Circulations and Thermodynamic Characteristics of Different Patterns of Rainstorm Processes in the Eastern Foot of Helan Mountain

Rainstorms are the results of the interactions between the high -, mid -, and low-latitude circulations and multi-scale synoptic systems (Ray^[1]; Ding^[2-3]; Wang et al.^[4]). To a large extent, the configuration of synoptic systems determines the location, distribution, and intensity of rainstorms (Houze^[5]; Mukhopadhyay et al.^[6]; Shepherd et al.^[7]; Tao^[8]) pointed out that the western Pacific subtropical high (WPSH) shows the closest relationship with rainstorms in China. According to the distribution characteristics of westerly circulation as well as the intensity and location of WPSH, the circulations of rainstorms in China are classified into the meridional, latitudinal, and transitional patterns. Moreover, combined with the influencing synoptic systems, the rainstorms can be further classified into 12 patterns, including the patterns of deep trough, two convergence lines located in the south and north, etc. In previous studies, large-scale circulation patterns of rainstorms in different regions of China are classified mainly by the WPSH as well. Some scholars proposed that the persistent extreme precipitation in eastern China can be classified into the double-blocking high pattern and the single-blocking high pattern (Tu et al.^[9]; Chen and Zhai^[10]). For rainstorms in Northwest China, the circulation situations are summarized as two patterns of southwesterly airflow on the northwest side of the subtropical high and the southerly airflow on the west side of the subtropical high (Bai and Xu^[11]), and further refinement and supplement have also been made (Wang et al.^[12]; Huang et al.^[13]; Li et al.^[14]). These studies have shown that the circulation situations of rainstorms in the east of Northwest China are mainly featured by high in the east and low in the west in terms of geopotential height. For rainstorms in Yunnan Province, the influencing synoptic systems are summarized as five patterns, including the periphery of tropical high pattern, the two-high convergence pattern, shear line pattern, tropical depression pattern and the Bay of Bengal trough pattern (Ma et al.^[15]). While the circulations causing sustained rainstorm during the annually first rainy season in South China are classified into four patterns, i. e., East Asian trough bottom pattern, two ridges and one trough pattern, multi-vortex pattern, and zonal pattern (Xu et al.^[16]).

The above classifications of circulation patterns based on subjective experience have played an important guiding role in rainstorm forecasts. However, the defects are also obvious-over reliance on subjective judgments and the inconsistency of classification results caused by different statistical samples and classification standards. At the same time, with the rapid development of meteorological modernization, as the meteorological data available for research are getting richer, objective circulation pattern classification technologies based on data mining have proved a more and more significant application value in actual weather operations. For example, by using the hierarchical clustering method based on the anomaly correlation coefficient and synoptic verification, the circulation situations for persisting extreme rainfall events in North China are classified into four patterns, namely meridional pattern, latitudinal pattern, weakened landing tropical cyclone pattern and early summer pattern (Zhou et al.^[17]). Furthermore, the impacts of frontal structures, atmospheric stratification state, the low-level jet related warm and humid airflow transport channels, and intensities under different synoptic systems on the spatial distributions of rainstorms are also investigated. The k-means clustering algorithm is applied to the number of rainstorm days in Hunan, and furthermore, the location and spatial distribution of typical rainstorms and associating synoptic systems are comparatively analyzed (Dai et al.^[18]; Chen et al.^[19]). By using the algorithm of simulated annealing and diversified randomization (SANDRA) in a software named cost733class, the circulation situations of hourly heavy rainfall in Beijing are classified based on the anomalous geopotential height fields (Li et al.^[20]). Based on the sea level pressure or 500-hPa geopotential height fields, some scholars applied the principle component analysis and clustering methods to objectively classify the circulation patterns of rainstorms over Mediterranean and Valencia of Spain, southern parts of Portugal and France, Iran and other areas (Romero et al.^[21]; Penarrocha et al.^[22]; Fragoso and Gomes^[23]; Nuissier et al.^[24]; Raziei et al.^[25]). In addition, the circulation configuration and key influencing factors for each pattern of rainstorm are also explored in-depth. The results show that the rainstorm distribution is directly related to the interaction of the warm and humid easterly at low level with the local topography.

The eastern foot of Helan Mountain (37.8°N-39.4° N, 105.7° E-107° E) is located in northern Ningxia Province, which is part of the arid area in the east of Northwest China, and it is also a region with complex terrains. The Helan Mountain features a northeast-southwest orientation (with the altitudes between 1500 and 3600 m). Hundreds of mountain flood ditches (with the altitudes between 1140 m and 1500 m) perpendicular to the mountain on the east slope and the Yinchuan Plain (with the altitudes between 1000 m and 1140 m) are distributed from west to east, with the largest altitude difference exceeding 2500 m. Although the average annual precipitation in the region is less than 200 mm, local rainstorms and even downpours characterized by short-time heavy rain occurred many times in this region (Cen et al.^[26]). Under the comprehensive impacts of the topography, underlying surface and climate background, the rainstorm amount in Ningxia generally presents a distribution of more in the south and less in the north. Therefore, previous classifications of circulation patterns based on subjective experience mainly revealed the characteristics of rainstorms in central and southern Ningxia (Feng et al.^[27]; Shao et al.^[28]). However, for extreme rainstorms in Ningxia in the recent decade, especially the only two torrential rain in this region, all these events occurred in the eastern foot of the Helan Mountain in northern Ningxia. Besides, the research in recent years are mostly based on the rainstorm in a single day or individual extreme event (Wang et al.^[29]; Chen et al.^[30-31]; Yang et al.^[32]). At present, the systematic research on the objective circulation classification of rainstorm processes in the eastern foot of Helan Mountain is few, and meanwhile the circulation configuration and thermodynamic characteristics of the rainstorm processes in this region are not clearly understood. Especially, the common characteristics of rainstorm events in this region under different circulation patterns have not been thoroughly studied.

For this reason, based on the reanalysis data with a high spatio-temporal resolution, this study uses the objective clustering algorithm and composite analysis method to compare the circulation characteristics and key thermal-dynamic impact factors of different categories of rainstorm. Then, we try to summarize the common features and differences of the rainstorm processes in the eastern foot of Helan Mountain under different circulation backgrounds. We hope this study could improve the understanding of weather forecasters on the formation mechanisms of rainstorms in this region, so as to improve the disaster prevention and mitigation ability against mountain torrents in arid areas and promote the development of the economic belt along the Yellow River.

The data used in this study include hourly precipitation, temperature, pressure, relative humidity, wind, lightning and other meteorological observations from 512 automatic weather stations in the eastern foot of Helan Mountain and the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis 5 (ERA5) products from 2006 to 2020. The ERA5 reanalysis data has a horizontal resolution of 0.25° × 0.25° and 17 layers in vertical direction, which are 1000 hPa, 950 hPa, 900 hPa, 875 hPa, 850 hPa, 825 hPa, 800 hPa, 775 hPa, 750 hPa, 700 hPa, 600 hPa, 500 hPa, 500 hPa, 300 hPa, 200 hPa, 100 hPa and 50 hPa. While the specifications for the rest data, the terrain of the study area, the distribution of the observation stations and the rules to select rainstorms can refer to Chen et al.^[26].The anomalies are the deviations to the average value during June, July and August from 2006 to 2020, and moreover, the standard Beijing time is also used in this study.

