1. Introduction
The Arctic Oscillation (AO), which refers to the leading empirical orthogonal function (EOF) of the Northern Hemisphere sea level pressure, has been the subject of numerous studies since the initial work of Thompson and Wallace (1998). The leading EOF of the midtropospheric geopotential height brings strong resemblance with the AO and both variabilities are usually referred to as the tropospheric northern annular mode (NAM) (Thompson and Wallace 2000; Quadrelli and Wallace 2004). The NAM pattern consists of three centers of action: one is located in the North Pacific, which mainly exhibits a one-sign large-scale geopotential anomaly centered in the middle latitudes; and the other two are located in the North Atlantic and strongly project onto the meridional dipolar anomaly of the North Atlantic Oscillation (NAO). There is a debate on the physical meaning of the NAM pattern as it is not clear how the Pacific and Atlantic centers of action are dynamically related (Deser 2000; Ambaum et al. 2001; Wallace and Thompson 2002; Itoh 2008). Honda and Nakamura (2001) and Honda et al. (2005) argued that the NAM is the result of a seesaw relationship between the fluctuations of the Aleutian and Icelandic lows, which itself is a signature of quasi-stationary Rossby waves propagating from the North Pacific to the North Atlantic. As such, the Pacific NAM pattern typically leads the Atlantic one by one month. However, as the typical time scale of the wintertime tropospheric NAM is much shorter, on the order of 10–15 days (Feldstein and Lee 1998; Feldstein 2000; Lorenz and Hartmann 2003; Rivière et al. 2010), the previously mentioned studies do not explain the major part of the NAM variability.
The tropospheric NAM variability is well known to be closely related to the strength of the polar vortex and most intraseasonal variabilities of the tropospheric NAM have been associated to the leading mode of the stratospheric geopotential height, that is, to the stratospheric NAM (Baldwin and Dunkerton 1999). There is often a downward propagation of the stratospheric NAM to the tropospheric NAM that lasts about 15 days (Christiansen 2001). This result is appealing as it indicates some potential predictability of the tropospheric NAM (Baldwin et al. 2003). Some authors have emphasized a pathway from land surface anomalies to the tropospheric NAM anomalies through the stratosphere (Cohen et al. 2007; Peings et al. 2012). But it is clear that there is some NAM variability intrinsic to the troposphere as the tropospheric NAM time scale is much smaller than that of the wintertime stratospheric NAM (Baldwin et al. 2003) and as the internal variability of the tropospheric NAM is large compared to the stratospheric influence (Gerber et al. 2009). Some studies have investigated short-term fluctuations of the combined tropospheric–stratospheric NAM (Black and McDaniel 2004; McDaniel and Black 2005). The purpose of the present paper is to focus on rapid fluctuations of the tropospheric NAM itself, which is expected to be more internally driven.
Compared to studies discussing the influence of the stratosphere onto the tropospheric NAM, those discussing intrinsic tropospheric NAM dynamics are less numerous. There are those considering the propagation of quasi-stationary Rossby wave trains (Honda and Nakamura 2001; Honda et al. 2005; McDaniel and Black 2005). There are others putting an emphasis on synoptic Rossby wave breaking at the hemispheric scale (Feldstein and Franzke 2006; Strong and Magnusdottir 2008b). Rossby wave–breaking events occurring in the two oceanic basins during the same period might be dynamically connected. For instance, anticyclonic wave-breaking events in the eastern Pacific favor the occurrence of those in the Atlantic sector through increased eastward wave activity fluxes (Strong and Magnusdottir 2008a). Woollings and Hoskins (2008) rather emphasized an upstream influence by showing how high-latitude Atlantic blockings precede the Pacific ones by few days with both blockings leading to negative NAM. Note finally that some theoretical studies have emphasized the key role played by synoptic eddies in the formation of low-frequency modes like the Arctic Oscillation and the Antarctic Oscillation (Jin et al. 2006).
More recently, Drouard et al. (2013, hereafter DRA13) and Drouard et al. (2015, hereafter DRA15) proposed a mechanism by which synoptic waves propagating from the North Pacific to the North Atlantic form the linkage between large-scale North Pacific anomalies and the NAO. Large-scale North Pacific anomalies may exert a downstream influence on synoptic wave propagation across North America and, as such, may largely determine the type of wave breaking in the North Atlantic sector and finally the phase of the NAO. More precisely, a large-scale ridge (trough) anomaly in the northeast Pacific favors equatorward (poleward) propagation of synoptic waves more downstream. This in turn triggers anticyclonic (cyclonic) wave-breaking events in the North Atlantic accompanied by an equatorward (poleward) deposit of westward momentum and a poleward (equatorward) deposit of eastward momentum (Rivière and Orlanski 2007; Vallis and Gerber 2008). It leads to a poleward-shifted (equatorward-shifted) Atlantic jet and the positive (negative) phase of the NAO. DRA13 showed evidence of such a process in idealized numerical experiments and DRA15 validated it using reanalysis data and showing monthly composites of the different phases of the El Niño–Southern Oscillation (ENSO), the Pacific–North America pattern (PNA), and NAM. The results on ENSO corroborate the findings of Li and Lau (2012b,a) to a large extent. The present paper investigates the rapid onset of NAM events using daily reanalysis datasets. The objectives are to determine the timing of appearance of the NAM anomalies in the two oceanic basins and the role played by the DRA13 mechanism in triggering these events.
