Links are sought between Madden-Julian oscillation (MJO)–related variations in the troposphere and stratospheric circulation. Tropospheric variations of equatorial MJO-filtered 200 hPa zonal winds define indices of MJO activity for two equatorial regions in the Indian and western Pacific oceans. These indices are used to define composite means of MJO-filtered Extended Eliassen-Palm (E-P) fluxes for eight height levels from the upper troposphere well into the stratosphere. Evidence is presented for significant and coherent MJO departures throughout the lower stratosphere. Significant departures of the vertical component of E-P flux flow into the lower stratosphere both in the tropics and at higher latitudes, especially over Canada. These are accompanied by horizontal flux departures in the upper troposphere and lower stratosphere from the central tropical Pacific into northern Canada. In this region, there is a divergence of Extended E-P flux, piling up wave energy leading to the observed increased cyclonic motion. Evidence supports the hypothesis that these high-latitude circulation variations in the stratosphere are due to a combination of two quite distinct mechanisms. In the first, poleward propagation occurs in the upper troposphere with vertical propagation at higher latitudes. In the second, upward propagation occurs in low latitudes into the lower stratosphere. This is followed by poleward propagation into higher latitudes and then farther upward propagation.
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 The Madden-Julian oscillation (MJO) was first identified by Madden and Julian [1972, 1994] as an eastward-propagating anomaly in tropical winds and surface pressure having a period of around 45 days. Many of the important properties of the MJO are summarized in the review article of Zhang . Weare [2010a] used tropospheric variations of equatorial MJO-filtered 200 hPa zonal winds to define indices of MJO activity for two equatorial regions in the Indian and western Pacific oceans. These indices were used to calculate composite means of MJO-filtered tropical and subtropical winds, temperature, and ozone mixing ratio for the eight height levels from the upper troposphere well into the stratosphere. Strong evidence was presented for significant and coherent MJO departures throughout the lower stratosphere. At 100 hPa, these departures show easterlies in the equatorial regions of the compositing centers and nearly symmetric anticyclonic centers at 25° poleward of those centers, which are associated with significant negative departures in both temperature and ozone mixing ratio. Near 40°N MJO departures of meridional velocity, temperature, and ozone mixing ratio generally tilt westward with height. The most important aspects of these features propagate eastward at a rate of about 5m/s in the Eastern Hemisphere and several times faster in the Western Hemisphere.
 This paper is aimed at better understanding how an MJO signal in the equatorial troposphere propagates into the tropical and Northern Hemisphere extratropical stratosphere. A number of authors have described the relationships in the troposphere between MJO variations in the tropics and anomalies in the middle and higher latitudes [e.g., Liebmann and Hartmann, 1984; Kiladis and Weickmann, 1992; Hsu, 1996; Kim et al., 2006]. The associated patterns in the higher latitudes of the upper troposphere are largely understood in terms of an equivalent barotropic response to the heating (divergence) pattern in the subtropics associated with the MJO together with the mean background flow [e.g., Hoskins and Karoly, 1981; Jin and Hoskins, 1995; Sardeshmukh and Hoskins, 1988; Pan and Li, 2008]. Use of this theory gives rise to waves along a great circle path in the Northern Hemisphere. A similar theory is probably applicable in the lower stratosphere. However, in addition to horizontal propagation of an MJO signal, vertical propagation is also necessary for a stratospheric response. Lindzen  outlines the general criteria for vertical propagation in the tropics and midlatitudes. In the tropics at MJO frequencies, shallow propagation is possible for all mean wind conditions. However, given MJO convection is known to be associated with higher-frequency variations [e.g., Mapes and Houze, 1993; Chao and Lin, 1994; Yanai et al., 2000], propagation into at least the lower stratosphere is possible [Lindzen, 1967]. In midlatitudes, the existence of vertically propagating waves is limited to conditions for mean westerly winds with magnitudes below a threshold. Two distinct possible paths exist for MJO responses in the high-latitude stratosphere. The first involves poleward propagation in the troposphere as has been observed, coupled with upward propagation at one or more higher-latitude sites. Alternately, vertical propagation may occur in the tropics and subtropics into the stratosphere, which is followed by poleward propagation in the stratosphere. One of the goals of this work is to attempt to assess whether or not one of these processes dominate.
