Introduction

The Madden-Julian Oscillation (MJO)1,2 is an eastward-propagating, planetary-scale disturbance that dominates tropical intraseasonal variability during the boreal winter3,4. Through tropical–extratropical teleconnections5, different phases and propagation types of the MJO have profound impacts on global rainfall patterns6,7, extreme precipitation occurrence8, tropical cyclone genesis9, monsoon circulations10,11, mid-latitude weather patterns12,13,14, atmospheric rivers15,16, Arctic amplification17, the El Niño-Southern Oscillation18,19, marine food chain20, and waterborne disease21. We will show that a fast-propagating MJO event would be considered perilous as it triggers extreme weather whiplash, such as precipitation whiplash22,23,24,25,26, and shortens the response time for hazard adaptation. Understanding the impending changes in MJO behavior is crucial for improving subseasonal-to-seasonal (S2S) forecasts and for timely decision-making in climate adaptations and agricultural and infrastructure planning27,28.

As a complex system governed by multiple factors, the future response of MJO to anthropogenic greenhouse gas (GHG) warming remains at the forefront of research. While the numerical experiments being performed differ, existing studies concluded that anthropogenic warming could shorten periodicity and zonal wavenumber, yielding a faster eastward propagation of the MJO29,30,31,32,33,34,35,36. However, the physical mechanism responsible for such an acceleration remains controversial33. Some stressed the role of enhanced low-level convergence and vertical moisture gradient east of the MJO in accelerating its propagation30,31,37,38, reasoning that an increased dry static stability would slow down the MJO by reducing vertical motions that would lead to weakened divergent flows39. Yet, theoretical studies predicted that increased dry static stability would instead accelerate the convectively coupled Kelvin wave speed, which is potentially favorable for the MJO’s eastward propagation40,41,42. Warming can invigorate the MJO’s convective center by increasing the water-vapor-holding capacity of the atmosphere following the Clausius-Clapeyron relation43. Meanwhile, it decelerates the moist gravity wave (GW) speed by wave dynamics40,44,45, which could eventually slow down the propagation of the MJO. To date, no study has quantitatively addressed the paradox of the differing roles of dry static stability and specific humidity in the future propagation speed of the MJO. Further, as far as climate resilience is concerned, our understanding of how the future MJO will shape the global distribution of compound dry and wet extremes and impact subseasonal climate predictability remains unclear.

To thoroughly understand the projected changes in the MJO requires a complete realization of its complex propagation behavior. Previous research noticed the existence of propagating and non-propagating MJO events46,47, with the latter failing to propagate through the Maritime Continent48,49. With the help of unsupervised k-means clustering, a recent study unfolded four outstanding MJO archetypes, including the standing, jumping, slow, and fast modes50, opening the door to an advanced understanding of the MJO’s complex propagation. Among the prevailing MJO theories, one school of thought regards the MJO as a dynamic moisture mode driven by both the moisture and dynamic feedbacks42,50,51,52,53,54,55,56,57. In contrast to the moisture-mode theory, which emphasizes the moisture and cloud radiation feedbacks58,59,60, the dynamic-moisture-mode theory takes into account also the wave dynamics and the boundary layer convergence feedback in a trio-interaction framework42,50,55,56,57,61, which were shown to explain the MJO’s westward-tilted, coupled Kelvin-Rossby wave structure by observations62,63,64,65,66,67. Through this framework, the origin of the diversified MJO behavior can be boiled down to two fundamental factors: the Kelvin-Rossby wave coupling strength and its structural asymmetry42,50,55,56,57,61. A tight coupling between the Kelvin wave response and the MJO’s major convection gives rise to a leading boundary layer moisture convergence (BLMC) and, thereby, the propagating modes. The structural asymmetry in the MJO’s coupled Kelvin-Rossby wave packet determines the slow and fast modes. The standing mode springs from a weak wave coupling that prevents a systematic eastward propagation, while the jumping mode is shaped by a strong, westward-propagating equatorial Rossby wave that hinders the MJO’s eastward propagation but initiates subsequent convection over the western Pacific Ocean68,69.

Here, we adopt the concept of MJO diversity to analyze the future changes in the MJO’s diverse propagation modes and their impacts and teleconnections—aspects that were overlooked in conventional climate projection research. This analysis is based on 28 coupled general circulation models (CGCMs) participating in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) under both mitigated (SSP2-4.5) and high-end (SSP5-8.5) shared socioeconomic pathways70. We seek to resolve the longstanding puzzle of the MJO’s future eastward acceleration by proposing a heuristic diagnostic of moist GW. This diagnostic demystifies the contrasting roles of atmospheric moisture and stability in the projected change in the MJO’s behavior in a systematic and quantitative manner. Notably, a recent report reveals a 31–66% increase in global subseasonal precipitation whiplashes since the mid-20th century71. This trend, exemplified by the 2022 severe drought and wildfire in California followed by record-breaking precipitation, suggests that the Earth’s hydroclimate variability has unusually intensified under climate change. Therefore, it is imperative to understand how future MJO diversity will influence the occurrence of global subseasonal precipitation whiplash and the medium-range prediction skills under ongoing global warming, as discussed in the following sections.

