The form of Newtonian cooling in atmospheric tidal theory

The different forms of the classical atmospheric tidal vertical structure equation derived by Lindzen and McKenzie (1967) and by Dickinson and Geller (1968) are shown to be due solely to their different treatment of the infrared radiative damping of tidal temperature perturbations. While both parameterize the infrared cooling as a Newtonian cooling, the former use the tidal temperature perturbation along a constant geometric height surface while the latter use the perturbation along a constant pressure surface. These two tidal temperature perturbations differ when the background atmospheric temperature varies with height. Scaling arguments show that for most applications the differences between the use of these two forms of Newtonian cooling are negligible. However, relative differences of 30% in amplitude and 15° in phase can occur in the Martian atmosphere, with its relatively short radiative time constants, for a possibly resonant planetary-scale Rossby tidal mode.