
Radiosonde data from the Dunhuang national reference station (40.15°N, 94.68°E) were obtained twice daily [0700 and 1900 Beijing Time (BT)] from 24 July to 21 August 2020. The data were obtained under qualitycontrolled conditions and included meteorological parameters such as wind speed, temperature, pressure, and humidity from the ground to 30 km. The data were used to analyze the variation in the QZWL. The sounding station location is shown by the asterisk in Fig. 1.
Figure 1. Location of the Dunhuang national reference station, where the asterisk indicates the sounding station.
The ERA5 data produced by the ECMWF were used to analyze the mechanism of QZWL variation by virtue of the diagnostic equations for zonal velocity, horizontal kinetic energy, and vertical wind shear. ERA5 is the fifth generation of ECMWF global atmospheric reanalysis data. The horizontal resolution is 0.25° × 0.25° with hourly intervals. There are 37 levels from 1000 to 1 hPa in the vertical direction. ERA5 is the global reanalysis data with the highest spatiotemporal resolution published by the ECMWF thus far (Liu et al., 2021). Due to the improvement in temporal and spatial resolution, ERA5 provides a more accurate depiction of weather systems and wind fields than its predecessor, ERAInterim (ECMWF atmospheric reanalysis data; Hersbach et al., 2020), and has more advantages in QZWL research.
Diagnostic equations used in this study are shown below.
The zonal motion equation can be written as:
$$ \dfrac{{\partial u}}{{\partial t}} = A + fv + B , $$ (1) where
$A =  {\boldsymbol{v}} \cdot \nabla u$ represents the threedimensional advection transport of zonal wind, v = (u, v, ω) represents the threedimensional velocity vector,$B =  \dfrac{{\partial \phi }}{{\partial x}}$ is the zonal gradient of geopotential height,$ \phi $ is potential height, and$ f $ is Coriolis parameter.The horizontal kinetic energy equation can be written as:
$$ \dfrac{{\partial K}}{{\partial t}} = H_{\text{1}} + H_2 + H_3 , $$ (2) where
$ K = \dfrac{1}{2}\left( {{u^2} + {v^2}} \right) $ represents horizontal kinetic energy,$H_{\text{1}}=  u\dfrac{{\partial \phi }}{{\partial x}}$ and$H_2{\text{ = }}  v\dfrac{{\partial \phi }}{{\partial y}}$ represent zonal and meridional advection of geopotential height, respectively, and$H_3 =  {\boldsymbol{v}} \cdot \nabla K$ is threedimensional advection transport of kinetic energy.The vertical wind shear equation in the isobaric coordinate system can be written as:
$$ \dfrac{\partial }{{\partial t}}\left( {\dfrac{{\partial u}}{{\partial p}}} \right) = U + W + L + H , $$ (3) where
$U =  {{\boldsymbol{v}}_{\rm{h}}} \cdot \nabla \left( {\dfrac{{\partial u}}{{\partial p}}} \right)$ represents the horizontal advection transport by vertical shear of zonal wind, v_{h} = (u, v) represents the horizontal velocity vector,$ W =  \omega \dfrac{\partial }{{\partial p}}\left( {\dfrac{{\partial u}}{{\partial p}}} \right) $ represents the vertical transport,$ L = \left( {f  \dfrac{{\partial u}}{{\partial y}}} \right)\dfrac{{\partial v}}{{\partial p}} + \dfrac{{\partial v}}{{\partial y}}\dfrac{{\partial u}}{{\partial p}} $ represents the tilt term, and$ H =  \dfrac{\partial }{{\partial p}}\left( {\dfrac{{\partial \phi }}{{\partial x}}} \right) $ is the zonal vertical gradient of geopotential height. 
