4.1 Vertical structure characteristics of SMJ
The EOF analysis for the SMJ and obtain two main modes. The two modes together contribute about 96% of the variance. The first mode reflects four levels of consistent variation (Fig. 2a), with a variance contribution rate of 65.66%, of which 850 hPa is the largest and 1000 hPa is the smallest. The second mode reflects the increase of 750hPa and the decrease of the other three levels (Fig. 2c), with a variance contribution rate of 30.35%. 850hPa is the smallest, and 925hPa and L1000hPa are similar, both greater than 850hPa, reflecting the vertical characteristics of the opposite variation. EOF mode's characteristics of SMJ are related to the results of Qiu and Sun (2013).
Comparing the strength of each level of SMJ (Fig. 2e), the core of SMJ is 925hPa, followed by 850hPa and 750hPa. The correlation analysis of SMJ in each level reveals that 750hPa is only 0.75 relate to 850hPa and not with other wind levels. The correlation between 925hPa and 1000hPa is good, reaching 0.88, followed by 850hPa is 0.72. The correlation between 850 hPa and 1000 hPa is 0.51 (all the above passes the 0.01 significance test). The correlation analysis results indicate a significant opposite variation within SMJ, and there may be different influencing factors.
4.2 Vertical structure characteristics of BOBCEF
The EOF analysis for the BOBCEF and obtain two main modes. The two modes together contribute nearly 99% of the variance. The first mode reflects that all levels are consistent (Fig. 3a). The variance contribution rate is 77.18%, of which 850 hPa and 925 hPa have good enhancement, but 750 hPa keeps the lowest enhancement. The second mode reflects the attenuation of 750hPa and 850hPa and the enhancement of the other two levels (Fig. 3c), with a variance contribution rate of 21.77%, of which 750hPa has the higher attenuation. The enhancement of 925 hPa and 1000 hPa is similar, reflecting the vertical characteristics' opposite variation.
Comparing the strength of each level of BOBCEF (Fig. 3e), the core of BOBCEF is 1000hPa in most years, rising to 925hPa in some years, while 850hPa and 750hPa become small. The correlation analysis of BOBCEF of each level shows that the correlation between 750hPa and 850hPa is 0.76, 925hPa is 0.35, and is not related to 1000hPa. The correlation between 925hPa and 1000hPa is good, reaching 0.99, followed by 850hPa is 0.85. The correlation between 850 hPa and 1000 hPa is 0.77. Except that 750 hPa and 925 hPa pass 0.05, the rest pass the 0.01 significance test. The results of correlation analysis demonstrate that BOBCEF also has a significant opposite variation, but compared with SMJ, the difference is less.
4.3 Vertical structure characteristics of SCSCEF
The EOF analysis of the SCSCEF displays that there are two main modes. The two modes together contribute more than 99% of the variance. The first mode reflects the consistent variation except for 750hPa (Fig. 4a). The first mode variance contribution rate is 86.81%, and the enhancement level of 850-1000hPa is identical. The second mode reflects the attenuation of 750hPa and 850hPa and the minor enhancement of the other two levels (Fig. 4c). The variance contribution rate of the second mode is 12.35%, of which 750hPa has the higher attenuation. Two modes of SCSCEF are different when compared with SMJ and BOBCEF. The first mode is only consistent with the lower three levels, and the second mode is inconsistent with all four levels because the enhancement of the lower two levels is almost negligible.
Comparing the strength of each level of the SCSCEF (Fig. 4e), the core of the SCSCEF always keeps at 925hPa, followed by 1000hPa, 850hPa, and 750hPa core becomes smaller and smaller with height. The correlation analysis of SCSCEF of each level shows that 750hP does not correlate with the other three levels (1000 ~ 850 hPa). The correlation between 925hPa and 1000hPa is good, reaching 0.99, followed by 0.91 with 850hPa. The correlation between 850hPa and 1000hPa is 0.77, all of which pass the 0.01 significance test. The results of correlation analysis show that the upper and lower levels of SCSCEF are very different, the change rates of the lower three levels are relatively similar, and 750hPa has its independence.
4.4 Vertical structure characteristics of CSCEF
EOF analysis of CSCEF displays two main modes. The two modes together contribute more than 99.6% of the variance. The first mode reflects the consistent variation (Fig. 5a), with a variance contribution rate of 97.10%, with a higher proportion of all CEFs. The 750hPa enhancement is weak, only less than half of the other three levels. The second mode reflects the attenuation of 750hPa and 850hPa and the negligibly slight enhancement of the 925 and 1000 hPa levels (Fig. 5c). The variance contribution rate is 2.5%, of which the attenuation of 750hPa is the largest, and the attenuation of 850hPa is the smallest. The second mode of CSCEF is similar to the second mode of SCSCEF, which may have identical influence factors.
