1. Introduction

Continuous wind measurements with high temporal-spatial resolution in the altitude range 15-60km, which are still rarely reported, are fundamental for the understanding of atmospheric dynamics. Chanin et al. first realize wind measurement in stratosphere up to 50 km [1–4]. Tepley et al. developed another technique for wind measurements up to 60 km using a single Fabry-Perot interferometer (FPI) [5–8]. A Rayleigh/Mie/Raman lidar developed in the ALOMAR research station has acquired simultaneous wind and temperature detection up to 80 km [9–11]. Recently, a direct detection system working at 589nm with a sodium filter was developed in Colorado [12]. The Goddard Lidar Observatory for Winds (GLOW) mobile Doppler lidar was implemented using a frequency tripled Nd:YAG laser working at 355 nm with a double-edge FPI for stratosphere wind measurement at NASA Goddard Space Flight Center [13]. As payload of Atmospheric Dynamics Mission Aeolus, space-borne Doppler wind lidar ALADIN has been demonstrated by airborne validation and scheduled to be launched in the near future [14–18].

Atmospheric gravity waves (GWs) are ubiquitous in the middle atmosphere and play important roles in influencing its state by transporting energy and momentum between widely separated regions and generating turbulences. A common feature in observed profiles of wind and temperature from a Lidar are fluctuations with vertical and temporal scales, which are characteristic of internal gravity waves. There has been variety of techniques applied to the study of the mesoscale fluctuations throughout the lower and middle atmosphere [19]. Considerable work has been done to study gravity waves using lidar. Alexander et al. investigated gravity wave activity in the upper stratosphere and lower mesosphere using temperature data retrieved from a Rayleigh lidar at Davis, Antarctica [20]. The ALOMAR research group has observed wind field gravity wave cases in the middle atmosphere with the combination of RMR (Rayleigh/Mie/Raman) lidar and Na lidar [21], and Chanin et al. detailedly analyzed the gravity waves using data from Rayleigh temperature lidar and rocketsonde [22,23]. In spite of this, there are no other reports about the gravity waves cases of wind field observed by Rayleigh Doppler wind Lidar in the region of 15-60km to the author’s knowledge.

Recently, a mobile Rayleigh Doppler lidar system based on the double-edge incoherent technique and integration technique was implemented and demonstrated capable to measure wind and temperature for the altitude range of 15-60km and 30-70km, respectively [24,25]. Observations were carried out over two periods of time: 3 months started from November 4, 2014 in Xinzhou, China (38.425°N, 112.729°E) and 2 months started from October 7, 2015 in Jiuquan, China (39.741°N, 98.495°E). In this paper we describe the detailed data processing of the gravity wave extracting from the wind field and show several typical gravity wave cases. The data are also compared with radiosonde, CIRA and MERRA data.

2. Instruments and database

The mobile Rayleigh Doppler lidar system is based on the double-edge technique to realize direct detection. The detailed description of double-edge technique is performed by Korb et al. [26, 27]. A triple channel FPI, which is capacitively stabilized and piezo-electrically tunable, is used as frequency discriminator to determine the wind velocity with its double-edge channels located in the wings of the thermally broadened molecular backscattered signal spectrum. The third channel is locking channel to lock the frequency of outgoing laser at the cross-point of the double-edge channels by monitoring the transmission changes of the outgoing laser on this channel. This locking procedure is used to remove the frequency drift of the laser and FPI for every one minute and a locking accuracy of 1.8MHz at 355 nm is realized, corresponding to a standard deviation error of 0.32 m/s in LOS wind velocity. Therefore, the wind signal also has to be accumulated for every one minute and we will accumulate the one-minute raw data to 30 minutes during the later wind retrieving process. The controlling of ambient temperature of the FPI is improved with an accuracy of ± 0.02K in sealed containers to weaken the influences of the thermal changes on the FPI cavity spacing, which decides the central wavelength of the FPI. For our system, an equivalent horizontal wind velocity bias of ± 0.6 m/s is obtained in condition of a maxima temperature variation of ± 0.1K. The system consists of three nearly identical independent subsystems pointing to three different fixed lines of sight (LOS), one points to the zenith and the two others are titled at 30° from the zenith and perpendicular to each other in the projection of horizontal (as shown in Fig. 1). The one pointing to the zenith is used as temperature detection during the observations in Xinzhou and Jiuquan for the reason that there will be chances to identify a gravity wave from different variables: temperature and horizontal wind. The system operates at eye-safe wavelength 354.7nm and adopts a Cassegrain telescope with 1 m in diameter and 0.09 mrad in field of view (FOV). A 200 µm diameter multimode fiber is used to guide the collected signal to the FPI, realizing all fiber structure of the receiver which is more suitable for mobile platform. More detailed description of the principle, optical layout, specifications and system calibration of this lidar system are presented in [24, 28–30].