The spatiotemporal distribution of the stratospheric QZWL was analyzed. Figure 2a shows the vertical distribution of the total wind speed at the Dunhuang sounding station from 24 July 2020 to 21 August 2020. The area with a low wind speed (horizontal wind speed < 5 m s^{−1}) during this period was mainly located between 18.5 and 23 km (50–70 hPa). The average height of the total wind speed was 20.5 km, which was the broadly defined QZWL (Chen et al., 2018). The westerly prevailed between 5 and 20 km, and the easterly prevailed above 20 km. The QZWL was located in the transformation area of the easterly and westerly belts.
Figure 2. Temporal and vertical crosssection at the Dunhuang national reference station from 24 July to 21 August 2020. (a) Full wind speed (shading; m s^{−1}), (b) pressure disturbance (shading; hPa), (c) temperature disturbance (shading; °C), and (d) density disturbance (shading; 10^{−5} kg m^{−3}). The black dotted lines denote the heights of 18 and 25 km, respectively. The black solid lines denote the upper and lower boundaries of the QZWL (m s^{−1}).
The average upper boundary height of the QZWL was 20.96 km during this period. The QZWL was uplifted to 22.39 km from 9 to 21 August 2020 and increased by 1.43 km. In contrast, the lower boundary of the QZWL did not change much, and its height increased from 19.06 to 19.26 km and increased by 0.2 km.
The variation in the QZWL accompanied the environmental evolution between 18 and 25 km. To analyze the environmental characteristics, pressure (
$p$ ), temperature ($T$ ), and density ($\rho $ , calculated from pressure and temperature data) could be decomposed into the basicstate quantity and disturbance quantity, namely,$$ p = \overline p + {p'} ,\; T = \overline T + {T'} ,\; \rho = \overline \rho + {\rho'} , $$ (4) where “
$ \overline {\;\;} $ ” denotes the time average and “′” denotes the deviation from the time average. With the radiosonde data from 24 July to 21 August 2020, the disturbances in pressure, temperature, and density were calculated and are shown in Figs. 2b–d. These disturbances all presented an oscillation with an approximate twoweek period. Their intensities gradually decreased with increasing height.From 5 to 9 August, a positive anomaly of pressure existed in the whole QZWL (Fig. 2b), corresponding to a negative disturbance of temperature (Fig. 2c) and a positive disturbance of density (Fig. 2d). After 9 August, the three disturbances all reversed, indicating that with the uplift of the QZWL upper boundary, the environmental thermal disturbance changed from a cold high to a relatively warm low. The two largescale circulation systems, the South Asian high (SAH) and the subtropical westerly jet, are geographically close to Dunhuang in summer. They can affect the environmental field and then the nearby QZWL. Therefore, the effects of these two circulation systems on the QZWL have been analyzed in the following study.

As the most stable and powerful circulation system at 100 hPa during the boreal summer (Flohn, 1957; Yeh et al., 1957; Mason and Anderson, 1963; Ye and Zhang, 1974), the SAH has an important influence on the structure and evolution of the stratospheric QZWL (Chen, 2018). As shown in Fig. 3, from 24 July to 21 August, radiosonde data were collected during the year when the SAH was most powerful and northerly.
Figure 3. Crosssection of the intensity of the SAH at 100 hPa over Dunhuang from 24 July to 21 August 2020 (the shaded part represents geopotential height; dagpm). (a) Crosssection along 40.15°N (the black dotted line indicates the longitude of Dunhuang) and (b) crosssection along 94.68°E (the black dotted line indicates the latitude of Dunhuang).
From 1 to 5 August, the SAH intensified eastward, and Dunhuang was located in the northeastern part of the SAH center. The maximum intensity of SAH occurred from 5 to 9 August, with the maximum meridional amplitude, and Dunhuang was closest to the high center. After 9 August, the SAH retreated westward, away from Dunhuang, weakened in intensity, and the upper boundary of the stratospheric QZWL began to rise significantly.
