A Case Study of the Stratospheric and Mesospheric Concentric Gravity Waves Excited by Thunderstorm in Northern China

In this paper, the complete process in which a concentric gravity wave (CGW), excited by a tropospheric thunderstorm, propagated into the stratosphere and mesosphere in Northern China is investigated. A strong thunderstorm developed in the middle of the Inner Mongolia autonomous region on the night of 10th August 2013. The stratospheric temperature perturbation, caused by the CGW, was observed by the Atmospheric Infrared Sounder (AIRS) at 02:11 LT 11th August 2013. An all-sky OH imager at the Shuozhou station (39.8◦ N, 112.1◦ E), supported by the Meridian Space Weather Monitoring Project, measured the mesospheric CGW between 22:00 LT to 23:00 LT on the night. It was certified that both the stratospheric and mesospheric CGWs were triggered by the aforementioned thunderstorm, and the excitation source was calculated to be located at (40.59◦ N, 108.67◦ E) by employing the dispersion relation. The CGWs were excited in the initial stage of the thunderstorm. The temperature and wind field data obtained by SABER and meteoric radar, respectively, were used to evaluate the background properties of the respective propagation regions. The result shows that an obvious thermal duct structure, with a positive squared vertical wavenumber (m2) existed around the OH layer.


Introduction
Gravity waves (GWs) are an important driver of the upper stratospheric and mesospheric circulation [1]. It is commonly recognized that deep convection (i.e., strong thunderstorms) can frequently excite GWs in the lower atmosphere [2]. In such a convectively unstable background environment, energetic and warm plumes rise rapidly to the upper troposphere. If enough energy is provided, the convective plume can overshoot the tropopause by up to 1-3 km into the stratosphere, dominated by the stable horizontal wind field. Then, the updraft collapses back down to the tropopause and spreads out horizontally as an anvil [3]. On one hand, the transitory air motion caused by overshooting causes the initial perturbation to initiate the GWs. On the other hand, latent heating and cooling (diabatic forcing) can also produce high-frequency GWs with dominant intrinsic periods between~7 min and 1 h in the lower stratosphere [4,5]. The above-mentioned processes may excite Atmosphere 2018, 9,489 3 of 14 from stratospheric and mesospheric waveforms. Section 5 provides the dispersion relation calculation to confirm that the CGWs were initiated by the thunderstorm in the center of the CGWs. Section 6 discusses the propagation circumstances and the thermal duct structure, and a concluding summary in Section 7 completes this paper.

AIRS Radiation Variation
AIRS is an infrared spectrometer and sounder onboard the NASA Aqua satellite. It is in a sun-synchronous polar orbit (13:30 local time, ascending node) at 705 km altitude with 99 min period [16]. The scanning time is 6 min for a single frame image. The footprint size is 13~14 km diameter at nadir view and the scan swath is~1600 km wide, which is sufficient to cover the horizontal scale of most GWs. The air thermal perturbations induced by GWs with vertical wavelengths longer than 10-15 km can be detected by the measurements [18,45]. AIRS radiance measurements at the 4.3 µm CO 2 fundamental emission band are most sensitive around 30-40 km altitude. Therefore, CO 2 radiance emission band with frequency ranging between 2299.80 cm −1 and 2422.85 cm −1 is used to measure the stratospheric air temperature perturbation in this study.

OH All-Sky Airglow Image
Since the first airglow measurement in the 1970s [46,47], airglow imaging technique has become an effective method to monitor nighttime airglow emission perturbations. Owing to the first no-gap all-sky OH airglow imagers network composed of six observation stations, established by the Meridian Space Weather monitoring Project (National Space Science Center, Chinese Academy of Sciences), the successional observations in northern China began in February 2012 [43]. In this work, the airglow data were observed by Shuozhou station (39.8 • N, 112.1 • E). The OH airglow all-sky imager is composed of a CCD detector (1024 × 1024 pixel), a near-infrared (NIR) band (715-930 nm) filter, a Nikon 16 mm/2.8D fisheye lens with a 180 • field of view, and an optical imaging system. The notch of NIR band filter centered at 865.5 nm at OH airglow layer (~87 km). The band-pass filter is sensitive to the emissions of the OH Meinel bands, and can suppress the O 2 (0-1) emission [48]. The image interval of the optical system is 1 min. The spatial resolution of the airglow imager is not uniform because of the distortion caused by the fisheye effect. With the increase of zenith angle, the spatial resolution is 0.27 km at the zenith, but about 5.5 km at the zenith angle of 80 • . On cloudless nights, the GWs can be viewed with the zenith angle smaller than 80 • , so the maximum observation radius is 420 km at OH airglow layer.