The definition of rainstorms in this study is given below.

Rainstorm process definition: The total precipitation amount during a rainfall process is defined as R_p. When R_p ≥ 50 mm, it is defined as rainstorm; when 50 ≤ R_p < 100 mm, it is defined as general rainstorm (GR); when 100 ≤ R_p < 200 mm, it is defined as heavy rainstorm (HR); when R_p ≥ 200 mm, it is identified as extraordinary rainstorm (ER).

When hourly precipitation (R_1h) ≥20 mm, it is defined as short-time rainstorm. Among them, when 20 ≤ R_1h < 40 mm, it is defined as general short-time rainstorm (GSR), and similarly, heavy short-time rainstorm (HSR) with 40 ≤ R_1h < 60 mm and extraordinary short-time rainstorm (ESR) with R_1h ≥ 60 mm.

Following the abovementioned definitions and combined with the statistical results from Chen et al.^[26], we have selected 22 rainstorms in the eastern foot of Helan Mountain during 2006-2020 (Table. 1).

The classification of large-scale circulation background patterns in synoptic dynamics is the precondition for composite analysis (Johns and Robert^[33]; Huth^[34]; Guerra et al.^[35]; Wang et al.^[36]). However, in composite analysis for rainstorms caused by atmospheric circulations with obvious differences, the characteristics of synoptic circulations and dynamic structures that are of synoptic indicating significance are easily concealed. By contrast, the common characteristics of rainstorms can be better revealed by composite analysis for rainstorms with similar circulation patterns (Wu et al.^[37]; Zhao et al.^[38]; Li et al.^[39]; Wang and Xiao^[40]). The objective classification is conducted based on similar circulation characteristics, and different circulation patterns have significantly different synoptic meanings (Lamb^[41]; Jenkinson and Collison et al.^[42]; Chen^[43]; Fragoso et al.^[23]; Zhou et al.^[44]). k-means clustering is a classic algorithm used to solve the clustering problems (Macqueen^[45]). When the dataset has a dense structure and the characteristics of objects in different clusters are obvious, the clustering result is good. Especially when dealing with huge amounts of data, this algorithm can provide high levels of scalability and work with large volumes of data efficiently. However, the k-means clustering solution needs to specify the number of clusters k in advance and the initial cluster center is randomly set, so the clustering result is unstable and easy to get stuck at locally optimal value, and the algorithm has a poor adaptability (Krishna and Murty^[46]; Hamerly and Elkan^[47]; Likas et al.^[48]; Pham et al.^[49]; Jain^[50]; Shi et al.^[51]). In comparison, hierarchical clustering is more objective. The biggest merit of hierarchical clustering method is that we do not need to determine the number of clusters in advance. By calculating the inertia weight, the most appropriate number of clusters (k value) can be obtained according to the elbow method. The biggest demerit of hierarchical clustering method is the irreversibility. Once the clustering result is obtained, it is impossible to re-cluster the samples. Its another demerit is the imprecision of clustering termination conditions. The main procedure of the hierarchical clustering algorithm is as follows. At the beginning, each object is considered as a cluster, and then the clusters close to each other are merged as one cluster. After each mergence, the number of clusters will decrease by one. The merging of samples will not stop until all of them are finally grouped into one cluster or meet some requirements. For instance, the number of clusters reaches the predetermined value, or the distance between the closest clusters reaches the predetermined threshold. Specific procedures of this algorithm can be referred in Murtagh^[52-53], Rani and Rohil^[54] and Nazari et al.^[55].

The rainstorm processes in the eastern foot of Helan Mountain are mainly convective precipitation (Chen et al.^[26]). According to the three basic conditions of water vapor, instability and uplift (Moller^[56]; Wilhelmson et al.^[57]; Yamane et al.^[58]), 500-hPa geopotential height (H₅₀₀), 700-hPa zonal (U₇₀₀), meridional winds (V₇₀₀), 850-hPa temperature, and humidity (pseudo equivalent potential temperature; θ_se850) are used for clustering analysis in the study. The reason is that severe convective weather that occurs under favorable conditions of large-scale circulation background is the result of the combined effects of thermal and dynamic factors. Therefore, 500-hPa geopotential height field is selected to represent the main influencing system in middle troposphere. 700 hPa is a transition layer between the middle and lower troposphere, which is not easily affected by the topography in the eastern part of Northwest China, and thus it can represent the dynamic effects in the lower layer. While 850-hPa temperature and humidity fields can represent the effects of heat and water vapor in the lower atmospheric layer.

The agglomerative hierarchical clustering algorithm AGNES (Agglomerative Nesting; Nazari et al.^[55]) is adopted in this study. First, the four variables (H₅₀₀, U₇₀₀, V₇₀₀ and θ_se850) in all the time steps of each rainstorm processes in Table 1 are averaged and normalized. Then, we use the principal component analysis (PCA) to conduct the data dimension reduction. Based on the variance contribution rate of 95%, 17 eigenvectors are obtained. The variance contribution rate of the first two principal components (PC1 and PC2, corresponding to the x-axis and y-axis in Fig. 1a, respectively) reaches 33.7%. Then the AGNES method is used for classification. The Euclidean distances among the 17 eigenvectors of all cases are calculated (Deza and Deza^[59]). In the beginning, each rainstorm process is considered to be a cluster, and then they are progressively merged into one cluster according to the principle of minimum distance coefficient. The clustering procedure is shown in Fig. 1b. The number of clusters is determined according to the following three principles. First, the distance coefficient of the members in the cluster should be as small as possible. Second, the distance coefficient between the clusters should be as large as possible. Third, by using the Pearson correlation coefficient (Pearson^[60]) as the similarity criterion, the above two distance coefficients should pass the t-test. The formulas of Euclidean distance, Pearson correlation coefficient and t-test are shown in Equation 1, Equation 2 and Equation 3, respectively.

Figure 1.  Classification results of 22 rainstorm processes in the eastern foot of Helan Mountain by hierarchical clustering. In Fig. 1a, the abscissa (PC1) and ordinate (PC2) represent the two components with the highest variance contribution rate in the principal component analysis. The number is the order of rainstorm processes (consistent with the order in Table 1). The red solid line in Fig. 1c is the 95% confidence level line.

where x_i' and x_j' are respectively the anomaly of the ith sample and jth sample, and k is the number of eigenvector, cov (x_i', x_j') is the covariance of the ith sample and jth sample, and s[x_i'] and s[x_j'] are respectively the variance of the ith sample and jth sample.

The results of clustering are shown in Fig. 1c. When the number of clusters is 3, there are sharp increases for maximum distance coefficients between clusters and minimum distance coefficients between objects in a single cluster. When the number of clusters is less than 3, neither of the two coefficients can pass the significance test at 95% confidence level (n=77361, t_0.05= 1.96, t=6.351, t > t_0.05) (Fig. 1c). Therefore, the 22 rainstorm processes in Table 1 are objectively classified into 3 categories in the study (Table 2).

