1. Introduction
The North Atlantic Oscillation (NAO), first identified by Sir Gilbert Walker (Walker 1924), is the most pronounced mode of atmospheric wintertime variability over Europe, eastern North America, and the Eurasian continent (van Loon and Rogers 1978; Hurrell 1995, 1996). The variability of the NAO is associated with changes in the location of the storm track over the North Atlantic region, as well as with precipitation and temperature anomalies over much of the North Atlantic and Eurasia (Hurrell 1995, 1996; Rogers 1990). A comprehensive review of the NAO can be found in Hurrell et al. (2003). Thompson and Wallace (1998) suggested that, rather than the NAO, the Arctic Oscillation (AO) more adequately represents the dominant mode of extratropical tropospheric atmospheric variability in the Northern Hemisphere. Compared to the NAO, the AO has an additional, relatively weak, center of action in the North Pacific and the northern center of the AO spreads more widely over the polar cap. However, the AO and the NAO have almost identical spatial structures over the North Atlantic region.
The preference by some authors for using the AO instead of the NAO is supported by the observation that the AO appears to be the tropospheric signature of the principal mode of variability of the wintertime stratospheric circulation (Perlwitz and Graf 1995; Kodera et al. 1996). Another notable justification for this preference is that the zonally symmetric component of the AO has a very similar counterpart in the Southern Hemisphere (Thompson and Wallace 1998, 2000; Hartmann and Lo 1998). In fact, these two patterns are now commonly referred to as the northern annular mode (NAM) and the southern annular mode (SAM). Furthermore, Thompson et al. (2000) found that the climatic trend noted for the Northern Hemisphere could be better resolved using the AO index. The bias of the NAM toward the North Atlantic sector is likely the consequence of the land–sea thermal contrasts and mountains in the Northern Hemisphere (Thompson and Wallace 1998). Although there is some debate regarding the differences between the AO and the NAO in the literature, many authors regard them as the same phenomenon.
Different mechanisms have been advanced to explain the variability of the AO/NAO. It has been established that the AO/NAO is, to a significant degree, an internal mode of variability of the atmospheric circulation. The spatial structure and amplitude of the AO/NAO can be well simulated in atmospheric general circulation models (AGCM) forced with fixed external forcing (Barnett 1985; Limpasuvan and Hartmann 1999). However, the external forcing cannot be entirely ruled out as contributing to its dynamics. Many studies showed that the NAO is the atmospheric response to regional forcing over the extratropical Atlantic Ocean (Kushnir 1994; Mehta et al. 2000). Recently, some studies pointed out a possible link between the AO/NAO and tropical forcing with time scales ranging from annual to decadal, a link which might be used to improve the prediction of the AO/NAO (Hoerling et al. 2001; Lin et al. 2002; Lin et al. 2005a, b). The dynamics that drive the subseasonal evolution of the AO/NAO, however, remain unclear. There is growing evidence that a coupling exits between the tropospheric AO and conditions in the stratosphere (Baldwin and Dunkerton 1999; Baldwin et al. 2003; Ambaum and Hoskins 2002; Norton 2003; Scaife et al. 2005). Baldwin and Dunkerton (1999) found a tendency for signals to propagate downward from the stratosphere to the troposphere within several weeks. Later studies showed that the stratospheric state can be used as a predictor of the AO in the troposphere, extending the predictability of the troposphere beyond the time scale of 10 days (Baldwin et al. 2003; Charlton et al. 2003; Christiansen 2005). However, AO events are also observed to be generated solely within the troposphere (Baldwin and Dunkerton 1999; Zhou et al. 2002). This stratosphere–troposphere connection, while of interest from the predictability point of view, is thus not seen as an essential component of the AO dynamics. Franzke et al. (2004) found that initial perturbations located upstream of the climatological Atlantic jet are important for the NAO formation. The NAO was found to be the remnant of breaking waves (Franzke et al. 2004; Benedict et al. 2004). Feldstein (2003) examined the fundamental mechanisms for the growth and the decay of the NAO using 300-hPa data. He examined the temporal evolution of each term in the streamfunction tendency equation and showed that both low- and high-frequency transients contribute to the growth of the NAO.