Results

Performance of CMIP6 models on historical MJO diversity

We evaluate the performance of 28 CMIP6 models in simulating the four MJO archetypes. To classify the MJO archetypes in the model, we first match the simulated MJO propagation patterns from the historical experiment over 1979–2014 to the most similar benchmark archetype from observation (see Methods). Model performance is then assessed by measuring their distances to all four benchmark propagation patterns combined together (Supplementary Fig. 1a). Here, we identify the 12 best models that realistically reproduced the historical MJO diversity with a normalized root-mean-square-error (RMSE) lower than 0.3 (Supplementary Fig. 1b). Sensitivity tests are performed based on different choices of the threshold when determining good models. The different choices reveal similar results of the future change of MJO diversity (Supplementary Fig. 2). Further, we confirm that the top-performing models based on individual MJO type are among the 12 good models using the original evaluation scheme (which is based on all four MJO types combined), and likewise for the poor models (Supplementary Fig. 3). These demonstrate the aptness of the model evaluation scheme adopted herein.

The multi-model ensemble mean (MME) of the 12 good models (MME12) closely resembles the overall benchmark patterns in terms of the convective intensity, the magnitude and the extent of accompanied subsidence, as well as the phase speed based on different MJO archetypes (Supplementary Fig. 4a–j). Though the model simulations were not perfect, the successful reproduction of the four propagation archetypes supports the effectiveness of the good models in accurately simulating MJO diversity. In contrast, the poor models (those with a normalized RMSE greater than 0.6) evidently fail to reproduce the overall propagation pattern, as well as the jumping and fast-propagating archetypes (Supplementary Fig. 4k–o). A common bias observed in both good and poor models is the over-simulation of standing and jumping cases with fewer propagating cases than observations. This bias is significantly more pronounced in the poor models, suggesting an intrinsic deficiency in their ability to simulate long-propagating MJO events adequately. The sources of model deficiencies in reproducing the MJO propagation diversity could stem from the inadequately simulated equatorial Kelvin-Rossby wave couplet61,72, an overly simulated effect of the Maritime Continent barrier48,49,73, and mean state bias74,75,76. Given the relatively accurate representation of MJO propagation archetypes and event frequencies by the 12 good models, the subsequent analyses are based on their MME.

Increased frequency of intense fast and jumping MJOs

The good models almost unanimously predict a burgeoning trend of more jumping and fast-propagating MJO events in future climates. Over the same 35 boreal winter seasons (November–April), the number of the fast-propagating MJO events is projected to increase significantly by about 40% on average during the far-future period (2064–2099) compared to the historical period (Fig. 1a, b). The stationary and slow-moving events will be slightly fewer or unchanged. Alongside the growth of fast-moving events, jumping MJO will increase by about 23%, with a notable propagation pattern transformation into a more eastward-propagating type. The signal of an increased frequency of fast-propagating and jumping MJO events is expected to emerge as early as 2028 to 2063, contributing to an overall rise in the total number of future MJO events under both mitigated and high-end scenarios. On convection extent, future warmer climates will witness a zonal expansion of the MJO convection (more to the east), which deepens as it travels eastward (Supplementary Fig. 5). On propagation speed, the lead-lag correlation analysis and the event-based composite analysis both show an overall acceleration of the MJO propagation speed by 17–20%. The upward trend of long- and fast-propagating cases indicates that the Maritime Continent barrier48,49,73 will become less insurmountable for the MJO as the climate warms.

Fig. 1: The preferred Madden-Julian Oscillation (MJO) propagation archetypes in future climate scenarios.
Fig. 1: The preferred Madden-Julian Oscillation (MJO) propagation archetypes in future climate scenarios.
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a Boxplots of changes in the number of events for each MJO archetype in the near- (2028–2063) and far-future (2064–2099) under the SSP2-4.5 and SSP5-8.5 scenarios compared to the historical period (1979–2014) based on the 12 good models. b Similar to panel a, but for relative percentage changes (%). Bars of a boxplot from bottom to top refer to the minimum, the lower (25th) quartile, the median, the upper (75th) quartile, and the maximum. Red dots denote the sample means. The yellow downward-pointing triangles indicate that the sample means significantly differ from zero at the 0.1 level (Student’s t test).

