1. Introduction
Numerous observational studies of the Madden–Julian oscillation (MJO; Zhang 2005) suggest strong coupling between its convection and circulation. However, the phase relationships between the convection and the circulation vary across the geographical regions as the MJO propagates eastward (Rui and Wang 1990; Hendon and Salby 1994; Adames and Wallace 2014). Strong MJO convection is confined within regions of high sea surface temperature (SST) while its circulation signal retains its strength throughout the global tropics (Knutson and Weickmann 1987; Hendon and Salby 1994). Over the warm pool where MJO convection is strong, the tropospheric and stratospheric circulation associated with the convection resembles a response pattern similar to a stationary anomalous heat source shown by Gill (1980): Rossby wave gyres westward and poleward of the convection and Kelvin response pattern east of the convection (Hendon and Salby 1996; Kiladis et al. 2005). It also includes anomalous cyclones in the upper troposphere poleward of the region of suppressed convection that result in part from climatological latent heat release not being achieved. These circulation response patterns are not often observed over the Western Hemisphere (WH) where MJO convection is usually weak, limited in meridional extent, or absent. Furthermore, the upper-tropospheric divergence and lower-tropospheric convergence are in phase with the convection over the warm pool during mature phases of MJO convection, but the divergence and the convergence begin to lead the convection over the central Pacific basins as MJO convection decays (Rui and Wang 1990; Hendon and Salby 1994). These changes in the relationship between MJO convection and circulation are documented in various studies, but these studies have not yet yielded a widely accepted explanation of MJO dynamics.
While some studies suggest that the main growth and decay mechanism of the MJO is the feedback between the moisture and convection (e.g., Sobel and Maloney 2013; Raymond and Fuchs 2009), some studies suggest that the interaction with extratropical circulation and circumnavigating waves are also critical for explaining the complete MJO dynamics (e.g., Ray and Zhang 2010; Haertel et al. 2015). Many studies have analyzed the relevance of the circumnavigating circulation and extratropical circulations to MJO convective initiation (e.g., Lin et al. 2000; Zhao et al. 2013; Ray and Zhang 2010; Kemball-Cook and Weare 2001; Ray and Li 2013; Kerns and Chen 2014; Heartel et al. 2015; Roundy 2014), but these works have not reached a consensus on their relative contribution. The circulation signal that often propagates throughout the global tropics is usually described as a Kelvin wave that is generated in response to deep convective heating in MJO convection when it is over the warm pool (Salby et al. 1994; Hendon and Salby 1996). Some authors argue that this Kelvin wave propagates eastward and generates the next MJO event when it returns to the Indian basin (Matthews 2000; Kikuchi and Takayabu 2003; Seo and Kim 2003; Heartel et al. 2015; Lavender and Matthews 2009). Some studies suggest that the westward-propagating Rossby wave associated with the suppressed envelope of MJO convection also helps adjust the environment for the next initiation of convection through moisture advection (Zhao et al. 2013; Kemball-Cook and Weare 2001; Seo and Kim 2003). The importance of precursor signals in circulation prior to the MJO convection is also suggested by Straub (2013), who found that the convective initiation of the MJO tends to be preceded by the upper-tropospheric anomalous westerly wind over the Indian Ocean that propagates from the WH, suggesting the potential role of the WH circulation on the convective initiation of the MJO. This arrival of the westerly wind over the Indian Ocean is followed by the easterly wind anomaly in the WH upper troposphere. Recently, Roundy (2014, hereafter R14) also found that the convective onset of the MJO over the Indian Ocean occurs concurrently with the upper-tropospheric easterly wind anomalies over the WH, and such convective events tend to become better organized and stronger compared to the ones preceded by westerly wind anomalies. The upper-tropospheric intraseasonal zonal wind often amplifies over the eastern Pacific and Atlantic after it decouples from the convection. If the intraseasonal wind is only a radiated Kelvin wave as a response to a deep convective heating associated with the MJO over the warm pool, another momentum source must exist to amplify the Kelvin wave after decoupling from MJO heat source. R14 suggested that the development of the easterly wind over the tropical WH is associated with an equatorward propagation of a midlatitude wave train and showed that the phase of the midlatitude waves coevolves with the change in sign of the intraseasonal zonal wind over the WH. Ferranti et al. (1990) found that forecast skill of the eastern Pacific tropical nondivergent component of 500-hPa winds improves when the midlatitude circulation is nudged toward analysis, which suggests that the interaction with the midlatitudes is important to the eastern Pacific tropical circulation.
These studies suggest that the development of upper-tropospheric zonal wind over the tropical WH is important for MJO convective initiation over the Indian Ocean. However, some of the explanation for the development of this wind remained qualitative in R14. This study follows R14 by using zonal momentum budget and composite analysis to further examine the dynamical processes that contribute to the changes in the upper-tropospheric zonal wind over the WH leading up to and during convective initiation. Lin et al. (2005) analyzed the development of intraseasonal zonal wind over the warm pool using budget analysis and found that vertical and zonal advection are important damping terms that slow down the zonal acceleration by the pressure gradient force. The present study focuses on the WH where the mechanism is expected to differ from that over the warm pool as a result of differences in background wind and much less intense deep convection. The existence of background upper-tropospheric westerly wind over the eastern Pacific and Atlantic basins makes the region favorable for more frequent midlatitude wave propagation into the tropics (Webster and Holton 1982; Hoskins and Ambrizzi 1993). Equatorward propagation of midlatitude synoptic wave trains and Rossby wave-breaking activity feed back onto MJO time scales by triggering convection or transporting momentum (Matthews and Kiladis 1999; Moore et al. 2010; Kiladis and Weickmann 1992). To examine the role of synoptic-scale and background circulations and their interactions with intraseasonal wind, we apply linear temporal decomposition of the zonal momentum budget. The main questions addressed herein are 1) Why do the upper-troposphere intraseasonal zonal winds amplify when they reach the eastern Pacific and Atlantic basins? and 2) What mechanisms determine the sign of that intraseasonal zonal wind at the time of the convective initiation of the MJO?
