The kinetic energy spectrum vis-à-vis a statistical model for geopotential

The relationship between a statistical model for geopotential height and the geostrophic eddy kinetic energy spectrum is elaborated. Ensemble spatial variability of the isobaric field is represented with a continuous linear stochastic model in the natural coordinates of a rotating sphere. The corresponding bi-frequency spectral density for the height field is derived, and a linear filter technique is applied to obtain a description of its implications for the eddy kinetic energy spectrum. The direct correspondence between spatially autoregressive models and bi-frequency spectra, and the companion correspondence between these autoregressive models and lag-correlation functions are discussed with regard to their combined potential for elucidating properties of the frequency (wave number) power spectrum.

The development produces an analytic tool for further investigation of the dependence of geostrophic kinetic energy on latitudinal and longitudinal wave numbers. It is argued that the somewhat simplistic nature of the approach is compensated by the sensitivity of the representations of distinct frequency components and the parsimony of statistical analyses based on the result. Possible implications for the retention of forecast-relevant energy distributions in objective analyses are considered.