The debate, however, is not completely closed as to whether or not the AO is a robust pattern, representative of the atmospheric variability in the Northern Hemisphere (Deser 2000; Ambaum et al. 2001; Wallace 2000; Wallace and Thompson 2002; Quadrelli and Wallace 2004; Wu and Straus 2004). As the AO and the NAO are highly correlated with each other, some studies question whether the AO and the NAO can be distinguished from each other. Using a rotated principal component analysis (RPCA), Rogers and McHugh (2002) argue that the AO and the NAO are inseparable, at least in winter. Feldstein and Franzke (2006) defined the AO as the leading empirical orthogonal function (EOF1) and the NAO as the first rotated EOF of the monthly mean sea level pressure (SLP) field of the Northern Hemisphere and came to the conclusion that the AO and the NAO are indistinguishable. Wallace (2000) suggested that the AO and the NAO could be distinct only if the NAO is defined in terms of station-based indexes. The above studies suggest that the distinction or lack thereof between the AO and the NAO is sensitive to the choice of definitions of the events. The AO is usually defined as the leading EOF of the Northern Hemisphere SLP field poleward of 20°N, while there is no unique way to define the NAO. The NAO index can be obtained from both pattern-based methods and station/gridpoint–based approaches. The station/gridpoint–based NAO amplitude is an index usually defined as the difference between the normalized SLP at Lisbon, Portugal, and Stykkisholmur, Iceland (Hurrell 1995). The pattern-based NAO indexes include the first EOF of the SLP over the North Atlantic (Hurrell et al. 2003), the rotated EOF of SLP (Rogers and McHugh 2002), or the streamfunction (Feldstein 2003) over the Northern Hemisphere. In some studies, zonally averaged indexes are used to define the NAO (Lorenz 1951; Namias 1950). Considering the above discussion, it would appear helpful to clarify the extent to which different definitions of the NAO lead to its different characteristics on the intraseasonal time scale.
In the present work we extend previous studies of the NAO on the intraseasonal time scale. We explore how the characteristics of the NAO are influenced by the choice of its definitions. We examine several aspects of the NAO, including its time-averaged spatial structures, the time evolutions of its spatial structures, the associated horizontal propagation of wave activity, and the mechanisms that drive it.
The paper is organized as follows. The data and diagnostic techniques are presented in section 2. Section 3 presents the time-averaged spatial structures of the NAO events. Section 4 describes and compares the growth rates and decay rates of the NAO events. The frequency distribution of the NAO duration is presented in section 5. Section 6 illustrates the time-evolving spatial structures of the NAO events. The wave activity fluxes during the setup stages and the mature stages, as well as the interaction between the transient eddies and the NAO, are discussed in section 7, followed by the conclusions in section 8.
2. Data and diagnostic techniques
This study uses daily mean National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data spanning 51 boreal extended winters (1 October to 31 March) from 1948/49 to 1998/99. The variables employed are SLP and the geopotential height at 1000, 925, 850, 700, 600, 500, 400, 300, 200, 150, and 100 hPa. The data retained cover the area from 20°N to the North Pole with a resolution of 5° in both latitude and longitude.
First, both the seasonal cycle (obtained as the calendar daily means over the 51 boreal winters) and linear trends are removed from the SLP and the geopotential height fields. Then the Fourier filter used by Lin and Derome (1999) is applied to remove the synoptic-scale transients (periods shorter than 10 days). Low-frequency eddies are defined as those with periods longer than 10 days. The introduction of satellite data during the 1970s has introduced some inhomogeneity in the data, but the influence of this on the life cycle of the NAO is very small. We verified this by dividing the data into two periods, 1948–77 and 1980–99. Analyzing the two periods of data separately, we found that the conclusions were valid for both periods.
