1 Introduction

Ozone is crucial for global climate change and environmental protection (Butchart et al. 2010). It absorbs and blocks ultraviolet radiation from the Earth’s surface, protecting humans and other organisms from damage (Slaper et al. 1996). In the mid-1980s, Farman et al. (1985) first discovered the South Polar ozone hole and proposed that human emissions of Freon were the primary cause of the dramatic depletion in Antarctic stratospheric ozone. This discovery caused a sensation in academia, and the ozone hole soon became a popular research direction in meteorology. Studies have shown that ozone layer depletion is the result of a combination of dynamic and chemical factors (Adams et al. 2012; Cicerone 1987). The Montreal Protocol, signed by governments in 1987, effectively reduced CFC emissions and restored stratospheric ozone (Solomon et al. 2016).

The Qinghai-Tibetan Plateau is one of the most ultraviolet-rich regions in the world. Intense UV radiation has serious effects on human health and ecosystems (Norsang et al. 2011). Therefore, the absorption of ozone is particularly critical to the ecosystems and climate change in the region. The changes in ozone levels in the Qinghai-Tibetan Plateau are of great concern to scientists. Zhou et al. (1995) analyzed the Total Ozone Mapping Spectrometer (TOMS) data and observed an ozone trough center on the Qinghai-Tibetan Plateau in summer. Zou (1996) also confirmed the existence of the ozone trough on the Qinghai-Tibetan Plateau by calculating the zonal deviation of global mean total ozone for each season from 1979 to 1991. With the development of technology, Guo et al. (2015), using Microwave Limb Sounder (MLS) data, found that there are two distinct ozone low centers in the UTLS region and the middle and upper stratosphere over the Qinghai-Tibetan Plateau, which indicates a double-center structure in the ozone trough of the Qinghai-Tibetan Plateau.

Since the UTLS on the Qinghai-Tibetan Plateau is the strongest low-value center in the double-center structure of the ozone valley, previous studies on ozone depletion on the Qinghai-Tibetan Plateau have mainly focused on this region (Wang et al. 2013; Xie et al. 2008). It is shown that the ozone trough in the UTLS region of the Qinghai-Tibetan Plateau is mainly influenced by dynamical processes, while chemical effects are weaker (Bian et al. 2011; Guo et al. 2015; Tian et al. 2008). Zhou et al. (1995) suggested that over the Qinghai-Tibetan Plateau, strong convective activity in summer causes the formation of ozone valley; Zou (1996) found that thermal forcing on the surface of the Qinghai-Tibetan Plateau during the hot summer season leads to ozone depletion and that the thermal and dynamical processes are unified. In 2006, Zhou et al. (2006) demonstrated that the exchange of material between the troposphere and the stratosphere is responsible for the ozone depletion over the Qinghai-Tibetan Plateau; Tian et al. (2008) showed that the formation of ozone low center in the UTLS region over the Qinghai-Tibetan Plateau is in association with large-scale rise and subsidence of the isentropic surface; Guo et al. (2015) found that there is a double-centered trough of ozone in summer on the Qinghai-Tibetan Plateau and noted that the ozone trough in the UTLS is mainly affected by anti-cyclone dispersion of the anticyclone. While ozone valley in the upper stratosphere is mainly influenced by chemical effects, it was pointed out that photochemical effects are the most important element in the formulation of upper stratospheric ozone trough over the Qinghai-Tibetan Plateau (Guo et al. 2015); Yan et al. (2022) used MLS data and the box model, showing that in summer the upper stratospheric ozone trough on the Qinghai-Tibetan Plateau is related to chemicals such as NO.

