A study of global mean temperatures applied to available potential energy, annual variations and static stability

This paper contains, for pedagogical purposes, a brief derivation of quasi-geostrophic, available potential energy using the parcel method and an approximate calculation of the work performed during the displacement. For the study, we have used 7 years of globally averaged temperatures. These data indicate a seasonal variation of the global mean temperature. The seasonal variation is determined from the data with respect to amplitude and phase, and a simple model is used to relate this variation to the seasonal variation of the planetary albedo. It is also demonstrated that the seasonal changes in the global mean temperature due to the ellipticity of the orbit are out of phase with the observed changes. The same data have been used to study the vertical variation of the static stability parameter entering in quasi-geostrophic models, as a function of pressure. The changes in the vertical direction are important for the determination of the vertical structure functions. In the first approximation, the parameter is inversely proportional to the square of the pressure, but deviations occur, depending on the number and position of the pressure levels. The error in the calculation of quasi-geostrophic, available potential energy due to an incorrect specification of the stability parameter is investigated using a specific example in Section 4.