The Roles of Westward-Propagating Waves and the QBO in Limiting MJO Propagation

: A recent study categorized the Madden-Julian Oscillation (MJO) during boreal winter season into four types including stand, jump, slow and fast MJO. This study focuses on the stand and jump MJO. Based on whether their convection penetrates the Maritime Continent (MC), stand and jump MJO are seen as non-penetrating (NP) MJO, while the rest two are seen as eastward-penetrating (EP) MJO. Results reveal the relative roles of the westward-propagating wave (WPW), as well as the QBO and ENSO, in limiting MJO propagation. Lack of the pre-moistening over the southern sea surface of the MC stops NP MJO from penetrating the MC. The active convection of the WPWs hinders the descending branch of the NP MJO circulation and therefore leads to the insuﬃcient meridional advective moistening over the southern sea surface of the MC. The independent convection over the Paciﬁc for jump MJO is inﬂuenced by a combined eﬀect of the QBO and ENSO. The tropopause instability induced by MJO is found to signiﬁcantly decouple from its convection over the Paciﬁc in the QBOW winters than in the QBOE winters. For jump MJO, the independent convection over the central Paciﬁc comes from local WPWs whose ampliﬁcation and further development into deep convection are correlated to jump MJO’s decoupled tropopause instability. For stand MJO, however, the seasonal-mean La Nina-like cool SST anomalies weaken the WPW activity over the central Paciﬁc and conﬁne WPWs within the western Paciﬁc. Therefore, the decoupled tropopause instability of stand MJO is out phase of WPWs and fails to induce an independent convection over the central Paciﬁc.

F . 1. Centriods by k-means cluster analysis on OLR Hovmöller diagrams of 104 boreal winter MJO events in 1979MJO events in -2013 the same data and method as in Wang et al. (2019). Hovmöllor diagrams are obtained by averaging the 20-70-day band-pass-filtered daily OLR between 10S and 10N. The reference day (day 0) is defined as when the 20-70-day band-pass-filtered box-mean (75E-95E, 10S-10N) OLR time series reaches its local minimum during each MJO lifespan. The cases with silhouette score lower than 0.06 are ruled out of the corresponding centroids after the cluster analysis. Numbers of MJO cases in four clusters after (before) the ruling out are indicated by the numbers before (after) the slash. Details of the data and methodology can be found in Wang et al. (2019).
Indian Ocean across the MC and into the western Pacific. Kim et al. (2014) suggest that the strongly suppressed convection to the east of MJO active convection is the key for the MJO's eastward propagation. The negative heating anomaly associated with the strongly suppressed phase of outgoing longwave radiation (OLR) would induce a local low-level anticyclonic Rossby gyre, which advects the moisture to the east of MJO convection. This moisture advection promotes the eastward propagation of the MJO. However, Wang et al. (2017) argue that such positive moisture tendency to the east of MJO convection comes from the vertical advection of the mean moisture induced by an anomalous intraseasonal ascending motion instead of the horizontal moisture advection. Such vertical moisture advection is disrupted by a dry Rossby-wave-like signal for nonpropagating MJO.
four types of MJO propagation are found, including stand, jump, slow, and fast MJO (Fig.1). The slow and fast MJO cases propagate eastward continuously from the Indian Ocean into the Pacific with different phase speeds. They are similar to the propagating MJO in Kim et al. (2014) and Wang et al. (2017). The stand and jump MJO are more like nonpropagating MJO with standing convection over the Indian Ocean. Jump cases have an independent convection that initiates and develops over the Pacific while the convection over the Indian Ocean decays. Therefore, the jump MJO propagates in a jumping-like behavior. Wang and Li (2021) investigated the diversity in MJO intensity and phase speed and found that the Sea Surface Temperature anomaly (SSTA) may influence the MJO diversity through tuning the background seasonal-mean moisture as well as the leading boundary layer moistening processes for MJO. Xiang et al. (2021) also investigated MJO diversity in a subseasonal-to-seasonal prediction system and found different QBO phase background as well as different predictability for four MJO types. Chen (2020) demonstrate the four types of MJO found in Wang et al. (2019) can excite significantly different extratropical teleconnections, and thus result in diverse global responses. Different extratropical teleconnections induced by slow and fast MJO are also noted in Yadav and Straus (2017).
Based on the four types of MJO propagation identified in Wang et al. (2019), this paper will attempt to understand the physical processes involved in limiting the propagation of the MJO from the perspective of the moisture mode theory by investigating the relative role of the intraseasonal WPWs in MJO propagation. Also, the potential QBO and ENSO phase preference among these four MJO types as well as their influences will be investigated. This work will also address the debate whether the horizontal or vertical moisture advection is more important for the propagation of the MJO through the MC.

