The low-frequency covariabilities of tropical sea surface temperature (SST) and the North Atlantic Oscillation (NAO) during twentieth-century winters are investigated by maximum covariance analysis (MCA) using reanalysis data. It was found that the positive NAO phase is positively correlated to an increase in tropical SST, especially during the recent decades. The western tropical Pacific SST displays high correlation with the NAO throughout the whole of the twentieth century. For this ocean region, the MCA homogeneous map has a SST spatial pattern with meridional gradients. It was also found that a cooling of tropical Atlantic SST is correlated with positive NAO. The influence of the tropical Atlantic SST on the NAO is strongest during the pre-1960s period.
A major part of the Northern Hemispheric flow changes in the second half of the twentieth century and projects onto the North Atlantic Oscillation (NAO) (Marshall et al. 2001). The NAO is a fluctuation in the sea level pressure between the Icelandic low and the Azores high (Hurrell 1995). The positive trend of the NAO in the recent 50 years was found to be related to global warming (e.g., Hurrell 1995).
The NAO on intraseasonal to interannual time scales is mainly an atmospheric internal phenomenon and thus sea surface temperature (SST) feedbacks on NAO variations are of secondary importance (Marshall et al. 2001; Czaja and Frankignoul 2002); whereas on decadal time scales, model results suggest that tropical and extratropical SST variabilities play a crucial role in the NAO evolution (Bader and Latif 2003; Hoerling et al. 2001, 2004; Hurrell 1995; Hurrell et al. 2004; Marshall et al. 2001; Mehta et al. 2000; Rodwell et al. 1999; Sutton and Hodson 2003). Variabilities at the low-frequency (e.g., decadal) time scales are sometimes referred to as trends. In other words, these modeling studies (same references as above and also Lu et al. 2004) suggest that a significant part of the NAO trend in the twentieth century is forced by a trend in tropical SST, although the magnitude of the NAO response to this low-frequency tropical SST forcing is still a subject requiring further study.
There may be confusion as to which oceans are more important. Some studies suggest that the Indian Ocean plays a dominant role in the period from 1950 to 1999 (e.g., Bader and Latif 2003; Hoerling et al. 2004; Hurrell et al. 2004), while others give more importance to the Atlantic Ocean (e.g., Sutton and Hodson 2003) throughout the whole of the twentieth century. Recently, Kucharski et al. (2006, hereafter KMB) reported a significant role of the western tropical Pacific in the decadal NAO variation. A possible ocean–atmosphere coupling has been suggested by them. Lu et al. (2004) also highlighted the ability of the western Indo–Pacific (they used 30°S–30°N, 60°E–180°, thus including the Indian Ocean as well as the western Pacific; see their Fig. 11) in forcing the observed response in amplitude in the North Atlantic sector. The perceived discrepancies can be due to various reasons. Sutton and Hodson (2003) used a detrended time series while Hoerling et al. (2004) purposely investigated the forcing of NAO by the tropical SST trends. Analyses using different subperiods of the twentieth century (e.g., post-1950 or pre-1950) may also emphasize the significance of different ocean regions because the influence of the oceans may be nonstationary (Sutton and Hodson 2003, e.g., found that this is true at least for the interannual cases).
The aim of this study is to investigate the observational evidence in the results of KMB. The connections between decadal variations of SST in the tropical oceans and the NAO during winters are examined using maximum covariance analysis (MCA). This method has been applied to study ocean–atmosphere interactions on intraseasonal and interannual time scales (e.g., Czaja and Frankignoul 2002; Wallace et al. 1992) and has been found to give robust results in comparison with other methods in situations of a low ratio of the number of time samples to the number of horizontal grid points. The MCA also has a number of other advantages, such as the ease of implementation and small systematic bias, and so is recommended for general use (Bretherton et al. 1992). MCA is carried out by performing singular value decomposition (SVD) on the cross-covariance matrix; it provides pairs of spatial patterns that account for the maximum covariance.
