## 1. INTRODUCTION

[2] Considerable progress has occurred in our understanding of middle atmosphere gravity waves in the four decades since the pioneering study by *Hines* [1960]. Indeed, interest in the field continues to expand as the many effects of gravity waves become better understood. Early results were reviewed extensively by *Fritts* [1984a], while subsequent reviews addressed specific aspects of gravity wave instability [*Fritts and Rastogi*, 1985], saturation [*Dunkerton*, 1989; *Fritts*, 1989], or climatologies and effects [*Vincent*, 1984a; *Schoeberl*, 1987; *Hamilton*, 1996; *McLandress*, 1998]. Arguably, the greatest quantitative advances in our understanding have been the most recent and have accompanied equally dramatic advances in observational and computational techniques and capabilities. This review will span middle atmosphere gravity wave dynamics and effects but will emphasize results subsequent to the review by *Fritts* [1984a].

[3] In retrospect, our understanding of middle atmosphere gravity waves in 1984 was quite limited. We had recognized the role of gravity waves in transporting energy and momentum, in contributing turbulence and mixing, and in influencing the mean circulation and thermal structure of the middle atmosphere, based on limited theoretical, numerical, and observational studies [*Lindzen*, 1981; *Holton*, 1982, 1983; *Vincent and Reid*, 1983]. However, we had little or no understanding of the characteristics of the gravity wave spectrum and of its behavior with altitude, of the variability imposed by sources and variable mean and low-frequency motions, of the global climatology of gravity waves and their effects, or of the processes and interactions that constrain wave amplitudes, effect spectral energy transfers, and account for turbulence, fluxes, and mixing. We also had explored only the most rudimentary schemes for describing gravity wave effects in large-scale models [*Lindzen*, 1981; *Holton*, 1982; *Matsuno*, 1982; *Dunkerton*, 1982a] and had no appreciation for the rich range of behaviors accompanying gravity waves throughout the middle atmosphere.

[4] More recent studies have yielded a more detailed understanding of middle atmosphere gravity waves on many fronts. In situ, ground-based, and space-based observational studies have contributed greatly to our knowledge of gravity wave scales, amplitudes, fluxes, and spectra. They have also addressed instability dynamics, vertical propagation, variations with altitude, and seasonal and geographic variability. Recent theoretical and numerical studies have addressed source characteristics and scales, spectral character, evolution, and energy transfers, instability dynamics, wave–wave and wave–mean flow interactions, and the implications of various parameterizations for atmospheric circulation and structure.

[5] Our purpose here is to review the contributions since 1984 that have led to our more advanced understanding of middle atmosphere gravity waves and their effects. In doing so, it will be impossible to cite all of the work that has been published. Instead, we will restrict ourselves to what we consider to be the more significant contributions in each area. We also will note, on occasion, where errors in interpretation have occurred and where debate over observational or theoretical implications continues to allow the reader to steer clear of mistakes and identify topics of current interest.

[6] We begin by reviewing the linear inviscid theory of gravity wave propagation as well as departures due to nonlinearity, dissipation via wave breaking, transience, localization, and variable environments, in section 2. Sources, propagation, and scales relevant to the middle atmosphere will be addressed in section 3. Spectral character and evolution, including evidence for and against universality, are reviewed in section 4. Section 5 summarizes what is known of gravity wave climatologies and their implications for sources and effects. Gravity wave interactions, instability dynamics, and wave-breaking or saturation processes are examined in section 6. Sections 7 and 8 describe efforts to parameterize gravity wave effects to date and their implementation and effects on the large-scale circulation and structure of the middle atmosphere. Our summary and recommendations are presented in section 9.