Data
Three datasets are used in this work. The daily averaged OLR data with a resolution of 2.5 × 2.5 from National Centers for Environmental Prediction /National Oceanic and Atmospheric Administration-interpolated OLR dataset (Liebmann and Smith 1996) is used to identify and categorize MJO cases. The daily wind components, temperature, geopotential, and specific humidity on 37 vertical levels (10-1000hPa) from the Era-Interim reanalysis dataset (Dee et al. 2011) provide the insight on MJO horizontal and vertical structure. Also, the monthly Sea Sur-7 Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-21-0691.1.
Unauthenticated | Downloaded 07/29/22 07:32 AM UTC face Temperature (SST) data from the Extended Reconstructed Sea Surface Temperature version 5 (ERSSTv5) dataset (Huang et al. 2017) is used to diagnose the seasonal SST background. The temporal range of the three datasets are the same, covering 1979 to 2013. The original resolution of the Era-Interim dataset is 0.75 × 0.75 . The original resolution of the ERSSTv5 dataset is 1.0 × 1.0 . They are both interpolated onto the same spatial grids as OLR before the analysis.

a. MJO identification and categorization
Methods for MJO identification and categorization in this work follow that in Wang et al. (2019).
They are briefly illustrated here. Details can be found in Wang et al. (2019).
To identify MJO events, the daily OLR anomalies are obtained by subtracting the daily climatology and its first three harmonics. Then, a 20-70-day band-pass Lanczos filtering is applied on OLR anomalies to extract its intraseasonal variations. A MJO event is identified when the box-mean band-pass-filtered OLR time series over the Indian Ocean (10 − 10 , 75 − 95 ) is below its -1 standard deviation for at least 5 successive days. The reference day, or day 0, for each MJO event is defined as the date when the time series reaches its local minimum. 104 MJO events are identified within the boreal winter seasons (November to April) of 1979-2013.
A k-means cluster analysis (Kaufman and Rousseeuw 2009) is applied to 104 Hovmöller diagrams of the intraseasonal OLR anomalies (10 − 10 ) to categorize them into four types. Four clusters are chosen because these MJO events can be optimally fitted into four clusters .
The cluster analysis domain in the Hovmöller diagram covers 30 days from day -10 to day 20 and a zonal range of 60 to 180 after applying a zonal three-point running mean and setting OLR > −5 / 2 to zero on diagrams. To determine how well each MJO event fits into its assigned cluster, a silhouette test (Kaufman and Rousseeuw 2009) is applied to each cluster member of the k-means cluster analysis. The silhouette score for each member ranges from -1 to 1. With a higher silhouette score, the member is more similar to the centroid of its assigned cluster than the other cluster centroids (Kaufman and Rousseeuw 2009). MJO events with silhouette score lower than 0.06 are identified as "outliers" not clearly belonging to any of the four clusters and excluded from the corresponding clusters after the k-means cluster analysis. 90 MJO events remain in the four clusters after removing 14 "outliers" as shown in Fig.1 To address the robustness of the k-means cluster analysis, a series of sensitivity experiments are conducted by changing the defined cluster number for k-means cluster analysis and the threshold for the silhouette test after the analysis, respectively (shown in Appendix). Results show that the cluster number of 4 is the best fit for this method, and the threshold for silhouette test set as 0.06 is reasonable.
The four types of MJO propagation, namely stand, jump, fast, and slow, are also seen in visual inspection of individual MJO events (not shown).