Future MJO is poised to induce stronger downpours, with the overall associated rain rate projected to increase significantly by about 38% (Supplementary Fig. 5e). Categorizing the MJO events by their propagation archetypes yields several important insights. Firstly, fast-propagating events produce the most significant rainfall accumulation among all archetypes in both past and future climates due to their long and persistent excursion (Fig. 2). Under the high-emission scenario, a fast-moving MJO event will, on average, produce a tropical mean (10°S–10°N) 20–70-day rainfall accumulation anomaly as high as 1804 mm (Fig. 2k). The greatest increase in rainfall occurs as the fast-moving MJO reaches the western Pacific warm pool (Fig. 2l). Secondly, whilst all types of MJO events are projected to accompany a greater rainfall intensity, the greatest uptick (+419 mm or +45%) in the resultant rainfall accumulation is found in future jumping events (Fig. 2e), followed by fast-propagating events (+329 mm or +22%) (Fig. 2k). Considering the projected increase in their occurrence as the climate warms, the gross hydrological impacts of fast-propagating and jumping MJO events are anticipated to be unprecedentedly severe. Thirdly, the MJO’s future jumping behavior will transform into an eastward propagation. This transformation results from intensified lower-level moistening and condensational heating across the EIO and the equatorial western Pacific (Supplementary Figs. 5f, 6d), promoting deep convection and closing the propagation gap between the two centers of convection (Fig. 2e). This burgeoning jumping pattern, plus the higher traveling speed of fast-propagating events, constitutes the overall eastward acceleration of the MJO.

Fig. 2: Future changes in different archetypes of Madden-Julian Oscillation (MJO) propagation and the associated rainfall.
Fig. 2: Future changes in different archetypes of Madden-Julian Oscillation (MJO) propagation and the associated rainfall.
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Hovmöller diagrams of the mean equatorial (10°S–10°N) 20–70-day rainfall anomaly (shading, units: mm day−1) and the outgoing longwave radiation (OLR) anomaly (contour, interval: 5 W m−1) averaged over all the standing MJO events in the (a) historical (1979–2014) and b far-future (2064–2099) SSP5–8.5 scenarios based on the multi-model ensemble mean of the 12 good models (MME12). c The difference between the two scenarios, with the shading showing the values with the sign agreed by ≥ 66% of the models. Dashed contours denote negative values, while solid ones denote positive values. The bottom right shows the tropical mean total 20–70-day rainfall accumulation associated with the MJO events. d–l Similar to panels a–c, but for d–f, jumping, g–i, slow, j–l, and fast events. The phase speed, with the uncertainty showing inter-model spread (±1 S.D.), is estimated using the regression approach (see Methods).

Role of the altering MJO diversity in global subseasonal precipitation whiplashes

More frequent fast and jumping MJO events are expected to trigger disruptive weather fluctuations worldwide. One important paradigm in this regard is precipitation whiplash22,23,24,25,26, characterized by rapid swings between wet and dry extremes. By identifying the subseasonal precipitation whiplash associated with the MJO (see Methods), we construct a global map showing the difference in precipitation whiplash occurrence between fast/jumping and slow/standing cases, normalized by the frequency of each MJO archetype (Fig. 3). Compared to the historical run, the future high-emission scenario will witness a substantially greater risk of precipitation whiplash occurrence heralded by increasing fast and jumping MJOs under climate change (Fig. 3a, b). The response of the precipitation whiplash occurrence between the historical and future warmer climates is considerably consistent, evidenced by a pattern correlation coefficient of 0.68. Hotspots of increased precipitation whiplash occurrence are expected to take place in central Africa, the Middle East, Central Asia, East Asia (or more specifically, the lower reaches of the Yangtze River basin), the Maritime Continent, equatorial Pacific Ocean, the northern Amazon rainforest, East Coast of the continental United States, coastal Argentina, South Atlantic Ocean, and West Antarctica. These precipitation whiplash hotspots, particularly those on land, can result in various forms of cascading hazards26 that pose unprecedented stress to ecosystem services, existing infrastructure, water and food security, and human safety.

Fig. 3: Future shift in the difference in precipitation whiplash frequency and circulation variability between fast/jumping and slow/standing Madden-Julian Oscillations (MJOs).
Fig. 3: Future shift in the difference in precipitation whiplash frequency and circulation variability between fast/jumping and slow/standing Madden-Julian Oscillations (MJOs).
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a Global map showing the difference in precipitation whiplash frequency (shading; see Methods for definitions) and the 500-hPa streamfunction variability (i.e., standard deviation) (contour, units: 105 m2 s−1) per fast/jumping event compared to that per slow/standing event in the historical simulation (1979–2014) based on the MME12. Stippling denotes that the difference in precipitation whiplash frequency is statistically significant at the 0.05 level across the models (Student’s t test). Solid (dashed) contours indicate positive (negative) values, with levels from −12 to −2 in an interval of 2, −0.5, 0.5, and from 2 to 12 in an interval of 2 (units: 105 m2 s−1). b Similar to panel a, but for the SSP5-8.5 simulation (2064–2099). Global hotspots of the heightened risk of precipitation whiplash are outlined in black. The pattern correlation coefficient of the significant difference in precipitation whiplashes between the historical and future periods is shown in the middle right.

