Probing the analytical cancellation factor relation using Na lidar and nightglow data from the Andes Lidar Observatory

The cancellation factor (CF) is a model for the ratio between gravity wave perturbations in the airglow intensity to those in the ambient temperature and is necessary to estimate the momentum and energy flux and flux divergence of gravity waves in the airglow emissions. This study tests the CF model using T/W Na Lidar data and zenith nightglow observations of the OH and O(1S) emissions. The dataset analyzed was obtained during the campaigns carried out in 2015, 2016, and 2017 at the Andes Lidar Observatory (ALO) in Chile. We have used an empirical method to fit the analytical function that describes the CF for vertically propagating waves and compared the quantities through the ratio of airglow wave amplitude registered as a dominant event in the images to the wave amplitude in the lidar temperature. We show that the analytical relationship underestimates the observational results. We obtained good agreement with respect to the theoretical value for the O(1S) emission line. In contrast, the observational CF ratio deviates by a factor of  ̃2 from the analytical value for the OH emission.

An analytical expression for the cancellation factor (CF) in the OH nightglow was first derived by airglow perturbations induced by gravity waves from simultaneous measurements in both layers. . 29 We present the first study for testing the analytical relationship of the cancellation factor using 30 Na Lidar data and nightglow all-sky imagery of the OH and O( 1 S) emissions during the observing 31 campaigns carried out through 2015, 2016, and 2017 at the Andes Lidar Observatory (ALO) in Chile. 32 We provide the magnitude of CF for multiple waves detected during these campaigns as well as 33 fundamental intrinsic wave parameters, and their uncertainties.  Table 1 and table 2.
The optical bench of the Na lidar (left) and the Na laser propagated to zenith and off-zenith (right) in the sky. In the long exposed image is captured the star trails and galactic centre.   coordinates with a resolution of 1 km/pix as shown in Fig. 4. The assumed altitudes for the OH  Table 3: 53 Figure 4. The OH (left) and O( 1 S) night airglow emissions is displayed at the right side, both images were captured through the ASI-1 at ALO. The camera field of view is about 1500 km 2 . The Na lidar is operated in zenith and off-zenith mode to measure the wind and temperature using 54 the three-frequency technique (She and Yu, (1994)[7]). The laser is locked at the Na resonance frequency 55 at the D2a line, and the two frequencies shifted by ±630 MHz in a sequence. The temperature and 56 line-of-sight wind are derived based on the ratios among the back-scattered signals at these three frequencies (Krueger et al., (2015) [4]). Profiles of Na lidar wind and temperature are shown in Fig. 5.

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The integration time in each direction varies between campaigns from 60 to 90 sec, that depends on the 59 signal-to-noise ratio retrieved from the photon return.

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The range of the relative amplitudes in temperature A T and airglow intensity A I have been 69 chosen to not break the linearity of the solutions. This way, the dispersion and polarization equations 70 remain valid throughout the analysis. We verify in this way that σ λ z increases while λ z decreases. The 71 uncertainty in λ z was derived using equations (8) and (12) reported in Vargas (2018)[11].

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The night airglow emission in response to AGWs perturbations was modeled using a linear, The intrinsic wave parameters (such as the horizontal wavelength (λ h ), wave orientation (θ), 86 wave phase (φ), wave period (τ), horizontal phase velocity (c), and the relative wave amplitude 87 (I /Ī)) have been obtained from the image dataset by performing usual pre-processing routines (i.e., 88 unwarping, star removal, coordinate transformation, detrending, and filtering) as described in Garcia 89 et al. (1997)[1]). In particular, wave intrinsic periods were inferred mean horizontal winds using from 90 the lidar.

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In order to compute the temperature perturbations, we removed the mean (T 0 ) from each 92 temperature altitude to determine T = T − T 0 . After selecting short wave periods (τ < 1 hour) from 93 prominent gravity wave events detected in imaging data, we estimate the observational cancellation 94 factor for the two nightglow emissions. 95 We have established the following criteria to filter out undesirable wave parameters obtained 96 from the image processing presented in Table 4. Here, z r is the altitude in kilometers to obtain the wave 97 amplitude in T for each nightglow layer, which is done by extracting the relative intensity (I /Ī) of the 98 wave, where I andĪ are the perturbed and non-perturbed airglow intensity. Also, T /T represents the 99 relative wave amplitude in the lidar temperature, and T is the perturbed temperature andT represents 100 the non-perturbed temperature. Thus, the ratio between I and T perturbations is an estimation of the 101 magnitude of CF.
We have detected prominent AGWs from the image processing in 85 out of 100 nights of the initial After filtering the data, 43 wave events remained along 9 nights in 2015, 50 waves appeared during 9 108 nights in 2016, and 98 AGWs throughout 5 nights in 2017.

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Finally, We have compared the observational cancellation factor as derived above) against the 110 analytical CF relationship as modeled in Vargas et al. 2007[10], and its uncertainties have been derived 111 by using equation (11) and their fitting coefficients presented in Table 1, and equation (12)

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The observational CF is estimated for both OH(6,2) and O( 1 S) emission lines during as shown in We have also used a statistical model to examine the correlation between the theoretical and 130 observational CF relationship for λ z > 20 km. We have computed the R 2 value of a linear regression 131 fit to the dataset of analytic CF agains observational CF as showed in Fig. 7. To estimate how far the data points fall from the CF analytic curve, we have built histograms and 137 kernel density estimators (KDE) using the filtered samples. Figure 8 shows the residuals between the 138 observational and theoretical CF data points. The sample have been filtered out using a 3σ standard 139 deviation to take out all the outliers. The KDE curve (solid red line) shows the density plot as a smoother version of the histogram.