2. Data and methodology
This study is based on two datasets. For SST, the Hadley Centre sea ice and SST (HadISST) dataset (Rayner et al. 2003), available from 1870 to present on a 1° × 1° grid, is used (we omit the first year from the time series). The SST data are interpolated to a 3.75° × 3.75° resolution in order to avoid the ratio of number of grid points to the number of time samples becoming too large. As an atmospheric variable, we used an updated historical sea level pressure (SLP) dataset from the University Corporation for Atmospheric Research–National Center for Atmospheric Research (UCAR–NCAR) (Trenberth and Paolino 1980); the dataset, online at http://dds.ucar.edu/datasets/ds010.1), is available from 1899 to present on a 5° × 5° grid in the Northern Hemisphere. The Hurrell NAO index (Hurrell 1995), online at http://www.cgd.ucar.edu/~jhurrell/nao.stat.winter.html, is available from 1864 to present and is also used. We consider winter data, December–March average, since the Hurrell NAO index is defined for the same months. To these seasonal means, filtering of 5-, 7-, 9-, and 11-yr running means are applied to allow a study of the sensitivity of the results to the filter widths.
The MCA following Bretherton et al. (1992) is applied to the filtered SST for the tropical regions (20°S–20°N) and SLP data in the North Atlantic (30°–70°N, 60°W–60°E). The resulting North Atlantic SLP structure is assessed in terms of its NAO resemblance by comparing the leading SST expansion coefficient time series with the Hurrell NAO index.
In applying the MCA, the SST and SLP fields are normalized at each grid point by their respective standard deviations. This is to avoid the dominance by regions of large standard deviations in the cross-covariance matrix. We briefly introduce some basic notations that are useful for presenting the results. Let 𝗦 and 𝗛 denote the two fields of interest (here the SST and SLP, respectively), and and their standardized counterparts. The corresponding expansion coefficients for the kth mode, ak and bk, are defined as
where pk and qk are the patterns from the kth mode of SVD. Of interest are the dimensional heterogeneous regression maps
because they indicate maps of anomalies in the SLP (SST) field based on the knowledge of the kth expansion coefficients of the SST (SLP), and the dimensional homogeneous regression maps
which are the regression of the SST (SLP) field on the kth expansion coefficients of the SST (SLP). The scaling of the homogeneous and heterogeneous regression maps is such that the values correspond to one standard deviation of the respective expansion coefficients and linear relationships between the two maps are preserved (see appendix A of Czaja and Frankignoul 2002).
In this paper, results are presented from the perspective that one can specify the SLP on the knowledge of the SST. Thus, for SST we will show only homogeneous maps, denoted HOM1(SST), and for SLP only heterogeneous maps, denoted HET1(SLP). The reason for choosing this point of view is that previous studies (as discussed in the introduction) suggest that tropical SST is forcing the NAO on these low-frequency time scales. However, it is important to caution that within merely the premise of MCA no firm conclusion can be made about any physical mechanism.
Only the maps related to the first singular values are shown because for all regions they produce the largest correspondence with the NAO. Note that for the time series ak an extended period can be considered, assuming that the pattern pk holds for the extended period to the beginning of the SST time series (i.e., pre-1899). To assess the temporal linkage of the first mode in each region with the Hurrell NAO index, the correlation r[a1, NAO] is evaluated. We comment here that the NAO index had been defined independently from the MCA. Usually at this stage, most previous MCA studies used r[a1, b1].
Since this paper deals with decadal variability of fields that have larger variability on an interannual time scale, it is informative to compare the typical interannual and decadal (for brevity only the 11-yr filtered data are considered here) standard deviations for SST in the tropical regions and SLP in the North Atlantic. The winter (December–March average) interannual and decadal standard deviations for the SLP, averaged in the region (30°–70°N, 60°W–60°E), are about 2.8 and 1 hPa, respectively. For SST, they are about 0.3 and 0.15 K for all regions of the Tropics (20°S–20°N) (only in the eastern Pacific the interannual standard deviation increases to about 0.5 K on interannual time scales). Thus, the ratios of decadal to interannual standard deviations are close to 1/2 for SST and 1/3 for the North Atlantic SLP.
