## 1. Introduction

During the past few decades, there has been a tremendous amount of research on teleconnection patterns, spatial patterns of the atmospheric flow that link remote locations around the globe. These patterns are detected with various techniques, such as 1) one-point correlation maps (Wallace and Gutzler 1981), 2) principal component analysis (Barnston and Livezey 1987), and 3) by using different station-based indices (Walker and Bliss 1932). It is the spatial patterns that arise from the use of these techniques that defines the teleconnection pattern.

Recent studies have questioned which of two very similar teleconnection patterns, the North Atlantic Oscillation (NAO) or the Northern Hemisphere annular mode (NAM; also referred to as the Arctic Oscillation or the AO), better represent the dominant form of low-frequency variability observed in the Northern Hemisphere. The NAO is generally regarded as being a pattern that is primarily confined to the North Atlantic, whereas the NAM is usually understood as being an annular or zonally symmetric pattern that is disrupted by zonal asymmetries in the lower boundary [see Wallace (2000), who carefully compares these two patterns]. One perspective, which favors the NAM, claims that the NAO is simply a regional manifestation of the larger scale NAM pattern (Thompson and Wallace 1998). The other perspective, which favors the NAO, claims that the NAM is not even a robust pattern, since the Atlantic and Pacific centers of action for the NAM are not significantly correlated with each other (Ambaum et al. 2001; Deser 2000). In contrast to these two perspectives, Wallace (2000) has questioned whether or not the NAO and NAM are distinct patterns, suggesting that the distinctiveness of the NAO and NAM patterns may simply depend upon their respective definitions. He suggests that the NAO may be regarded as distinct from the NAM only if the NAO is defined with a local station-based index, rather than from time-dependent projections onto a hemispheric field.

Other studies have also made important contributions to this debate. For example, Christiansen (2002) performed a rotated empirical orthogonal functions (EOF) analysis of the 500-hPa geopotential height field and found that the NAM is best understood as a physical mode and not an artifact of the mathematical analysis. In another rotated EOF analysis, Rogers and McHugh (2002) found for the sea level pressure (SLP) field that the NAO and NAM are separate patterns during the spring, summer, and autumn seasons, but not during the winter. Cohen and Saito (2002) developed a test for annularity, which indicates that the first empirical orthogonal function (EOF1) of the Northern Hemisphere 50-hPa geopotential height is annular whereas the corresponding EOF of the SLP field is not.

The above three statistical techniques, one-point correlation maps, principal component analysis, and calculations based on station-based indexes, all exhibit serious drawbacks when applied to atmospheric data. For example, these methods impose a linear relationship between opposite phases of the patterns (Chen and van den Dool 2003; Feldstein 2002a, 2003). Furthermore, principal component analysis is subject to mathematical constraints on spatial and temporal orthogonality; because these constraints lack a sound physical basis, it is possible that the precise spatial form of the teleconnection pattern is seldom observed in the atmosphere (Dommenget and Latif 2002). Given these limitations, rather than arguing over the merits of either pattern, we focus instead on addressing the question first raised by Wallace (2000) on the statistical distinctiveness of the NAO and NAM patterns. For this purpose, we shift our attention away from the spatial structure of the NAO and NAM teleconnection patterns, as determined by the various statistical techniques listed above, and instead examine this question on distinctiveness by calculating composites of different atmospheric variables averaged over time periods when the atmosphere has a large projection onto either teleconnection pattern. This approach is much simpler to interpret because the composites, which will be found to be statistically significant, correspond to averages of patterns that are actually observed in the atmosphere. The primary method to be used in this study is to specify the null hypothesis that composites of NAO and NAM persistent events are indistinguishable (persistent events will be precisely defined in the following section). Stated mathematically, our null hypothesis is that positive phase NAO and NAM persistent events are drawn from the same population of maps or patterns. Similarly, the null hypothesis for the negative NAO and NAM events is that they also come from the same population. We then examine with standard statistical techniques whether or not this null hypothesis can be rejected.

Both phases of the NAO have been shown to undergo a life cycle of growth and decay that takes place over a period of about two weeks (Feldstein 2003; Benedict et al. 2004; Franzke et al. 2004). Furthermore, these studies have shown that the spatial structure of the NAO anomalies undergoes changes during the life cycle. (As we will see, similar changes in the anomaly spatial structure are also observed for the NAM life cycle.) Therefore, for the sake of conciseness, our focus will be on time averages of the composite NAO and NAM life cycles.

