On the annual variation and spectral distribution of atmospheric energy¹

1 Research supported by the National Science Foundation, GP-2561. Contribution So. 110, Department of Meteorology and Oceanography, University of Michigan.

Abstract

A study is made of the annual variation of the six components, A_Z, A_E, K_E, K_Z, K_S, and K_M, of the energy in the atmosphere based on data from a complete year, February 1963–January 1964, and on eight vertical levels. The distribution of the energy with respect to pressure and time of the year is investigated with the result that all forms of energy have a maximum in the beginning of the year and a minimum during the month of July.

The energy conversions C(A_Z, A_E), C(K_E, K_Z) and C(K_S, K_M) are also investigated during the period. The most remarkable result is the annual variation of C(KE, KZ) showing a maximum during the fall, a phenomenon also observed during the previous year.

Fourier analysis of the data in time is employed to determine the amplitude and phase of the first few components. The first component contains a considerable fraction of the annual variations, but the second component is in certain cases, as for example C(K_E, K_Z), very important in describing the annual behavior. A similar analysis is made of three years of data with essentially the same results. The latter set of energy data is used to determine the annual variation of the generation of available potential energy and the frictional dissipation using the energy equations, while the data for 1963 are used to calculate the energy conversion C(A, K) and the generation G(A) based on the energy equations and an assumption concerning the frictional dissipation.

The last section of the paper contains a description of the results of an investigation of the energy spectra showing that in the range of wave numbers 8 ≤ n ≤ 15 we can approximate the form of the spectra by a power law: E = a = n-b. a and b are determined by regression analysis.