Comments on ``Atmospheric Tides'' by A. Palumbo [Journal of Atmospheric and Solar-Terrestrial Physics 60 (1998) 279-287]

Palumbo (1998), starting from the equation of state in differentiated form p sub(n) /p sub(m) = [f] sub(n) /[f] sub(m) + rho sub(n) / rho sub(m) + T sub(n) /T sub(m) + rho sub(n) T sub(n) / rho sub(m) T sub(m) with p sub(m) , rho sub(m) , T sub(m) , [f] sub(m) being the mean background pressure, density, temperature, and water vapor pressure, respectively, and p sub(n) , etc., the tidal wave amplitudes (n greater than or equal to 1) of the n-th harmonic with a basic period of one solar day, maintains that the observed semidiurnal tidal pressure wave p sub(2) , which is about twice as large as its diurnal component p sub(1) , results from a nonlinear interaction between the diurnal temperature wave T sub(1) and the diurnal density wave rho sub(1) (the product rho sub(1) T sub(1) in eqn (1)). The phase difference between rho sub(1) and T sub(1) has been measured to be such that both wave components interfere destructively. Thus, the diurnal component p sub(1) becomes smaller than the semidiurnal component p sub(2) generated by the product rho sub(1) T sub(1) in eqn (1). This scenario is not very convincing for the following reasons: (a) Palumbo introduced a factor of k = rho sub(1) / rho sub(m) = T sub(1) /T sub(m) in order to estimate the phase relationship between rho sub(1) and T sub(1) from eqn (1). From the numerical values given at the beginning of his section 6 (p. 286), I derive a number of k = 2B/A | cos 91 degrees | [perspective to] 0.1 which would yield a diurnal temperature amplitude of T sub(1) = kT sub(m) [perspective to] 29 K, certainly an unrealistic number. (The number of K super(2) = 0.20 on p. 286 seems to be a misprint.) On the other hand, one finds from the numbers given in tables 1-3 values of Th sub(1) and D sub(1) of the order of, e.g., | Th sub(1) | = R rho sub(m) T sub(1) [perspective to] 10 hPa (or mb). Thus k = | Th sub(1) | /p sub(m) [perspective to] 0.01. Evidently, which such small value of k, his mechanism of nonlinear interaction does not work. Typical values for global-scale diurnal tidal pressure waves measured near the ground are of the order k [perspective to] 1/1000 (e.g., Chapman and Lindzen, 1970), and the same order of magnitude holds for the temperature and density waves. Local-scale daily variations may have values of k up to one order of magnitude larger. My conclusion is therefore, that Palumbo (1998) measures essentially local-scale daily variations. (b) Atmosphere dynamics is described by the set of hydrodynamic