The paper is composed as follows. Section 2 presents the reanalysis datasets, the selected NAM events, and the various diagnostic tools to analyze the generation, propagation, and breaking of synoptic Rossby waves. Section 3 is dedicated to the detailed analysis of the time-lag daily composites of the selected NAM events. We show how North Pacific anomalies first appear and then influence the formation of the North Atlantic anomalies via the downstream propagation and breaking of synoptic waves in the Atlantic sector. In section 4, the tropical origin of the North Pacific anomalies is discussed. Section 5 shows a low-frequency streamfunction budget to more quantitatively compare the different processes into play. Section 6 provides a discussion on the possible role played by the stratosphere and section 7 provides the conclusions.
2. Data and methodology
a. Data
We use daily means of ERA-Interim datasets (Dee et al. 2011) from the European Centre for Medium-Range Weather Forecast (ECMWF) on a 1.5° × 1.5° grid from 16 October to 15 April during the 1979–2014 period. The geopotential, temperature, and three-dimensional wind components on isobaric surfaces and potential vorticity on isentropic surfaces are used. After removing the seasonal cycle, we obtain the synoptic-scale and planetary-scale anomalies by decomposing the field into high- and low-frequency parts. The filter is defined by a nine-point Welch window, which has a 10-day cutoff period.
b. The selected NAM events
The daily NAM index is defined as follows. An EOF analysis is first applied to the monthly geopotential at 300 hPa from November to March between 20° and 90°N. We then project the 300-hPa low-frequency daily geopotential anomaly onto the leading monthly EOF in the same area and normalize the projection. We finally obtain the daily NAM index by applying again the low-pass filter to the previous normalized projection to smooth out short-term fluctuations. The variations of the 300-hPa NAM index (NAMI) during the recent boreal winters are shown in Fig. 1. The same procedure is applied to the 10-hPa geopotential field to obtain the 10-hPa NAM index.
The NAM index series based on the first principal component of an EOF analysis of the 300-hPa geopotential. Each panel corresponds to a given winter season from mid-October to mid-April. The 8-day intervals preceding the peak of the selected positive and negative NAM events are indicated by the red and blue lines and the peak of the events by the red and blue circles, respectively.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
Before describing how we selected the various tropospheric NAM events, let us first present some basic intraseasonal and interannual variations of NAMI during the recent decade. As the NAO index is close to NAMI, well-known extreme NAO winters are highlighted on the figure. The 2009/10 winter was characterized by a very strong and persistent negative NAO leading to extremely cold temperatures over Europe (Ouzeau et al. 2011; Li and Lau 2012a; Santos et al. 2013; Harnik et al. 2014). The winter was marked by two negative NAO events whose peaks were reached in mid-December and mid-February (Fig. 1b). The origin of such an extremely negative NAO winter is debated. One possibility is the anomalous tropical heating in the Pacific associated with a strong El Niño event (Li and Lau 2012a; Harnik et al. 2014). The other possibility is linked to the stratosphere, which was marked by a weak polar vortex (Ouzeau et al. 2011). A major stratospheric warming occurred in late January (Dörnbrack et al. 2012; Kuttippurath and Nikulin 2012), which might have played a role in triggering the second negative NAO/NAM event of mid-February. Note that these two origins could be dynamically connected (Castanheira and Graf 2003). There were also winters when the positive NAO phase was dominating. For instance, the 2011/12 winter was a mainly positive NAO type, except for some days in February (Fig. 1d), and was accompanied by a La Niña event (Santos et al. 2013). The 2013/14 winter was also a positive NAO winter with a strong westerly Atlantic jet and a well-marked stormy season in northwestern Europe (Kendon and McCarthy 2015). It is interesting to note that during some years the early and late wintertime periods have contrasting NAO/NAM phases as was the case for the 2010/11 winter. The early 2010/11 winter was dominated by a negative NAO, which might be due to the reemergence of sea surface temperature anomalies of the previous winter (Taws et al. 2011), whereas the late 2010/11 winter was dominated by a positive NAO.
To investigate the rapid onset of NAM events, we selected them as follows: (i) NAMI has a local extremum exceeding 1.5 standard deviations at a given time, which is labeled the zero-lag day and (ii) it increases (or decreases) by 1.0 standard deviation between lag −8 days and the zero-lag day or by 1.5 standard deviations between lag −15 days and the zero-lag day. Step (ii) is designed to select a rapid increase in NAMI. When applied to all the years between 1979 and 2014 from mid-October to mid-April, 28 positive and 37 negative NAM events are found. The zero-lag day of all these events is indicated in Table 1, together with the value of NAMI at the same lag. Selected events belonging to the last six winters are highlighted in Fig. 1 in blue and red for negative and positive NAMI, respectively. Even though the criterion (ii) does not require any monotonic variations of NAMI, it appears to be systematically the case from lags −8 days to the zero-lag day. Criteria (i)–(ii) are rather strict in the sense that the thresholds used select very rapid onset of extreme NAM events. For instance, the rapid decrease in NAMI in late November 2010 or the rapid increase in NAMI in late October 2013 are not selected by the algorithm because both of them do not satisfy criterion (i) as their corresponding NAMI do not exceed 1.5 standard deviations. Replacing 1.5 standard deviations by 1.0 standard deviation doubles the number of detected cases. It does not change most of the results but it usually leads to less contrasting behaviors and less significant anomalies.
