AbstractA diagnostic study has been performed to investigate the prospects for developing a time-averaged statistical-dynamical model for making long-range weather forecasts. Estimates are made of nearly all terms in the equations describing the evolution of the time-mean quantities (ū, v̄, T̄, ) and the horizontal second-order eddy statistics (u2, v2, uv, uT) and vT. These calculations were performed over northwestern Europe, using radiosonde observations of wind, temperature and height for the winter of 197611977. Geostrophic winds were estimated from objective analyses, while vertical velocities were determined with a quasi-geostrophic baroclinic model. For each equation, approximate balances are presented on the basis of these estimates.In the equations for the mean quantities the time derivatives are more than one order of magnitude smaller than the unknown second-order eddy statistics. The same holds for the time derivatives of second-order eddy statistics compared with the unknown third-order and ageostrophic terms in the equations for these eddy fluxes. We therefore conclude that the system of time-averaged equations has no capability of describing the evolution of the atmosphere from one specific mean state to another mean state in the futuresince for this purpose a closure of the system or a parameterization of second- order or third-order terms has to be extremely accurate. Even in the case in which only the stationary waves of the mean flow are treated, a higher order closure scheme does not seem to be feasible, for third-order terms and ageostrophic second-order terms are probably large and very difficult to parameterize. This implies that a preferable approach is to explore in greater depth the possibility of parameterizing the second-order statistics directly.
Journal of the Atmospheric Sciences – American Meteorological Society
Published: Oct 19, 1979
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