A torrential rainstorm occurred in Xinjiang, China during June 16–17, 2016. Precipitation was mainly concentrated in Yili Valley and distributed along the Borohoro Mountains from the northwest to southeast (Fig. 1). Xinjiang, the largest province in China, has an extensive variety of landforms given its uneven topography. Xinjiang contains few meteorological observation stations; thus, there is apparent discontinuity in the precipitation zone shown in Fig. 1. Heavy rainfall (over 48 mm within 24 h) mainly occurred in Nilka County and Gongliu County, and to a lesser extent in Yining County, Turks County, Xinyuan County, and Huocheng County. The maximum rainfall was recorded in the boundary area between Yining County and Nilka County, with a 24 h accumulated rainfall of more than 96 mm, defining a torrential rainstorm based on the local operational standard set by Xinjiang Province. This rainstorm was characterized by high intensity, concentrated location, and spatial and temporal inhomogeneity, indicating that it was a typical mesoscale weather process.

Fig. 1.

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	Fig. 1. Observed 24 h accumulated precipitation (mm) from 12:00 UTC, June 16, 2016 to 12:00 UTC, June 17, 2016.

During the rainstorm, a South Asian high increasingly strengthened and moved westwards, with a high-pressure center stably maintained over the Tibetan Plateau (Figs. 2(a) and 2(d)). At the same time, a high-level trough and the South Asian high increased the speed of the upper-level jet stream, with Yili Valley to the left of the exit of the upper-level jet stream. The divergence to the left of the exit of the upper-level jet stream at 200 hPa promoted convergence on the surface at Yili Valley. The synoptic background at 500 hPa (Figs. 2(b) and 2(e)) exhibited the classic weather pattern of two troughs and one ridge; one trough was located to the west of Lake Balkhash and the other was over northeastern China, extending from the northeast China cold vortex to the Changjiang-Huaihe basin, with the ridge situated over Lake Baikal. The trough to the west of Lake Balkhash gradually developed into a cold vortex to the west of Xinjiang, such that Xinjiang was under the control of the southwesterly flow in front of the trough. Under these favorable weather conditions, a cyclonic circulation formed to the west of Yili Valley (Figs. 2(c) and 2(f)). The northwesterly flow around Lake Balkhash steered the cold air in Siberia southwards. When the cold air reached Central Asia, it turned right and entered Yili Valley along the North Tianshan basin, providing sufficient moisture to promote the development of the torrential storm in the Yili Valley area of Xinjiang Province.

Fig. 2.

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Fig. 2. Upper, middle and lower-level synoptic weather patterns at (a)–(c) 12:00 UTC, June 16, 2016 and (d)–(f) 06:00 UTC, June 17, 2016, respectively. (a), (d) Geopotential height (solid lines, dagpm) and wind speed ≥ 30 m/s (vectors, m/s) at 200 hPa; (b), (e) geopotential height (solid lines, dagpm), temperature (dashed lines, ○C), and wind speed (vectors, m/s) at 500 hPa; (c), (f) geopotential height (solid lines, dagpm), wind speed (barbed lines, knots), and wind speed ≥ 8 m/s (shaded areas, m/s) at 700 hPa; the rectangular area represents the domain of the simulation area.

The water vapor originated mainly from the Arctic Ocean (Fig. 3(a)). Northerly flows to the east of the arctic high transported the water vapor southwards to Western Siberia. The water vapor was driven by the northerly flow to the east of the Ural high pressure zone to move southwards into Kazakhstan, then turned right and entered Yili Valley along the North Tianshan basin where the water vapor converged at last with the maximum absolute value of water vapor flux divergence, which exceeded 5 × 10⁻⁷ g·cm⁻²·s⁻¹·hPa⁻¹. The convergent water vapor was forcedly uplifted by the steep terrain, and water vapor in the atmosphere further condensed into rainwater, finally leading to the occurrence of the torrential rainstorm. At 12:00 UTC, June 17 (Fig. 3(b)), the convergence of water vapor in Yili Valley significantly weakened, and the convergence center moved northeastwards to Altay Prefecture, then the heavy rains in Yili Valley gradually decreased.

