The NECV dataset during 2000–2019 is from Huang and Cui (2022).

The precipitation data are derived from the hourly precipitation dataset of national surface automatic weather stations (AWSs) in the warm seasons (May–September) from 2000 to 2019 provided by the China Meteorological Administration (CMA). Strict quality controls, including climatological extremes, internal consistency, and temporal consistency, have been performed for the dataset (Ren et al., 2015). To avoid the impact of missing values, the AWS will be excluded if the rate of missing values exceeds 5%. Figure 1 shows the spatial distribution of 220 trusted national AWSs (black dots) in the NEC after the quality control of time continuity. Considering that there are only four trusted national AWSs in the HulunBuir region and all of them are distributed in the lower altitude region in the east of HulunBuir, they cannot represent the characteristics of precipitation of the whole region. Thus, all AWSs in HulunBuir are removed, and 216 AWSs in the NEC are finally selected for the following analysis.

A rainstorm day is defined as a day in which the accumulated precipitation is greater than or equal to 50 mm from 0800 local standard time (LST, LST = UTC + 8 h) to 0800 LST of the next day for an AWS. A rainstorm day associated with NECVs is defined as a rainstorm day occurring during the influence period of NECVs. A total of 306 rainstorm days associated with NECVs are identified during the warm seasons of 2000–2019 for the study of objective circulation classification.

NCEP/NCAR reanalysis data (Kalnay et al., 1996) with a horizontal resolution of 2.5° × 2.5° from 1991 to 2020 are used for the objective classifications and subsequent synthetic analysis. The variables include geopotential height, wind, relative humidity, and specific humidity.

Cost733class (Philipp et al., 2014) is a widely used classification software. There are five groups of objective classification methods in the Cost733class, including classifications based on principal component analysis (PCA), classifications using the leader algorithm (LDR), hierarchical cluster analysis (HCL), optimization algorithms (OPT), and random classifications (RAN). In this study, ten objective circulation classification methods are utilized and evaluated (Table 1).

PCA (or empirical orthogonal functions) aims to select principal components (PCs) by decomposition and then assign each case to a PC according to some rule. Both PCT (Huth, 1993) and PTT (Philipp, 2009) are in T-mode, but PCT uses oblique rotation while PTT uses orthogonal rotation.

Methods based on LDR can also be called “correlation-based” methods. The main idea is to find leader patterns by considering the number of elements that are similar to the potential leader pattern exceeding a certain threshold. In LND (Lund, 1963), at first, set Pearson correlation coefficient (r > 0.7) to determine leader patterns, and then assign each case to the type of the most similar leader. KIR (Kirchhofer, 1974) is similar to LND but takes similarity in all parts of the map into account. And the threshold in KIR is usually 0.4.

HCL (Murtagh, 1985) is also a widespread classification method that first splits up all cases into two types according to some criterion. On a second hierarchy level, it splits up one of these types again into two types, and so on.

OPT works non-hierarchically and can be considered a standardized method. The aim of OPT is to minimize within-type variability and achieve optimal partitioning. CKM (Enke and Spekat, 1997) modifies the minimum distance to produce the seeds for k-means clustering. KMD (Kaufman and Rousseeuw, 1990) is similar to k-means, but it employs given data points as centers of the clusters. SOM (Michaelides et al., 2007) arranges types defined by their features (grid point values) in a structure where similar types are adjacent to each other (a map).

RAN (Philipp et al., 2014) randomly selects any arbitrary number as type number for each case and chooses the best result according to the explained cluster variance after 1,000 iterations. RAC (Philipp et al., 2014) is similar to RAN, except for any arbitrary case used as a centroid for each type. All the other cases are then assigned to these centroids by the minimum Euclidean distance.

In this study, the 500 hPa geopotential height anomaly at 08 LST is used to classify the circulation background of rainstorm days associated with NECVs in the warm seasons from 2000 to 2019. The region is set as 90–150°E, 20–70°N. The geopotential height anomaly is calculated by the 500 hPa geopotential height minus the monthly mean of 30 years (1991–2020).

Generally, a better objective classification method should achieve smaller within-type differences and bigger between-type differences. The following evaluation indicators are used in this study to obtain the optimal objective classification method and the corresponding number of types.

