Vertical profiles of temperature, horizontal wind speed, and ozone concentration are first re-sampled with a 5 m vertical resolution applying a cubic spline interpolation. Profiles of LOAC aerosol concentration are interpolated at every 50 m using a nearest neighbour interpolation. Then, vertical profiles are filtered using a discrete wavelet transform (DWT) also called multiresolution analysis. Multiresolution is well adapted for the analysis and the decomposition of multiscale wave-like structures in geophysical signals (Kumar and Foufoula-Georgiou, 1997; Domingues et al., 2005). Conventional filters often alter amplitudes and/or phase of the original signal when filtering out high-frequency structures. Implementing finite impulse response filters with properties, such as perfect flatness in the passband, very fast decay at the frequency cut-off, and linear phase response, is difficult and expensive. In this study, the wavelet decomposition consists of the fast application of an orthogonal filter bank; i.e. a set of iterations such that the remaining signal (the approximation) becomes coarser and coarser after each iteration. Then the signal can be perfectly reconstructed by adding all details and the approximation of the signal at the nth order of the iteration (refer to Eq. 1 in Chane Ming et al., 2000a). The smoothness or the number of vanishing moments of the wavelet are important in theoretical and practical studies (Pollicott and Weiss, 2008) because it ensures fast decay and limits the wavelet to capture high-order polynomial behaviour in a noisy signal. But more wavelet values are needed to capture most of the energy of the signal when the smoothness of the wavelet increases; i.e. the support of the wavelet is less compact (Walker, 2008). Compact support orthogonal bases with high orders of smoothness, such as the eighth-order Daubechies wavelet, ensures energy conservation and a very good localisation both in space and frequency for the analysis of GWs in the lower and middle atmosphere. Applications of the pyramid algorithm and the eighth-order Daubechies wavelet coefficients are described in Chane Ming et al. (1999, 2000a). In this way, fine structures with λv<0.32 km are efficiently removed from re-sampled profiles.

Perturbation profiles are then extracted from filtered data using a numerical Butterworth infinite impulse response high-pass filter with a specific vertical wavelength cut-off between 5 and 7 km for temperature, horizontal wind, and ozone concentrations. Background temperature and horizontal wind profiles result from the difference between the original and perturbation profiles. A high-order Butterworth filter is commonly used to simulate an ideal filter with maximally flat and linear phase responses in the passband. A fourth-order Butterworth filter provides a good compromise between the cost of implementation and the frequency decay (-80 dB decade-1). Because of the high variability of aerosol concentration with altitude, the DWT is used to extract perturbations of aerosol concentration with a vertical wavelength cut-off of 6.4 km.

Figure 1 shows examples of 50 m interpolated continuous vertical distributions of aerosol concentrations with diameters of 0.2–50 µm in the troposphere and the stratosphere up to an altitude of 35 km. Different shapes of vertical distribution are observed. In particular, Fig. 1c visualises a stratospheric aerosol layer with high values of aerosol concentration in which thin layers of strong local enhancements are embedded. Severe storms with numerous lightning strikes occurred in France for cases in Fig. 1a, c, and d. The examination of the whole aerosol data set indicates a day-to-day variability of aerosols in the UTLS. Other cases reveal that aerosol content was low in the UTLS during the 2013 ChArMEx.

Cases, for which aerosol layers are visualised in the UTLS, are analysed by the continuous wavelet transform (CWT) to detect GW signatures (Chane Ming et al., 2000a). The continuous wavelet transform with Morlet complex-valued mother wavelet is applied to perturbation profiles of temperature, horizontal wind speed, ozone and concentration of aerosols to produce altitude–wavelength representations of the modulus of CWT coefficients, also called scalograms. For vertical profiles in Fig. 1, scalograms capture similar signatures of wave-like structures with vertical wavelengths between 1 and 4 km in dynamical parameters and tracer constituents of ozone and aerosols in the UTLS, which are explained by the presence of GWs. The case on 27 June 2013 is described in Sect. 4.

The European Center for Medium-Range Weather Forecasts (ECMWF) model is an operational numerical weather prediction model, which can explicitly resolve stratospheric GWs with horizontal and vertical wavelengths > 200 km and > 2 km respectively (Shutts and Vosper, 2011; Chane Ming et al., 2014; Preusse et al., 2014). Distributions of vertical velocity and horizontal wind divergence produce snapshots of GW structures. A one-dimensional (1-D) fast Fourier transform (FFT) in latitude is applied on 6-hourly ECMWF operational analyses with 1.125∘ × 1.125∘ resolution at 50 hPa (about 21 km) in the LS to produce spectral densities of dominant GWs as a function of latitudes and horizontal wavelengths.

