Abstract
Abstract An energetics formulation is here introduced that enables an explicit evaluation for the conversion rates between available potential energy and kinetic energy, the nonlinear interactions of both energy forms, and their generation and dissipation rates, in both the zonal wavenumber and vertical mode domains. The conversion rates between available potential energy and kinetic energy are further decomposed into the contributions by the rotational (Rossby) and divergent (gravity) components of the circulation field. The computed energy terms allow one to formulate a detailed energy cycle describing the flow of energy among the zonal mean and eddy components, and also among the barotropic and baroclinic components. This new energetics formulation is a development of the 3D normal-mode energetics scheme. The new formulation is applied on an assessment of the energetics of winter (December–February) circulation in the 40-yr ECMWF Re-Analysis (ERA-40), the 25-yr Japan Meteorological Agency Reanalysis (JRA-25), and the NCEP–Department of Energy Reanalysis 2 (NCEP-R2) datasets.
Highlights
The net conversion rate of available potential energy into kinetic energy is mostly due to the conversion of potential energy of the rotational adjusted mass field into kinetic energy by the work realized in the eddy divergent motion
An energetics formulation has been introduced that enables an explicit evaluation for the conversion rates between available potential energy and kinetic energy, the nonlinear interactions of both energy forms, and their generation and dissipation rates, in both the zonal wavenumber and vertical mode domains
An energetics analysis was assessed for the DJF climate from three reanalysis datasets (ERA-40, JRA-25, and National Centers for Environmental Prediction (NCEP)– Department of Energy Reanalysis 2 (NCEP-R2))
Summary
Since the global energy cycle in the atmosphere was introduced by Lorenz (1955), the energetics of the atmospheric general circulation has been further investigated with orthogonal projections of the circulation field onto various basis functions. Saltzman (1957) presented the energetics in the zonal wavenumber domain, using a zonal harmonic expansion, which allows for the analysis of energy amounts and energy conversion/transfer rates in eddies of given wavenumber as well as the interaction between the eddies. Kao (1968) and Hayashi (1980) extended the approach of Saltzman (1957) to the wavenumber–frequency domain using a two-dimensional Fourier expansion. The 3D normal-mode energetics (NME) combines three one-dimensional spectral energetics in domains of zonal wavenumber n, a meridional mode number l, and a vertical mode number k. The scheme complement the standard energetics in the zonal wavenumber domain, since it can diagnose the 3D spectral distribution of energy and energy interactions, the energetics characteristics of Rossby waves and gravity waves, and the energy interaction between the barotropic and baroclinic modes (Tanaka and Kung 1988). By summing up the 3D NME terms within the same physical categories, the energetics characteristics can be assessed separately, for the zonal mean and eddy components, and for the barotropic and baroclinic modes, and for the Rossby and gravity waves.
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