List of the selected positive and negative 300-hPa NAM events. The first value in parentheses is the 300-hPa NAM index and the second value is the 10-hPa NAM index.
Figure 2 presents the time evolution of the composited NAM index for the selected positive and negative NAM events (solid lines). At the peak of the events (the zero-lag day), the NAM index exceeds the 2.0 standard deviations threshold. The onsets of the opposite NAM events are rather symmetric but the decay stages differ. The negative NAM event is significantly more persistent than the positive NAM event as NAMI at lag +20 days is −0.5 and near zero for the former and latter, respectively. Similar asymmetries were found for the NAO (Barnes and Hartmann 2010; Woollings et al. 2010). The stronger persistence of the negative phase seems to be due to a more active positive eddy feedback when the jet is anomalously shifted equatorward (Barnes and Hartmann 2010).
Composites of the 300-hPa NAM (solid lines), the 10-hPa NAM (short-dashed lines), and the vertically averaged vertical velocity between 600 and 300 hPa in the area 10°S–0°, 220°–120°W (long-dashed lines) for the selected positive (red) and negative (blue) 300-hPa NAM events. The zero-lag day corresponds to the peak of the selected events. Thick lines correspond to t values exceeding the 98% confidence level for a two-sided t test.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
c. Diagnostic tools
The Rossby wave–breaking (RWB) detection algorithm of Rivière (2009) and Rivière et al. (2010) is used. The algorithm detects local overturnings of circumglobal potential vorticity contours on isentropic surfaces. When the locally overturned contour is southwest–northeast (northwest–southeast) oriented, it is considered as belonging to an anticyclonic (cyclonic) wave-breaking event. Overturnings of potential vorticity contours on the 300-, 315-, 330-, and 350-K isentropic surfaces every 0.5 potential vorticity unit (PVU; 1 PVU = 10−6 K kg−1 m2 s−1) were systematically detected over the whole period of interest. The RWB frequencies of occurrence obtained on these four isentropic surfaces were then vertically averaged.
3. The dynamical link between the North Pacific and North Atlantic anomalies of the NAM
Composites of different quantities have been made over the selected positive and negative NAM events, denoted as NAM+ and NAM−, respectively. Figure 3 presents the time lag composites of the 300-hPa low-frequency geopotential for NAM+. At lag −12 days (Fig. 3a), NAMI is already positive but rather weak (around 0.4). The largest region of significant geopotential anomalies is in the North Pacific with negative values at high latitudes and positive values in middle latitudes. The positive values reveal the presence of a localized large-scale high anomaly centered at 40°N, 140°W. On the other hand, in the North Atlantic sector, the area covered by significant anomalies is much smaller, the only significant pattern being the high anomaly over the United Kingdom. While the high anomaly in the North Pacific already projects onto the North Pacific center of action of the NAM, the high anomaly in the North Atlantic is displaced relative to the positive center of action of the NAM in that sector (cf. with the zero-lag day in Fig. 3d). It shows that the North Pacific anomalies of NAM+ appear before the North Atlantic ones. At lag −8 days (Fig. 3b), the NAO anomalies begin to show up but the geopotential anomaly with the highest amplitude is still located in the North Pacific. Note that there is no obvious presence of low-frequency Rossby wave trains coming from the Pacific to the Atlantic in contrast with those shown by Honda et al. (2001) on longer time scales. At lag −4 days (Fig. 3c), the dipolar anomaly of the positive NAO more clearly emerges with the Greenland low anomaly being deeper. There are two high anomalies in the North Atlantic: one in the subtropical western Atlantic and another over Europe. It is a typical feature of the EOF of the upper-tropospheric geopotential in the Northern Hemisphere [see, e.g., Fig. 1b of Honda et al. (2007), or Fig. 8a of DRA15]. At the zero-lag day (Fig. 3d), NAMI exceeds 2.0 standard deviations, the anomalies reach their maximum amplitude and are more zonally oriented than the preceding days. At lag +4 and +8 days (Figs. 3e and 3f), the anomalies decrease in amplitude, and the decrease in NAMI at positive lags is as fast as the increase at negative lags.
