A TEST OF NUMERICAL PREDICTION METHODS BASED ON THE BAROTROPIC AND TWO-PARAMETER BAROCLINIC MODELS

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Abstract
A two-parameter baroclinic model for vertically integrated flow is derived under the assumption of an isogonal geostrophic wind shear, and constitutes a generalization of the theory of equivalent baroclinic flow. The computational procedures used to apply both this theory and that for purely barotropic flow to the production of numerical forecasts are described in detail, and this is followed by a brief summary of the results of an extensive series of numerical integrations of the equations of both the barotropic and thermotropic models. In all, a total of 120 24-hour forecasts were made every 12 hr from a series of especially prepared maps throughout the entire month of January 1953, the largest collection of numerical forecasts assembled to the present time. From a preliminary summary of the results supported by the discussion of several individual cases, it appears that the major characteristics of this series of numerical forecasts are: (1) the lack of a significant difference between the barotropic and thermotropic 500-millibar forecasts, the correlation between the predicted and observed 24-hr 500-mb height changes being 0.74 in each case, (2) the marked effects of a number of purely mathematical errors or errors of method, especially those introduced by the lateral boundary conditions and by the use of the finite-difference approximation, and (3) an important effect of the Rocky Mountain barrier on the forecasts. These results are interpreted as demonstrating the quasi-barotropy of the atmosphere at mid-tropospheric levels when considered on a day-to-day basis over a monthly period. The 1000-mb forecasts computed from the baroclinic theory, while displaying an average correlation between predicted and observed 24-hr height changes of only 0.62, show considerable synoptic “skill,” especially over the eastern United States. These forecasts are felt to demonstrate conclusively the applicability of numerical prediction techniques to operational forecasting. Further research on the effects of both the physical and mathematical approximations of the methods of numerical prediction is suggested.

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