Atmospheric gravity waves are meso-small-scale oscillations propagating through perturbing stable layers and are closely associated with many meso-small-scale weather phenomena. The propagation and fragmentation of gravity waves in the atmosphere have important impacts on local as well as global atmospheric circulation, momentum transfer, material exchange, and chemical composition distribution (Fritts 1984; Garcia and Solomon 1985; Holton 1983; Xu et al. 2016). Previous studies indicate that meso-small-scale atmospheric gravity waves interacting with the unique topography of the Qinghai-Tibetan Plateau cause strong stratospheric and tropospheric material exchange during propagation, which allows stratospheric ozone to enter the troposphere, resulting in stratospheric ozone deficit. Wei et al. (2016) simulated the Qinghai-Tibetan Plateau gravity wave process from 00:00 to 06:00 UTC on May 1, 2008, and analyzed the stratospheric-tropospheric material exchange (STE); In 2018, Xu et al. (2018) showed that meso-small-scale gravity waves on the Qinghai-Tibetan Plateau can be uploaded to the medium and upper layers of the atmosphere, affecting the exchange of matter and energy and the distribution of atmospheric constituents and thus influencing the weather and climate change regionally and globally; Chang et al. (2020) investigated a gravity wave event occurring on the Qinghai-Tibetan Plateau from May 3 to 4, 2014 and gave an estimate of the impact of the gravity waves on ozone in the UTLS. However, most of studies on the upper stratospheric ozone valley on the Qinghai-Tibetan Plateau have focused on chemical processes (Guo et al. 2015; Yan et al. 2022), and the studies on the effects of meso-small-scale atmospheric gravity waves on the upper stratospheric ozone valley on the Qinghai-Tibetan Plateau are limited. Thereby, it is of great scientific value to investigate the relationship between the stratospheric ozone layer and the dynamical mechanisms of gravity waves on the Tibetan Plateau.

Based on ERA5 reanalysis data, the WRF model simulates the mechanism of gravity waves propagation over the Qinghai-Tibetan Plateau. It focuses on the impact of gravity waves on the upper stratospheric ozone valley and provides a relevant basis for further research. The first section is the introduction. The second section introduces the data methods and models used in the study. The third section analyzes the ERA5 data and the results of the WRF simulations. The final section serves as the conclusion.

2 Data and methodology

2.1 Data

The ERA5 reanalysis data is a global reanalysis dataset provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) with hourly horizontal temporal resolution of 0.25° and 37 vertical layers covering the atmospheric pressure range from 1000 to 1 hPa. The ERA5 dataset provides global, high-quality historical meteorological data on a wide range of parameters such as latitudinal winds, temperature, vertical velocity, potential vorticity, ozone mixing ratios, and more. They are widely used in different meteorological studies and applications (He et al. 2023; Montoya Duque et al. 2021). In the Qinghai-Tibetan Plateau region, this dataset is frequently used. Chang et al. (2020) used ERA5 reanalysis data to analyze the gravity wave event on the Qinghai-Tibetan Plateau and described in detail the process of material exchange in the stratosphere; Liu et al. (2021) evaluated the effect of the ERA5 dataset on air temperature and snow depth on the Qinghai-Tibetan Plateau and discovered that this dataset can help to solve the problem of data sparsity over the Tibetan Plateau, with better performance than the ERA5 dataset. The study found that this dataset helps to solve the problem of sparse data over the Tibetan Plateau and has better performance; Xu et al. (2021) used the ERA5 dataset to analyze the tropospheric water vapor trends on the Qinghai-Tibetan Plateau with high feasibility. This manuscript presents an analysis of the gravity waves on the Qinghai-Tibetan Plateau from 15:00 on July 29 to 06:00 on July 30, 2015, and the effect on upper stratospheric ozone based on the ERA5 data.

2.2 Methods

This study further analyses the variation in the gravity wave characteristics and the ozone concentration using ERA5 reanalysis data. Atmospheric gravity waves are fluctuating phenomenon of propagating energy and momentum that cause periodic deformation of atmospheric air masses. The rising or falling motion of the air mass will deviate from the equilibrium position, and the air mass will periodically vibrate upward and downward in the vertical direction due to the force of gravity. When the air mass rises, the vertical velocity is positive, and when it moves downward, the vertical velocity is negative, so the signals of gravity waves can be identified using alternating positive and negative changes in vertical velocity (Chen et al. 2014; Wei et al. 2016). When gravity waves propagate in the atmosphere, temperature wave guide phenomena are generated (Li and Zhang 2010). Therefore, the method of extracting gravity waves by using temperature perturbation is widely used (Wang et al. 2019; Zhang et al. 2011). In this paper, temperature perturbation is used to extract gravity wave signals with the original temperature subtracted from the background temperature on the basis of the linear theory of gravity waves. In addition, the WRF model can accurately characterize the evolution of meso-small-scale gravity waves due to its high resolution. Furthermore, the model is used to simulate the gravity wave processes.