Time-lag composites of the 300-hPa low-frequency geopotential anomaly (contour interval: 300 m2 s−2) for the selected positive NAM events. Light and dark shaded areas indicate positive and negative t values, respectively, that exceed the 95% confidence level for a two-sided t test.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
The time lag composites of the low-frequency geopotential for NAM− are shown in Fig. 4. At lag −12 days (Fig. 4a), NAMI is near zero. Similar to NAM+, the largest significant anomalies first emerge in the North Pacific sector. They are mainly composed of large-scale high and low anomalies at 20° and 45°N, respectively, which accelerate the North Pacific jet. In the North Atlantic, there is a significant high anomaly over the east coast of the United States, but it has a much less spatial extent than those in the North Pacific. Interestingly, at that lag, the North Pacific anomalies already project onto the North Pacific anomalies of the NAM as seen by comparing with the zero-lag day (Fig. 4d). The North Atlantic anomalies of the NAM only show up at lag −8 days on the eastern side of the basin (Fig. 4b). This is to be contrasted with NAM+ composite, which already exhibits significant anomalies over North America and in the western Atlantic at the same lag. Then, at lags −4 days (Fig. 4c), the dipolar negative NAO anomaly is well formed. It increases in amplitude until reaching the zero-lag day (Fig. 4d), together with the large-scale trough anomaly in the North Pacific. NAMI reaches a value close to −2.0 standard deviations. Finally, the decrease in NAMI at positive lags is slightly slower than the increase in NAMI at negative lags.
As in Fig. 3, but for the selected negative NAM events.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
Composites of the meridional temperature gradient at 700 hPa, which is a good indicator of low-level baroclinicity, are shown in black contours in Fig. 5. In the North Atlantic, during NAM+ (left column), the baroclinicity is increased and reaches high values over a broad range of longitudes from the eastern coast of the United States to the northeastern Atlantic. On the contrary, during NAM− (right column), the baroclinicity is significantly reduced in the North Atlantic, especially at positive lags, and reaches high values over the eastern coast of the United States only. It is consistent with the difference between the opposite NAO phases highlighted by Pinto et al. (2009). In the North Pacific, it is almost the converse. The baroclinicity is strong and eastward extended during NAM−, consistent with a zonal acceleration of the North Pacific jet and the dipolar geopotential anomaly of Fig. 4. The baroclinicity is less eastward extended during NAM+ and shifted poleward in the northeastern Pacific in accordance with the large-scale high anomaly shown in Fig. 3 and the poleward-shifted Pacific jet in that region.
Time-lag composites of the vertically averaged baroclinic conversion from eddy potential energy to eddy kinetic energy (shadings; units: m2 s−3) and the 700-hPa low-frequency temperature gradient (black contours; contour interval: 3 × 10−6 K m−1 with the thick contour corresponding to 9 × 10−6 K m−1) for the selected (left) positive and (right) negative NAM events.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
The baroclinic conversion from eddy potential energy to eddy kinetic energy 
Figure 6 represents the composites of the eddy total energy fluxes (arrows) and their magnitude (shadings). At lag −8 days, the two opposite NAM phases roughly present the same magnitude of energy fluxes in the two storm-track regions and over North America. However, for NAM+, near the North Pacific high anomaly, regions of intense eastward fluxes are poleward deviated reaching their maximum amplitude at 35°N west of 160°W, at 50°N between 160° and 120°W, and then near 40°N over North America. On the contrary, for NAM−, as the Pacific jet is already more zonal, regions of intense energy fluxes fluctuate less in latitude and the fluxes themselves are more zonal. A major difference between NAM− and NAM+ appears at lag −4 days. Over North America, in the longitudinal band between 120° and 100°W, the energy fluxes are 3 times larger in amplitude for NAM+ than NAM−. It means that during the days prior to the peak events, downstream propagation of eddy energy from the North Pacific to the North Atlantic is significantly intensified and reduced for NAM+ and NAM−, respectively. This difference comes from both the advective and dispersive components of the fluxes (not shown) with the former being roughly twice greater than the latter. Even though this difference over North America is largest at lag −4 days, it is still present until lag +4 days but disappears at lag +8 days. Other differences can be noticed in the storm-track regions. In the Atlantic sector, for NAM−, there is a decrease in energy fluxes magnitude from negative to positive lags. For NAM+, their magnitude is strong at all lags with a peak at the zero-lag day. In the Pacific sector, for NAM−, energy fluxes generally reach large amplitude whatever the lag. For NAM+, they are intense prior to the event, but decrease significantly at positive lags.
Time-lag composites of the high-frequency eddy total energy flux (arrows) and its magnitude (shadings; units: m3 s−3) for the selected (left) positive and (right) negative NAM events. The black contours correspond to the 300-hPa low-frequency geopotential anomaly (contour interval: 300 m2 s−2).
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
The composites of eddy total energy shown in Fig. 7 are rather similar to those of the energy flux magnitude and baroclinic conversion. First, in the northeast Pacific, the eddy energy follows the anomalous position of the jet with a well-marked poleward deflection for NAM+. The energy decreases significantly at positive lags for NAM+, while it remains rather constant for NAM− in that sector. Second, over North America, NAM+ has much more eddy energy than NAM−. Third, in the Atlantic sector, for NAM−, the energy is strong between lags −8 and −4 days but rapidly decreases after the zero-lag day. For NAM+, the energy remains strong during the whole event with a peak amplitude reached at the zero-lag day.
