The Variance Spectrum of Tropospheric Winds over Eastern Europe

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Abstract

Daily values of the 500 mb wind at 72 radiosonde stations in eastern Europe during July 1966 are analyzed. Variance is extracted for groups of contiguous stations occupying increasingly large areas, and for the whole set of stations over increasing time periods. Covariance over the month is computed for all possible station pairs as a function of length and direction of the separation vector and for observations at the same station as a function of separation in time. Efforts to extract variance spectra by direct inversion or transformation of these statistics fail, and they are, therefore, compared with those appropriate to several hypothetical variance spectra. In the spatial-scale range 500–2500 km, the data are consistent with a k5/3 spectrum which implies a dissipation rate of 1.5–2 ergs g−1, if interpreted as an energy-cascading inertial range. More variance is associated with this scale range than can reasonably he explained on the hypothesis of a k−3 spectrum. Within this scale range, spatial and temporal statistics are found to transform linearly by application of a mean wind speed (Taylor transformation). All results are compatible with an analysis, previously published by other authors, of a 2 h series of observations taken over the same month at a single station central to the group of 72.

Because the analysis differs in some important respects from that used by previous workers, particularly in the use of transforms appropriate to a two-dimensional vector field, elementary derivations are given of the methods used.

Abstract

Daily values of the 500 mb wind at 72 radiosonde stations in eastern Europe during July 1966 are analyzed. Variance is extracted for groups of contiguous stations occupying increasingly large areas, and for the whole set of stations over increasing time periods. Covariance over the month is computed for all possible station pairs as a function of length and direction of the separation vector and for observations at the same station as a function of separation in time. Efforts to extract variance spectra by direct inversion or transformation of these statistics fail, and they are, therefore, compared with those appropriate to several hypothetical variance spectra. In the spatial-scale range 500–2500 km, the data are consistent with a k5/3 spectrum which implies a dissipation rate of 1.5–2 ergs g−1, if interpreted as an energy-cascading inertial range. More variance is associated with this scale range than can reasonably he explained on the hypothesis of a k−3 spectrum. Within this scale range, spatial and temporal statistics are found to transform linearly by application of a mean wind speed (Taylor transformation). All results are compatible with an analysis, previously published by other authors, of a 2 h series of observations taken over the same month at a single station central to the group of 72.

Because the analysis differs in some important respects from that used by previous workers, particularly in the use of transforms appropriate to a two-dimensional vector field, elementary derivations are given of the methods used.

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