Three-dimensional Scaling and Structure of Atmospheric Energetics

Abstract

Three-dimensional structure functions characteristic of atmospheric energy are developed from data samples and presented. The horizontal dependence is based on known functions in spherical surfaces whereas the vertical dependence is derived from data. Three-dimensional scaling of these functions is determined from the properties of the functions as well as their ability to satisfy the potential vorticity equation. The distribution of observed planetary energy represented by these functions is presented in terms of their scale. Two-dimensional energy distributions in each of the vertical modes are also described. Power law relationships of energy versus scale with slope of ?3 appear in the statistics, but not under all conditions. The results of the study may be useful in parameterizing non-resolved model scales for closure. The structure functions may be utilized for fully three-dimensional spectral modeling. The scaling of the structure functions indicates appropriate vertical resolution for given horizontal model truncation as well as the appropriate vertical levels to be selected.