Time-lag composites of the E vectors (arrows), the low-frequency horizontal wind magnitude (black contours; contour interval: 10 m s−1), and high-frequency eddy total energy (shadings; units: m2 s−2) at 300 hPa for the selected (left) positive and (right) negative NAM events.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
A key difference between NAM− and NAM+ shown in Fig. 7 concerns the orientation of the E vectors. For NAM+, the E vectors are poleward and equatorward oriented upstream and downstream of the North Pacific ridge anomaly, respectively. The consequence is that, over North America, the eddies are anticyclonically tilted and keep this anomalous tilt until reaching the North Atlantic. On the contrary, the Pacific jet being more zonal for NAM−, the E vectors are more zonally oriented over North America. They also have much less amplitude as their amplitude (i.e., the eddy kinetic energy) is significantly reduced in that region. The results on the E-vectors orientation support the mechanism proposed by DRA13 and DRA15.
Wave-breaking frequencies of occurrence are presented in Fig. 8. At lag −8 days, not much difference between NAM− and NAM+ is noticed. In the northeast Pacific, slightly more anticyclonic wave-breaking (AWB) and less cyclonic wave-breaking (CWB) events occur in NAM+ than in NAM- in accordance with the different latitudinal positions of the Pacific jet in the two opposite NAM phases. It reflects the positive eddy feedback exerted by synoptic Rossby waves onto the latitudinal fluctuations of the mean jet (Rivière 2009). The poleward eddy momentum fluxes associated with AWB (CWB) tend to push the jet poleward (equatorward), which in turn favors the occurrence of AWB (CWB). Differences in wave-breaking statistics between NAM− and NAM+ appear more clearly at lag −4 days. There are much more AWB and much less CWB events in both oceanic basins in NAM+ than in NAM−. Generally speaking, these distinct RWB events increase in frequency until reaching the zero-lag day and then decrease at positive lags.
Time-lag composites of the AWB (red contours; contour interval: 0.05 day−1 for values greater than 0.10 day−1) and CWB (blue contours; contour interval: 0.05 day−1 for values greater than 0.10 day−1) frequencies of occurrence averaged on the 300-, 315-, 330-, and 350-K isentropic surfaces for the selected (left) positive and (right) negative NAM events. The shadings correspond to the composites of the 300-hPa horizontal wind magnitude (units: m s−1).
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
Let us first discuss RWB anomalies for NAM−. In the North Atlantic, more CWB events occur predominantly at 55°N over a large domain from the east coast of Canada to the mid-Atlantic. An interesting feature is the peak in the AWB frequency of occurrence at the same latitude but located more eastward over northwestern Europe. Such a dipolar structure with CWB events more upstream and AWB events more downstream reflects the occurrence of 
For NAM+, in the North Pacific, AWB events occur more frequently at negative lags than at positive lags, consistent with the decrease in eddy energy as lag increases. It is also in accordance with the more poleward deviation of the jet in the northeast Pacific at negative lags. As already mentioned, such a deviation favors an equatorward propagation of synoptic waves over North America, which in turn triggers AWB events more downstream in the Atlantic sector. The peak in AWB events occurs at the zero-lag day where they strongly accelerate the Atlantic jet northeastward.
To summarize the time evolution of the opposite NAM events, different spatial averages of synoptic eddy statistics have been made in the two storm-track regions and over North America (Fig. 9). For NAM+, the baroclinic conversion in the North Pacific is greater than the climatological mean at negative lags until lag −4 days with a 95% confidence level whereas it is less than the climatological mean at positive lags without being statistically significant (Fig. 9a). This eddy generation is followed by an increase in AWB events in the Pacific sector between lags −4 and +2 days (Fig. 9b), consistent with the anomalously poleward-shifted Pacific jet and the effect of the jet latitude on the type of wave breaking (Rivière 2009). The strong eddy generation in the Pacific also leads to more eastward eddy energy fluxes over North America between lag −4 days and the zero-lag day (Fig. 9c). The E vectors are significantly more equatorward oriented during the intense downstream propagation of eddy energy from the Pacific to Atlantic sectors from lag −6 days to the zero-lag day. Such an anomalous anticyclonic eddy tilt is rapidly suppressed at positive lags (Fig. 9d). Then, in the North Atlantic, baroclinic conversion is strong between lags −4 and +6 days (Fig. 9e) while AWB events reach their maximum frequency between lags −2 and +6 days (Fig. 9f). For NAM+, there is therefore an obvious downstream influence of the Pacific sector onto the Atlantic sector through downstream propagation of synoptic waves, which is more intense and more equatorward than usual.