The first selected evaluation index is the explained variation (EV), which can be used to quantify the proportion of variance of the dependent variable as well as to represent within-type differences (Buishand and Brandsma, 1997; Beck and Philipp, 2010; Casado et al., 2010). EV can be calculated as follows: E V = 1 − W S S T S S (1) W S S = ∑ j = 1 k ∑ i = 1 n y j i − y ¯ j 2 (2) T S S = ∑ i = 1 n y i − y 2 (3) WSS and TSS represent the within-type sum of squares and the total sum of squares, thereby taking into account the number of all elements (n) and types (k), respectively. y ¯ j denotes the mean value for elements of each type (1, …, k) and y is the mean value for all elements. EV ranges from 0 to 1, with a value closer to 1 indicating better quality of classifications.

The second evaluation index is the pseudo-F statistic (PF) (Calinski and Harabasz, 1974; Broderick and Fealy, 2015), which is the ratio of the between-type sum of squares (BSS) to WSS, and its formula is: P F = B S S k − 1 W S S n − k (4) B S S = ∑ j = 1 k y ¯ j − y 2 (5)

The larger PF implies bigger between-type differences and better quality of the classification.

Figure 2 shows the evaluation results of different objective classification methods using EV and PF, respectively. Except for KIR and RAN, other classification methods exhibit better ability for classification. Among all the classification methods, SOM performs best in both EV and PF. However, when the number of types is increasing, EV of all the classification methods shows a tendency to increase. It indicates that the within-type differences decrease, and the proficiency of classification improves at the same time. The result of PF shows opposition compared with EV. Based on the evaluation results of EV and PF, SOM can be decided as the optimal classification method.

For the optimal classification number of types based on SOM, a new evaluation index (EVPF) is created by considering both EV and PF. First, to eliminate the dimensional influence between EV and PF, min-max normalization is performed on these two indices: X ′ = X − X min X max − X min (6) In which X ′ represents the normalized result of EV or PF when X represents EV or PF, X min and X max are the minimum and maximum values of EV or PF, respectively.

The new evaluation index can be expressed as: E V P F = E V ′ × P F ′ (7)

EVPF ranges from 0 to 1. A larger EVPF value indicates better classification quality.

With min-max normalization, EVPF equals 0 when the number of types is 2 or 15. Therefore, Figure 3 presents the evaluation results of EVPF for the optimal classification method (SOM), with the number of types between 3 and 14. It can be found that SOM shows a better classification performance when the number of types is between three and six. The highest value of EVPF is 0.467 when the number of types is five. If the number of types is larger than five, the quality of classification grows worse.

Based on the above results, SOM is finally determined as the optimal objective circulation classification method to classify the rainstorm days associated with NECVs in the warm seasons from 2000 to 2019, and the optimal classification number is five.

Figure 4 shows the five types of rainstorm days associated with NECVs in the NEC over the warm seasons from 2000 to 2019 based on the 500 hPa geopotential height anomaly at 08 LST by SOM.

Type 1 accounts for about 17% (Figure 4A). In this type, the western Pacific subtropical high (WPSH) extends west to the east coast of Taiwan Island and north to the southwest coast of Japan, which is connected to the mid-latitude ridge in the east of the NEC. In addition, the centers of the high-pressure anomalies are located in the eastern part of the NEC and East Siberia. In the northwest of Lake Baikal, there is a low-pressure anomaly, and a mid-latitude westerly trough is in the west of the NEC. The mean intensity of NECVs is the weakest (5,638 gpm) and the mean size is also the smallest (766 km) of all types.

Type 2 accounts for about 25.2%, which is the majority (Figure 4B). Except for the region where the WPSH is occupied, the other region of this type is controlled by the low-pressure anomaly, and the two centers of the low-pressure anomalies at 500 hPa are located in the NEC and its north. There is an obvious trough in the NEC. Compared with type 1 (Figure 4A), the WPSH retreats southeasterly. NECVs of this type have the strongest mean intensity (5,575 gpm) and their mean size (856 km) is larger than that of type 1.

The proportion of type 3 is the least of all five types, at roughly 13.4% (Figure 4C). In this type, the region north of 45°N is controlled by a strong high-pressure anomaly. The low-pressure anomaly shrinks to the south of the NEC, and the NEC is controlled by the cut-off low vortex. Compared with the above two types, the WPSH retreats further to the southeast. The mean intensity of NECVs (5,635 gpm) is similar to that of type 1, while the mean size (1,014 km) is the largest.

Type 4 accounts for nearly 19.6% of the total (Figure 4D). The high-pressure and low-pressure anomalies are distributed alternately from north to south. The center of the low-pressure anomaly is located in the west of the NEC. The WPSH at 500 hPa is the most westward of these five types, reaching the Taiwan Strait. The mean intensity of NECVs (5,587 gpm) is a little weaker than that of type 2, with the mean size (889 km) larger than both type 1 and 2.

