Jurnal Internasional Suatu Prosedur Objektif untuk Mendefinisikan Vortex Circumpolar – Bushra – 2019 – Ilmu Bumi dan Luar Angkasa
5.1 Validation Approach
The results show that the new approach identifies stronger relationships with the teleconnection index, compared to those reported for the same time period by Wrona and Rohli ( 2007 ). In particular, 12 (12) were significant ( α = 0.05) correlation with area ( R c ) identified, compared to 10 (6) by Wrona and Rohli (  2007), for 6 months analyzed (Table 2 ). In general, the similarity of magnitude and sign of correlation in the matrix (besides being stronger in this study) between this study and Wrona and Rohli's research ( 2007 ) corroborates these findings.
|Months||Current research||Wrona and Rohli ( 2007 ) 1945-1914|
|AO||PNA||PDO||SOI||NIÑO3.4||AO||NAO||PNA||POD  SOO] .4|
| r Value
|r Value|| p Value
 r Value
|Value|| r Value
|p Value||r r ] Value||p Value||Value of|| p
| r Value
 p Value
|p Value||Value|| p
|r Value|| p p ] Values
|Des||−0.454||0.030||−0.397||0.023||0.240||0.852||0.360||0.046||– 0.116 ||0.598||−0,709||−0,527||0.010||19709  0.356||0.065  0.076||0.730||– 0.012||0.960||−0,540||0.042||– – 0,289||0.078||0.337||– 0.005||0.981||– 0,270||0.089||0.116  0.599||−0,649||– 0.412||0.051||0.333||0.120  0.368||0.061||– – 0.267  0.219||0.339||0.112|
|February||−0,678 [0000||−0,530 19659309] – 0,204||0.351||– 0.139||0.527||0.340||0.032||−0.669||−0,647||.50,562||0.005||0.218||0.317||0.276||0.203||– 0.112||0.612||0.119||0.588||−0,567||0.005||0.034||0.877||1930  1930] 0.332||– 0.205||0.348||0.099||0.653||0.003||−0.415 [1965930119309 1930] 1930 0.419||0.052  – 0.198||0.365||0,380|
|Jul||−0,631||0.001||−0,466 19659309 ||0.159||– 0.077||0.726||– 0.012||0.957||– 0.386||0.069||0.258||0.344||0.136||−0,549||0.007  19659325] Oct||– 0.221||0.312||−0,358||0.043||– 0.103||0.639||– 0.107||0.626||– 0.027||0.903||– 0.240||0.269||– 0.289||0.181||– 0.262||0.227||0,170||0.366||0.086||– – 0.087||0.693||– 0.117 ||0,594|
|R c 19459012|
|Des||0.541||0.008||0.125 1971||−0.375||0.048||0,416||0.048||– 0.264||0.095||0.157||0.475||0.491||0.017||0.526||– 0.398||0.060||– 0.144||0.512||– 0.138||0.529||0.3121|
|Jan||0.152||0.488||0.230||0.091||0.091||] – 0.304||0.082||0.523||−0,360||0.049||0.214||0.328||−0,660||– 0.289||0.180||0.050||0.821||– 0.004||0.984|
|February||0.074||0.736||– 0.182||0.406||−0.423||0.044|| – 0.163
|– 0.006||0.979||– 0.067||0.763||0.142||– 0.126||0.565||– 0.254||0.242||– 0.292||0.176||0.003||– 0.045||0.838|
|Apr||0.629||0.001||0.178||0.416||– 0.295||0.172||– 0.285||0.079||0.243||0.264||– 0.186 ||0.396||0.163||0.457  0.393||0.064||– – 0.129||0.558||– 0.261||0.230||0.147||0.502||– 0.174||0.430|
|Jul||0.630||0.001||0.622||0.002||…||…||] …||0.076||0.286||– 0.166||0.448||0.057||0.797||0.253||0.244||…||…||0.294||0.174||19689306  Oct||0.551||0.006||0.353||0.098||– 0.181||0.409||0.079||0.248||0.254||0.004||0.986||0.445  0.033||0.114|| 1930] 1930
- Notes . Significant correlations on 
AO had the strongest and most significant relationship for the CPV area and R c with results consistent with those reported by Wrona and Rohli ( 2007 ), as shown in Table 2 . Especially, in every winter month, and also in April and July, the warm (cold) phase of AO is related to CPV which is smaller and more circular (bigger and more non-circular). These results support the theoretical arguments of smaller (larger) CPV when midlatitudes are warmed (cooled), as in the positive (negative) AO regime. The midline high gradient that is strengthened (attenuated) as long as AO is positive (negative) (Thompson et al., 2000 ) also induces more (less) circular CPV, with thermal conditions of warm (cold) phases tends to shrink (expand) CPV. Likewise, with a characteristic increase in zality (meridionality), the positive (negative) phase of NAO is associated with smaller (larger) and more (less) circular CPV but with fewer months showing a significant relationship. Because AO and NAO are related to each other (Marshall et al., 2001 ; Rogers & McHugh, 2002 ), similarities in correlation between NAO and CPV also corroborate the findings.