Fig. 3.

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	Fig. 3. Water vapor flux (streamlines, g·cm−1·s−1·hPa−1) and water vapor flux divergence (shaded areas, 10−7g·cm−2·s−1·hPa−1) at (a) 18:00 UTC, June 16, 2016; and (b) 12:00 UTC, June 17, 2016.

We used the WRF model version 3.7.1 to simulate the torrential storm with a single domain with 539 × 384 grid points in the north-south and east-west directions, and a horizontal grid spacing of 3 km. The simulation was performed for the storm occurring over a period of 48 h, from 00:00 UTC, June 16, 2016 to 00:00 UTC, June 18, 2016. The initial and boundary conditions were derived from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) GFS reanalysis dataset, with a resolution of 0.25^○ × 0.25^○. The main parameterizations used in the model are as follows: a microphysics scheme with ice, snow and graupel processes suitable for high-resolution simulation (Thompson); a boundary scheme from the asymmetric convective model with a non-local upward mixing and local downward mixing closure scheme (ACM2); a two-layer scheme from the Pleim–Xiu land surface model with vegetation and sub-grid tiling (PX LSM); a longwave radiation scheme from the rapid radiative transfer model (RRTM). The model was set up to provide output every 10 min. The simulation area and topographic distribution are presented in Fig. 4 (red line indicates the cross-section referred to below).

Fig. 4.

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	Fig. 4. Terrain height (in units of m) in the numerical simulation domain. Red line indicates the cross-section studied in depth.

Rainfall was mainly concentrated along the southern foot of Borohoro Mountain during 12:00–18:00 UTC, June 16, 2016 (Fig. 5). Two rainfall centers, in Nilka County and Xinyuan County, experienced a maximum rainfall over 6 h of > 48 mm, the definition of a large rainstorm based on the Xinjiang Province local operational standard. There were two zonal precipitation belts distributed in Zhaosu County and the region between Changji and Urumqi. The model simulated the precipitation process well, with little deviation from the observations; for example, the simulated rainfall in Yining County was stronger than that observed, and the location of the simulated precipitation cell was to the northwest of the observed cell. The precipitation cell simulated in Nilka County was slightly weaker than that observed, and its location was to the north of the observed cell. Between 18:00 UTC, June 16 and 00:00 UTC, June 17, the rainfall along the Borohoro Mountains increased rapidly, and the precipitation cell was located in the western part of Nilka County, with a maximum rainfall of > 96 mm occurring over 6 h. The precipitation zone was characterized by a clear zonal distribution along the Borohoro Mountains, with precipitation on the windward slope; the model reproduced the characteristics of the precipitation along the south foot of Borohoro Mountain well, except that three strong precipitation centers were observed, whereas only two precipitation centers appeared in the simulation.

Fig. 5.

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	Fig. 5. The 6 h accumulated rainfall (mm) during (a), (b) 12:00–18:00 UTC, June 16, 2016 and (c), (d) between 18:00 UTC, June 16, 2016 and 00:00 UTC, June 17, 2016. (a), (c) simulation; (b), (d) observation.

There were differences in the precipitation intensity and location of precipitation cells between simulation and observation; however, overall, the precipitation areas and precipitation development trend were very similar. In other words, the model reproduced the precipitation process well, and the high-resolution model output was sufficiently accurate to analyze gravity wave characteristics during the torrential rainstorm.