The rise in global subseasonal precipitation whiplash can be explained by the disparate teleconnection patterns across the MJO archetypes14,28. In contrast to the slow and standing ones, fast and jumping cases typically link to stronger poleward-propagating Rossby wave trains77 into the mid-latitudes in both hemispheres, as indicated by the 500-hPa streamfunction variability difference (Fig. 3a). Global warming is expected to amplify such a difference in Rossby wave responses, particularly in the northern hemisphere. The increased subseasonal precipitation whiplashes in extratropical regions, including East Asia, the East Coast of the continental United States, and Central Asia, juxtapose with the enhanced circulation variability (Fig. 3b). Even with a weaker change over the tropics and West Antarctica, the increased 500-hPa streamfunction variability still elucidates the heightened risk of precipitation whiplash there. With the expected rise in fast and jumping events (Fig. 1), the risk of global precipitation whiplash is anticipated to significantly intensify (Supplementary Fig. 7). The findings underscore the collective role of anthropogenic warming and the fast-propagating and jumping MJO teleconnection in amplifying global risks of compound hazards. The widening contrast in global teleconnection of compound hazard risks across the archetypes will likely be missing in conventional MJO analysis that disregards propagation types.

The physical origin of the MJO acceleration under anthropogenic warming

A classic conundrum remains unresolved: Why does the MJO accelerate with anthropogenic GHG warming? Observational and theoretical evidence have demonstrated that a standing MJO convective complex is characterized by a vertical alignment of convection and moist static energy (MSE) without a tilt of ascending motion and MSE (or equivalent potential temperature)61,72,78. In contrast, an eastward propagating MJO complex is characterized by a rearward tilt of ascending motion and MSE led by the BLMC ahead of the MJO convection. The trio-interaction theory57 suggests that the MJO propagation is closely tied to pre-existing BLMC that accumulates MSE, generates convective instability, couples the convective heating and the equatorial Kelvin-Rossby wave packet, and eventually propels the convective core eastward. In the following, we will elucidate the collective role of atmospheric and oceanic forcings in shaping the strength and asymmetry of the Kelvin-Rossby wave couplet, shedding light on the physical origin of the MJO’s future eastward acceleration.

Regarding atmospheric forcings, GHG warming accelerates the moist gravity (or Kelvin) wave speed and deepens the skewness of the Kelvin-Rossby wave packet structure. The good models simulate an iconic Matsuno-Gill response of the atmosphere to the MJO’s diabatic heating, as manifested in an equatorial trough of Kelvin wave response east of the MJO convection and two off-equatorial lows of the Rossby wave response to the west79,80 (Fig. 4a). Of particular interest is a stronger Kelvin wave response with enhanced convectively coupled easterlies during future MJO events (Fig. 4b, c). The MJO is closely coupled with moist, long Rossby and Kelvin waves, forming a wave structure less skewed than the Gill pattern57,80. A shape parameter for this pattern is the Rossby-Kelvin (R-K) ratio42,57,61, which is defined as the ratio of the equatorial (10°S–10°N) Rossby wave westerly averaging over 40° to the west of the MJO convection and the Kelvin wave easterly averaging over 120° east of it.

Fig. 4: Future changes in the Madden-Julian Oscillation (MJO) circulation structure and background mean states.
Fig. 4: Future changes in the Madden-Julian Oscillation (MJO) circulation structure and background mean states.
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Composites of the mass-weighted integral of the 1000–850-hPa 20–70-day moisture convergence (shading, units: mm day−1) and the 850-hPa winds (vectors, units: m s−1) associated with the MJO events in (a) historical (1979–2014) and b SSP5-8.5 (2064–2099) scenarios based on the MME12. c The difference between the two scenarios, with shading and vectors showing the values with the sign agreed by ≥ 66% of the models. The box region west of the MJO centroid (denoted by a blue dot) refers to the region where the Rossby westerlies (RW) are averaged, while the east of it indicates the region where the Kelvin easterlies (KE) are averaged. d–f Similar to panels a–c, but for the background 3-month running mean 1000–500-hPa MSE (units: 108 J m−2). The tropical Indian Ocean (20°S–10°N, 50°–110°E) and western-central Pacific Ocean (20°S–10°N, 110°E–150°W) where the MJO convective activity prevailing are outlined in black, with the value showing the regional mean.

The R-K ratio describes the relative strength of the Rossby and Kelvin wave components in the structure of the MJO. The R-K ratio describes the relative strength of the Rossby and Kelvin wave components in the structure of the MJO. A higher R-K ratio suggests the Rossby wave is more dominant, while a lower ratio indicates a greater contribution from the Kelvin wave. This ratio affects how the MJO moves: the Rossby wave, excited by MJO heating, tends to push the MJO complex westward, whereas the Kelvin wave component drives it eastward. The Kelvin wave component is a low-pressure system located to the east of MJO convection57. A stronger Kelvin wave component enhances boundary layer moisture convergence, which boosts MSE, atmospheric convective instability, and shallow convection east of the MJO convection, thereby promoting its eastward movement.