In the processes mentioned above, the SAH presented obvious quasibiweekly oscillation characteristics. The date of the SAH strengthening eastward first and then weakening westward was consistent with the previous analysis results of the environmental field. In addition, the east–west oscillation of the SAH was about 4 days earlier than the height variation of the stratospheric QZWL on 9 August 2020 in this case; the time difference may be used as one of the indicators for predicting the stratospheric QZWL in future studies.

The intensity of the subtropical westerly jet and the height of the jet stream core also affected the stratospheric QZWL. As shown in Fig. 4, during the observation period, the subtropical westerly jet over Dunhuang was mainly located in the range of 5–20 km, and the maximum wind speed center (jet stream core) was located in the range of 10–15 km. On 9 August, the speed of the jet stream core increased to 56 m s^{−1}, and the uplift of the upper boundary of the stratospheric QZWL over Dunhuang was observed. After 12 August, the intensity of the westerly jet weakened, although the height of the upper boundary of the stratospheric QZWL decreased slightly and was still higher than that before 9 August. As the jet stream core increased, the vertical range of the zonal westerly wind increased, and the altitude of east–west wind conversion was lifted, thus pushing up the height of the stratospheric QZWL.
Figure 4. Wind speed profiles over Dunhuang from 24 July to 21 August 2020 (the gray shaded part is the area of the QZWL and the color shaded part is the minimum total wind speed; the blue solid line is the average height of the QZWL and the yellow solid line is the maximum wind speed of the westerly jet).
Since the wind speed of the stratospheric QZWL is minimal between the upper troposphere and the lower stratosphere and the wind speed of the upperlevel jet stream reaches a maximum in the upper troposphere, the vertical shear of horizontal wind (
$\dfrac{{\partial V}}{{\partial p}}$ , where$V$ is the horizontal wind speed and$p$ represents the vertical pressure coordinate) should be minimal in both places, so$\dfrac{{\partial V}}{{\partial p}}$ can represent the above two weather systems simultaneously. Figure 5 shows the vertical shear of horizontal wind changes over time; a positive value indicates that wind speed decreases with height, while a negative value indicates the opposite. A narrow black area occurs between 200 and 150 hPa, which represents the height of the maximum wind speed of the westerly jet over Dunhuang, and another narrow black area near 50 hPa represents the stratospheric QZWL.Figure 5. Time–height profile of vertical shear of the total wind speed (10^{−2} m s^{−2}) over Dunhuang from 24 July to 21 August 2020.
On 9 August, the westerly jet suddenly strengthened (Fig. 4), and the height of the jet stream core increased (Fig. 5), which lifted the zonal westerly to a greater height, thereby increasing the wind speed above it. As the altitude increased, gradually approaching the lower stratospheric easterly zone, the wind speed between 100 and 50 hPa decreased rapidly and then increased the height of the stratospheric QZWL.

To analyze the causes of the stratospheric QZWL height variation more intuitively and quantitatively, the zonal motion, horizontal kinetic energy, and vertical wind shear equations were used to diagnose the zonal wind, kinetic energy, and vertical wind shear, respectively. Detailed description of these equations can be found in Section 2, and diagnostic calculations used ERA5 data.
Comparing the total wind speed between the radiosonde data from Dunhuang station and the ERA5 data from 24 July to 21 August 2020 (Fig. 6), it can be seen that the distribution of the two figures is almost the same. For the westerly jet, the wind speed between 300 and 250 hPa decreased on 25 July firstly and then increased and weakened again on 6–7 August. Two highspeed centers occurred on 9–13 August. For the QZWL between 70 and 50 hPa, height elevation occurred on 9 August. Therefore, the description of the wind field from ERA5 data was consistent with the observational data and was suitable for QZWL analysis.
Figure 6. Full wind speed (m s^{−1}) above Dunhuang national reference station from 24 July to 21 August 2020 based on (a) radiosonde data and (b) ERA5 data.
ERA5 data were used to calculate each item in Eqs. (1) and (2) and to analyze the main physical factors responsible for local variations in zonal wind and kinetic energy to explain the causes of the stratospheric QZWL height variation.