2.3 Numerical simulation

The WRF model was simulated for about 15 h in the area of 65°E to 110°E and 20°N to 45°N with a horizontal resolution of 10 km. In order to accurately monitor the spatiotemporal development of gravity waves and detect exchange of atmospheric matter and energy associated with this process, the model was vertically divided into 80 layers. In the WRF model, the ERA5 data were interpolated from 1 to 0.1 hPa using an interpolation method. The WRF model’s top position is set to 0.1 hPa. The numerical simulation experiments were performed using the Kain-Fritsch cumulus convection scheme (Kain and Fritsch 1990) and the WSM 6-class graupel scheme (Hong and Lim 2006) were conducted. The WRF model was simulated starting at 15:00 UTC on July 29, 2015, and initial fields were derived using ERA5 data. Non-rigid or elastic boundary conditions were used to simulate gravity waves in order to allow fluctuations to pass through the top boundary of the model without artificial reflections. The results were collected at half-hourly intervals in time steps of 180 s. After 15 h of simulation, the process concluded at 06:00 UTC on July 30, 2015. The initial time for the model was specified as the first three hours, and the last twelve hours of model output data were analyzed for diagnostic purposes.

It has been shown that WRF model is quite effective in simulating meso-small-scale gravity waves process. Chen et al. (2013) simulated gravity waves triggered by Typhoon Matsa with a horizontal resolution of 27 km and a vertical resolution of 300 m. Wei et al. (2016) simulated the STE process caused by gravity waves in UTLS on the Qinghai-Tibetan Plateau with WRF model with a horizontal resolution of 80 km and a vertical model divided into 46 layers. The results show that vertical velocity distribution of WRF model simulates the gravity wave signals well, and is consistent with the results of the MERRA (Modern-Era Retrospective Analysis for Research and Applications) reanalysis data. In 2020, Chang et al. (2020) used the meso-scale WRF model to simulate gravity waves on the Qinghai-Tibetan Plateau, and the comparison results show that the horizontal and vertical distributions of the vertical velocities of the WRF simulation results is consistent with the ERA5 data, and it can give the details of gravity wave dynamical processes better.

3 Results

3.1 Analysis of gravity wave characteristics by ERA5 reanalysis data

The atmospheric gravity wave event took place between 15:00 UTC on July 29 and 06:00 UTC on July 30, 2015. Figure 1 shows the horizontal distribution of vertical velocities at an altitude of 40 km during this period. Within the region of 80°E − 100°E and 20°N − 45°N (black box), vertical velocities alternated between positive and negative signals between 29 July 21:00 UTC and 30 July 03:00 UTC, indicating the presence of a gravity wave. The clear arc-wave structure appeared at 21:00 UTC on July 29. The signal gradually weakened from 00:00 to 03:00 UTC on July 30 and eventually dissipated.

Fig. 1
figure 1

The horizontal distribution of vertical velocity (unit: cm·s−1) at 40-km altitude obtained by ERA5 data from 15:00 UTC on July 29 to 06:00 UTC on July 30, 2015. Black box: 80°E − 100°E, 20°N − 45°N

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On the basis of the linear theory of gravity waves, the perturbation temperature is \({T}{\prime}=T-\overline{T }\), where denotes the original temperature and \(\overline{T }\) is the back \(T\) ground temperature. The results of the perturbation temperature at 40-km altitude from 15:00 UTC on July 29 to 06:00 UTC on July 30, 2015 are shown in Fig. 2. Within the region of 80°E − 100°E and 20°N − 45°N (black box), a magnitude of the temperature perturbation was large from 18:00 to 21:00 UTC on July 29, and at 21:00 UTC, there was a more obvious fluctuating structure. The temperature perturbation in this region weakened from 00:00 to 03:00 UTC on July 30.