Four frequently used NAO indexes are examined in this study. One is a station/gridpoint-based index and the other three are pattern-based indexes. The station/gridpoint-based NAO index is defined as the difference between the normalized SLP at the two grid points closest to Lisbon, Portugal, and Stykkisholmur, Iceland. Monthly averages of this time series correlate with Hurrell’s (1995) NAO index at a level of 0.95 over the 51 winters common to both series. Second, an EOF analysis is conducted on the mean monthly SLP data over the North Atlantic region (20°–80°N, 90°W–40°E). The NAO appears as the first EOF, explaining 32% of the total variance. Then the daily mean SLP is projected onto this EOF to get the corresponding daily NAO time series. The third and fourth NAO indexes are obtained by a rotated EOF of the monthly mean SLP and of the monthly mean 500-hPa geopotential height poleward of 20°N. The NAO appears as the second rotated EOF while the first rotated EOF is the Pacific–North American (PNA) pattern in both analyses. These four NAO indexes are named NAO1, NAO2, NAO3, and NAO4 index, respectively. Considering the close relationship between the AO and the NAO, the AO index is also examined in this study. To obtain the spatial structure of the AO, an EOF analysis is conducted on the mean monthly SLP data poleward of 20°N. The first EOF, explaining 20% of the total variance, is the AO. The AO index is obtained by projecting the daily mean SLP onto this EOF.
All the AO and NAO daily time series are then normalized by their respective standard deviations. The correlations among these daily time series over the 51 boreal winters are given in Table 1. We see that NAO indexes defined by pattern-based methods are more highly correlated to each other than with the station/gridpoint–based NAO1 index. The best correlation between the NAO1 and the other three pattern-based NAO indexes is only 0.75, while the correlations among the NAO2, NAO3, and NAO4 indexes are all higher than 0.85. Examination of the correlations between the AO and NAO indexes shows that the AO index is best correlated (0.93) to the NAO2 index, while the correlation between the AO index and the NAO1 index is only 0.64. All correlations are significant at the 99% confidence level according to a Student’s t test. In the following, we will focus on a comparison of the NAO1 and the NAO2. Considering the high correlation between the AO and the NAO2 (0.93), it is reasonable to suggest that the conclusions derived from the comparison of the NAO1 and the NAO2 in this study can serve as a reference in interpreting the differences and similarities between the AO and station/gridpoint–defined NAO. The other NAO definitions will also be discussed briefly.
To define the NAO events we use a method similar to that of Lin and Derome (1999) in their study of the PNA pattern. The NAO events were selected using low-pass-filtered SLP data. First, the amplitude of the daily time series is required to exceed (be less than) 0.4 (−0.4) standard deviation of the index. Second, in each case, the amplitude meeting the first criterion must persist for at least 10 days. Third, the beginning and the ending day of each event must be at least 10 days away from 1 October and 31 March. This last condition is included to ensure that the time evolution of the events selected is not cut off by the calendar date. Also, the time interval between two events must be more than 10 days, to ensure that they are separate events. Based on these criteria, 74 positive NAO1 and 81 negative NAO1 events are selected. As for the NAO2 events, 80 positive and 86 negative events are selected. The first criterion is obviously arbitrary. However, while using other thresholds to select events, such as 0.6, 0.8, and 1 standard deviation, changes the number of selected events, the basic results to be discussed are unaltered. To see the extent to which the NAO1 events and the NAO2 events overlap in time, we compared the days selected for the NAO1 and NAO2 events. We found that the selected days common to positive NAO1 and positive NAO2 events occupy 42% of the total selected days of the positive NAO1 and 38% of those of the positive NAO2. For the negative polarities, 50% of the negative NAO1 days and 49% of the negative NAO2 days are common to them. Thus there is some overlap between the NAO1 and the NAO2, but it is far from complete.
The first day when the amplitude meets the first criterion is defined as the onset day (S0 day), while the first day when the amplitude falls below the first criterion is termed the decay day (D0 day). The days between the onset day and the decay day are termed the mature stage. We will concentrate on the setup period, that is, a few days before and after day S0, although the decay period is also briefly discussed in sections 4 and 7. The time evolution of the spatial structures of the NAO is constructed by simply averaging all the events relative to the onset days and, separately, relative to the decay days.