Baroclinic conversion (units: m2 s−3) averaged in (a) the Pacific sector and (e) the Atlantic sector (see the green boxes in Figs. 5e,f). RWB frequencies of occurrence (long-dashed and solid lines for CWB and AWB, respectively; units: day−1) averaged in (b) the Pacific sector and (f) the Atlantic sector (see the red and blue boxes in Figs. 8e,f for AWB and CWB events, respectively). (c) Eastward component of the eddy total energy flux (units: m3 s−3) and (d) angle of the E vector (units: °) with respect to the x axis averaged over North America (see the blue box shown in Figs. 6e,f). The red and blue curves correspond to the selected positive and negative NAM events, respectively. In (a),(c),(d), and (e), the black solid line corresponds to the climatological value and the black short-dashed lines correspond to values exceeding the 95% confidence level for a two-sided t test. In (b) and (f), the black lines correspond to the climatological values of cyclonic and anticyclonic frequencies of occurrence, respectively.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
In contrast, for NAM−, the role played by the Pacific anomalies in triggering the event is less obvious. The more zonal Pacific jet prevents the occurrence of anticyclonic tilt over North America and the propagation of synoptic waves is indeed more zonal (Fig. 9d). But more importantly, there is a drastic decrease in downstream propagation of eddy energy between lags −4 and +4 days (Fig. 9c). The suppression of upstream seeding might be partly due to the decreased zonal wind over North America as seen from the poleward-oriented geopotential anomaly gradient in that region (Fig. 6f). Even though the jet is eastward accelerated in the mid-Pacific, it is also rapidly decelerated farther east. The suppression of upstream seeding is a favorable situation for CWB events to occur as shown in Orlanski (2005). The first statistically significant anomaly in eddy characteristics appears in the North Atlantic domain where a peak in baroclinic conversion occurs at lag −8 days (Fig. 9e). This is followed by major CWB events in the North Atlantic with a peak reached at lag −2 days just before the peak of the NAO− anomalies (Fig. 9f). The AWB events decrease in frequency during that period but remember that the average is made in the southern part of the midlatitudes between 20° and 50°N (see the red box in Fig. 8). Hence, the AWB events occurring farther north, which reinforce the blocking situation over Europe, are not included in the spatial average. To conclude, the CWB events occurring in the North Atlantic domain are triggered by strong cyclogenesis in the northwestern Atlantic in presence of small-amplitude zonally propagating upper-level waves coming from North America. As the major CWB events occur, there is first the formation of a blocking in the northeastern Atlantic and then a transition toward NAO− characterized by a more zonally oriented equatorward-shifted jet. Then, the CWB events and high-latitude anticyclonic anomalies are displaced westward toward the Pacific at positive lags. These results, therefore, suggest that there is a two-way interaction between the Pacific and Atlantic anomalies during NAM−. First, near the peak of the event, the downstream propagation of synoptic waves is altered across North America and, in that sense, influences the type of breaking in the North Atlantic. Second, after the event, a more upstream influence occurs with a westward displacement of the high-latitude anticyclonic anomalies or high-latitude blockings following the terminology of Woollings and Hoskins (2008).
4. The origin of the North Pacific anomalies
As the NAM anomalies first emerge in the North Pacific, their initiation stage is here discussed. There is much evidence in the literature that North Pacific low-frequency anomalies may arise from anomalous convection in the tropical Pacific (Jin and Hoskins 1995; Franzke et al. 2011; Li and Wettstein 2012). To check if it is the case in our selected NAM events, composites of the vertically averaged vertical velocity from 600 to 300 hPa are shown in Fig. 10, the vertical velocity being a good indirect measure of latent heat release in the tropics (Li and Wettstein 2012; Harnik et al. 2014). Both NAM− and NAM+ show significant anomalies in the western tropical Pacific between 10°S and the equator, especially at negative lags. NAM− presents anomalous upward motions in that region between 220° and 120°W with the peak amplitude reached at lag −8 days. There is the formation of a high streamfunction anomaly between 0° and 30°N, more or less at the same longitudes consistent with Jin and Hoskins (1995), and farther north a trough anomaly shown in Fig. 4. It creates an acceleration of the Pacific jet similar to the positive PNA phase (Franzke et al. 2011), El Niño events (Li and Lau 2012b), and the composites of strong western Pacific convection of Li and Wettstein (2012). On the contrary, NAM+ presents anomalous downward motions between 220° and 160°W with most significant anomalies appearing at lag −12 days. This is associated in the Northern Hemisphere subtropical region with a low streamfunction anomaly between 160° and 120°W and a high anomaly in the northeast Pacific already seen in Fig. 3.
Time-lag composites of the vertically averaged vertical velocity between 600 and 300 hPa (shadings; units: Pa s−1; blue and red for upward and downward motion, respectively) and the 200-hPa low-frequency streamfunction anomaly (green contours). Dashed and solid black contours indicate positive and negative t values, respectively, exceeding the 95% confidence level for a two-sided t test.
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
We defined a normalized index by horizontally averaging the vertically averaged vertical velocity in the western tropical Pacific area (10°S–0°, 220°–120°W). Its time evolution is shown in Fig. 2, together with NAMI. For NAM+, the index reaches a maximum value of about +0.6 standard deviation at lag −12 days. For NAM−, the index reaches a mininum value of about −1.0 standard deviation at lag −8 days. These values are highly significant (98%). In both composites, the extrema of tropical convection anomalies in the western Pacific precede the peaks of the NAM events by more than 1 week. At positive lags, the convection index approaches zero but differently for the two phases. For NAM+, the vertical velocity rapidly changes direction while for NAM− the decrease toward zero slowly occurs and never reverses sign. The stronger persistence of tropical convection anomalies for NAM− provides another explanation for its stronger persistence mentioned earlier in the paper.