Figure 7a shows that at 70 hPa over Dunhuang from 8 to 9 August, the zonal gradient of geopotential height [B in Eq. (1)] contributed the most to local changes in the zonal wind. For the local change in kinetic energy, the most important forcing terms were zonal and meridional advection of geopotential height [H_{1} and H_{2} in Eq. (2); Fig. 7b], so the geopotential height gradient was the most basic physical factor that caused the variation in kinetic energy in the stratospheric QZWL.
Figure 7. Evolution of the forcing terms of (a) the zonal motion equation (units of B and A are 10^{−3} m s^{−2} and 10^{−4} m s^{−2}, respectively) and (b) kinetic energy equation (units of H_{1}, H_{2}, and H_{3} are 10^{−2} m^{2} s^{−3}, 10^{−3} m^{2} s^{−3}, and 10^{−3} m^{2} s^{−3}, respectively) of 70 hPa over Dunhuang from 1400 BT 8 to 2000 BT 9 August 2020, based on ERA5 data.
Figure 8 shows the 70hPa geopotential height and its zonal and meridional gradient distributions over Dunhuang. From 8 to 9 August, the SAH gradually moved to the southwest, and Dunhuang is located in the northeast of the SAH (Figs. 8a, b). With the southward retreat of high pressure, the geopotential height in this area gradually decreased, and the contour lines became denser (Figs. 8c, d). The zonal gradient of geopotential height appears in an area with large values near Dunhuang (Figs. 8g, h), and was smaller in magnitude than the meridional gradient, showing a state of alternating positive and negative fluctuations.
Figure 8. Distributions of (a–d) geopotential height (dagpm), and (e–h) its zonal (10^{−4} dagpm m^{−1}) and (i–l) meridional gradient (10^{−4} dagpm m^{−1}) at 70 hPa over Dunhuang from 8 to 9 August 2020, based on the ERA5 data.
In general, the meridional gradient of geopotential height was stronger than the zonal gradient, presenting a relatively consistent positive value (Figs. 8i–l). The intensity of the zonal gradient was weaker, and its distribution was uneven, reflecting the zonal oscillation during the westward retreat of the SAH.
In conclusion, the movement of the SAH center, which first strengthens to the east and then weakens to the west, causes the zonal and meridional gradient adjustment of geopotential height and then leads to the evolution of zonal wind and kinetic energy to adapt to the changes in the geopotential height of the SAH. This result is consistent with previous analyses of the influence of the SAH on the stratospheric QZWL. This result also indicates that the wind field in the upper troposphere and lower stratosphere has the dynamic characteristics of adapting to the geopotential height field or the mass field.
As previous analyses have shown that vertical wind shear can adequately indicate the position of the stratospheric QZWL, the zonal wind vertical shear equation was used to further analyze the mechanism of the stratospheric QZWL height variation.
Figure 9 shows the changes in the total forcing of local vertical wind shear with time and height
$\left[\dfrac{\partial }{{\partial t}}\left( {\dfrac{{\partial u}}{{\partial p}}} \right)\right]$ , which was the sum of the H, U, L, and W terms on the righthand side of Eq. (3). On 9 August, 100–50 hPa was a region with high total forcing values with a quasibiweekly variation cycle, which was similar to the oscillation cycle of the SAH. The occurrence time of the highvalue region corresponded to the intensification of the westerly jet and the uplift of the stratospheric QZWL. Figure 10 shows the horizontal distribution of the H, U, L, and W terms on the righthand side of Eq. (3) at 70 hPa. A belt with high values was shown by the horizontal distribution of the H term, and Dunhuang was located in the southern part of the belt (Fig. 10a). The horizontal distribution of the U and L terms shows significant positive and negative fluctuations along the northwest to the southeast (Figs. 10b, c), and Dunhuang was near the extreme value center of the W term (Fig. 10d). Figure 11 shows the regional average of these four terms. The total forcing of the local vertical wind shear was mainly caused by the H term (zonal vertical gradient of geopotential height), while the contribution of the U, L, and W terms was relatively small.Figure 9. Time–height profile of
$\dfrac{\partial }{{\partial t}}\left( {\dfrac{{\partial u}}{{\partial p}}} \right)$ in Eq. (3) over Dunhuang from 24 July to 21 August 2020 (the black line is the strength of the SAH at 100 hPa, based on ERA5 data).Figure 10. Contribution of each compulsion item [(a) H (10^{−8} m Pa^{−1} s^{−2}), (b) U (10^{−9} m Pa^{−1} s^{−2}), (c) L (10^{−9} m Pa^{−1} s^{−2}), and (d) W (10^{−10} m Pa^{−1} s^{−2})] in Eq. (4) over Dunhuang at 70 hPa at 0200 BT 9 August 2020, based on ERA5 data.
