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The daily and monthly mean data used in this study come from the NCEP−NCAR reanalysis (Kalnay et al., 1996) for May from 1948 to 2017. The geopotential height and zonal wind are archived on a 2.5° × 2.5° horizontal grid at 17 vertical pressure levels from 1000 to 10 hPa. Data of the surface air temperature at 2 m (T2m) are available on a T42 Gaussian grid with 192 × 94 points. We also use the gridded daily precipitation data on a 0.5° × 0.5° grid over Eurasia (15°S−84°N, 15°E−165°W) for 1951−2007 from the Asian Precipitation—HighlyResolved Observational Data Integration Towards Evaluation (APHRODITE) of Water Resources Project by the Research Institute for Humanity and Nature (RIHN) and the stateoftheart daily precipitation datasets on highresolution grids for Asia developed by the Meteorological Research Institute of Japan Meteorological Agency (MRI/JMA; Yatagai, 2012). Finally, this study adopts the monthly teleconnection pattern indices in May, which are provided for 1950−2017 by the CPC (http://www.cpc.ncep.noaa.gov/data/teledoc/telecontents.shtml). The indices include the NAO index, Scandinavian pattern (SCA) index, East Atlantic pattern (EA) index, East Atlantic/West Russia pattern (EAWR) index, and POL index.
In this study, the POL pattern is defined in May by using the SOM method based on the daily Z500 field for the study area (40°–80°N, 60°W–180°). The following preprocessing procedure is undertaken before the SOM classification. (1) In each year, the daily areamean (40°–80°N, 60°W–180°) values of Z500 are calculated for 1–31 May, constituting a time series of 31 days. Then, the seasonal trend of this areamean time series is calculated. (2) An “anomaly” field (referred to as ZA500 field) is obtained by subtracting the seasonal trend of the areamean time series from the original daily Z500 fields for 1–31 May of that year. The daily ZA500 fields with a sample length of 2170 days (70 × 31 days) are taken as input samples for the SOM analysis. In the preprocessing steps, the purpose of removing the areamean trend is to highlight the spatial heterogeneity of the input field, eliminate the longterm climate trend associated with global warming, and retain consistent signals of daily “anomaly” fields. In addition, for convenience of discussion, a climatological mean ZA500 field in May is also defined and calculated in a similar manner as the daily ZA500 field. Specifically, the climatological mean ZA500 field in May is obtained by first subtracting the areamean Z500 quantity from the monthly mean Z500 field in each year and then averaging the results over 70 yr (1948–2017).
In the SOM classification process, the larger the cluster number (N_{C}), the smaller the differences among members of each cluster and the average distances with respect to all pairs of clusters. However, in practice, N_{C} should not be excessively large. Instead, N_{C} should be small enough to allow for the classification results to be practically meaningful. Following the method of Lee et al. (2017), we determine the optimal N_{C} through the following steps: (1) all the classification results with 2 ≤ Nc ≤ 20 are obtained through repeating the SOM classification process, and (2) the mean pattern correlation coefficient (R) is calculated for N_{C} clusters, as noted in Lee at al. (2017). A large N_{C} corresponds to a high R, and vice versa (Fig. 1a). An optimal N_{C} can be searched if (1) R is as high as possible to ensure the overall similarity among members of each cluster, and (2) the average distance (D) with respect to all pairs of clusters is as large as possible to ensure significant differences among all clusters. D can be calculated based on the Ward’s distance between each pair of clusters (Ward, 1963; Xu et al., 2013). A large N_{C} corresponds to a low D, and vice versa (Fig. 1b). The details of the determination of an optimal N_{C} will be exemplified in Section 3.1.
Figure 1. Variation of (a) the average pattern correlation coefficient (R) between each member and the corresponding centroid of clusters, (b) the average distance between each pair of clusters (Ward’s distance; D), and their corresponding slopes with the number of nodes ( N_{C}) in the SOM neural network.
In this study, the highfrequency transient eddy kinetic energy (EKE) anomalies at 300 hPa are used to characterize the variability of major storm tracks and the intensity of transient synoptic wave processes. The EKE is calculated with a highpass filter with an 8day cutoff period based on daily 300hPa horizontal wind data (Pelly and Hoskins, 2003; Lehmann et al., 2014; Xie and Bueh, 2017a). The daily EKE can be expressed as follows:
$${\rm{EKE}} = {{({u'^{2}} + {v'^{2}})} /2},$$ (1) where u' and v' are 8day high passfiltered 300hPa zonal and meridional winds, respectively.
