1. Introduction
The Madden–Julian oscillation (MJO; Zhang 2005) is a dominant mode of intraseasonal variability in tropical convection and circulation. A number of observational studies have documented that the anomalous tropical convection associated with the MJO modulates the global circulation. This modulation is expressed through changes in atmospheric angular momentum (AAM) or through quasi-stationary Rossby waves or Rossby wave dispersion (Kiladis and Weickmann 1992; Matthews et al. 2004; Weickmann et al. 1992). Some studies have shown that the MJO interacts with some extratropical teleconnection patterns such as the Arctic Oscillation, the North Atlantic Oscillation, and the Pacific–North America pattern (Cassou 2008; L’Heureux and Higgins 2008; Lin et al. 2009; Mori and Watanabe 2008; Frederiksen and Lin 2013). Straus and Lindzen (2000) found strong coherence between eastward-moving planetary-scale zonal winds in the subtropics and tropics and suggested a linkage between planetary-scale baroclinic instability in the subtropics and the organization of the tropical convection. Furthermore, the modulation of the global circulation by the MJO is not restricted to intraseasonal time scales. Several studies have shown that the MJO modulates the propagation characteristics of high-frequency extratropical transient eddies (Matthews and Kiladis 1999), characteristics and frequency of breaking Rossby waves (Moore et al. 2010), and tropical cyclogenesis (Liebmann et al. 1994; Maloney and Hartmann 2000; Frank and Roundy 2006), as well as violent tornado outbreak frequency in North America (Thompson and Roundy 2013).
While a number of studies have shown variability of the extratropical circulation associated with the MJO, some studies have suggested that extratropical waves can trigger tropical convection and influence the initiation of convection in the MJO (Ray and Zhang 2010; Zhao et al. 2013). Propagation of extratropical waves into the tropics can trigger tropical convection and circulation responses that resemble convectively coupled equatorial waves such as equatorial Rossby waves or Kelvin waves (Kiladis 1998; Straub and Kiladis 2003). Therefore, the higher-frequency wave activity in the extratropics that is modulated by the MJO can then feed back onto the intraseasonal or background state through momentum transfer or by triggering convection in the tropics. Through idealized modeling, Zhao et al. (2013) showed that MJO activity diminishes when model variables in the subtropics were damped to climatology, suggesting the importance of communication between the tropics and extratropics on the organization of the MJO. A model study by Ray and Zhang (2010) also suggested that extratropical circulation patterns can initiate MJO events. Both observational and modeling studies suggest that interaction between the tropics and extratropics is part of MJO dynamics. Roundy (2014) showed that the extratropical circulation response to MJO convection includes intraseasonal wave signals that propagate back into the tropics over the Western Hemisphere, where they influence the direction and intensity of the zonal wind in the equatorial waveguide. While the MJO modulates the extratropical circulation, its organization and characteristics may also be determined or influenced by the extratropical circulation, including both signals dependent on or initially independent from the MJO. However, the extent to which these modulations of the synoptic- to planetary-scale extratropical circulation help drive the MJO circulation is not yet well understood.
One aspect of the MJO and its interaction with the extratropics that is yet to be examined is how the subtropical jet streams and global zonal mean circulation vary with the MJO. The subtropical jet acts as a waveguide of extratropical Rossby waves and as a storm track. Changes in its strength and structure associated with the MJO influence the pathway and baroclinic life cycle of synoptic waves. Therefore, examination of the mechanisms whereby the subtropical jet varies with the MJO would improve our understanding of consequential influences on the transient eddies and synoptic weather events such as wave breaking and blockings. The changes in synoptic wave activity could then also feed back onto the intraseasonal to lower-frequency background circulation, resulting in complicated multiway interactions. To understand such complicated multiway interactions from a simplified point of view, this study examines the association of variability of 200-hPa zonal mean zonal wind with the MJO. The intraseasonal variability in 200-hPa zonal mean zonal wind generally resembles variability of AAM equatorward of around 35°N and 35°S (Weickmann et al. 1997), but Hsu (1996) showed that the zonal mean zonal winds at 850 and 200 hPa shift out of phase with each other at higher latitudes. Therefore close examination on one level in the upper troposphere avoids averaging out the higher-latitude zonal circulation that is still associated with the MJO instead of focusing on vertically integrated angular momentum. This study diagnoses the role of the zonal mean and eddy circulations across multiple time scales and their interactions with the 200-hPa zonal mean zonal wind variability associated with the MJO through budget analysis.
2. Data and methodology
a. Data and MJO indices
Interpolated outgoing longwave radiation (OLR; Liebmann and Smith 1996) data obtained from the National Oceanic and Atmospheric Administration (NOAA)/Earth System Research Laboratory is applied as a proxy for moist deep convection in the tropics. Wind data are obtained from National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis data (Saha et al. 2010) with 2.5° horizontal resolution on isobaric surfaces. The period of the study is December–February (DJF) from 1980 to 2010. Indices for the MJO are calculated as in MacRitchie and Roundy (2012), except the intraseasonal time scale is defined as 30–100 days. These indices are similar to the real-time multivariate MJO indices in Wheeler and Hendon (2004, hereafter WH04) that are generated from combined empirical orthogonal function (EOF) analysis of 200- and 850-hPa zonal winds and OLR anomalies averaged from 15°N to 15°S but are derived using filtered OLR and wind data. Filtering the data reduces inclusion of signals from other convectively coupled equatorial waves such as Kelvin or equatorial Rossby waves (Roundy et al. 2009) and other noise. The structure of the resultant multivariate EOFs used for calculating the index are similar to those of WH04, where the first EOF has enhanced convection over the warm pool and the second EOF has suppressed convection over the Indian Ocean (see Fig. 1 in WH04). Straub (2013) found that the multivariate indices in WH04 are more heavily weighted toward the wind components. To emphasize the convective signals of the MJO, only the OLR component of the EOFs is projected to generate the MJO indices in this study. Here we refer to these MJO indices as MJOI1 and MJOI2.
b. Zonally averaged zonal momentum equation
Scale analysis showed that the only terms that contribute to the intraseasonal time scales in the dynamical processes that modulate zonal mean winds (term 1 and term 2) are the terms that represent interaction between the background and the intraseasonal band [see (5)]. These terms are considered pseudolinear terms since the background state can be considered constant within the intraseasonal time scale. Whereas for the convergence of eddy flux terms (term 3 and term 4), nonlinear upscale momentum transfer from transient circulations plays an important role as well [see (6)]. The important terms for driving intraseasonal zonal mean zonal wind that will be discussed in the rest of the paper are summarized in Table 1.