To estimate the robustness of the linkage between NAM and the anomalous convection in the tropical Pacific, time-lagged correlations between the tropical Pacific vertical velocity index and the NAM index over the whole period have been computed. A peak of about 0.23 was obtained at lags −12 days, which is statistically significant at the 90% confidence level. As such, the tropical Pacific index explains about 5% of the variance of the NAM.
These results corroborate those of Cassou (2008) on the impact of the Madden–Julian oscillation (MJO) onto the NAO. He showed that phases 3 and 6 of the MJO, which correspond to reduced and intensified convection in the western tropical Pacific, act as precursors of NAO+ and NAO−, respectively. An initiation of low-frequency Rossby wave trains in the Pacific by such anomalous convection is clearly seen in our composites. However, a wave train propagation of the type of a great-circle path, as seen in Jin and Hoskins (1995) for instance, is not visible. However, the propagation of low-frequency Rossby wave trains may occur even in the absence of great-circle wave train (Qin and Robinson 1993). Such a possibility is investigated in the next section by providing a more quantitative analysis.
5. Streamfunction budget analysis
The projections of the composited fields for the two opposite NAM events and different sectors are shown in Fig. 11. Let us first analyze the characteristics of the projections in the Northern Hemisphere (Figs. 11a,b). The sum 
The time-lagged projections onto (left) positive and (right) negative NAM streamfunction anomalies of 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
Interesting features can be noticed by analyzing the projections in the Pacific and Atlantic sectors. In the North Pacific, the projection of the linear term reaches a peak of about 10−6 s−1 at lag −14 days for NAM+ and lag −16 days for NAM−. In the North Atlantic, the same projection has a maximum few days later, at lag −10 days for NAM+ and NAM−, which does not exceed 6 × 10−7 s−1. The time lag between the Pacific and Atlantic peaks supports the idea that low-frequency anomalies are initiated in the Pacific and then propagate farther downstream in the Atlantic sector. The forcing is due to the linear term being stronger in the Pacific than in the Atlantic; hence, linear processes are more important in the Pacific. At the later stage of the NAM development, the strongly positive projection of the nonlinear term explains the rapid formation of the NAM events in all sectors.
The projection of the nonlinear eddy fluxes is separated into high- and low-frequency eddy parts in Fig. 12. The high-frequency component dominates over the low-frequency one in most cases and is responsible for both the triggering and maintenance of the NAM events. The low-frequency part triggers the events but participates in their decay. These features are consistent with previous studies using the same methodology (Feldstein 2003; Michel and Rivière 2011). To conclude, the propagation of low-frequency Rossby wave trains triggered by anomalous tropical convection in the Pacific explains the initiation of the NAM events while Rossby wave breaking, mainly of synoptic scale, is responsible for the rapid setting of the events at the later stage.
As in Fig. 11, but by decomposing the projection of the nonlinear term 
Citation: Journal of the Atmospheric Sciences 72, 12; 10.1175/JAS-D-15-0069.1
6. Discussion on the eventual role played by the stratosphere
An alternative hypothesis for connecting the North Pacific and North Atlantic NAM anomalies could be through the stratospheric control as suggested by Castanheira and Graf (2003) and Ineson and Scaife (2009). We have computed a 10-hPa NAM index in the same way as NAMI, and its composites are shown in Fig. 2 for the two types of selected events. The 10-hPa NAM index has the same sign as NAMI but is less than 0.4 standard deviation for all time lags and its extrema are reached at positive lags. A Student’s t test shows that the confidence level exceeds 95% at some positive lags for NAM+ but the 90% confidence level is never reached at negative lags whatever the NAM phase. Besides, as seen in Table 1, extreme tropospheric NAM events may occur in presence of opposite-signed stratospheric NAM events. For instance, for NAM+, there are 7 cases for which the 10-hPa NAM index is above 1.0 standard deviation but also 3 cases for which it is below −1.0 standard deviation. For NAM-, there are 10 cases for which the 10-hPa NAM index is below −1.0 standard deviation and 6 cases for which it is above 1.0 standard deviation. But if we consider the 1.5 standard deviation threshold, extreme opposite-signed tropospheric and stratospheric NAM events occurring concomitantly are more unlikely. Among the 65 selected NAM events, there are 6 events with the 10-hPa NAM index greater than 1.5 standard deviations, two of them belong to NAM− and four others to NAM+. There are also 6 events with the 10-hPa NAM index below −1.5 standard deviations. They all belong to NAM− and correspond to six stratospheric sudden warmings listed in Hitchcock et al. (2013) (see their Table 1). Hence, we cannot discard the possibility that the stratosphere plays a role in some specific cases because there is a preference for extreme same-signed tropospheric and stratospheric NAM events, which is more visible for the negative phase. But the stratospheric path is certainly not the main mechanism implied in our selected NAM events.