If the NAO and NAM patterns are indeed indistinguishable, then our results will have implications for other properties of the NAO and NAM patterns. For example, if these two patterns are indistinguishable, then 1) the NAO cannot be a regional manifestation of the NAM, 2) both patterns are physical, neither being a statistical artifact, and 3) either one of the two patterns should be regarded as redundant. In addition, the indistinguishability will lead us away from comparing the merits of the two patterns, and instead lead us to addressing the question of whether the NAO/NAM pattern is better understood as being annular or being confined to the North Atlantic.

In section 2, we present the data and diagnostic techniques. This is followed in section 3 by a brief summary of the characteristics of the NAO and NAM persistent events. In section 4, we test the null hypothesis that the NAO and NAM persistent events are indistinguishable. Section 5 shows the wave-breaking characteristics for the NAM pattern as observed along the tropopause, and the conclusions are given in section 6.

## 2. Data and diagnostic techniques

For this study, we examine SLP, 40- and 300-hPa streamfunction, and potential temperature on the tropopause [the two potential vorticity unit surface (PVU: 1 PVU = 10^{−6} m^{2} s^{−1} K kg^{−1})]. All data are from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis dataset. The data used cover the years 1958 through 1997 for the months of December through February. For the SLP and the 40- and 300-hPa streamfunction fields, the seasonal cycle is removed at each grid point. All quantities for which the seasonal cycle is subtracted are referred to as anomalies. The seasonal cycle is obtained by applying a 20-day low-pass digital filter to the calendar mean for each day. For the 2-PVU potential temperature field, the seasonal cycle is retained in order to compare the wave-breaking characteristics during the NAM life cycle with those of the NAO (Benedict et al. 2004; Franzke et al. 2004). The SLP field is on a 2.5° latitude–longitude grid, and the 300-hPa and 40-hPa streamfunction fields and the 2-PVU potential temperature field are on the Gaussian grid for a rhomboidal 30 truncation.

We define the NAM as the EOF1 of monthly mean SLP poleward of 20°N (this definition for the NAM is the same as that used by Thompson and Wallace (1998)). The NAO is defined as the first rotated empirical orthogonal function (REOF1) of the monthly mean SLP field. We chose this definition for the NAO simply because the pattern is objectively derived from hemispheric data, rather than depending upon particular station-based indices. Furthermore, the rotation of EOFs yields patterns that tend to be local, as is the NAO pattern. For the rotated EOF analysis, the covariance matrix is used with a varimax rotation. Also, the gridpoint values are weighted by the square root of the cosine of the latitude, in order to account for the reduction in area with latitude. For the results to be shown in this study, eight unrotated EOFs are retained. The sensitivity of the NAO/REOF1 pattern to the number of retained unrotated EOFs was also examined. Over a range of between eight and 20 unrotated EOFs, extremely little sensitivity was found. These patterns, which we refer to as the NAO/REOF1 and NAM/EOF1 patterns, are illustrated in Figs. 1a,b, respectively. As can be seen, the NAO/REOF1 pattern takes on a dipole structure in the North Atlantic, and the NAM/EOF1 pattern resembles the NAO/REOF1 pattern except for the presence of a third center of action in the North Pacific.

Daily amplitude time series for the NAO/REOF1 and NAM/EOF1 patterns are obtained by projecting the daily SLP field onto the corresponding NAO/REOF1 and NAM/EOF1 spatial patterns. These time series are referred to as the NAO/REOF1 and NAM/EOF1 index time series, respectively. We also use the daily NAO and NAM indices of the Climate Prediction Center (CPC; referred as the NAO/CPC and NAM/CPC indices, respectively). For these calculations, we use the NAO index from the CPC that was generated before the 1 June 2005 changes in their definition of the NAO were adopted. The NAO index used by the CPC prior to 1 June 2005 was based on the methodology of Barnston and Livezey (1987), which determined teleconnections by applying a rotated EOF analysis to the 700-hPa geopotential height field. The linear correlations between each of these daily indices are shown in Table 1. As the NAM/EOF1 and NAM/CPC indices have such a high linear correlation, for the remainder of this study, we consider only the NAM/EOF1 pattern, and refer to this pattern and its time series with the shorter acronym NAM. Also, the *e*-folding time scales of each of the indices is similar, being 8 and 9 days for the NAO/CPC and NAO/REOF1, respectively, and 11 days for both the NAM/REOF1 and NAM/CPC. These values are close to those found by (Feldstein 2000, 2002b) for the NAO and NAM patterns. Furthermore, it is important to note that the NAO/EOF1 and NAO/CPC indices both attain their maximum linear correlation with the NAM index at lag 0 days. This implies that the NAO is not evolving into the NAM, nor vice versa.