2. Data and methodology
Daily interpolated outgoing longwave radiation (OLR) data (Liebmann and Smith 1996), with 2.5° horizontal resolution are used as a proxy for tropical convection. Other meteorological data are obtained from NCEP Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) with daily 2.5° horizontal resolution on 30 isobaric surfaces from 1000 to 30 hPa. The analysis period is during December–February (DJF) from 1979 through 2010.
a. MJO index
This study uses an MJO index that is derived similarly to real-time multivariate MJO (RMM) index of Wheeler and Hendon (2004, hereafter WH04) except using only OLR filtered in time and space for the MJO band of the wavenumber–frequency domain as done by R14. The use of OLR data alone to generate the index eliminates explicit dependence on zonal winds, which tend to dominate the RMM index (Straub 2013). To derive the index, empirical orthogonal function (EOF) analysis is applied to extract two leading modes of convection from the OLR anomalies that are averaged meridionally from 15°N to 15°S and filtered for periods of 20–100 days and wavenumbers 0–10, including eastward propagation only. All data are filtered by transforming the data into Fourier coefficients, then applying the inverse transform while retaining only the coefficients inside the selected bands. Time series of principle components (PCs) are obtained by projecting the two leading EOFs onto the filtered OLR. The PCs are normalized by their standard deviations and shifted to best match the phasing of the WH04 RMM index. The two PC time series are then used to categorize the MJO into eight phases as by WH04. The amplitude of MJO convection is determined by the square root of the sum of the squared PCs. Note that no index for the MJO can include all of its variability while perfectly excluding other signals, but composite events based on this index are not statistically different from composites based on other similarly derived indexes.
Events of MJO convective initiation are identified following R14, including 323 days when the MJO index is in phase 1 and its amplitude is greater than or equal to 0.5 during DJF. The sample includes 64 distinct events. These MJO events are then stratified into two sets based on the sign of the WH zonal wind index (WHZI). The WHZI is derived by averaging 200-hPa intraseasonal zonal wind in the region 2.5°N–2.5°S, 140°–40°W. The intraseasonal time scale herein is defined to be between 20 and 100 days. Hereafter, the MJO phase-1 events with negative WHZI and positive WHZI are referred to as easterly and westerly wind events. Note that the corresponding wind anomaly index of R14 is not filtered for intraseasonal time scales. Despite this difference, similar numbers of the easterly and westerly events are found since the intraseasonal anomaly dominates the total anomaly that occurs over this wide region. Using the WHZI, 70% (45 events) of the phase-1 events are categorized as easterly wind events and 30% (19 events) are categorized as westerly wind events.
b. Zonal momentum budget
The overbar indicates the background state, the asterisk indicates the intraseasonal time scale, and the prime indicates the transient time scale. The background state includes the seasonal cycle and lower-frequency variability such as El Niño–Southern Oscillation (ENSO). The seasonal cycle is defined as an annual cycle with its first three harmonics.
Each term in (3) as well as various other fields is composited based on the list of dates of the easterly and westerly wind events of MJO phase-1 events, with time lags. Day 0 is defined as the center day of each MJO event in phase 1. Positive time lags indicate days following the phase-1 events and negative time lags indicate days preceding the events. The statistical significance of composite anomalies from zero is tested using the Student’s t test with the number of degrees of freedom equal to the number of events. The two-sample Student’s t test is also used to examine whether the means of the easterly and westerly wind events are statistically significantly different from each other (i.e., whether the difference is statistically significantly different from zero). All statistical significance tests herein are tested at the 95% confidence level.
3. Results
This section first examines the subsequent development of MJO convection following the upper-tropospheric intraseasonal easterly and westerly wind events over the WH in section 3a. Then the results of budget analysis are presented in section 3b. Section 3c examines the sources of intraseasonal zonal wind anomalies in the layer between tropopause and lower stratosphere, which contributes a portion of the wind anomalies at 200 hPa in the WH.
a. The evolution of MJO convection in easterly and westerly wind events
Figure 1 shows a longitude–time composite evolution of intraseasonal OLR and 200-hPa zonal wind anomalies about the equator, with the longitudes spanning from 180°W to 180°E. During the easterly wind events (Figs. 1a and 1d), the 200-hPa easterly wind anomaly first appears around day −12 over the central Pacific as a convergent circulation associated with the suppressed convection over the western Pacific basin. The easterly wind then begins to propagate eastward at a faster speed (5–10 m s−1) than the convection and amplifies over the eastern Pacific basin (120°–80°W). Its amplitude then weakens as it passes South America (80°–40°W) but it amplifies again as it reaches the Atlantic Ocean (40°W–10°E) where it seems to couple again with an envelope of enhanced convection. During the westerly wind events (Figs. 1b and 1e), 200-hPa easterly wind anomalies also develop over the eastern Pacific basin, but they peak around day 20, roughly 15 days later than in the easterly wind events. Even though amplification of the easterly wind anomalies over the eastern Pacific basin during the westerly wind events lags the similar signal during the easterly wind events, Indian basin MJO convection between the two sets of events does not show much phase lag (this timing is fixed by the MJO index). However, as shown by R14, the amplitude of MJO convection over the Indian Ocean from days 4 through 10 is significantly greater in the easterly wind events than in the westerly wind events (Fig. 1c), while it is not statistically significantly different prior to those days. This result suggests that the difference in the upper-tropospheric zonal wind over the WH is not the result of a difference in the initial state of the Indian Ocean convection but suggests, instead, that the difference in the sign of the zonal wind influences the subsequent development of the convection.
Longitude–time diagram of composite intraseasonal (a)–(c) OLR anomaly (W m−2) and (d)–(f) 200-hPa intraseasonal zonal wind anomaly (m s−1) averaged over 10°N–10°S for (a),(d) easterly wind events and (b),(e) westerly wind events and (c),(f) their difference. The area where the anomalies are statistically significantly different from zero at the 95% confidence level is outlined with thin black lines.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
Figure 2 shows the plan views of intraseasonal OLR and 200-hPa velocity potential from day −6 through day +6 at a 6-day increment for the easterly and westerly wind events. The hatching indicates that the OLR anomalies are statistically significantly different from zero. Thin blue and red lines indicate the results of the same significance test for the velocity potential. Figure 3 shows intraseasonal 200-hPa geopotential height and wind on the same days as shown in Fig. 2. In Fig. 3, only the wind anomalies that pass the statistical significance test are plotted.
