Growth Rate of Gravity Wave Amplitudes Observed in Sodium Lidar Density Proﬁles and Nightglow Image Data

: Amplitude growth rates of monochromatic gravity waves were estimated and compared from multiple instrument measurements carried out in Brazil. Wave dynamic parameters were obtained from sodium density proﬁles from lidar observations carried out in Sao Jose dos Campos (23 ◦ S, 46 ◦ W), while all-sky images of multiple airglow layers provided amplitudes and parameters of waves over Cachoeira Paulista (23 ◦ S, 45 ◦ W). Growth rates of gravity wave amplitudes from lidar and airglow imager data were consistent with dissipative wave behavior. Only a small amount of the observed wave events presented freely propagating behavior. Part of the observed waves presented saturated amplitude. The general saturated or damped behavior is consistent with diffusive ﬁltering processes imposing limits to amplitude growth rates of the observed gravity waves.

, where A 1 and A 2 are 47 the amplitudes of a gravity wave at the altitude levels 1 and 2, respectively, and ∆z is the distance 48 between these levels. Here we refer to β as the growth rate of monochromatic waves in general, to 49 distinguish from α = 1 2H , the growth rate of freely propagating waves (non dissipative waves), where 50 H is the scale height.   1 shows how the monochromatic waves were identified in sodium lidar data. Fig. 1(a) shows 56 a temporal series of vertical sodium profiles from 75-110 km, with temporal (spatial) resolution of 3 min 57 (250 m). The sodium density profiles are first spatially and temporally low-pass filtered with cutoffs of 58 about 1.5 km and 20 minutes, respectively. Coherent downward phase progression can be seen in Fig.   59 1. Additionally, Fig. 1(b) shows a single [Na] profile superposed to an estimated unperturbed [Na] 60 profile. The relative wave amplitude perturbing the Na layer is given in Fig. 1(c), showing a decreasing 61 wave amplitude as it propagates upward. For this specific case, the wave presents vertical wavelength 1 β =-24 km. Wave periods, horizontal wavelengths, and phase velocities can be also estimated by using 64 the technique described by [8]. 65 On the other hand, a multicolor nightglow imager operating at Cachoeira Paulista (23 • S, 45 • W) 66 provided images of the mesospheric nightglow layers for three emissions during 1999, 2000, 2004 and 67 2005. A description of this imaging system is given in [9].

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In order to obtain dynamic parameters of observed gravity waves, we first preprocess the image 69 dataset by performing usual corrections in every image (i. e., unwarping, star removal, coordinate 70 transformation, detrending, and filtering).
[10] present the preprocessing methodology used in this 71 study. We focus in wave events occurring quasi-simultaneously in two or three nightglow layers. The same set of images smoothed by a Butterworth spatial band pass filter with cutoff spatial frequencies at 1 100 km −1 and 1 10 km −1 . The straight lines indicate the pixels whose relative intensity values were extracted to estimate the wave amplitude for each layer.

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The location of a spectral maximum in the amplitude periodogram indicates the horizontal 89 wavelength of the perturbing wave. By integrating below that maximum value we obtain an estimation 90 of the relative wave amplitude. Because the vertical distance ∆z between the centroid of two given 91 airglow layers is known, the amplitude growth rate is estimated by solving β = ln(A 2 /A 1 ) ∆z . As the wave 92 perturbs all three layers at the same time, we observe a finite phase difference for every spatial series 93 pair ( Fig. 3(c)).

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By applying the procedure above to the images in Fig. 2

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[8] identified 45 gravity events from analysis of ten years of sodium density profiles recorded 100 by lidar, and we have identified 52 gravity events events from analysis of 4 years of airglow images. wavelength accessed with imager is limited by the field of view of the instrument. The lower limit is 117 determined by the spatial resolution (ds) of each pixel , which is 1 km/pixel in this study. Spectral 118 analysis of the events studied in here showed λ h ranging from ∼14 to ∼78 km. The analysis of spatial 119 series extracted from images revealed relative wave amplitudes ( ∆I I ) ranging from 0.6% to 15% for the 120 OH, from 0.5% to 8.5% for O 2 , and from 0.5% to 8.5% for O( 1 S) emissions, respectively. responsible to limit the wave amplitude.

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The linear saturation theory (LST) predicts that the wave amplitude will reach the saturation behavior, suggesting that processes other than diffusivity have to be considered in order to explain the 160 observed wave amplitude characteristics and growth rates. is between -10< β <-8 within the over-damped region of the distribution.

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Also, 51.6% of imager-observed waves were found in the strong dissipation region (β <-6), 172 against only ∼9% of these type of waves in the lidar dataset. Gravity waves observed in lidar density 173 profiles support the diffusive filtering theory, which states the dissipation of wave energy is mainly 174 due to diffusivity processes acting on the wave amplitude.
Funding: This research received no external funding by CNPq grant number 04/07695-5 and National Science