3. Time-averaged spatial structure
The NAO events have been selected on the basis of SLP data. However, considering the equivalent barotropic nature of the extratropical low-frequency variability, the spatial patterns to be discussed in this paper are vertically averaged using geopotential height data at 11 levels, from 1000 to 150 hPa. Similarly, the vorticity budget of section 7 is also vertically averaged. In the following, we will refer to the positive polarity of the NAO as “+NAO” and to the negative polarities as “−NAO.” When used without the “+” and “−,” the term NAO will refer to both polarities.
The time-averaged composites for the NAO1 and the NAO2 from day S0 to day D0 are shown in Figs. 1a,b,d,e, respectively. We also want to examine the extent to which the time average of the positive and negative polarities of the NAO events can be viewed as the mirror images of each other. The sums of the two polarities of the NAO1 and NAO2 are shown in Figs. 1c,f, respectively. Naturally, if they are mirror images, the sum of the positive and negative phases should be zero. We see that the dipole over the North Atlantic, the well-known central feature of the NAO, is evident. As expected, the structures of the time-averaged NAO1 and the NAO2 are similar to each other. The composites of the NAO1 (Figs. 1a,b) are quite similar to those of Hurrell (1995). For the composites of the NAO2 (Figs. 1d,e), they are quite similar to the AO of Thompson and Wallace (1998). This is not surprising if we consider the high correlation between the AO and NAO2 indexes. The sum is seen to be very small for the NAO2 (Fig. 1f), indicating that the two polarities of the NAO2 tend to have very similar structures and amplitudes but different signs. The same is not true, however, for the NAO1. The amplitude of the −NAO1 over the North Atlantic is clearly larger than that of the positive polarity, and the northern center of the −NAO1 is located somewhat farther west than that of its positive counterpart, as can be seen more clearly from Fig. 1c. This phase difference is consistent with Cassou’s (2001) study of climate regimes in the North Atlantic, whose results are included in Hurrell et al.’s (2003) review. By comparing Figs. 1a,b and 1d,e, we can also see that the northern center of the NAO2 extends across more of the polar region than does that of the NAO1.
When obtained from the NAO3 and NAO4 indexes, the two phases of the NAO (not shown) are more nearly antisymmetric to each other than the NAO1 presented above. The fact that the time-averaged composites for the two phases of the NAO1 are not as nearly antisymmetric as those of the NAO2, NAO3, and NAO4 should not be surprising if we consider the way we define these events. The EOF technique includes a built-in assumption of antisymmetry between the two polarities of the patterns, whereas the two-point definition of the NAO1 index has no such constraint.
4. Composites of the time series
To estimate the time scales of the NAO, we examine the composites of their time series. This is done separately for the positive and negative NAO and separately for the growth and decay phases. Taking the positive phase as an example, we recall that each event entering a composite has an amplitude of at least 0.4 standard deviation on day S0 for the growth phase and less than 0.4 standard deviation on day D0 for the decay phase. The decay phase is treated separately from the growth phase, because, as will be seen later, there is a considerable range in the lifetime of the different events, some lasting little more than 10 days (our minimum) while others last several times longer. Aligning all events on day S0 and compositing them over, say, 30 days, would smear the decay phase over widely different events and lead to unrepresentative results. As done here, day D0 is the first day for which the amplitudes falls below 0.4 standard deviation for all positive events, regardless of their previous duration.
We only show the composites of the time series for the NAO1 as an example as it is found that the conclusion also applies to the other indexes. From Fig. 2 we see that the growth and decay rates of the NAO are similar to each other. In addition, the growth and decay rates are approximately the same for the positive and negative polarities (Fig. 2). The amplitude develops most rapidly within a few days after the onset day, reaches a maximum 4 or 5 days after day S0, and remains relatively stable or decays somewhat in the remaining period. In all cases the amplitude starts to decay about 1 week before day D0 and reverses sign at about day D1. When the above composites were repeated with unfiltered data, the resulting curves were slightly noisy, as expected, but the results described above remained essentially unchanged. The composites of the time series obtained here are similar to those in Feldstein (2003), with the exception that in his results, the growth rate is faster than the decay rate. The difference is caused by our aligning the events to day D0 to obtain the decay phase separately.