Conventional methods detailed in Chane Ming et al. (2010), such as the hodograph analysis, the SPARC Gravity Wave Initiative Radiosonde Data, and Stokes' parameter methods (Eckermann, 1996; Vincent et al., 1997), are applied to RS vertical perturbation profiles to provide characteristics of GWs (energy densities, momentum fluxes, and spectral parameters). The hodograph analysis computes the intrinsic frequency from the elliptical axis ratio, which is determined from variances of horizontal wind perturbations as a function of altitude. Combined conventional methods (CCM) based on the SPARC and Stokes' parameter methods ensure good estimation of GW spectral characteristics. The wavenumber, the direction of horizontal propagation, and the phase speed of horizontal propagation are derived from the SPARC method and the intrinsic frequency is obtained from the Stokes' parameter method.

At a given altitude, the horizontal wavelength can be deduced from adjacent vertical profiles of temperature close in time and space in order to observe the same GW packet. If the time variation in the phase difference is neglected (refer to Eq. 5 in Wang and Alexander, 2010), the phase shift divided by the distance provides the horizontal wavenumber projected along the line connecting the two profiles. Ern et al. (2004) introduced this method to estimate a horizontal wavelength of GWs and global absolute values of vertical flux of horizontal momentum at 25 km altitude from adjacent temperature profiles from Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA). The method is adapted to pairs and triads of RO temperature profiles using the S-transform and CWT in the altitude range of 17.5–22.5 km with temporal windows of 4 and 2 h (Wang and Alexander, 2010; Faber et al., 2013). To better constrain estimated horizontal wavelengths and momentum fluxes, Schmidt et al. (2016) used temporal and spatial windows of 15 min and 250 km

The GW parameters are used to initialise a model based on the simplified linear wave polarisation relations for vertically propagating internal waves in a rotating fluid (Gill, 1982; Chane Ming et al., 2002) to produce synthetic vertical profiles of temperature and horizontal winds with GW signatures. Input parameters are vertical wavelength, intrinsic frequency, direction of horizontal propagation, localisation, altitude range, amplitude of temperature perturbation, and mean profiles of temperature and horizontal winds. The horizontal wavelength is derived from the GW–dispersion relationship. A Gaussian-shaped sinusoidal pulse is first computed at the observed altitude range from temperature perturbations. Based on the simplified linear wave polarisation relations, vertical wind perturbations are derived from temperature perturbations. Then the horizontal wind perturbations result from the vertical wind perturbations when the rotated frame of reference is aligned along the horizontal wavenumber. The direction of horizontal wave propagation is finally used to rotate the frame of reference to obtain observed horizontal wind perturbations. The synthetic profiles result from the sum of perturbations and observed background profiles.

The gravity wave regional or global ray tracer (GROGRAT) is a 4-D ray-tracing model of the propagation and amplitude evolution of non-hydrostatic GWs in a rotating, stratified, compressible slowly varying background described by numerically gridded fields of temperature, wind, and pressure or geopotential height in the lower and middle atmosphere. It is based on the dispersion and refraction of the ray paths and includes parameterisations of turbulent and radiative wave damping and of wave–amplitude saturation. A full description of the model can be found in Marks and Eckermann (1995) and Eckermann and Marks (1997).

The validity of the Wentzel–Kramers–Brillouin (WKB) condition based on the slow variation of the vertical wavenumber with height ensures an approximate solution of the GW ray-tracing equations. Previous studies have shown that GROGRAT is an efficient tool to identify GW sources (Guest et al., 2000, 2002; Pramitha et al., 2015) and to simulate GW-background interactions such as GW effects, wave filtering, space and time variability of GW activity and characteristics (Wei and Zhang, 2015). For example, GROGRAT simulations help to interpret global GW observed morphology derived from satellite observations (Preusse et al., 2009). In this study, the model GROGRAT is run with observed GW spectral characteristics in a regional background of 6-hourly operational ECMWF analyses of temperature, horizontal wind, and geopotential height with resolutions of 25 pressure levels (1000–1 hPa) and 1.125∘ × 1.125∘ in the horizontal plane.