Figure 2 and Table 2 present the distributions of precipitation amounts and frequencies of rainstorm with different magnitudes for three rainstorm patterns in the study area.

Figure 2.  Precipitation amounts (units: mm) and rainstorm days (units: d) for rainstorm processes of three patterns in the eastern foot of Helan Mountain. The bold black line indicates the terrain height of 1200 m. In Figs. 2a-2c, the shadings are the mean rainfall, and the colored dots are the total days of rainstorms. In Figs. 2d-2f, the colored dots and triangles show the days of heavy and extraordinary rainstorms, respectively.

Figures 2a and 2d reveal that the eight rainstorm processes of pattern Ⅰ mainly occurred in July (about 75%) and early August. The large-value areas with the multi-process averaged rainfall ≥40 mm correspond to the weather stations where ER occurs, which are all located at the junction between Yinchuan and Helan on the Helan Mountain side. Compared with rainstorms of patterns Ⅱ and Ⅲ, the lightning stations, the number of stations and days of ER, the total stations of short-time rainstorm, and the stations of GSR and ESR are all higher for pattern Ⅰ. At the same time, the precipitation amount during rainstorm processes and hourly rainfall intensity are the largest, while the rainstorm duration is the shortest, indicating that the convective rainstorm is the most extreme.

For rainstorms of pattern Ⅱ (Figs. 2b and 2e), five processes occurred in early summer (early and middle June) and early autumn (early September, accounting for 60%). Most of the processes are rainstorms in continuous rainy weather. The regions with multi-process averaged rainfall of ≥40 mm accord with the weather stations that exhibit high frequency of rainstorms, which are distributed throughout the whole Helan Mountain, mainly at the section from Yinchuan to PingLuo. For rainstorms of pattern Ⅱ, the lightning stations, HR stations, ER stations and the stations of different grades of short-time rainstorm are the fewest, and total precipitation amount during the rainstorm processes and hourly rainfall intensity are the smallest. However, the total rainstorm stations and days, and the stations and days of GR are the highest, the rainstorm duration is the longest and the average rainfall is the largest, indicating obvious characteristics of stable and large-scale persistent precipitation.

For rainstorms of pattern Ⅲ (Figs. 2c and 2f), nine processes are mainly distributed from July to early and middle August (the number of processes occurred in August account for 56%). The large-value areas with multi-process averaged rainfall ≥40 mm are consistent with the weather stations that exhibit high frequency of ER, which are mainly located at the junction of Yinchuan and Helan on the Helan Mountain side. Compared with the rainstorms of other two patterns, the lightning is the strongest, the stations and days of HR, the stations of HSR and ESR are the highest, and the average rainfall is the smallest for rainstorms of pattern Ⅲ, indicating obvious characteristics of local strong convection.

The above analysis shows that the topography of Helan Mountain has an important influence on the distribution of rainstorms in the eastern foot of Helan Mountain, and the determinant for the formation of rainstorm center is the precipitation intensity rather than the rainfall duration. The areas with multi-process averaged rainfall ≥40 mm correspond to weather stations with high-frequency rainstorms, especially those with severe rainstorms, which are concentrated in mountainous areas. Particularly, rainstorm processes of patterns Ⅰ and Ⅲ mainly occur in middle summer (accounting for 77% of the total processes). The stations with high-frequency rainstorms of these two patterns, especially those with HR and ER, are consistent with the large-value areas of multi-process averaged rainfall. Rainstorms of the two patterns have short duration, small range, large accumulated rainfall, large hourly rainfall intensity and strong convection. Comparatively, the rainstorms of pattern Ⅰ are more extreme, while those of pattern Ⅲ have obvious characteristics of local strong convection. However, there are few rainstorm processes of pattern Ⅱ in the early summer and early autumn. As these processes are rainstorms during relatively stable continuous rainy weather, they are featured by long duration, broader range, small number of stations and days of large magnitude rainstorms, and weak convection.

According to previous studies (Yao et al.^[61]; Huang et al.^[62]; Chen et al.^[31]), it can be concluded that the rainstorms in Northwest China mostly occur under some specific large-scale circulation situations, which is closely related to the westerlies, and subtropical and tropical systems. The distributions of large-scale circulations and configurations of main weather systems for rainstorms of three patterns are comparatively analyzed as follows.

Given the multi-year average, the ridge line of the characteristic line of the South Asian high (SAH), i. e. the 1252 dagpm isoline, locates near 25° N, with the northern boundary in 35° N. The western ridge point the of characteristic line of WPSH (588 dagpm isoline) locates near 130° E, and the northern boundaries of the 588 and 584 dagpm isolines locate near 25°N and 32°N, respectively (Fig. 3). Compare with the multi-year average, the SAH and WPSH are the strongest and northernmost for the rainstorms of pattern Ⅲ, followed by pattern Ⅰ, and those of pattern Ⅱ are close to the multi-year averages.

Figure 3.  Composite circulation and anomaly fields for rainstorm processes of three patterns in the eastern foot of Helan Mountain, and the green lines indicate the multi-year averages. In Figs. 3a-3c, the black contour line is the average geopotential height (units: dagpm) at 200 hPa, the green contour line is the 1252 dagpm isoheight, and the shading is the sea level pressure (units: hPa) anomaly. In Figs. 3d-3f, the black contour lines are the average geopotential height at 500 hPa, green lines are isoheights of 588 dagpm and 584 dagpm, and the shading indicates the geopotential height anomaly at 500 hPa.

The circulation anomaly is shown in Fig. 3. As can be seen, for pattern Ⅰ and pattern Ⅲ the westerlies prevail in middle-upper levels in mid-high latitudes; for pattern Ⅱ the meridional circulation prevails in mid-high latitudes. For pattern Ⅰ, the 500 hPa geopotential height anomaly is large in the east and small in the west. The Hetao area is located in the weak positive anomaly area (less than 2 dagpm) along the northeast-southwest oriented gradient zone of geopotential height, and the positive anomaly center is located near 130° E with the intensity exceeding 8 dagpm. While weak negative anomalies (absolute value less than 2 dagpm) appear from the eastern Tibet Plateau to the ocean in the south (Fig. 3d and Fig. 5a). The anomaly of sea level pressure (SLP) is positive in the east and negative in the west. The absolute value of the negative SLP anomaly is less than 1 hPa in the eastern foot of Helan Mountain, and the absolute value of SLP negative anomaly to the south of Hetao area is larger than 2 hPa (Fig. 3a and Fig. 5a). For pattern Ⅱ, the 500-hPa geopotential height anomaly field presents a negative-positive-negative distribution from east to west in mid-high latitudes, that is, a two-trough and one-ridge pattern. The Hetao area is located at the negative anomaly zone of geopotential height (absolute value larger than 2 dagpm), which is the transition area from positive anomaly in the east to negative anomaly in the west. The center of positive anomaly is located at about 120° E, with the central intensity exceeding 4 dagpm. There are two centers of negative anomaly (absolute value larger than 4 dagpm) over the regions west to Hetao area and over the ocean surface in the east (Fig. 3e and Fig. 5b). On the anomaly field of SLP, there is positive anomaly in most of the areas in China. The positive anomaly in the Hexi Corridor is over 8 hPa, and is 2-4 hPa in the eastern foot of Helan Mountain (Fig. 3b and Fig. 5b). For pattern Ⅲ, the 500 hPa geopotential height anomaly is also large in the east and small in the west. The Hetao area is located in the positive anomaly area (larger than 4 dagpm) along the east-west oriented gradient zone of geopotential height, and the positive anomaly center is located near 120° E with the intensity exceeding 6 dagpm. The negative anomalies (absolute value larger than 2 dagpm) appear over the ocean in the south (Fig. 3f and Fig. 5c). The anomaly of SLP is positive in the north and negative in the south. There is positive SLP anomaly in most of the regions to the north and west of Ningxia. There is negative SLP anomaly in the Hetao area and the coastal areas of South China. The SLP anomaly in the eastern foot of Helan Mountain is − 1 hPa, and the absolute value of SLP negative anomaly to the southeast of Hetao area is larger than 2 hPa (Fig. 3c and Fig. 5c).