Type 5 accounts for about 24.8% (Figure 4E). The two low-pressure anomalies are distributed southwest to northeast, with their centers located in the west of the NEC and East Siberia, respectively. A northeast-southwest trough line can be found in the westerly trough, and the WPSH at 500 hPa is similar to that of type 2. The mean intensity of NECVs ranks third (5,601 gpm) and the mean size (892 km) is similar to that of type 4.

The wind at 850 hPa of each type corresponding to NECV systems presents cyclonic vortexes except for type 1, where there is a deep low trough. However, the morphology, size, and location of the cyclonic vortexes of each type at 850 hPa are slightly different (Figure 4).

It is observed in Figure 4 that the large-scale circulation backgrounds of rainstorm days associated with NECVs under different types present distinct discrepancies. Different large-scale circulation backgrounds can lead to differences in water vapor transport and convergence, as well as different precipitation characteristics of rainstorms associated with NECVs.

Rainstorm days associated with NECVs frequently occur from June to August, especially in July (132 times), accounting for about 43% of the total (not shown). Figure 5 further presents the semi-monthly variation of the frequency of rainstorm days associated with NECVs under different synoptic circulation patterns in the warm seasons during 2000–2019. Rainstorm days associated with NECVs in type 1 mainly occur in the second half of July and the second half of June. The frequency of rainstorm days associated with NECVs in type 2 peaks in the first half of July at 28, followed by the second half of July (14 times), while the frequencies in other periods of the warm seasons are all less than 10. Type 3 is mostly in the second half of July to the first half of September, while type 4 predominantly appears from June to August, especially in the first half of July and August. Rainstorm days associated with NECVs in type 5 are more frequent in the second half of July, which ranks second only to type 2 in the first half of July.

In different synoptic circulation patterns, the daily precipitation characteristics of rainstorms associated with the NECVs in the warm seasons differ dramatically (Figure 6). Under the control of NECVs, rainstorms occur in the NEC with strong local characteristics (Bai andJin, 1993), which can also be found in Figure 6C. For type 1 and 5, the mean number of AWSs reaching the rainstorm level is about five in a rainstorm day, which is more than that of other types. The mean daily precipitation of rainstorm days associated with NECVs in type 1 is the largest among all five types, reaching 76 mm. The extreme value exceeds 280 mm/24 h and hits the level of an extremely heavy rainstorm, while the extremes of daily precipitation of other types are all less than 200 mm. Meanwhile, the mean hourly maximum of this type is more than 25 mm/h, which is stronger than the others. However, the hourly extreme of rainfall on rainstorm days associated with NECVs appears in type 4, reaching about 130 mm/h. Note that in type 1, the high-pressure anomaly hinders the upstream NECV from moving to the east (Figure 4A). This configuration is favorable for water vapor transport to the NEC and results in more daily precipitation and large-scale rainstorms (Figures 6A,C). A similar configuration of the high-pressure anomaly block can also be found in type 5 (Figures 4E, 6C). Moreover, type 4 frequently occurs in the first half of July and the first half of August (Figure 5), when the WPSH is active and extends most westward among all types. The NEC of this type is in the narrow zonal low-pressure anomaly with a little stronger NECVs (Figure 4D). It is favorable to the eastward movement of the low-value systems in the upstream area of the NEC, further leading to extreme hourly precipitation (Figure 6D). In addition, the maximum hourly precipitation in type 2 can reach 100 mm/h (Figure 6B). The low-value system is also active in mid and high latitudes, and the mean intensity of NECVs is the strongest. Similar to type 4, the NEC is also mainly controlled by a low-pressure anomaly (Figure 4B), which is also conducive to the occurrence of stronger hourly precipitation (Figure 6B).