Composite maps of 200-hPa intraseasonal velocity potential (m2 s−1; shading) and intraseasonal OLR anomaly (W m−2). Intraseasonal OLR anomaly is contoured in black with an interval of 5 W m−2, where dashed lines indicate positive and solid lines indicate negative. Thin dark blue and red lines outline the velocity potential anomalies where they are statistically significantly different from zero at the 95% confidence level. The same statistical significance is indicated by hatching for the OLR anomalies. (a),(d),(g) Composites of the easterly events, (b),(e),(h) composites of the westerly wind events, and (c),(f),(i) the difference between the easterly and westerly wind events at time lags from (top) day −6 through (bottom) day 6 incremented every 6 days.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
As in Fig. 2, but for 200-hPa intraseasonal geopotential height (shading) and 200-hPa intraseasonal wind anomalies (m s−1; vectors). The geopotential height anomaly is normalized by the local standard deviation during DJF to highlight the structure over the tropics. The same statistical test as in Fig. 2 is applied and indicated by thin blue and red lines for the geopotential height anomaly. The wind vectors are only plotted where they pass the statistical test.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
On day −6, both sets of the events have an envelope of suppressed convection propagating away from the Indian Ocean and an envelope of enhanced convection propagating into the eastern Pacific basin between 180° and 150°W (Figs. 2a and 2b). However, the convection over the central Pacific basin is significantly more enhanced during the westerly wind events (Fig. 2c). Figure 1c also shows that the central Pacific convection is significantly stronger in the westerly wind events from day −30 through day 0. This intensity difference is reflected in the strength of upper-tropospheric divergence suggested by 200-hPa velocity potential. During the westerly wind events on days −6 and 0, the upper-tropospheric divergence remains over the eastern Pacific basin associated with an ongoing deep convective heat source, which sustains the upper-tropospheric westerly wind anomaly on its east (cf. Figs. 2b,e and Figs. 3b,e). On the other hand, during the easterly wind events, the upper-tropospheric divergence decouples from the central Pacific convection and propagates farther eastward where it later couples with the convection over South America and Africa (Figs. 2a and 2d). This decoupling of upper-tropospheric divergence as the central Pacific convection decays typically occurs during an average MJO life cycle, where the upper-tropospheric divergence propagates across the WH at a faster speed than the convection (Hendon and Salby 1996; Salby and Hendon 1994).
On day 0, by selection, intraseasonal easterly wind occurs over the eastern Pacific region during the easterly wind events while the wind remains westerly during the westerly wind events (Figs. 3c,e). This persistence of the westerly wind over the eastern Pacific basin in the westerly wind events seems to be associated with the central Pacific convection and a pair of troughs about the equator collocated with the equatorial westerly anomalies. The pair of troughs over the eastern Pacific basin develops as the westerly wind amplifies on the equator, while the easterly wind over the same basins during the easterly wind events is associated with a pair of ridges. These structures in both sets of events differ from the horizontal structure of theoretical Kelvin waves, which would have easterly wind together with negative geopotential height anomalies and westerly wind with positive geopotential height anomalies (Matsuno 1966).
On day 0, an envelope of developing convection over the Indian Ocean during the westerly wind events is associated with a much stronger 200-hPa ridge and weaker divergence aloft than the one during the easterly wind events (Figs. 2f and 3f). Six days later, the envelope of enhanced convection over the Indian basin becomes significantly stronger and zonally broader following the easterly wind events (Fig. 2g) than the westerly wind events (Fig. 2h).
These results confirm that MJO convection is more likely to have lower amplitude following the westerly wind events than the easterly wind events. However, a few of the westerly wind events do subsequently develop strong convection in the MJO band over the Indian basin as indicated by the MJO index. The westerly wind events that exceed amplitude 1 of the MJO index at lag +10 days are associated with weak delayed easterly wind over the eastern Pacific basin as observed in Fig. 1e, while the events that do not exceed amplitude 1 do not develop easterly wind at any time lags. Although the sign of the WH upper-tropospheric intraseasonal easterly wind during phase 1 is not a necessary condition for the strength of the following MJO convection, it is clearly more favorable for the development of strong convection than westerly wind, and most events that develop stronger convection ultimately are associated with easterly wind in that region.
b. Low-frequency background state
Section 3a shows that MJO convection persists longer and stronger over the central Pacific basin in the westerly wind events. Enhanced activity of MJO convection over the central Pacific is often observed during El Niño events (Kessler 2001; Vincent et al. 1998). Therefore, this section briefly examines the potential biases in the low-frequency background state between the easterly and westerly wind events. Figure 4 shows cumulative probability distribution of SST averaged over the Niño-3.4 region (5°N–5°S, 170°–120°W) and zonally averaged 50-hPa zonal wind to test possible differences in ENSO and QBO state. Both the SST and 50-hPa zonal wind are filtered for periods longer than 100 days and their seasonal cycles are removed to represent the low-frequency anomaly. No clear differences in SST in the Niño-3.4 region appear in Fig. 4a and other ENSO indices (Niño 1+2, 3, and 4) show no differences as well (not shown). A small tendency for positive low-frequency anomalies of SST is observed in the subtropical central Pacific Ocean poleward of 5°N or 5°S (not shown), so that this signal could also occur during ENSO cold states. This higher SST off the equator does not project onto the conventional ENSO indices but it might contribute to the longer lifetime of MJO convection over the central Pacific Ocean during the westerly wind events.
Cumulative probability distribution of (a) low-frequency SST anomaly over Niño-3.4 region and (b) low-frequency zonal-mean 50-hPa zonal wind anomaly on the dates of easterly (blue) and westerly (red) wind events. The 95% confidence intervals from 10 000 bootstrap resampling tests in each set of events are shown with dashed line in its respective color.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
On the other hand, low-frequency 50-hPa zonal wind in Fig. 4b shows that westerly wind events occur relatively more frequently during westerly phase of the QBO. The same tendency is evident using the zonal wind at 70 hPa but not with the 30-hPa wind. Section 3c discusses the potential influence of the phase of the QBO on the sign of upper-tropospheric intraseasonal zonal wind. Testing to diagnose a potential subseasonal bias in the occurrence of westerly and easterly wind events within DJF showed no statistically significant difference between the two sets of events (not shown).
c. Zonal momentum budget analysis
This section analyzes the zonal momentum budget to understand the development of the easterly and westerly wind over the WH.