We define blocking events with the method proposed by Pelly and Hoskins (2003). From a potential vorticity (PV) perspective, Pelly and Hoskins (2003) defined a onedimensional blocking high index B (also called PH03 index) according to the reversal of the potential temperature (θ) at dynamic tropopause. The dynamic tropopause is defined as the 2 PVU (1 PVU = 10^{−6} m^{2} s^{−1} K kg^{−1}) surface. In this method, a daily B index at every grid (λ_{0}, φ_{0}) along the latitude of the maximum climatological mean EKE is calculated as
$$B = {2 / \Delta }\varphi \int_{{\varphi _0}}^{{\varphi _0} + {{\Delta \varphi } / 2}} {\theta {\rm d}\varphi }  {2 / \Delta }\varphi \int_{{\varphi _0}  {{\Delta \varphi } / 2}}^{{\varphi _0}} {\theta {\rm d}\varphi },$$ (2) where Δφ is set to 30°. The B index at a particular longitude is designated as 1 if B is positive for at least 15° of longitude, and there are grid points with positive B values within 10° of longitude of the particular longitude for at least 4 consecutive days; otherwise, it is specified as 0. Obviously, the B index represents a largescale meridional gradient of θ.

Based on the method of determining the optimal N_{C} as described in Section 2, all classification results with 2 ≤ Nc ≤ 20 are obtained through repeating the SOM classification process with the same daily ZA500 field input to 1 × N_{C} grid maps. As shown in Fig. 1, as N_{C} increases, R gradually increases (Fig. 1a), and D gradually decreases (Fig. 1b). Notably, as N_{C} increases to a large number, the absolute change rates of both R and D tend to be stabilized. To illustrate the change rates of R and D, the slopes of R and D curves are also drawn in Fig. 1. As N_{C} increases from 2 to 7, R increases gradually. However, as N_{C} turns greater than 7, R reaches a relatively stable value, as indicated by the slope of R. A similar variation is also observed for D. These facts suggest that daily ZA500 fields can be categorized into at least 7 clusters, allowing for sufficient intracluster similarities and intercluster differences, thereby meeting the classification requirements. To highlight the spatial continuum of representative patterns in the topological ordering, we adopt a 3 × 3 SOM grid, rather than a 1 × 7 SOM grid. The 3 × 3 SOM patterns incorporate the 7 SOM patterns with pattern correlation coefficients from 0.66 to 0.98.
Figure 2 shows nine SOM patterns over 40°–80°N, 60°W–180° in May over 1948–2017. The number of occurrence days of each SOM pattern is indicated in brackets. As explained by Kohonen (1990, 1997), in the SOM neural network, similar SOM patterns are arranged on neighboring nodes, whereas dissimilar patterns are separated on distant nodes. Thus, differences among SOM patterns can be indicated by distances among nodes. For convenience, the nth SOM pattern is referred to as SOMn (e.g., the first and second SOM patterns are referred to as SOM1 and SOM2, respectively). To facilitate comparison between each SOM pattern and the corresponding climatological mean field, the climatological mean ZA500 field in May is shown in Fig. 3. Because the areamean value is subtracted from the ZA500 field, the zero contour lines (the thick blue and green solid lines in Fig. 2 and the thick blue solid line in Fig. 3) can approximately reflect the alignment and shape of the polar vortex. As demonstrated in Fig. 2, significant differences among the nine SOM patterns are primarily reflected in the polar vortex activity and the associated wavelike circulation over middle and high latitudes. In both the SOM1 and SOM5 patterns, the polar vortex is active over the subarctic region of the Eurasian continent. However, the polar vortex activities differ between these two SOM patterns. Specifically, the polar vortex apparently intrudes towards northern Europe in the SOM1 pattern, whereas it mainly invades southward to the Asian continent in the SOM5 pattern (Figs. 2a, 2e, 3). The polar vortex activity over the subarctic region of the Eurasian continent is relatively weak in both the SOM7 and SOM9 patterns. However, the mid and highlatitude wavelike circulations differ significantly between these two SOM patterns (Figs. 2g, 2i, 3). In particular, the SOM5, SOM7, and SOM9 patterns are related to anomalous polar vortex activities over the subarctic Asia; therefore they may represent the POL pattern. In the SOM3 and SOM4 patterns (Figs. 2c, d), the region of Iceland/Greenland is controlled by a planetary ridge and trough, respectively. Thus, these two patterns may be related to NAO. The SOM2, SOM6, and SOM8 patterns are characterized by three distinct wavelike circulations over the North Atlantic/Europe (Figs. 2b, f, h).