To estimate the statistical significance of the results, the MCA for each region and each filter width was repeated 200 times (many longer trials were actually conducted, but 200 was deemed sufficient to obtain good estimates) using temporally scrambled tropical SST and the original North Atlantic SLP data (see e.g., Czaja and Frankignoul 2002). The SST is the suitable field to shuffle because we can be certain that an NAO signal in the SLP is still present, but any high-correlation (in r[a1, NAO]) event found in the shuffled MCA trials would be regarded as insignificant. The quoted significance levels indicate the percentage of events (denoted by p) with correlations or squared covariance (SC), which equals or exceeds the values being tested (i.e., values from the unshuffled MCA).
The ocean regions considered are the whole Tropics, western tropical Pacific (140°–190°E), Indian Ocean (40°–100°E), eastern Pacific (225°–280°E), and the tropical Atlantic Ocean (60°W–0°); all for 20°S–20°N. The results for these regions are summarized in Tables 1 –4 for the 5-, 7-, 9-, and 11-yr filtered data, respectively. The values presented are the statistical significance level, p, and the correlations are given in parentheses. Statistically significant results are highlighted in bold numbers. Generally, only the 5-yr running mean MCA results show statistically significant correlations in r[a1, b1] for all of the regions except the eastern Pacific. However, only the whole Tropics, western Pacific, and Atlantic regions show statistically significant r[a1, NAO] for the 5-yr running-mean filtered data.
For the 7-, 9-, and 11-yr filtered data, only the western tropical Pacific and the Atlantic give statistically significant r[a1, b1], and significant r[a1, NAO] correlations are found only for the western tropical Pacific. Based on these results, figures will be presented for all regions only for the 5-yr filtered case, while those for the western tropical Pacific in the 11-yr filtered case will also be presented (the 7-, 9-, and 11-yr filtered cases are very similar to each other for the western tropical Pacific).
a. Whole of tropical oceans
We only consider the whole tropical belt from 20°S to 20°N for the 5-yr filtered data because, for this region, only this filter width produces statistically significant correlations. The HOM1(SST) and HET1(SLP) maps are shown in Figs. 1a and 1b, respectively. The squared covariance fraction (SCF) of this leading MCA pattern is 0.53. HET1(SLP) resembles the NAO (i.e., negative pressure anomaly near Iceland and positive anomaly close to the Azores). The magnitude reaches about 1 hPa. The expansion coefficient time series (crosses), a1, is compared with the Hurrell NAO index (open circles) in Fig. 1c (the NAO index is filtered accordingly). Good agreement between the curves is seen, particularly in the last 30 years, when both curves show a strong upward trend. The temporal correlation coefficient of a1 with the Hurrell NAO index, r[a1, NAO], is 0.61, whereas r[a1, b1] = 0.68. The significance levels of the coupled signal are p(r[a1, b1]) = 3% and p(r[a1, NAO]) = 0%. The HOM1(SST) map shows a pattern of global warming of about 0.1–0.2 K. There are only two regions in which no warming, or even a slight cooling, occurs: the tropical Atlantic at about 10°N and the western Pacific at about 10°N, 150°E. Referring to HOM(SST) and HET1(SLP), we find that 5 hPa in the North Atlantic SLP would be linearly connected to about 1 K in the tropical SST, which is comparable to the North Pacific SLP relationship to interdecadal changes in (El Niño–Southern Oscillation) ENSO-related SST variations (Zhang et al. 1997).