 

Fig. 1 Schematic view of the lidar’s three lines of sight. The mobile platforms are set in different directions in Xinzhou and Jiuquan.

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During the 3-months observation from November 2014 in Xinzhou, China (38.425°N,112.729°E) and the 2-month observation from October 7 in Jiuquan, China (39.741°N, 98.495°E), measurements of the temperature and horizontal wind started from 6:00 pm to 7:00am on clear nights as a routine. Radiosonde observations from the local meteorological station were operated twice at the same place on 7:00 pm and 7:00 am, realizing a daily comparison between radiosonde and lidar profiles. In some other conditions, radiosonde observations were operated at other local times deliberately to realize more convincing comparison between lidar and radiosonde at the time far from the routine time of 7:00 am and 7:00 pm. An accumulating time of 30 min is adopted during the wind inversion. Two perpendicular components (15° from the north and east anticlockwise in Xinzhou and 45° from the north and east in Jiuquan) of the horizontal wind are measured by the two 30°-leaned subsystems and temperature is measured by the vertical-pointing one. The 15° offset in Xinzhou and 45° offset in Jiuquan of the two perpendicular components from the zonal and meridional direction results from the space limit of the field which means the mobile system can only be fixed at this particular direction despite zonal and meridional directions are more usual (The different directions of south relative to the mobile platform in Xinzhou and Jiuquan are shown in Fig. 1). The zenith angle of 30° determines that each perpendicular component of the horizontal wind velocity equals twice the corresponding LOS wind velocity. In the following sections, we use X wind to represent the horizontal component which is 15°(in Xinzhou) or 45°(in Jiuquan) anticlockwise from the east and Y wind to represent the horizontal component which is 15°(in Xinzhou) or 45°(in Jiuquan) anticlockwise from the north. The measured components of the horizontal wind (twice the LOS wind velocity) have a vertical resolution of 0.2 km (below 40 km) and 1 km (above 40 km). After we get the wind profiles from the raw photo counts data with this kind of resolution, the resolution above 40 km was changed from 1 km into 0.2 km using linear interpolation to get equally spaced wind profiles. This step of resolution change is necessary for the bandpass filtering and Fourier analysis of the wind profiles. The Radiosonde data was given in a pattern of wind velocity and wind direction originally. Therefore, it was decomposed into two components in the directions of the measured wind components to realize the comparison between lidar and radiosonde. The times shown below are all in local time. The local time is 7 hours (in Jiuquan) and 8 hours (in Xinzhou) faster than the universal time.

3. Fluctuation extracting and results

Despite only a part of the data has been individually studied in details, some wave patterns are very frequently observed. The wave cases presented below are characteristics of these observations and they are selected because they correspond to a long measurement period which provides a view of long-hours gravity wave propagation. Meanwhile, one of these cases was given with simultaneous wind and temperature measurements. The fluctuation analysis of the wind is directly applied in the two components of the horizontal wind: X wind and Y wind rather than in the zonal and meridional winds for the reason that this will avoid the vector composition of two components measured by the two subsystems of the lidar, which have a conceivable phase delay with each other due to the distance between the two different measuring locations of the two subsystems. To be more specific, the distance between two measured horizontal wind components is related to altitude:

3.1 Temperature relative perturbations

The temperature measurements are based on the using of Rayleigh backscatter. The backscattered light from the pulsed laser beam sent vertically into the atmosphere (Mie scattering could be ignored and resonant line is absent above 30 km), is due to Rayleigh scattering from neutral molecules and is thus proportional to the atmospheric density. The absolute temperature profile can be deduced from the relative density measurements by assuming hydrostatic equilibrium, applying the ideal gas law and fitting the temperature profile with the CIRA (COSPAR International Reference Atmosphere, 1986) model at the upper altitude of the measurement [22]. It should be noted that it is equivalent to consider the density or the temperature relative fluctuations because they are equal within the assumption of hydrostatic equilibrium. In the process of retrieving the temperature from the photo counts, the reference height is selected at the maximum height where the SNR is bigger than 17. In clear night, the reference height can reach up to 75-80km. The time resolution of the temperature profiles is 15 minutes and the height resolution is the same as the wind measurements (0.2 km below 40 km and 1 km above 40 km). The resolution above 40 km also changes from 1 km to 0.2 km using leaner interpolation after the process of temperature retrieving (same as the wind measurements).