Summary of the linearly decomposed components of the first four terms on rhs of (1) that are relevant on intraseasonal time scales.
c. EOF analysis
To extract the dominant modes of intraseasonal variability in the upper-level zonally averaged zonal wind, EOF analysis is applied to 30–100-day filtered zonally averaged 200-hPa zonal wind data during DJF. The difference in gridbox area with latitude is taken into account by multiplying by the cosine of latitude before the EOF analysis is applied. Figure 1 shows the first two leading EOFs of the zonal wind anomalies, which explain around 33% and 21% of the variance, respectively. The first EOF shows a westerly and an easterly oscillation of intraseasonal zonal wind in the tropics. The second EOF captures meridional shifts of the Northern and Southern Hemisphere subtropical jets that occur symmetrically about the equator.
First two leading EOFs of the zonally averaged intraseasonal zonal wind at 200 hPa with an amplitude of one standard deviation of each PC.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
Auto- and cross correlations between the resultant principal components (PCs) and MJO indices are calculated to examine the correlation and time-lag relationship between the dominant intraseasonal zonal wind variability and the MJO. The first and the second leading PCs are referred to as PC1 and PC2, respectively. Figure 2 shows that PC1 and PC2 are most correlated with each other at about ±13-day time lag with correlation coefficients of about −0.70 and 0.55 when PC1 leads PC2 and when PC2 leads PC1, respectively (suggested by stronger coefficient magnitude at day +13 than at day −13 in Fig. 2a and the opposite in Fig. 2b). The higher correlation when PC2 lags PC1 suggests that the equatorial intraseasonal signal tends to precede the subtropical meridional shifts, while reduced correlations when PC1 lags PC2 suggest that the tropical wind signal following the anomalous meridional shift of the subtropical jets may vary more in periodicity and amplitude. The maximum amplitude of lagged correlation coefficients between PC1 or PC2 and higher PCs (i.e., PC3, PC4, etc.) drops rapidly to about 0.17 or less (not shown), suggesting that the two leading EOFs are much less associated with higher EOFs when time lags are considered. Imperfection in the correlation between PC1 and PC2 is associated with slight differences in the preferred frequency bands of the two time series. PC1 has zero autocorrelation at about 13.5 days, suggesting that its dominant period is around 54 days, while PC2 has a zero autocorrelation around 11.5 days (suggesting a 46-day period), slightly shorter than for PC1.
Auto- and cross correlation of (a) PC1 and (b) PC2 with each other and MJO indices.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
Figure 2 shows that the leading two PCs are also highly correlated with the MJO indices with some time lags. The maximum correlation between the first two leading PCs and the MJO indices exceeds 0.6 but the maximum correlation between the higher PCs and the MJO indices drops to around 0.2 or less. Thus, the first two leading EOFs of the zonally averaged intraseasonal zonal wind are most closely coupled to the part of MJO activity that is captured by the MJO indices. However, the structures of the zonal wind associated with the leading PCs do not represent all of the intraseasonal zonal wind variability associated with the MJO and they contain some signal independent from the MJO. Therefore, this study examines the structure and driving mechanism of the intraseasonal zonal wind from two points of view—namely, signals associated with the first two leading PCs in sections 3a–c and the ones associated with the MJO indices in section 3d.
d. Lagged regression and composite techniques
The association between the zonal mean zonal wind and the MJO is examined based on the dominant spatial structure of intraseasonal zonal wind variability extracted by EOF analysis shown in section 2c. To capture the evolving wind tendency and to assess its driving mechanisms and the signals of MJO convection associated with the EOF patterns, lagged regression is used with the PCs as predictors. The gridded fields are regressed against the normalized PCs with time lags. The patterns in the fields associated with the indices are then reconstructed using the regression coefficients and one standard deviation of the predictor PC. Statistical significance of the regression coefficients is tested at each grid point by using the Student’s t test with the degrees of freedom calculated by following (31) in Bretherton et al. (1999).
3. Results
This section first shows the evolution of the contributing dynamical terms that are linearly associated with the first leading EOFs of the zonally averaged intraseasonal zonal wind. Because PC1 and PC2 are highly correlated given a time lag, the following results focus on examination of the mechanism associated with the development of the EOF1 pattern only. The same analysis was repeated using PC2 as a predictor, but results suggest a similar mechanism with signals occurring at different lead times to that suggested by analysis of EOF1. The analysis of EOF1 is then compared with the composite analysis based on the MJO indices.
a. Evolution of the zonal wind signal associated with the leading EOF
Figure 3a shows the evolution of intraseasonal zonal wind and its time tendency, as linearly associated with PC1 using the regression technique described in section 2d. The strong intraseasonal wind signal starts over the tropics and propagates poleward. The wind amplitude is stronger in the Northern Hemisphere (NH) but it tends to extend farther poleward in the Southern Hemisphere (SH). The intraseasonal zonal wind in the NH also decreases its speed of meridional propagation as it propagates away from the tropics. Another difference between the hemispheres is the equatorward propagating wind anomaly from higher latitudes in the NH that has the opposite sign from the one that propagates from the tropics. A similar equatorward-propagating signal does not appear in the SH. The DJF climatological zonal mean jets peak at around 30°N and 50°S (Fig. 4a). Therefore, when the opposite-sign zonal wind anomalies approach from the equator and the pole toward the NH jet stream, it results in a several-degree latitudinal shift of the jet and adjusts amplitude by a few meters per second. In the SH, without the strong anomalies moving equatorward from higher latitudes, the zonal wind anomalies that propagate from the equator modify the jet by changing its meridional width but do not necessarily shift the latitude of maximum wind.