b. QBO and ENSO indices
The monthly global mean of the equatorial (5 − 5 ) zonal wind at 50hPa from Era-Interim reanalysis is used as the QBO index to diagnose the QBO phase. Following Son et al. (2017), the easterly and westerly phase of the QBO are defined when the monthly global mean of the zonal wind is below and above one half of its standard deviation, respectively.
The widely used Nino3.4 index is used to diagnose the ENSO phase, which is computed by averaging the monthly sea surface temperature (SST) anomalies from ERSSTv5 within the centraleastern Pacific (5 − 5 , 170 − 60 ).

c. Composite analysis
Composite analysis is used to diagnose the MJO vertical structure and the seasonal mean background state of the four types of MJO with the reference day defined in Sec.2a. The composite analysis of MJO-related structures is performed using 20-70-day band-pass-filtered variables.
Composite analysis of the seasonal mean background states uses monthly, three-month running mean and seasonal mean (April to November) variables. A Student-t test is conducted to validate these composite results are significantly different from zero. Unauthenticated | Downloaded 07/29/22 07:32 AM UTC convection and circulation highly resemble that of the canonical MJO with a continuous eastward propagation (Zhang 2005(Zhang , 2013Yadav and Straus 2017). At day -10, weak convection can already be seen over the central-western Indian Ocean with leading lower-troposphere easterlies. The organized convection gets amplified from day -10 to day 0. At day 0, the strong MJO convective envelope over the Indian Ocean is accompanied by suppressed convection over the MC. The leading equatorial easterlies and lagging westerlies are well organized. The off-equatorial cyclones in both hemispheres are also evident in the coupled circulation pattern, indicating the well-developed Rossby wave gyres of the MJO. With the help of leading easterlies as well as the off-equatorial meridional winds, EP MJO events penetrate the MC with a southward detouring over the sea surface between the MC and Australia, consistent with previous studies on MJO propagation (e.g., Kim et al. 2017). During their propagation through the MC, the convection over the Indian Ocean turns from an active to a suppressed phase at day 10.

a. Horizontal evolution
For NP MJO events, the convection and circulation evolution are different than that of EP MJO events. At day -5 to day 5, when the MJO convection is over the Eastern Indian Ocean, the suppressed convection over the MC is very weak or even missing (Fig.2). The leading easterlies of NP MJO are disrupted. For stand MJO events, such disruption can be seen over the middle-eastern MC in the southern hemisphere at day 0, and it is coupled with a smaller-scale convective dipole mode over the same region. Also, the lower-troposphere leading easterlies vanish from day 5, over the western Pacific also starts to decay from day 10 and turns to the suppressed phase at day 20.
Although the convective envelope of NP MJO events highly resembles that of EP MJO events at day 0, their disrupted leading easterlies at the lower troposphere over the MC indicate a different coupled circulation than that for EP MJO events. Also, the convective dipole mode over the western Same as in Fig.2, but for the composited vertical sections (10 − 10 ) of specific humidity (shadings) and vertical circulation (vectors) from day -10 to day 10. The wet (dry) anomalies indicating the potential WPWs for stand and jump MJO are marked out by thick green (red) arrow lines, respectively. jump MJO, the new shallow convection over the central Pacific gets amplified from day 0. It is noteworthy that the descending motions to the east of NP MJO convection are still evident at day -5, but they are replaced by shallow ascents at day 0.
The WPWs for NP MJO can be more clearly seen in Fig Fig.1, but for the equatorial (10 −10 ) intraseasonal OLR (lines) and column-integrated (100hPa to surface) specific humidity (shadings). The specific humidity anomalies over the 95% significance level are stippled. are evident as early as from day -10 over the Pacific, separated from the suppressed-convection MJO phase over the Indian Ocean. The WPWs for stand MJO are weaker than that for jump MJO.
Also, the WPWs are mainly over the western Pacific for stand MJO while those for jump MJO occupy the whole central-western Pacific during their propagation.
The lower-tropospheric wind and the column-integrated specific humidity related to the WPWs for NP MJO are shown by Fig.5. These WPW horizontal structures are obtained by applying the westward-filtering on the intraseasonal anomalies. Noted that such filtering may also include the signals from any standing mode. The WPWs for NP MJO have a dipole mode with wet anomalies over the equatorial Pacific and dry anomalies to the west in the southern (northern) hemisphere for stand (jump) MJO at day -5. The westward propagation of the dipole mode is led by lowertropospheric westerlies to the west of wet anomalies, which is the equatorial part of the coupled cyclonic gyres in both hemispheres symmetric about the equator. These westerlies induced by WPWs over the eastern MC disrupt the leading easterlies there for stand and jump MJO (Fig.2).
As the WPWs reach the MC, they propagate to higher latitude as shown by the wet anomalies in 14 Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-21-0691.1.
F . 5. Composited maps for the westward-filtered intraseasonal wind at 850hPa (vectors) and the columnintegrated specific humidity (shadings) over the central-western Pacific from day -5 to day 5 for (a) stand and (b) jump MJO. The specific humidity anomalies over the 95% significance level are stippled, and the wind vectors over the 95% significance level are represented by thick black arrow lines.
the southern hemisphere at day 5 for stand MJO and the dry anomalies over the northeastern MC at day 0 to day 5 for jump MJO, respectively.