The relative perturbations of temperature T’/T0 are extracted by subtracting a third-order polynomial fit of the whole-night mean temperature profile from the raw temperature profiles. This process is carried out in height range of 30-70km because the backscatter is affected by the aerosol below 30 km. 70 km is the upper limit of the temperature measurements and the actual max height of the temperature profile depends on the signal-to-noise ratio (SNR). One example of the raw temperature profile and the third-order polynomial fit of the whole-night mean temperature profiles are shown in Fig. 2(a) with error bars. The profiles are compared with the temperature of the CIRA model and MERRA (Modern Era Retrospective-analysis for Research and Applications) data. The MERRA data’s resolution is about 1.25° in longitude and latitude. We selected the 2 × 2 grids of the MERRA data nearest from the lidar location and calculated an average vertical temperature and wind profile of the four grids. MERRA raw data uses universal time with a time resolution of 3 hours and we converted it to local time when comparing them with lidar profiles. The profile of relative perturbations of the temperature is shown in Fig. 2(b). There is clearly wavelike disturbance growing in amplitude with height.

 

Fig. 2 (a) raw temperature profile with error bars at 00:15 on December 14, 2014, Xinzhou and the third-order polynomial fit of the whole-night mean temperature profiles (blue), compared with the CIRA 86 model (red) and MERRA temperature (green) at local time of 23:00 on December 13. (b) The relative perturbation of the temperature profile

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3.2 Horizontal wind perturbations

The wind measurements can catch up to altitude of 60 km, lower than the max height of temperature measurements. This is because the two wind subsystems both will separate the Rayleigh backscatter into two signal channels to realize double edge technique by detecting the outcoming light intensity from the two channels of the FPI. In the meantime, the fibers of the wind subsystems which collect the backscatter light from the telescope have a smaller numerical aperture than the fiber of the temperature subsystem, in order to match the aperture of the FPI channels. A smaller numerical aperture will cause more signal loss when coupling the focusing spot of the telescope into the fiber. As a result of the two main reasons, the signal of the wind channels is weaker than the temperature signal by almost one order of magnitude. The X and Y wind (This name has been explained in section 2) fluctuations are extracted by subtracting the background wind. The background wind is a fourth-order polynomial fit of the whole-night mean wind profile. In the most conditions, the wind profiles have a more complex background than the temperature profiles so a third-order polynomial fit can hardly coincide with the expected background wind. This is the reason why we use a fourth-order polynomial fit onto the wind profile and a third-order polynomial fit onto the temperature profiles. After subtracting the background wind, a band pass filtering will be applied onto the residual of the wind speed. The cutoff wavelengths of the bandpass filter will change in different cases in order to highlight the most dominant oscillatory mode with different wavelengths.

Figure 3(a) shows a Y wind profile with an accumulating time of 30 minutes at 23:30 on October 27, 2015, Jiuquan and the polynomial fit of the whole night mean profile compared with the radiosonde and MERRA data. We select three MERRA wind profile (the MERRA’s horizontal wind has been projected onto the Y component direction) on the time nearest to the observation time of the Y wind profile. The MERRA profiles have a similar shape with the lidar profile: the absolute wind speed decreases with height below 30 km and increases with height above 30 km. The radiosonde data on that day only reached up to 20 km. The wind speed difference between the lidar and radiosonde is less than 3 m/s, which is within the uncertainty expected from the difference of measuring time and location between them. The residual between Y wind profile and the estimated background wind profile is shown in Fig. 3(b). The amplitude of the fluctuations increases with height. This behavior is typical for upward propagating gravity waves and the amplitude scale height is about [31]: $H\approx 2H_p$ and $H_p$ is the pressure scale height of about 7 km. This is estimation in the condition of a monochromatic freely propagating wave. We fitted an envelope to the residual profile in the form of $Y=a+\exp ((h+b)/H)$, where h refers to height and $Y$refers to the residual of Y wind. The parameters we get from this fitting are: $a=2.3m/s$, $b=13.5km$and $H=24.4km$, which means the amplitude scale height is about 24.4 km. This scale height is larger than expected from a monochromatic freely propagating wave (about 14 km). Thus the wave structure we observed in this case was probably generated by several different wave modes or it’s a dissipative wave losing its energy while propagating upward. A bandpass filter with cutoff wavelengths at 0.33 km and 10 km was applied on the residual profiles of this night and the filtering result is also shown in Fig. 3(b) as blue line. From the filtered profile in this figure we can see that the wave structure was highlighted and smoothed after the filtering but the amplitude of the wave was affected (smaller than the original amplitude). We use the filtering step only to highlight the evolution of the wave pattern with the wavelengths within the bandpass cutoff wavelengths.