Although there was no significant relationship with the area found, the PNA pattern also had a strong association with CPV R c . As expected, the amplification (deamplification) of the ridge configuration was associated with significantly lower (higher) R c in each of the three winter months. The implication is that the strengthening of the Rossby wave train across significant parts of the hemisphere encourages the amplification of the adjacent Rossby ridge configuration in response, while significantly changing the net CPV area. Another implication is that the smoothing algorithm was introduced here performed well, because it preserved the relationship that is known with most certainty to exist; waviness (or lack thereof) in the PNA pattern should coincide with low (or high) R c . Furthermore, the results are again the corroborate of those of Wrona and Rohli ( 2007 ), but the method was used to display the statistically significant results of the winter month of January.
As suggested in previous research (Angell, 1992 ; Frauenfeld & Davis, 2003 ), ENSO also shows some relationships to the CPV area and R c as identified in this research. Specifically, smaller CPV occurs during the La Niña (El Niño) phase, with significant associations occurring in December and February (as defined by the SOI, which defines the El Niño phase negative values) or February only (as defined by Niño3.4, which represents the El Niño phase through positive SST anomalies). The implication is that the polar front is shifted anomalously southward (northward) by the presence of a colder (warmer) than a normal winters during La Niña (El Niño). Notably, the insignificant correlations in other months are often of opposite signs. As for the cases for AO, NAO, and PNA patterns, the ENSO relationships described here were undetected by Wrona and Rohli ( 2007 ); instead, they found a relationship only in July (Table 1945-1913), but because of the known strength of ENSO associations in winter, our results are more plausible.
Finally, a negative relationship between the PDO and R c was observed but only in December (Table 2 ). This is a negative phase, or warm (cold), phase of the PDO (which is characterized by a long-term (20-30 years) periodic oscillations in the tropical central and eastern Pacific Ocean) creates greater (lesser) undulation in the ridges and troughs of CPV and thus decreases (increases) the NHTCPV's circularity (Newman et al., 2003 ). Because of the long-term periodic nature of the PDO, a 23-year study period may not represent the true nature of the PDO-induced variability. Moreover, this relationship was undetected by Wrona and Rohli ( 2007 ), who instead found a (negative) relationship only in October.
5.2 Extension of the Time Series
The time series is extended to all 12 months of the January 1979 to December 2017 period. Many, but not all, of the patterns that emerge are similar to those of the shorter time series. The AO remains the most direct correlation with the CPV. In 9 of the 12 months, a warm (cold) AO is linked to a smaller (larger) CPV (Table  3 ). In contrast to the 1979–2001 period, this correlation is somewhat weaker in winter than the other months, with 2 of the 3 months lacking a significant relationship are January and February. The findings for R c  also echo those for the shorter time series, as 10 of the 12 months show that warm (cold) AO is linked to more (less) circular CPV. Interestingly, again January and February are the months in which this relationship is not significant.
