JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. A8, PAGES 14,141-14,152, AUGUST 1, 1991 On the Nonlinear Response of Airglow to Linear Gravity Waves J. R. ISLER 1 AND T. F. TUAN PhysicsDepartment, University of Cincinnati, Cincinnati, Ohio R. H. PICARD Optical Environment Division, Geophysics Directorate, Phillips Laboratory, Hanscorn Air Force Base, Bedford, Massachusetts U. MAKHLOUF 2 Physics Department, University of Cincinnati, Cincinnati, Ohio The questionof whether a linear gravity wave will give rise to nonlinear effects in ground-based airglow observations is important for the proper interpretation of gravity wave dynamics.In this paper we obtain a closed form solution for the integrated airglow response to a linear gravity wave, containing all the higher-order nonlinearresponse terms. A comparison is made to the linear response, and the higher orders are seen to be significant.In addition, the wave-induced airglow intensity fluctuationsare shown to be much greater than the corresponding major speciesdensity fluctuations. 1. INTRODUCTION Ground-basedairglow observations have often been used for studying middle and upper atmosphericdynamics. The common assumption has been that the airglow intensity (or "brightness") fluctuations correspond directly to atmo- spheric disturbances. However, if the airglow response is nonlinear, many of the airglow power spectrumpeaks may be due to the nonlinearity of the airglow response,rather than an indication of the actual dynamic behavior of the atmosphereas a whole. This paper deals primarily with the purely dynamical effects of a linear gravity wave on airglow as observed by ground-based equipment. We ignore, as have other authors, photochemistry, quenching, and molecular/ eddy diffusion on the time scale of the wave period. Minor speciesinvolved in airglow reactions often have a layered structure, i.e., a sharplypeaked unperturbed density profile, with a very steep vertical gradientjust below the peak. As a consequence, it has been realized for some time that the fluctuation of the minor constituent's density, in- duced by a linear gravity wave, can be very large at a point where its unperturbed gradient is steep. For example, a linear gravity wave which producesa 10% density fluctua- tion in the major species may induce a 50-100% density fluctuationin the minor species at the samepoint. Thus the local response of the minor species at particular heightlevels may not be amenable to a linear treatment. Weinstock [1978] computed the first-order, linear airglow response and the unperturbed background airglow for O•.(•Z +•7)emissions. He also attempted to calculate the nonlinear response. Hines and Tarasick [1987] (hereafter 1Now at Geophysical Institute, University of Alaska, Fairbanks. 2Now at Optical Environment Division, Geophysics Directorate, Phillips Laboratory, HanscomAir Force Base, Bedford, Massachu- setts. Copyright 1991 by the American GeophysicalUnion. Paper number 91JA01323. 0148-0227/91/91JA-01323505.00 referred to as HT87) have recently questionedthe necessity of invoking the higher-order nonlinear responseterms pro- ducedby the steepgradient. They have reasonedthat, while the local response may be nonlinear, the integrated response as measured from the ground should be linear, since the effect of the large density gradient can be removed by the integration. They have demonstrated this by means of a transformation from the Eulerian to the semi-Lagrangian frame, in which the air parcels in motion due to the gravity wave are mapped back to their original resting positions (before the onset of the gravity wave). This is a very important result, since it permits, if true, a great simplifica- tion in calculatingthe column-integrated responseof airglow to a gravity wave. Radar or resonancelidar which measures the local response of a minor species must contend with nonlinearities associated with steep gradients, leading to harmonicsnot present in the original wave perturbation; on the other hand, passiveinstrumentssuchas photometersand radiometers, which measure total column brightness, effec- tively filter out such nonlinear responses. In this paper we reexamine the higher-order nonlinear terms in the semi-Lagrangian formulation of HT87 (for convenience "semi" will be dropped for the remainder of the paper). We propose to show that while the steep vertical density gradient of the minor speciesno longer shows up in the Lagrangian system, the higher-order response terms remain important. This is because a new nonlinearity is introduced by the Lagrangian transformation itself. In general, an atmospheric field variable (for example, pressure or density) which is linear in its dependence on velocity at a fixed point (in Eulerian coordinates) may be nonlinearalong a Lagrangiantrajectory passing through that point. For example, while the density may fluctuate with a small amplitude at a fixed point, along a trajectory passing through that point it may fluctuate with a much larger amplitude, due in part to the large variation in background density and pressureexperienced during vertical motion. By a simpleextensionof the procedurein HT87, it is possible to obtain the total airglow response to a generalgravity wave in 14,141