1) Area-averaged budget terms over the eastern Pacific basin
The area averages of the terms are first presented to examine their temporal phase relationships with the actual zonal wind time tendency. The region of greatest interest here is the eastern Pacific basin where the intraseasonal zonal wind first amplifies, where the difference between the easterly and westerly wind events is the greatest (Fig. 1). The intraseasonal anomalies of the zonal wind time tendency and dynamical terms on the rhs of (1) are averaged over the region 10°S–5°N, 110°–80°W (Figs. 5a,b). The dots on Fig. 5 indicate that the plotted terms are statistically significantly different from zero. The peak in easterly acceleration occurs at around day −6 in the easterly wind events and day +5 in westerly wind events. The gray dashed line shows the sum of all the plotted dynamical terms. The sum of the dynamical terms replicates the actual tendency well, suggesting that the dynamical terms estimated from the reanalysis data balance realistically. The sum of the pressure gradient force and the Coriolis torque (magenta line) is nearly equal to the pressure gradient force alone owing to the small Coriolis parameter near the equator. In both easterly and westerly wind events, none of the terms dominate the intraseasonal zonal wind tendency. In both cases, easterly wind acceleration peaks when all terms are weakly negative. However, an opposite case does not occur during the days of westerly wind acceleration. Similarly, no single term seems to dominate the difference between the easterly and westerly wind events at all time lags (Fig. 5c). Traditionally, the fast eastward-propagating zonal wind signal over the WH was often simply thought of as a dry Kelvin wave radiated from the deep convective heat source of the MJO over the warm pool (e.g., Hendon and Salby 1996; Salby and Hendon 1994; Milliff and Madden 1996; Sobel and Kim 2012). A theoretical Kelvin wave propagates its zonal momentum eastward through interaction between the pressure gradient force in quadrature with mass divergence (Matsuno 1966). Therefore, if the zonal wind propagates as a pure dry Kelvin wave, the pressure gradient force (magenta line) should dominate the zonal wind tendency (black line). However, the results here indicate that it is not the leading mechanism that drives the intraseasonal zonal wind.
Time-lag plot of intraseasonal zonal wind tendency (black), zonal advection (red), meridional advection (blue), vertical advection (green), the sum of pressure gradient force and the Coriolis torque (magenta), and sum of all the above (dashed gray) averaged over the region 10°S–5°N, 110°–80°W for (a) the easterly wind events, (b) the westerly wind events, and (c) the difference between the easterly and westerly wind events. Dots indicate that the values are statistically significantly different from zero at the 95% confidence level.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
The same analysis is repeated at various longitudes and the sum of all budget terms represents the zonal wind tendency well in different regions as well (not shown). Over Africa and the western Indian Ocean at 200 hPa, the pressure gradient force is generally in phase with the zonal wind tendency during the easterly wind events (not shown), suggesting it is the main driver of the zonal wind and that Kelvin wave dynamics dominate that region. However, this relationship does not occur elsewhere. This result shows that the dynamics that drive upper-tropospheric zonal wind continuously change as it propagates.
To deepen our understanding of what drives the intraseasonal zonal wind over the eastern Pacific area, the linearly decomposed and expanded terms in (3) that include interactions with background and transient winds are examined. Each row of Fig. 6 shows a different subset of the expanded terms on the rhs of (3) and the y axis of each row in Fig. 6 is on different scales to highlight the structure of the plotted terms. Figures 6a and 6b show zonal, meridional, and vertical advection of intraseasonal zonal wind by the background wind (
(a),(b) Time-lag plots of total advection of intraseasonal zonal wind by background wind and its three components averaged over the same region as Fig. 5. (c),(d) Same area-averaged time plots of zonal, meridional, and vertical advection of background zonal wind by intraseasonal wind, intraseasonal zonal pressure gradient force, and sum of the four terms. (e),(f) Same area-averaged time plots of total advection of intraseasonal zonal wind by intraseasonal wind, its zonal advection component, total advection of transient zonal wind by transient wind, and its meridional advection component. (a),(c),(e) The easterly wind events and (b),(d),(f) the westerly wind events. Dots indicate statistical significance as in Fig. 5. The scales on the y axis change in each row to better present the structure of the plotted terms.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
Figures 6c and 6d show the zonal, meridional, and vertical advections of background zonal wind by intraseasonal wind (
The differences in the temporally decomposed dynamical terms shown in Fig. 6 are plotted in Fig. 7, which shows that the difference between the easterly and westerly wind events is not dominated by a single term but rather results from a net balance between multiple terms. The westerly wind events have stronger westerly acceleration around day −10, which leads to the longer persistence of westerly wind anomaly and delayed development of easterly wind anomaly. The term that contributes the most strongly to the difference is 
As in Fig. 6, except showing the difference between the easterly and westerly wind events. Differences between each term shown in (a) Figs. 6a and 6b, (b) Figs. 6c and 6d, and (c) Figs. 6e and 6f.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
2) The spatial patterns of important budget terms
The spatial patterns of intraseasonal zonal wind tendency and some of the terms on the rhs of (3) and in Fig. 6 are shown in Figs. 8 and 9 to examine how these terms are driven. The top rows show the sum of all the terms on the rhs of (3) in shading and the tendency calculated by finite differencing in time of the intraseasonal zonal wind shown in black contours. Even though the horizontal resolution is coarse and the reanalysis data do not have a closed budget, the sum of all the terms captures the general spatial structure of the actual zonal wind tendency. From Figs. 6 and 7, 
Composite maps of different terms for (a),(c),(e),(g) easterly events and (b),(d),(f),(h) westerly events on day −6. (a),(b) Intraseasonal zonal wind time tendency (black contour; 2 × 10−6 m s−2 interval) and estimated time tendency (shading; m s−2). A 1–2–3–2–1 filter is applied to smooth the estimated time tendency. (c),(d) Vertical advection by background wind (shading; m s−2) and 200-hPa background vertical motion (black contours; 8 × 103 Pa s−1 interval). (e),(f) Zonal advection of background zonal wind by intraseasonal wind (shading; m s−2), background zonal wind (black contour; 4 m s−1 interval), and intraseasonal horizontal wind (vectors). The vectors are plotted where the wind anomalies are statistically significantly different from zero at the 95% confidence level. (g),(h) Meridional advection by transients (shading; m s−2). For all line contours, solid lines indicate positive values and dashed lines indicate negative values. The thin lines outline the shaded anomalies where their values are statistically significantly greater (red) or less (blue) than zero at the 95% confidence level.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
As in Fig. 6, except on day 0.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
On day −6 (Fig. 8), the spatial pattern of vertical advection by background wind corresponds well to the pattern of zonal wind tendency in the easterly wind events over the eastern Pacific basin. The background flow descends over the eastern Pacific basin, which advects intraseasonal zonal wind anomalies downward. This background subsidence is shown with black contours in Figs. 8c and 8d and it has also been observed over the eastern Pacific basin as part of the Walker circulation by previous studies (Walker 1923; Webster 1983; Krishnamurti et al. 1973). The maximum amplitude of the vertical advection of easterly wind is about −0.5 m s−1 day−1, and this advection is statistically and physically significant in the region enclosed by a blue contour in Fig. 8c over the eastern Pacific basin where it coincides with the region of strongest net easterly wind acceleration. This result suggests that the intraseasonal zonal wind anomaly appears aloft first and then progresses downward. However, no or weakly positive acceleration is driven by the vertical advection during the westerly wind events (Fig. 8d).