 The approach of this work follows the general procedure of Weare [2010b], which defined El Niño/Southern Oscillation (ENSO) composites of Extended Eliassen-Palm (E-P) fluxes [Plumb, 1985] to better identify ENSO-associated propagation into the stratosphere. In this case, Extended E-P fluxes have been calculated for each day and filtered with an MJO bandpass filter. The MJO features of these fluxes and their divergences are identified by using the same compositing technique as by Weare [2010a].
2.1. ERA-40 Data
 ERA-40 [Uppala et al., 2005] involves comprehensive use of traditional observations and satellite data, including TOVS, SSM/I, ERS, and ATOVS and cloud motion winds, in a start-of-the-art forecast model to derived gridded data fields. In this case, a three-dimensional variational technique was applied using the T159L60 version of the European Centre forecast model. The current analysis uses 00 UHT daily values zonal (u) and meridional (v) wind, temperature (T) ,and geopotential (Φ) at 10, 20, 30, 50, 70, 100, 150, and 200 hPa on a 2.5° × 2.5° grid for 1980–2001. To identify the MJO, the 22 year daily means of these data at every grid point are first removed, Then, these anomalies are filtered using a high-quality 150 point Lanczos band-pass filter [Duchon, 1979] capturing well the 20–100 day periodicities.
2.2. Extended E-P Fluxes
 Following Weare [2010b], the zonal, meridional, and vertical Extended E-P flux components may be written in spherical coordinates as
where the very standard notation is that of equation (7.1) of Plumb . In equation (1) primes denote daily departures from daily mean zonal means, and derivatives are calculated using centered differences. Kuroda  and Palmer  have shown that the quasi-geostrophic equations used here include divergence and are thus applicable to planetary motions. In addition at the equator the terms involving sin(2ϕ) are replaced by the averages of the points just north and south of the equator. The Extended E-P fluxes calculated in this way include the influence of both the quasi-stationary and transient eddies.
 These fluxes satisfy a conservation equation for wave activity A, such that
where C is a nonconservative tendency, p is pressure, q′2 is the square of the departure of potential vorticity from the zonal mean (positive definite), Q is the zonal mean potential vorticity, E is wave energy density (positive definite), and U is the zonal mean zonal wind. In the quasi-geostrophic framework A is proportional to the square of geopotential perturbations [Vallis, 2006]. As summarized by Weare [2010b], these fluxes are approximately parallel to the flow of wave energy and their divergences (convergences) may be associated with a piling up (export) of that energy. When interpreting the quasi-geostrophic equations for the globe for a range of elevations, one must add a further caveat. Based on equation (2)A blows up if either zonal mean zonal wind or the zonal mean potential vorticity gradient changes sign. However, these criteria are not strictly applicable to the following composites, since in a region in which the composite mean changes sign, there may be periods in which the sign is positive or negative, but not changing.
 Following Plumb , the traditional E-P fluxes are calculated as the zonal means of and Fz. Similarly, the divergences of the traditional E-P fluxes are calculated as the zonal means of the divergences of these components. Positive divergences are associated with the acceleration of the zonal mean zonal wind. Also, as for the Extended E-P fluxes the direction of the traditional fluxes is parallel to the wave group velocity.
 As in the work of Weare [2010a], indices of filtered equatorially symmetric variations in 200 hPa zonal wind between 10°S and 10°N are calculated for the Indian Ocean (60°E–90°E) and western Pacific (140°E–170°E). This procedure identifies time periods in which each region has relatively strong easterlies that are symmetric about the equator. These indices for the Indian Ocean and the western Pacific are illustrated in Figure 1 of Weare [2010a]. The illustrated mean easterlies usually exceed the threshold for a number of consecutive days, identifying the growth and decay of those easterlies in each region. In general, these symmetric easterly winds are strongest in the Northern Hemisphere winter half of the year. Often, but not always, strong symmetric easterlies in the Indian Ocean are followed by those in the western Pacific a few days later. However, there is generally little relationship between the magnitudes of the Indian and western Pacific easterly anomalies. The dates, when the Indian Ocean and western Pacific indices are nonzero [see Weare, 2010a], are used to calculate the composite means of the approximately 1000 days of MJO-filtered anomalies of the Extended E-P fluxes and their divergences for the 10, 20, 30, 50, 70, 100, 150, and 200 hPa levels.