5. The lifetime distributions
We now examine the frequency of the NAO events as a function of their duration. As can be seen from Fig. 3, the duration range for the NAO2 is wider than that of the NAO1. The NAO2 has similar distributions for both polarities, but this is not the case for the NAO1. One notable feature is that more than 50% of the −NAO1 events last less than 2 weeks, which results in a sharply decaying distribution of lifetimes compared to the +NAO1. The averaged duration for both polarities of the NAO2 and for the +NAO1 is 17 days, while for the −NAO1 it is 15 days. The chi-square goodness-of-fit test has been used to test the frequency distribution of the NAO1 and the NAO2 to estimate whether or not the distributions are significantly different. It was found that the difference in the frequency distributions of the two phases of the NAO1 marginally passes the 10% significance level, which is not the case, however, for the NAO2. From this perspective the frequency distributions of the two phases of the NAO1 are seen to be somewhat more asymmetric than those of the NAO2.
6. The temporal evolution of the spatial structures
The composites of the vertically integrated geopotential height for the period day S−7 through day S3 with a 2-day interval for both phases of the NAO1 are shown in Figs. 4 and 5. The corresponding figures for the −NAO2 appear in Fig. 6. The time evolution of the +NAO2 is not shown as it is essentially the mirror image of the −NAO2. Areas with significance level over 95% according to a Student’s t test are shaded. As expected, the NAO1 and the NAO2 share some similarities during their setup stages. We will take the −NAO2 as an example to describe several of their common characteristics. We will later turn to the differences between them during their respective growth phases.
From Fig. 6 we can see that 1 week before the −NAO2 onset day, three anomalies appear: a pronounced negative anomaly over the North Atlantic at about 70°N, a positive anomaly to the south at about 50°N, and another positive anomaly over Scandinavia. This pattern obviously projects negatively onto the −NAO, as could be expected from Fig. 2 where it was found that the composite time series of the −NAO starts from a positive value. Subsequently, the two positive anomalies develop with time and merge together just 3 days before the onset day to form the northern center of the −NAO2. The negative anomaly first weakens then develops and moves southward, forming the southern center of the −NAO2 over the North Atlantic. The −NAO2 pattern becomes apparent after day S−1 and is quite stable thereafter. Both the NAO1 and the NAO2 exhibit these characteristics during their setup processes. The negative anomaly of the −NAO2 over eastern Asia appears at day S−1. It develops primarily locally and intensifies with time.
Some differences also appear during the setup stages between the NAO1 and the NAO2. The setup process of the NAO2 is quite antisymmetric for the two polarities, while for the NAO1 there are some noticeable differences between its two phases (Figs. 4, 5). In particular, the +NAO1 evolution (Fig. 4) shows, starting at day S−5, an upstream wave train pattern from the eastern Pacific across North America to the North Atlantic. The wave train signal for the +NAO1 was also noted by Feldstein (2003) using 300-hPa data. After the onset day, the anomaly centers develop and intensify over time downstream toward the NAO region. Finally, for the −NAO1 (Fig. 5), starting at day S−7, a pronounced anticyclone appears over northern Russia (about 60°E). It develops with time, moves westward and merges with another positive anomaly off the west coast of Europe. It then remains almost stationary over the east coast of Greenland from day S−1 onward. We observe a similar (albeit initially weaker) evolution of the opposite sign in the case of the +NAO1 (Fig. 4). In contrast to the +NAO1, however, no upstream wavetrain signal is found over the PNA region during the growth of the −NAO1. Comparing Figs. 4 and 5, it is also found that the polar NAO1 center migrates from the west or the east depending on the NAO phase, for example, the northern center of the +NAO1 develops from a negative anomaly originating from the western North Atlantic while the northern center of the −NAO1 migrates from northern Russia.
The temporal evolution of the NAO obtained using the NAO3 and NAO4 indexes have also been examined. It was found that the evolution of the NAO obtained using these two indexes are similar to that of the NAO2, as expected, considering the high correlations between them. These results are also consistent with Feldstein and Franzke’s (2006), where they used SLP data to examine whether or not the AO and the NAO are distinguishable. As both the AO and NAO were defined using pattern-based approaches, they found that the temporal evolution of the AO and the NAO are overall very similar.
