The Arctic Oscillation (AO), the North Atlantic Oscillation (NAO) and the Cold Ocean-Warm Land Pattern (COWL) have been identified as important modes of variability in the Northern Hemisphere winter sea-level pressure field. However, which one is most fundamental in describing this variability and the relationship between them are still important open questions. A key uncertainty is our lack of knowledge of the linkages between the Arctic, North Atlantic and North Pacific Oceans that are manifest in these modes. In this study, the authors investigate these linkages through a frequency dependent decomposition of the variability in the Northern Hemisphere sea-level pressure field. In particular, the authors show that the spatial expression of the variability in this field has a frequency dependence that results in a NAO-like pattern on inter-annual timescales, an AO-like pattern on inter-decadal timescales and a COWL-like pattern on multi-decadal timescales.
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 The North Atlantic Oscillation (NAO), the Arctic Oscillation (AO) and the Cold Ocean-Warm Land Pattern (COWL) are the most important modes characterizing Northern Hemisphere (NH) climate variability during the boreal winter [Hurrell, 1995; Wallace et al., 1995; Thompson and Wallace, 1998; Wallace and Thompson, 2002; Wanner et al., 2001; Quadrelli and Wallace, 2004; Wu and Straus, 2004]. The NAO is a meridional dipole in the North Atlantic sea-level pressure (SLP) field with two centers of action, one near Iceland and the other near the Azores. The AO is the leading mode in an EOF decomposition of the NH winter monthly mean SLP anomaly field which is characterized by a center of action over the Arctic Ocean with centers of opposite sign over the North Atlantic and North Pacific Oceans. The COWL pattern in the SLP has two negative centers of action of the same sign over the North Pacific and Arctic Oceans and a center of action of the opposite sign over the North Atlantic Ocean.
 However, much of our knowledge of the climate expression of these modes stems from linear analysis techniques such as Empirical Orthogonal Function (EOF) decomposition and regression analysis [Storch and Zwiers, 1999]. Recently, non-linear relationships between modes of climate variability have begun to be identified. For example, Hoerling et al.  argued that a non-linear relationship between sea surface temperatures and deep convection over the tropical Pacific was responsible for the approximate 35° longitudinal shift in the centers of action of the Pacific North America (PNA) teleconnection pattern between warm and cold phases of the El-Nino Southern Oscillation (ENSO). ENSO-related non-linearities have also been identified in the North America and North Atlantic climate as well as in tropical rainfall [Hoerling et al., 2001a; Pozo-Vazquez et al., 2001]. Zhao and Moore  identified a non-linear amplitude dependent expression of the NAO in the North Pacific that was associated with the Aleutian Low and the East Asian jet stream. Recently, H. X. Zhao and G. W. K. Moore (Temporal variability in the expression of the Arctic Oscillation in the North Pacific, submitted to Journal of Climate, 2006, hereinafter referred to as Zhao and Moore, submitted manuscript, 2006) argued that there exists temporal variability in the Pacific center of action in the AO mode, which is associated with the non-linear regime shifts resulting from the Pacific Decadal Oscillation (PDO). In particular, they argued that this nonstationarity can result in a finding as to the dominance of either the AO or the NAO as a paradigm for understanding the NH tropospheric climate variability that is dependent on the time period under investigation.
 The results of Zhao and Moore (submitted manuscript, 2006) suggest that there may be a time-dependence in the expression of these modes of climate variability. In this study, we extend these results by means of a frequency dependent decomposition of the variability in the NH mean SLP into three periods: the inter-annual (less than 10 years), the inter-decadal (10–40 years) and the multi-decadal (longer than 40 years) during the 20th century. Through this decomposition, the authors show that variability in the NH winter SLP takes on a NAO-like pattern on inter-annual timescales, an AO-like pattern on inter-decadal timescales and a COWL-like pattern on the multi-decadal timescales.
2. Data and Methods
 We will make use of the SLP data set, HadSLP1, produced by the U.K. Meteorological Office [Basnett and Parker, 1997]. This data set makes use of all available SLP data to produce an internally consistent time series of the global monthly mean SLP field over the period 1871–1998. There is concern as to the lack of observations over the North Pacific ocean prior to the early part of the 20th century [Trenberth and Hurrell, 1994]. As a result, we restrict our attention to the period after 1900.