Lag regression time–latitude diagram of (a) intraseasonal zonal wind tendency, (b) sum of the all dynamical terms, and (c) residual (m s−2), all onto PC1 (shaded) and intraseasonal zonal wind (black contour with interval of 0.5 m s−1), with the value of PC1 set to one standard deviation. Gray dots indicate statistical significance of the difference of the regression coefficients from zero at the 95% confidence level.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
(a) The 200-hPa zonal mean zonal wind (m s−1) averaged over DJF. (b) Plan view of the 200-hPa zonal wind averaged over DJF (shading), along with OLR between 25°S and 25°N (contoured where it is less than 240 W m−2 for every 10 W m−2).
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
The sum of all the calculated terms and the residual from the total intraseasonal zonal wind tendency are regressed in the same way as the zonal wind tendency onto one standard deviation of PC1 (Figs. 3b,c). The residual is calculated by subtracting the actual zonal wind tendency from the sum of all the calculated terms on the rhs of (1). In general, the calculated total tendency tends to underestimate the actual tendency in the tropics and overestimate it in higher latitudes. The magnitude of the residual becomes of the same order as the actual zonal wind tendency at higher latitudes in both hemispheres, especially poleward of 40°S or 40°N. However, this large residual does not necessarily mean that the results are not statistically significant for interpretation. Regression analysis captures signals that more consistently occur with base indices although there may be a bias in the estimation of the amplitude. Despite the fact that the reanalysis is not adjusted to close the budget and despite the coarse resolution in time and space, the sum of the calculated terms is able to capture the overall structure of the zonal wind tendency, especially in the tropics and the subtropics.
Figure 5 maps the longitudinal structures of the intraseasonal zonal wind and MJO convection at days −15, −5, +5, and +15. The structures of the mean DJF 200-hPa zonal wind and OLR are also shown in Fig. 4 to examine how the intraseasonal anomalies evolve with respect to the background state. Zonal mean tropical zonal wind begins to become anomalously westerly when the subtropical jets are shifted poleward and when convectively active MJO is over the warm pool of the western Pacific Ocean (positive PC2; Fig. 5a). The poleward shift of the subtropical jets is indicated by the anomalous westerly wind poleward and the anomalous easterly wind equatorward of the climatological location of the jet streams, especially in the NH. As the MJO active convection propagates to the central Pacific basin (positive MJOI2), the tropical intraseasonal zonal wind anomaly reaches its maximum westerly state (positive PC1; Fig. 5b). At the same time, a suppressed convective phase of the MJO develops over the Indian Ocean. As the suppressed convection moves out from Indian Ocean (negative MJOI1), the tropical intraseasonal westerly wind anomaly starts to decay (Fig. 5c). The subtropical jet shifts equatorward with the decay of the tropical westerly wind anomaly (negative PC2; Fig. 5d), followed by the anomalous zonal mean tropical zonal wind switching to easterly as the suppressed convective phase of the MJO moves to the central Pacific.
Map of intraseasonal zonal wind (shaded) and intraseasonal OLR anomalies (black solid contours indicate negative and dashed indicate positive values; interval of 2 W m−2) regressed onto PC1 with the value of PC1 set to one standard deviation at time lags of (a) −15, (b) −5, (c) +5, and (d) +15 days. (left) The profiles show zonally averaged intraseasonal zonal wind at each time. (right) Intraseasonal wind fields are plotted as vectors over regions where the intraseasonal zonal wind is correlated above the 95% significance level. Regions of statistically significant OLR anomalies are shown by gray hatching.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
The intraseasonal upper-tropospheric zonal mean zonal wind anomalies are associated with anomalous meridional circulation throughout the troposphere. Figure 6 shows the meridional overturning circulation that evolves with the intraseasonal poleward-propagating zonal mean zonal wind at 200 hPa for the same days as shown in Fig. 5. The convectively enhanced MJO convection over the warm pool at day −15 induces zonally averaged anomalous ascent in the tropics and descent in the subtropics, suggesting enhancement of the Hadley cell. These meridional overturning cells propagate poleward with the zonal mean zonal wind anomalies. At day −5, a counterclockwise circulation begins to develop in the upper troposphere over the NH tropics while a clockwise circulation develops in the lower troposphere at the equator (Fig. 6b). These two anomalous cells continue to amplify and propagate poleward, thus weakening the Hadley circulation and shifting the subtropical jets equatorward (Figs. 6c,d).