During the westerly wind events at day −6, the zonal advection of background zonal wind by intraseasonal wind is strongly positive over the eastern Pacific basin (Fig. 8f), while the term does not induce any significant acceleration during the easterly wind events (Fig. 8e). Over the eastern Pacific, the background zonal wind switches from westerly to easterly from west to east, resulting in its zonal convergence. The presence of the background zonal wind convergence (
Six days later at day 0 (Fig. 9), in the easterly wind events, the easterly acceleration due to vertical advection strengthens slightly and also begins to accelerate easterly wind over the Atlantic basin. The zonal advection of background zonal wind by intraseasonal wind becomes strongly negative, maintaining and amplifying the easterly wind over the eastern Pacific basin (Fig. 9e). In the westerly wind events, the intraseasonal westerly wind remains over the eastern Pacific basin. Therefore, zonal advection of background zonal wind by intraseasonal wind remains positive (Fig. 9f) but the zonal wind tendency becomes negative as a result of the negative pressure gradient force, zonal advection of intraseasonal zonal wind by background wind, and nonlinear terms (see Fig. 6). The spatial patterns of the terms (shown in Figs. 8 and 9) support that the background subsidence and meridional convergence of transient flux contribute to the development of the intraseasonal zonal wind over the eastern Pacific basin and its difference between the easterly and westerly wind events, and the intraseasonal zonal wind is maintained and amplified by its zonal advection by the background wind in the presence of the background zonal wind convergence.
3) Meridional convergence of transient flux
The most important nonlinear term that contributes to the easterly wind acceleration during the easterly wind events is the meridional convergence of transient flux 
The easterly acceleration by the meridional convergence of transient flux on day −6 (Fig. 8g) results from the meridional flux of transient zonal wind (
Composite maps of 200-hPa transient streamfunction anomaly during days −5 through −7 of (a) the easterly wind events (31 days) and (b) westerly wind events (13 days) when the 200-hPa transient meridional wind averaged over the region 10°–15°N, 150°–145°W minimized (shading; m2 s−1). Statistically significant transient streamfunction anomaly is outlined in red and blue lines for positive and negative values, respectively. Black contour lines show the climatological structure of the streamfunction at the selected region, which is composited based on all days when the meridional wind minimized (contours; 1 × 106 m2 s−1 interval). The thick solid and dashed black lines show estimated climatological ridge and trough axes, respectively, calculated by finding the maximum and minimum points from the climatological streamfunction composite and estimating their slopes.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
This result indicates that the intraseasonal circulation serving as background to the midlatitude waves modifies the structures of the waves, which then feeds back onto the intraseasonal circulation on the equator. Although these nonlinear terms are small relative to other terms, the dynamical explanation of the development of the intraseasonal zonal wind over the eastern Pacific basin is incomplete without them.
d. Sources of the tropopause–lower-stratospheric intraseasonal wind anomaly
The budget analysis in section 3c shows that one of the processes that contributes to the development the intraseasonal zonal wind at 200 hPa is 
Time–pressure diagrams of intraseasonal zonal wind anomaly (m s−1; shading) and its vertical advection by background vertical wind (black contours; solid lines indicate positive values and dashed lines indicate negative values; 1.0 × 10−6 m s−2 interval) averaged over 10°N–10°S, 110°–80°W in (a) easterly wind events and (b) westerly wind events.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
This section further examines the vertical structure of the intraseasonal circulation in the tropics to understand the sources of the intraseasonal zonal wind above 200 hPa by decomposing the intraseasonal circulation fields into eastward-propagating and westward-propagating anomalies. After removing the zonal-mean values, the anomalies are further decomposed into eastward- and westward-propagating components by applying the Fourier transform as described in section 2a. Fourier coefficients with positive wavenumber with intraseasonal time scales are retained to filter for the eastward-propagating component and the coefficients with negative wavenumber are retained for the westward-propagating components.
1) Easterly wind events
Figure 12 shows the zonal-mean vertical profiles and the longitude–pressure cross sections of eastward- and westward-propagating intraseasonal zonal wind and geopotential height anomaly on days −6, −3, and 0 during the easterly wind events. The region of focus in the budget analysis (110°–80°W) is indicated by a gray cross-hatched box for reference. The budget analysis shows that on day −6, the background subsidence begins to advect intraseasonal easterly wind downward toward 200 hPa in the easterly wind events (Figs. 6a, 8c, 11a). On this day, both the eastward- and westward-propagating easterly wind anomaly appears within and above the hatched box, inducing a negative vertical gradient of the intraseasonal zonal wind with height and its negative vertical advection by background subsidence within the box.