 

Fig. 3 (a)Y wind profile with error bars at 23:30 on October 27, 2015, Jiuquan, compared with the radiosonde data at 19:00 on October 27 (blue dots) and MERRA data (green lines in three different times on this night). The polynomial fit of the whole night mean profile is also shown (red dash-dot line) (b)Y wind fluctuation profile after (blue) and before bandpass-filtering(black). The red solid lines represent the fitting result of the fluctuation’s amplitude.

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The process of fluctuation extraction and bandpass filtering of the residuals on this night is shown in Figs. 4(a)-4(c) in a form of height-time map of the successive vertical profiles from left to right by steps. We only plotted up to 50 km because on this night clouds sometimes appears in the troposphere and SNR is not enough above 50 km in most of the time. After 3:00 am in the morning, clouds became thicker and the max height of measurements decreases lower than 45 km. To be specific, Fig. 4(a) shows the measured Y wind, Fig. 4(b) shows the residual of wind speed between the Y wind and the estimated background wind, and Fig. 4(c) shows the bandpass filtering result of the residual. A wavelike structure with a slow downward phase velocity can be easily recognized in the map of the measured Y wind in Fig. 4(a) and this structure is highlighted in the residual map after subtracting the background wind in Fig. 4(b). The fluctuations below 23 km shown in Figs. 4(b) and 3(b) are clearly mixed with some background components which is probably caused by the imperfect of the background wind estimation. However, this background component is gone after the bandpass filtering with cutoff wavelengths at 3.3 km and 10 km. Thus the filtering step will help us to highlight the evolution of the wave in the condition of this imperfect of subtracting background procedure. To identify the characteristics of this case, we plotted the two-dimensional spectra (function of vertical wavenumber and apparent frequency) of the filtered residuals in Fig. 4(d). A dominant low-frequency (corresponding to a period of about 10 hours) and low wavenumber (corresponding to a wavelength of about 4.3 km) wave modes are easily identified. The frequency term of the phase of this dominant wave mode is generally positive, which implies a downward vertical phase velocity, indicative of an upward energy flux. The 2-D spectra analysis is applied from 15km to 50km, thus the dominant frequency and wavenumber is an imprecise mean value of the whole height and time scale. However, we can find in Figs. 4(a)-4(c) that the waves have somewhat higher frequencies in high ranges (30-50 km) than in lower level.

 

Fig. 4 (a) Y wind map on October 27/28, 2015, Jiuquan (b) residual of Y wind speed after subtracting background (c)filtering result of the residual (d) 2-D spectra analysis of the perturbations.