Figure 2. (a–i) Composite ZA500 fields of nine SOM patterns (SOM1–SOM9) over 40°–80°N, 60°W–180° in May during 1948–2017, with the number of occurrence days shown in the bracket. The ZA500 is constructed by removing the seasonal trend of areamean (40°–80°N, 60°W–180°) Z500 in each year, representing an anomaly with respect to the areamean (see text for details). The contour interval is 30 m. The thick blue line represents the zero line; the red solid line and blue dashed line represent positive and negative values, respectively; and the green line represents the zero line in May of the climatological mean ZA500 field.
Figure 3. As in Fig. 2, but for the climatological mean ZA500 field in May over 1948–2017.
For comparison with conventional teleconnection patterns, Fig. 4 shows the composite Z500 anomaly fields corresponding to the nine SOM patterns in May over 1948–2017. Each composite field is calculated based on all members of the corresponding SOM pattern (the sample number of each cluster is indicated in brackets). For convenience, such composite patterns are referred to as the first to ninth circulation patterns (C1–C9) in sequence. Here, Z500 anomalies are calculated relative to the climatological mean Z500 field and differ from the input “anomalies” of the SOM analysis (i.e., ZA500). To eliminate the interdecadal variation and climate trend, a dynamic climatological mean state is used in this study. Following the CPC’s new method of calculating the Oceanic Niño index (L’Heureux et al., 2013), we assign a fixed 30yr average to each 5yr period centered on the first year of that 5yr period as the climatological mean. For example, anomalies in the period 1956–1960 are relative to the climatological mean of the period 1941–1970, anomalies in the period 1961–1965 are relative to the climatological mean of the period 1946–1975, and so on. In total, eight fixed 30yr climatological mean states are applied in the current study (see Table 1).
Figure 4. (a–i) Composite fields of Z500 anomalies (shading, m) of the nine circulation patterns (C1–C9), with respect to the climatological mean Z500 field in May over 1948–2017 (see text for details). The value in each bracket denotes the sample number of the corresponding SOM pattern shown in Fig. 2; only composite anomalies in the 95% confidence interval are shaded; and the lowest point in each panel is drawn at 30°N, 90°E.
5yr 1948–1970 1971–1975 1976–1980 1981–1985 1986–1990 1991–1995 1996–2000 2001–2017 30yr 1948–1980 1956–1985 1961–1990 1966–1995 1971–2000 1976–2005 1981–2010 1986–2017 Table 1. Information on the 30yr climatological mean period centered on the first year of each 5yr period (or equivalent)
Because there is a onetoone correspondence between Figs. 2 and 4, the C1–C9 patterns in Fig. 4 characterize the nine prevalent physical modes in May over North Atlantic/Eurasia. The patterns clearly reflect significantly different polar vortex activities and wave trainlike circulation anomalies. Of the nine patterns, the C5, C7, and C9 patterns are similar to the conventional POL pattern, and all reflect anomalous polar vortex activities over the subarctic Asia. In the following section, we identify the POL pattern by analyzing the C1–C9 patterns.

We recognize the attributes of C1–C9 patterns by analyzing their spatial and temporal correlations with the conventional teleconnection patterns defined by the CPC. It should be noted that conventional EOF analysis embodies linear characteristics, whereas SOM analysis reflects nonlinear characteristics. Therefore, differences would undoubtedly be identified between the circulation patterns obtained by the SOM method and those defined by the CPC.
To facilitate comparisons, the POL pattern in May defined by the CPC (Barnston and Livezey, 1987) is shown in Fig. 5, which is obtained by regressing the Z500 anomaly fields in May against the time series of the CPC’s POL index in the same month over 1948–2017. As seen in Fig. 5, the conventional POL pattern in May is characterized by a meridional dipole pattern with an anomaly center over the subarctic region of the Eurasian continent and another anomaly center with an opposite sign over Lake Baikal.