We follow an approach similar to that of Feldstein (2002a, 2003) and define a persistent event, or a life cycle, to have taken place when the pattern correlation for the daily SLP field stays above a particular threshold value for five or more consecutive days. This technique is based on the methodology of Horel (1985) and Mo (1986). The threshold value for these pattern correlations is chosen to correspond to the 95% confidence level for a one-sided *t* test. A zero null hypothesis is used. The number of degrees of freedom, *N*, is obtained from the Fisher’s *Z* transformation, where the variance of *Z* is equal to (*N* − 3)^{−1}. These pattern correlations are applied to the entire Northern Hemisphere. The onset day is defined as the first day of the persistent event. If the amplitude of the NAO/REOF1, NAO/CPC, or NAM index time series exceeds a value of one standard deviation on the onset day, then an NAO/REOF1, NAO/CPC, or NAM persistent event is defined to have taken place. To ensure that each persistent event is independent, we require that each persistent event be separated by more than 15 days.

## 3. Persistent event characteristics

We illustrate the temporal evolution of the anomalous composite SLP field for both phases of the NAO/REOF1 and NAM patterns (Figs. 2 and 3). As can be seen, the SLP anomalies for the NAO/REOF1 and NAM are overall very similar. For the positive phase, prior to the establishment of the NAO/REOF1 and NAM patterns (Figs. 2b and 3b), there is a Rossby wave train that extends over the North Pacific and North America (Figs. 2a and 3a). For the negative phase, the blocking anticyclone that is over Greenland (Figs. 2f and 3f) is preceded by a retrograding anticyclonic anomaly that was previously located over northern Europe (Figs. 2e and 3e).

We next examine the composite NAO/REOF1 and NAM SLP anomalies averaged from lag 0 to lag +6 days, a time period over which the NAO/REOF1 and NAM indices typically exceed 1.25 standard deviations (Fig. 4). As can be seen, the time-averaged NAO/REOF1 and NAM composite patterns appear to more closely resemble each other rather than their respective teleconnection patterns (Fig. 1). Also, over the North Pacific, with the exception of the NAO/REOF1 positive phase (Fig. 4a), all of the time-averaged NAO/REOF1 and NAM composites have a spatial structure that appears to be intermediate between that of the REOF1 and EOF1 patterns (Fig. 1). To verify this visual impression, we calculate the pattern correlations between each of the time-averaged SLP composites and the REOF1 and EOF1 patterns (see Table 2). The values of the pattern correlations range from 0.67 to 0.79. In contrast, the pattern correlation between the time-averaged NAO/REOF1 and NAM SLP composites has a value of 0.96 and 0.97 for the positive and negative phases, respectively, much larger than those shown in Table 2. (The pattern correlation between the REOF1 and EOF1 patterns is 0.88.) These pattern correlations verify that the time-averaged SLP composites for the NAO/REOF1 and NAM are much more similar to each other than to their respective teleconnection patterns. It is this result that motivates the question raised in the introduction of whether there is any statistically significant difference between the NAO and NAM.

We next consider the question of why the pattern correlations between the time-averaged NAO and NAM SLP composites are much larger than those with their respective teleconnection pattern. For this question, a series of composite calculations is first performed for those days when the amplitude of the NAO and NAM teleconnection patterns exceeds 1.5 standard deviations. The pattern correlations between these NAO and NAM composites is 0.88 for the positive phase and 0.93 for the negative phase. For both the NAO and NAM, the pattern correlations between these composites and their respective teleconnection patterns yields similar values, ranging between 0.82 and 0.91. These results are rather different from those in the above paragraph for the time-averaged composites. To interpret these findings, we first note that the time-averaged composites are based on two requirements, 1) that the SLP field must have a large projection onto the corresponding teleconnection pattern (this requirement also applies to the above composites with a large teleconnection pattern amplitude), and 2) that the SLP spatial pattern must persist for five or more consecutive days. With regard to the first requirement, for both the NAO and NAM, amongst the days with large projections, there is much variability in the spatial patterns. Thus, our results suggest that the similarity between the time-averaged NAO and NAM SLP composites arises from the requirement of persistence, which leads to the selection of a subset of large NAO and NAM projection days for which the SLP field simultaneously projects onto very similar spatial patterns. These persistence patterns are somewhat different from the NAO and NAM teleconnection patterns.