The parcel advection method is based on an analytical formula for the linear response of minor constituents to non-dissipating hydrostatic internal GW motions when photochemical response of the constituent can be negligible, especially for long-lived tracers. The method was used for GW-induced perturbations in ozone, water vapour, and other constituents such as nitrogen dioxide and sodium (Randel et al., 1990; Teitelbaum et al., 1994). When the photochemical response of the constituent is negligible, in the linear simplified case, normalised ozone mixing ratio perturbations as a function of altitude are linked to normalised potential temperature perturbations by a coefficient R(z), which is the ratio of vertical gradients of ozone and of the potential temperature background. Chane Ming et al. (2000b) illustrated the method to produce a climatology of laminae with vertical wavelengths < 5 km induced by GWs and horizontal advection in the UTLS near the southern subtropical barrier. The method also revealed the presence of GWs on vertical ozone profiles collected at Macquarie Island (54∘ S, 159∘ E) during the Airborne Southern Hemisphere Ozone Experiment/Measurements for Assessing the Effects of Stratospheric Aircraft (ASHOE/MAESA) observation programme in 1994 (Chane Ming et al., 2003). Eckermann et al. (1998) formalised the method to derive analytical formulas for the response of vertical constituent profiles of arbitrary shape to adiabatic GWs. In particular, they showed that the parcel method becomes inaccurate for non-hydrostatic GWs and if the wave-induced photochemical response produces a significant diabatic feedback on the GW for shorter-lived constituents.

Figure 3 visualises filtered resampled vertical profiles of temperature, potential temperature, horizontal winds, and ozone from radiosondes and the vertical profile of LOAC aerosol concentrations with diameters of 0.2–0.7 µm on 27 July at 23:03 UTC above Ile du Levant.

In our study, GW analyses are applied on the sum over the size classes between 0.2 and 0.7 µm of continuous vertical profiles of aerosol concentrations to derive a mean continuous vertical profile of aerosol concentrations. Because of the synoptic meteorological event, a sheared tropospheric jet is observed at 10 km height with maximum wind velocities < 20 ms-1 at altitudes of 6 and 14 km, whereas larger amplitudes (≈ 40 ms-1) are observed at longitudes < 2.5∘ W at heights of about 12.5 km. Perturbation profiles are obtained from subtraction between original and background profiles (Chane Ming et al., 2010). They show evidence of wave-like structures with short vertical wavelengths of 2–3 km in temperature and horizontal wind at heights of 13–20 km. Maximum temperature and wind perturbations are about 3 ∘C and 5–7.6 ms-1 respectively, near the tropopause located at a height of 15 km. Large variations in ozone and aerosol perturbations are also observed at altitudes of 15–20 km. Thus the CWT is applied on vertical profiles of perturbations to localise wave-like structures in altitude–wavelength representations at heights below 23 km (refer to Sect. 3.2). The scalograms of the dynamical variables (temperature, wind) reveal a spectral signature with 2.6 km vertical wavelength at heights 10—20 km (Fig. 4a, b, c). For ozone and aerosols, similar peaks are found above 15 km (Fig. 4d, e). Such a pattern is also observed on CWTs of each vertical aerosol concentration profile of the five smallest size classes. Analyzing normalised ozone perturbation profiles would enhance the ozone peak at 13 km because of low level tropospheric ozone background whereas the use of ozone perturbation profiles focuses on wave-like structures observed at 15–23 km heights. The cross-sections of potential vorticity and ozone mixing ratio at 43∘ N indicate that the peak at 13 km heights results from a local stratospheric intrusion at longitudes of 7–12∘ W. The longitude–latitude maps at 250–300 hPa support the presence of a filament structure of potential vorticity and ozone mass mixing ratio during the jet-streak event (not shown). These observations also suggest that aerosols observed on the LOAC profile at the same altitude are of stratospheric origin on 27 July at 12:00 UTC (Plumb et al., 1994).