Figure 4 shows the composite circulation and the anomalies for rainstorm processes of the three patterns in the eastern foot of Helan Mountain. As can be seen, for all the rainstorm processes, the westlies prevail in mid-high latitudes at 200 hPa, and there is an upper-level jet with wind speed larger than 30 m s^-1 at 40°N. At 700 hPa and 850 hPa, the southerly and southeasterly wind prevails in the Hetao area, and there is low-level jet in the central-south Hetao area. For patterns Ⅱ and Ⅲ, the wind speed of upper-level jet is higher than 38 m s^-1, and the range of the upper-level jet core in pattern Ⅲ is wider than that in pattern Ⅱ. The wind speed of upper-level jet core in pattern Ⅰ is 30 m s^-1. For patterns Ⅰ and Ⅱ, the fore-end of the 700 hPa jet axis moves northward to central Ningxia around 38° N, while for pattern Ⅲ the jet axis is more southerly (around 36 °N). The intensity of the low-level jet is the most intense for pattern Ⅱ (larger than 13 m s^-1), and it is 12 m s^-1 for patterns Ⅰ and Ⅲ. At 700 hPa, there is a cyclonic circulation (marked by"C"in Fig. 4d) in the southeast of the Tibetan Plateau for pattern Ⅰ, which locates to the left of the jet axis. The wind anomaly in the cyclonic circulation region is 2-8 m s^-1 (Fig. 5g). There are cyclonic circulations in the western Inner Mongolia (marked by"C"in Figs. 4e and 4f) for patterns Ⅱ and Ⅲ. The cyclonic circulation locates in the left front of the jet axis, where the wind anomaly is weak (1-2 m s^-1) (Figs. 5h and 5i). At 850 hPa, for patterns Ⅰ and Ⅲ the southeasterly jet at 850 hPa over the southeast Hetao area is discontinuous and dispersed, and the jet core has a velocity of 9 m s^-1. The 850 hPa jet axis in pattern Ⅲ is two latitudes northward than that in pattern Ⅰ, while in pattern Ⅱ the 850 hPa jet locates in Shanxi and eastern Gansu with the jet axis locating around 38°N and 107°E, and the jet core has a velocity of 11 m s^-1. For pattern Ⅰ, there is a cyclonic circulation in the Helan Mountain areas (marked as "C"in Fig. 4g), where the wind anomaly is weak (less than 2 m s^-1) (Fig. 5j). For pattern Ⅱ, there is a south-north oriented shear line in central Ningxia (marked as"C"in Fig. 4h) where the wind anomaly is larger than 4 m s^-1 (Fig. 5k). For pattern Ⅲ, there is a cyclonic circulation in the eastern foot of Helan Mountain (marked as"C"in Fig. 4i) where the wind anomaly is larger than 4 m s^-1 (Fig. 5l). For all the three patterns, the cyclonic circulation and shear line all locate in the fore-end of the low-level jet.

Figure 4.  Composite circulation fields and anomaly fields for rainstorm processes of three patterns in the eastern foot of Helan Mountain. The mark"C"indicates the cyclonic circulation or shear line. In Figs. 4a-4c, wind vector anomaly≥1 m s⁻¹, the wind vectors are the composite u- and v-components at 200 hPa, blue contour lines indicate the upper-level jet with average wind speed (units: m s⁻¹) larger than 30 m s⁻¹ at 200 hPa, and the shading is the positive divergence anomaly at 200 hPa (units: 10⁻⁶ s⁻¹). In Figs. 4d-4f, the wind vectors are the anomalies of composite u- and v-components at 700 hPa, the solid green lines indicate the low-level jet with average wind speed ≥10 m s⁻¹ at 700 hPa, and the shading is the anomaly of the integral of water vapor flux from 875 hPa to 700 hPa (units: 10² kg m⁻¹ s⁻¹). In Figs. 4g-4I, the wind vectors are the anomalies of composite u- and v-components at 850 hPa, the solid green lines indicate the low-level jet with average wind speed ≥8 m s⁻¹ at 850 hPa, and the shading is the negative divergence anomaly at 850 hPa. In Figs. 4j-4l, the black contour lines are anomalies of the K index (units: ℃), and the shading shows the anomalies of convective effective potential energy (units: J kg⁻¹).

Figure 5.  The t-test results for the three patterns of rainstorm in the eastern foot of Helan Mountain. The red shading and blue shading are positive value and negative value, respectively. The areas indicated by the contours and shadings with absolute value from small to large have passed the t-test at 90%, 95% and 99% confidence levels, respectively. Figs. 5a-5c show the anomalies of 500 hPa geopotential height and sea level pressure. Figs. 5d-5f present the anomalies of 200 hPa divergence. Figs. 5g-5i present the anomalies of 700 hPa wind and the vertically integrated water vapor flux from 875 hPa to 700 hPa. Figs. 5j-5l present the anomalies of 850 hPa wind and divergence. Figs. 5m-5o present the anomalies of K index and convective available potential energy.

Overall, in the rainstorm processes of pattern Ⅰ, there are no obvious cold air activities in the low levels. The East Asian summer monsoon from the South China Sea and the Bay of Bengal converges along the periphery of the WPSH and leads the 700-hPa southerly air flow and 850-hPa southeasterly air flow to the north, which combine with the low-pressure systems over the southeastern Tibet Plateau and the northern Hetao to form strong convective rainstorms in warm sector. In the rainstorm processes of pattern Ⅱ, the high-pressure ridges (the ridge line is at 120° E) over East China overlap from the upper troposphere to the lower troposphere in the same phase, which forms a strong high-pressure ridge across high and low latitudes. Moreover, the background circulation with the distribution of high in the east and low in the west is beneficial to the formation of southwest monsoon to the west of the ridge. It converges with the easterly flow carried by the weakened tropical cyclone on the north side of 588 dagpm WPSH, which further leads the 700-hPa warm and humid southerly air flow and the 850-hPa easterly air flow in the lower layer to move westwards and northwards. Then these air flows encounter with the eastward-moving cold trough, and the confluence of the cold airflow and warm airflow results in the formation of continuous precipitation. In the rainstorm processes of pattern Ⅲ, the South Asia high, WPSH and the thermal low over Hetao area develop strongly. In the middle troposphere, there is no obvious cold air activity, while weak cold air moves eastwards and southwards from Xinjiang and Mongolia on the near-surface layer. Besides, the East Asian summer monsoon from the ocean in the south is anomalously strong, leading the 700-hPa southerly airflow and 850-hPa southeasterly airflow to move westwards and northwards, which further climbs along the weak front, and thus strong convective rainstorm forms.