Fig. 2
figure 2

The horizontal distribution of perturbation temperatures (unit: °C) at 40-km altitude obtained by ERA5 data from 15:00 UTC on July 29 to 06:00 UTC on July 30, 2015. Black box: 80°E − 100°E, 20°N − 45°N

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In a stable atmospheric junction, the vertical movement of the fluid particle occurs in response to disturbance. The equilibrium position is regained due to the combined influence of gravity and buoyancy, with the oscillation frequency referred to as buoyancy frequency:

$${N}^{2}=g\frac{d\mathit{ln}\overline{\theta }}{dz}.$$

If N2 > 0, the atmosphere is stable; otherwise, an unstable atmosphere is prone to convective activity. One study analyzed the characteristics of the buoyancy frequency to judge the stability of the atmosphere (Wei et al. 2016). Therefore, in order to indicate the stability of the atmospheric junction, it can be analyzed based on the zonal profile of buoyancy frequency.

This paper shows the ERA5 reanalysis data of the buoyancy frequency latitudinal profile along 28°N in the height range of 550 − 1 hPa from 12:00 to 21:00 UTC on July 29, 2015. We define the dynamic troposphere top height as \(2 {\text{PVU}}\) (the white solid line) (Shi et al. 2018). According to the WMO (World Meteorological Organization) defined temperature decline rate \(\Gamma =2 {\text{K}}/{\text{km}}\), take the typical value \(\rho \approx 0.35 {\text{kg}}\bullet {{\text{m}}}^{-3},\theta \approx 320 {\text{K}},f\approx {10}^{-4}{{\text{s}}}^{-1},\) of the peak height \(PV=\frac{f}{g\rho }\theta {N}^{2}\approx 3.5 {\text{PVU}}\) (the yellow solid line) (Gettelman et al. 2011), where \(1 {\text{PVU}}={10}^{-6}{{\text{m}}}^{2}{{\text{s}}}^{-1}{{\text{Kkg}}}^{-1}\). As shown in Fig. 3, the top of the tropopause on the Qinghai-Tibetan Plateau is at a height of about 16 km, the magnitudes of the buoyancy frequencies are all positive, and the atmosphere remains stable during the propagation of gravity waves, which makes convective activity unlikely to occur. In general, the \({{\text{N}}}^{2}\) increases uniformly with increasing height. In particular, over the region of 80°E − 100°E (the Qinghai-Tibetan Plateau), low values of buoyancy frequency occur within 350 − 150 hPa and high values within 20 − 3 hPa. The region of buoyancy frequency anomalies is associated with perturbation and fragmentation during the uploading of the gravity waves (Chang et al. 2020; Wei et al. 2016). This suggests that gravity waves were not caused by deep convection, but rather excited by large topography of the Qinghai-Tibetan Plateau.

Fig. 3
figure 3

The latitudinal profile of buoyancy frequency (unit: \({10}^{-3}{{\text{s}}}^{-2}\)) along 28°N in the area of the gravity waves occurrence from 12:00 to 21:00 UTC on July 29, 2015, calculated by ERA5 reanalysis data. The white line represents the dynamic convection layer top (\(2 {\text{PVU}}\)) and the yellow solid line represents the thermal convection layer top (\(3.5\mathrm{ PVU}\))

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In order to gain a more complete understanding of the gravity wave activity, this study presents the zonal profile of vertical velocity. Using ERA5 reanalysis data, Fig. 4 exhibits the latitudinal profile of vertical velocity along 28°N, within the height range of 550 − 50 hPa. At 15:00 UTC on July 29, the vertical velocity showed an alternating distribution of positive and negative values in the area of 80°E − 100°E and 450 − 50 hPa (black box), where the gravity wave signals originated. On July 29, the fluctuation signals increased from 15:00 to 18:00 UTC, and at 18:00 UTC, the signals were clear at 450 − 50 hPa. During the period between 18:00 and 21:00 UTC on July 29, the gravity wave signals were evident at 250 − 50 hPa. It can be seen that under the effect of topography of the Qinghai-Tibetan Plateau, gravity waves are uploaded from the surface (450 hPa) and tilt to the east with the increase of height. Figure 5b–d estimates that the horizontal wavelength of gravity wave is about 480 km. Bian et al. (2005) used the dispersion relation

$$\left({\widehat{\omega }}^{2}-{f}^{2}\right){m}^{2}={N}^{2}{k}_{h}^{2}$$

to derive the horizontal wave number \({k}_{h}\), where the vertical wave number \(m\) and buoyancy frequency \({N}^{2}\) are known. The intrinsic frequency \(\widehat{\omega }\) can be obtained from formula