Comparing the strength of each level of CSCEF (Fig. 5e), the core of CSCEF always keep at 925hPa, followed by 1000hPa, 850hPa, and 750hPa becomes smaller and smaller with height, which is consistent with SCSCEF. The correlation analysis of CSCEF at each level shows that 750hP and 850hPa is 0.49, 925hPa is 0.35, and 1000hPa is 0.33. The correlation between 925hPa and 1000hPa is better, reaching 1.0, and 850hPa is 0.98. The correlation between 850hPa and 1000hPa is 0.97(All the above pass the 0.01 significance test). The results of correlation analysis show that the differences between upper and lower SCSCEF are relatively small, and the changes between upper and lower SCSCEF are comparably similar, which are strongly affected by the same factors.
4.5 Vertical structure characteristics of NGCEF
EOF analysis of CSCEF shows that there are two main modes. The two modes together contribute more than 99.6% of the variance. The first mode reflects the consistent variation of all levels (Fig. 6a), with a variance contribution rate of 92.72%. The 750hPa enhancement is weak, and one-third of the other three core levels are similar. From Fig. 6c, the second mode has reflected the attenuation of 750hPa and 850hPa and the slight enhancement with the two levels (1000 hPa and 925 hPa). The variance contribution rate is 6.89%, of which 750hPa is the largest and 850hPa is the smallest. The two modes of NGCEF and CSCEF are almost identical, and the two CEFs are similar in space and may have similar influence factors.
Comparing the strength of each level of NGCEF (Fig. 6e), the core of NGCEF always keep at 925hPa, followed by 1000hPa, 850hPa, and 750hPa are smaller and smaller with height. The correlation analysis of CSCEF at each level shows that the correlation between 750hP and 850hPa is only 0.56, and the correlation between 925hP and 1000hPa is better, reaching 1.0, followed by 850hPa is 0.92. The correlation between 750hP and 850hPa is 0.89, all of which pass the 0.01 significance test. The correlation results reveal that NGCEF has a higher difference from upper to lower, and there may be different influencing factors.
4.6 Vertical structure characteristics of EPCEF
EPCEF obtains two main modes from EOF analysis. The two modes together contribute about 90% of the variance. The first mode is the mode with the opposite variation (Fig. 7a), and the variance contribution rate is 68.53%, which reflects the increase of 750hPa. The other three levels are weak, and the extent of weakening is close to and significantly higher than the increase of 750hPa. The second mode reflects a significant decrease of 850hPa, a slight decrease of 750hPa, almost unchanged of 925hPa, and a significant increase of 1000hPa (Fig. 7c). The variance contribution rate is 21.87%, also reflects the opposite variation. The two modes of EPCEF are opposite variations, and the changes are not consistent when compared with the upper and lower levels of NGCEF have higher differences.
Comparing the strength of each level of the EPCEF (Fig. 7e), the core of the EPCEF is 1000hPa in most years, but it shifts to 925hPa in some years, 850hPa and 750hPa become small, and 750hPa is north wind in most years. The correlation analysis of EPCEF in each level indicates 750hPa is not related to 850hP and has a correlation of -0.52 and − 0.35 with 925hPa and 1000hPa (through 0.01 and 0.05 significance tests). The correlation between 925hPa and 1000hPa is 0.73, and the correlation with 850hPa is 0.76 (through 0.01 significance tests). There is no correlation between 850hPa and 1000hPa. The results of correlation analysis also show that the EPCEF has a higher difference from upper to lower. The thickness of the south wind is thin.
4.7 Vertical structure characteristics of ALCEF
EOF analysis obtains two main modes from EOF analysis. The two modes together contribute more than 93% of the variance. The first mode is the mode with the opposite variation (Fig. 8a), and the variance contribution rate is 74.77%, which reflects the increase of 750hPa. The other three levels are weak, and the degree of weakening is 925hP and 1000hPa stronger, and 850hPa is weak, and both are significantly greater than the increase of 750hPa. The second mode reflects a significant decrease of 750hPa and 850hPa, a slight increase of 925hPa and 1000hPa (Fig. 8c), and the variance contribution rate is 18.6%, which is also the opposite variation. The two modes of ALCEF are opposite variations, which is consistent with EPCEF, indicating that there are higher differences between the upper and lower levels of ALCEF, and the changes are inconsistent.
Comparing the intensity of each level of ALCEF (Fig. 7e), the core of EPCEF is 1000hPa in most years, 925hPa, 850hPa, and 750hPa will become smaller and smaller with the increase of height. The correlation analysis of ALCEF at each level shows that 750hP has nothing to do with 850hP, and the correlation with 925hPa and 1000hPa is -0.36 and − 0.42, respectively, through the 0.05 significance test. The correlation between 925hPa and 1000hPa is better, reaching 0.94, followed by 850hPa is 0.6. The correlation between 850 hPa and 1000 hPa is 0.48, passing the 0.01 significance test. Correlation analysis also shows that ALCEF varies significantly from upper and lower, and there is a negative correlation between the 750hPa and lower levels, although not as significant as EPCEF.