The spatial distribution of accumulated precipitation on rainstorm days associated with NECVs in the warm seasons during 2000–2019 demonstrates remarkable non-uniformity and differences under different synoptic circulation patterns (Figure 7). In addition, the spatial distribution of the frequency of rainstorms shows consistencies with accumulated precipitation (not shown). The rainstorms mostly concentrate near Changbai Mountain and the narrow northeast plain regions in the middle of Liaoning Province, which reflects the effect of topography on the rainstorms. Rainstorms of type 1 mainly occur in the central plain of Liaoning province and central Jilin Province (Figure 7A). The extreme precipitation center of type 2 is mostly located near Changbai Mountain, especially in the southern part of Changbai Mountain in Liaoning Province (Figure 7B). The accumulated precipitation of rainstorms in type 3 and 4 is weaker than that of other types, and the precipitation center in type 3 is in the southwest of Changbai Mountain (Figure 7C). Unlike in other types, the precipitation centers in type 4 are scattered around the topography (Figure 7D). The extreme precipitation centers of type 5 are found near Changbai Mountain and the coastal areas in the southeast of Liaoning Province. The sub-extreme center is distributed in the northwest of Heilongjiang Province where Greater and Lesser Khingan Mountains intersect (Figure 7E).

Previous research has revealed that the local topography of the NEC has a great impact on the circulation and rainfall of NECVs (Wang and Xie, 1994; Zhong, 2011). Moreover, our study also shows that the interaction of local topography and different large-scale circulations can lead to different water vapor transport and convergence ascending processes, which can partially explain the unique precipitation characteristics of different circulation types.

In type 1 (Figure 8A), a low-pressure vortex center at 925 hPa is located in the northwest NEC, and there is a positive equivalent potential temperature ( θ e ) anomaly greater than 12 K in the southeast NEC. The NEC is controlled by warm and moist southerly airflows. Under the low-pressure vortex, a northwest-southeast-oriented high- θ e belt can be found in the north of the NEC, and northerly dry and cold air flows to the west of the NEC. In this type, the upstream low-value system in the NEC is blocked by the WPSH and the high-pressure ridge, resulting in a relatively small size of the NECVs (Figure 4A). The warm and moist air consistently interacts with dry and cold air, which is conducive to the occurrence of more accumulated daily precipitation (Figure 6A). The low-pressure vortex center of type 2 (Figure 8B) is located near the border of Heilongjiang Province and Inner Mongolia. Under the influence of the low-pressure circulation, the high- θ e region shrinks to the south compared with type 1, but there is still a high- θ e anomaly center in the southeastern part of the NEC. In this type, the cold air at middle-high latitudes is active, and the mean intensity of the NECVs is the strongest (Figure 4B). The warm and cold air collaborating with the terrain near Changbai Mountain results in rainstorms (Figure 7B). The center of the low-pressure vortex of type 3 (Figure 8C) is to the south of that of type 2, with the warm air and rainstorm scope (Figure 7C) also located farther south. In type 4 (Figure 8D), the location of the low-pressure vortex center is similar to that in type 3 (Figure 8C), but the vortex is more east-west oriented. The central and southern parts of the NEC are controlled by warm and moist air. There is a high- θ e anomaly center of more than 8 K in the southeast of the NEC. Although the location of the center of the low-pressure vortex and the spatial distribution of the high- θ e in type 5 (Figure 8E) are similar to type 2 (Figure 8B), the northeast-southwest stretch of the low-pressure vortex is more remarkable. The northeastward transport of warm and moist air is more obvious, and the high- θ e anomaly center in the southeastern NEC is also stronger, which leads to a larger scope of rainstorms (Figure 7E) than that of type 2 (Figure 7B).

Water vapor transport and convergence are indispensable for the occurrence of heavy precipitation. Figure 9 shows water vapor transport and convergence in the whole atmosphere layer under different circulation patterns. In the NEC, southwesterly wind transport and convergence are apparent in type 1 and 5, whereas westerly wind transport and convergence are dominant in type 2 and 4, and the wind convergence of type 3 is stronger than that of other types, resulting in different heavy precipitation characteristics (Figures 6, 7). Differences can also be found in the ratio of rainstorm-day accumulated precipitation under different circulation types. The AWSs of type 1, accounting for more than 50%, are concentrated in the central and southern parts of the NEC (Figure 9A). The AWSs of type 2 are mostly located in the northeast and southwest parts of the NEC (Figure 9B). Only four AWSs in type 3 account for more than 50%, which is the least among all five types (Figure 9C). The AWSs accounting for more than 50% of type 4 are also mainly in the west-southwest to the east-northeast direction (Figure 9D), while those of type 5 (Figure 9E) are widely distributed in the southwest-northeast orientation. The distribution of ASWs with a high proportion of precipitation shows consistency with water vapor convergence areas of different circulation patterns. Furthermore, the precipitable water in the NEC can reach more than 40 mm (not shown). However, for a rainstorm, water vapor of this magnitude is obviously insufficient. Therefore, the transport and convergence of water vapor under the influence of different circulations are of vital importance.