Latitude–pressure cross sections of zonal mean zonal wind (shaded; m s−1) and meridional overturning circulation (black lines) calculated by regressing zonal mean meridional wind onto one standard deviation of PC1 with (a) −15-, (b) −5-, (c) +5-, and (d) +15-day time lags. Black solid line indicates positive and dashed indicates negative, with a 2 × 108 kg s−1 interval. Statistically significant regions of the overturning circulations are hatched in gray at the 95% confidence level.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
b. Dynamical processes influencing zonal mean and eddy flows
Contributions of the different dynamical terms in (1) from all time frequencies to the intraseasonal poleward-propagating zonal wind signal are first examined here before considering the role of scale interactions. Figure 7 shows different terms and intraseasonal zonal wind. A quadrature relationship, where a term leads the wind signal, suggests that its dynamical process contributes to the development of the wind signal that will be referred to as a positive quadrature relationship, whereas if the term leads the wind signal in opposite sign, its dynamical process is acting to slow down the developing wind signal and will be referred to as a negative quadrature relationship. In-phase relationships between the dynamical term and the intraseasonal wind indicate that the term acts to maintain the wind signal while out-of-phase relationships indicate that the term is decaying the wind signal. All terms in Fig. 7 except term 5 show asymmetrical patterns about the equator even though the wind pattern is relatively symmetrical. This hemispheric difference suggests that most of the terms contribute differently across the latitudes. The advection and Coriolis terms associated with zonal mean flows (term 1, term 2, and term 5) and the flux convergence terms associated with zonally asymmetric flow or eddies (term 3 and term 4) contribute approximately in equal magnitude to the zonal mean intraseasonal zonal wind time tendency although the latitudes of their strong contributions differ among the terms.
As in Fig. 3, except shading represents (a) term 1, (b) term 2, (c) term 3, (d) term 4, (e) term 5, and (f) the sum of all other terms.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
In the NH subtropics, term 1 drives most of the poleward propagation of the intraseasonal zonal wind. However, it becomes more in phase with the wind as it propagates poleward of 20°N. North of 30°N, term 1 slows down the development of wind as shown by the negative quadrature relationship. Term 2 weakly develops the intraseasonal wind around 20°N while it slows down and decays the wind over the tropics (Fig. 7b). This slowdown and decay of wind anomalies by term 2 across the tropics is counteracted by the flux convergence by eddies (term 3 and term 4). Term 3 and term 4 (Figs. 7c,d) become key drivers of the intraseasonal wind evolution north of 25°N, where the zonal mean zonal wind maximizes climatologically. Another weak but important term over the tropics is the zonal acceleration by convective mixing, which makes up most of the contributions in the tropics by X (Fig. 7f). Term 5 is out of phase with the zonal wind at all latitudes (Fig. 7e). Therefore, term 5 decays the intraseasonal zonal mean zonal wind oscillation. Since the zonal mean of the geostrophic meridional wind is zero, only the ageostrophic and mostly divergent parts of the wind contribute to term 5. The out-of-phase relationship between the zonal wind and term 5 suggests that the meridional wind associated with the anomalous mass convergence in the tropics acts to decay the intraseasonal wind anomaly and to bring the circulation back to equilibrium. Comparison of the error (Fig. 3c) and term 5 (Fig. 7e) shows that their patterns are similar. This similarity suggests that the error might result from overestimation of term 5 or underestimation of term 3 or term 4 that counteract term 5. The error becomes larger at higher latitudes where the eddy flux terms, term 3 and term 4, are more important. The lack of fine grid resolution to capture the small-scale eddies suggests likelihood of underestimation of the flux convergence from unresolved small-scale eddies that are more important at higher latitude.
In the SH, flux convergence by eddies (term 3 and term 4) appears to be the main driver of intraseasonal wind while advection by the zonal mean circulation (term 1 and term 2) contributes little. The contribution of the zonal mean flow to driving the intraseasonal zonal wind is smaller in the SH than in the NH.
c. Scale interactions
Decomposition of each term into nonlinear and cross-frequency components gives further insights about the mechanism of poleward propagation and feedbacks between the synoptic- and planetary-scale circulations. This section examines the contribution of different scale interaction to each dynamical term that was shown in section 3b.
1) Zonal mean advection terms (term 1 and term 2)
At 200 hPa, both term 1 {
As in Fig. 3, except shading represents (a) term 1a, (b) term 1a-1, and (c) term 1a-2.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
As in Fig. 3, except shading represents (a) term 2a, (b) term 2a-1, and (c) term 2a-2.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
Similar to term 1a, term 2a (shown in Fig. 9a) can also be decomposed into the advection of intraseasonal zonal wind by background vertical motion {term 2a-1; 
Regressed latitude–pressure cross sections for comparison with (a) Fig. 9b and (c) Fig. 9c at time 0. Contribution by (a) term 2a-1 and (b) term 2a-2 are contoured in gray with a 2 × 10−7 m s−2 interval. Shaded is the (a) intraseasonal zonal wind and (b) background zonal wind. Vectors show (a) background vertical velocity and (b) intraseasonal vertical velocity (Pa s−1) and are plotted where term 2a-1 and term 2a-2 are correlated with PC1 at the 95% significance level.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
The temporal decomposition of the meridional and vertical advection by zonal mean flow shows that the most important temporal interaction that develops the intraseasonal zonal wind comes from advection of the intraseasonal zonal wind by background flow. The background flow plays a key role in the northward propagation of the intraseasonal zonal wind anomalies and the decay of these anomalies in the tropics and subtropics. The analysis of the zonal mean advection terms shows that the evolution of the zonal mean intraseasonal wind is determined by how it is advected by the background flow rather than how it advects the background flow. It indicates that the changes in the background state would have strong influence on the zonal mean circulation associated with the MJO. However, the zonal mean advection alone cannot explain the change in the equatorial intraseasonal zonal wind anomaly and why the anomaly is able to extend poleward of 30°N or 30°S.
2) Eddy flux convergence terms (term 3 and term 4)
(i) Interaction between background and intraseasonal eddies
Figure 11a shows that important contributions to the development of the tropical intraseasonal zonal wind comes from term 3a (
As in Fig. 3, except shading represents (a) term 3a, (b) term 4a, (c) term 3b, and (d) term 4b at 200 hPa.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
(a) (right) Term 3 (
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
Poleward of 20°N and 20°S, the vertical flux convergence of intraseasonal zonal momentum due to interaction between the background wind and wind at intraseasonal time scales (
Both term 3a and term 4a in the middle latitudes help develop and maintain the intraseasonal zonal mean zonal wind. These results indicate the importance of interaction between the zonally varying background and intraseasonal circulation for the evolution of the zonal mean circulation. The role played by the zonally varying circulation suggests that the zonally averaged global circulation associated with the MJO may vary from event to event owing to the variability of the zonal structure of the MJO as well as the background state.