 As an index for the NAO (NAOI), we will use that of Hurrell , which uses the difference of the normalized Lisbon Portugal and the Stykkisholmur Iceland SLP data. This index, available on a monthly-mean basis from 1821 to 2000, is the most widely used in studies of climate variability associated with the NAO [Wanner et al., 2001]. To describe climate variability in the North Pacific, we make use of the North Pacific index (NPI), an area-weighted average of the monthly SLP over the region 30–65°N, 160°E–140°W. More information on this index is detailed in Trenberth and Hurrell .
 We will use the winter mean fields/indices defined as the mean of three months: January, February and March (JFM) in this study. We have tested the winter mean with other months such as December through February and December through March and found that there are no significant differences in our conclusions.
 Empirical Orthogonal Function (EOF) decomposition is a commonly employed data compression technique used to extract modes or spatial patterns that maximize the amount of variance explained in a given data set [Richman, 1986]. The EOFs are usually defined as the leading eigenvectors of the covariance matrix of a given data set [Preisendorfer et al., 1988]. Because the EOFs do not necessarily represent physical modes, care must be used in the interpretation of such analyses [Richman, 1986; Ambaum et al., 2001]. Therefore, a strategy for identifying physical modes of climate variability through the use of multiple techniques including EOF decomposition and regression analysis is recommended by Dommenget and Latif . We will adopt this strategy in this paper.
 The statistical significance of our results was assessed with a resampling method [Gershunov and Barnett, 1998] that makes use of synthetic time series, with the same statistics as the time series in question, to estimate the characteristics of the underlying probability distribution. In this instance, the synthetic time series were constructed by randomizing the phase of the Fourier transform of the time series in question, thus insuring that the synthetic time series have the same power spectrum as the original time series [Ebisuzaki, 1997; Rudnick and Davis, 2003]. It is found that the resampling test results are very similar to those using a more conventional Student's t-test that takes into account the reduction in the degrees of freedom that arises from the application of the filters [Gao and Stanford, 1988].
Figure 1 shows the power spectra of the normalized winter mean (JFM) NPI and NAOI for the period 1900–2000 using the multi-taper method [Mann and Lees, 1996]. Both spectra have minima for periods near 10 and 40 years that result in a partitioning of power into distinct bands characterized by: inter-annual variability (periods less than 10 years); inter-decadal variability (periods between 10 and 40 years) and multi-decadal variability (periods longer than 40 years). The NPI power spectrum (Figure 1a) is dominated by two peaks with periods of 100 and 50 years that reach the 99% significance level. This variability is most likely that identified by Minobe . For the inter-decadal band, there is a peak with a period around 30 years that is significant at the 95% level. In the inter-annual band, there is a peak with period between 2 and 3 years that is significant at the 95% level. In contrast, the NAOI power spectrum is dominated by inter-annual oscillations with periods between 7–10 years and 2–3 years that are significant at the 95% level [Hurrell and VanLoon, 1997]. In the inter-decadal and multi-decadal bands, there are peaks with periods around 16, 50 and 75 years. However none of these peaks are statistically significant.
 To understand the implications of this partitioning in the frequency domain on the coupling between the North Pacific and North Atlantic Oceans, we show in Figure 2 the filtered NAOI and NPI time series obtained by using a transform filter [Walters and Heston, 1982] that captures variability in these three bands.
 With regard to inter-annual variability (Figure 2a), we see that there is weak correlation between the two indices on these timescales. This is confirmed by the small correlation coefficient (CC = 0.05) that is not statistically significant. For inter-decadal variability, the two indices exhibit some degree of correlation. Indeed the correlation coefficient (CC = 0.42) is statistically significant at the 90% level. With regard to multi-decadal variability, the indices are negatively correlated with a correlation coefficient (CC = −0.33). However according to our tests, this correlation is only statistically significant at the 65% level. This result is indicative of the relatively short length of the underlying indices especially when filtered to remove all but the lowest frequency signals.