Time-averaged composites are also determined for the NAO/CPC time series (Fig. 5). As can be seen, the time-averaged NAO/CPC patterns very much resemble those for the NAO/REOF1 and NAM (Fig. 4), which lack a strong center of action in the North Pacific.

## 4. Tests of statistical significance

*t*distribution for the difference of means, by testing whether the variable (see von Storch and Zwiers 2002)whereexceeds the 80% confidence level, for a two-sided

*t*test, where the variable

*T*do not exceed the 80% confidence level over a sufficiently large area [this particular fractional area is determined by examining field significance (Livezey and Chen 1983)], then we claim that our null hypothesis that the NAO and NAM are indistinguishable cannot be rejected (since our focus is on the acceptance of the null hypothesis, we use the more strict 80% confidence level rather than the more commonly used 95% confidence level). The quantity

*n*

_{1}(

*n*

_{2}) is the number of persistent events within the NAO (NAM) composite,

*S*

_{1}(

*S*

_{2}) is the standard deviation of the NAO (NAM) composite, and

*λ*and

*θ*are latitude and longitude, respectively. The approach taken is to calculate (1) separately for each of the seven lags between lag 0 and lag +6 days, and then to average the

*t*values over these seven lags.

For the field significance calculations, a Monte Carlo approach is used. The onset days for these calculations are randomly selected, with *n*_{1} onset days being chosen for the NAO and *n*_{2} onset days for the NAM. The composites, *S*_{1} and *S*_{2}, are then separately calculated for the NAO and the NAM, for all lags between lag 0 and lag +6 days. This is followed by a calculation of the *t* values at each lag and then a time-average of the *t* values over the lag 0 to lag +6 day interval. This procedure is performed 1000 times. For the SLP composites, it is found that 20% of the time-averaged difference composites have more than 17.8% of the area of the Northern Hemisphere with *t* values above that for the 80% confidence level (this threshold level is very similar for both the NAO/REOF1 and NAO/CPC patterns). It is important to note that this threshold is less than 20% of the Northern Hemisphere because of the 7-day time-averaging. [Consistent with our expectations, for difference composites without the time-averaging, 50% (20%) of the difference composites have more than 20% (24%) of the hemispheric fractional area with *t* values above the 80% confidence level.] Therefore, if the fractional area of the difference composites does not exceed this 17.8% threshold, we will claim that the null hypothesis cannot be rejected at the 80% confidence level.

Before presenting the field significance results, it is important to note that there are many NAO and NAM persistent events that coincide. This is not surprising, because of both the large overlap in the NAO and NAM spatial patterns (Figs. 4 and 5) and the high temporal correlation between the various NAO and NAM index time series (Table 1). As an example, amongst the 30 NAO/REOF1 and 23 NAM positive phase persistent events, there are 18 events that coincide. For the 29 NAO/REOF1 and 31 NAM negative phase events, there are 24 events that coincide. As the difference of means *t* test requires that the NAO and NAM events be independent, to retain this independence and yet maximize the sample size, we adopt the following procedure. For both NAO and NAM phases, each of the coinciding events are placed in chronological order and then designated alternately as either even or odd. Composites are then calculated from a combination of all the nonoverlapping events together with either the odd or the even events. For example, we calculate two composite patterns, one for the NAO that includes both the nonoverlapping and the odd events, and the other for the NAM that is comprised of both the nonoverlapping and the even events. The statistical significance of the difference between these NAO (odd) and NAM (even) composites is then calculated with (1). An analogous calculation is also performed for the NAO (even) and NAM (odd) composites. These odd and even difference composites are calculated both for the NAO/REOF1 and NAO/CPC patterns.