7. The wave activity flux and the barotropic vorticity equation
In this section we present the wave activity flux associated with the composite NAO, as discussed in section 2, during its setup and mature stages, that is, from day S−5 to day S10. In the expression Eq. (2) for the wave activity flux, ψ′ is the streamfunction of the composite field at 500 hPa and U, V are the velocity component of the climatological mean of the 51 winters. The fluxes for the positive and negative NAO1 are shown in Figs. 7 and 8, respectively, and those for the −NAO2 in Fig. 9. The wave activity flux of the +NAO2 is not shown as it is similar to that of its negative counterpart. We plot the wave activity flux from day S−5 to day S−1 with a 1-day interval and the time-averaged wave activity flux from day S0 to day S10 since, as noted in section 4, the NAO pattern is almost stationary after day S0.
From day S−5 through day S−1, the wave activity flux for both phases of the NAO1 originates from the Labrador coast of Canada, indicating a source there, and is directed eastward. For the +NAO1, an additional flux from upstream appears across North America at day S−3, suggesting a Pacific influence on the North Atlantic area. In contrast, for the −NAO1 (Fig. 8), no upstream wave activity flux is observed over the PNA region during this period. Similarly to the NAO1, the wave activity flux for the −NAO2 also originates from the Labrador coast of Canada. It is primarily in the zonal direction and penetrates deeply into the northern Eurasian continent. During the mature stage (from day S0 to day S10), the wave activity flux for both phases of the NAO1 is mostly concentrated over the North Atlantic. More equatorward propagation appears between 30°W and 0° than for the −NAO2. Examination of the divergence of the wave activity flux (not shown) indicates that during the mature stage a flux divergence occurs over the high latitudes of the North Atlantic region, as can also be inferred from the time-averaged wave activity flux from day S0 to day S10. This happens for both of the NAO1 and the NAO2. It is not possible from the above to identify the mechanisms responsible for these sources of wave activity, but in the following we will examine the contribution of the transients to the vorticity budget to see if this can yield some insight.
We use the barotropic vorticity equation to see the influence of the first four terms on the rhs of Eq. (4) on the tendency of the geopotential height anomalies. We first examine the spatial structures of the Nhh and Nll terms, considering their importance as pointed out by Cai and Van den Dool (1994). Having seen that the spatial structures of Nll and Nhh have little phase shift during the setup and the mature stages, we averaged their spatial structures before (from day S−6 to day S−1) and after (from day S3 to day S9) the onset day for the −NAO1 (Fig. 10) and the −NAO2 (Fig. 11). The main results also apply to the positive phases (not shown). Several characteristics are immediately apparent. First, the Nll term has a larger magnitude than the Nhh term. The centers of the Nhh term are concentrated over the North Atlantic and are in phase with the centers of the NAO events, while the Nll term has additional pronounced centers outside the North Atlantic. We recall that the NAO events are selected on the basis of data with periods 10–182 days, while the Nhh term is computed with data with shorter periods (2–10 days). The Nhh term can then be viewed as a forcing by the high frequency on the low-frequency NAO events. We see from Figs. 10 and 5 that, during the −NAO1 growth phase, the Nhh term is in phase with the observed height tendency, while during the mature phase, it is in phase with the −NAO1 itself. The vorticity flux convergence/divergence by the high-frequency transients is thus seen to contribute to the growth and maintenance of the −NAO1. The relationship of the Nll term to the growth and maintenance of the −NAO1 is more complex. During the period day S−6 to day S−1 (Fig. 10), the Nll term contributes to the development of the −NAO1 centers over and south of Greenland and over Europe (Fig. 5, day S−7 to day S−1). During the mature stage, however, (i.e., for the period day S3 to day S9) the phase relationship between the Nll term and the −NAO1 is not as clear. Calculations to be described shortly show that the Nll term projects negatively onto the −NAO structure.