Longitude–pressure diagrams of composite intraseasonal zonal wind (shading; m s−1) and intraseasonal geopotential height anomalies (black contours; 2-m interval) that are averaged over 10°N–10°S and decomposed into (a),(d),(g) zonal mean, (b),(e),(h) eastward-propagating components, and (c),(f),(i) westward-propagating components for (a)–(c) day −6, (d)–(f) day−3, and (g)–(i) day 0 of the easterly wind events. (left) Zonal-mean intraseasonal zonal wind anomaly is shown in blue and geopotential height anomaly is shown in black. Gray hatched box indicates the region of focus (110°–80°W) in the budget analysis in section 3c(1).
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
On day −6, the eastward-propagating easterly wind over the central to eastern Pacific basins is associated with a positive geopotential anomaly (Fig. 12b). The relationship between the zonal wind and geopotential height anomalies over those longitudes does not resemble the theoretical Kelvin structure by Matsuno (1966) or the observed structure of convectively coupled Kelvin waves by Wheeler et al. (2000). In contrast, over the Indian and western Pacific basins, positively correlated zonal wind and geopotential height anomalies tilt eastward with height, replicating the theoretical structure of dry Kelvin waves in the stratosphere (Wallace and Kousky 1968) as generated by MJO convection (Kiladis et al. 2001; Zhou and Holton 2002). This upper-tropospheric to lower-stratospheric Kelvin wave propagates downward and eastward as it disperses energy upward and eastward (Holton 2004; Roundy and Janiga 2012). However, the structure of the zonal wind and geopotential height anomalies over the WH differs from theoretical Kelvin waves, suggesting that Kelvin wave energy dispersion is not the initial source of the easterly wind anomaly over the central and eastern Pacific basins. Wu et al. (2001) found that the response pattern of circulation to a heat source in Gill (1980) can vary depending on the strength of damping effects, but none of their theoretical solutions can explain the out-of-phase relationship between the eastward-propagating zonal wind and geopotential height anomaly that is observed over the WH in Fig. 12.
The zonal-mean component (Figs. 12a,d,g) suggests the downward propagation of zonal-mean zonal wind anomaly, which is generally in phase with the geopotential height anomaly. This downward propagation of the zonal-mean momentum has been observed in the intraseasonal atmospheric angular momentum anomaly by Weickmann et al. (1997). The in-phase relationship between the zonal-mean zonal wind and geopotential height anomaly might come from the zonally asymmetric amplitude of a planetary-scale (near wavenumber-1) Kelvin wave, which projects onto the zonal-mean quantities (i.e., stronger amplitude of the wavenumber-1 Kelvin wave over some wide range of longitudes than the other longitudes projects onto the zonal mean). The zonal-mean easterly wind anomaly begins to appear in the upper troposphere on day −3, but the initial development of the easterly wind in the WH around day −6 is associated with eastward- and westward-propagating positive geopotential height anomalies. Thus, the initial development of easterly wind in the region west of South America is not associated with Kelvin waves or zonal-mean atmospheric angular momentum.
The westward-propagating component (Figs. 12c,f,i) over the WH has a slight westward tilt with height, consistent with the theoretical structure of stratospheric n = 1 equatorial Rossby waves (Lindzen and Matsuno 1968). The horizontal structure of the westward-propagating components also supports the conclusion that the westward-propagating easterly wind on the equator is associated with an equatorial Rossby wave (Figs. 13b,d,f). The 100-hPa westward-moving intraseasonal easterly wind signal on the equator near 70°W in Fig. 13b and farther west in Figs. 13d and 13f is clearly associated with anticyclonic circulations associated with ridges (labeled “A”). The zonal and meridional widths of the gyre pattern and its phase speed of 2.5–4 m s−1 are consistent with the theoretical structure (Matsuno 1966) and these scales are also consistent with observational analysis of equatorial Rossby waves by Wheeler et al. (2000). This equatorial Rossby wave initiates over South America around day −15, coinciding with an equatorward propagation of a midlatitude ridge that remains present over the Atlantic in Fig. 13a (labeled “B”).
(a),(c),(e) Composite maps of 100-hPa eastward-propagating intraseasonal geopotential height anomaly (m; shading), OLR (black contours; 3 W m−2 interval; only negative values are plotted), and intraseasonal horizontal wind (vectors) during easterly wind events. (b),(d),(f) As in (a),(c),(e), but for westward-propagating anomalies. The geopotential height is normalized by local DJF standard deviation of total zonally asymmetric anomalies (sum of the eastward- and westward-moving components). The OLR anomalies that are statistically significantly different from zero are shown by hatching. Anomalies are shown on (a),(b) day −12, (c),(d) day −6, and (e),(f) day 0.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
The left column of Fig. 13 shows eastward-propagating components that include eastward and equatorward-propagating midlatitude wave trains. These wave trains evolve on the same time scales as the MJO or they would not appear in the composites. The equatorial easterly wind anomalies in the eastern Pacific basin on days −12 and −6 (Figs. 13a,c) are associated with a pair of subtropical ridges (“C”). These ridges merge with an equatorward-propagating midlatitude ridge in the NH eastern Pacific basin. As suggested in Fig. 12b, this structure associated with the easterly wind is dissimilar to a theoretical Kelvin wave. The same budget analysis as in section 3c applied at 100 hPa suggests that the intraseasonal zonal wind at 100 hPa over the eastern Pacific basin is driven by similar mechanisms as at 200 hPa, and the horizontal pressure gradient force does not significantly contribute to the initial easterly acceleration (not shown). Over the Atlantic basin, the circulation associated with a midlatitude ridge (B) initiates the eastward-propagating easterly wind on the equator as it propagates into the equator around 60°–50°W from day −12 to day −6. Therefore, the easterly wind anomaly around 60°W at the tropopause to lower-stratosphere layer (also in Fig. 12b) initiates in association with an intraseasonal equatorward-propagating midlatitude wave train (B). The equatorward-propagating midlatitude troughs from the NH and SH also trigger convection on their downstream sides over the eastern Pacific and Atlantic basins (Fig. 13a). Intraseasonal convection over tropical South America has previously been observed to occur in association with SH midlatitude wave trains (Liebmann et al. 2004; Mo and Paegle 2001), but our results also suggest that NH waves play prominent roles in the circulation associated with the MJO in the region.