 The statistical assessment as to whether a composite mean at each point is different from zero is determined by the t test [Von Storch and Zwiers, 1999],
where N is the effective number of samples in the composite mean, and and σX are the mean and standard deviations of the variable X. In the following discussion, values of t are often called normalized MJO departures. Since the composite means are calculated from data that are highly filtered and thus have substantial autocorrelations, N is smaller than the number of days contributing to the means. This N is estimated using the procedure described by Lieth , which uses the lag correlations to determine the ratio of the effective number of samples relative to the total number. In these analyses, N is generally about one tenth of the number of sample days in the composite means. Absolute values of t greater than 2 and 2.4 are judged to be statistically different than zero at approximately the 95% and 97.5% significance levels.
 To further illustrate the properties of the composites, Figure 1 shows the composite mean filtered outgoing longwave radiation (OLR) for the Indian Ocean center for time periods 10, 5, and 0 days before the reference period. The patterns correspond to those of phases 2, 3, and 4 shown in Figure 8 of Wheeler and Hendon . Their figure clearly indicates an eastward propagation of convection along the equator. Both the Wheeler and Hendon results and those shown here also show that the convective anomalies stretch north and south of the equator at least 15° of latitude. The maps associated with the western Pacific center suggest similar patterns shifted to the east (not shown).
Figure 2 illustrates MJO composites based on the western Pacific region for geopotential Φ and stream function (based on u and v departures) for four levels between 200 and 20 hPa. At 200 hPa near the equator in the Eastern Hemisphere, the pattern corresponds to that described by Gill  for a heating near 90°E. In this case to the east of the heating Kelvin waves induce an easterly equatorially trapped flow, whereas to the west Rossby waves lead to westerlies near the equator and cyclonic centers just off the equator. However, the full flow associated with the MJO heating is considerable more complex [Jin and Hoskins, 1995].
 The full 200 hPa pattern is broadly comparable to that in Figure 2b of Kiladis and Weickmann , Figure 2d of Hsu , and Figure 2d of Kim et al. . Unfortunately, the details at higher latitudes of all of these plots differ considerably from each other. This is partially explained by the modeling work of Jin and Hoskins , who show that the response to an equatorial heating is a function of the location of that heating relative to the background vorticity field. In fact the pattern in Figure 2a corresponds well to that corresponding to a heating at 120°E with a realistic background flow. At 100 hPa the pattern in Figure 2b is similar to that at 200 hPa and is comparable to the negative of that shown in Figure 9b of Kiladis et al. . At both the 100 and 200 hPa levels, two dominant features are the anticyclone pair north and south of the composite center. In addition northward of the Northern Hemisphere anticyclone is a strong cyclonic anomaly. Both of these Northern Hemisphere features weaken with increasing elevation. On the other hand a low over North America and a high over Asia have increasing magnitudes with height, giving a pattern that is dominated by a strong wave number 1 with a low center over northern Canada. This feature tilts westward with increasing height, suggesting the importance of Rossby wave dynamics. The MJO composites for the Indian Ocean center are of nearly opposite sign and weaker at higher elevations (not shown). This is consistent with the results of Kiladis and Weickmann  and Matthews and Kiladis , who show that the 200 hPa flow response to MJO is sensitive to the location of the convection or the phase of the MJO.
Figure 3 shows longitude/height cross sections of the normalized departures of u, v, and Φ for the MJO composites based on the Indian Ocean and western Pacific regions. At lower elevations, the patterns for the Indian and western Pacific composites are roughly the negatives of each other. For both composites, the zonal winds have a wave number 1 pattern, whereas those of the meridional wind are wave number 2. The western Pacific geopotential composite has a wave 1 pattern; the Indian Ocean departures are largely insignificant at the 95% level. For both composites there is generally a westward tilt with height of the departures. At higher elevations the apparent response to MJO at higher latitudes is stronger for the western Pacific composites, which have a westward tilt with height, again suggesting the importance of Rossby wave dynamics. Figures 2 and 3 suggest that the MJO has not only a large-scale response in the troposphere but also a significant response in the higher latitudes of the stratosphere, especially for the western Pacific composite. The goal of this paper is to better understand the processes involved in these higher-latitude, higher-elevation responses.