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The histogram is normalized by default so that it has the same y-scale as the density plot. Also, we  The main contribution of this work is to test the analytical CF relationship using the observational 152 data, and we have verified that the theoretical model underestimate the observations. It is important 153 to measure this discrepancy to make correction to the theoretical relationship for both emissions. To 154 do so, we have evaluated the discrepancy between observed and analytical CF, and add them to the 155 corresponding analytical CF for each layer to obtain corrected predictions.
To estimate teh discrepancy, we define the weighted mean and the standard deviation of the mean 157 of the corrected cancellation factor as CF = . We computed the weighted 158 mean and standart deviation as they serve as a measure of the spread in the data. The smaller the 159 spread, the higher accuracy of the measurements. These will have larger influence on the mean and 160 uncertainties, and is a better estimator than the arithmetic mean and standard deviation, which just 161 ignore the magnitude of the error in each measurement. The results are listed in Table 6.
162 We summarize next the results from the observational CF weighted mean computation. The the OH emission as the estimated weighted mean is higher than the theoretical CF, CF theo (OH) = 3.8.

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However, our findings help to correct the theoretical CF relationship for the OH emission. Uncertainties 167 derived for CF dir data points have been computed for both emissions. They show that the dispersion 168 of the data set is small compared to its weighted mean. Using the weighted mean values as measure of 169 the discrepancies between CFs, we add them to the analytical curve to adjust its magnitude according 170 to the observation. Figure 9 shows the corrected theoretical CF for both emissions.

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We have tested the analytic relationship of the cancellation factor (CF) presented in Vargas et al.
from the Andes Lidar Observatory (ALO). 175 We report perturbations in the airglow intensity in response to the AGWs through the wave 176 cancellation effect using the empirical method that considers a windless and isothermal atmosphere 177 with upward propagating and saturated waves (β = 1, the wave amplitude does not change with 178 altitude). Figure 6 shows the cancellation factor in both layers as functions of λ z . It is clearly seen 179 from the CF definition that smaller CF represents stronger cancellation and that the CF increase 180 asymptotically with increasing λ z .

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The intensity perturbations with small vertical scale (λ z < 10 km) have strong cancellation in the 182 layer because of the finite thickness of the airglow layers, which implies that these short λ z waves 183 do not show significant amplitudes from ground observations (Liu and Swenson (2003)[5]). Thus, 184 the airglow is not sensitive to these waves. Equation (11) in Vargas (2018) [11] shows that the analytic 185 function describing CF increases monotonically with λ z < 13.86 km for OH band emission and 186 λ z < 10.37 km for O( 1 S) emission line, therefore, for λ z lower than these limits the cancellation effect 187 gets stronger.

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The centroid heights and thickness (FWHM) of the unperturbed and standard deviation of the 189 VER profiles derived for the OH layer is larger than that the O( 1 S) layer (see Table 1 in Vargas et al.

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We have found discrepancies between the theoretical model and the observational CF for the OH 202 emission as showed in Table 5. These discrepancies likely come from the photochemical scheme used

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Also, based on a full−wave model with the relevant chemistry to the airglow emissions that 219 considers more physical processes such as propagating gravity waves in a non-isothermal mean state, 220 windy (background winds as a function of height = 0), and viscous atmosphere, the cancellation factor can vary considerably by a factor of two greater than their isothermal and windless values for gravity 222 waves of short horizontal wavelength with phase velocities less than 100 (m/s), and by a factor of one 223 hundred for phase speeds less than 40 (m/s) (Hickey and Yu (2005)[3]).

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Having tested the analytic CF relationship against observational data for two airglow layers, 225 we have found that the theoretical model underestimated the observations for both emissions. 1. Fig. 6 shows consistency between the analytic and observational CF relationships for the O( 1 S) 242 emission in the range 20 < λ z < 60 km, considering the error bar and 95% confidence levels 243 showed. Using a linear regression model to estimate the correlation between the theoretical and 244 observational CF relationships, we have found a weak correlation for the OH band emission and 245 a larger correlation for the O( 1 S) emission line as showed in Table 5.
246 247 2. We have found that the analytic relationship underestimates the observational CF. The 248 disagreement showed in Figure 6 were examined through its correlation presented in Table 5 249 for OH emission. It comes from the fact that dissipative and freely propagating waves co-exist 250 with saturated waves, and we have not separated waves by their kind in this study. That 251 is due to the fact we do not measure individual waves simultaneously in different layers.

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That would be the only way to assure how the wave amplitude is affect as it moves upwards.

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Another possible source of inaccuracy could be introduced by the photochemical scheme used to 254 model the cancellation factor. As we explained earlier, the model does not use realistic atomic 255 oxygen data (see Vargas et al., (2007)[10]) to obtain the CF magnitude. As the atomic oxygen the discrepancies as well. By accounting for those effects, it will allow to adjust the coefficients 262 and associated errors of the fitting function for the CF I for both airglow layers.