
In this section, we will review the physical mechanisms relevant to MJO eastward propagation and initiation, with an emphasis on latest development in the recent decade. The most striking feature of MJO is its slow eastward phase propagation along equatorial Indian Ocean and western Pacific after being triggered over the western Indian Ocean (Madden and Julian, 1972; Zhao et al., 2013). The anomalous circulation associated with MJO has a zonal wavenumber1 structure with a Kelvin wave type circulation to the east and a Rossby wave gyre circulation to the west (Hendon and Salby, 1994; Wang and Li, 1994; Li and Zhou, 2009). Vertically it has a firstbaroclinic mode structure in the free atmosphere and a phase lead of moisture and convergence anomalies in the planetary boundary layer (PBL), relative to the MJO convection (Wang and Rui, 1990; Sperber, 2003; Hsu and Li, 2012). Compared to the MJO, the BSISO exhibits a more complicated propagating characteristic with pronounced northward propagation over northern Indian Ocean and South China Sea and northwestward propagation over western North Pacific (e.g., Yasunari, 1979; Lau and Chan, 1986; Wang and Rui, 1990; Hsu and Weng, 2001; Lawrence and Webster, 2002; Jiang et al., 2004; Li and Wang, 2005; Tsou et al., 2005).

Various theories have been proposed to understand MJO eastward phase propagation. Early studies assumed that the oscillation is a Kelvin wave forced by convective heating through a so called wave–CISK mechanism (Lau and Peng, 1987; Chang and Lim, 1988; Wang, 1988a). The major promise of this mechanism is that heating effect can be represented by wave induced moisture convergence so that its net effect is the reduction of atmospheric static stability and thus the slowingdown of atmospheric Kelvin waves in the tropics. The weakness of this mechanism is that it prefers maximum growth in small scale, which is against the observation.
The second theory is the WindInduced Surface Heat Exchange (WISHE) feedback (Emanuel, 1987; Neelin et al., 1987), which assumes a conditionally unstable atmosphere so that surface heat flux anomaly may trigger atmospheric heating to the east of MJO main convection under the equatorial mean easterly. However, in reality, the observed mean flow over the IndoPacific warm pool is dominated by westerly flow. As a result, this mechanism favors a westward rather than an eastward phase propagation (Wang, 1988b; Wang et al., 2017).
The third theory emphasized the role of a PBL frictional effect (Wang, 1988a; Wang and Li, 1994). A PBL convergence anomaly appears to the east of MJO main convection, which causes the column integrated moisture convergence center shifting slightly to the east of the MJO center, results in eastward moving tendency (Li and Wang, 1994; Wang and Li, 1994). But such a heating tendency depends on model convective parameterization. Idealized numerical experiments with an aquaplanet atmospheric GCM show that there is no clear eastward propagation when perturbation moisture asymmetry is removed even though PBL convergence asymmetry is still presented (Hsu et al., 2014).
Recently, two distinctive moisture mode theories were proposed. Both of the theories emphasize the important role of MJOscale moisture anomaly in its eastward propagation. The first moisture mode theory emphasizes the role of zonal asymmetry of perturbation moisture in the atmospheric PBL (Hsu and Li, 2012). The other moisture mode theory stresses the importance of zonal asymmetry of time tendency of column integrated moist static energy (MSE) anomaly, regardless of whether or not the perturbation moisture, particularly in PBL, is zonally asymmetric (Sobel and Maloney, 2012, 2013; Jiang et al., 2015; Adames and Kim, 2016; Wang et al., 2017). In the following, we discuss physical mechanisms behind the two moisture mode theories.
Observational analyses showed that while lowertropospheric moisture anomaly is in phase with MJO convection, PBL moisture anomaly leads the MJO convection (Sperber, 2003; Kiladis et al., 2005; Hsu and Li, 2012). Figure 2 illustrates the composite zonal–vertical distribution of MJOfiltered moisture and its phase relationship with the MJO convection (represented by a negative OLR center). While in the middle troposphere the maximum moisture anomaly is colocated with the MJO convection, in the PBL there is a clear zonal asymmetry in the perturbation moisture field; that is, a positive (negative) center is located to the east (west) of the OLR center. Because of this asymmetry, the maximum moisture content line tilts eastward and downward.