Under the SSP5-8.5 scenario, the R-K ratio of the MJO is projected to plunge by 0.27, from an average of 1.41 to 1.14 (Fig. 4b, c). This change implies that the MJO’s Kelvin-Rossby wave couplet shows a disproportionately stronger Kelvin wave easterly to the east of the convection, while the Rossby wave westerly to the west will weaken. Such an alternation suggests an enhanced zonal asymmetry in the wave couplet, which is associated with a future accelerated MJO. To illustrate their relationship further, we construct a scatter plot of the MJO phase speed against the R-K ratio simulated by all 28 CMIP6 models. We show an inverse relationship wherein the smaller the R-K ratio (i.e., the stronger the Kelvin wave response), the faster the eastward propagation speed of the MJO will be (Fig. 5a). The Sen’s slope and Mann-Kendall test aptly captures such a relationship, albeit with the existence of outliners. Notably, these outliners, including CanESM5, CMCC-ESM2, MPI-ESM1-2-LR, INM-CM4-8, and INM-CM5-0, are among those that inadequately reproduce MJO propagation and its diverse behavior (Supplementary Fig. 1b).

Fig. 5: Future Madden-Julian Oscillation (MJO) acceleration driven by the stronger effect of warming-induced atmospheric stabilization than moisture destabilization.
Fig. 5: Future Madden-Julian Oscillation (MJO) acceleration driven by the stronger effect of warming-induced atmospheric stabilization than moisture destabilization.
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Scatter plots showing the relationship of the mean MJO propagation speed (\({C}_{{MJO}}\), units: m s−1) against (a) the coupled Rossby-Kelvin (R-K) ratio (unitless) and b the regional mean-state moist gravity wave (GW) speed (\({C}_{1},\) units: m s−1) averaged over 10°S–10°N, 50°–150°E based on 28 CMIP6 models. The regression is estimated using Sen’s slope. The equation and the Kendall rank correlation coefficient are shown on the bottom left. c A bar plot showing the effects of static stability (SS) and moisture destabilization (MD) on the future change of moist GW speed (\(\Delta {C}_{1}\)) (units: m s−1) averaged in 10°S–10°N, 50°–150°E during the SSP5-8.5 (2064–2099) scenario, compared to the historical run (1979–2014). The quantities are computed based on the background 3-month running mean fields (see Methods), with the central month being the month of day 0 of each MJO event. The MME12 mean value and the percentage change with respect to the historical regional mean \({C}_{1}\) (41.35 m s−1) are shown, with the uncertainties representing the inter-model spread from the 25th to 75th percentile of the values output by the 12 good models.

On the other hand, the background moist GW speed is positively correlated with the MJO phase speed, as adequately represented by most CMIP6 models (Fig. 5b). It is important to note that the changes in the moist GW speed and the horizontal structure (R-K ratio) affect MJO propagation speed independently and jointly. The moist GW speed is an intrinsic geophysical parameter determining the propagation speed of large-scale equatorial waves and MJOs. The Kelvin wave propagates with the GW speed, while the long Rossby wave speed is about one-third of the GW speed79. The moist GW speed is collectively determined by the competing effects of dry static stability and moisture destabilization40. A more stratified fluid, namely, a more stabilized atmosphere, in this case, would induce a faster internal GW speed44. On the other hand, a stronger vertical moisture gradient would instead slow it down since the latent heat released as moisture condenses can effectively reduce the static stability felt by the wave45. Quantitatively, the future change in the moist GW speed, \(\Delta {C}_{1},\) can be decomposed into the changes in the dry static stability, \(\Delta {S}_{2}\), and moisture destabilization, \(\Delta \bar{q}\), based on our heuristic diagnostic equation (See Methods for definitions and the derivation):

$$\Delta {C}_{1}=\frac{\delta {p}^{2}}{4{C}_{1}}\left[\left(1-I+A\bar{q}{S}_{2}^{-1}\right)\Delta {S}_{2}-A\Delta \bar{q}\right],$$
(1)

The decomposition suggests that the impact of enhanced dry static stability overtakes that of moisture destabilization, yielding a net increase in the moist GW wave speed that aids in the MJO’s eastward propagation speed in future warming scenarios (Fig. 5c). The high-emission run sees the strongest effect of enhanced dry static stability offsetting the moisture effect by contributing to 8.39 m s−1 (+20.3%) in moist GW wave speed, while moisture destabilization acts to reduce it by 6.26 m s−1 (−15.1%) compared to the historical value of the moist GW speed (41.35 m s−1) (Supplementary Fig. 8). The above decomposition is robust, evidenced by a narrow inter-model spread and a negligible residue. A similar result is obtained for the projected changes in the moist GW wave budget under the mitigated scenario (Supplementary Fig. 9). Notably, the increase in the background moist GW speed is not uniform (Supplementary Fig. 8). The GW speed will stay almost the same as its historical value in the tropical eastern Pacific Ocean where moisture destabilization becomes strong enough to completely offset the effect of dry static stability due to the El Niño-like warming (Fig. 4f). In contrast, the slower rate of sea surface warming (SST) warming in the Indian Ocean-western Pacific sector produces a weaker enhancement in the moisture destabilization and is thus dominated by the uniform boost in dry static stability by the GHG forcing (Supplementary Fig. 6). This explains the increased background moist GW speed concerning the EIO MJO acceleration.