TIMED/SABER and Meteor Doppler Radar Data
Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) is a sensor on board the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite, for detecting the profile of air temperature and several kinds of tracer components. The satellite was launched in January of 2002 at an altitude of 625 km with an inclination angle of 74.1 • . SABER scans the atmosphere from 0 km to 180 km in 58 s, and can cover the latitude circle from winter hemisphere 53 • to the summer hemisphere 83 • [49,50]. SABER grid data has an excellent vertical spatial resolution of as high as~0.4 km of Level-2A products [16]. In this work, kinetic temperatures from CO 2 emissions are employed as the background temperature and 1.6 µm OH emission is used to extract OH airglow CGWs.
The meteor Doppler radar measures the wind velocity profiles in the mesosphere and lower thermosphere from 70 to 110 km with a height interval of 2 km. Its transmit power is 7.5 kW and received frequency is 38.9 MHz with an integration time of 1 h. In this work, the data of Beijing station (39.98 • N, 116.37 • E) which is 100 km east of the Shuozhou station boundary is used.

Processing of All-Sky Image Data
Both low-frequency background emissions and the distortion caused by fisheye lenses are the main error source for all-sky image data. Thus, processing of the raw image data is necessary before the wave parameters can be extracted from the airglow images. First, the difference between two consecutive raw images is found so that time-difference (TD) images can be created to eliminate the background information [27,51,52]. In the TD images, the high-frequency perturbation caused by GWs from irregular, abrupt background changes can be recognized exactly. Next, in order to correct the distortion by the fisheye lens, the TD images are projected onto the geographic coordinate with 512 × 512 km grid, assuming the altitude of the OH airglow layer to be 87 km [26,38,53].

Boussinesq GW Dispersion Relation
The basic rules of GW propagation have been investigated by numerical simulation and observations for several years [8,54]. The Boussinesq GW dispersion relation has become an effective method to explain the propagation characteristics [7,55,56]. The GWs dispersion relation has been used to estimate the position of the GWs' excitation source and the propagation time from the excitation altitude to the upper mesosphere and lower thermosphere (MLT) [12,57,58].
Due to the atmospheric dispersion relation, the GW with longer horizontal wavelengths can propagate longer distances under the assumption of zero wind. The Boussinesq GWs dispersion relation is [30,59] where λ h is the horizontal wavelength, N is the Brunt-Väisälä frequency, and R is the horizontal distance from the center of the observed CGW at an altitude of~87 km. Considering the generation mechanism of convective CGWs is convective overshooting in the upper troposphere, by assuming that the CGWs are launched from the tropopause, the height from the tropopause to the OH layer is ∆z = Z OH − Z ctop . If the measured horizontal wavelength is close to the estimated value calculated by Equation (1), the convective source can be confirmed as the CGWs excitation source. Both the background temperature and wind field are determinant factors for GW propagation. Previous studies have shown that the temperature inversion layer and obvious wind shear are distinctly associated with the formation of mesospheric GW ducts during propagation processes [13,14,60]. The square of the Brunt-Väisälä frequency (N 2 ) represents the influence of the temperature where g = 9.54 ms −2 , T is the kinetic temperature measured by SABER, dT/dz is the vertical gradient of temperature, and c p = 1005 J·kg −1 ·K −1 is the specific heat capacity at constant pressure. The vertical wave number m = 2π/λ z describes the vertical propagation condition, and can be expressed using the GW dispersion relation as [61]: where k h = 2π/λ h is the horizontal wave number. u is the horizontal wind velocity in the direction of the CGW's propagation, obtained by the meteor radar. u zz is the second derivative of u wind velocity with height z. The vertical profile of m 2 is the most significant criterion in indicating the existence of the ducting structure [12].