Figure 2. (Upper panel) Zonal–vertical distributions of 0°–10°S averaged MJOfiltered specific humidity (contour, 10^{−4} kg kg^{−1}) and specific humidity tendency (shading, 10^{−10} kg kg^{−1} s^{−1}). (Bottom panel) Zonal distributions of 0°–10°S averaged MJOfiltered OLR (blue dashed line, W m^{−2}), OLR tendency (blue solid line, 10^{−6} W m^{−2} s^{−1}), and columnintegrated specific humidity tendency (red line, 10^{−7} kg m^{−2} s^{−1}) during the active phase of MJO in the eastern Indian Ocean.
To demonstrate how the PBL moisture asymmetry affects the MJO growth and evolution via atmospheric destabilization, the vertical profile of the intraseasonal equivalent potential temperature (θ_{e}′) was examined by Hsu and Li (2012). As shown in the top panel of Fig. 3, a significant increase of lowlevel θ_{e}′ is found, consistent with PBL moistening, to the east of the MJO convection. If defining a convective instability parameter as the difference of θ_{e}′ between the PBL (850–1000 hPa) and the middle troposphere (400–500 hPa), one may find that the atmosphere is more (less) potentially unstable to the east (west) of the MJO convective center (bottom panel of Fig. 3). Therefore, a phase leading of a positive lowlevel moisture anomaly may set up a relatively unstable stratification and generate a favorable environment for potential development of new convection to the east of the MJO convective center.
Figure 3. As in Fig. 2, but for MJOfiltered equivalent potential temperature (θ_{e}′, upper panel) and the convective instability index (bottom panel) defined as the difference of θ_{e}′ between the PBL and the middle troposphere [i.e., 1000–850hPa averaged θ_{e}′ minus 500–400hPa averaged θ_{e}′]. Unit: K. From Hsu and Li (2012).
A moisture budget analysis was conducted to reveal the cause of the PBL moistening in front of MJO convection. The diagnosis result showed that the largest positive contribution is anomalous vertical moisture advection; that is, the advection of the mean moisture (which has a maximum at the surface and decays exponentially with height) by anomalous ascending motion, the latter of which is associated with the PBL convergence. This indicates that the boundary layer convergence and associated ascending motion play an important role in moistening the PBL to the east of deep convection.
Physically, two factors may contribute to the moistening in PBL. The first factor is the boundary layer convergence, and the second factor is the surface evaporation. Hsu and Li (2012) showed that the lowlevel convergence presents an eastward shift to the MJO convection, whereas the surface evaporation tends to decrease to the east of MJO convection. The result indicates that the boundary layer convergence is a major process that causes the observed phase leading of PBL moisture.
The decrease of surface evaporation, along with the increase of downward shortwave radiation, leads to the change in SST (Jones and Weare, 1996; Shinoda et al., 1998; Araligidad and Maloney, 2008). As a result, a warm (cold) sea surface temperature anomaly (SSTA) appears to the east (west) of MJO convection.
How does the warm SSTA contribute to the eastward propagation? According to Lindzen and Nigam (1987), a warm SSTA may induce a boundary layer convergence through the change of the boundary layer temperature and pressure. However, it is not clear to what extent the observed PBL convergence is contributed by the underlying SSTA. Figure 4 is a schematic diagram illustrating key processes that contribute to the phase leading of the boundary layer convergence. Firstly, the midtropospheric heating associated with MJO deep convection induces a baroclinic freeatmosphere response, with a Kelvin (Rossby) wave response to the east (west) of the convective center. The anomalous low pressure at top of the PBL associated with the Kelvin wave response may induce a convergent flow in the boundary layer, while a PBL divergence may occur to the west of the convective center between two Rossby wave gyres. Thus, the first convergencegeneration process is associated with the midtropospheric heating and equatorial wave responses to the heating. The second generation process is associated with the SSTA forcing. As a warm SSTA is generated to the east of the MJO convection, the warm SSTA may drive boundary layer flows through induced hydrostatic effect on sea level pressure (Lindzen and Nigam, 1987). Therefore, the convergence in the atmospheric boundary layer may be connected to the underlying positive SSTA and associated SSTA gradients to the east of the MJO convection.