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3.3 Gravity wave cases

Including this case, the observed waves exhibit a slow downward vertical phase velocity of the order of a few tens of centimeters per second (estimated by the ratio of wavelength and period) and a higher frequency in higher ranges in most of the cases. Figures 5 and 6 show another two cases. In Fig. 5, three days’ continuously filtered perturbations of measured X wind from December 3-6, 2014 are plotted together. A bandpass filter with cutoffs at 3.3 km and 12 km is used. Although lidar can’t acquire valid data in daytime (shown by white), we can easily identified a dominant wave mode with period longer than 10 hours (lidar only operates during nighttime of about 12 hours thus the estimated period value is not as accurate as we need) and wavelength of about 6-7 km below 35 km. The wave pattern in 35-40 km is not as clear as below 35 km, whereas the wave mode with a downward phase velocity can still be identified in 35-40 km. Above 40 km altitude, the low-frequency waves seem partially dissipated. In the time period from 18:00 to 21:00 on December 4, two unexpected peak appears at 33 km and 20 km and the wave pattern can’t coincide with the estimated wave mode very well in 15-20 km, suggesting a superposition of other wave modes. In this case we can also found that frequencies are somewhat higher above 35 km than in the lower level. Figure 6 shows a case simultaneously observed by temperature and wind systems on December 29/30, 2014. In this case we found dominant wave modes with longer wavelengths so the bandpass filter was selected with cutoffs at 5 km and 20 km. Temperature measurements reaches up to 70 km and Y wind measurements reaches up to 60 km on account of the clear weather and good performance of the system. The two height-time maps are using the same height and time scales in order to compare the wave structure in the map of these two different variables. From this figure we can find that the wind and temperature perturbations generally have the similar dominant wave mode with wavelength around 14 km and low downward phase velocity in height range 30-60 km which is covered by both wind and temperature measurements. However, there are lots of differences between these two wave structures, especially in the range highlighted by the black dashed square frame, suggesting that there are probably other wave modes. The wind perturbation below 35 km have a downward phase in the beginning of the night but changes to nearly upward structure later. This similar phenomenon was also found in temperature map in altitude of 30-45 km, where the downward wave changes to nearly stationary on the second half of the night, suggesting another wave mode has been probably generated at about 23:00. This can also explain why the differences in the square frames happened. However, more quantitative analysis of the wave’s polarization relationships (i.e., the relationships between temperature and wind perturbations) and the coupling mechanisms of different perturbed variables are beyond the scope of this work.

 

Fig. 5 Height-time maps of X wind perturbations on Dec. 03-06, 2014, Xinzhou. Lidar only operates in nighttime thus daytime is shown as white in this figure. The time scale is continuous and linear.

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Fig. 6 Height-time maps of simultaneous Y wind and temperature relative perturbations on Dec. 29/30, 2014, Jiuquan.

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For most of the gravity waves cases observed by this lidar, the vertical phase velocity of the dominant gravity waves is very generally directed downward indicating an upwards energy flux. Above 40 or 45 km altitude the lower-frequency waves frequently seem partially dissipated. And the frequency is higher in higher altitude ranges. Such similar wave cases have been observed in this height range from other Rayleigh temperature lidar [22] and rocket soundings [32, 33]. These findings are generally in agreement with the results of our observation, suggesting that most part of the waves is generated in the troposphere or lower stratosphere. More kinds of database covering different altitude and regions around the observation place will help to assess possible wave-generation mechanisms.

4. Summary and conclusions

In this paper we performed several gravity waves observations of wind field in stratosphere using the data from a Rayleigh Doppler lidar. This mobile Rayleigh Doppler lidar can realize simultaneous high-time-spatial-resolution wind and temperature measurements (15-60 km for wind and 30-70 km for temperature) with height resolution of 0.2 km (below 40 km) or 1 km (above 40 km) and time resolution of 30 minutes (wind) or 15 minutes(temperature).

The wind and temperature fluctuations have been shown and analysis in some particular cases which are characteristic of typically observed wave patterns. The dominant wave mode with large period, around 10 hours, and large vertical wavelengths, from 4 to 14 km, is generally observed in the stratosphere. Meanwhile, the observed cases generally shows a downward phase velocity and the frequencies are higher in higher altitude range, suggesting an upward energy flux and a strong damping of the lower frequency waves in the upper stratosphere. These results are basically in agreements with the observations of gravity waves by other temperature Rayleigh lidar and rocket soundings. These gravity waves cases observed by the Rayleigh Doppler lidar demonstrates its capability to realize continuously observation of gravity waves of wind field and temperature in stratosphere. And the simultaneous wind and temperature measurements will make it possible to more clearly identify a gravity wave, compared with measuring only one variable. At the same time, the measure wind field and gravity wave activities will help to understand the atmosphere dynamics and the mechanism of momentum transporting, which is a basis to realize forecasting evolution of atmosphere and monitoring the dynamical environment of air craft, aerostat platforms or rockets.

In the future research, statistical analysis of these gravity waves’ characteristics in this region of Asia will be performed. Other kinds of database covering different altitude and regions around the observation place will acquire our attention to assess possible wave-generation mechanisms. The optimizing of the optical systems to improve the SNR will be one of our goals to realize more accurate wind and temperature measurements with a higher altitude range.