On day 0 (Fig. 13e), pairs of eastward-propagating ridge anomalies (C and B) persist and enhance the equatorial easterly wind anomaly over the eastern Pacific and Atlantic basins, while the equatorial easterly wind between those basins becomes associated with a negative geopotential height anomaly. The eastward-propagating signal in the equatorial WH thus includes both a Kelvin wave and a midlatitude Rossby wave circulation together on day 0, but the earlier development of the easterly wind anomaly in the WH at 100 hPa is associated with subtropical and midlatitude ridges. The equatorial easterly wind also has a relative maximum in its amplitude over the longitudes where it coincides with subtropical ridge anomalies (Figs. 12h and 13e).
Therefore, during the easterly wind events, the initial development of the easterly wind anomaly in the WH above 200 hPa is associated with equatorial Rossby wave ridges and midlatitude and subtropical Rossby wave ridges, while the zonal-mean easterly wind anomaly arrives above 200-hPa later (around day −3) as the easterly wind anomaly maximizes at 200 hPa. The arrival of the equatorial easterly wind associated with the Rossby ridges above 200 hPa provides an additional source of intraseasonal easterly wind that is farther advected downward by the background subsidence.
2) Westerly wind events
In the westerly wind events, equatorial westerly wind and negative geopotential height anomalies persist over the eastern Pacific basin in fields filtered for eastward- and westward-propagating signals (Fig. 14). The plan-view map at 100 hPa shows that the midlatitude wave train over the NH eastern Pacific basin tends to propagate zonally with a smaller equatorward propagation component than in the easterly wind events (Figs. 15a,c,e). A pair of troughs (labeled “D”) over the equatorial eastern Pacific basin propagates from the west with equatorial westerly wind. In the westward-propagating components (Figs. 15b,d,f), the Rossby wave ridges that are associated with the equatorial easterly wind in the easterly wind events are absent in the westerly wind events. Instead, a pair of troughs occurs over the equatorial Atlantic and eastern Pacific basin (labeled “E”). These results suggest that a different midlatitude wave-train pattern contributes to the different development of intraseasonal zonal wind in the lower stratosphere–upper troposphere layer, which leads to the different sign of 200-hPa intraseasonal zonal wind in the easterly and westerly wind events.
As in Fig. 12, but for the westerly wind events.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
As in Fig. 13, but for the westerly wind events.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
The zonal-mean component of the intraseasonal zonal wind also remains westerly during the westerly wind events (Figs. 14a,d,g). A zonal-mean easterly wind anomaly and a negative geopotential height anomaly appear in the lower stratosphere (70–100-hPa layer) from day −6 through day 0, but its amplitude and downward propagation appear weaker. Since the zonal-mean zonal wind and geopotential height anomalies are generally in phase during the westerly wind events, they probably include planetary-scale Kelvin wave that has zonally asymmetric amplitude. Section 3b shows that the westerly wind events tend to occur during the westerly phase of QBO, which reduces or prohibits the upward energy dispersion of Kelvin waves and weakens their amplitudes in the lower stratosphere (Randel and Wu 2005). This reduction of Kelvin wave activity due to the QBO state would lead to less downward propagation of the planetary-scale intraseasonal easterly wind anomalies in the upper troposphere over the WH during the westerly wind events.
Figure 16 shows longitude–time diagrams of 100-hPa total zonally asymmetric zonal wind anomaly and its intraseasonal eastward- and westward-propagating component. The zonal wind anomalies associated with the features labeled in Figs. 13 and 15 are also labeled in Fig. 16 with corresponding letters. The total zonal wind anomalies are shown with shading and they include all time scales. The westward propagation of the easterly wind (labeled A in Fig. 16c) from day −10 through day +10 over 120°–60°W is apparent in the total anomaly, suggesting that the westward-propagating component is not a statistical artifact of filtering a standing oscillation. Consistent with this interpretation, the eastward- and westward-propagating easterly wind anomalies crossing each other around 100°W on day 0 (A and C) have different phase speeds and zonal scales [similar to the interacting eastward- and westward-propagating intraseasonal waves discussed by Roundy and Frank (2004)]. Around day 0 of the westerly wind events, the westerly wind anomalies associated with the westward- and eastward-propagating troughs (E and D) around 110°W are weak, resulting in a weakly positive total wind anomaly over the eastern Pacific basin.
Longitude–time diagrams of 100-hPa total zonal wind anomaly (m s−1; shading) and its intraseasonal component (black contours; 0.5 m s−1 interval) that is propagating (a),(b) eastward and (c),(d) westward averaged from 10°N to 10°S for (a),(c) easterly wind events and (b),(d) westerly wind events.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0293.1
The results in this section show that the differences in the midlatitude and subtropical waves and equatorial Rossby waves contribute to the difference in the sign of the WH intraseasonal zonal anomaly above 200 hPa, and these differences are then extended to lower layers by advection by the background vertical wind.
4. Conclusions
Consistent with the results of R14, our results indicate that MJO convection over the Indian Ocean more frequently develops into stronger and zonally broader envelopes when the WH intraseasonal wind on the equator is easterly during convective initiation. This study uses budget and composite analysis techniques to examine the driving mechanisms of this upper-tropospheric intraseasonal easterly wind over the WH and compares evolution of events that include this easterly wind anomaly with events that are instead associated with westerly wind anomalies at the same stage of initiating MJO convection over the Indian Ocean.