 To identify the spatial structures associated with this frequency dependent variability, we show in Figure 3 the leading EOF of the NH winter (JFM) mean SLP field after the application of the various filters. These leading modes were well separated from the other EOFs [North et al., 1982]. The leading EOF of the SLP field filtered to include variability on inter-annual timescales (variance explained 37%) is a NAO-like pattern (Figure 3a). This result is consistent with the low correlation between the NAOI and NPI on inter-annual timescales (Figure 2a). When the SLP field is filtered to include inter-decadal variability, the leading EOF (variance explained 39%) is an AO-like pattern (Figure 3b). This is again consistent with the positive correlation between the NAOI and NPI on inter-decadal timescales (Figure 2b). Finally, the leading EOF (variance explained 66%) of the SLP field that is filtered to include multi-decadal variability is a COWL-like pattern (Figure 3c). This is also consistent with the negative correlation between the NAOI and NPI on multi-decadal timescales (Figure 2c).
 Following the example of Dommenget and Latif , we will complete the presentation of our results by showing in Figure 4 the regressions of the winter mean SLP against the winter mean NAOI after the application of the filters. The statistical significance of the regression was assessed by the methods described in Section 2. A comparison between Figures 3 and 4 show strikingly similar structures that are for the most part statistically significant at the 90% level. In particular, the regression of the winter mean SLP field filtered to retain variability on the inter-annual time scales against the similarly filtered NAOI results in dipolar structure over the North Atlantic and Arctic Oceans that resembles the classical NAO pattern (Figure 4a). In contrast, the regression that retains variability in the SLP field and NAOI on inter-decadal timescales has an AO-like pattern (Figure 4b), while the regression that retains variability on multi-decadal timescales has a COWL-like pattern (Figure 4c).
 In this study, variability in the NH winter SLP field has been partitioned into three bands in the frequency domain: the inter-annual band (periods less than 10 years), the inter-decadal band (periods between 10–40 years) and the multi-decadal band (periods larger than 40 years). This particular partition was based on power spectra of two key indices of climate variability in the North Pacific, the NPI, and the North Atlantic, the NAOI. When these indices were filtered to retain variability on these time-scales, we found strikingly different behavior. In particular, there was no correlation between the two indices when only inter-annual variability was retained. In contrast, the two indices were positively correlated when only inter-decadal variability was retained and were negatively correlated when only multi-decadal variability was retained.
 The spatial patterns associated with this frequency dependent variability were identified through the use of both an EOF decomposition and regressions against the filtered NAOI. With regard to the variability in the NH winter mean SLP on the inter-annual time scales, both the EOF and regressions produced similar results that are consistent with previous studies [Quadrelli and Wallace, 2004], which show a stationary dipole structure centered on the Arctic and North Atlantic with opposite sign leading to an apparent NAO-like or weak AO-like pattern. On inter-decadal time scales, both techniques produce a more complete AO-like or northern annular mode (NAM) pattern, which is similar to the bidecadal pattern [Minobe et al., 2002] and the intraseasonal pattern [Quadrelli and Wallace, 2004]. Finally, on multi-decadal time scales, both techniques produce a pattern that has centers of action of same sign in the Arctic and the North Pacific regions but of opposite sign in the North Atlantic. This configuration is similar to the COWL pattern [Wallace et al., 1995].
 Recently, we have showed that there exist non-linear linkages between the two basins of Atlantic and Pacific oceans [Zhao and Moore, 2004]. The further finding of temporal variability in the Pacific center of action in the AO mode (Zhao and Moore, submitted manuscript, 2006), which is associated with the non-linear regime shifts resulting from the PDO, contributed to understanding the dominance of either the AO or the NAO as a paradigm in the NH tropospheric climate variability. This study suggests that the NAO-like pattern is associated with inter-annual timescale oscillations [Hurrell and VanLoon, 1997], the AO-like pattern is associated with inter-decadal [Minobe et al., 2002; Jevrejeva et al., 2004] or seasonal timescale oscillation [Thompson and Wallace, 1998; Deser, 2000], while the COWL-like pattern is associated with multi-decadal timescale oscillations [Hoerling et al., 2001b; Lu et al., 2004].
 The Natural Sciences and Engineering Research Council of Canada and the Canadian Foundation for Climate and Atmospheric Sciences funded this research. The North Atlantic Oscillation index was provided by the Climate Research Unit of the University of East Anglia. The NPI was provided by the Climate Analysis Section, NCAR, Boulder, USA.