The Morlet CWT local maxima also called “skeleton” (Chane Ming et al., 2000a) provide a continuous distribution of dominant wave-like structures with the vertical wavelength of 2–3 km at heights between 3 and 25 km with maxima at heights of 13–18 km in zonal wind perturbations (not shown). The mean vertical wavelength is estimated at about 2.5 km at altitudes of 3–7 km. The amplitudes as well as the mean vertical wavelength decrease rapidly at altitudes above 19 km likely because waves are filtered near the critical level where intensity of zonal wind approaches zero. The FFT also supports the presence of wave-like structures with vertical wavelengths of 2–3.5 km at heights of 13–23 km in all analysed parameters (Fig. 4f). The DWT decomposition reveals that RS horizontal wind perturbations (u′ and v′) with dominant vertical wavelengths of 2–3 km are in quadrature at heights of 14–26 km in agreement with the linear GW–polarisation relationship. The hodograph of wind perturbations visualises elliptical structures with characteristics of GWs with vertical wavelength of about 2 km at heights of 14–24 km. The sign change at heights of 9–12 km with anticyclonic (cyclonic) rotation of the ellipse above 12 km (below 9 km) indicates an upward (downward) flux of GW energy. This suggests that GW sources are localised at heights between 9 and 12 km.

The analyses of vertical velocities in pressure coordinates (ω= dp/ dt) derived from ECMWF operational analyses indicate that the numerical weather prediction model captures some wave-like structures on 27 July 2013 at 18:00 UTC in the LS (Fig. 5a). Figure 5a depicts mesoscale structures located over the eastern part of France. Spectral density of vertical velocities is calculated for longitudes of 10∘ W–20∘ E at latitudes between 42 and 48∘ N. In particular, the energy of mesoscale wave-like structures with horizontal wavelengths in the east–west direction (λx<500 km) is well localised at the latitude of 46∘ N, which corresponds to the latitude of the exit region of the jet streak. Figure 5b displays the energy distribution of dominant wave-like structures at latitudes of 42–48∘ N for horizontal wavelengths λx<1200 km. In particular, it highlights a continuous spectrum of GWs with horizontal wavelengths λx of 400–800 km with a dominant mode of 400 km at latitudes of about 46∘ N. The spectral densities at latitudes of 42–48 and 46∘ N confirm that the mode of 400 km is dominant at 46∘ N within the wavelength range of 400–800 km (Fig. 5c). The vertical velocity data also reveal that the structure with amplitudes < 0.2 Pas-1 extends at longitudes (latitudes) between 4∘ W to 10∘ E (42 to 52∘ N).

The waves from this event can be identified in GPS-RO soundings as well. Figure 6a shows an overview of the GPS-RO soundings over western Europe for 26 to 29 July 2013. We selected profiles for longitudes of 2.5–6∘ E and latitudes of 40–50∘ N for spectral analysis of the altitude range of 10–20 km. The results are shown in Fig. 6b. The individual spectra are labelled by the day and UTC of the measurement (e.g. 2605 for 26 July; 05:00 UTC) and also marked accordingly in Fig. 6a. As one can see from results for consecutive days, GWs are enhanced starting from 27 July, peak at 28 July and are still active on 29 July. Spectral density peaks are found for wavelengths 2–3.5 km, especially from 27 July at 06:00 UTC to 29 July in the morning with a maximum observed on 28 July early in the morning.

The hodograph analysis and the CCM (refer to Sect. 3.3) are applied on RS temperature and wind perturbations on 27 July at 23:03 UTC above Ile du Levant to compute spectral characteristics such as vertical and horizontal wavelengths, intrinsic frequencies, periods, directions of horizontal wave propagation, and wave energy densities (Table 1). Consistent spectral parameters are obtained by the two methods. In particular, the hodograph analysis reveals the presence of mesoscale inertia GWs with vertical and horizontal wavelengths of 2.6 and 440–510 km respectively, a period of about 12 h, propagating southward at heights of 13–20 km. Eastward dominant modes with similar vertical wavelength, a period of about 15 h and longer horizontal wavelengths (≈1300 km) are observed at heights of 20–26 km. The horizontal phase speed of the mesoscale GW is estimated at about 6.8 ms-1 (7.9 ms-1) at heights of 13–20 km (20–26 km). GWs with 1300 km horizontal wavelength have larger phase speed of about 24 ms-1 at heights of 20–26 km. Consistent large values of total energy densities of about 16 Jkg-1 and vertical flux of horizontal momentum of 0.05 m2 s-2 (vertical flux of zonal momentum u′w′‾≈0.045 m2 s-2) defined in Vincent et al. (1997) are calculated at heights of 13–20 km. Our computed value of vertical flux of horizontal momentum (about 8 mPa) is well beyond values of 1 mPa and 0.02 m2 s-2 observed in the LS in summer midlatitudes respectively, by Ern and Preusse (2012) over Europe from High Resolution Dynamics Limb Sounder (HIRDLS) observations and Zhang et al. (2014) from radiosondes over North America. Thus the value of vertical flux of horizontal momentum supports our statement that the case on 27 July 2013 represents a stronger GW event.