Figure 4. Schematic diagram of boundary layer convergence induced by freeatmospheric wave dynamic and SSTA. Cloud stands for the MJO convection with heating. Solid (dashed) gyres with H_{K} (L_{K}) and H_{R} (L_{R}) indicate the high (low) pressure anomaly associated with Kelvin and Rossby waves response to convection, respectively. Red and blue shadings denote the positive and negative SSTAs, respectively. Solid green arrows indicate the anomalous ascending motion, dashed green arrows represent the boundary layer convergence, and p_{s} and p_{e} are pressure levels at the bottom and top of the PBL, respectively.
To examine quantitatively the relative roles of the SSTA gradient induced pressure gradient force and the heating induced freeatmospheric wave dynamics in determining the PBL convergence, a boundarylayer momentum budget was diagnosed by Hsu and Li (2012). Following Wang and Li (1993), the PBL momentum equation may be written as
$$ f{{k}} \times {{V}}_{\rm{B}}{'} + E{{V}}_{\rm{B}}{'} =  \nabla \phi _{\rm{e}}{'} + \frac{R}{2}\frac{{\left({{p_{\rm{s}}}  {p_{\rm{e}}}} \right)}}{{p_{\rm{e}}}} \nabla T_{\rm{s}}{'}, $$ (1) where a prime denotes the MJO component, f is the Coriolis parameter, k is the unit vector in the vertical direction, V_{B} denotes the vertically averaged horizontal wind in the boundary layer,
$\nabla $ is the horizontal gradient operator, ϕ_{e} denotes the geopotential at the top of the boundary layer, R is the gas constant of air, p_{s} and p_{e} are pressures at the bottom and top of the PBL respectively, T_{s} is the surface temperature, and E is the friction coefficient (equal to 10^{−5} s^{−1}). The first term in the right hand side of Eq. (1) represents the freeatmospheric wave effect. The second term in the right hand side of Eq. (1) represents the SSTA forcing effect. To test the sensitivity of the result to the boundary layer depth, two different PBL depths, 1000–850 and 1000–700 hPa, are applied.Figure 5 reveals the diagnosis results for the PBL convergence. The free atmospheric wave effect in response to the MJO heating plays a major role in determining the boundary layer convergence. It accounts for 90% and 75% of the total boundary layer convergence in the case of p_{e} = 850 and p_{e} = 700, respectively. The warm SSTA induced by decreased latent heat flux ahead of MJO convection, on the other hand, also plays a role. It contributes about 10%–25% to the observed boundary layer convergence. Since the PBL convergence is a major factor affecting the moisture asymmetry, the result above suggests that both the heating induced equatorial wave response and the underlying SSTA contribute to the eastward propagation of MJO.
Figure 5. (From left to right) Total boundary layer convergence (sum) averaged over 0°–10°S, 130°–150°E, induced by both the freeatmospheric wave dynamic (atm_wave) and SSTA, and relative contributions of wave dynamic and SSTA effect in the case of p_{e} = 850 (filled bars) and p_{e} = 700 hPa (hollow bars). Unit: 10^{−6} s^{−1}. From Hsu and Li (2012).