Fig. 4
figure 4

The latitudinal profile of the vertical velocity (unit: cm·s−1) along 28°N from 12:00 to 21:00 UTC on July 29, 2015 obtained by ERA5 data. The white line represents the dynamic convection layer top (\(2 {\text{PVU}}\)) and the yellow solid line represents the thermal convection layer top (\(3.5 {\text{PVU}}\)). Black box: 80°E − 100°E, 450 − 50 hPa

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Fig. 5
figure 5

The profile of the vertical velocity (unit: cm·s−1) and latitudinal wind (black dotted lines, unit: m·s−1) along 28°N from 15:00 UTC on July 29 to 03:00 UTC on July 30, 2015 obtained by ERA5 reanalysis data. The white line represents the dynamic convection layer top (\(2 {\text{PVU}}\)) and the yellow solid line represents the thermal convection layer top (\(3.5 {\text{PVU}}\)). Black box: 80°E − 100°E, 20 − 3 hPa

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$$\frac{\widehat{\omega }}{\left|f\right|}=\sqrt{\frac{{\lambda }_{1}}{{\lambda }_{2}}} .$$

The connecting line of the endpoints of the horizontal wind speed vector \(\left.\left(u\left(z\right),v\left(z\right)\right.\right)\) generated by the gravity wave is an ellipse, which is obtained by fitting the wavelengths

$${\lambda }_{\mathrm{1,2}}=\frac{\left[\overline{{u }^{{\prime}2}}+\overline{{v }^{{\prime}2}}\pm \sqrt{{\left(\overline{{u }^{{\prime}2}}-\overline{{v }^{{\prime}2}}\right)}^{2}+4{\overline{{{u }{\prime}v}{\prime}}}^{2}}\right]}{2},$$

where the wave signals were selected to be highly averaged over the 400–50 hPa range in which the wave signals were evident. Based on \({\lambda }_{h}=\frac{2\pi }{{k}_{h}}\) and \({\lambda }_{z}=\frac{2\pi U}{{k}_{h}}\), the horizontal wavelengths \({\lambda }_{h}\) and vertical wavelengths \({\lambda }_{z}\) can be calculated, where U is the latitudinal wind speed. The above coefficients allow the computation of the group velocity

$${(c}_{gh},{c}_{gz})=(\frac{\partial \omega }{\partial {k}_{h}},\frac{\partial \omega }{\partial m})=(\overline{{u }_{h}},0)+\frac{\left({k}_{h}{N}^{2},-m\left({\widehat{\omega }}^{2}-{f}^{2}\right)\right)}{\widehat{\widehat{\omega }{m}^{2}}}.$$

The calculation results in a horizontal wavelength of about 590 km, a vertical wavelength of about 4 km, a horizontal group velocity of about 6 m/s, and a vertical group velocity of about 0.5 m/s. From the above, it can be concluded that the horizontal wavelengths estimated by the ERA5 reanalysis data and the theoretical horizontal wavelengths are similar to the results. The propagation area of these gravity waves corresponds to the large terrain of the Qinghai-Tibetan plateau, and the horizontal wavelengths are parallel to the horizontal scale of the terrain. According to the gravity wave-related parameters, combined with Fig. 2, it can be judged that gravity waves are triggered by the topography of the Qinghai-Tibetan Plateau. Further analyses are necessary to determine whether the gravity wave can continue to propagate upwards into the higher atmosphere.

For a more accurate description of the dynamic process of gravity wave propagation, vertical velocity and latitudinal wind profiles in the stratosphere are given. Figure 5 shows the profile of vertical velocity and latitudinal wind along 28°N obtained from ERA5 data for a height range of 250 − 1 hPa. From 18:00 to 21:00 UTC on July 29, an enhanced gravity wave signal was observed in the region of 80°E − 100°E and 250 − 10 hPa, with the wave train tilted to the east with time. At 21:00 UTC on July 29, the gravity waves were uploaded to the vicinity of the atmosphere at 3 hPa (about 40 km), and there were clear positive–negative alternating signals in the 20 − 3 hPa region (black box). The signals then weakened until 03:00 UTC on July 30. Combining Figs. 1 and 4, we infer that the gravity waves propagated from the surface of Qinghai-Tibetan Plateau (450 hPa) to the upper stratosphere (3 hPa) between 15:00 and 21:00 UTC on July 29. At 03:00 UTC on July 30, there was a strong easterly jet near the 3 hPa atmosphere (about 40 km), with maximum wind speed of − 30 m/s. When the gravity waves propagated in the shear wind field, they were subjected to the dissipative effect of the critical layer, which resulted in a large loss of energy and thus caused the gravity waves to break up (Bretherton 1966).