Figure 4 shows normalized departures of the traditional E-P fluxes and flux divergences for the Indian and West Pacific composites. In the tropics, the patterns of flux divergence are nearly opposite sign for the two composites, such that there is acceleration of the zonal flow for the western Pacific composite and deceleration for the Indian Ocean composite. For the Indian composite in the lower stratosphere, there are upward and poleward fluxes out of the subtropics. The associated divergence differences imply a significant acceleration of the zonal mean westerly flow near 50°N up to about the 30 hPa level. For the West Pacific composite, there are also significant upward and poleward fluxes through the 20 hPa level from the subtropics into the high latitudes of the Northern Hemisphere. For the western Pacific center, this is associated with weak divergence, hence deceleration of the zonal flow. The contrasting flux and divergence patterns between the Indian and western Pacific composites are consistent with the differences in high-latitude responses diagnosed in Figure 3. Furthermore, the strong, more significant fluxes at the higher elevations of the higher latitudes for the western Pacific composite are also consistent with the strong response seen in these locations in Figures 2 and 3.
Figure 5 shows the Extend E-P flux composites for the Indian Ocean center for 200 hPa and for the western Pacific center for 200, 100, and 70 hPa. Most striking in Figure 5 are regions of coherent, statistically significant flux departures over a broad tropical swath in the troposphere and lower stratosphere. At 200 hPa near the equator, the largest vertical fluxes are near 120°E for both compositing regions. For both regions, there is a flux out of the Pacific, especially along the coast of North America; this is generally weaker for the Indian composite. For the western Pacific composite, the upward fluxes at 200 hPa are generally associated with downward fluxes above and vice versa. At 70 hPa the extratropical vertical fluxes are similar to those at 100 hPa, but generally less significant. Broadly, they show convergent flows near the regions of upward motion and vice versa. In the lower latitudes there is the strong suggestion that most of the important features of the West Pacific composites are shifted eastward of those of the Indian composites about 60° of latitude (not shown). Most importantly, the western Pacific departures imply a pronounced anomalous horizontal flow of wave energy across the eastern Pacific into the North American region of strong cyclonic anomalies (Figures 2 and 3) at all three elevations. These horizontal flows are accompanied by a modestly significant up/down dipole of wave energy in this locale. The horizontal flows are in qualitative agreement with the idealized example illustrated by Plumb .
 The E-P flux divergence composites, comparable to the fluxes illustrated in Figure 5, are shown in Figure 6. In the equatorial zone at all three pressure levels (200, 100, and 70 hPa), there are coherent regions of statistically significant convergence and divergence. For instance at 200 hPa near both composite centers, there are positive divergence departures with convergence anomalies to both the east and west. Since the mean zonal winds do not change sign convergence implies a piling up of wave energy and vice versa. At 200 hPa, there are few regions of significant divergence anomalies at higher latitudes. However, in the lower stratosphere, there are significant divergence departures not only near the equator but also north of 50°N, especially over northern Canada. The dipole pattern over Canada has a similar relation to the low geopotential anomaly shown in Figure 2, as that found by Caballero and Anderson  in an analysis of ENSO departures. A comparison of the E-P fluxes in Figure 5 and the flux divergences in Figure 6 illustrate that caution must be used in interpreting apparent flux divergences based solely on the horizontal flux vectors. Oftentimes, the vertical flux gradients, which cannot be inferred from a single level, dominate (not shown).
Figure 7 shows examples of vertical/longitude cross sections of the MJO composites of Extended E-P fluxes for 15°N and 60°N. There are statistically significant, spatially coherent departures at both latitudes for both composites. Figures 7a and 7b for 15°N highlight the meridional flux departures, whereas the maps in Figure 5 tend to emphasize the vertical flux departures. For instance, near both composting centers, there are significant equatorward fluxes in the troposphere and lower stratosphere. These are accompanied by poleward fluxes to the east of the centers. Also, to the east of the centers there are significant upward and eastward fluxes of wave energy. For the western Pacific composites, these extend upward to 50 hPa; those for the Indian are weaker and shallower. All of these departures have a noticeable eastward tilt with height, suggesting the importance of Kelvin wave dynamics. This is consistent in this region with Kelvin waves associated with the eastward propagation found for composites of temperature and winds by Weare [2010a].