b. Western tropical Pacific
KMB suggested a special role of the western tropical Pacific in interacting with the NAO. According to them, this is due to the sensitivity of atmospheric heating to the SST gradient seen in the region 20°S–20°N, 140°E–170°W. We have chosen this subregion first to verify their findings. Indeed, from Tables 1 –4, the western tropical Pacific shows statistically significant correlations for all filter widths considered here. The results are presented for the 5-yr filtered data as well as for the 11-yr filtered data (the 7-, 9-, and 11-yr filtered results are very similar). The HOM1(SST) and HET1(SLP) maps for the 5-yr filtered data are shown in Figs. 2a and 2b, respectively (SCF = 0.54). The HET1(SLP) map resembles an NAO. The amplitude of the negative northern anomaly exceeds −2 hPa in this case. The HOM1(SST) map shows a cooling mainly at the north of the equator, but the gradient structure with a sign change at about 5°N, as reported by KMB, is also observed. The time series a1 shown in Fig. 3c gives r[a1, NAO] = 0.51, with p(r[a1, NAO]) = 1%. The strong covariability of SST in the western tropical Pacific and the NAO becomes even clearer when an 11-yr filter is considered, as demonstrated in Fig. 2f. In this case good agreement with the Hurrell NAO index is found throughout the 121-yr period and r[a1, NAO] = 0.82 and r[a1, b1] = 0.84. This coupled signal is extremely significant as there is no event in the trials with r[a1, NAO] larger than or equal to 0.82; that is, p(r[a1, NAO]) = 0%. It is also found that p(r[a1, b1]) = 5%. Figure 2d shows clearer than Fig. 2a the gradient structure in the SST pattern that KMB discussed extensively. Figure 2e closely resembles the NAO. For the western Pacific, 10 hPa of the North Atlantic SLP corresponds to about 1 K in the tropical SST.
We comment here that the HOM1(SST) map is similar to the empirical orthogonal function corresponding to the second PC (not shown here) for the western tropical Pacific SST.
c. Other regions
In this section we summarize the results for the other regions. However, from Tables 1 –4 it is clear that only the Atlantic Ocean shows statistically significant correlation with the NAO for the 5-yr filtered data (r[a1, NAO] = 0.44, with p(r[a1, NAO]) = 4%), whereas the Indian Ocean is statistically significantly correlated with a pattern different from the NAO (r[a1, b1] = 0.59, p(r[a1, b1]) = 5%, but r[a1, NAO] = 0.28, p(r[a1, NAO]) = 20%). For the 7-, 9-, and 11-yr filtered data no significant correlations with the NAO could be identified. Thus, only results for 5-yr filtered data will be presented. Figures 3a,c,e show the HOM1(SST) maps for the tropical Indian Ocean (20°S–20°N, 40°–100°E), the eastern Pacific (20°S–20°N, 225°–280°E), and the Atlantic (20°S–20°N, 60°W–0°), and Figs. 3b,d,f show the corresponding HET1(SLP) maps (the SCFs of these leading MCA patterns are 0.8, 0.67, and 0.8, respectively). Results from the Indian Ocean indicate the dominance of increased pressure over Europe, but relatively small anomalies near Iceland, whereas for the Atlantic region it is found that the negative pressure anomaly close to Iceland is dominating. This result is similar to that obtained for the western tropical Pacific when a 5-yr running mean is considered.
The HOM1(SST) maps show warming patterns for the Indian Ocean. For the Atlantic Ocean, it is found that a cooling corresponds to the positive NAO phase. The latter result is consistent with the findings of Sutton and Hodson (2003). For the Indian Ocean and tropical Atlantic regions, 1 K in the SST corresponds to about 3 and 10 hPa in North Atlantic SLP, respectively. The time series of a1 for the tropical Indian Ocean, eastern Pacific, and Atlantic are shown in Figs. 4a,b,c. The Indian Ocean shows an upward trend in the last 30 years, consistent with an overall warming of the Indian Ocean.