(ii) Feedbacks from transient eddies
Transient eddy flux convergence terms, term 3b (
(right) As in Fig. 5, except shading represents the intraseasonal anomalous meridional flux of zonal wind by transient eddies (
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
The structural and track changes in the transient eddies are evidenced in Fig. 14 at day −15 and day +5 by first identifying the days of local peaks in PC1 with its amplitude greater than one standard deviation. Then from among these days, the subset of days during which transient eddy meridional winds at 30°N, 170°W were southerly and had local time maxima within 2 days before and after 15 days prior and 5 days after the peaks in PC1 are composited. The composite 200-hPa transient eddy streamfunction (shading in Fig. 14) is compared with its climatological structure (contoured in black in Fig. 14), which is composited based on all days when the transient eddy meridional wind at the same location was southerly during DJF. Statistical significance for these composites is tested by 1000 sample bootstrap resampling tests as described by Roundy et al. (2010). In this test, the distribution of the 1000-time resampled composite days are compared with 1000 composites based on sets of the same number of dates selected at random from DJF. At each grid point, if 95% of the distribution of the resampled composite is greater or less than the top or bottom 95% of the distribution based on the random composite, the result is considered statistically significantly different from zero. The regions of statistical significance are indicated by white hatching.
Composite maps of times when 200-hPa transient eddy meridional wind at 30°N, 170°W had a local time maximum and was positive within 2 days before and after (a) −15 and (b) +5 days from the peak of PC1 with greater than one standard deviation (see text for more details). The transient eddy streamfunction (m2 s−1) is shaded and its climatological composite is contoured in black with a 106 m2 s−1 interval [N = (a) 18 and (b) 19 days]. Hatched regions indicate anomalies that are statistically significantly different from zero at the 95% confidence level using a bootstrap resampling test for the shaded anomalies.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
Figure 14a shows that the transient eddies tend to be slightly more positively tilted with latitude (anticyclonically sheared) and their track has shifted slightly northward compared to the climatology at day −15. While at day +5, they are more north–south oriented. Figure 5 shows that, at these days, there is imposed planetary-scale intraseasonal anticyclonic (−15 days) and cyclonic (+5 days) shear on the subtropical jet in the NH. These results suggest that the anomalous intraseasonal shear influences the baroclinic life cycle of the synoptic eddies as anticyclonic (LC1) and cyclonic (LC2) Rossby wave breaking tends to occur in background anticyclonic and cyclonic shear, respectively (Thorncroft et al. 1993). These modulated structures of the synoptic eddies induce anomalous flux that feeds back onto the intraseasonal time scale by accelerating intraseasonal easterly wind at −15 days and westerly wind +5 days to the south of climatological jet. Similar changes occur across the North Pacific and over the North Atlantic basins as well (not shown). Along with other mechanisms, this positive feedback develops midlatitude intraseasonal zonal wind variability associated with the MJO.
While the changes in the horizontal structure of the transient eddies positively feed back to develop the observed zonal mean intraseasonal zonal wind (shown by term 3b), Fig. 11d shows that vertical flux convergence by the transient eddies (term 4b) feeds back negatively by slowing down the intraseasonal zonal mean wind acceleration. Figure 15 shows the NH latitude–pressure cross sections of zonal mean zonal wind and 
(a)–(c) Regressed latitude–pressure cross section of background zonal wind [shaded in (a)] and intraseasonal zonal wind [shaded in (b),(c)]. Black contours show DJF-mean zonal mean of meridional flux by transient eddies (
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
At day −5, amplitudes of the NH westerly wind and 
d. Intraseasonal zonal wind and estimation of budget terms based on the MJO indices
This section examines how the zonal wind and the contributing dynamical terms may differ when they are composited based on the MJO indices. WH04 divided the global evolution of the MJO into eight phases based on the phase angle created by RMM1 and RMM2 (see WH04 for more details). In this study, the cycle is divided into 16 phases (22.5° phase angle in each phase) and labeled 0.5, 1, 1.5, …, 8 in order to capture more detailed time evolution of the zonal wind and the dynamical terms. The composite based on each phase includes only days when the amplitude of the MJO indices was greater than one standard deviation. The number of days composited in each phase varied from 118 in phase 2.5 to 156 in phase 5. The statistical significance of the composite fields is tested by bootstrap resampling tests as described in section 3c(2)(ii).
The evolution of the intraseasonal zonal wind and the dynamical terms composited based on the MJO indices shows a similar pattern and driving mechanism to the regressed intraseasonal zonal wind derived from PC1. However, some differences between the analysis based on the two leading PCs of the zonal mean zonal wind and the MJO indices appear in term 3a and term 3b (not shown). Significant contribution of term 3b on accelerating the intraseasonal zonal wind in midlatitudes is not apparent in the composite. The possible cause of this result could be wide event-to-event variability of the MJO in its temporal and spatial characteristics. One index might capture a given part of the signal, while another index might not. No index for the MJO could diagnose all aspects of its preferred types of variability, and different indexes would highlight particular aspects of its evolution (e.g., Straub 2013; Kiladis et al. 2014). When the amplitude, duration, and structure of the MJO convection are different, the circulation response to the released latent heat and its interaction with background state would be different. The zonally varying circulation and changes in the characteristics of the transient eddies may differ substantially depending on the characteristics of the MJO as diagnosed by a particular index. The composite method used here also does not take into the account the MJO state preceding the events in each phase. The regression analysis based on PC1 is able to capture its linearly associated signal with its time evolution. The MJO indices only capture the days when the 15°N–15°S-averaged intraseasonal convection projects well onto its two leading EOF structures. The state of the extratropics may depend more on the preceding progression of the MJO convection. In that case, the composited terms in the extratropics based on the MJO indices may not show any significant signals if there is a wide variety of the MJO structure and characteristics that precede the composited days. In fact, regression of term 3b patterns onto MJOI1 or MJOI2 showed statistically significant contributions to intraseasonal zonal wind. This result confirms that modulation of the characteristics of the transient eddy feedback onto the intraseasonal zonal mean circulation when examined based on the MJO indices as well. However, this signal is not captured by the composite method applied here owing to some event-to-event variability of the MJO. Term 3a has more amplitude in the NH subtropics when it is composited based on the MJO indices than when it is regressed onto PC1 (not shown). This difference contributed to the secondary maximum in intraseasonal zonal wind in the NH subtropics in the composite that is not apparent in association with PC1.