A comparison of Figs. 6 and 11 for the −NAO2 leads to similar conclusions as for the −NAO1, namely, 1) that the Nhh term clearly contributes to the development and maintenance of the −NAO2, whereas 2) the Nll term contributes to the growth of the −NAO2 but is out of phase with it during the mature period.
An arguably more succinct way of looking at the roles of the terms on the rhs of Eq. (4) is to project the spatial distribution of their composites onto that of the time-averaged composites of the NAO (Fig. 1). The projection illustrates the contribution of each term to the time tendency of the NAO index (Feldstein 2002). When the composites of the vertically integrated geopotential height are quasi stationary and resemble the time-averaged composites of the NAO, the projection illustrates the contribution of those terms to the tendency of the NAO patterns. We apply the projection technique for the NAO during the setup stage (day S−4 to day S10) (Fig. 12, left side of panels) and during the decay stage (day D−8 to day D4) (Fig. 12, right side of panels) separately when the patterns are quasistationary. We only show the projections for the NAO2 as an example as it is found that the projections for the NAO1 are similar to those of the NAO2. As can be seen from Fig. 12, during the setup stage, the projections of Nhh remain positive while the projections of Nll become negative just a few days after the onset day. This result is consistent with Figs. 10 and 11 where we found that the centers of the Nhh spatial structures in phase with the NAO while the Nll spatial structures reverse sign after the events are established. These results are also consistent with previous studies (Feldstein 2003; Franzke and Feldstein 2005). The high-frequency eddies maintain the NAO through a positive feedback process (Lau 1988; Branstator 1992; Nakamura et al. 1997). The ADV term also plays an important role during the development of the events, while the role of the DIV term is found to be just opposite to the Nll term, that is, it delays the growth of the events before the onset day and a few days after the onset day it helps to maintain them. Figure 12 shows that during the decay stages, the low-frequency transients and the vorticity advection are dominant, while the DIV term helps to delay the decay of the events.
There are some differences between the projection results we present here and those presented by Feldstein (2003), especially for the DIV term. The differences are mainly caused by the fact that we vertically integrated the terms, whereas Feldstein did not. We also used only the 300-hPa data to examine the roles of the above four terms (not shown) and obtained results consistent with his.
8. Summary and discussion
The purpose of this study was to make some contribution to the question as to how the characteristics of the NAO events are influenced by the choice of their definitions and to what extent do the NAO events obtained using different definitions differ from each other. We examined the influence of four definitions of the NAO index on the characteristics of the NAO on the intraseasonal time scale. One NAO index was based on the pressure difference between two points in space and three NAO indexes were pattern based. The pattern-based NAO (NAO2, NAO3, and NAO4) were found to be similar to each other, while some notable differences were observed when the NAO was defined using a station/gridpoint–based index (NAO1). Emphasis has been placed on comparing the characteristics of the NAO obtained using the NAO1 and NAO2 indexes.
We saw that the time-averaged spatial structures for the two polarities of the NAO1 are less antisymmetric than those of the NAO2. The time-averaged spatial structures for the NAO2 expand across more of the polar region, while the NAO1 are more concentrated over the polar North Atlantic and the amplitude of the −NAO1 is larger than that of the +NAO1. The frequency distributions of the durations of the two phases of the NAO1 are more asymmetric than those of the NAO2. The −NAO1 was found to be less persistent than other events.
The time evolutions of the spatial structures of the NAO1 and NAO2 display some common characteristics during their setup processes. They develop starting from weak patterns of opposite sign 1 week before their onset day. The northern center of the events evolves from two anomaly centers with one anomaly center originating in high latitudes of the North Atlantic and the other one originating from northern Scandinavia. The southern center of the dipole pattern is found to develop in situ. Some differences between the NAO1 and the NAO2 have also been noted. Most notable is the observation that the +NAO1 shows a wave train signal over the PNA region during the days before the onset day, while the −NAO1 is found to develop locally over the northern Europe–North Atlantic area. The setup processes for the two polarities are more nearly the mirror images of each other for the NAO2 than for the NAO1.