On the contrary, the Atlantic (Fig. 4c) shows the best agreement with the NAO from the beginning of the data until the mid-1960s, but fails to capture the upward trend in the final 30 years. We believe that, since tropical Atlantic SST actually anticorrelerates with the NAO, the background warming of that ocean in the recent decades has reduced its correspondence with the NAO whose linear trend is upward during the final 30-yr period.
The correlation coefficients r[a1, NAO] are 0.28 and 0.44 for Indian Ocean and Atlantic, respectively, whereas r[a1, b1] = 0.59 and 0.71, respectively. For the significance levels, it is found that p(r[a1, b1]) = 5% and 0%, and p(r[a1, NAO]) = 20% and 4%, for Indian Ocean and Atlantic, respectively. We have excluded the eastern Pacific from the discussion because their correlations with NAO are not found to be statistically significant. This should not be taken to imply that the eastern Pacific is not forcing the NAO in other time scales not considered here.
4. Discussion and conclusions
MCA is performed on winter-averaged 5-, 7-, 9-, and 11-yr filtered tropical SST and North Atlantic SLP data to investigate the connections between the low-frequency tropical SST variations and the NAO. The main findings are as follows:
The western tropical Pacific shows the most robust connection with the NAO, providing statistically significant correlations for all of the 5-, 7-, 9-, and 11-yr filtered data. Correlations are particularly high for 7-, 9-, and 11-yr filtered data (second columns in Tables 1 –4). Here a SST gradient appears to be correlated with the NAO (Fig. 2). This result supports the findings of KMB, who found that the atmosphere is particularly sensitive to SST anomalies in the western Pacific warm pool region.
The Atlantic Ocean shows statistically significant correlations with the North Atlantic SLP for 5-, 7-, 9-, and 11-yr filtered data. However, the correlation with the NAO is only statistically significant for the 5-yr filtered data (fifth columns in Tables 1 –4), where it was found that the cooling of the Atlantic Ocean (Figs. 3e,f) is moderately correlated with the NAO (r[a1, NAO]=0.44). This finding is in agreement with Sutton and Hodson (2003).
Recent model studies (Hoerling et al. 2004; Hurrell et al. 2004; Hoerling et al. 2001; Bader and Latif 2003) suggested an important role of the tropical Pacific and Indian Ocean in forcing the NAO in the last 50 years. Our analysis confirms that the upward NAO trend seen in the last three decades corresponds to an upward trend in the SST expansion coefficient time series in the whole tropical oceans.
The correlations from the whole Tropics, western tropical Pacific, and Atlantic Ocean that have been identified could indicate forcing of the NAO by tropical SST. However, other reasons for the identified correlations cannot be ruled out. For example, KMB suggest an ocean–atmosphere coupling at work where the NAO feeds back onto the western Pacific SST via a cold ocean–warm land (COWL) pattern (Wallace et al. 1996). Another possibility is that a common external forcing is responsible for the correlations found here. The last 30 years are dominated by an upward trend in tropical SST (see e.g., Fig. 1). It is possible that this trend is due to “external forcing” such as the increased greenhouse gases (Shindell et al. 1999). Such a forcing could possibly influence both tropical SST and North Atlantic SLP independently. These questions cannot be addressed by MCA alone. However, a considerable number of modeling studies that investigated the connection between SST and the North Atlantic atmosphere in the last 50 years (e.g., Bader and Latif 2003; Hoerling et al. 2001, 2004; Hurrell et al. 2004; Lu et al. 2004; Mehta et al. 2000; Rodwell et al. 1999; Sutton and Hodson 2003; KMB) suggested that the oceans are forcing the atmosphere on decadal time scales. They indicated that, although an external forcing is present, the interaction with the climate system is taking place mainly by warming of tropical and extratropical SST that then influences the atmosphere via diabatic heating. Under this hypothesis the correlations presented here (despite being demonstrated mostly through a trend in the last 30 years) can indicate physical interaction of SST and North Atlantic SLP. The possibility that an external forcing can at the same time directly influence both SST and North Atlantic SLP independently cannot be ruled out, as this is a subject still under debate and investigation.