4. Summary and discussion
The budget analysis of zonal mean intraseasonal zonal wind revealed insight about the driving mechanisms of the observed global circulation associated with the MJO. To diagnose the role of cross-time-scale interaction and nonlinear effects by the zonal mean and eddy circulation, all wind fields are linearly decomposed into three temporal bands: a 30–100-day intraseasonal period and periods shorter or longer than the intraseasonal period. Results show that the first two leading EOFs of the zonal mean intraseasonal zonal wind in DJF vary with the MJO. These two EOFs together represent a poleward propagation of intraseasonal zonal wind anomalies that starts from the equator and whose amplitude remains relatively stronger in the NH as it moves poleward.
The mechanisms of the poleward propagation of the zonal mean intraseasonal westerly momentum from the tropics are summarized in the schematics in Fig. 16. At day −15 (Fig. 16a) when the tropical zonal wind anomaly begins to switch from easterly to westerly, the MJO active convection is over the Maritime Continent to the western Pacific basin. The change in the strength and structure of the climatological seasonal-mean subtropical eddies due to the intraseasonal circulation associated with the MJO accelerates the tropical westerly wind. At the same time, anomalous vertical motion in the subtropics associated with the MJO convection interacts with the background zonal circulation to help accelerate easterly wind in the midlatitudes, shifting the subtropical jets poleward. At day −10 (Fig. 16b), as the westerly wind anomaly begins to develop over the tropics, it is advected poleward because of the background zonal mean meridional wind. At the same time, the intraseasonal meridional wind also advects the background zonal wind to accelerate westerly wind in the tropics and easterly wind in the NH subtropics. At day 0 (Fig. 16c), at the peak of intraseasonal westerly wind in the tropics, the westerly wind continues to be advected poleward by the background wind. But at the same time, strong background ascending motion in the SH tropics advects intraseasonal easterly wind upward, thus decaying the tropical westerly wind in the upper troposphere. At day +5 (Fig. 16d), suppressed MJO convection over the Maritime Continent imposes planetary-scale cyclonic shear on the subtropical jets associated to the anomalous westerly wind that was advected poleward from the tropics. This anomalous cyclonic shear causes the transient eddies to shift their tracks equatorward and causes their structures to become more meridionally elongated. These changes in the structure of the transient eddies are consistent with the changes in the characteristics of wave breaking events with the MJO as discussed by Moore et al. (2010). They found that when the envelope of enhanced MJO convection moves to the central Pacific basin, during a state similar to that at +5 days, the preferred location of anticyclonic wave breaking events shifts eastward and the frequency of cyclonic wave breaking increases slightly to the north of the subtropical jet. They also found the opposite when MJO convection is located over the warm pool: increased anticyclonic and decreased cyclonic wave breaking at the exit region of the subtropical jet. The change in the structure of the transient eddies positively feeds back to the intraseasonal zonal wind by inducing anomalous flux convergence and divergence equatorward and poleward, respectively, helping to accelerate the zonal mean westerly wind equatorward of the subtropical jets, thus shifting the jet equatorward. At the same time, Coriolis torque by the equatorward meridional wind associated with the suppressed MJO convection damps the westerly wind acceleration in the subtropics. The role of interaction between different scales in driving the intraseasonal AAM was also emphasized by Feldstein (1998), but a clearer explanation of the mechanism is achieved in this paper.
Schematics of the mechanics of the poleward propagation of the intraseasonal westerly anomaly from the tropics shown in maps and latitude–pressure cross sections at days (a) −15, (b) −10, (c) 0, and (d) +5 from the peak in PC1. Circulations are drawn in black and intraseasonal zonal wind accelerations are drawn in red.
Citation: Journal of the Atmospheric Sciences 71, 10; 10.1175/JAS-D-13-0304.1
The significant contribution of dynamical processes that involve interaction between the intraseasonal and background flow to the intraseasonal flow indicates that the variability in the background state and the MJO characteristics can interact to produce variability in the zonal mean global circulation associated with the MJO. Therefore, as expected, the zonal mean global circulation signal associated with the MJO differs by seasons or ENSO phases as both the background circulation and the characteristics of the MJO change substantially (Hendon et al. 1999; Pohl and Matthews 2007; Zhang and Dong 2004; Roundy et al. 2010). Our results also suggest that the MJO circulation is associated with changes in the characteristics of synoptic waves, including wave breaking. These synoptic signals might be a necessary part of the system that drives changes in the observed global intraseasonal circulation and the circulation of the MJO itself. Some such synoptic wave events might be initiated by synoptic-scale convective events embedded within or otherwise modulated by the MJO, implying two-way coupling between the MJO and synoptic events. Using the quantification method of Rossby wave sources by Sardeshmukh and Hoskins (1988), some authors have shown that as the MJO interacts with background absolute vorticity (Hsu 1996; Tyrrell and Karoly 1996), it generates Rossby waves. These results suggest wave signals associated with the MJO act on its own time scales, but since the MJO also modulates convective events of shorter time scales, the MJO would also influence the timing and characteristics of synoptic wave events. This study shows that the feedbacks from those synoptic waves are intrinsic parts of the global intraseasonal circulation that is observed in association with the MJO. The global circulation associated with the MJO does not purely result as a linear response to the convection, but it involves complicated interaction with the background state and feedbacks from modulated synoptic-scale circulations.