We began by calculating the running average values of vertical velocity every 4 h, after which FFT was used to obtain the mean characteristics of the waves along the red line indicated in Fig. 4 between 12:00 UTC, June 16, 2016 and 12:00 UTC, June 17, 2016. A power spectrum analysis for different altitudes showed that wave signals were most prominent at an altitude of 19 km, with a clear single peak and narrow spectrum (Fig. 6). The wave numbers ranged from −0.024 km⁻¹ and −0.009 km⁻¹ (corresponding to horizontal wavelengths of 40–110 km) and the main wave frequencies varied from 0.0063 min⁻¹ to 0.02 min⁻¹ (corresponding to wave periods of 50–160 min) in the region of maximum wave energy density. These results indicate that the main wave signals were classic meso-β scale waves with horizontal wavelengths of 40–110 km and periods of 50–160 min. The wave phase velocities were concentrated in the range of −25 m/s to −10 m/s, where the negative sign indicates that the waves were propagated in the westward direction.

Fig. 6.

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	Fig. 6. Power spectrum density (m2·s−2) of the vertical velocity at an altitude of 19 km along the line shown in Fig. 4(a). Solid lines represent the wave phase velocities of −5 m/s, −10 m/s, and −25 m/s.

A phase difference of 90^○ between the vertical vorticity and horizontal divergence was selected as the criterion to identify IGWs based on the polarization of gravity waves.^[29] We calculated the phase spectrum and correlation spectrum of the vertical vorticity and the horizontal divergence using cross-spectral analysis to identify IGWs along the red line indicated in Fig. 4 during the rainstorm. For example, the phase spectrum and correlation spectrum of different wavenumbers calculated for 11:00 UTC, June 17, 2016 are presented in Fig. 7. The phase difference in the vertical vorticity and horizontal divergence with wavenumbers of 0.015–0.022 km⁻¹ and 0.033–0.036 km⁻¹ approached 90^○ (Fig. 7(a)). At the same time, the vertical vorticity and horizontal divergence had a high correlation coefficient, with values greater than 0.8 for waves with wave numbers of 0.016–0.020 km⁻¹ (Fig. 7(b)). Taken together, the waves with wavenumbers of 0.016–0.020 km⁻¹ (corresponding to horizontal wavelengths of 50–60 km) were identified as IGWs. IGWs with wavenumbers of 0.016–0.020 km⁻¹ were determined to be in the region of maximum wave energy density according to the power spectrum density analysis (Fig. 6), indicating that IGWs were the crucial waves in the torrential rainstorm.

Fig. 7.

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	Fig. 7. (a) Phase spectrum and (b) correlation spectrum between the horizontal divergence and vertical vorticity at an altitude of 19 km at 11:00 UTC, June 17, 2016 along the line shown in Fig. 4(a).

Based on the cross-spectral analysis, we were able to identify IGWs with detailed wavelengths and periods; however, the disadvantage of the cross-spectral analysis is that it could not be used to obtain the spatiotemporal characteristics of IGWs. Based on the phase spectrum, correlation spectrum, and amplitude spectrum of the vertical vorticity and horizontal divergence calculated using wavelet cross-spectral analysis, we obtained the spatiotemporal characteristics of IGWs along the red line indicated in Fig. 4. There was an extreme value in the 79.17–79.93^○E, 81.10–81.45^○E, and 81.50–82.00^○E regions (Fig. 8(a)). The phase differences in vertical vorticity and horizontal divergence at 79.17–79.93^○E and 80.69–82.21^○E both approached 90^○, particularly at 81.83–82.21^○E, where the phase difference was exactly equal to 90^○ (Fig. 8(b)). There were three regions where the correlation coefficients were close to 0.9: near 79.55^○E, near 80.5^○E, and along 81.4–82.21^○E, particularly along 81.83–82.21^○E, where the correlation coefficients were exactly equal to 0.98 (Fig. 8(c)). There were clear gravity wave signals along 79.17–79.83^○E, 81.35–81.45^○E, and 81.5–81.83^○E, particularly along 81.83–82.21^○E where the correlation coefficients were close to 0.98 and the phase differences were exactly equal to 90^○. Compared to the 1 h accumulated precipitation (Fig. 8(b)) along the cross-section line shown in Fig. 4, the region experiencing maximum rainfall corresponded well with the IGWs described above.

Fig. 8.