Mesospheric CGW
Concentric rings were observed in the mesosphere by the all-sky airglow imager from 22:00 LT to 22:30 LT. During this period, two groups of obvious waveforms of this CGW event were chosen, as shown in Figure 1. Both of the groups of CGWs maintained consecutive waveforms for~20 min, and were initiated by the expansion of the same circular rings. Thus, they were part of the same CGW event. Group A was north of Shuozhou station, and its semi-period, where wave crests switched to troughs, was 4.28 min. The wave period and horizontal wavelength were 8.56 min and 34.06 km for group A, respectively, while they were 10.72 min and 22.61 km for group B, located to the southwest of Shuozhou station. Group A with longer horizontal wavelength can reach longer horizontal distance than group B.
Atmosphere 2018, 9, x FOR PEER REVIEW 5 of 15 u wind velocity with height z. The vertical profile of m 2 is the most significant criterion in indicating the existence of the ducting structure [12].

Mesospheric CGW
Concentric rings were observed in the mesosphere by the all-sky airglow imager from 22:00 LT to 22:30 LT. During this period, two groups of obvious waveforms of this CGW event were chosen, as shown in Figure 1. Both of the groups of CGWs maintained consecutive waveforms for ~20 min, and were initiated by the expansion of the same circular rings. Thus, they were part of the same CGW event. Group A was north of Shuozhou station, and its semi-period, where wave crests switched to troughs, was 4.28 min. The wave period and horizontal wavelength were 8.56 min and 34.06 km for group A, respectively, while they were 10.72 min and 22.61 km for group B, located to the southwest of Shuozhou station. Group A with longer horizontal wavelength can reach longer horizontal distance than group B. wave troughs (dark parts) are marked with red and green dots, respectively, in Figure 1. The least square method [29,62] was employed to obtain a more accurate fitting result from the eight fringes. The best fitting center of circles and radii minimized the total residual sum of the squares, S [28][29][30]. LT) were chosen to estimate the center of the CGWs. The wave crests (bright parts) and wave troughs (dark parts) are marked with red and green dots, respectively, in Figure 1. The least square method [29,62] was employed to obtain a more accurate fitting result from the eight fringes. The best fitting center of circles and radii minimized the total residual sum of the squares, S [28][29][30]. where r ik is the distance between the hypothetic center and the i-th marked point on the k-th wavefront. The distance r ab between a(λ a , φ a ) and b(λ b , φ b ) is calculated by the formulae of spherical trigonometry.
where R 0 is the radius of the Earth. n k is the number of points on the wavefront. Here, the mean radius, r k , can be written as The fitted center, located at (40.59 • N, 108.67 • E), is represented by the red triangle in Figure 1. The convective center, fitted by only two rings, was located at (40.47 • N, 108.90 • E) [63]. The deviation between the two results is less than 0.5 • . Therefore, the number of marked points results in negligible deviation, and does not affect the fitting results.

Stratospheric CGWs
When CGWs propagate into the stratosphere, the radiance temperature perturbations can be observed by AIRS in the 4.3 µm channel. The stripy waveforms propagated northeastward at 02:11 LT on 11th August, as shown in Figure where ik r is the distance between the hypothetic center and the i-th marked point on the k-th ( ) where 0 R is the radius of the Earth. k n is the number of points on the wavefront. Here, the mean radius, k r , can be written as The fitted center, located at (40.59° N, 108.67° E), is represented by the red triangle in Figure 1. The convective center, fitted by only two rings, was located at (40.47° N, 108.90° E) [63]. The deviation between the two results is less than 0.5°. Therefore, the number of marked points results in negligible deviation, and does not affect the fitting results.