Composite analysis of the zonal mean intraseasonal wind based on the MJO indices shows similar poleward-propagating patterns and reveals similar driving mechanisms to those shown by the regression analysis based on PC1. However, the inconsistency between the analyses based on the PCs and MJO indices in the contribution of the feedback from transient eddies suggests that the response of transient eddies to anomalous tropical convection varies with event-to-event variability in the characteristics of the MJO circulation and convection. The authors plan to continue to explore the possible sensitivity of the zonal mean intraseasonal circulation and its driving mechanism to the temporal characteristics of the MJO and its simultaneous interaction with the background state.
Acknowledgments
Funding was provided by the National Science Foundation Grant 1128779 to Paul Roundy. The NOAA PSD provided OLR and reanalysis data.
REFERENCES
Bretherton, C. S., M. Widmann, V. P. Dymnikov, J. M. Wallace, and I. Bladé, 1999: The effective number of spatial degrees of freedom of a time-varying field. J. Climate, 12, 1990–2009, doi:10.1175/1520-0442(1999)012<1990:TENOSD>2.0.CO;2.
Cassou, C., 2008: Intraseasonal interaction between the Madden–Julian oscillation and the North Atlantic oscillation. Nature, 455, 523–527, doi:10.1038/nature07286.
Feldstein, S., 1998: An observational study of the intraseasonal poleward propagation of zonal mean flow anomalies. J. Atmos. Sci., 55, 2516–2529, doi:10.1175/1520-0469(1998)055<2516:AOSOTI>2.0.CO;2.
Frank, W. M., and P. E. Roundy, 2006: The role of tropical waves in tropical cyclogenesis. Mon. Wea. Rev., 134, 2397–2417, doi:10.1175/MWR3204.1.
Frederiksen, J. S., and H. Lin, 2013: Tropical–extratropical interactions of intraseasonal oscillation. J. Atmos. Sci., 70, 3180–3197, doi:10.1175/JAS-D-12-0302.1.
Hendon, H. H., C. Zhang, and J. D. Glick, 1999: Interannual variation of the Madden–Julian oscillations during austral summer. J. Climate, 12, 2538–2550, doi:10.1175/1520-0442(1999)012<2538:IVOTMJ>2.0.CO;2.
Holton, J. R., 2004: The zonally averaged circulation. An Introduction to Dynamic Meteorology, F. Cynar, Ed., Elsevier Academic Press, 316–328.
Hsu, H.-H., 1996: Global view of the intraseasonal oscillation during northern winter. J. Climate, 9, 2386–2406, doi:10.1175/1520-0442(1996)009<2386:GVOTIO>2.0.CO;2.
Jeong, J.-H., B.-M. Kim, C.-H. Ho, and Y.-H. Noh, 2008: Systematic variation in wintertime precipitation in East Asia by MJO-induced extratropical vertical motion. J. Climate, 21, 788–801, doi:10.1175/2007JCLI1801.1.
Kiladis, G. N., 1998: Observations of Rossby waves linked to convection over the eastern tropical Pacific. J. Atmos. Sci., 55, 321–339, doi:10.1175/1520-0469(1998)055<0321:OORWLT>2.0.CO;2.
Kiladis, G. N., and K. M. Weickmann, 1992: Circulation anomalies associated with tropical convection during northern winter. Mon. Wea. Rev., 120, 1900–1923, doi:10.1175/1520-0493(1992)120<1900:CAAWTC>2.0.CO;2.
Kiladis, G. N., J. Dias, K. H. Straub, M. C. Wheeler, S. N. Tulich, K. Kikuchi, K. M. Weickmann, and M. J. Ventrice, 2014: A comparison of OLR and circulation-based indices for tracking the MJO. Mon. Wea. Rev., 142, 1697–1715, doi:10.1175/MWR-D-13-00301.1.
Kim, B.-M., G.-H. Lim, and K.-Y. Kim, 2006: A new look at the midlatitude–MJO teleconnection in the northern hemisphere winter. Quart. J. Roy. Meteor. Soc., 132, 485–503, doi:10.1256/qj.04.87.
L’Heureux, M. L., and R. W. Higgins, 2008: Boreal winter links between the Madden–Julian oscillation and the Arctic Oscillation. J. Climate, 21, 3040–3050, doi:10.1175/2007JCLI1955.1.
Liebmann, B., and C. A. Smith, 1996: Description of a complete (interpolated) outgoing longwave radiation dataset. Bull. Amer. Meteor. Soc., 77, 1275–1277.
Liebmann, B., H. H. Hendon, and J. D. Glick, 1994: The relationship between tropical cyclones of the western Pacific and Indian Oceans and the Madden-Julian oscillation. J. Meteor. Soc. Japan, 72, 401–411.
Lin, H. L., G. Brunet, and J. Derome, 2009: An observed connection between the North Atlantic Oscillation and the Madden–Julian oscillation. J. Climate, 22, 364–380, doi:10.1175/2008JCLI2515.1.
MacRitchie, K., and P. E. Roundy, 2012: Potential vorticity accumulation following atmospheric Kelvin waves in the active region of the MJO. J. Atmos. Sci., 69, 908–914, doi:10.1175/JAS-D-11-0231.1.