Figure 11. Contribution and total income and expenditure of each forced term in Eq. (4) over Dunhuang at 70 hPa at 0200 BT 9 August 2020, based on ERA5 data; from left to right, the units are as follows: 10^{−8} m Pa^{−1} s^{−2}, 10^{−8} m Pa^{−1} s^{−2}, 10^{−9} m Pa^{−1} s^{−2}, 10^{−9} m Pa^{−1} s^{−2}, and 10^{−10} m Pa^{−1} s^{−2}.
According to the hydrostatic equilibrium (Zhang, 2006), the H term can be written as
$\dfrac{R}{{p{{\left(\dfrac{{{p_{\rm{s}}}}}{p}\right)}^{\frac{R}{{{c_p}}}}}}}\left( {\dfrac{{\partial \theta }}{{\partial x}}} \right)$ , where R is the gas constant for dry air, c_{p} is the specific heat at constant pressure, p_{s} = 1000 hPa, p is environmental pressure as in Eq. (4), and$ {\dfrac{{\partial \theta }}{{\partial x}}} $ is the zonal gradient of potential temperature. Figure 12 shows the horizontal distribution of the potential temperature and its zonal gradient at 70 hPa. The potential temperature over Dunhuang was high in the north and low in the south, and zonal fluctuation existed in the equal potential temperature curve (Figs. 12a–d). The zonal gradient of potential temperature over Dunhuang was positive at 2000 BT 8 August (Fig. 12e). After reaching a maximum at 0200 BT 9 August, the gradient began to weaken and gradually became negative (Figs. 12g, h). This trend indicates that, from the thermal perspective, zonal and vertical gradient changes in the geopotential height on 9 August followed the potential temperature evolution. Under the control of the SAH, a cold highpressure disturbed area occurred over Dunhuang at 70 hPa. With the westward retreat of the SAH, the cold high disturbance turned into a relatively warm and low disturbed area, which was also consistent with previous analyses.Figure 12. (a–d) Potential temperature (K) and (e–h) its zonal gradient distribution (K m^{−1}) of 70 hPa over Dunhuang from 8 to 9 August 2020, based on ERA5 data.
The evolution of the stratospheric QZWL height over Dunhuang can be summarized as follows: during 5–8 August 2020, the SAH continued to strengthen as it moved toward the northeast. The upper troposphere over Dunhuang was controlled by a cold high disturbance. After 9 August, the SAH retreated westward and weakened, and the upper troposphere over Dunhuang turned into a relatively warm and low disturbance. The zonal gradient of geopotential height was the main reason for the change in the wind speed at 70 hPa. At the same time, the westerly jet strengthened, the height of the jet axis lifted, and the horizontal gradient of the thermal potential temperature increased, eventually increasing the upper boundary height of the stratospheric QZWL.
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Yuan, Y., Y. Liu, L. K. Ran, et al., 2022: Height variation in the summer quasizero wind layer over Dunhuang, Northwest China: A diagnostic study. J. Meteor. Res., 36(4), 618–630, doi: 10.1007/s1335102212072 
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