An Alternate Scale Representation of Atmospheric Energy Spectra

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  • 1 Dept. of Atmospheric Science, Colorado State University, Fort Collins
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Abstract

Although it is known that all spatial scales are nonlinearly interrelated in any prediction model of the atmosphere, truncation demands a limit to scale resolution. One is therefore compelled to parameterize sub-resolution scales, hopefully in such a manner that they describe observed statistics. Such statistics have been shown frequently as energy spectra of synoptic scales in terms of the planetary wavenumber. An alternate representation is the presentation of the energy in terms of the degree of a Legendre polynomial expansion; this representation may be more advantageous insofar as it presents a two-dimensional spectral index. Arguments are presented which indeed suggest the appropriateness of the index. Two months of atmospheric wind data at five pressure levels and on a hemispheric grid were analyzed to establish energy spectra. The spectra are described both as a function of time and as a function of wavenumber for time averages. Using a five-level linear baroclinic model, stability characteristics for each wave component for the observed zonal and vertical profiles were established. Based on these results, the energy data were fit logarithmically by least squares to the wavenumber (both planetary wavenumber and Legendre polynomial degree). Energy slopes show values close to −3 when utilizing the two-dimensional index in the non-baroclinically forced scale range. These results suggest the use of this index in studying scale parameterization.

Abstract

Although it is known that all spatial scales are nonlinearly interrelated in any prediction model of the atmosphere, truncation demands a limit to scale resolution. One is therefore compelled to parameterize sub-resolution scales, hopefully in such a manner that they describe observed statistics. Such statistics have been shown frequently as energy spectra of synoptic scales in terms of the planetary wavenumber. An alternate representation is the presentation of the energy in terms of the degree of a Legendre polynomial expansion; this representation may be more advantageous insofar as it presents a two-dimensional spectral index. Arguments are presented which indeed suggest the appropriateness of the index. Two months of atmospheric wind data at five pressure levels and on a hemispheric grid were analyzed to establish energy spectra. The spectra are described both as a function of time and as a function of wavenumber for time averages. Using a five-level linear baroclinic model, stability characteristics for each wave component for the observed zonal and vertical profiles were established. Based on these results, the energy data were fit logarithmically by least squares to the wavenumber (both planetary wavenumber and Legendre polynomial degree). Energy slopes show values close to −3 when utilizing the two-dimensional index in the non-baroclinically forced scale range. These results suggest the use of this index in studying scale parameterization.

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