|r Value||p Value|| r Value
|r Value||p Value||r Value|| p Value
|p Value||r Value||p p ] Value|
|Dec||−0,325||0.043||– 0.061||0.712||0.462||0.003||0.0793||0.327||0.064||– 0.189||0.249|
|Jan||– 0.034||0.835  0.356||0.026||0.401||– 0.056||0.733||– 0.154||0.350  0.287||0.077|
|February 19,192,9063 0.990||0.286||0.078||0,167||– 0.164||0.317  0.130||0.430||– 0.216||0.186|
|Apr  170.517||0.001||0.724||0.218||0.183||0.239||0.143||– 0.190||0.246||0.180||0.272|
|−0,524||0.001||– 0.221||0.177||0.044||0.790||0.038||0817||– 0.193||0.238||– 0.178||0.278|
|Jun||– 0.495||0.001||−0.409||0.010||0.198||0.227||0.147||0.373||– 0.275||0.0 90||– 0.102||0.535||−0,712||−0,503||0.001||0.210||0.201||0.183||0.266||– 0.235||0.150||0.153||0.353|
|Aug||– 0.398||0.055||0.175||0828||0.656||0.011||0.948||– 0.067||0.684||– 0.107 ||0.515|
|Sep||−0,541||0,000||0.120||0.468||0.418||0.008  – 0.055||0.737||0.092||– 0.170||0.302|
|Oct||−0.403||0.048||.30.352||0.028||0.772||– 0.045||0.786|| – 0.041
|– 0.196||0.231||−0,493||0.001||– 0.173||0.292||0.382||0.016||0.317||0.049||0.031||0.852||0.115  0.487|
|R c 19459012|
|Dec||0.401||0.011||0.090||0.586||−0.456||0.004||– 0.288||0.076||– 0.254||0.118||0.190||0.248|
|Feb||0.302||0.052||0.016||0.921||−0,503||0.001||– 0.127||0.442||0.149||0.365||– 0.120||0.466|
|Apr||0.606||0.099||0.548||0.017||−0.330||0.040||0.221||0.175||– 0.252 1945.||0.122|
|May||0.570||0.271||0.095||−0,370||0.021  – 0.165||0.316||0.204||0.213||0.038||0.818|
|Jun||0.489||0.338||0.035||−0.405||0.011||] – 0.231||0.157||0.179||0.035||0832|
|Jul||0.731||0.604||−0.363||0.023||– 0.253||0.120||0.284||0.080||– 0.262||0.108|
|Aug||0.502||0.001||– 0.027||0868||−0,590||0.064||0.699||0.087||0.599||0.112 [1 9659063] 0.496|
|Sep||0.503||0.001||– 0.172||0.294||−0,344|| 0.032||– 0.052||0.753||190.330||0.040||0.157||0.341|
|Oct||0.555 ||0.604||0.277||0.088||0.021||0.900||0.085||0.608||0.068  0.680|
|Nov||0.594||0.294||0.069||−0,664||−0,391||0.014||– 0.092||0.578|| 0167 |
 0311  Note [1945901million]. Correlations significant at α
The linkages to the NAO also largely echo the results of the 1979–2001 period and corruption relationships between the NAO and AO (Table 3 ). Four months (March, June, July, and October) have CPV areas with significant positive relationships to the NAO, and only 1 month (January) shows a significant negative correlation. (June, July, and October) also shows a positive link between the NAO and R c . Thus, a positive (negative) NAO is associated with smaller and more (circular) circular CPV, at least for June, July, and October.
While the PNA pattern shows no links to CPV areas in the shorter time series, the patterns of exposure to PNA are significantly positive in relation to area, in December, August, September, and November ( Table  3 ). While at first glance, this result might suggest a smoothing algorithm, in which adjacent troughs might be connected instead of separated by a ridge, the relationship between the shorter time series, along with the presence of significant negative relations between the PNA index and R c  in 11 of the 12 months, suggesting that the smoothing algorithm succeeded.
Looking to the Pacific Ocean, the PDO displays few relationships to the CPV (Table 3 . Only November has been correlated with both area and R c with a positive (negative) PDO coincident with larger (smaller) and less (more) circular CPV. March and April share this same PDO- R c relationship but display no significant link between PDO and area.
ENSO shows a weaker relationship to the CPV than occurred over the shorter time series. None of the relationships between CPV areas and ENSO that appeared in 1979–2001 period were evident over the 1979–2017 period (compare Tables 1945-1913 2 and 1945-1955 3 . However, the relationships to R c  are mostly the same over the two time series with ENSO, as defined by both the SOI and Niño3.4 indices . El Niño (La Niña) in January is associated with a less (more) circular CPV. September, which was not analyzed in the shorter time series analysis because it was not analyzed by Wrona and Rohli (2007), also shows some evidence of an ENSO link to Rc but only when ENSO is defined by SOI and in the opposite direction as January; El Niño (La Niña) in September is associated with a more (less) circular CPV.