### a. SLP

The SLP difference composites together with the corresponding *t* values are shown for the NAO/REOF1 and NAM in Fig. 6 and for the NAO/CPC and NAM in Fig. 7. In these figures, we evaluate the difference between the odd composite of the NAO and the even composite of the NAM, and vice versa. As can be seen (cf. Figs. 6a,c, Figs. 6b,d, Figs. 7a,c, and Figs. 7b,d), the two difference composites for each phase are very different from one another. If the NAO and NAM patterns were truly distinct, then we would expect that the two difference composites for the same phase would be similar. This result alone suggests that the difference composites are not statistically significant. The sensitivity of the results shown in Figs. 6 and 7 to the time averaging interval was found to be small for time intervals between 5 and 9 days.

The field significance results are shown in Table 3. For both phases of the NAO/REOF1 and NAO/CPC patterns, compared with the two phases of the NAM, the fraction of area with *t* values greater than that for the 80% confidence level is always under the 17.8% threshold. These results suggest that we cannot reject the null hypothesis that the NAO and NAM persistent events are indistinguishable, or equivalently, that they come from the same population. As is seen in Table 3, the fractional area for the NAO/CPC difference composites are mostly larger than those for the NAO/REOF1 difference composites. This result is to be expected, because the linear correlation between the NAO/CPC index and both NAM indices is smaller than that between the NAO/REOF1 index and the two NAM indices (see Table 1).

### b. *ψ*_{40} and *ψ*_{300}

We next examine the field significance of the difference composites for the stratospheric (40 hPa) and upper-tropospheric (300 hPa) streamfunction fields. These two levels are investigated because of the finding that the NAO originates from the breaking of synoptic-scale waves in the upper troposphere (Benedict et al. 2004; Franzke et al. 2004) and because there are numerous NAM studies that focus on its stratospheric component (e.g., Baldwin and Dunkerton 1999).

For the 300-hPa level, the threshold value for the field significance tests is found to be 11.2% of the Northern Hemisphere, markedly smaller than that for the SLP difference composites. The fractional areas for the various *ψ*_{300} difference composites are shown in Table 3. As can be seen, with the exception of the NAO/CPC (odd)/NAM (even) positive phase composite, all fractional areas are less than the threshold value. This one exception indicates that either the NAO or NAM patterns are not entirely distinct at 300 hPa, or that this exception corresponds to the 20% of cases, which randomly exceed the statistical significance threshold. For the 40-hPa level, the threshold level for the field significance test is found to be 22.9% of the Northern Hemisphere. As can be seen from Table 3, the fractional area in all of the 40-hPa difference composites is always less than this value. These results suggest that the NAO and NAM patterns at the surface and stratosphere are indistinguishable but that slight differences may exist in the upper troposphere.

## 5. Wave-breaking characteristics of NAM life cycle

The dynamical processes that describe the NAO life cycle were recently examined by Benedict et al. (2004) and Franzke et al. (2004). These studies showed that the positive NAO phase arises from the anticyclonic^{1} wave breaking of two synoptic-scale waves, whereas the negative NAO phase develops from the cyclonic wave breaking of a single synoptic-scale wave. It is the remnants of these wave breakings that comprise both NAO phases. Given the results of the previous section, we would expect that the NAM shows the same wave-breaking properties.

Our interest in examining whether the NAM pattern arises from wave-breaking stems from the question raised in the introduction as to whether the dominant pattern of low-frequency variability in the Northern Hemisphere is annular or is confined to the North Atlantic. If the NAM does arise from wave breaking, as has been shown for the NAO, then it is unlikely that the NAM can be an annular pattern. This is simply because most breaking waves lead to the formation of locally confined, rather than zonally uniform, anomalies.

A sequence of maps of the composite potential temperature field on the 2-PVU surface (the tropopause) is shown for the positive NAM phase in Fig. 8. To aid in the visualization of the wave breaking, values of potential temperature below 315K are shaded. For the positive phase, at lag −1 days (Fig. 8a), anticyclonic wave breaking can be seen over the western United States and the adjacent Pacific Ocean. At lag 0 days, anticyclonic wave breaking begins to develop over the subtropical and midlatitude North Atlantic. This wave breaking intensifies during the next two days. The primary impact of this wave breaking is to advect warm air over much of the midlatitude North Atlantic. A close look at the potential temperature contours also reveals the advection of cold air into the high-latitude North Atlantic during the same days. This sequence of anticyclonic wave breakings and thermal advection closely matches the synoptic description of the positive NAO phase in Benedict et al. (2004) and Franzke et al. (2004).