c. Moisture budget analysis of MJO propagation
The lower-troposphere pre-moistening to the east of the MJO convection is considered as the key  The WPWs have potential impacts on both the horizontal and vertical moisture advection over the MC. The descending motion induced by the suppressed convection of the WPWs could directly weaken the shallow convection over the MC, and the local vertical moisture advection will be weakened as a result. The ascending motion of the WPWs may weaken the MJO descending motion to the east of the MC, so that the dry Rossby wave over the MC is also weakened. As a result, the horizontal moisture advection over the MC induced by the Rossby wave wind anomalies would be insufficient. Therefore, to address the question how MJO propagation over the MC is influenced by the intraseasonal WPWs, it is essential to investigate how the moisture tendencies vary over the MC among NP and EP MJO and the roles of the horizontal and vertical moisture advection play in that variability. The moisture budget analysis (Yanai et al. 1973) is conducted over the eastern Indian Ocean and the MC to answer these questions. The moisture budget equation is, The left-hand term in Eq.1 is the moisture tendency term. The four terms on the right-hand side of Eq.1 are the zonal advection, meridional advection, column process, and the surface evaporation term, respectively. We combine the vertical advection and precipitation together as the column process term here because the vertical moisture advection naturally has greater amplitude due to the great background vertical moisture gradient. And the vertical moisture advection is largely canceled out by the condensation induced by precipitation within the atmosphere column. The tilde represents the 20-70-day band-pass-filtering and the bracket symbol represents the column integration from the surface to 100hPa.
The moisture tendencies over the MC for NP MJO events are different from that for EP MJO events. Fig.6 shows the composited maps of the intraseasonal OLR and column-integrated moisture three harmonics. Since the temporal resolution of the dataset is daily, the timescale of 2-20 days is retained after the high-pass-filtering. The horizontal advection term is therefore decomposed into nine terms, including − · / , − · / , − ℎ · / , − · / , − · / , − ℎ · / , − · ℎ / , − · ℎ / , and − ℎ · ℎ / . These nine terms are then vertically integrated and band-pass-filtered to extract their intraseasonal variation.
To quantify the contribution of each decomposed term to the leading pre-moistening processes over the southern sea surface of the MC, the box-mean values of these nine terms over that region (20 − 10 , 100 − 140 ) at day 0 are calculated for EP and NP MJO, respectively (Fig.9).
For EP MJO events, the meridional moisture advection responsible for the pre-moistening over the southern sea surface of the MC is mainly contributed by the seasonal mean moisture advection induced by the intraseasonal meridional wind anomalies. For NP MJO events, this term is largely reduced as shown in Fig.9b. It is found that such reduction for NP MJO is due to the missing intraseasonal off-equatorial meridional wind anomalies over that region as displayed in Fig.10.

19
Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-21-0691.1. This indicates that the dry Rossby wave induced by the MJO descending motion to the east of MC is not well developed. This is probably related to the active convection of the WPWs as it disrupts the MJO descending motions starting from day 0 ( Fig.3a and Fig.3b). The lower-tropospheric leading easterlies over the eastern MC for NP MJO are also disrupted as displayed in Fig.10b. This is probably due to the involvement of the lower-tropospheric westerlies induced by WPWs over the same region as shown in Fig.5 F . 10. Climatology of boreal winter column-integrated (from surface to 100hPa) specific humidity (top row) as well as the differences between the background moisture for NP and EP MJO and the climatology (shadings in the bottom row). The composited MJO-scale horizontal wind components at 850hPa (vectors in the bottom two rows) are superposed. The region for box-mean as in Fig.8 and Fig.9 are marked by dashed red rectangles on the map. The climatology state of boreal winter humidity is computed by averaging November to April monthly fields from 1979 to 2013. The background state for each MJO event is obtained by applying the three-month running mean of specific humidity field centered with the calendar month of day 0. In the bottom row, only the MJO-scale horizontal wind components exceeding 95% confidence level are displayed.