 At 60°N (Figures 7c and 7d) there are coherent significant vertical flux departures through the full depth of the domain for both composites. These have strong wave number 2 patterns, which generally have westward tilts with height. The latter is suggestive of the importance of Rossby wave dynamics in this region. For the West Pacific composite, the meridional fluxes are poleward near 40°E, 140°E, and most importantly 80°W throughout the stratosphere. This latter region corresponds to the large flow changes shown in Figure 2. Few significant departures of the meridional fluxes are evident for the Indian composite. Overall, in the tropics there are upward and poleward fluxes east of the longitudes of the composite centers in the troposphere and lower stratosphere. At higher latitudes, these poleward flux departures evolve into large flux departures throughout the stratosphere.
Figure 8 illustrates the associated height/longitude profiles of Extended E-P flux divergence composites at 5°N and 60°N. Near the equator, there are highly significant positive departures in the flux divergences near both composting regions stretching from the troposphere into the lower stratosphere. This is accompanied by flux convergences both to the east and west. These patterns are all very consistent with the map views in Figure 6. Since near the equator both the composite mean zonal mean zonal winds and vorticity gradients are of constant sign (not shown), these divergence/convergence patterns may be associated with a significant export or piling up of wave energy in the general region of the low anomaly, shown in Figures 2 and 3. For both the divergent and convergent zones, there is evidence of eastward tilt with height up to at least the 50 hPa level, which again suggests the importance of Kelvin waves in this region. At the upper levels the divergence patterns are quite noisy.
 At 60°N near the longitudes of both centers, there are broad regions of Extended E-P flux convergence departures extending from 200 to 10 hPa. These are associated with a wave number 2 pattern of convergence/divergence departures. For both composite centers, the departures have a westward tilt of at least 60° over the depth analyzed, suggesting the importance of Rossby waves. The high-latitude stratospheric responses to forcing at the West Pacific center is shifted about 120° east of those of the Indian Ocean center. This is a larger shift than is evident near the equator. At the higher latitude for both compositing regions, the mean zonal wind and mean vorticity gradients are positive so that positive divergences may be unambiguously interpreted as being associated with increases in wave energy and vice versa. Comparing Figures 2b–2d and 8d, it is evident that positive divergence departures are broadly associated with low geopotential anomalies for western Pacific compositing region.
4. Conclusions and Discussion
 Traditional and Extended Eliassen-Palm fluxes have been filtered with an MJO bandpass filter. The features of these fluxes and their divergences associated with the MJO are identified by using two composites centered on the equatorial Indian and western Pacific oceans. The traditional E-P flux composites suggest for both composites an upward and poleward flux of zonal momentum in the Northern Hemisphere. The Indian Ocean composite flux divergences tend to accelerate the zonal mean flow, and those of the western Pacific tend to decelerate it. Departures for the western Pacific composites are generally more significant at higher elevations than those for the Indian Ocean region.
 For the Extended E-P fluxes at levels from 200 hPa into the lower stratosphere, there are significant vertical and meridional fluxes over nearly all of the equatorial Eastern Hemisphere associated with both the Indian and western Pacific MJO composite centers. At the low latitudes there are coherent zones of statistically significant Extended E-P flux convergence and divergence, implying a piling up or export of wave energy. There is also evidence for the importance of Kelvin wave dynamics. At higher latitudes these changes are associated with northward and upward flux departures to the east of the composite centers spanning much of the stratosphere. Many of the significant changes are focused on northern Canada, the region of significant dynamical departures associated with the western Pacific center. These fluxes of wave energy lead to significant flux divergence departures at higher latitudes over much of the stratosphere, which are dominated by wave number 2 variations. These higher-latitude divergence departures generally tilt westward with height, suggesting the importance of Rossby wave dynamics.