The corresponding sequence of composite 2-PVU potential temperature maps for the negative NAM phase is shown in Fig. 9. For this phase, cyclonic wave breaking is observed over the middle- and high-latitude North Atlantic. This wave breaking first become noticeable at lag 0 days (Fig. 9b) off the east coast of Canada, and then gains strength over the next two days. As can be seen, warm air is being advected into the high-latitude North Atlantic, while cold air is advected toward the middle-latitude North Atlantic. Also, as with the negative NAO phase, there is no indication of wave breaking occurring over the North Pacific. Again, this pattern of wave breaking and thermal advection closely matches that described for the NAO negative phase (Benedict et al. 2004; Franzke et al. 2004).

## 6. Conclusions

In this study, we examined composites of the SLP, 40-hPa, and 300-hPa streamfunction fields during NAO and NAM persistent events to test our null hypothesis that these two teleconnection patterns are indistinguishable. Standard statistical techniques were used, such as *t* tests for the differences of means. Except for one result for the 300-hPa level, our results showed that the null hypothesis cannot be rejected, even at the 80% confidence level. From a mathematical perspective, these results imply that the NAO and NAM events are drawn from the same population, as has been hypothesized by Wallace (2000). Furthermore, we also compared the dynamical characteristics of the NAO and NAM patterns. Recent studies have shown with potential temperature on the tropopause (2-PVU surface) that the anomalies for both NAO phases are remnants of breaking synoptic-scale waves (Benedict et al. 2004; Franzke et al. 2004). An examination of the wave-breaking characteristics during the NAM life cycle reveals the same properties as those for the NAO.

The results of our study also contribute toward the ongoing argument as to whether the NAO or NAM is a better representation of the dominant form of Northern Hemispheric low-frequency variability. Our finding that persistent events of the two patterns are statistically indistinguishable suggests that both patterns are of equal importance. This statistical indistinguishability also implies that the NAO should not be viewed as a regional manifestation of the NAM, as has been suggested by some studies, and that neither the NAO nor the NAM is a statistical artifact, a point that has also been raised in various studies. In addition, the indistinguishability implies that either one of the two patterns should be regarded as redundant. Furthermore, there is also the question of whether the NAO/NAM would be better understood as a pattern that is confined to the North Atlantic; that is, the NAO perspective, or whether the NAO/NAM should be regarded as an annular pattern with some local distortions because of zonal asymmetries in the lower boundary; that is, the NAM perspective. The composite calculations of this study suggest that perhaps neither picture is quite appropriate. This is because even though our composite NAO and NAM patterns both show a strong dipole in the North Atlantic, for some lags, there is a weak but statistically significant anomaly in the North Pacific. The small amplitude and lack of statistical significance at all lags for the North Pacific anomaly suggest that the NAO/NAM pattern should not be seen as annular. However, because the NAO/NAM pattern is associated with a weak North Pacific anomaly, the NAO/NAM is not entirely confined to the North Atlantic. This weak linkage between the North Atlantic and North Pacific is consistent with Benedict et al. (2004), Franzke et al. (2004), and Feldstein (2003) who find that the positive NAO is preceded by breaking synoptic-scale waves over the North Pacific, which last for 2 to 3 days, much shorter than the time scale for the entire persistent event.

This research was supported by the National Science Foundation through Grant ATM-0351044 and CMG Grant DMS-0222133. We thank Drs. Sukyoung Lee, Mike Wallace, and two anonymous reviewers for their beneficial comments. We would also like to thank the NOAA Climate Diagnostics Center for providing us with the NCEP–NCAR reanalysis data.

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Linear correlations between various daily NAO and NAM indices.

Spatial correlation between the NAO (REOF1) and NAM (EOF1) teleconnection patterns and the time-averaged composite SLP fields.

The fraction of the area of the Northern Hemisphere with *t* values that are above the 80% confidence level.

^{1}

Following Thorncroft et al. (1993), anticyclonic (cyclonic) wave breaking is characterized by southwest–northeast (southeast–northwest) tilt of the trough–ridge pair.