On the Radiative Damping of Atmospheric Waves

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Abstract
General expressions for computing time constants for radiative decay of harmonic temperature perturbations in planetary atmospheres are developed. Previous studies have not taken into account the inhomogeneity of planetary atmospheres or, more important, the role of the planetary surface. These omissions lead to significant overestimates of the radiative time constant in a number of cases. Four spatial scales are shown to he generally important. the scale height of the atmospheric absorber, the absorption mean–free–path for thermal radiation, the altitude above the planetary surface, and the wavelength of the temperature perturbation. Atmospheric inhomogeneity is particularly important when the radiation mean free path and the vertical wavelength divided by 2π both exceed the absorber scale height. The surface is very important for decay of waves at attitudes less than a few radiation mean tree paths. The effect of the surface depends on a comparison of the surface response time and the lifetime of the atmospheric perturbation. The surface response time depends on the conducting and emitting properties of the surface material and on the strength of turbulence in the planetary boundary layer. Highly conducting surfaces have very long response times and lead to much shorter radiative time constants than insulated surfaces which have very short response times. The additional influence of chemical reactions and phase changes on radiative damping is discussed and several assumptions inherent in the development of the general expressions for time constants are evaluated. Terrestrial examples are used for purposes of illustration but the development is kept sufficiently general so that the results remain applicable to most situations on other planets.

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