The Relation between the North Atlantic Oscillation and SSTs in the North Atlantic Basin

Transcription

1 4752 JOURNAL OF CLIMATE VOLUME 17 The Relation between the North Atlantic Ocillation and SST in the North Atlantic Bain WEILE WANG, BRUCE T. ANDERSON, ROBERT K. KAUFMANN, AND RANGA B. MYNENI Department of Geography, Boton Univerity, Boton, Maachuett (Manucript received 14 October 2003, in final form 19 April 2004) ABSTRACT The author ue the notion of Granger cauality to invetigate the relationhip between the North Atlantic Ocillation (NAO) index and the ea urface temperature (SST) over the Northern Hemiphere. The Granger cauality analyi enure that any apparent oceanic influence upon the atmophere (a meaured by the NAO) i provided by the ocean and i not related to preexiting condition within the NAO itelf (and vice vera when looking at the atmopheric influence upon the ocean). Although thi tatitical technique doe not imply phyical forcing of one field on the other, it i generally more reliable compared to the imple lead/lagged correlation. Uing thi technique, the author find that on eaonal time cale, the preceding NAO anomalie influence on the wintertime SST field i rather retricted. Converely, preceding SST anomalie have a tatitically ignificant caual effect on the wintertime NAO. However, the caual relation between preceding SST and the wintertime NAO i limited to the Gulf Stream extenion; in contrat to the canonical tripole SST pattern typically aociated with the NAO, the author do not find that SST anomalie in either the Greenland or ubtropical region have a ignificant caual effect on the NAO. Thee reult ugget that the Gulf Stream SST have an important influence in initiating diturbance of the atmopheric circulation over the wintertime North Atlantic. 1. Introduction The North Atlantic Ocillation (NAO), which i uually defined by the difference in ea level preure between Iceland and the Azore, i the dominant pattern of atmopheric variability over the North Atlantic region, epecially in winter (Hurrell 1995; Kuhnir 1999). The NAO i trongly correlated with large-cale change in ea urface temperature (SST) acro the bain (Bjerkne 1964). However, the role that air ea interaction play in the dynamic of the NAO i not fully undertood. It i generally believed that atmopheric forcing dominate interaction over the North Atlantic bain and generate SST anomalie through turbulent heat fluxe or anomalou wind tre (Frankignoul 1985; Cayan 1992). Alternatively, ome ugget that the ocean participate in the dynamic via the influence of SST anomalie. Becaue the well-mixed ocean upper layer ha a large heat capacity, an oceanic thermal ignal can perit for everal month, which allow for a peritent thermal forcing of the overlying atmophere (Frankignoul 1985; Kuhnir et al. 2002). Evidence for oceanic forcing of the NAO i uggeted by tudie of climate model (e.g., Rodwell et al. 1999) Correponding author addre: Dr. Weile Wang, Department of Geography, Boton Univerity, 675 Commonwealth Ave., Boton, MA wlwang@bu.edu and obervational data (e.g., Czaja and Frankignoul 1999, 2002, hereafter referred to a CF99 and CF02, repectively). The latter (CF99; CF02), which ue maximum covariance analyi (MCA), indicate a ignificant correlation between the wintertime NAO (the firt MCA mode of 500-hPa anomalie in their analyi) and the leading mode of anomalou SST from the previou ummer. The link between ocean and atmophere at uch long lead eem to be a reult of the long peritence of the North Atlantic SST anomalie and thu erve a evidence for the oceanic forcing of the NAO (Kuhnir et al. 2002). However, imple correlation technique can be problematic when ued to aign caual order in highly coupled ytem uch a the atmophere and the ocean. The correlation between the wintertime NAO anomaly and SST anomalie from earlier eaon may be due to the peritence, or even influence, of preceding atmopheric anomalie, which alo influence the underlying SST during the previou eaon. Thu the reult decribed by Kuhnir et al. (2002) cannot exclude the poibility that the apparent oceanic forcing ignal i not uniquely provided by the ocean, but alo may have exited within the atmophere. To expand imple correlation between the NAO and SST anomalie, we introduce the notion of Granger cauality (Granger 1969). Granger cauality ha been ued to invetigate phyical ytem (Kaufmann and Stern 1997; Kaufmann et al. 2003) and i baed on the notion 2004 American Meteorological Society