Stratospheric CGWs
When CGWs propagate into the stratosphere, the radiance temperature perturbations can be observed by AIRS in the 4.3 μm channel. The stripy waveforms propagated northeastward at 02:11 LT on 11th August, as shown in Figure 2. Radiance temperature perturbations occurred in the region of 40°-45.5° N and 109°-116.5° E, north of Shuozhou station. The green dashed lines mark the peaks of the CGWs. The average horizontal wavelength of the three streaks in Figure 2 was 151.70 km, which is close to the most common value observed by AIRS of ~100 km [64].  The average propagation distance of group A and group B was 174.25 km and 149.64 km away, respectively. The stratospheric propagation distance was 516.92 km. In the horizontal direction, the greater propagation distance of stratospheric CGW is caused by the longer propagation time,~4 h more than that of the mesospheric CGW.
Although the background emission will bring disturbance into the OH images [27,52], the relative variation is still a credible parameter to evaluate the perturbation caused by GWs [43]. The luminous Atmosphere 2018, 9, 489 7 of 14 intensity variation indicates the amplitude of GWs. The relative luminosity intensity, extracted from raw unwrapped OH images, is defined as ∆I/I, and the relative radiation temperature was defined as ∆T/T. In Figure 3, the average perturbation amplitude of ∆I/I is 6.14%, while the average perturbation amplitude of ∆T/T is 5.01%. The disparate methods and observation principles can cause the systematic deviation between the amplitudes of ∆I/I and ∆T/T, and wave amplitude damping caused by observational filters must be considered [15]. Smaller amplitudes in the stratosphere could be explained by gradual energy dissipation with the increase in horizontal propagation distance.
The average propagation distance of group A and group B was 174.25 km and 149.64 km away, respectively. The stratospheric propagation distance was 516.92 km. In the horizontal direction, the greater propagation distance of stratospheric CGW is caused by the longer propagation time, ~4 h more than that of the mesospheric CGW.
Although the background emission will bring disturbance into the OH images [27,52], the relative variation is still a credible parameter to evaluate the perturbation caused by GWs [43]. The luminous intensity variation indicates the amplitude of GWs. The relative luminosity intensity, extracted from raw unwrapped OH images, is defined as ΔI/I, and the relative radiation temperature was defined as ΔT/T. In Figure 3, the average perturbation amplitude of ΔI/I is 6.14%, while the average perturbation amplitude of ΔT/T is 5.01%. The disparate methods and observation principles can cause the systematic deviation between the amplitudes of ΔI/I and ΔT/T, and wave amplitude damping caused by observational filters must be considered [15]. Smaller amplitudes in the stratosphere could be explained by gradual energy dissipation with the increase in horizontal propagation distance.

CGWs Excitation Source
The dispersion relation is widely used to estimate the position and time of a GW's excitation source by verifying actual wave parameters in accordance with the theoretical dispersion relationship. Yue et al. [30] and Fovell et al. [65] used 12 km as the height of the tropopause, while at the Shuozhou station = 13 ctop Z km, as per the NCEP (National Centers for Environmental Prediction) reanalysis data. Therefore, = 87 -13 = 74 z Δ km is the vertical distance from the tropopause to OH airglow layer (~87 km) in Equation (1). In Figure 4, group A propagated a greater distance than group B, and so the horizontal wavelength of group A is obviously longer than group B. The uncertainties in the horizontal wavelengths are due to the difference between each waveform and the average value, which is caused by wave interference and noise when identifying the bright or dark bands in the airglow image. Comparing the observed horizontal wavelengths with their theoretical propagation curves, it could be seen that, in the OH airglow layer, the wavelengths and propagation distance approximately satisfied the 150 min curve (red line) in  Figure 5. Therefore, the excitation time of the CGWs in the AIRS layer was 19:11 LT on 10th August. The excitation time difference of OH airglow layer and AIRS layer was ~27 min. It probably because the waves were excited at different instants by the same source, once the waves have different parameters at the stratosphere and mesosphere, respectively. Moreover, the dispersion relationship is a theoretical estimation for actual atmospheric GWs' propagation characteristics under the assumption of weak

