Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere .1. Basic formulation

This paper presents a parameterization of gravity-wave momentum and energy deposition in the middle atmosphere, given a wave spectrum incident from below and arbitrary temperature and wind profiles through which it progresses upward. An associated turbulence diffusivity is also obtained. The work constitutes an extension and application of the author's previous analysis of gravity-wave saturation in the middle atmosphere. In that analysis the dissipation of waves, and so too the momentum and energy deposited by them, is controlled largely by a Doppler spreading caused by the fluctuating winds that are induced by the waves themselves, acting via the Eulerian advective nonlinearity. The present work adds the effects of Doppler shifting caused by the background winds of the region and parameterizes the whole. Implementation of the parameterization requires the adoption of some specific incident spectrum in vertical wavenumber m. The question of suitable spectra and their implementation is discussed in Part 2 of this paper, where too some modifications associated with quasi monochromatic spectra are introduced. Modelers who wish to go straight to the operational relations as exemplified by these spectra will find them in Part 2. Copyright (C) 1996 Elsevier Science Ltd.