2 15 DECEMBER 2004 WANG ET AL of predictability. In general, in a coupled ytem that involve two interacting field, Granger cauality tet whether pat value of one field (X) tatitically help to predict the current value of the other field (Y) better than uing pat value of Y alone. Should pat value of X contain information about current value of Y beyond that contained in the preceding Y equence (or any other variable contained in the information et), variability in the X field i aid to Granger caue (hereafter caue for implicity) variability in the Y field. Similarly, we can tet whether previou value of Y caue variability in the preent value of X. In thi paper, we ue Granger cauality to examine the relationhip between the NAO and SST. Section 2 decribe the methodology that i ued to tet for Granger cauality. Section 3 decribe the dataet, and the reult are decribed in ection 4. The implication for the link between SST anomalie and the NAO anomaly are ummarized in ection Methodology We tet for the preence and direction of Granger cauality between the NAO and SST anomalie following the procedure outlined by Kaufmann and Stern (1997). Thi procedure include two tep. In the firt tep, the two-way interaction between the NAO anomaly and each gridpoint SST anomaly are decribed uing a vector autoregreion (VAR) given by Eq. (1) and (2): t 1 1i t i 1i t i 1t NAO NAO SST e (1) and t 2 2i t i 2i t i 2t i-1 SST NAO SST e, (2) where,, and are regreion coefficient, e are error term, and i the lag length, which i determined with a likelihood ratio tet developed by Sim (1980). Equation (1) and (2) are derived from a tructural VAR (not hown), in which the current value of NAO and SST are a function of lagged value of the dependent variable and the current and lagged value of the independent variable (Ender 1995). The tructural VAR pecification [a well a the tandard form given in Eq. (1) and (2)] i conitent with the undertanding that the current (winter, e.g.) value of the eaonal NAO and SST anomalie depend not only on the concurrent anomalie of the other variable, but alo on their pat value, that i, from the previou fall, ummer, etc. To determine the direction of caual order, we etimate retricted form of Eq. (1) or Eq. (2) in which the caual variable i eliminated. For example, to tet whether SST anomalie caue variability in the NAO, we etimate a retricted form of Eq. (1) in which we eliminate the SST anomalie. Thi i done tatitically by retricting in Eq. (1) to zero a follow: t 1 1i t i 1t NAO NAO e. (3) Converely, we tet whether the NAO caue SST anomalie by etimating a retricted verion of Eq. (2) in which we eliminate the lagged value of the NAO index. The next tep i to tet whether the retricted etimate are tatically ignificantly different from the unretricted etimate. To do thi, we calculate a tet tatitic a follow: (RSSr RSS u)/, (4) RSS u/(t k) in which RSS i the um of the reidual quared; the ubcript r and u refer to the retricted and unretricted verion of Eq. (1) or Eq. (2), repectively; T i the number of obervation; k i the number of regreor in the unretricted verion of the equation; and i the number of coefficient retricted to zero in Eq. (3). The tet tatitic can be evaluated againt an F ditribution with and T k degree of freedom in the numerator and denominator, repectively, in order to evaluate the null hypothei that the variable eliminated from Eq. (1) (SST in the given example) doe not caue variability in the dependent variable (i.e., the NAO). For thi paper, value of that exceed the 5% threhold reject the null hypothei of no caual order, which indicate that the variable eliminated from the unretricted equation caue variability in the dependent variable. A tatitically ignificant increae in the RSS of the retricted verion of Eq. (3) relative to the unretricted verion of Eq. (1) indicate that the lagged value of SST have information about the current value of NAO beyond that in the lagged value of NAO alone. Eliminating the lagged value of SST reduce the explanatory power of the VAR, which increae the reidual um of quare. The tatitic quantifie the information uniquely contained in the lagged SST value and repreent the tatitical power of Granger cauality relative to imple correlation technique. A written, Eq. (1) and (2) aume that air ea interaction are contant over eaon. That i, the 1-eaon lag interaction between the SST and NAO i the ame regardle of the eaon under conideration (i.e., pring/ ummer, ummer/fall, or fall/winter). To relax thi retrictive aumption, we allow the coefficient to vary with lag length and eaon. Becaue winter i the eaon of interet, we modify Eq. (1) and (2) a follow: Winter 1 1i Winter i 1i Winter i 1t NAO NAO SST e and (5) SST NAO Winter 2 2i Winter i 2i Winter i 2t SST e. (6)