CGWs Excitation Source
The dispersion relation is widely used to estimate the position and time of a GW's excitation source by verifying actual wave parameters in accordance with the theoretical dispersion relationship. Yue et al. [30] and Fovell et al. [65] used 12 km as the height of the tropopause, while at the Shuozhou station Z ctop = 13 km, as per the NCEP (National Centers for Environmental Prediction) reanalysis data. Therefore, ∆z = 87 − 13 = 74 km is the vertical distance from the tropopause to OH airglow layer (~87 km) in Equation (1). In Figure 4, group A propagated a greater distance than group B, and so the horizontal wavelength of group A is obviously longer than group B. The uncertainties in the horizontal wavelengths are due to the difference between each waveform and the average value, which is caused by wave interference and noise when identifying the bright or dark bands in the airglow image. Comparing the observed horizontal wavelengths with their theoretical propagation curves, it could be seen that, in the OH airglow layer, the wavelengths and propagation distance approximately satisfied the 150 min curve (red line) in Figure 4. According to the observation, the excitation times of group A and group B were 19:37 LT and 19:39 LT on 10th August, respectively.
At AIRS observation height of 41 km, ∆z = 41 − 13 = 28 km from Equation (1), and the propagation time approximately conformed with the 7 h curve (red line) in Figure 5. Therefore, the excitation time of the CGWs in the AIRS layer was 19:11 LT on 10th August. The excitation time difference of OH airglow layer and AIRS layer was~27 min. It probably because the waves were excited at different instants by the same source, once the waves have different parameters at the stratosphere and mesosphere, respectively. Moreover, the dispersion relationship is a theoretical estimation for actual atmospheric GWs' propagation characteristics under the assumption of weak wind, and it will lead to certain errors. Accordingly, it is acceptable that the deviation of excitation time was almost 30 min in this case.
The convection cell, especially in the case of the overshooting process at the top of the convective cloud, has been proven to be the initial excitation of CGWs [9,21,66]. According to the excitation position and time, the excitation source of CGWs is a thunderstorm in the region of 40.5 • -41.5 • N and 108 • -109 • E. In accordance with the investigation by Wen et al. [63], the convection began at 19:00 LT and developed for~6 h. The CGWs were excited in the initial stage of the thunderstorm, between 19:30 LT and 20:00 LT. In this stage, the strong and rapid development of convection was advantageous for overshooting, which is known to be important for initial perturbation [2,3,29,37,65].
Atmosphere 2018, 9, x FOR PEER REVIEW 8 of 15 wind, and it will lead to certain errors. Accordingly, it is acceptable that the deviation of excitation time was almost 30 min in this case.  The convection cell, especially in the case of the overshooting process at the top of the convective cloud, has been proven to be the initial excitation of CGWs [9,21,66]. According to the excitation position and time, the excitation source of CGWs is a thunderstorm in the region of 40.5°-41.5° N and 108°-109° E. In accordance with the investigation by Wen et al. [63], the convection began at 19:00 LT and developed for ~6 h. The CGWs were excited in the initial stage of the thunderstorm, between 19:30 LT and 20:00 LT. In this stage, the strong and rapid development of convection was advantageous for overshooting, which is known to be important for initial perturbation [2,3,29,37,65].

Propagation Background Circumstances
Both propagation and breaking are the main phenomena of GWs and they are dictated by the horizontal prevailing wind in the stratosphere [67]. Therefore, the zonal wind is the principal factor wind, and it will lead to certain errors. Accordingly, it is acceptable that the deviation of excitation time was almost 30 min in this case.  The convection cell, especially in the case of the overshooting process at the top of the convective cloud, has been proven to be the initial excitation of CGWs [9,21,66]. According to the excitation position and time, the excitation source of CGWs is a thunderstorm in the region of 40.5°-41.5° N and 108°-109° E. In accordance with the investigation by Wen et al. [63], the convection began at 19:00 LT and developed for ~6 h. The CGWs were excited in the initial stage of the thunderstorm, between 19:30 LT and 20:00 LT. In this stage, the strong and rapid development of convection was advantageous for overshooting, which is known to be important for initial perturbation [2,3,29,37,65].