The ratio between kinetic and potential energy of GWs provides a spectral index (p) of about 2.6–2.9, which is larger than the values of p∼5/3 in the middle atmosphere (Vincent et al., 1997). Hertzog et al. (2002) found values of p in the range 1.5–2.2 for high-frequency GWs from super-pressure balloon measurements in the stratosphere. However, they suggest that values greater than 5 could be caused by enhancements of the velocity spectrum near the inertial frequency. A large decrease of total energy densities above heights of 20 km indicates that most tropospheric GWs are not transmitted to higher stratospheric layers. The wave energy propagates upward from the troposphere with a fraction of upward energy Fup>86 % (95 %) at heights of 13–20 km (20–26 km). In addition the hodograph analysis reveals the presence of mesoscale structures propagating south-westward with vertical and horizontal wavelengths of 2.6 and 161–451 km respectively, with periods of 10–15 h at heights of 3–7 km in the lower troposphere. The Fup value of about 60 % suggests that wave energy equally propagates upward and downward below the dominant GW tropospheric source. Finally, conventional methods provide good estimates of spectral GW parameters as can be seen from consistent values of the two methods and the standard deviation computed for the hodograph analysis in particular for the observed dominant mesocale wave-like structures at heights of 13–20 km. Similar results at heights of 13–20 km are also obtained by the CWT method described in Chane Ming et al. (2002, 2003).

Figure 7a visualises temperature profiles from RS at 23:03 UTC (hereafter called RS2723) on 27 July above Ile du Levant and RO at 02:00 UTC (hereafter called RO2802) and 12:00 UTC (hereafter called RO2812) on 28 July. As observed on the RS2723 temperature profile, GPS RO temperature profiles also show evidence of small-scale perturbations in the troposphere and the LS. Scalograms of RO2802 and RO2812 temperature perturbations support the presence of dominant GW structures with vertical wavelengths of 2.5–3 km at heights of 10–18 km on 28 July (Fig. 7b, c). By assuming that the same GW packet is observed on RS2723 and RO2802 profiles in the LS, the phase shift (Φ) between perturbation profiles is calculated at the altitude of 17 km taking into account of the time variation (refer to Sect. 3.3) using a GW period of 12 h at heights of 15–20 km and a time difference of 1.8 h at the altitude of 17 km between RS and RO measurements. Using a distance of 179.14 km between temperature profiles, the phase shifts (Φ) of 1.67 radians provide a horizontal wavelength of 673.6 km. The estimated horizontal wavelength is larger than the “real” value by a factor of 1/cos⁡α, where α is the angle between the connecting line of the two profiles and the real horizontal wave vector (Preusse et al., 2002). Thus, the “real” horizontal wavelength is ranged between 396 and 674 km (Phi = 200 ± 29∘). The result is consistent with values of horizontal wavelengths derived from applying conventional methods on RS2723 profiles at heights of 13–20 km. Using Eq. (7) reported in Ern et al. (2004), the vertical flux of momentum is estimated at 0.017–0.03 m2 s-2 at heights of 10–20 km. The estimate is somewhat lower but compatible with the value of 0.05 m2 s-2 derived from the RS measurements. The characteristics of these GWs are consistent with previous observations of inertia GWs associated with a jet stream exit region (Thomas et al., 1999; Ravetta et al., 1999; Bertin et al., 2001).

Thus, both observations and ECMWF analyses suggest that the strong activity of GWs with vertical and horizontal wavelengths of 2–5 km and < 1200 km with dominant mesoscale structures of 400 km horizontal wavelength is associated with the jet-front system from 27 July afternoon to 28 July in the morning in the eastern part of France (refer to the following Sect. 5.1).

The observed characteristics at heights of 13–20 km are used in the next section to provide a simplified synthetic profiles of perturbations and to identify GW sources.