3 4754 JOURNAL OF CLIMATE VOLUME 17 FIG. 1. (a) The detrended wintertime (DJF) NAO, normalized uch that the variance i unity; (b) concurrent correlation map of NAO and SST during wintertime. Correlation coefficient (r) are hown in contour: the interval i 0.1, the minimum contour i 0.2, and poitive value are haded. The thick dark line how region where r exceed the 5% critical value. In Eq. (5) and (6), only winter value of the anomalou NAO and gridpoint SST appear on the left-hand ide. Thee winter value are predicted baed on value from previou eaon. Becaue the current time i winter, a lag length of 1 denote the previou fall, a lag length of 2 denote the previou ummer, and o on. The timing of thee lag implie that the tatitical methodology tet whether the SST (NAO) field from previou eaon contain information about the winterime NAO (SST) that i not contained in the preceding value of the NAO (SST) itelf. We recognize that the detection of Granger cauality doe not necearily imply a phyical caual mechanim between the two field. Concluion about the preence and direction of cauality depend on the validity of the tatitical model. Etimate may be biaed by the omiion of relevant variable [e.g., the ummer extent of now cover over northern North America and northern Euraia (Saunder et al. 2003)] that are in fact the caual variable. Depite thee limit, the cauality tet i more rigorou than lagged correlation tatitic becaue it remove fale poitive in which relation with lagged value are in fact the reult of autocorrelation within the predicted field (ee below). 3. Dataet The NAO index time erie i defined in Hurrell (1995) and Jone et al. (1997). Data for ea urface temperature are taken from the National Center for Environmental Prediction National Center for Atmopheric Reearch (NCEP NCAR) reanalyi monthly mean SST dataet, which ha global coverage with 192 (longitude) 92 (latitude) grid point at Triangular-62 reolution (approximately 2 latitude and longitude). A decription and evaluation of the reanalyi SST dataet can be found in Hurrell and Trenberth (1999). Thi analyi ue SST within the domain of 75N 20 S and The extenion of the SST domain beyond the North Atlantic bain reflect the conideration that SST over other ocean [e.g., the tropical Indo-Pacific region (Hoerling et al. 2001)] alo may influence the atmopheric circulation over the North Atlantic. Both the NAO index and the SST data are available monthly from January 1948 to December Monthly anomalie are created by ubtracting the monthly climatology ( ) from the monthly data. In addition, a linear trend i removed from the NAO time erie and the SST time erie at each grid point (concluion are the ame when a time trend i explicitly included in the tatitical model a oppoed to detrending the data a priori). Seaonal-average anomalie are calculated by averaging the three monthly value in the correponding eaon. The eaon are defined a March April May (MAM) for pring, June July Augut (JJA) for ummer, September October November (SON) for fall, and December January February (DJF) for winter.

4 15 DECEMBER 2004 WANG ET AL FIG. 2. Granger cauality analye uing eaonal data for the winter (DJF): (a) SST gridpoint variability caued by NAO and (b) NAO variability caued by each SST grid point. The color bar how the value of ( ru 2 rr 2 ), the difference between the r 2 tatitic for the unretricted and the retricted equation; the white contour how region where value of the tatitic exceed the 5% threhold. The meaning for thee tatitic i explained in the text. 4. Analyi reult Firt, we regre the detrended winter NAO index onto the concurrent (winter) SST field (Fig. 1a). The correlation map (Fig. 1b) how the well-known tripole pattern over the North Atlantic bain. Near the outheat of Greenland (GL; N, W) and in the ubtropic (ST; N, W), the SST i negatively correlated with the NAO. Between thee two negative center i an area of poitive correlation located over the extenion of the Gulf Stream (GS; N, W). Thi tripole pattern i conitent with many other tudie, including thoe mentioned above. For example, the leading MCA mode of SST in CF02, termed the North Atlantic Horehoe (NAH), ha a imilar tructure but i hifted to the northeat. Figure 1b alo how a imilar but weaker correlation pattern over the North Pacific Ocean. It reflect the fact that the NAO i cloely related to the Arctic Ocillation (AO) and indeed ha an impact beyond the Euro Atlantic half of the Northern Hemiphere (Thompon and Wallace 1998, 2001). Next, for SST anomalie at each grid point, we tet both whether the preceding NAO caue variability in the wintertime SST and