3.2 Impact of a gravity wave process on the upper stratospheric ozone valley

To demonstrate the effect of gravity waves on ozone valley in the upper stratosphere, Fig. 6 displays the latitudinal distribution of ozone mixing ratio along 28°N within the height range of 50 − 1 hPa using ERA5 reanalysis data. In Fig. 8, it can be seen that between 03:00 and 06:00 UTC on July 30, the ozone mixing ratio was reduced from about 8.0 ppmv to 7.9 ppmv in the area of 80°E − 100°E and 20 − 3 hPa (black box). Over the Qinghai-Tibetan Plateau, ozone is primarily affected by kinetic and chemical effects. On this occasion, the ozone concentration was reduced for only three hours, so the chemical effect on ozone was minimal. In addition, the atmospheric knots were relatively stable and there was no deep convective activity. Therefore, it can be inferred that the decrease of upper stratospheric ozone is connected to the dynamical process of gravity waves.

Fig. 6
figure 6

The latitudinal distribution of ozone mixing ratio (unit: ppmv) along 28°N between 15:00 UTC on July 29 and 06:00 UTC on July 30, 2015 obtained by ERA5 data. Black box (80°E − 100°E, 20 − 3 hPa) represents the region of variation in ozone mixing ratio

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Atmospheric gravity waves are oscillatory motions on small to medium scales. Influenced by factors such as rapids, the breakup of gravity waves leads to turbulent mixing of matter and energy, which affects the matter exchange process (Alexander et al. 2020; Chen et al. 2014). Thus, the propagation, fragmentation, and dissipation of gravity waves cause changes in the potential vorticity, and it has been investigated to describe the turbulent mixing process by determining the vertical flux of the potential vorticity (Chang et al. 2020; Wei et al. 2016). The vertical flux of mean potential vorticity \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) is calculated to determine the energy change due to gravity wave fragmentation.

This paper gives the changes in the mean potential vorticity vertical flux \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) (the orange line) and the mean ozone mixing ratio (the blue line) calculated from ERA5 data. The analysis focuses on the region between 80°E and 100°E, spanning altitudes from 20 to 3 hPa. Figure 7 shows that from 02:00 to 03:00 UTC on July 30, the observed changes in \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) and ozone mixing ratio are small due to the weakening of the gravity waves. However, at 03:00 UTC, \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) reached a critical point. By 05:00 UTC, there was a rapid increase from about -0.032 \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\) to 0 \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\). The mean ozone mixing ratio reached an extreme value at 03:00 UTC on July 30. Subsequently, a relatively small change in the mean ozone mixing ratio occurred between 03:00 and 04:00 UTC, with a drop of about 0.01 ppmv. The average ozone mixing ratio decreased sharply between 04:00 and 05:00 UTC, from about 7.924 ppmv to 7.910 ppmv. It can be tentatively concluded that the gravity waves broke up at 03:00 UTC on July 30, releasing the potential and leading to the drastic change of the average ozone mixing ratio in the 20 − 3 hPa region (upper stratosphere). After the breakup, the ozone concentration started to decrease at 03:00 UTC and dropped sharply after 04:00 UTC, with the mean ozone mixing ratio decreasing by about 0.024 ppmv from 03:00 to 05:00 UTC.

