## Abstract

A cascade-type energy conversion diagram is proposed for the purpose of diagnosing the atmospheric general circulation based on wave–mean flow interactions. Mass-weighted isentropic zonal means facilitate the expression of nongeostrophic wave effects, conservation properties, and lower boundary conditions. To gain physical insights into energetics based on the nonacceleration theorem, the wave energy *W* is defined as the sum of the eddy available potential energy *P _{E}* and the eddy kinetic energy

*K*.

_{E}The mainstream of the energy cascade is as follows: The diabatic heating produces the zonal mean available potential energy *P _{Z}*, which is converted into the zonal mean kinetic energy

*K*through the mean meridional circulation. The

_{Z}*K*is mainly converted to

_{Z}*W*through zonal wave–mean flow interactions and the rest is dissipated through friction. Not only the dynamical conversion but also the diabatic heating generates

*W*, which is dissipated through friction.

A diagnosis package is designed to analyze actual atmospheric data on the standard pressure surfaces. A validation study of the package is made by using the output from a general circulation model. The scheme accurately expresses tendencies of the zonal mean and eddy available potential energy equations, showing the diagnosis capability. On shorter time scales, *P _{E}* changes in accordance with

*K*, good correlation indicating the relevance of the definition of wave energy.

_{E}A preliminary study is made of the climate in December–February (DJF), and June–August (JJA), using the NCEP–NCAR reanalysis. The dynamical wave energy generation rate *C*(*K _{Z}*,

*W*) is about 60% of the conversion rate

*C*(

*P*,

_{Z}*K*), which means that

_{Z}*K*is dissipated through friction at a rate of about 40%. In the extratropics,

_{Z}*C*(

*K*,

_{Z}*W*) is almost equal to

*C*(

*P*,

_{Z}*K*), as is expected from quasigeostrophic balance. In the subtropics, however,

_{Z}*C*(

*K*,

_{Z}*W*) is much smaller than

*C*(

*P*,

_{Z}*K*), which suggests the importance of nongeostrophic effects on the energetics. The energetics is substantially different between the two solstices. Both

_{Z}*C*(

*P*,

_{Z}*K*) and

_{Z}*C*(

*K*,

_{Z}*W*) are about 30% larger in DJF than those in JJA, reflecting differences in wave activity. Stationary waves contribute considerably to energy conversions in the Northern Hemispheric winter, while baroclinic instability waves do more in the Southern Hemispheric winter than in the Northern Hemispheric winter.

*Corresponding author address:* Toshiki Iwasaki, Dept. of Geophysics, Graduate School of Science, Tohoku University Aramaki, Aoba-ku, Sendai 980-8578, Japan. Email: iwasaki@wind.geophys.tohoku.ac.jp