Figure 5. Z500 anomalies in May regressed against the CPC POL index in May over 1948–2017 with one standard deviation. The contour interval is 5 m. The solid (dash) lines represent positive (negative) anomalies, and the zero lines are omitted. Light (dark) shading marks the region where the anomalies are significant at the 90% (95%) confidence level. The lowest point is drawn at (30°N, 90°E).
The pattern correlation coefficients (R_{s}) of the C1–C9 patterns with the NAO, SCA, EA, EAWR, and POL patterns defined by the CPC are summarized in Table 2. The spatial correlations are calculated in the same domain (40°–87.5°N, 0°–357.5°E). The NAO, SCA, EA, and EAWR patterns are obtained by the same regression method of constructing the POL pattern in Fig. 5.
NAO SCA EA EAWR POL C1 −0.28 −0.45 0.24 0.05 0.32 C2 −0.18 −0.48 −0.31 0.31 0.02 C3 −0.71 0.23 −0.34 0.20 −0.32 C4 0.69 −0.38 0.52 0.17 0.37 C5 0.07 0.20 −0.00 0.56 0.70 C6 −0.33 0.72 −0.19 −0.09 −0.17 C7 0.15 −0.42 0.17 −0.45 −0.46 C8 0.35 0.13 0.09 −0.59 0.10 C9 0.16 0.28 −0.14 −0.55 −0.75 Note: CPC teleconnection patterns are obtained by regressing the Z500 anomalies against the standardized CPC teleconnection pattern indices in May over the domain of 40°–87.5°N, 0°–357.5°E. The bold numbers signify that the absolute values of the correlation coefficients exceed 0.65. Table 2. Pattern correlation coefficients between the composite Z500 anomaly fields of the nine circulation patterns (C1–C9) and CPC teleconnection patterns
Meanwhile, the projection indices of the C1–C9 patterns are calculated by projecting the Z500 anomaly fields in May over 1948–2017 onto the C1–C9 patterns using the following formula (Goss et al., 2016; Lee et al., 2017):
$${P_{(t)}} = \frac{{\sum\nolimits_i {\sum\nolimits_j {{\varPhi '}({\lambda _i},{\varphi _j},t){\varPhi ^ * }({\lambda _i},{\varphi _j})\cos {\varphi _j}} } }}{{\sum\nolimits_i {\sum\nolimits_j {{{[{\varPhi ^ * }({\lambda _i},{\varphi _j})]}^2}\cos {\varphi _j}} } }},$$ (3) where λ_{i} (0° ≤ λ_{i} ≤ 357.5°E) is the longitude and φ_{j} (40°N ≤ φ_{j} ≤ 87.5°N) is the latitude for grid point (i, j); t is time; and Φ^{*}(λ_{i}, φ_{j}) represents the Z500 anomaly field in each of the C1–C9 patterns (Fig. 4) and Φ′(λ_{i}, φ_{j}, t) is the original Z500 anomaly field in May of each year (relative to the dynamic climatological mean state; Table 1). The temporal correlations (R_{t}) of the P_{(t)} with the NAO, SCA, EA, EAWR, and POL indices (provided by the CPC) are summarized in Table 3.