The above analysis indicates that all rainstorm processes of the three patterns in the eastern foot of Helan Mountain are under a relatively stable background circulation and weather systems. Among them, both pattern Ⅰ and Ⅲ are dominated by straight zonal westerly airflow. The South Asian high and WPSH high are stronger and northerly than normal years, and the tropical system over the ocean in the south is active. The study area is controlled by warm air flow from the lower troposphere to the upper troposphere, and the strong convective characteristics of rainstorm are significant. Compared with rainstorms of pattern Ⅰ, the circulations of pattern Ⅲ are featured by stronger and more northward South Asian high and WPSH and more active tropical systems, and the rainstorms formed by the intrusion of weak cold air in middle and high latitudes are more localized and convective than the warm-sector rainstorms of pattern Ⅰ. Rainstorms of pattern Ⅱ display a distribution of high in the east and low in the west in terms of geopotential height, that is, an obvious meridional circulation. The tropical system over the ocean in the east is active, and the frontal system in the middle and lower troposphere is anomalously active. The upper-level jet stream is stronger and more southward, the two low-level jets are stronger and more northward, and the rainstorm formed by the confluence of the warm and cold airflows has a long duration but weak convection.

Some previous studies indicated that the formation of rainstorm in the eastern part of Northwest China is closely related to abundant water vapor transport, continuous upward movement and repeated reconstruction of convective environment, while these three conditions are closely related to the low-level jet stream (Tao and Ding^[63]; Qian et al.^[64]; Yan et al.^[65]; Chen et al.^[26]). It indicates that most of the rainstorms in the eastern foot of Helan Mountain are accompanied with low-level jet streams that provide sufficient water vapor and thermal-dynamic conditions to the formation of the rainstorms.

Specifically, for rainstorms of pattern Ⅰ, the water vapor from the ocean in the south is transported mainly by the two low-level jets (Figs. 4a, 4d, 4g, 4j, 4d, 5g, 5j, 5m and 6a). The 850-hPa easterly air flow on the south side of the WPSH and surface high turns northwards, and converges with the 700-hPa southerly air flow that passes through the middle and low latitudes over the southeastern Hetao area. The convergence area of the two air flows is also the area with the largest positive anomaly (larger than 80 × 10² kg m^-1 s^-1) of the water vapor flux integral in the low-level. Besides, it is also the large-value area of K index and CAPE positive anomaly, where the rainstorm center is located to the left of the positive anomaly center of these physical quantities, which is also the left of the low-level jet axis. The water vapor contributing to rainstorms of pattern Ⅰ mainly comes from the 700-hPa southerly jet. Comparatively, the 850-hPa jet is more eastward and southward, with weaker intensity, smaller range and discontinuous distribution, while 700-hPa jet is more complete, concentrated and stronger. The rainstorm area is located in the strong divergence area on the south side of the 200 hPa upper-level jet, where the divergence at the positive anomaly center exceeds 24 × 10⁻⁶ s⁻¹. However, the negative divergence anomaly at 850 hPa only appears over the southeast of the rainstorm area, while the areas near the Helan Mountain and Yinchuan plain are dominated by weak positive divergence anomaly. The reason is that when the 850-hPa southeasterly wind encounters with the Helan Mountain, a flow around the mountain generates, presenting a weak positive divergence anomaly, and the strong convergence center in low layer is mainly located over the middle of Ningxia. It is also confirmed by the latitude-height cross section along 106° E (Fig. 6a), where a weak anomalous descending motion at 650 hPa and below is found over the northern part of the rainstorm area (39°N-40°N). The area with the value of 0.1 Pa s⁻¹ at the vertical velocity anomaly center is located at the top of the areas with positive anomalies of both relative humidity and θ_se near 800 hPa. The abnormal ascending motion over the south of the rainstorm area penetrates through the whole troposphere, and the center of −0.2 Pa s⁻¹ is located at 800-300 hPa over 34° - 38° N within the abnormal southerly flow. Meanwhile, the regions with positive θ_se anomaly are broad and deep, which appear at 600 hPa and below in the middle and lower troposphere, where the values at 800 hPa and below are larger than 12 K and the horizontal gradient of θ_se is close to 0, suggesting that there is strong convective instability ($ \frac{{\partial {\theta _{{\rm{se}}}}}}{{\partial p}} > 0$)in the middle and lower troposphere over the rainstorm area. Besides, there is also strong vertical wind shear in the lower troposphere. Although the whole troposphere is in the positive anomaly region with relative humidity ≥ 20% over the rainstorm area, the positive anomaly region with relative humidity ≥30% is mainly located at 700 hPa and below, indicating that the atmospheric stratification with "dry in the upper-layer and wet in the lower-layer" is obviously unstable. It can be concluded that under the westerly circulation background, the warm-sector rainstorms of pattern Ⅰ are mainly strong convective precipitation, and the extremities of both rainfall and rainfall intensity are prominent. Therefore, the 700-hPa southerly jet across the whole middle and low latitudes is not only beneficial to water vapor transport, but also crucial to the repeated formation of convective instability, enhancement of dynamic uplift mechanism and systematization of convective system in the rainstorm area. These are the main features of warmsector rainstorm.

Figure 6.  Cross sections of mean circulation anomaly fields during rainstorm processes of three patterns in the eastern foot of Helan Mountain. The black shading represent the topography, the red line indicates the rainstorm area, the solid lines indicate positive values and the dotted lines indicate negative values. Wind vector anomaly≥1 m s^-1. Figs. 6a and 6c are latitude-height cross-sections along 38oN. Fig. 6b is longitude-height cross-section along 106oE. The black contour line is the anomaly of pesudo-equivalent potential temperature (units: K), the green contour line indicates the vertical velocity anomaly (units: Pa s^-1), the vector is the wind anomaly (units: m s⁻¹), and the shading is the relative humidity anomaly (units: %).

