Analytical models for the responses of the mesospheric OH* and Na layers to atmospheric gravity waves

Analytic models are developed to describe gravity wave induced perturbations in the high nu OH* Meinel Band emissions and in atomic Na density. The results are used to predict the fluctuations in OH* intensity and rotational temperature, Na abundance, and the centroid heights of the OH* and Na layers. The OH* model depends critically on the assumed form for the atomic oxygen profile. In this study the O profile is modeled as a Chapman layer, which is in excellent agreement with MSIS-90. We. also neglect the wave-induced redistribution of O-3 because the chemical lifetime of oz;one in the mesopause region is short compared to most gravity wave periods. Under these conditions the OH* response is Delta V/V-u similar or equal to -3[1 - (z - Z(OH))/h(OH) + (z - z(OH))(2)/sigma(1)(2)] Delta rho/rho(u), where Delta V/V-u are the relative emission rate fluctuations, Delta rho/rho(u) are the relative atmospheric density fluctuations, z(OH) similar or equal to 89 km is the layer centroid height, h(OH) similar or equal to 3.6 km, and sigma(1) similar or equal to 8.0 km. By using these results, we show that cancellation of the induced perturbations in emission intensity and rotational temperature is significant for short vertical wavelengths. The amplitude attenuation in both parameters is proportional to exp(-m(2) sigma(OH)(2)/2), where m = 2 pi/lambda(z) and sigma(OH) approximate to 4.4 km is the rms thickness of the OH* layer. For example, at lambda(z) = 15 km, the predicted rotational temperature perturbation is only 20% of the atmospheric temperature perturbation. Because the most sensitive instruments are only capable of accuracies approaching +/-2 K, there are few reported observations of waves with lambda(z) less than or equal to 15 hm. The cancellation effects are not as limiting in OH intensity observations because the relative intensity perturbations;are larger than the relative temperature perturbations, and intensities can be measured more accurately than temperature, especially with broadband instruments. Fluctuations in the emission rate are largest on the bottomside of the OH* layer, similar to 3.75 km below the layer peak (similar to 89 km), where the effects due to the redistribution of atomic oxygen dominate. Fluctuations in rotational temperature are largest near the peak of the OH layer, where the volume emission rate is largest. The similar to 3.75 km separation between the maxima of the intensity and rotational temperature perturbations is largely responsible for the phase differences observed in the fluctuations of these parameters. Rotational temperature and Krassovsky's ratio are found to be very sensitive to the form of the background temperature profile. Wave-induced OH* layer centroid height fluctuations coupled with the mean lapse rate of the background temperature profile can contribute significantly to the observed rotational temperature fluctuations, especially for the shorter wavelength waves lambda(z) less than or equal to 15 km. The OH* intensity fluctuations are relatively insensitive to the temperature profile as well as variations in atomic oxygen density and therefore appear to be excellent tracers of gravity wave dynamics. OH temperature observations are best suited for studying long-period waves, including tides, with lambda(z) greater than or equal to 15 km.