Fig. 7
figure 7

The change of mean potential vorticity vertical flux \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) (the orange line, unit: \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\)) and the mean ozone mixing ratio (the blue line, unit: ppmv) obtained from ERA5 data in 80°E − 100°E and 20 − 3 hPa region from 02:00 to 05:00 UTC on July 30, 2015

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3.3 The results of WRF simulations

The ERA5 dataset has an hourly temporal resolution and a spatial resolution of 0.25° × 0.25°. It reanalyzed data has a high spatiotemporal resolution, but it can be filtered for meso-small-scale gravity waves. The exclusion of tiny structural features of gravity waves leads to an incomplete explanation of the dynamic process of gravity waves. For a more detailed description of this process, this paper simulates the gravity wave event using the WRF model with higher spatial and temporal resolution to reveal the role of atmospheric gravity waves on ozone in the upper stratosphere.

The WRF model was used to simulate the horizontal distribution of vertical velocities at 40 km over the Qinghai-Tibetan Plateau during 15:00 UTC July 29 to 06:00 UTC on July 30, 2015 (Fig. 8). Alternating positive and negative vertical velocities are observed in the 80 − 100°E and 20 − 45°N regions (black box) between 21:00 UTC on July 29 and 03:00 UTC on July 30 and the gravity waves show an arc-shaped structure. The WRF simulation results are compared with the results of the ERA5 data (Fig. 1) in terms of the presence of gravity waves in the region, time of intensity display and the structural features are basically the same.

Fig. 8
figure 8

The horizontal distribution of vertical velocity (unit: cm·s−1) at 40-km altitude simulated by the WRF model from 15:00 UTC on July 29 to 06:00 UTC on July 30, 2015. Black box: 80°E − 100°E, 20°N − 45°N

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In comparison to the ERA5 reanalysis data zonal profile of vertical velocity (Fig. 4), this research also employed the WRF model to replicate the latitudinal profile of vertical velocity along 28°N, in the range of height 550 to 50 hPa (Fig. 9). The outcomes reveal that the WRF model's simulation of the gravity wave propagation process is more prominent. Figure 9 shows that the alternating vertical velocity signals from 15:00 to 18:00 UTC on July 29 are obvious in the region of 80°E − 100°E and 450 − 50 hPa (black box), and the gravity wave signals are obvious in the region of 250 − 50 hPa between 18:00 and 21:00 UTC on July 29, and the vertical structure is gradually tilted to the east. The WRF simulation results are roughly the same as the ERA5 data results, and the WRF results can show uploading process of the gravity waves and the characteristic structure more clearly. Therefore, the WRF model is a more effective simulation method, which can describe the dynamic propagation of gravity waves more accurately and in detail.

Fig. 9
figure 9

The latitudinal profile of vertical velocity (unit: cm·s−1) along 28°N from 12:00 to 21:00 UTC on July 29, 2015 simulated by the WRF model. The white line represents the dynamic convection layer top (\(2 {\text{PVU}}\)) and the yellow solid line represents the thermal convection layer top (\(3.5 {\text{PVU}}\)). Black box: 80°E − 100°E, 450 − 50 hPa

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To further confirm whether the gravity waves propagate to higher levels, this paper also gives the latitudinal profile of the vertical velocity along the 28°N in the height range of 250 − 2 hPa (Fig. 10). At 21:00 UTC on July 29, there were clear wave signals in the area of 80°E − 100°E and 20 − 3 hPa (black box), which indicated that the gravity waves propagated from the surface of Qinghai-Tibetan Plateau (450 hPa) to the upper stratosphere (20 − 3 hPa). The vertical structure of gravity waves tilted to the east with time can be clearly seen in the figure. The simulation results obtained by the WRF model are consistent with those shown in Fig. 5, and the WRF simulation results can more clearly show the characteristics of the vertical direction of gravity waves.

Fig. 10
figure 10

The latitudinal profile of vertical velocity (unit: cm·s−1) along 28°N from 18:00 UTC on July 29 to 03:00 UTC on July 30, 2015 simulated by the WRF model. The white line represents the dynamic convection layer top (\(2 {\text{PVU}}\)) and the yellow solid line represents the thermal convection layer top (\(3.5 {\text{PVU}}\)). Black box: 80°E − 100°E, 20 − 3 hPa