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	Fig. 8. (a) Wavelet amplitude spectrum, (b) phase spectrum, and (c) correlation spectrum between the horizontal divergence and vertical vorticity at an altitude of 19 km at 11:00 UTC, June 17, 2016 along the line shown in Fig. 4(a). Red line in panel (b) represents the 1-hour accumulated precipitation (mm).

To obtain the temporal characteristics of the IGWs in the rainstorm, we performed wavelet cross-spectral analysis of the vertical vorticity and horizontal divergence over time. Figure 9 shows the result of this analysis along 81.68^○E at an altitude of 19 km between 00:00 UTC, June 16, 2016 and 00:00 UTC, June 18, 2016, where the horizontal axis is time in 10-min intervals. Between 06:00 and 12:00 UTC, June 17, 2016, there was an extreme value in the amplitude spectrum (Fig. 9(a)); the phase difference in vertical vorticity and horizontal divergence approached 90^○ (Fig. 9(b)) and the correlation coefficient exceeded 0.9 (Fig. 9(c)). This gives a clear IGW signal during that period. A precipitation peak appeared at 10:00 UTC, when the phase difference in the vertical vorticity and horizontal divergence approached 90^○ (Fig. 9(b)), indicating that the precipitation peak and IGWs agreed well in time.

Fig. 9.

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	Fig. 9. (a) Wavelet amplitude spectrum, (b) phase spectrum, and (c) correlation spectrum between the horizontal divergence and vertical vorticity at an altitude of 19 km along 81.68○E. Red line in panel (b) represents the 1 h accumulated precipitation (mm).

According to our analysis of IGWs, we chose IGWs during the rainstorm with periods of 60–120 min, horizontal wavelengths of 50–60 km, and phase velocities of −10 m/s to –20 m/s for reconstruction by filtering the vertical velocity with the IFFT method. The westward propagation of gravity waves is clearly evident in Fig. 10(a). In three time periods (07:00–09:00 UTC, June 16; 13:00–14:00 UTC, June 16; and 09:00–14:00 UTC, June 17), the IGWs were clear, particularly during the period 09:00–14:00 UTC, June 17, when the IGW signal intensity along 80.4–82.21^○E was strongest, corresponding well to our previous analysis. Precipitation was mainly concentrated along 80.4–82.21^○E during 07:00–13:00 UTC, June 17 (Fig. 10(b)), with a precipitation peak at 11:00 UTC, June 17 near 81.4^○E, corresponding well to the strongest waves shown in Fig. 10(a) and further revealing the close correlation between IGWs and rainstorms.

Fig. 10.

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	Fig. 10. (a) Time–longitude cross-section of reconstructed vertical velocity (m·s−1) at an altitude of 19 km. Time on the Y-axis is formatted ‘ddhh’. (b) Time–longitude cross-section of the 1 h accumulated precipitation (mm).

Figure 11 shows the reconstruction of the vertical velocity along the time-latitude cross-section. As shown in Fig. 11, gravity waves were active at a height of 12–20 km. Gravity waves propagated strongly westward during 10:40–11:30 UTC, June 17. A clear gravity wave signal was present along 80.69–82.21^○E, which corresponded well to the precipitation signal shown in Fig. 10, again revealing correspondence between the gravity waves and the precipitation. While propagating westwards, gravity waves along 80.69–82.21^○E weakened gradually, with a limited intensity during 10:40–11:10 UTC, June 17; however, at 11:20 UTC, June 17, gravity waves suddenly became very weak, reflecting the transience of gravity wave characteristics. Gravity waves along 79.17–79.93^○E enhanced with time from 11:30–11:40 UTC, June 17. Apart from the change in intensity of the gravity waves, the clearest trend was their upward propagation (Fig. 11).

Fig. 11.

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	Fig. 11. Height–longitude cross-section of reconstructed vertical velocity (m·s−1) at an elevation of 19 km from 10:40 UTC, June 17, 2016 to 11:30 UTC, June 17, 2016 calculated every 10 min. Selected horizontal wavelengths for reconstruction are 50–60 km, and periods are 60–120 min.