The generation of available potential energy, according to Lorenz’ exact and approximate equations

Abstract

The generation of available potential energy (APE) in the atmosphere according to Lorenz’ (1955a, b) exact and approximate equations is investigated in the space-time domain. The generation is determined from the fields of diabatic heating and temperature. The heating is evaluated by the residual method, using 4 × daily ECMWF-(European Centre for Medium-Range Weather Forecasts) initialised analyses for the January months of 1986—1992 and the July months of 1985—1991. The contributions of different parts of the atmosphere to the exact and approximate generation are investigated, and the differences between these contributions are explained. In the derivation of the equation of the approximate generation, Lorenz made several approximations. The most serious one appears to be that the average pressure on an isentropic surface is approximately equal to the pressure of the isobaric surface, for which the average potential temperature is equal to the potential temperature of the isentropic surface. Our results show that the largest differences between the contributions to the exact and approximate generation occur in the extratropical low troposphere. Here the contribution to the exact generation of eddy APE is up to 10 × smaller than in the approximation, and the contribution to the exact generation of zonal- and time-mean APE is weakly positive, whereas for the approximation it is strongly negative. Other main differences occur in the tropical middle troposphere where the contribution to the exact generation of mean APE is about two times as small as the approximate value. Despite these large differences, the globally averaged exact generation of mean APE, which is 2.29 W/m² in January and 1.88 W/m² in July, differs less than 3% from its approximation. The globally averaged exact generation of stationary eddy APE, which is 0.26 W/m² in January and 0.45 W/m² in July, is about 25% smaller than its approximation. In most individual months the globally averaged exact generation of transient eddy APE is weakly positive (about 0.01 W/m²), whereas the approximation is weakly negative (about — 0.08 W/m²). The globally averaged generation of mean APE is not sensitive to the period and kind of the circulation data. The sensitivity of the globally averaged generation of stationary and transient eddy APE is about 0.1 W/m².