A wave activity flux for stationary eddies has been computed for the NAO1 and the NAO2 during their setup and mature stages. The wave activity flux for the NAO2 is primarily in the zonal direction. This flux propagates from the Labrador coast of Canada and penetrates deeply into the Eurasian continent. For the NAO1, on the other hand, the wave activity flux is mostly concentrated over the North Atlantic. The flux also propagates starting from the Labrador coast of Canada, but there is a pronounced equatorward component between 30°W and 0°. For the +NAO1, a clear wave activity flux appears over the PNA region before the onset day.
The vorticity budget analysis shows that the roles of the high- and low-frequency transients, advection, and divergence terms are qualitatively similar for the NAO1 and the NAO2. During the setup stage, the high-frequency transients contribute to the growth and maintenance processes. The low-frequency transients help set up the NAO events but subsequently contribute to decay them. The vorticity advection also contributes to the time tendency of the NAO index while the horizontal wind divergence delays the development of the events. During the decay stage, the low-frequency transients and the vorticity advection play the dominant roles, while the horizontal wind divergence acts to delay the decay of the events.
This study shows how the intraseasonal characteristics of the NAO depend on its definitions, more specifically, on whether it is defined through an EOF analysis (regional or hemispheric and rotated) or through a pressure difference between two points in space. It makes it clear that the differences among the subseasonal NAO events defined using varied definitions are minimized when they are all defined through an EOF analysis. Some notable differences are found, on the other hand, when the NAO is defined through a two-point pressure difference, as is commonly done, such as the time-averaged spatial structures, the frequency distribution of their durations, and the temporal evolution of their spatial structures.
The EOF-based definition, as mentioned above, has a built-in assumption of antisymmetry between the two polarities of the EOF. The station/gridpoint–based index does not have this constraint and would appear better suited to show the differences between the two phases of the NAO, as was the case in this study. Some interesting characteristics of the NAO can only be seen through the NAO1, as for example, the influence of the upstream Pacific Ocean on the NAO. Also the pronounced equatorward wave activity flux off the west coast of Europe, indicating an interaction between the high- and low-latitude flows, is clear only with the NAO1 index.
Acknowledgments
This research was funded by the Natural Sciences and Engineering Research Council of Canada and the Canadian Foundation for Climate and Atmospheric Sciences through the Canadian Climate Variability Research Network. We are grateful to Lisa LeBlanc for her many useful comments. We also thank the editor and the anonymous reviewers for their insightful comments and valuable suggestions for improving the manuscript.
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Composites of the time-averaged (a) +NAO1, (b) −NAO1, (d) +NAO2, and (e) −NAO2. The sum of the composites for the (c) NAO1 and (f) NAO2. Contour interval is 15 m. Areas with significance level over 95% are shaded.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Composites of the time series for the NAO1 for the setup stage (left curves) and for the decay stage (right curves). Solid lines are for the positive polarity and dashed lines are for the negative polarity.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
The frequency distributions as the function of the duration for the (left) NAO1 and (right) NAO2.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Composites of the vertically integrated geopotential height at 11 levels for the +NAO1 from day S−7 to day S3. Contour interval is 15. Solid contours are positive and dashed contours are negative. Areas with significance level over 95% are shaded.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Composites of the wave activity flux defined by Takaya and Nakamura (2001) for the +NAO1 from day S−5 to day S−1 with a 1-day interval and the time average of the wave activity flux from day S0 to day S10. The geopotential height anomaly patterns are overlaid (shaded). Contour interval is 15 m. Solid contours are positive and dashed contours are negative.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Time-averaged composites of the Nll (see text) for the −NAO1 (top left) before the onset day and (bottom left) after the onset day. (right) Similar to left panels, but for the Nhh. Contour interval is 2 × 10−5 m s−1. Similarly for the Nhh (see text) on right panels.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Same as in Fig. 10, but for −NAO2.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Projections of Nhh, Nll, ADV, and DIV (see text) onto (top) +NAO2 and (bottom) −NAO2. Solid line is ADV, dashed line is DIV, solid line with circle is Nhh, and dashed line with square is Nll. The ordinate has units of 0.01 m2 s−1.
Citation: Journal of Climate 20, 24; 10.1175/2007JCLI1408.1
Correlations between the NAO indexes and the AO index.