The budget analysis focuses on the eastern Pacific basin where the intraseasonal zonal wind tends to amplify first and the largest difference between the easterly and westerly wind events is observed. The intraseasonal circulation in the WH associated with the MJO is often described as a dry Kelvin wave radiated from MJO convection (e.g., Salby et al. 1994; Hendon and Salby 1996; Haertel et al. 2015). However, the budget analysis shows that the horizontal pressure gradient force, which drives the eastward propagation of zonal wind in a theoretical Kelvin wave, is not the main driving mechanism of the upper-tropospheric zonal wind in the WH (Fig. 5). Instead, multiple processes including the interaction with background and transient time-scale circulation balance to induce the net intraseasonal zonal wind tendency. The main amplification mechanism of the intraseasonal zonal wind over the eastern Pacific basin is advection of the background wind by intraseasonal wind (
Since the background zonal wind is quasi stationary on intraseasonal time scales, the sign and amplitude of 
The first source of the difference between the easterly and westerly wind events is the strength of previous MJO convection over the central Pacific. During the westerly wind events, an envelope of enhanced convection from the previous MJO persists longer and stronger over the central Pacific basin (Figs. 1 and 2). This stronger convection is reflected in the longer persistence of upper-tropospheric divergence centered on the convection and westerly wind anomaly east of the convection. This continued source of westerly wind and the delayed arrival of the easterly wind from the west due to the enhanced convection over the central Pacific basin delay the decay of the westerly wind during the westerly wind events.
The second significant source of difference between the easterly and westerly wind events is the lack of equatorial easterly acceleration by the transient circulation in the westerly wind events (Fig. 7c). In the easterly wind events, easterly acceleration is partially initiated by the meridional convergence of transient flux (
The third source of difference occurs in the layer between the lower stratosphere and the tropopause. During the easterly wind events, easterly intraseasonal zonal wind develops in this layer in association with equatorial Rossby waves and midlatitude and subtropical Rossby wave ridges. The resultant easterly momentum anomalies are then advected downward by background subsidence. The downward propagation associated with the Kelvin wave signal catches up later to induce a more zonally uniform upper-tropospheric easterly wind anomaly. However, during the westerly wind events, both the subtropical and equatorial Rossby waves induce equatorial westerly wind, and the QBO westerly wind weakens the stratospheric Kelvin wave activity.
5. Broader implications to MJO dynamics
One of our key findings is that the intraseasonal zonal wind over the WH cannot be simply explained as a Kelvin wave that is zonally radiated from a deep convective heat source associated with previous MJO convection over the western Pacific warm pool. In further support of the argument that the eastern Pacific circulation signals are inconsistent with pure Kelvin waves, the budget analysis is repeated with the nondivergent and irrotational components of the intraseasonal zonal wind. The results show that 200-hPa intraseasonal zonal wind over the eastern Pacific is mostly nondivergent (not shown). In that region, the nondivergent circulations associated with midlatitude waves and equatorial Rossby waves are important. The presence of the background westerly wind in the WH tropics would allow the midlatitude waves to approach the equator and to directly modulate the tropical circulation (Thompson and Lorenz 2004; Matthews and Kiladis 1999; Kiladis and Weickmann 1992). Although the initial circulation over the WH in the tropics cannot be explained as a pure Kelvin wave, it begins to resemble Kelvin wave structure and dynamics with time as it reaches Africa and the Indian Ocean basin. Further studies are needed to understand what causes this transformation of the structure and dynamics of the circumnavigating circulation as it propagates from the WH into the Eastern Hemisphere.
Our results provide some insights about the observed variability in periodicity and strength of MJO convection. Previous studies have labeled most MJO events as secondary (Matthews 2008; Straub 2013), preceded by circumnavigating signal from previous events. However, we find that the circumnavigating signal is tightly coupled with the midlatitude circulation, which suggests that the roles of the circumnavigating signal and the midlatitude waves on the MJO dynamics cannot be completely separated. The global circulation response to the MJO includes modulation of the extratropical circulation, and our results therefore suggest that one MJO event can affect the evolution of the subsequent event through its circulation response in the extratropics. However, the interaction with the variability in the midlatitudes independent from the MJO could contribute to the event-to-event variability in the periodicity and strength of MJO events. Weare (2010) also found a strong association between the upper-tropospheric intraseasonal zonal winds over the Indian Ocean with the midlatitude circulation over western North America, suggesting the importance of tropical extratropical interaction over the WH to the subsequent MJO event.
Further analysis on the dynamical understanding of how the WH upper-tropospheric zonal wind impacts MJO convection over the Indian Ocean is an ongoing work. Tromeur and Rossow (2010) suggested that an interaction between the large-scale circulation in the lower to middle troposphere and convection induces a positive feedback that amplifies MJO convection. We hypothesize that a similar positive feedback occurs with intraseasonal large-scale upper-tropospheric circulations as well. The large-scale divergence associated with the upper-tropospheric easterly wind approaching the western Indian Ocean would lead to a drop in surface pressure, thereby reinforcing lower-tropospheric convergence. The surface pressure change by the horizontal divergence is estimated by vertically integrating the horizontal divergence on isobaric surfaces (Trenberth 1991), which shows that the upper-tropospheric divergence dominates the lower-tropospheric convergence over the western Indian basin at the initiating stage of MJO convection (not shown). Although the surface pressure tendency budget cannot be closed using reanalysis data (Trenberth et al. 1995; Trenberth 1991), results are sufficiently large to suggest that the divergence in the upper half of the troposphere contributes substantially to the surface pressure drop. Ling et al. (2013) also found that wavenumber-1 surface pressure anomalies that propagate eastward into the Indian Ocean basin distinguish the MJO and nonpropagating intraseasonal convection. Similarly, the upper-tropospheric zonal wind over the WH also has half wavenumber-1 structure, suggesting some dynamical links between the upper-tropospheric circulation and surface pressure anomalies. Given the absence of large-scale convection at the time, the upper-tropospheric divergence ahead of easterly wind might cause the planetary-scale drops in surface pressure anomalies that precede MJO convective initiation. The authors intend to further investigate the dynamical link between the upper-tropospheric circulation in the WH and MJO convection.
Acknowledgments
We acknowledge George Kiladis, Zhaohua Wu, and four anonymous reviewers for their helpful comments. Funding was provided by National Science Foundation Grant 1128779 to Paul Roundy. The NOAA PSD provided OLR and reanalysis data.
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