7. Conclusions
Rapid onsets of positive and negative tropospheric NAM events during boreal winters have been studied using ERA-Interim datasets. The NAM anomalies first show up in the North Pacific in connection with anomalous convection in the western tropical Pacific around 2 weeks before the peak of the NAM event. The negative NAM anomalies are characterized by a zonal acceleration of the central Pacific jet and triggered by enhanced convection in the western and central tropical Pacific in accordance with the positive PNA phase (Franzke et al. 2011), El Niño events (Horel and Wallace 1981; Hoerling and Ting 1994), and various intraseasonal variabilities unrelated to ENSO (Higgins and Mo 1997; Li and Wettstein 2012). The positive NAM anomalies present a midlatitude ridge anomaly in the northeast Pacific that is associated with a weaker and poleward-shifted Pacific jet in its exit region. This anomaly is likely due to reduced convection in the western Pacific similar to the negative PNA phase and La Niña events. The North Pacific NAM anomalies can be thus interpreted as resulting from Rossby wave propagation excited by anomalous tropical convection. The reduced and enhanced convection in the western Pacific lead to positive and negative NAO, respectively, similarly to the results of Cassou (2008) on the impact of the Madden–Julian oscillation on the NAO.
Even though low-frequency Rossby wave trains forming a great-circle path are not visible over North America and in the North Atlantic, a low-frequency streamfunction budget suggests that the NAO anomalies of the NAM are initiated by the downstream propagation of low-frequency wave activity around 10 days prior to the events. Then, during the last onset week when the most rapid change in the NAM index occurs, synoptic wave propagation and breaking form the cornerstone of the linkage between North Pacific and North Atlantic NAM anomalies. Statistically significant anomalies of various synoptic eddy measures emerge at that time. During the last onset week of the positive NAM, the generation of baroclinic waves in the North Pacific is strong and the downstream propagation of eddy energy is strong, too. The intense eddies mainly tilt anticyclonically during their propagation across North America because the northeast Pacific ridge anomaly deflects the synoptic wave trains and favors their equatorward propagation downstream of it. As a consequence, waves break anticyclonically when they reach the North Atlantic domain, which is accompanied by poleward eddy momentum fluxes. This pushes the Atlantic jet poleward, favors the emergence of the positive NAO phase, and validates the mechanism proposed in DRA13 and DRA15.
On the contrary, during the week preceding the peak of the negative NAM event, the more zonal Pacific jet favors a more zonal propagation of synoptic waves across North America. There is also a drastic decrease in downstream propagation of synoptic eddy energy that can be partly attributed to a rapid deceleration of the jet in that particular sector. The zonal propagation of small-amplitude upper-tropospheric waves added to the strong baroclinic generation over the northeast coast of the United States favors the occurrence of cyclonic wave-breaking events in the North Atlantic. These events first lead to the generation of a blocking in the northeastern Atlantic and then to the formation of the Greenland anticyclone characteristic of the negative NAO phase. Such a transition from the European blocking to the negative NAO phase is supported by Michel and Rivière (2011) and Michel et al. (2012). Then, the westward displacement of high-latitude anticyclonic anomalies and cyclonic wave-breaking events continues toward the Pacific after the peak of the negative NAM phase, consistent with Woollings and Hoskins (2008).
Both the intensity and orientation of synoptic wave propagation across North America seem to be important in setting the different phases of the NAM. The key role played by the orientation of wave propagation in the formation of the NAO phases was clearly shown by DRA15 but the role played by the intensity of wave propagation was found to be less systematic (see, e.g., their Figs. 2a,b). Less upstream seeding usually favors the occurrence of cyclonic wave breaking and the negative NAO phase according to the observational study of Benedict et al. (2004) or the numerical experiments of Orlanski (2005). However, the El Niño composites of Li and Lau (2012a) and DRA15 based on the Niño-3 index showed a zonal Pacific jet extended across North America, which favors intense downstream development, in particular at low latitudes. The relatively strong and zonally propagating upper-level waves lead to cyclonic wave-breaking events and negative NAO. Such a scenario does not emerge in our selected negative NAM events as the zonally oriented Pacific jet rapidly decelerates before reaching North America. These distinct negative NAO events may explain why there is no clear signal in the intensity of downstream development in negative NAO composites.
Finally, the stratosphere is not found to be the main driver connecting the North Pacific to the North Atlantic anomalies of the NAM as a significant number of tropospheric NAM events occur in the presence of opposite-signed stratospheric NAM. However, the stratosphere may play a role in specific cases like the six selected NAM events occurring during major sudden warmings, which all correspond to negative NAM.
Besides the emergence of the North Pacific low-frequency anomalies triggered by anomalous tropical convection, the role of precursor played by an enhancement of baroclinic wave generation in one of two storm-track regions has been pointed out. For NAM+, an enhancement of baroclinic wave generation in the North Pacific was found during the onset stage, which further increases the amount of waves coming from the Pacific to the Atlantic. This eddy generation is completely suppressed during the decay stage. For NAM−, the same scenario occurs but in the North Atlantic. Further investigation is needed to more clearly establish the importance of these storm-track anomalies in triggering the NAM events, especially for NAM− whose narrative appears more complicated than that for NAM+.
Another future direction of research would be to more systematically compare slow, intermediate, and fast onsets of the annular mode phases. We expect the role played by planetary-scale low-frequency eddies to be more important for slower variations and that played by synoptic eddies to dominate for rapid variations.
Acknowledgments
The authors would like to acknowledge the three anonymous reviewers for their suggestions that helped to significantly improve the manuscript.
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