Mean values of spectral parameters observed at heights of 13–20 km (a vertical wavelength of 2.6 km, a period of 11.7 h, a direction of horizontal wave propagation clockwise from north of 204∘) with upward propagation of energy at heights of 12.8 km with a height range of 14 km are used to produce simplified synthetic RS profiles (refer to Sect. 3.4) with signatures of dominant mesoscale GWs with horizontal wavelengths of 499.9 ± 45.7 km. Filtered and simulated amplitudes, and phase relations of perturbations are in good agreement for the temperature and the horizontal wind (Fig. 8). The hodograph analysis and the CCM are applied on simulated profiles to retrieve spectral parameters (Table 1). The two methods provide good estimates of the input spectral parameters. These estimates are also in agreement with observed ones at heights of 13–20 km in terms of energy densities and the mean horizontal phase speed. The wave energy propagates upward from the troposphere with a fraction of upward energy Fup>93 % and a horizontal phase speed of 6.44 ms-1 at heights of 13–20 km. In conclusion, the simplified synthetic RS profiles are consistent with observed RS profiles at heights of 13–20 km for the case study on 27 July 2013. Thus, mean characteristics of observed mesoscale inertia GW structures agree well with simplified linear GW theory and are the most energetic structures observed in the RS profiles on 27 July at heights of 13–20 km. Thus, because of the shape of the mean wave-like structure observed at heights of 13–20 km, the Morlet complex-valued mother wavelet reveals to be well adapted to analyse such a structure. The simplified synthetic RS profiles are used in the next section to interpret the impact of GWs on stratospheric tracers and aerosols.

The GROGRAT model (refer to Sect. 3.5) is used to identify sources of observed dominant mesoscale GWs at heights of 13–20 km. Taking into account spreads of spectral parameters (refer to values of the two methods between parentheses in Table 1), spectral characteristics of the mesoscale inertia GW with horizontal wavelengths of 300–550 km (step of 20 km), ω/f of 1.4–1.8 (step of 0.1) and horizontal propagation direction of 200∘ at heights of 19 km from 28 July at 00:00 UTC provide a discrete spectrum of 65 individual components to initialise the model. Backward ray trajectories are computed with the same parameterisations used in Guest et al. (2000). Almost all rays can be traced back to 12–17 h before release on 28 July at 00:00 UTC. Projected ray paths on the georeferenced infrared GMS-3 image at 12:00 UTC and the latitude–height cross section of zonal wind at longitude 0∘ at 12:00 UTC reveal that ray paths terminate at the location of the cold frontal zone and at about heights of 10 km in the jet core on 27 July at 12:00 UTC at 2–0∘ W longitudes and 42.5–45∘ N latitudes (Fig. 9a, b). Because rays pass over a convective region when the front system moves eastward, some GWs produced by convective sources might also be captured.

Figure 9c shows the evolution of the mean horizontal wavelength and the mean normalised intrinsic frequency as a function of altitude and mean time. The mean horizontal wavelength (mean period) decreases (increases) slowly from 440 km (10 h) at 17 km heights to 290 km (14 h) at 10 km heights. A given combination of wave parameters might preferentially be observed depending on the background wind field. A sensitivity test on the horizontal propagation direction varying between 170 and 230∘ (with a step of 10∘) produces similar results. The characteristics of GWs are consistent with numerical modelling studies of Zhang (2004) and Wang et al. (2009) on the generation of GWs in upper tropospheric jet-front systems. These studies reveal the production of mesoscale GWs lasting more than 24 h with very similar spectral characteristics (λh=100–500 km, λv=2 km, ω/f≈1.5) in the troposphere and LS.

In conclusion, the GROGRAT simulation indicates that mesoscale GWs with a whole range of parameters around the mean parameter could be excited by the front and propagate to the location of Ile du Levant at heights of 13–20 km.