The second type of the moisture mode theory excludes the aforementioned asymmetric PBL moisture effect but emphasizes the zonal asymmetry of column integrated MSE tendency. To unveil dynamics behind MJO eastward propagation, Wang et al. (2017) conducted an MSE budget for observations and outputs from 27 global models that are separated into good and poor MJO groups based on their 20yr simulation performance. MSE (m) is defined as
$m = {c_p}T + gz + {L_{\rm{v}}}q$ , where T is temperature, z is height, q is specific humidity, c_{p} is the specific heat at constant pressure (1004 J K^{−1} kg^{−1}), g is the gravitational acceleration (9.8 m s^{−2}), and L_{v} is the latent heat of vaporization (2.5 × 10^{6} J kg^{−1}). The columnintegrated MSE budget can be written following Neelin and Held (1987) as$$ \left\langle {{\partial _t}m} \right\rangle =  \left\langle {\omega {\partial _p}m} \right\rangle  \left\langle {{V} \cdot \nabla m} \right\rangle + {Q_{\rm{t}}} + {Q_{\rm{r}}}, $$ (2) where the angle bracket represents a massweighted vertical integral from the surface to 100 hPa, p is pressure,
${V}$ is horizontal wind vector, and$\omega $ is pressure velocity. The lefthandside term represents MSE tendency, the first and second terms on the righthandside represent the vertical and horizontal advection, respectively. Q_{t} represents the sum of surface latent and sensible heat fluxes, and Q_{r} represents the sum of vertically integrated shortwave and longwave heating rates. For the observational diagnosis, Q_{r} is calculated from MERRA (Modern Era Retrospective Analysis for Research and Applications) and the other terms are derived from ERA_I (ECMWF Interim Reanalysis) data.Figure 6 (upper panels) shows lagged time–longitude diagrams of regressed rainfall and column MSE anomalies for the observation as well as good and poor model groups. A marked feature from the observation is that column integrated MSE anomaly is approximately in phase with the rainfall anomaly and they both show clear eastward propagation (Fig. 6a). For the good models (Fig. 6b), a robust eastwardpropagating intraseasonal mode is visible, which has a feature similar to the observation. By contrast, eastward propagation is not seen in the poor model composite (Fig. 6c). The result implies that to the first order of approximation, MJO convective anomaly may be regarded as an MSE envelope, moving eastward.
Figure 6. (Upper panels) Longitude–time evolution of rainfall anomalies (shaded, mm day^{−1}) and columnintegrated Moist Static Energy (MSE) anomalies (contour, J m^{−2}; contour interval is 1 × 10^{6}, with zero line omitted) averaged over 10°S–10°N by lag regression against 20–100day bandpassfiltered anomalous rainfall averaged over the equatorial eastern Indian Ocean (5°S–5°N, 75°–85°E). (Lower panels) Regressed day 0 columnintegrated MSE tendency anomaly (shaded, W m^{−2}) overlaid by MSE anomaly itself (contour, J m^{−2}; contour interval is 2 × 10^{6}, with zero line omitted). (a, d) are calculated from GPCP observation and ERA_I reanalysis, (b, e) are the good MJO model composite, and (c, f) are the poor MJO model composite. The rectangle in (d) marks the projection domain (10°S–10°N, 40°–160°E). From Wang et al. (2017).
To examine what causes the eastward movement of the column integrated MSE anomaly, one may examine the horizontal pattern of the MSE tendency at a given time. The horizontal patterns of the MSE tendency anomaly (shaded) overlaid by the MSE anomaly (contour) at day 0 are shown in lower panels of Fig. 6. Both the observation and the good model composite show a positive tendency anomaly to the east of maximum MSE anomaly center and a negative tendency anomaly to the west. Such zonal asymmetry of the MSE tendency favors the eastward propagation of the MSE maximum. The poor model composite, however, does not have a clear zonal asymmetry in the MSE tendency distribution. In these poor models, a positive tendency anomaly is observed flanking both sides of the MSE maximum, and the tendency to the west is even slightly stronger than that to the east, possibly explaining the hint of slight westward propagation shown in Fig. 6c.