NAO SCA EA EAWR POL C1 −0.43* −0.49* 0.27 0.09 0.46* C2 −0.26 −0.47* −0.41* 0.44* 0.06 C3 −0.73* 0.20 −0.29 0.19 −0.30 C4 0.70* −0.29 0.41* 0.16 0.35* C5 0.09 0.17 −0.02 0.58* 0.75* C6 −0.48* 0.69* −0.17 −0.14 −0.24 C7 0.24 −0.40* 0.16 −0.54* −0.58* C8 0.44* 0.09 0.11 −0.67* 0.10 C9 0.17 0.23 −0.11 −0.56* −0.78* Note: The symbol * marks values that are significant at the 99% confidence level, and the bold numbers signify that the absolute values of the correlation coefficients exceed 0.65. Table 3. Correlation coefficients between the projection indices of the nine circulation patterns (C1–C9) and the CPC teleconnection pattern indices
As shown in Figs. 4, 5, the C5, C7, and C9 circulation patterns resemble the POL pattern in their spatial distributions. The negative anomaly center of the C5 pattern anchors over the northern Taimyr Peninsula, and its two positive anomaly centers are located over Lake Baikal and Northeast Atlantic/northern Europe, respectively. As displayed in Tables 2, 3, among the C1–C9 patterns, the C5 pattern has the highest R_{t} (0.75) and R_{s} (0.70) with the positive POL pattern. This finding suggests that the C5 pattern represents the positive phase of the POL pattern. For the C9 pattern, the subarctic region of the whole Eurasian continent is dominated by a positive anomaly band with its strongest center around the Barents Sea and by a negative anomaly band extending from Lake Balkhash to the Sea of Okhotsk. Among the C1–C9 patterns, the C9 pattern has the strongest negative R_{t} (–0.78) and R_{s} (–0.75) with the POL pattern (Tables 2, 3). This finding suggests that the C9 pattern represents the negative phase of the POL pattern. Regarding the C7 pattern, the positive anomaly zone is located over the subarctic Asia and extends eastward to the Bering Strait and Alaska, while its two negative anomaly centers are located over northeastern Atlantic/northern Europe and Lake Baikal, respectively. Among the C1–C9 patterns, the C7 pattern has the second strongest negative R_{t} (–0.58) and R_{s} (–0.46) with the POL pattern (Tables 2, 3). This finding suggests that the C7 pattern represents another negative phase of the POL pattern. Although both C7 and C9 patterns show the features of negative POL pattern, their horizontal structures differ considerably. In the SOM neural network (figure omitted), the distance between the C5 and C9 patterns is remarkably large, which is indicative of a significant difference between them. As representatives of the positive and negative phases of the POL pattern, the C5 and C9 patterns are not antisymmetrical in horizontal spatial structure. The C5 circulation pattern exhibits a notable wave trainlike distribution, whereas the C9 pattern is primarily characterized by a meridional dipole structure. Interestingly, the C5 and C7 patterns are antisymmetrical to each other in horizontal spatial structure; however, the positions and intensities of their anomaly centers over North Atlantic and East Asia slightly differ. Hereafter, the C5, C9, and C7 patterns are referred to as POL^{+}, POL1^{–}, and POL2^{–} patterns, respectively.
As anticipated, the R_{t} (R_{s}) values of the C3 and C4 patterns with the conventional NAO pattern are –0.73 (–0.71) and 0.70 (0.69), respectively (Tables 2, 3). These findings suggest that the C3 and C4 patterns correspond to the negative and positive phases of the NAO pattern, respectively. In addition, the C4 circulation pattern is also positively correlated with the EA pattern. As indicated in Tables 2, 3, the C6 pattern corresponds to the positive phase of the SCA pattern and is negatively correlated with the NAO pattern. The C8 pattern corresponds to the negative phase of the EAWR pattern and is simultaneously positively correlated with the NAO pattern. The C1 and C2 patterns can be considered as combinations of three conventional teleconnection patterns (Tables 2, 3). The C1 pattern is a combination of the NAO, SCA, and POL patterns; while the C2 pattern combines the SCA, EA, and EAWR patterns. Of the nine circulation patterns identified in this study, six of them (i.e., C3, C4, C5, C6, C8, and C9) notably correspond to different phases of the NAO, POL, SCA, and EAWR patterns defined by Barnston and Livezey (1987). However, a onetoone correspondence does not exist between the C1–C9 patterns identified in this study and the conventional teleconnection patterns.

Figure 6 shows the total number of occurrence days of POL^{+}, POL1^{−}, and POL2^{−} patterns in May over 1948–2017. On average, all these patterns (POL^{+}, POL1^{−}, and POL2^{−}) occur on approximately three days in May. However, they all exhibit remarkable interannual variability. For example, the POL^{+} pattern prevailed for 27 days in 1990, the POL1^{−} pattern occurred for 21 days in 1954, and the POL2^{−} pattern occurred for 13 days in 2005. In contrast, the patterns are absent in some years. In addition, all the POLlike patterns exhibit a notable interdecadal variation. The POL^{+} pattern occurred frequently in the 1960s and during the mid1980s to mid2000s, but it occurred less frequently in other periods. On the interdecadal timescale, as shown in Fig. 6, the periods when the POL^{+} pattern occurs frequently basically correspond to the periods when the POL1^{−} pattern occurs less frequently, and vice versa. The POL2^{−} pattern occurred frequently during mid1980s to mid1900s and in the 2000s.