whether the preceding SST caue variability in the wintertime NAO. The tet of Granger cauality are run on VAR [Eq. (5) and (6)] with lag length of 2, 3, and 4 eaon. Figure 2 how the reult obtained by etting maximum lag length to 3 eaon (the previou pring). Figure 2a indicate that preceding eaonal anomalie in the NAO Granger caue wintertime SST variation in only mall and pare area. Converely, Fig. 2b identifie a large, patially conitent area of the Gulf Stream extenion where SST Granger caue anomalie of the wintertime NAO. Thi region correpond to the poitive center on the correlation map (Fig. 1) with a northeatern hift. The Fig. 2b value, which repreent the difference between the r 2 tatitic for the unretricted and the retricted equation, indicate that SST from previou eaon reduce the unexplained variance by up to 20%, relative to the lagged value of the NAO. In contrat, Fig. 2b indicate that there i no tatitical evidence for a caual influence of SST near Greenland or the ubtropical region upon the NAO. The Granger cauality tet are alo applied uing alternative maximum lag length etting ( 2, 4). For 2 eaon, the influence of the NAO on the SST field remain inignificant. However, the influence of

5 4756 JOURNAL OF CLIMATE VOLUME 17 FIG. 3. Correlation coefficient (r) of the wintertime NAO and previou SST: (a) SST from SON and (b) SST from both JJA and SON. The contour interval i 0.1, the minimum contour i 0.2, and poitive value are haded. The thick dark line how region where r exceed the 5% critical value. the NAO increae when increae to 4 eaon (not hown). Thi increae may be aociated with the peritence of uburface temperature anomalie that reappear the following winter (Rodwell and Folland 2002). In contrat, all tet of the caual relation from preceding SST to the wintertime NAO confirm the reult in Fig. 2b; that i, over the North Atlantic bain, only SST around the Gulf Stream extenion have a ignificant caual relationhip with the winter NAO. Figure 2b alo identifie ome area over the Indian Ocean and the wetern/tropical Pacific where SST have a ignificant caual relationhip with wintertime NAO variation. Generally, thee relationhip are weaker and le peritent than thoe found in the Gulf Stream extenion. On the other hand, if realitic, they eem to upport the idea that oceanic influence on the NAO may not be retricted to the North Atlantic bain. Although thee caual relationhip deerve more invetigation, they will not be dicued further in thi paper. One limitation of uing the NAO index (a defined in Jone et al. 1997) i that it may not capture the movement of the center of the NAO pattern in eaon other than winter. To addre thi iue, we repeat the analyi uing another NAO index compiled by the U. S. Climate Prediction Center (CPC). The CPC index i computed from the rotated empirical orthogonal function analyi of monthly mean 500-mb geopotential height (Barnton and Livezey 1987) and therefore i expected to better reflect the eaonal patial change of the NAO. The reult obtained uing the CPC index are quantitatively the ame a thoe in Fig. 2. Thi imilarity indicate that the eaonal hift of the NAO pattern do not eem to have a major influence on the reult hown in Fig. 2. A dicued previouly, the reult of Fig. 2 ugget that the preceding NAO doe not contain ignificant explanatory information about wintertime SST over mot part of the North Atlantic bain (other than that found in the preceding SST themelve). In contrat, SST around the Gulf Stream from the previou ummer and pring contain information related to the NAO during the following winter that i not contained in the previou value of the NAO. The firt reult indicate weak atmopheric forcing at eaonal time cale. Thi lack of a caual relationhip may be due to the fact that the peritence time cale of the NAO i on the order of day and that the urface turbulent heat fluxe are dominated by hort time-cale weather change (Frankignoul 1985; Deer and Timlin 1997). In fact, repeating our analyi with monthly data how that the NAO anomalie from the previou two or three month ignificantly caue SST anomalie during wintertime (not hown). For eaonal anomalie, however, thee high-frequency ignal are filtered out, and the caual influence may be retricted. On the other hand, the large heat capacity of the ocean allow an SST ignal to perit for month to eaon. Therefore, it i poible for a peritent SST ignal to initiate and force a eaonaltype anomaly in the atmophere. Thee reult are im-

