# Global diagnostic energetics of five state-of-the-art climate models

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## Abstract

In this study, the global energy cycle of five state-of-the-art climate models is evaluated in the wave number domain for all seasons. The energy cycle estimates are based on 30 years of 6-hourly data obtained at pressure levels of all models. The models energetics are compared to those obtained from three reanalysis datasets (ERA-40, JRA-25 and NCEP-R2). The results show that the distributions of the energetics integrands and the shape of the various wave number spectra are reasonably well simulated. Many important features can be found in most models, namely both the upscale and downscale energy cascade for the wave–wave interactions of kinetic energy, the downscale energy cascade for the wave–wave interactions of available potential energy and the downscale energy transfer for the zonal–wave interactions of kinetic energy. However, the magnitude in the integrands distributions is generally excessive, yielding too much energy and an overactive energy cycle in the models. Accordingly, this energy excess is also reflected in the various spectra, specially but not exclusively, at the synoptic scale wave numbers for the energy conversion/transfer rates. The well known cold pole bias and the too strong tropospheric jets, along with their dislocation in some cases, still persist in the climate models. These are some of the deficiencies in the models directly implicated in the energy cycle. Apparently, simply increasing the horizontal and vertical resolutions is not enough to eliminate these deficiencies due to somewhat opposite effects achieved by refining both spatial resolutions. Therefore, more accurate physics parameterisations as well as improved numerical schemes and resolution dependence of parameterisations seem to be essential for a significant improvement in the models energetics. Moreover, efforts should be made to improve the physical processes controlling the generation of zonal available potential energy and dissipation of eddy kinetic energy, in which the synoptic scale should be fundamental, as inferred from the excessive energy conversion/transfer rates in the models spectra.

### Keywords

Atmospheric energetics Wave number Climate models Reanalysis### Abbreviations

*A*_{Z},*P*(0)Zonal available potential energy or total available potential energy in zonally averaged temperature distribution

*P*(*n*)Total available potential energy in eddies of wave number

*n**A*_{E}Eddy available potential energy \(\left(=\!\sum_{n=1}^{N} P(n)\right)\)

*K*_{Z},*K*(0)Zonal kinetic energy or total kinetic energy in zonally averaged motion

*K*(*n*)Total kinetic energy in eddies of wave number

*n**K*_{E}Eddy kinetic energy \(\left( =\!\sum_{n=1}^{N} K(n)\right)\)

*R*(*n*)Rate of transfer of zonal available potential energy to eddy available potential energy in wave number

*n**C*_{A}Rate of transfer of

*A*_{Z}to*A*_{E}\(\left( =\!\sum_{n=1}^{N} R(n)\right)\)*S*(*n*)Rate of transfer of available potential energy to eddies of wave number

*n*from eddies of all other wave numbers*C*_{Z},*C*(0)Rate of conversion of zonal available potential energy to zonal kinetic energy

*C*(*n*)Rate of conversion of available potential energy of wave number

*n*to eddy kinetic energy of wave number*n**C*_{E}Rate of conversion of

*A*_{E}to*K*_{E}\(\left( =\!\sum_{n=1}^{N} C(n \right))\)*M*(*n*)Rate of transfer of kinetic energy to the zonally averaged flow from eddies of wave number

*n**C*_{K}Rate of transfer of

*K*_{E}to*K*_{Z}\(\left( =\!\sum_{n=1}^{N} M(n)\right)\)*L*(*n*)Rate of transfer of kinetic energy to eddies of wave number

*n*from eddies of all other wave numbers*G*_{Z},*G*(0)Rate of generation of zonal available potential energy due to the zonally averaged heating

*G*(*n*)Rate of generation of available potential energy of wave number

*n*due to nonadiabatic heating*G*_{E}Rate of generation of \(A_E \left( =\!\sum_{n=1}^{N} G(n)\right)\)

*D*_{Z},*D*(0)Rate of viscous dissipation of zonal kinetic energy

*D*(*n*)Rate of viscous dissipation of the kinetic energy of eddies of wave number

*n**D*_{E}Rate of dissipation of \(K_E \left( =\!\sum_{n=1}^{N} D(n)\right)\)

*N*Maximum wavenumber for the analysis (=72 in a 2.5 degree grid)

*a*Mean earth radius

*c*_{p}Specific heat at constant pressure

- dm
Element of mass

*g*Acceleration of gravity

*h*Diabatic heating rate

*i*Square root of (−1)

*m*,*n*Zonal wave numbers

- \({\mathcal{M}}\)
Total mass of the atmosphere

*p*Pressure

*R*Dry air gas constant

*t*Time

*T*Temperature

*u*Zonal wind

*v*Meridional wind

*x*Eastward viscous force per unit mass

*y*Northward viscous force per unit mass

*Z*Geopotential height

*α*Specific volume

*ϕ*Latitude

*γ*Stability parameter

*λ*Longitude

*θ*Potential temperature

*ω*Vertical

*p*-velocity*Φ*Geopotential

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