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In order to validate the results obtained from the ERA5 data on the effect of gravity waves on upper stratospheric ozone, WRF model simulated the mean potential vorticity vertical flux in the region of 80°E − 100°E and 20 − 3 hPa for the period of 02:00 to 05:00 UTC on July 30, 2015 in conjunction with mean ozone mixing ratio obtained from ERA5 data (Fig. 11). The figure shows an increase in the mean potential vorticity vertical flux \(\overline{P{V }{\prime}{\omega }{\prime}}\) from approximately − 0.015 \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\) to − 0.005 \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\) from 02:30 to 03:00 UTC on July 30. \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) increased rapidly from about − 0.028 \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\) to − 0.018 \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\) between 04:00 and 05:00 UTC. The drop in ozone concentration in the 20–3 hPa region (upper stratosphere) during the period of 03:00 to 04:00 UTC on July 30 was not significant, from about 7.933 to 7.923 ppmv. However, the average ozone mixing ratio decreased rapidly after 04:00 UTC. That is, between 04:00 and 05:00 UTC, the mean ozone mixing ratio decreased by about 0.014 ppmv. Overall, the ozone mixing ratio decreased by a total of 0.024 ppmv during the process of gravity wave fragmentation. The high resolution of the WRF can bring out the detailed features of the atmospheric gravity waves. Combined with the analyses in Figs. 1 and 8, it can be seen that the partial fragmentation of gravity waves occurred at 02:30 UTC, which led to the beginning of the drop of ozone concentration at 03:00 UTC, but the gravity wave signals were still present. At 04:00 UTC, the gravity waves were completely fragmented, leading to a sharp drop of the ozone mixing ratio, which indicated that a significant ozone responded to the gravity wave breakup. It also further proves that WRF model simulates medium and small scale gravity waves in a detailed and efficient way.

Fig. 11
figure 11

The change of mean potential vorticity vertical flux \(\overline{P{V }^{\prime}{\omega }^{\prime}}\) (the orange line, unit: \({\text{PVU}}\bullet {\text{m}}\bullet {{\text{s}}}^{-1}\)) simulated by the WRF model and the mean ozone mixing ratio (the blue line, unit: ppmv) obtained from ERA5 data in 80°E − 100°E and 20 − 3 hPa region from 02:00 to 05:00 UTC on July 30, 2015

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4 Conclusions

The study analyzed the atmospheric gravity wave process on the Qinghai-Tibetan Plateau, specifically between 15:00 UTC on July 29 and 06:00 UTC on July 30, 2015. It also examined the effect of this event on the ozone valley in the upper stratosphere. The data are derived from the Global Climate Five Generation Atmospheric Reanalysis dataset ERA5 and the WRF model simulation. The key results are outlined below:

  1. 1.

    The atmospheric gravity wave process took place within the region of 80 − 100°E and 20 − 45°N. The gravity wave signals propagated from the surface of the Qinghai-Tibetan Plateau (450 hPa) to the upper stratosphere (20 − 3 hPa) between 15:00 and 21:00 UTC on July 29. In the upper stratosphere, the gravity wave signal gradually weakened after 21:00 UTC on July 29 and disappeared after 03:00 UTC on July 30. The gravity waves have an arc-shaped structure and are vertically inclined to the east with increasing altitude.

  2. 2.

    The upper stratospheric ozone valley on the Qinghai-Tibetan Plateau responded significantly to the atmospheric gravity waves, with gravity wave signals generated in the upper stratosphere (40-km altitude) at 21:00 UTC on July 29. The gravity waves partially broken up near 3 hPa at 02:30 UTC on July 30 due to an easterly surge, but the gravity wave signals were still present, and the ozone concentration began to decrease 30 min later (03:00 UTC). At 04:00 UTC, the gravity waves completely broke up and the ozone concentrations changed significantly in the 80 − 100°E and 20 − 3 hPa regions. From 04:00 to 05:00 UTC, the mean ozone mixing ratio dramatically decreased by about 0.014 ppmv, indicating that the upper stratospheric ozone valley responded well to the atmospheric gravity waves.

  3. 3.

    By comparing ERA5 data, WRF model accurately simulates the time, region, structure, and propagation characteristics of gravity waves, which indicates its reliability in gravity wave research. Additionally, owing to its high resolution capabilities, the WRF model accurately captures the detailed features of gravity waves, revealing that gravity waves breakup lead to a dramatic decrease in ozone mixing ratio.