Since the MJO tendency is controlled by four terms in the right hand side of Eq. (2), a natural question is what causes the observed asymmetry of the MSE tendency. Wang et al. (2017) projected each of the terms onto the observed MSE tendency field over the domain of 10°S–10°N, 40°–160°E shown in Fig. 6d. If a tendency term has a similar asymmetric pattern as in Fig. 6d, the projection coefficient should be a positive value. If a tendency term is exactly the same as that shown in Fig. 6d, the projection coefficient should be equal to 1. Thus, the projection coefficient can be used to measure whether or not and to what extent a term may contribute to the eastward propagation. Through this projection analysis, one may diagnose the fractional contribution of each budget term to the observed asymmetric MSE tendency.
Figure 7 shows the projection coefficients from the ERAI reanalysis and from the good and poor model group composites as well as their difference. Based on the observational diagnosis, one may see clearly that both horizontal and vertical MSE advection terms contribute to MJO eastward propagation, while the surface heat flux and column integrated atmospheric radiation terms contribute to westward propagation. A net effect of these terms causes a slow eastward phase speed (Li and Hu, 2019).
Figure 7. Projection of regressed columnintegrated MSE budget terms against the observed MSE tendency anomaly at day 0 over 10°S–10°N, 40°–160°E. Bars from left to right represent MSE tendency, vertical advection (W_{adv}), horizontal advection (H_{adv}), turbulent heat fluxes (Q_{t}), radiation heating rate (Q_{r}) and sum of budget terms (Sum). (a) is calculated from ERAI reanalysis, and (b) and (c) are the good and the poor model composite, respectively. (d) is the difference between the good and poor composite results (good minus poor). From Wang et al. (2017).
In the good model composite, the vertical and horizontal advections show positive coefficients with comparable magnitudes with the observation. Q_{t} and Q_{r} show negative coefficients, indicating that they hinder the eastward propagation. These results are in good agreement with the observations (Fig. 7a). By contrast, the poor model group presents negative projections for the vertical advection (blue bar, Fig. 7c) and much weaker projection for the horizontal advection (pink bar, Fig. 7c), compared to the good model group. The nearzero projection of MSE tendency (black bar, Fig. 7c) in the poor model composite is thus primarily a consequence of both the reversed sign of vertical advection and the weaker horizontal advection projection. Figure 7d shows the difference of MSE budget terms between the good and the poor model composites. As one can see, the difference is primarily attributed to the vertical MSE advection, followed by the horizontal MSE advection.
How do the vertical and horizontal advection terms contribute to MJO eastward propagation? Figure 8 is a schematic diagram illustrating how this mechanism works (see Wang et al., 2017 for detailed description). To the east of the MJO convection, downward anomaly appears in the upper troposphere and upward anomaly appears in the lower troposphere; to the west, upward anomaly in association with stratiform cloud appears in the upper troposphere while downward anomaly appears in the lower troposphere. Given that the mean MSE profile minimizes in the middle troposphere, such a distribution of secondbaroclinic mode vertical velocity anomalies would induce a positive (negative) columnintegrated MSE advection to the east (west), promoting the eastward propagation of MJO. Wang et al. (2017) demonstrated that the existence of stratiform cloud in the rear of the MJO convection is critical in generating zonally asymmetric vertical motion distribution in the upper troposphere.
Figure 8. Schematic diagram illustrating the role of anomalous vertical MSE advection in generating a zonal asymmetric MSE tendency. The tall cloud describes gross feature of an MJO, which has a largescale deep convection over its center and a stratiform cloudlike structure in the rear in the upper troposphere. The small clouds to the east of MJO convection indicate the shallow convection. The green curves denote climatological mean MSE profiles. The orange arrows denote the second baroclinic mode vertical velocity anomalies.