e. QBO and ENSO phase preferences
Apart from the intraseasonal WPWs presented above, the MJO propagation over the MC is also influenced by ENSO and QBO phases. Wang et al. (2019) already found that the composited seasonal mean SST anomalies for stand MJO events show a La Nina-like pattern, while that for fast MJO events show an El Niño-like pattern. The QBO's influence on MJO propagation is found to be more dominant than that of ENSO (e.g., Son et al. 2017). Xiang et al. (2021) found that stand MJO shows a QBOW phase background while slow MJO shows a QBOE phase background.
However, it is meaningful to investigate whether different QBO phase preferences still stand in our analysis since we focus on a different and longer time period from 1979 to 2013 which provides more MJO cases for study.
There are indeed certain phase preferences among MJO types as shown by the QBO-ENSO phase diagram for MJO events (Fig.11). NP MJO including stand and jump MJO events show a QBOW preference. Among all the NP MJO events, 19 of them occur during the QBOW phase, while only 6 of them happen during the QBOE phase. Such QBOW phase preference is not seen for EP MJO events, consistent with the conclusions of previous studies that during the QBOW F . 11. Phase diagram of QBO and ENSO for MJO events. X axis refers to the QBO index defined as global mean of equatorial (5 − 5 ) monthly zonal wind. Y axis refers to the ENSO index using monthly Nino3.4 index. Solid lines represent the climatology mean of two indices. Dashed gray lines parallel to X axis represent 1 below and above the climatology mean of monthly Nino3.4. Dashed gray lines parallel to Y axis represent 1/2 standard deviation above and below the climatology mean of monthly QBO index. Each dot represents one MJO event with different colors indicating the corresponding MJO type. Four stars tell the mean values of QBO and ENSO indice for four types of MJO. Also, numbers of MJO events lying in each quadruplet of the phase diagram are labeled, respectively. phase, MJO is less active over the Pacific with more events failing to penetrate the MC (Nishimoto and Yoden 2017;Son et al. 2017;Wang et al. 2019;Zhang and Zhang 2018). For the ENSO phase preference, which is already revealed in Wang et al. (2019), stand MJO shows a La Nina phase preference while fast MJO shows an El Niño phase preference. It is worth noting that the ENSO phase preferences are statistically significant as the composited 3-month running mean of monthly SST anomalies over the central-eastern Pacific exceed the 95% confidence level (shown by Fig.5 in Wang et al. (2019)). However, the composited 3-month running mean of monthly zonal wind at 50hPa fails to pass the 95% confidence level (not shown). This is probably due to both the limited number of cases for NP MJO and the fact that a few NP MJO events happen when the stratospheric zonal wind anomalies at 50hPa are extremely strong easterlies (6 NP MJO in the QBOE phase indicated in Fig.11). Both factors increase the standard deviation for the samples and make the composited background stratospheric zonal wind not significant. Therefore, the possible QBOW phase preference for MJO propagation is not entirely clear. state for slow MJO. This is possibly due to the decadal variability of the MJO-QBO connection since we use different time period for our analysis. We find that there are changes of the MJO case distribution among four types before and after the 1990s. In the 1980s, the case number for EP MJO is more than the twice of that for NP MJO. However, beginning with the 1990s, the case number of NP MJO increases so that it is almost about the same as that for EP MJO (not shown here). The time period of our analysis is not long enough to confirm that the decadal variability is robust. Therefore, possible decadal variation needs further investigation.