For rainstorms of pattern Ⅱ (Figs. 4b, 4e, 4h, 4k, 5e, 5h, 5k and 5n), the meridional circulation displays a distribution pattern of high in the east and low in the west in terms of geopotential height, which is different from those of patterns Ⅰ and Ⅲ, and the water vapor sources and transport paths are also different. Because the tropical systems over the ocean in the east during rainstorm processes of pattern Ⅱ are more active, the southeast jet and southeast wind anomalies at 850 hPa are stronger than those of patterns Ⅰ and Ⅲ. 700-hPa and 850-hPa jet streams during rainstorm processes of pattern Ⅱ are the strongest in terms of the range and intensity among the three patterns, and their positions are the most northward or westward. The easterly flow carried by the tropical cyclone on the north side of 588 dagpm WPSH and the 700-hPa southwest flow led by the southwest monsoon on the west side of the ridge of high pressure over East China converge over the southeastern Hetao area, forming two extremely strong low-level jets. From the distribution of the water vapor flux integral anomaly, the values of positive anomaly in the rainstorm area are consistent with those of pattern Ⅰ, which are less than 20 × 10² kg m^-1 s^-1. This water vapor distribution is caused by the fact that the strong cold air moving southwards along the Qilian Mountains affects the further northward transport of water vapor during rainstorm processes of pattern Ⅱ. There are positive divergence anomalies of 12 × 10⁻⁶ s⁻¹ at 200 hPa and negative divergence anomalies of − 40 × 10⁻⁶ s⁻¹ at 850 hPa over the rainstorm area, which are conducive to the dynamic uplift over the rainstorm area due to the weak divergence at the upper level and strong convergence at the lower level. The K index positive anomaly center over the rainstorm area reaches 8℃, while the CAPE shows a weak positive or negative anomaly of less than 100 J kg⁻¹ over this area. That is, the condition for thermal instability is the worst among the three patterns. The longitude-height cross-section along 38° N shows that the relative humidity anomalies over the rainstorm area exceed 30% or 40% below 450 hPa in the middle and lower troposphere. Compared with patterns Ⅰ and Ⅲ, the humidity in the middle and lower troposphere is higher and the wet layer is thicker. Meanwhile, the the humidity in the middle and lower troposphere is higher and the wet layer is thicker. Meanwhile, the northerly and southerly wind anomalies at 700 hPa and below in the lower troposphere are stronger than those of patterns Ⅰ and Ⅲ. The abnormal ascending motion penetrates through almost the whole troposphere, with the center of −0.3 Pa s⁻¹ located within 800-300 hPa, which is consistent with the area of the strongest lowlevel wind convergence, corresponding to the rainstorm area. The abnormal ascending motion is not only deep, but also has a strong intensity in its center, which is the strongest among the three patterns. Positive θ_se anomalies only appear at 750-700 hPa over the rainstorm area, with the central value being 1 K, indicating that the stratification instability in the middle and lower troposphere is relatively weak ($ \frac{{\partial {\theta _{{\rm{se}}}}}}{{\partial p}} \approx 0$). Combined with the characteristics of much stronger horizontal gradient of θ_se anomaly (larger than 5 K) than its vertical gradient (1 K), strong ascending motion anomaly and strong humidity condition, these features indicate that the convective activity during the rainstorm processes of pattern Ⅱ is not as intense as that of the zonal pattern, and the characteristics of mixed precipitation or stable persistent precipitation in frontal area are more clear. That is why the accumulative precipitation, hourly rainfall intensity, frequencies of short-time rainstorm and lightning during rainstorm processes of pattern Ⅱ are obviously lower than those of convective rainstorm. However, the total precipitation amount during the processes and GR stations are higher. This is because although the rainstorm processes of pattern Ⅱ are weaker in the intensity and magnitude than those of convective rainstorm, they present better persistence, larger precipitation range, and more uniform spatial distribution. These are the main features of frontal rainstorm.

For rainstorm processes of pattern Ⅲ, the circulation background is similar to that of pattern Ⅰ, so are the distributions of water vapor transport, dynamic uplift and atmospheric stratification (Figs. 4c, 4f, 4i, 4l, 5f, 5i, 5l and 5o). The difference is that the 850-hPa southeast jet and southeast wind anomaly over the southeast Hetao area are stronger, the 700-hPa southerly jet is more southward, and the South Asian high and subtropical high are stronger and more northward. Therefore, the positive anomalies for the integral of water vapor flux, K index and CAPE are stronger in the lower layer over the rainstorm area. The positive divergence anomaly at 200 hPa and negative divergence anomaly at 850 hPa are located over the rainstorm area, where the positive divergence anomaly center (20 × 10⁻⁶ s⁻¹) is located over the Helan Mountain, and the negative divergence anomaly center (−40×10⁻⁶ s⁻¹) over the east and south of the rainstorm area. Affected by the flow around, the Helan Mountain is dominated by weak positive divergence anomaly. As shown in Fig. 6c, the latitude-height cross-section along 106°E indicates that there is a clear θ se front tilting northwards with the height. The mid-lower troposphere shows a anomalously strong convective instability ($ \frac{{\partial {\theta _{{\rm{se}}}}}}{{\partial p}} > 0$) at 550 hPa and below, where the positive θ_se anomaly at 850 hPa and below is more than 20 K, and the maximum abnormal intensity is about 1.6 times of that of pattern Ⅰ. In addition, the vertical gradient of θ_se anomaly in the middle and lower troposphere (20 K) is much larger than the horizontal gradient (4 K). Correspondingly, there is a northward-tilting ascending motion anomaly along the front, and a descending motion anomaly over the north side of the rainstorm area (38°N-39°N) at 650 hPa and below. However, both the positive and negative anomalies are weak, particularly the ascending motion anomaly that is the weakest among the three patterns, with the central value being only 0.1 Pa s⁻¹. Besides, there is also strong vertical wind shear anomaly in the lower troposphere. In terms of relative humidity, there is positive anomaly above the rainstorm area, but the area with positive relative humidity anomaly of ≥40% is mainly concentrated at 800 hPa and below, where the relative humidity is larger and wet layer is thinner than those of pattern Ⅰ. Combined with the vertical distribution of positive θ_se anomaly, it is indicated that for the same atmospheric stratification distribution pattern of "dry in the upper-layer and wet in the lowerlayer", the convective instability of pattern Ⅲ is stronger and the convective system is deeper than those of pattern Ⅰ. The maintenance mechanisms of the convective instability near the top of the unusually warm and humid tongue and the conditional symmetric instability near the θ se front can be very important for severe convective rainstorm processes of this pattern, and the continuous warm and humid air advection by the low-level jet is also very important for the maintenance of instability. Therefore, the rainstorm processes of pattern Ⅲ is generally related to the convective heavy precipitation process forced by weak frontal system. The convective precipitation under the background of synoptic-scale situation and thermal-dynamic instability is of high intensity and high degree of organization, which may be the synoptic causes contributing to the fact that the area with the maximum mean rainfall during the rainstorm processes overlaps with the area where high-frequency of ER occurrences are observed at weather stations. The stronger and more northward WPSH leads to stronger humidity and unstable energy in the lower layer. Furthermore, the state of deep unstable atmospheric stratification is the direct reason for the stronger convective rainstorm formed by the ascending of the southerly warm and humid air along the weak front that is more obvious than the warm-sector rainstorm of pattern Ⅰ under the same background of zonal circulations. These are the main features of strong convective precipitation.