 Insight into the high-latitude changes associated with the western Pacific composite may be gained by comparing Figures 2 and 3 with Figures 5–8. Figure 5 indicates large departures of the vertical component of E-P flux extending into the lower stratosphere both in the tropics and at higher latitudes, especially over Canada. In the tropics upward fluxes are possible for all mean zonal wind conditions [Lindzen, 1967]. Propagation into at least the lower stratosphere is possible because intraseasonal MJO variations have imbedded higher-frequency components [Yanai et al., 2000]. In the middle latitudes vertically propagating waves are generally only possible when the mean zonal winds are westerly [Charney and Drazin, 1961], which is true for both composites for all heights for latitudes north of about 25°N (not shown). These vertical flux changes are accompanied by horizontal flux departures at all levels shown from the central tropical Pacific into northern Canada, where geopotential departures are strongly negative. Figure 2 shows that the associated changes are equivalent barotropic and thus may be described by the relatively simple wave dynamics of Hoskins and Karoly . However, Figure 7 also indicates significant vertical E-P flux departures in the higher latitudes. Figures 6c, 6d, and 8d also show that in this Canadian region there is a divergence of Extended E-P flux, piling up wave energy leading to the observed perturbed cyclonic motion. Broadly, these same relationships are apparent for the Indian Ocean composite. However, both the associated wind/geopotential and Extended E-P flux departures are weaker and less significant than for the western Pacific composite.
 Evidence summarized in Figures 5–8 strongly supports the hypothesis that high-latitude circulation variations shown in Figures 2 and 3 are due to a combination of two quite distinct mechanisms. Figure 9 shows a simple schematic of these processes that may work in the latitude/height plane for the zonal mean flow or along a great circle from equator to pole for zonally varying flows. A key element of this diagram and the conclusions of this analysis is that the development of the large cyclonic zone over Canada is due to a combination of two sets of processes. The first (red lines in Figure 9) is associated with poleward propagation in the troposphere followed by vertical propagation directly into the stratosphere at high latitudes. The poleward propagation in the troposphere has been previously observed [e.g., Kiladis and Weickmann, 1992; Hsu, 1996; Matthews and Kiladis, 1999; Kim et al., 2006] and may be described by the now classic equivalent barotropic poleward propagation resulting from a subtropical perturbation [Hoskins and Karoly, 1981]. The associated vertical motion is shown in Figure 7d. The second mechanism (blue lines in Figure 9) results from a combination of vertical propagation in the tropics and subtropics into the lower stratosphere, horizontal propagation northward within the stratosphere, and farther upward propagation in the stratosphere at higher latitudes. The vertical propagation into the lower stratosphere in the subtropics is shown in Figures 5c and 7b. The implied vertical wavelength of at least 10 km is consistent with the analysis of various tropical waves made by Wheeler et al.  (see for instance their Figures 7 and 11). This mechanism appears to be mediated by an anomalous subtropical circulation in the lower stratosphere as shown in Figures 2b and 5c. The horizontal transport in the stratosphere is apparent in Figures 2b, 2c, 5c, and 5d. Vertical propagation in the higher latitudes associated with both mechanisms is illustrated in Figures 5c, 5d, 7c, and 7d. Hints of the this pathway are also observed in the traditional EP flux analysis, shown in Figure 4. Overall, this latter mechanism is comparable to the observed link between El Niño/Southern Oscillation (ENSO) in the tropics with the higher-latitude stratosphere [Manzini, 2009]. Presently, it does not seem possible to ascribe a relative importance to the two paths.
 A number of follow-up studies should clarify the MJO/stratospheric links shown in this study. One somewhat arbitrary aspect of nearly all MJO studies is the specification of indices used in composite or correlation analyses. Other such indices could be used to test the robustness of the present results. Additional efforts are also required to better specify the stratospheric pathway described above. Furthermore, since Figure 4 suggests relationships between MJO and zonally mean flows in the stratosphere, possible interactions with other phenomena, such as the Quasi-Biennial Oscillation and Sudden Stratospheric Warmings, should be explored. Finally, similar methods could be used on model output to assess how well models reproduce the full range of MJO/stratosphere interactions. The overall goal would be to use the better understanding of MJO signal propagation to improve both tropical and extratropical weather and climate forecasts.
 ERA-40 data were provided by the European Centre for Medium-Range Weather Forecasting from their Web site at http://data.ecmwf.int/data/d/era40_daily/. This work was partially supported by NSF grant ATM0733698.