As a further robustness test, the analyses have been repeated using data omitting the final 30 years (N.B. This is the period where many authors put a linear upward trend; on the other hand, the NAO time series shows only a weak trend if considering the whole 100-yr record used for the MCA). In these tests, it was found that for MCA on the 7-, 9-, and 11-yr filtered data, the western tropical Pacific does not show statistically significant correlations with the NAO anymore; although the 5-yr filtered data still remains robust with r[a1, NAO] = 0.52 and p(r[a1, NAO]) = 5%. The Atlantic Ocean, however, shows statistically significant correlations with the NAO for all filter widths (an improvement from the untruncated MCA in which only the 5-yr filtered data produces significant r[a1, NAO], see the fifth column of Tables 1 –4}. In fact, for the tropical Atlantic, the correlations r[a1, NAO] for all filter widths have also increased to about 0.65 by omitting the last 30 years, compared to 0.44 for MCA on the complete 5-yr filtered data.
With regard to the robustness check above, it should be noted that the last few decades of the data contain a large part of the total variance (the final 30 years amount to one-third of the data used for MCA, and the variability increases toward the last decades). Truncating these data points reduces the degree of freedom considerably. Therefore, it is not surprising the western tropical Pacific, which relies on the last three decades of the data to produce high covariances with North Atlantic SLP, loses its statistical significances (except for the 5-yr filtered data) when these final 30 data points were removed. The tropical Atlantic Ocean, on the hand, benefits from this truncation because as mentioned in the penultimate paragraph in section 3c, its correlation with the NAO index is better from the beginning of the time series until about the mid-1960s. This point probably reinforces the conclusion by Sutton and Hodson (2003) who reported good correlation of tropical Atlantic and NAO throughout the whole period because, we believe, the data were detrended in all subperiods.
The robustness of the results using unstandardized data was also checked. We found that the resulting patterns and correlations are very similar to the ones presented here. However, the relevant patterns may shift to the second modes as first modes with the highest SC are dominated by the high variance in the subpolar North Atlantic region.
Another issue is that the SST modes identified in different regions show global covariances (see e.g., Fig. 1d of KMB). Thus, if the SSTs are forcing the North Atlantic SLP there are likely influences from SST outside the region in which MCA was performed here. Further investigation of the nature of such interactions using the analysis of coupled models is necessary.
Finally, it is worth mentioning two important aspects not considered in detail in this study. The first is that MCA extracted the linear signals whereas nonlinear interactions of tropical SST and extratropical responses can also exist (e.g., Lin and Derome 2004). Second, there is evidence that the influences of the oceans are nonstationary (e.g., Sutton and Hodson 2003 found that this is the case for interannual variability). In other words, the relative importance of the different ocean regions is not the same if different subperiods are considered. As far as our study is concerned this is likely to be true for the Indian Ocean and tropical Atlantic (see Figs. 4a,c) where there is a switch in the dominant role between them near 1960 (particularly regarding their linear trends). Indeed, the correlation r[a1, NAO] for the Indian Ocean changes sign between the periods from 1874 to 1960 (r[a1, NAO] = −0.22) and from 1961 to 2000 (r[a1, NAO] = 0.66).
This study is a contribution to the “International Climate of the 20th Century Project” (C20C) coordinated by the Hadley Centre for Climate Prediction and Research (U.K.) and the Center for Ocean–Land–Atmosphere Studies (Calverton, Maryland). We thank Tim DelSole and Franco Molteni for their comments and suggestions. We have also benefited from the careful and very constructive reviews.
* Current affiliation: Arctic Region Supercomputing Center, and International Arctic Research Center, University of Alaska Fairbanks, Fairbanks, Alaska
Corresponding author address: Fred Kucharski, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy. Email: email@example.com