However, the acceleration of moist GW speed and the increased skewness of the MJO’s Kelvin-Rossby wave couplet cannot account for the MJO acceleration to the fullest. Additional factors must be considered. We notice that the models project more pronounced condensational heating from enhanced precipitation and convection east of future MJO (Supplementary Fig. 10). This asymmetric heating likely results from a more intense BLMC contributed by the accelerated Kelvin wave easterlies (Fig. 4c) and elevated background lower-level specific humidity (Supplementary Fig. 6d). The BLMC favors the development of shallow and congestus clouds east of the MJO’s deep convection, forming asymmetric condensational heating that further amplifies the Kelvin-Rossby wave asymmetry for more fast-propagating MJO cases. Further, the increased MJO-coupled dry anomaly in the central and eastern Pacific Ocean suggests an anomalous MJO-related Walker circulation (Supplementary Fig. 10c), promoting equatorial easterly winds and contributing to the development of the BLMC.

The asymmetric diabatic heating coupled with the MJO likely springs from oceanic forcings—an asymmetric equatorial sea surface temperature (SST) warming. Future high-end scenario projects a rise in tropical mean SST by approximately 2.6 °C in an El Niño-like pattern, with the most intense SST warming expected in the equatorial eastern Pacific (Supplementary Fig. 11a–c). One remarkable phenomenon regarding a fast MJO event is its inclination to occur during El Niño episodes50,81. Therefore, the mean-state El Niño-like warming in future climates is expected to promote fast-propagating MJO. Existing idealized experiments have demonstrated that a faster propagation of the MJO occurs with an increased zonal scale in response to an eastward extended warm pool56. The mean state MSE is an energy source for MJO development that controls the extent of the convectively coupled equatorial waves82,83. We show that the mid-lower tropospheric (1000–500-hPa) MSE is projected to intensify and expand eastward, as most evident in the high-end scenario (Fig. 4d, e). In tandem with the El Niño-like warming, future MSE increase over the maritime continent and the western-central Pacific tends to be higher than in the Indian Ocean (Fig. 4f). We substantiate that this difference is robust by eliminating mean-state differences across the models (Supplementary Fig. 12). The enhanced zonal asymmetry of tropical MSE across the Indo-Pacific basin is expected to stretch the convectively active zone eastward (Supplementary Fig. 5f), enhancing the Kelvin wave response to the east, and deepening the asymmetry of the Kelvin-Rossby couplet (Fig. 4c). These processes, driven by GHG and asymmetric oceanic forcings, collectively clarify the physical origin of the MJO’s eastward acceleration in a future warmer climate, as depicted in the schematic diagrams in Fig. 6.

Fig. 6: Key physical processes associated with the Madden-Julian Oscillation (MJO)’s eastward acceleration.
Fig. 6: Key physical processes associated with the Madden-Julian Oscillation (MJO)’s eastward acceleration.
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Schematic diagrams depicting the three-dimensional structure of the MJO and its dynamics (a), in the past and (b), in future warmer climates. Panel b details the key changes in the physical processes that contribute to the MJO’s eastward acceleration. BLMC stands for boundary-layer moisture convergence.

Discussion

Analyzing climate projections from the 12 top-performing CMIP6 models unravels a notable shift in the MJO propagation diversity under anthropogenic GHG warming. A future increase in MJO events is driven primarily by a significant uptick of 40% in fast-propagating events, followed by a 23% rise in jumping events under the far-future SSP5-8.5 scenario, while stationary and slow-moving events are expected to decrease or remain stable. The shifted diversity suggests a less insurmountable barrier to future MJO events in the Maritime Continent as the climate warms. Overall, future MJO events are projected to propagate 22% faster and generate 38% more precipitation over their lifespan than historical events. The predicted growth in fast and jumping events is expected to trigger a global increase in precipitation whiplashes. As the GHG forcing causes a more statically stable atmosphere with a greater water-vapor-holding capacity, our analysis using a simple two-layer model suggests the dominance of increased dry static stability over moisture destabilization in future warmer climates, resulting in faster moist GW and bolstering the MJO eastward acceleration. Hence, contrary to conventional wisdom, we propose that enhanced dry static stability accelerates rather than decelerates the MJO propagation. Additionally, the pivotal oceanic forcing of the mean-state El Niño-like warming will expand the core region of tropical convective instability to the east, thereby increasing the skewness of the MJO’s Kelvin-Rossby wave structure and resulting in its future eastward acceleration. Some of these projected trends are already evident in the present-day climate, such as the rapidly expanding Indo-Pacific warm pool84,85 and the rising frequency of central Pacific El Niño episodes50,84,86. These observations provide compelling evidence of the anticipated changes in the MJO diversity based on CMIP6 projections.87

What practical insights can we gain from the understanding of the MJO diversity and its impending shift? Firstly, it sheds light on the surging risks of intraseasonal compound hazards. The propagation of MJO heralds alternating pluvial and dry spells10,88. The projected increase in fast and jumping events, alongside their eastward acceleration and heavier precipitation intensity, are expected to reduce the interval between wet and drought conditions, leading to greater weather fluctuations and the emergence of MJO-coupled precipitation whiplash hotspots globally (Fig. 3). These challenges can severely impact the climate resilience of existing infrastructure and should be carefully considered in future agricultural practices, urban planning, multi-hazard early warning systems, and climate mitigation. On exposure and vulnerability, the global population is expected to rise from 8 billion to between 9.4 and 12.7 billion by 2100, with an unprecedented increase in the proportion of elderly individuals reaching 22.4%89,90. The combination of demographic growth and aging foreshadows a greater impact of the emerging subseasonal precipitation whiplashes associated with the far-reaching impacts of the changing MJO diversity.