While the vertical MSE advection is primarily attributed to upper tropospheric process, the horizontal advection is mainly determined by meridional MSE advection in the lower troposphere (Wang et al., 2017). Figure 9 shows a schematic diagram of this mechanism. In response to MJO heating, lower tropospheric easterly anomalies associated with Kelvin wave response are generated. Decent anomalies appear to the east in association with this Kelvin wave response, which induces a negative heating anomaly in situ. The negative heating further induces an anticyclonic Rossby gyre with poleward flows in the lower troposphere. The poleward flows cause a positive MSE advection because maximum mean MSE appears near the equator. Thus, a positive MSE tendency appears to the east of MJO convection. Meanwhile, lowlevel cyclonic flows to the west associated with Rossby wave response advect low MSE air equatorward, leading to a negative MSE tendency. The processes above lead to the east–west asymmetry of the column integrated MSE tendency, promoting eastward propagation (Kim et al., 2014).
Figure 9. Schematic representation of key processes through which the zonal asymmetry of anomalous horizontal MSE advection is generated. The shaded and contour denote the horizontal distribution of boreal winter mean humidity and MSE averaged over 600–800 hPa. The green arrows denote the key anomalous flows in the lower troposphere that induce positive (negative) MSE advection to the east (west). The red arrow at 80°E denotes ascending motion or positive heating associated with MJO deep convection while the orange arrow over the western Pacific Ocean denotes descending motion or negative heating in association with Kelvin wave response.

Observational analyses (e.g., Zhao et al., 2013) showed that MJO convection is often initiated over the western equatorial Indian Ocean (WIO). A longterm hypothesis is that MJO initiation arises from the circumnavigation of a preceding MJO event that travels around the global tropics (e.g., Lau and Peng, 1987; Wang and Li, 1994; Matthews, 2000, 2008; Seo and Kim, 2003). The promise behind the circumnavigating hypothesis is that the eastwardpropagating uppertropospheric divergence signal associated with MJO may trigger deep convection over relatively moist and warm Indian Ocean after it passes the African continent. As demonstrated by idealized numerical model experiments (Zhao et al., 2013) and observational analyses (Li et al., 2015), this circumnavigating process is not crucial for MJO initiation.
Based on a 20yr observational data analysis, two major initiation mechanisms were proposed by Zhao et al. (2013). The first one is relevant to successive MJO events, that is, a suppressedphase MJO, after it moves to eastern IO, may trigger a convectivephase MJO, through the lowlevel horizontal moisture advection. Figure 10 presents the horizontal patterns of the mean specific humidity field and the MJO wind perturbation field derived based on a 10day average prior to MJO convective initiation in WIO. As expected, maximum mean specific humidity is located over EIO, where SST is higher compared to WIO. The MJO flow during the initiation period is dominated by anomalous easterlies and two anticyclonic Rossby gyres over the tropical IO. Such a wind anomaly resembles the Gill (1980) pattern and is typically observed when the suppressed MJO convection is located in the EIO. The easterly anomalies advect the high mean moisture westward, leading to the increase of the lowertropospheric moisture over the initiation region (20°S–0°, 50°–70°E).
Figure 10. Vertically (1000–700hPa) integrated intraseasonal wind (vector, m s^{−1}) and the lowfrequency background state specific humidity (shaded, g kg^{−1}), averaged during the initiation period (from day –10 to day 0, with day 0 defined as the time when the areaaveraged OLR anomaly over the WIO initiation region switches its sign from a positive to a negative value). From Zhao et al. (2013).
The second initiation mechanism is through extratropical or midlatitude wave processes, a mechanism possibly applicable to primary MJO events. A case study by Hsu et al. (1990) suggested a possible midlatitude wave source from the Northern Hemisphere (NH). Such a hypothesis, however, was challenged by Zhao et al. (2013), who pointed out, based on their idealized numerical model experiments, that the Southern Hemispheric Rossby wave forcing is more critical. Although the NH wave activity is stronger in boreal winter, it is difficult for wave fluxes to cross the equator, and thus hardly for them to affect MJO initiation, which happens south of the equator.
