On the concept of available potential energy

Abstract

The available potential energy of the atmosphere is defined as the property of the atmosphere for which the source is energy generated by the distribution of the heat sources and sinks, i.e. their deviations from the mean heating rate, and the sink its conversion to kinetic energy; the unavailable potential energy is defined as having as its source the mean (uniform) heating rate and its sink the energy made available for conversion by the heating distribution, i.e. the APE source. These definitions lead to an expression for the APE which, to a good approximation, is proportional to the global mean temperature variance. This partitions into zonal and eddy components and, in addition, a component involving the mean temperature distribution in the vertical. Associated with the latter is a source term determined by the mean heating distribution in the vertical and sink terms corresponding to its conversion to the other two components, these terms being proportional to the conversions to KE. This additional component is referred to as the static stability component of available potential energy (SAPE). The zonal and eddy components, which depend on the temperature variance on isobaric surfaces, are together referred to as the baroclinicity component of the APE. The relationship between this form of the APE and that proposed by Lorenz is discussed in detail. The physical interpretation of the conversion between zonal and eddy APE, associated mainly with poleward heat (enthalpy) transport down the mean meridional temperature gradient is found to have its analogue in the conversion from the static stability component to the other two components which is associated with upward heat transport down the vertical temperature gradient. The concepts are illustrated for a numerical simulation of the life cycle of an idealized baroclinic wave. It is further shown that this definition of APE extends quite naturally to the description of the energetics of dry and moist convection and its conversions can be calculated without difficulty even if there exist regions in which the lapse rate is dry adiabatic. The roles of frictional and non-frictional heating in the general atmospheric circulation are discussed and, finally, comments are made on the concept of adiabatic mass redistribution and the definition of a reference state for APE in the light of the approach adopted here.