f. A combined effect of the QBO and ENSO on MJO propagation
The jump MJO events are also characterized by an independent convection developing over the central Pacific from day 0 (Fig.2b). Both the longitude-height cross section (Fig.2b) and the Hovmöller diagrams of the jump MJO convection (Fig.4b) indicate that the independent convection over the Pacific shows a westward propagation. Does this independent convection for jump MJO events develop from the WPW? Hendon and Abhik (2018) demonstrate that during the QBOW phase, the tropopause instability induced by the MJO is less in phase with its convection over the Pacific. Is it possible that the less-coupled tropopause instability tends to enhance other convective systems over the Pacific during the QBOW phase? Also, the phase diagram of the QBO and ENSO for MJO events (Fig.11) show that besides the QBOW phase preference shared by both stand and jump MJO events, stand MJO events also have a La Nina phase preference which is not seen for jump MJO events. Does this particular La Nina phase preference prevent the development of an independent convection over the Pacific for stand MJO?
The temperature anomalies induced by the MJO convection vary among MJO types. Fig.12 shows the longitude-height section of MJO-induced heating and circulation. For EP MJO, the MJO-induced heating is well confined around the MJO convection with the maximum heating centered in the middle troposphere and a westward-tilted vertical structure in the middle-lower troposphere. In the middle-higher troposphere, MJO-induced heating exhibits an eastward-tilted vertical structure. Such heating is overlain by an anomalous cooling at around 100hPa, which is a result of adiabatic adjustment to maintain hydrostatic balance in response to the diabatic warming of the troposphere induced by enhanced convection (Holloway and Neelin 2007). The anomalous heating below anomalous cooling around the tropopause leads to the tropopause instability (Hendon 23 Accepted for publication in Journal of Climate. DOI 10.1175/JCLI-D-21-0691.1. Noted that the covariances are normalized by the variance of the box-mean 20-70-day-band-pass-filtered OLR timeseries over the Indian Ocean (10 − 10 , 75 − 95 ) from day -25 to day 25 for MJO events in QBOE and QBOW phases, respectively. decoupling is then quantified by the covariance between the OLR and tropopause stability. The covariance is then normalized by the variance of the box-mean intraseasonal band-pass-filtered OLR timeseries over the Indian Ocean (10 − 10 , 75 − 95 ) from day -25 to day 25 for MJO events in QBOE and QBOW phases, respectively. The normalization is applied to remove the influence of the stronger MJO magnitude in QBOE phase than in QBOW phase. As shown by Fig.13c, the normalized covariance between MJO convection and its tropopause instability is very strong over the Indian Ocean in both QBOE and QBOW boreal winters. During QBOE phases, such normalized covariance remains strong over the Pacific Ocean although with slight decreases over the MC, and it gradually decreases with longitude, reaching to zero at the dateline. However, during the QBOW phase, the normalized covariance shows a rapid drop to below zero over the MC and remains weak over the whole Pacific. Such contrast in the normalized covariance over the Pacific between the QBOE and QBOW phases again indicates that the coupling between the MJO tropopause instability and its convection is highly related to and possibly influenced by the QBO phase.
The lack of independent convection over the central Pacific for stand MJO events can be attributed to their La Nina phase preference. As displayed in Fig.14, the WPW activity is largely influenced by the ENSO while the QBO has very slight influence. In the boreal winters with El Ninõ conditions, F . 14. Maps for (a) westward-filtered intraseasonal OLR variance, (b) the composited differences of the westward-filtered intraseasonal OLR variance between QBOE and QBOW phase, and (c) same as in (b)  stand MJO, such amplification of WPW convection over the MC is disrupted and the wet anomalies over the MC vanish after day 10 (Fig.3a). suggests that both the low-level pre-moistening processes and the high-level tropopause instability structure are important for the diversity in MJO propagation.