The good news is that fast-propagating MJO tends to be more predictable than other propagation archetypes. Drawn from a 20-year, ten-ensemble S2S hindcast by the Geophysical Fluid Dynamics Laboratory (GFDL) Seamless System for Prediction and Earth System Research (SPEAR) coupled model, a recent report28 uncovered that fast-propagating MJO events had the highest prediction skill, achieving accuracy up to 38 days in advance. In contrast, slow-moving and jumping events demonstrated a prediction skill of 31 days, while the standing events were the least predictable, with a lead time of only 23 days. Similar results were attained based on another global climate model91. Hence, forecasting the ever-growing, fast-moving MJO events in a warmer climate will promisingly push the current prediction limit closer to the maximum attainable range of 35–45 days shown by modern S2S forecasting systems92. However, future improvement in MJO forecasting hinges ultimately on the capability of S2S prediction models to accurately simulate the MJO diversity and its evolving patterns. Models that can capture the fast and jumping events and their trends will likely extend their prediction range beyond four to five weeks, providing more time for decision-making in hazard preparedness and emergency response to minimize casualties and property damage.

The conceptual framework of MJO diversity has been instrumental in identifying physical processes responsible for propagation-type changes and in uncovering model deficiencies. The good and poor CMIP6 models, chosen based on their reproducibility of the historical MJO diversity (Supplementary Fig. 1b), align well with those selected by lag-regression diagnostic49, wave spectrum93, or sophisticated criteria of moisture-mode properties94. The agreement upon model selection reveals two important insights: On the one hand, accurately simulating the moist processes and coupled equatorial wave structure could be the key to reproduce the various facets of the MJO propagation diversity. On the other hand, evaluating model performance in reproducing the historical MJO diversity can be a simple and straightforward technique for distinguishing good models from poor ones. CMIP6 models tend to simulate more standing and jumping but fewer propagating cases than observations (Supplementary Fig. 4). Even for the good models at higher spatial resolutions, the simulated intraseasonal OLR variability of the propagating events is apparently weaker than observations. These common biases in MJO propagation diversity and variability suggest critical gaps in fundamental model physics, such as improper parameterizations of the coupling between shallow convection and boundary-layer circulation55,72,78 and Kelvin wave response55,56,61,93, as well as a relatively limited understanding of the Maritime Continent’s impact on the MJO propagation49,95. Addressing these grand challenges in numerical simulations can be of utmost importance for advancing the prediction of the growing prevalence of hazard-triggering fast and jumping MJO events in a warmer world.

In this study, the explanation of the physical processes changing MJO propagation was underpinned by the trio-interaction theory. However, several other theories have also been proposed in the literature40,41,54,57,60,96,97,98,99. Among them, four theories specifically address the MJO’s propagation and selection mechanisms for the spatial and temporal scales87: the skeleton theory54, the ‘moisture-mode’ theory60, the gravity-wave theory100, and the trio-interaction theory57. One fundamental feature discovered by Madden and Julian (1972)2—which was not used to verify the theories—is the sea-level low pressure is ahead of eastward propagating MJO convection. Numerous observational studies have shown that the boundary layer convergence associated with the low-pressure anomaly leads the MJO, which shows a salient vertical tilted structure against its propagation in the fields of MSE, specific humidity, and vertical velocity42,64,72,78,101,102. This vertical structure and the characteristic coupled Rossby-Kelvin wave structure are essential for verifying the theories. Among the four theories, only the trio-interaction theory effectively captures the characteristic vertical and horizontal structure by incorporating the boundary layer dynamics and convective interaction with the Kelvin and Rossby waves. The trio-interaction theory unravels an inherent linkage between the MJO circulation structure and its eastward propagation. It suggests that different cumulus parameterization schemes can lead to different R-K ratios and, thus, different propagation speeds. The skeleton theory and moisture-mode theory can be viewed as a special form of the trio-interaction under a generalized theoretical framework that uses different cumulus parameterization schemes42. Various theories may interpret MJO eastward propagation speed differently. For instance, in the “moisture-mode” theory, the eastward propagation of the MJO is mainly maintained by large-scale horizontal and vertical moisture advection58,59,60. This theory would interpret the future rise in fast-moving MJO events as the result of an increased horizontal advection of moisture that causes a positive column- or lower troposphere-integrated moisture (or MSE) tendency to the east34,47,83,103. However, the positive moisture tendency ahead of MJO can arise from both the intensification of the MJO convection and its eastward movement, making it a less clear indicator of propagation speed. It may also overlook the impact of dry static stability in accelerating moist GW waves and the MJO. Future research on aspects such as the extent to which the BL frictional coupled Kelvin‐Rossby feedback is important compared to other processes, such as moisture and cloud-radiative feedback, in both the present and future climates, will facilitate the reconciliation of existing theories and further advance our understanding of future changes in MJO diversity and dynamics.