Propagation Background Circumstances
Both propagation and breaking are the main phenomena of GWs and they are dictated by the horizontal prevailing wind in the stratosphere [67]. Therefore, the zonal wind is the principal factor

Propagation Background Circumstances
Both propagation and breaking are the main phenomena of GWs and they are dictated by the horizontal prevailing wind in the stratosphere [67]. Therefore, the zonal wind is the principal factor controlling the GW's propagation processes. The wind direction opposite to the direction of the GW's horizontal propagation facilitates upward propagation in the upper atmosphere. Using the ECMWF (European Centre For Medium-Range Weather Forecasts) reanalysis data, the horizontal background wind field was statistically analyzed between the tropopause (~13 km) and the mid-stratosphere (~30 km) above the excitation thunderstorm at 18:00 LT. It is usually observed that eastward winds reverse direction to become westward winds at the bottom of the stratosphere. As shown in the wind-rose diagram (Figure 6), this region was mainly controlled by the background westward wind, and the maximum wind velocity was less than −22 m/s (westward winds). According to the classical wave theory, stratospheric westward wind cannot filter out eastward fluctuation propagation, so the CGWs which originated by the convection plume can reach the region over the Shuozhou station.
background wind field was statistically analyzed between the tropopause (~13 km) and the mid-stratosphere (~30 km) above the excitation thunderstorm at 18:00 LT. It is usually observed that eastward winds reverse direction to become westward winds at the bottom of the stratosphere. As shown in the wind-rose diagram (Figure 6), this region was mainly controlled by the background westward wind, and the maximum wind velocity was less than −22 m/s (westward winds). According to the classical wave theory, stratospheric westward wind cannot filter out eastward fluctuation propagation, so the CGWs which originated by the convection plume can reach the region over the Shuozhou station. The background wind field was observed by the meteor radar (Beijing station), the location of which is marked as a yellow triangle in Figure 1. The wind hodograph from the night of 10-11th August 2013 is presented in Figure 7. The westerly wind controlled the whole layer between 80 km and 100 km until 22:00 LT, with a maximum velocity of 42.67 m/s. After 23:00 LT, the easterly wind gradually displaced the weak westerly wind from 86 km to 106 km, with a maximum velocity of −60.39 m/s, followed by a reduction in the westerly wind. It is noted that the obvious wind shear between 86 km and 90 km and CGWs occurred practically at the same time: between 22:00 LT and 23:00 LT.
The thermal duct and wind duct structure have been proven to play important roles in the propagation of GWs [13,60,[68][69][70]. The temperature inversion, which is the sudden increase around the mesopause in the vertical temperature profile, is a typical phenomenon of a thermal duct [38,43]. On the night of 10-11th August 2013, TIMED/SABER scanned the CGWs region four times (red crosses in Figure 1). An obvious temperature inversion layer, with a peak of 200 K, can be seen between the altitudes 85 km and 91 km (dotted lines in Figure 8a). The amplitude of the temperature inversion layer is ~30 K and it is as sharp as the previous observation in Northern China [38,43]. Remsberg et al. [71] assessed the quality of the temperature profiles observed by TIMED/SABER and calculated the root-sum-square (RSS) uncertainties of the temperature to present the random and bias errors. The RSS uncertainties are marked by green error bar in Figure  8a. Using Equation (2), the squared Brunt-Väisälä frequency (N 2 ) can be derived from the temperature profile.
The peak of the 1.6 μm average OH emission profile is at 87 km in Figure 8b. According to the excitation source location and the arcs of the eastern half of CGWs (group A and group B) observed by the all-sky imager, the direction of propagation is eastward. Thus, the average u component of the meteor radar wind is used as the wind velocity in the propagation direction. The wind profile The background wind field was observed by the meteor radar (Beijing station), the location of which is marked as a yellow triangle in Figure 1. The wind hodograph from the night of 10-11th August 2013 is presented in Figure 7. The westerly wind controlled the whole layer between 80 km and 100 km until 22:00 LT, with a maximum velocity of 42.67 m/s. After 23:00 LT, the easterly wind gradually displaced the weak westerly wind from 86 km to 106 km, with a maximum velocity of −60.39 m/s, followed by a reduction in the westerly wind. It is noted that the obvious wind shear between 86 km and 90 km and CGWs occurred practically at the same time: between 22:00 LT and 23:00 LT.   The thermal duct and wind duct structure have been proven to play important roles in the propagation of GWs [13,60,[68][69][70]. The temperature inversion, which is the sudden increase around the mesopause in the vertical temperature profile, is a typical phenomenon of a thermal duct [38,43]. On the night of 10-11th August 2013, TIMED/SABER scanned the CGWs region four times (red crosses in Figure 1). An obvious temperature inversion layer, with a peak of 200 K, can be seen between the altitudes 85 km and 91 km (dotted lines in Figure 8a). The amplitude of the temperature inversion layer is~30 K and it is as sharp as the previous observation in Northern China [38,43]. Remsberg et al. [71] assessed the quality of the temperature profiles observed by TIMED/SABER and calculated the root-sum-square (RSS) uncertainties of the temperature to present the random and bias errors. The RSS uncertainties are marked by green error bar in Figure 8a. Using Equation (2), the squared Brunt-Väisälä frequency (N 2 ) can be derived from the temperature profile.
The peak of the 1.6 µm average OH emission profile is at 87 km in Figure 8b. According to the excitation source location and the arcs of the eastern half of CGWs (group A and group B) observed by the all-sky imager, the direction of propagation is eastward. Thus, the average u component of the meteor radar wind is used as the wind velocity in the propagation direction. The wind profile was vertically interpolated at 1 km per hour intervals (Figure 8c). Below 93 km, the wind direction is east, with a peak velocity at 85 km of 34.95 m/s. was vertically interpolated at 1 km per hour intervals (Figure 8c). Below 93 km, the wind direction is east, with a peak velocity at 85 km of 34.95 m/s.  The squared vertical wavenumber m 2 is a criterion for the vertical propagation of GWs. In the layer where m 2 is positive, surrounded by evanescent regions (where m 2 is negative), the structure The squared vertical wavenumber m 2 is a criterion for the vertical propagation of GWs. In the layer where m 2 is positive, surrounded by evanescent regions (where m 2 is negative), the structure of CGWs is sustained, allowing them to propagate over longer distances. As Equation (3) reveals, m 2 is controlled by the N 2 term (the first term) and the curvature term (the second term), which represent the effects of temperature gradients and wind shear in the propagating environment, respectively. There is a thermal duct between 82 and 88 km in Figure 8d. Due to the lack of the original meteor radar data set, the random error of wind profile cannot be given. The average of the wind profile, during 21:00 LT to 23:00 LT, is used to decrease the effect of uncertainty in the wind profile. Thus, the deviation of m 2 is propagated by the RSS uncertainties of temperature (red error bar in Figure 8d). The altitude of the duct region is associated with the peak of the wind profile. Figure 8d also illustrates that the curvature term contributes more towards m 2 than the N 2 term in the main ducting region.

