Testing a Global Multivariate Statistical Objective Analysis Scheme with Observed Data

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Abstract
A multivariate statistical analysis procedure has been developed for estimating geopotential height h and wind (u, v) on a global latitude-longitude grid. Estimates are obtained by modifying the “first guess” from a prediction model by a linear combination of forecast errors deduced from observed data. Because the scheme is multivariate, the regression coefficients (weights) are matrices, which depend upon covariance among forecast errors in h, u and v. These covariances are modeled mathematically with geostrophic constraints. In the tropics, however, only the wind field is analyzed, covariances are modeled under the constraint of nondivergence, and heights are obtained from a balance equation. At high latitudes, analyses are performed in polar stereographic coordinates. The objective analysis scheme fits observed data as well as the “Cressman scheme” that was used operationally at the National Meteorological Center until recently and also as well as a skilled analyst. In data-rich areas, the analyses are insensitive to the type of fist guess. Realistic ageostrophic and divergent components are present in the analyzed winds, and the kinetic energy spectrum at 40°N is reasonable at zonal wavenumbers less than 20. When both wind and height observations are plentiful, two univariate schemes (one for height, one for wind) fit the data as well as the multivariate scheme, but forecasts based upon the latter are consistently better. Experiments suggest that for a fixed amount of initial data, small gains in forecast accuracy can be made by improving the analysis procedure.

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