A Cascade-Type Global Energy Conversion Diagram Based on Wave–Mean Flow Interactions

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 PE and the eddy kinetic energy KE. The mainstream of the energy cascade is as follows: The diabatic heating produces the zonal mean available potential energy PZ, which is converted into the zonal mean kinetic energy KZ through the mean meridional circulation. The KZ is mainly converted to 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, PE changes in accordance with KE, good correlation indicating the relevance of the definition of wave energy. 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(KZ, W) is about 60% of the conversion rate C(PZ, KZ), which means that KZ is dissipated through friction at a rate of about 40%. In the extratropics, C(KZ, W) is almost equal to C(PZ, KZ), as is expected from quasigeostrophic balance. In the subtropics, however, C(KZ, W) is much smaller than C(PZ, KZ), which suggests the importance of nongeostrophic effects on the energetics. The energetics is substantially different between the two solstices. Both C(PZ, KZ) and C(KZ, 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.

Future Changes of Atmospheric Energy Cycle in CMIP5 Climate Models

“…This indirect estimation may suffer from numerical calculation errors. The results of a previous study showed that the energy generation rates of direct and indirect estimations of the diabatic heating rate differ (Uno & Iwasaki, 2006). This difference may affect the future changes of these terms.…”

“…Subsequently, it is converted into wave energy through wave-mean flow interactions C(K Z , W). In the extratropics, these two dynamic conversion rates become equivalent under geostrophic balance (Uno & Iwasaki, 2006). In the tropics, By comparing the JRA-55 and CMIP5 models, we examined the performances of the selected climate models with respect to the energy diagram for the present climate.…”

“…The MIM correctly expresses wave-mean flow interactions and mass stream-functions, even in the lower troposphere (Iwasaki, 1989(Iwasaki, , 1992. These two energy conversions are geostrophically related (Uno & Iwasaki, 2006) and mainly driven by the baroclinic instability (Iwasaki & Kodama, 2011). This simple energy diagram has been employed in several climate variability studies (Kodama & Iwasaki, 2009;Kodama et al, 2010;Uno & Iwasaki, 2006).…”

“…These two energy conversions are geostrophically related (Uno & Iwasaki, 2006) and mainly driven by the baroclinic instability (Iwasaki & Kodama, 2011). This simple energy diagram has been employed in several climate variability studies (Kodama & Iwasaki, 2009; Kodama et al., 2010; Uno & Iwasaki, 2006). Kodama and Iwasaki (2009) carried out aqua‐planet experiments with different sea surface temperature (SST) distributions to mimic idealized global warming and showed that a smaller meridional SST gradient suppresses the wave energy, whereas a uniform SST shift of +3 K in‐significantly changes the wave energy.…”

Mass-Weighted Isentropic Zonal Mean Equatorward Flow in the Northern Hemispheric Winter

“…MIM represents a cascade-type energy conversion diagram, if the wave energy is defined as a sum of eddy available potential energy and eddy kinetic energy (Iwasaki 2001;Uno and Iwasaki 2006). The ETD circulations convert zonal mean available potential energy to zonal mean kinetic energy, and wave-mean flow interactions do zonal mean kinetic energy to wave energy.…”