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

Abstract

Analytic models are developed to describe gravity wave induced perturbations in the high ν 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 O3 because the chemical lifetime of ozone in the mesopause region is short compared to most gravity wave periods. Under these conditions the OH* response is ΔV/Vu ≃ −3[1 ‐ (z ‐ zOH)hOH + (z − zOH)2/σ12]Δρ/ρu, where ΔV/Vu are the relative emission rate fluctuations, Δρ/ρu are the relative atmospheric density fluctuations, zOH ≃ 89 km is the layer centroid height, hOH ≃ 3.6 km, and σ1 ≃ 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(−m2σ2OH/2), where m = 2π/λz and σOH ≃ 4.4 km is the rms thickness of the OH* layer. For example, at λz = 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 λz ≤ 15 km. 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, ∼ 3.75 km below the layer peak (∼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 ∼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 λz ≤ 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 λz ≥ 15 km.