Conclusions and Discussion
This paper reported the observation of typical stratospheric and mesospheric CGWs in northern China on the night of 10th August 2013. Two groups of mesospheric CGWs started to appear at 22:00 LT on 10th August and a series of arcs were observed by AIRS at 02:11 LT on 11th August. The CGWs were excited by a thunderstorm located at (40.59 • N, 108.67 • E). The stratospheric CGWs propagated horizontally for 516.92 km and the average horizontal wavelength was 151.70 km. In the mesosphere, group A propagated horizontally for 270.57 km and the average horizontal wavelength was 34.06 km. Group B propagated horizontally for a distance of 179.60 km and the average horizontal wavelength was 22.61 km. Compared with the mesospheric CGWs, the horizontal wavelengths of the stratospheric CGWs were much longer. The dispersion relationship was used to estimate the excitation source of the stratospheric and OH airglow CGWs. Although a brief analysis of mesospheric CGWs was completed by Wen et al. [63], more, different groups of waveforms have been extracted to fit the center in this work. Both of the fitting results are feasible; they describe all of the basic CGWs parameters and the propagation process of the intact CGWs event, while the CGWs were excited by the same thunderstorm. The horizontal wavelength values of CGWs (21.6 ± 2.5 km) investigated by Xu et al. [43] are similar to the observations in this paper, but the time scale was longer (~3 h) and the spatial scale was larger (~800 km). It is worth noting that, in this case, the horizontal propagation distance is much shorter in spite of the thermal duct observed.