Maloney, E. D., and D. L. Hartmann, 2000: Modulation of hurricane activity in the Gulf of Mexico by the Madden-Julian oscillation. Science, 287, 2002–2004, doi:10.1126/science.287.5460.2002.
Matthews, A. J., and G. N. Kiladis, 1999: The tropical–extratropical interaction between high-frequency transients and the Madden–Julian oscillation. Mon. Wea. Rev., 127, 661–677, doi:10.1175/1520-0493(1999)127<0661:TTEIBH>2.0.CO;2.
Matthews, A. J., B. J. Hoskins, and M. Masutani, 2004: The global response to tropical heating in the Madden–Julian oscillation during the northern winter. Quart. J. Roy. Meteor. Soc., 130, 1991–2011, doi:10.1256/qj.02.123.
Moore, R. W., O. Martius, and T. Spengler, 2010: The modulation of the subtropical and extratropical atmosphere in the Pacific basin in response to the Madden–Julian oscillation. Mon. Wea. Rev., 138, 2761–2779, doi:10.1175/2010MWR3194.1.
Mori, M., and M. Watanabe, 2008: The growth and triggering mechaisms of the PNA: A MJO-PNA coherence. J. Meteor. Soc. Japan, 86, 213–236, doi:10.2151/jmsj.86.213.
Pohl, B., and A. J. Matthews, 2007: Observed changes in the lifetime and amplitude of the Madden–Julian oscillation associated with interannual ENSO sea surface temperature anomalies. J. Climate, 20, 2659–2674, doi:10.1175/JCLI4230.1.
Ray, P., and C. Zhang, 2010: A case study of the mechanics of extratropical influence on the initiation of the Madden–Julian oscillation. J. Atmos. Sci., 67, 515–528, doi:10.1175/2009JAS3059.1.
Roundy, P. E., 2014: Some aspects of Western Hemisphere circulation and the Madden–Julian oscillation. J. Atmos. Sci., 71, 2027–2039, doi:10.1175/JAS-D-13-0210.1.
Roundy, P. E., C. J. Schreck, and M. A. Janiga, 2009: Contribution of convectively coupled equatorial Rossby waves and Kelvin waves to the real-time multivariate MJO indices. Mon. Wea. Rev., 137, 469–478, doi:10.1175/2008MWR2595.1.
Roundy, P. E., K. MacRitchie, J. Asuma, and T. Melino, 2010: Modulation of the global atmospheric circulation by combined activity in the Madden–Julian oscillation and the El Niño–Southern Oscillation during boreal winter. J. Climate, 23, 4046–4059.
Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc., 91, 1015–1057, doi:10.1175/2010BAMS3001.1.
Sardeshmukh, P. D., and B. J. Hoskins, 1988: The generation of global rotational flow by steady idealized tropical divergence. J. Atmos. Sci., 45, 1228–1251, doi:10.1175/1520-0469(1988)045<1228:TGOGRF>2.0.CO;2.
Straub, K. H., 2013: MJO initiation in the real-time multivariate MJO index. J. Climate, 26, 1130–1151, doi:10.1175/JCLI-D-12-00074.1.
Straub, K. H., and G. N. Kiladis, 2003: Extratropical forcing of convectively coupled Kelvin waves during austral winter. J. Atmos. Sci., 60, 526–543, doi:10.1175/1520-0469(2003)060<0526:EFOCCK>2.0.CO;2.
Straus, D. M., and R. S. Lindzen, 2000: Planetary-scale baroclinic instability and the MJO. J. Atmos. Sci., 57, 3609–3626, doi:10.1175/1520-0469(2000)057<3609:PSBIAT>2.0.CO;2.
Thompson, D. B., and P. E. Roundy, 2013: The relationship between the Madden–Julian oscillation and U.S. violent tornado outbreaks in the spring. Mon. Wea. Rev., 141, 2087–2095, doi:10.1175/MWR-D-12-00173.1.
Thorncroft, C. D., B. J. Hoskins, and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behavior. Quart. J. Roy. Meteor. Soc., 119, 17–55, doi:10.1002/qj.49711950903.
Tyrrell, G. C., and D. J. Karoly, 1996: Links between tropical convection and variations of the extratropical circulation during TOGA COARE. J. Atmos. Sci., 53, 2735–2748, doi:10.1175/1520-0469(1996)053<2735:LBTCAV>2.0.CO;2.
Weickmann, K. M., S. J. S. Khalsa, and J. Eischeid, 1992: The atmospheric angular-momentum cycle during the tropical Madden–Julian oscillation. Mon. Wea. Rev., 120, 2252–2263, doi:10.1175/1520-0493(1992)120<2252:TAAMCD>2.0.CO;2.
Weickmann, K. M., G. N. Kiladis, and P. D. Sardeshmukh, 1997: The dynamics of intraseasonal atmospheric angular momentum oscillations. J. Atmos. Sci., 54, 1445–1461, doi:10.1175/1520-0469(1997)054<1445:TDOIAA>2.0.CO;2.
Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time multivariate MJO index: Development of an index for monitoring and prediction. Mon. Wea. Rev., 132, 1917–1932, doi:10.1175/1520-0493(2004)132<1917:AARMMI>2.0.CO;2.
Zhang, C., 2005: Madden-Julian Oscillation. Rev. Geophys., 43, RG2003, doi:10.1029/2004RG000158.
Zhang, C., and M. Dong, 2004: Seasonality in the Madden–Julian oscillation. J. Climate, 17, 3169–3180, doi:10.1175/1520-0442(2004)017<3169:SITMO>2.0.CO;2.
Zhao, C., T. Li, and T. Zhou, 2013: Precursor signals and processes associated with MJO initiation over the tropical Indian Ocean. J. Climate, 26, 291–307, doi:10.1175/JCLI-D-12-00113.1.