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Energetics

The atmospheric energy in a model can be stored in the form of potential energy and kinetic energy, which can be described with energetics. The Lorenz atmospheric energy cycle describes the general circulation from a perspective that emphasizes energy transformation - how the incoming solar radiation generates potential energy that is converted to kinetic energy and is finally lost to frictional dissipation. These statistical characteristics of the global atmospheric energy cycle are useful for validation of general circulation models since they constitute constraints that must be satisfied.

The LC-LRFMME developed its model assessment system based on balance equation. We calculated the energy cycle and the connecting links between the various energy forms. A schematic box diagram of energy cycle is provided in Fig. 1.

Fig. 1. Schematic box diagram of the energy cycle in the atmosphere showing the rates of generation, conversion, and dissipation of the various forms of energy.

  • PM: mean available potential energy
  • PE: eddy available potential energy, which is composed of PSEand PTE
  • PSE: stationary eddy available potential energy
  • PTE: transient eddy available potential energy
  • KM: mean kinetic energy
  • KE: eddy kinetic energy, which is composed of KTEand KSE
  • KTE: transient eddy kinetic energy
  • KSE: stationary eddy kinetic energy
  • C(A,B) : conversion rate of A to B

The balance equations for the four basic forms of energy are summarized as follows:

Where, C, G, D, means conversion, generation and dissipation rates respectively, and the eddy available potential energy PE and the eddy kinetic energy KEare divided into two terms for elaboration as follows:

The mean available potential energy is converted into eddy available potential energy by the growing baroclinic disturbances. Some of the eddy available potential energy may be dissipated by a greater loss of infrared radiation to space in warm rather than in cold air and by a similar heat exchange with the earth's surface. However, latent heating is believed to surpass these effects, leading to a small positive generation of PE. The eddy available potential energy PEis then converted into eddy kinetic energyKEthrough the sinking of relatively cold air and the rising of warm air in the eddies. Some of the eddy kinetic energy KEis converted into kinetic energy of the mean flow KMin a barotropic process leading to a decascade of energy from the small into the larger scales, which can be interpreted as a negative viscosity phenomenon. However, the bulk of the kinetic energy of the large-scale eddies is dissipated by friction in a normal cascade regime. Finally, some of the mean zonal kinetic energy KMis dissipated by friction and turbulence, while a small residual is converted into mean zonal available potential energy PMby the combined action of the direct and indirect mean meridional circulation. If one compares the total amount of kinetic energy with the rate of dissipation of kinetic energy we find that it would take about seven days to dissipate the kinetic energy.