To identify GW induced perturbation in tracers, the parcel advection method (refer to Sect. 3.6) is applied on profiles of ozone and potential temperature perturbations normalised by the background profiles on 27 July at 23:03 UTC (Fig. 10a). The normalised potential temperature perturbations are multiplied by smooth vertical profiles of coefficient R(z) (Fig. 10b) and superimposed on normalised ozone perturbations. The amplitudes of perturbations exhibit comparable values at heights of 4–7 and 14–24 km for perturbations with vertical wavelengths < 5 km. This supports the presence of GW signatures. The parcel advection method is not valid at heights of 7–14 km because the vertical gradient of the ozone background is very small, R(z) strongly varies with altitude, and other tropospheric structures are present at 7.5 and 12.5 km (Chane Ming et al., 2000b). The parcel method also identifies GW signatures in temperature and ozone perturbation profiles on 28 July at 13:30 UTC (Fig. 10c and d). In comparison with Fig. 3, smaller values of normalised potential temperature perturbations are observed in the LS. It means that the intensity of stratospheric GWs is decreasing in the afternoon of 28 July. The Morlet CWTs of ozone and temperature perturbations depict similar monochromatic structures with vertical wavelength of about 1.5–3 km at heights of 10–15 km. For these two cases, GW signatures can be observed in the lower troposphere above 3 km. The parcel advection method is also valid for temperature and humidity mixing ratio. Figure 10e visualises wave-like structures on specific humidity profiles at heights above 3 km. The spectral densities of perturbations (Fig. 10f) reveal wave-like structures of 1.5–3 km vertical wavelengths. The amplitudes of temperature and specific humidity perturbations are π out of phase above 4 km height, which is in agreement with the parcel advection method with regards to signs of mean gradients. Thus, evidence of GW signatures in ozone and humidity in the lower troposphere supports that the dominant GW source is located in the jet core with an upward (downward) propagating energy above (below) the source. Thus, observations lead to the conclusion that mesoscale GWs observed on 27 July 2013 affected the variability of stratospheric ozone-tracer fields.

Effects of GWs on stratospheric aerosols are investigated in perturbations of aerosol concentrations and dynamical parameters in the LS. The DWT is applied to aerosol concentrations to retrieve perturbations of aerosol concentrations with vertical wavelengths of 1.6–3.2 km and the mean profile with vertical wavelengths > 3.2 km (Fig. 11). Dominant wave-like structures with vertical wavelengths of 2–2.5 km are observed in the LS (15–20 km). The amplitudes of aerosol concentration perturbation strongly decrease at heights of 20 km likely because of partial transmission of GWs through the wind field and the presence of two layers of stratospheric aerosols with different origins. The superimposition of synthetic vertical perturbation aerosol upon concentration perturbation profiles of the mean dominant mesoscale GW (Fig. 8b) indicates that perturbations of aerosol concentration and simulated vertical wind are in phase at heights of 15–19 km (Fig. 11b). The phase relationships do not agree with the parcel advection method for which perturbations should be in quadrature (refer to Eq. 24 in Eckermann et al., 1998). Aerosols behave differently from tracer gases with production and growth processes in the stratosphere. This case study suggests a possible correlation between vertical transport and the distribution of aerosol concentration in the LS. In addition, large amplitudes of stratospheric vertical wind with maximum values of ±40 mms-1 are induced by the mean mesoscale GW in comparison with monthly averaged amplitudes of stratospheric vertical wind of about ±5 mms-1 with an annual averaged of ±1 mms-1 (Gryazin and Beresnev, 2011). Recent theoretical studies reveal possible substantial effects of a background vertical motion on stratospheric aerosol distribution. Using a 4-D continuity equation for particles undergoing growth process, Li and Boer (2000) investigated the relative roles of condensation, particle fall velocity, vertical motion, and diffusion in determining the aerosol size distribution. Vertical motion could broaden the size distribution of the stratospheric background aerosol, which would tend to support a broader size distribution of the stratospheric background aerosol in the tropics. Gryazin and Beresnev (2011) suggested that the relative aerosol concentration is mostly controlled by the action of the vertical wind for particles with a size < 2.5 µm. Nilsson et al. (2000) proposed the use of the phase shift in perturbations of aerosol concentration and vertical wind to separate the influence of turbulent fluxes of aerosols from the effect of nucleation responding on waves or turbulence. Perturbations should be 3π/4 out of phase if nucleation dominates, whereas turbulence would cause perturbations to be in phase. With regard to GWs effects on cirrus clouds, the combination of a mountain wave and the jet-streak GW producing a wave-induced upward motion > 10 cms-1 can cause ice supersaturation and trigger the formation of a cirrus cloud in the UT (Spichtinger et al., 2005). A strong link has been established between GW-induced mesoscale variability in vertical velocities and climate forcing by cirrus (IPCC, 2007). Haag and Kärcher (2004) investigated the impact of aerosols and GWs on cirrus clouds at northern mid-latitudes. They emphasise the importance to include small-scale temperature fluctuations caused by GWs for a good prediction of cloud physical properties in global models as well as to represent correctly changes in GW activity in a future climate. In the present study, strong modulation is also observed on amplitudes of stratospheric aerosol concentration background with size class of 0.2–0.7 µm up to 60 % of the background amplitude with the vertical spectral characteristic of the observed stratospheric mesoscale GW.