The above analysis shows that rainstorm processes in the eastern foot of Helan Mountain are generally related to frontal dynamic processes under different configurations of weather systems. However, due to the differences in structural characteristics of the front, the state of environmental atmospheric stratification and the low-level jet related transport channel as well as intensity of humid and warm flow, the intensity, magnitude, and spatial distribution of heavy rainstorm vary under different circulation backgrounds. The zonal circulation background of patterns Ⅰ and Ⅲ are similar, and the warm and humid airflow from the ocean in the south is mainly transported to the rainstorm area by 700-hPa southerly jet and 850-hPa southeast jet through the middle and low latitudes. The unstable atmospheric stratification of "dry in the upper-layer and wet in the lower-layer" is obvious and the conditions of dynamic uplift are relatively weak, which are conducive to the triggering and organization of convective system, leading to the high-degree overlap between the area with heavy rainfall and the stations with heavy rainstorm. In particular, due to stronger and more northward WPSH during rainstorms of pattern Ⅲ, higher humidity in the lower layer and the conditions of more abundant water vapor and more unstable energy, the rainstorm caused by the ascending of the warm and humid air along the weak front in the lower layer is more convective and localized, but the warm-sector rainstorm of pattern Ⅰ is more extreme. While for rainstorms of pattern Ⅱ, the synoptic situations are mainly characterized by prominent meridional circulations, which present a distribution of high in the east and low in the west in terms of geopotential height. Besides, the water vapor from the ocean in the east is transported to the rainstorm area by two jets together. The WPSH is weaker and more southward, the frontal system within westerlies is active, and the cold and warm air are comparable in their power. Combined with high humidity, thick wet layer, anomalously deep and strong ascending motion, and weak stratification instability, all these conditions are conducive to the persistence of frontal precipitation, and thus the area with heavy precipitation highly overlap with the stations where the GR is highly frequent. These were the main features of frontal precipitation or someone particular rainstorm type.

The observations at Yinchuan station, which is the only radiosonde station in the study area, are used in the study. Table 3 presents 14 convective parameters representing thermal and dynamic instabilities as well as their combined effects. The changes of convective parameters before and during the rainstorm processes of three patterns are investigated, aiming to provide quantitative indicators for rainstorm forecasts in arid areas.

During 6-12 h before the rainstorm process, there were increases in the parameters of CAPE, K, EHI, SWEAT, thickening in Hwarm and Hwet, decreases in CIN, LS, LI, SI, T75 and lowering in LCL and LFC. This indicates that with the establishment, development, northward or westward movement of the low-level jet as well as the increases of the temperature, humidity and energy in the lower-layer of the rainstorm area, the atmospheric instability increases and thus the convective potential further increases. According to the magnitudes of convective parameters, when Ls < − 40℃, LI < 2℃ and SI < 3℃, K > 30℃, T85 > 20℃, T75 > 13℃, SWEAT > 200, Hwarm > 3 km, Hwet > 3 km, LCL > 800 hPa and LFC < 750 hPa, convective rainstorms are prone to occur in the eastern foot of Helan Mountain. In addition, the CAPE (EHI) have a large-magnitude-range within 10⁰-10² J kg⁻¹ (from −10⁰ to 10²), respectively. In general, the larger the absolute values of these convective parameters are, the more conducive to the occurrence of severe convective precipitation in arid areas.

In comparison, the absolute values of most convective parameters of patterns Ⅰ and Ⅲ are 1-3 times higher than those of pattern Ⅱ before and after the rainstorm occurs. The results indicate that the characteristics for strong convective rainstorms of patterns Ⅰ and Ⅲ are more obvious, and the anomalously warm and humid environment in lower-layer is more conducive to the triggering and maintenance of convective systems. In contrast, the intrusion of the weak dry cold air from middle and high latitudes intensifies the instability of the environmental atmosphere in pattern Ⅲ. Although the wet layer is thinner in pattern Ⅲ than in pattern Ⅰ, the absolute values of convective parameters are significantly higher for pattern Ⅲ, especially the CAPE value which is 1.4 times higher in pattern Ⅲ than in pattern Ⅰ. Therefore, the convective instability energy is more sufficient, and thus the convective instability is more intense. The strong convective characteristics for pattern Ⅲ, including higher frequencies of HR and HSR and more intense lightning activities, are thus more prominent. The wet layer of pattern Ⅰ is 0.6 km thick than that of pattern Ⅲ, and the LFC of pattern Ⅰ is 55.7 hPa lower than that of pattern Ⅲ, which is more conducive to the occurrence of extreme rainstorm. Comparatively, the convective characteristics of pattern Ⅱ are relatively weaker. The wet layer is thicker (> 4.5 km), LCL is lower (> 860 hPa) and the CAPE is less than 20 J kg⁻¹, which is more conducive to the occurrence of relatively stable continuous heavy rain.

As precipitation and temperature are the two main observing elements in intensified ground observations (accounting for 80%) in the study area, all 22 rainstorm centers are located in areas where both two elements are observed. Considering the precipitation intensity and amount during rainstorm processes and the observing elements, the Helan Mountain Yanhua station from July 22 to 23, 2018 (pattern Ⅰ, Fig. 7a), Pingluo station from August 31 to September 1, 2018 (pattern Ⅱ, Fig. 7b), and Dawukou station on July 19, 2018 (pattern Ⅲ, Fig. 7C) are selected as representatives of the three patterns of rainstorm processes. The variations of meteorological elements including atmospheric temperature, atmospheric pressure, relative humidity, wind speed and wind direction before and after the rainstorm processes are compared.

Figure 7.  Variations of meteorological elements at representative stations during rainstorm processes of three patterns in the eastern foot of Helan Mountain. The black solid line indicates atmospheric pressure (units: hPa), the dash line indicates temperature (units: ℃), the dotted line represents relative humidity (units: %), and the bar represents precipitation (units: mm).

Figure 7 shows that the variations of the temperature, wind and relative humidity are most obvious before and after the rainstorm processes of pattern Ⅲ. Specifically, the easterly or southerly wind before the processes turns to westerly or northwesterly wind in pattern Ⅲ. The pressure and relative humidity increase first and then decrease in patterns Ⅰ and Ⅲ, while the temperature decreases first and then increases. For pattern Ⅱ, the pressure and temperature decrease first and then increase, the relative humidity increases first and then decreases, and the magnitude of the decrease is obviously higher than that of the increase. The main peak of precipitation appears in the period with increasing wind speed and relative humidity and decreasing air temperature. The precipitation peak of pattern Ⅰ (Ⅲ) appear in the period with decreasing (increasing) atmospheric pressure. While the main (secondary) precipitation peak of pattern Ⅱ appears in the period with decreasing (increasing) atmospheric pressure. During the precipitation period, the atmospheric pressure, temperature and relative humidity are the largest in pattern Ⅱ and smallest in pattern Ⅰ, while the situation for wind speed is the opposite. Comparatively, the changes of meteorological elements in pattern Ⅰ and Ⅲ are more obvious than those in pattern Ⅱ.

