible to explain a significant fraction of the variance by still more strongly truncated models of the idealized form proposed by Charney and Egger. Our analysis indicates that all degrees of freedom of the truncated system (28 or 68) contribute significantly to the dynamics of the large-scale components. The most important processes are the wave/mean-flow interaction and the beta effect, followed by the nonlinear interactions among waves and the annually varying thermal forcing. Interactions with orography and frictional effects are generally negligible. The residual variance not represented by the model cannot be parameterized in a simple manner in terms of the components of the truncated model itself and must be treated as external stochastic forcing. Thus for a realistic description of large-scale atmospheric variability, low-order spectral models must be augmented by a significant stochastic forcing component in addition to the internal interactions.DOI: 10.1111/j.1600-0870.1986.tb00449.x
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