To obtain the statistically robust signal of the midlatitude impact, Zhao et al. (2013) examined the upper tropospheric (200hPa) geopotential height anomaly pattern and associated wave activity flux during the MJO initiation period using the same 20yr reanalysis data (Fig. 11). Note that the geopotential height anomaly displays a wave train pattern, with high pressure centers located southeast of South America and southeast of Africa, and low pressure centers in between and to the east of Madagascar. There are pronounced eastward wave activity fluxes over midlatitude Southern Hemisphere (SH), indicating that the Rossby wave energy propagates eastward. The eastward wave activity fluxes turn northward and converge onto the tropical IO. The wave flux convergence implies that the wave energy is accumulated over the region. Thus, SH midlatitude Rossby wave perturbations may trigger MJO initiation in the tropical IO through wave energy accumulation process.
Figure 11. The observed 20–90day filtered geopotential height anomaly (contour, m^{2} s^{−2}), Rossby wave activity flux (vector, m^{2} s^{−2}), and wave flux divergence (shaded, 10^{−5} m s^{−2}; only negative values are shaded over the Indian Ocean) at 200 hPa during the initiation period from day –10 to day 0. From Zhao et al. (2013).
The third initiation mechanism is through air–sea interaction process. Li et al. (2008) proposed a delayed air–sea interaction mechanism in which a preceding active phase MJO may trigger an inactive phase MJO through a delayed effect of induced SSTA over the IO. Figure 12 shows the evolution of the 20–90day filtered SST, wind stress, and OLR anomalies during a composite MJO cycle over the IO in northern winter (DJF). The regression is based on 20–90day bandpass filtered zonal wind stress averaged over the domain of 5°–12.5°S, 50°–65°E. All fields shown in Fig. 12 are regressed onto the index. A warm SSTA appears along 10°S in pentad –2, due to a delayed ocean response to a preceding suppressed phase MJO. In pentad –1, westerly wind stress and negative OLR signals associated with an active phase of MJO appear in the tropical IO. This leads to rapid decrease of the initial warm SSTA due to both the increased surface latent heat flux and reduced shortwave radiation associated with the active phase MJO. Because background mean wind is westerly along 10°S, a positive westerly anomaly increases evaporative cooling in the region. This gives rise to the inphase relationship between the anomalous surface shortwave radiation and the latent heat flux, and together they act with the ocean entrainment to strongly cool the SST. As a result, a cold SSTA appears along 10°S in pentad 0. In pentad +1, the cold SSTA is enhanced over the western to central IO along approximately 10°S (see Fig. 12). One pentad later, a positive OLR anomaly appears at about 55°E, collocated with the cold SSTA there. The positive OLR anomaly subsequently expands eastward and grows. It is noteworthy that suppressed convection tends to develop over the location where cold SSTA is already present for 5 to 10 days, as inferred from the sequence of charts from pentad +1 to +3. This phase relationship between the SST and convection implies a delayed air–sea interaction scenario for MJO initiation; that is, on the one hand, an ocean cooling is induced by the wet phase of the MJO through combined cloud radiative forcing and surface evaporation/ocean vertical mixing, and on the other hand, the soinduced WIO cold SSTA in turn initiates a subsequent dry phase of the MJO. Thus, air–sea interactions play an important role in the reinitiation of the MJO over the WIO in boreal winter.
Figure 12. Regressed SST (shading, K), wind stress (arrow), and OLR (solid contours for positive and dashed contours for negative values; starting from ± 5 W m^{−2}, interval: 2.5 W m^{−2}) anomalies for the lag of pentad (a) –2, (b) –1, (c) 0, (d) +1, (e) +2, and (f) +3 for northern winter (DJF) season. Only wind stress and SST (OLR) anomalies that exceed 95% (90%) significance level are shown.
This ocean feedback mechanism was recently confirmed with a longterm integration of a coupled general circulation model (Chang et al., 2019). The ocean feedback process becomes less effective in boreal summer when the mean SST is low in western IO and intraseasonal SST variability in the IO is weaker (Zhang et al., 2019).
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Li, T., J. Ling, and P.C. Hsu, 2020: Madden–Julian Oscillation: Its discovery, dynamics, and impact on East Asia. J. Meteor. Res., 34(1), 20–42, doi: 10.1007/s1335102091533. 
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