The changes of meteorological elements are related to the configuration of weather systems and the properties of precipitation. Pattern Ⅱ is mainly featured by continuous rain formed by the confluence of cold and warm air, with strong cold and warm air, high pressure, low temperature, high humidity and small wind speed. The changes of meteorological elements are relatively stable during precipitation processes of this pattern. While patterns Ⅰ and Ⅲ are strong convective weather with weak cold air, strong warm air, low pressure, high temperature, low humidity and large wind speed. The changes of meteorological elements before and after the processes are relatively obvious. The cold air activity in pattern Ⅰ is mainly found in the middle and upper layer, while there is no obvious frontal zone, and the atmospheric pressure is generally smaller that in pattern Ⅲ. In general, the stronger the convection is, the stronger the rainfall intensity is; the lower the temperature, pressure and humidity are, the stronger the wind is.

By using the hierarchical clustering method, 22 rainstorm processes in the eastern foot of Helan Mountain from 2006 to 2020 are objectively classified into three patterns. On this basis, the characteristics of precipitation distribution, circulation configuration, water vapor transport, thermal dynamics, convective parameters and meteorological elements for rainstorms of three patterns under different circulation backgrounds are comparatively analyzed through the composite analysis method.

In the eastern foot of Helan mountain, the formation of most rainstorm processes is closely related to the interactions between weather systems at different layers and those in middle and low latitudes, the strengthening of the unstable stratification caused by the long distance transport of the warm and humid air flow to the rainstorm area, and the development of dynamical uplifting mechanism. Rainstorm centers are located on the left of the large-value centers of water vapor and thermal instability in the lower layer, that is, the left side of the low-level jet axis.

Under different synoptic backgrounds, the weather situation and rainfall distribution of rainstorm processes are quite different. For rainstorm processes of patterns Ⅰ and Ⅲ, the westerly circulation backgrounds are similar, the SAH and WPSH are stronger and more northward than in normal years, and the tropical systems over the ocean in the south are active. The 700 hPa southerly jet, 850 hPa southeasterly jet and the fronts in westerlies are weak, and the rainstorm process is mainly dominated by the localized convective precipitation. The extremity of the warm-sector rainstorms of pattern Ⅰ is prominent. For pattern Ⅲ, the local strong convective characteristics related to the intrusion of weak dry cold air from middle and high latitudes are more obvious. For rainstorms of pattern Ⅱ, there is obvious meridional circulation with high geopotential height in the east and low geopotential height in the west. The SAH and WPSH are weaker and more southerly. Besides, the tropical system over the ocean in the east is active. The 700 hPa and 850 hPa low-level jets are relatively stronger and more northward (westward). The confluence of cold air and warm air can cause the wide-range and long-lasting rainstorm with weak convection.

The water vapor transportation is different in different patterns of rainstorm. For rainstorm processes of the patterns Ⅰ and Ⅲ, the water vapor over the ocean in the south is mainly transported to the rainstorm area by the 700-hPa southerly low-level jet. For rainstorm processes of the patterns Ⅱ, the 700 hPa southerly jet and the 850 hPa southeasterly jet transports the water vapor from the oceans in the east to the rainstorm area. As for the three patterns, pattern Ⅰ (Ⅱ) has low (high) relative humidity and thin (thick) wet layer, while pattern Ⅲ has the most abundant water vapor in the lower troposphere.

The thermodynamic characteristics of different patterns of rainstorms are different. For patterns Ⅰ and Ⅲ, the dynamic uplift anomalies are relatively weak. The atmospheric structure of "dry in the upper-layer and wet in the lower-layer" is extremely unstable, and the vertical wind shear in the lower troposphere is quite significant, which is more conducive to the formation and development of convective systems. For rainstorms of pattern Ⅲ, the convective instability is stronger and deeper than that of pattern Ⅰ, and the absolute values of convective parameters are also larger, which is more conducive to the triggering and strengthening of convective systems. For rainstorms of pattern Ⅱ, the dynamic lifting is deep and intense, but the thermal conditions are poor and the values of convective parameters are small, which are conducive to the persistence of frontal precipitation.

The changes of meteorological elements before and after the rainstorm processes are related to weather systems and precipitation properties. The stronger the convection is, the more severe the changes of meteorological elements will be. Processes of pattern Ⅱ are accompanied by strong cold and warm air, high atmospheric pressure, low temperature, high humidity and small wind speed. Processes of patterns Ⅰ and Ⅲ are accompanied by weak cold air, low atmospheric pressure, high temperature, low humidity, and high wind speed, while those of pattern Ⅰ have higher surface temperature and lower pressure. The variations of meteorological elements are the most significant in pattern Ⅲ and weakest in pattern Ⅱ.

In this paper, the precipitation distribution, circulation configuration and thermal dynamic characteristics of rainstorm processes in the eastern foot of Helan Mountain under different circulation backgrounds are compared by objective clustering and composite analysis methods. Due to limited space, only the large-scale circulation characteristics are analyzed, and the detailed characteristics of local circulations near the rainstorm area would be explored in the future. Specifically, high-resolution numerical simulations and sensitivity tests will be conducted on typical rainstorm processes to investigate the distribution characteristics of local circulations for rainstorms in the eastern foot of Helan Mountain. Furthermore, the triggering, development and dissipation mechanism of rainstormrelated mesoscale systems over complex terrains will also be explored, aiming to figure out the formation mechanisms of rainstorms in this particular area.

Appendix:

(a) Illustrations of some of the figures and tables

All the statistics in Table 1 and Table 2 are obtained based the 22 rainstorm processes, and only the stations in the study area are concerned. In the two tables, average rainfall (units: mm) denotes the average accumulated rainfall of all stations. Rainstorm stations denote the number of stations with accumulated rainfall reaching 50 mm or above. GR stations, HR stations and ER stations are the number of stations with accumulated rainfall reaching 50-100 mm, 100-200 mm, more than 200 mm, respectively. Short-time rainstorm stations denote the number of stations meeting the standard of short-time rainstorm. GSR stations, HSR stations and ESR stations denotes the number of stations with hourly rainfall reaching 20-40 mm, 40-60 mm and more than 60 mm, respectively. Lightning stations denote the number of stations with lightning during the rainstorm process. Note that, when calculating the station of short-time rainstorm, GSR, HSR, ESR and lightning, one station could be counted several times in a rainstorm process. Maximum rainfall (units: mm) denotes the maximum accumulated rainfall among all the stations in the study region. Maximum hour rainfall denotes the maximum hourly rainfall among all the stations in the study region during the rainstorm process. Max lightning intensity (units: KA) denotes the maximum lightning intensity during the rainstorm process.

The days in Fig. 2 (units: day) denotes the number of days meeting the standard of different grades of rainstorms at each station.

(b) Abbreviations

ECMWF: the European Centre for Medium-Range Weather Forecasts

ERA5: the European Centre for Medium-Range Weather Forecasts reanalysis 5

WPSH: western Pacific subtropical high SAH: South Asia high

GR: general rainstorm

GSR: general short-time rainstorm HR: heavy rainstorm

HSR: heavy short-time rainstorm ER: extraordinary rainstorm

ESR: extraordinary short-time rainstorm AGNES: Agglomerative Nesting

PCA: principal component analysis