6 15 DECEMBER 2004 WANG ET AL FIG. 4. Correlation of the detrended winter NAO (DJF) and the SST indice averaged from Jun to Nov: (a) GL, (b) GS, and (c) ST. See text for averaging domain. All of the indice are normalized uch that they have unit variance. ilar to thoe reported by CF02; however, the apparent tripole pattern (NAH) dicued in that paper diappear in our analyi uing the Granger cauality technique. Thi dicrepancy may be partially due to the fact that we tet the whole SST field intead of decompoing it into everal leading mode. Furthermore, it ugget that the anomalou SST around the Gulf Stream may be more important in initiating diturbance of the atmopheric circulation over wintertime North Atlantic, while the tripole pattern may be generated by poitive feedback between thee two field (CF02). To compare the reult generated by Granger cauality with thoe from imple lagged correlation analyi, we calculate the correlation coefficient between the wintertime NAO and SST from the previou fall and ummer (Fig. 3). In both Fig. 3a and 3b, the NAO time erie i correlated with the earlier SST around the Gulf Stream (the averaged value of the correlation coefficient r in thi region i about 0.5). Thee reult are conitent with thoe in Fig. 2b. We note that uch agreement i not alway preent. For example, the winter NAO i ignificantly correlated with gridpoint SST during the following pring, that i, when the NAO lead the SST by a eaon (not hown). However, the Granger cauality tet of the influence of the wintertime NAO on the following pringtime SST (not hown) indicate that much of thi correlation i actually related to the tate of the wintertime SST field itelf and therefore cannot be uniquely attributed to the preceding NAO field. A uch, the Granger cauality tet i tricter and more reliable than imple lagged correlation. To validate our analyi, we compile three SST in-

7 4758 JOURNAL OF CLIMATE VOLUME 17 TABLE 1. Correlation coefficient (r) etimated for the relation between the wintertime NAO and SST indice of different eaon. Value that exceed the 5% threhold are in boldface. GL SST GS SST ST SST Spring Summer Fall Winter dice by patially averaging SST over the previouly identified GL and ST region, which how ignificant concurrent correlation with the wintertime NAO (Fig. 1), along with the GS region, which how ignificant caual relation with the wintertime NAO (Fig. 2). The SST indice averaged for the proceeding June November are hown in Fig. 4. All the concurrent SST indice correlate well with the NAO in winter, and the ign of the correlation agree with the negative poitive negative tripole pattern (Table 1). However, only the value from the Gulf Stream SST region have ignificant (p 0.05) lead correlation with the winter NAO. In addition, the Granger cauality tet alo indicate that only the GS SST caue variability in the NAO (not hown). Thee reult are conitent with modeling tudie by Wu and Gordon (2002), which indicate that Gulf Stream variability in autumn can influence the wintertime atmophere over the NAO region on decadal/interdecadal time cale. Here we find a imilar relationhip within the oberved and analyzed field, indicating that thi influence alo may be apparent on horter time cale. 5. Concluion Here, we ue the notion of Granger cauality to invetigate the relationhip between the NAO and SST over the North Atlantic bain. Although the concurrent correlation map of the wintertime NAO and SST how the well-known tripole pattern, the influence of the preceding eaon NAO anomalie on the wintertime SST field are very limited. Intead, the preceding tate of the ocean how a ignificant caual relation with the dominant wintertime atmopheric circulation pattern. Thi influence i mainly centered over the Gulf Stream (GS) area. Thee reult agree with imple lagged correlation map of the winter NAO and preceding SST from earlier eaon; however, we believe the Granger cauality i a more rigorou tet for the caual order within the coupled ytem. To further evaluate thee reult, we define three SST indice by area-averaging the SST near the center of the typical tripole pattern, including the Greenland (GL), the GS, and ubtropic (ST), repectively. It i found that only the GS SST index how ignificant lead correlation with the winter NAO. In addition, the GS index i alo the only one that Granger caue anomalie in the winter NAO. Thee reult ugget that the anomalou Gulf Stream SST are important in initiating diturbance of the atmopheric circulation over the wintertime North Atlantic. In addition, the reult ugget that the full tripole pattern (e.g., a identified in CF02) may intead repreent the overall effect of poitive feedback between the ocean and the atmophere in thi region. 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