Summary and Discussions
The moisture budget analysis reveals that the intraseasonal WPWs are able to influence the MJO propagation across the MC mainly through suppressing the meridional moisture advection over the southern sea surface of the MC, which is responsible for the insufficient pre-moistening there. For EP MJO events, the meridional moisture advection over the southern sea surface of the MC is related to local off-equatorial meridional winds which are part of the dry Rossby gyre over the MC induced by the descending motion of the MJO circulation (Kim et al. 2014). For NP events, the active convection of the WPWs weakens this descending motion and the meridional moisture advection is therefore insufficient for them to propagate. While this mechanism is identified in composite analysis, it is also evident in individual events (see supplementary information for details). Note that although the column process term differences between EP and NP MJO are small over the southern sea surface of the MC, they are large over the equatorial MC (Fig.7). For EP MJO, the column process term contributes to the moistening tendencies around the equator (Fig.6b) and helps parts of the EP MJO convection to penetrate MC over the islands (Fig.2). We also found that for jump MJO events, the WPWs induce intraseasonal dry anomalies over the northeastern MC and these dry anomalies are advected by local seasonal-mean northeasterlies into the MC, responsible for the overall drying tendencies over the MC for jump MJO (see supplementary information for details). Some differences in the seasonal-mean moisture background among four MJO types are also found and this is probably related to the background ENSO state as presented in the supplementary information.  Gonzalez and Jiang (2019). It demonstrates the essential role of the pre-moistening for MJO propagation, as supported by four schools of MJO theory (Zhang et al. 2020). This paper links the physical mechanism for the influences of WPWs on horizontal moisture advection to their active convection through hindering the vertical descending motion of MJO circulation, rather than focusing on the role of the intraseasonal dry anomalies of WPWs such as dry precursors in DeMott et al. (2018).
Previous studies have emphasized the tropopause instability as the potential mechanism by which the QBO impacts MJO (Hendon and Abhik 2018). In this study, we confirmed the decoupling of the tropopause instability with MJO convection during the QBOW phase from an event-based view. We also quantified such decoupling by the normalized covariance between the tropopause instability and the MJO OLR (Fig.13). We found that the decoupled tropopause instability for NP MJO will enhance the intraseasonal WPWs over the central Pacific, complicating the local intraseasonal variability. The combined effects of QBO and ENSO were also proposed by Sun et al. (2019). However, they explain such effects solely as a result of changes in the seasonal zonal mean gradients of moisture and vertical velocity in the equatorial region. We identify another mechanism for the combined effects through the changes in the tropopause instability influenced by the QBO as well as the WPW activity influenced by the ENSO-related SST anomalies (Fig.14).
The QBO phase preferences found in this paper are somewhat different from that found in Xiang et al. (2021). This is probably due to the different time periods used (1979-2013 for our study and 2000-2019 in Xiang et al. (2021)). This indicates a possible decadal variation for the MJO-QBO connection. We investigated the case number distribution of these four MJO types as a function of decade and found an apparent change in the ratio of NP to EP MJO case number before and after the 1990s (not shown). During the 1980s, the number of EP MJO is more than twice of that for NP MJO. However, from the 1990s, the EP MJO case number is about the same as that for NP MJO. Due to the limited time period of 35 years in our study, robust conclusions about this decadal variability will require further investigation.
Unauthenticated | Downloaded 07/29/22 07:32 AM UTC A complete understanding of the relationship between the QBO and MJO remains elusive from the results of this study. The tropopause instability occurs at a very high level of the atmosphere.
How such high-level instability amplifies the shallow convection, such as for jump MJO over the central Pacific and for stand MJO around the MC, remains a open question. However, our study suggests that these two processes are highly correlated. The cloud-radiative feedback is another very potential mechanism for the QBO-MJO connection Zhang and Zhang 2018).
We investigated this mechanism through the linear regression coefficients between the net radiative heating rate and precipitation rate over the Indo-Pacific (not shown). But the result does not show much differences among four MJO types. Due to limited sample size available in the reanalysis dataset used, the proposed mechanism for the QBO-MJO connection remains elusive. In particular, there are only 14 jump MJO events and whether the QBOW phase preference is robust for these types of events is not clear. Future work will explore this relationship in model simulations and sensitivity experiments.

Robustness of the k-means Cluster Analysis
The robustness of the k-means cluster analysis is examined in sensitivity experiments by varying the pre-defined number of clusters, as well as the threshold value ( ) of the silhouette score. A higher silhouette score indicates an MJO event is well-matched to its assigned cluster. The goal is to find optimal value such that the number of clusters is robust when varied and the threshold chosen allows the most MJO events to be successfully classified into a cluster. Fig.A1 demonstrates that the MJO cases can be best fit into 4 clusters using the k-means cluster analysis. The number of cases passing the silhouette test is always the highest for 4 clusters with a threshold from 0.05 to 0.07.