Methods

Observational datasets and reanalysis

The satellite-based National Oceanic and Atmospheric Administration (NOAA)-interpolated OLR dataset104 is adopted as a benchmark to evaluate CMIP6 model performance in simulating the MJO diversity. The hourly, 1° × 1° pressure-level and surface environmental fields are retrieved from the fifth-generation European Centre for Medium-Range Weather Forecast (ECMWF) reanalysis (ERA5)105 for diagnosis. Leap days are omitted from all observational and reanalysis datasets, as most CMIP6 models use a 365-day calendar. Given its superior advantages over the other filters106, a 20–70-day bandpass Butterworth filter is adopted to extract the intraseasonal anomalies from the daily data for MJO event detection and analysis. A 3-point zonal running mean is applied to all analyses to remove small-scale noises50. The mean state is computed based on the period of interest. The extraction of intraseasonal anomalies is independent of the mean state.

CMIP6 models and experiments

The CMIP6 archive provides state-of-the-art climate projections in response to anthropogenic and natural forcings. Here we examined 28 CMIP6 models (Supplementary Table 1) with complete output of daily outgoing longwave radiation available—the key proxy for identifying the MJO-related disturbances10. Models based on a 360-day calendar were omitted from our analyses. Experiments considered here are historical (with all natural and anthropogenic forcings), a mitigated scenario that produces a radiative forcing at 4.5 W m−2 in 2100 (SSP2-4.5), and a high-emission scenario that produces a radiative forcing at 8.5 W m−2 in 2100 (SSP5-8.5)70.

Detection of MJO events and propagation diversity

Following Wang et al. (2019)50, an MJO event was identified if the regional mean 20–70-day OLR anomaly over the eastern Indian Ocean (EIO; 10°S–10°N, 75°–95°E) was negative and had a magnitude greater than one S.D. for five consecutive days during the boreal cold season (from November through April). The event day 0 was chosen when the averaged OLR anomaly reached the minimum. We then computed the 10°S–10°N averaged lag-longitude diagrams (from day −10 to day 20 and 60°E to 180°) of each event, which were smoothed by a 3-point zonal running mean and with the OLR anomalies greater than −5 W m−2 set to zeros. k-means clustering107 with the correlation distance metric was then applied to the smoothed lag-longitude diagrams to assign events to four clusters. The clustering was iterated for a maximum of 10,000 times to achieve convergence, and the run was repeated 10 million times with random initializations to select the optimal clustering with the minimum total sum of distances. Among the 105 MJO events over the EIO using NOAA-interpolated OLR from 1979 to 2014, we retained 88 that are considerably well-matched to the centroid of their clusters with a Silhouette score greater or equal to 0.06. The composites of the well-match events reconstruct the four MJO propagation archetypes (Supplementary Fig. 4b–e), which serve as benchmarks for matching the MJO propagation patterns from CMIP6 simulations.

Matching CMIP6 MJO events to the four archetypes

The k-means method is an iterative algorithm that seeks to minimize the average square distance between points within the same cluster108. The classification results are therefore entirely subject to the inherent structure and bias of the data fed into the algorithm. For this reason, the four k-means clusters derived from a CMIP6 model simulation would differ from the four MJO archetypes from observational data. To permit a simple, objective, and effective assignment of the CMIP6 MJO events to the four archetypes, we matched them to the most similar archetype based on the highest pattern correlation coefficient (PCC) between its lag-longitude pattern and the four benchmark patterns. After the matching, we evaluate the model performance in simulating the historical MJO diversity by concatenating the composites of the four propagation patterns based on the CMIP6 historical simulations and compared them against the four benchmarks simultaneously (Supplementary Fig. 1a). The 12 top-performing models exhibiting a normalized RMSE less than 0.3 were selected for the main analysis of this study (Supplementary Fig. 1b). The six poor models with a normalized RMSE of greater than 0.6 were selected for comparison and discussion.

Regression-based approach in estimating MJO propagation speed

The MJO propagation speed was measured based on the lag-longitude OLR diagram using the following procedures. Firstly, we identify the largest deep convection with the OLR anomaly less than −3 W m−2 in the diagram. Secondly, we locate the points with minimum OLR anomaly at each longitude of the object. Thirdly, we perform simple linear regression on these points to obtain Sen’s slope, which is resistant to outliers and more robust than an ordinary least-square fit109. The statistical significance of the slope is verified by the non-parametric Mann-Kendall test110,111,112. With appropriate unit conversion, the inverse of the slope coefficient yields the phase speed of the MJO event.

MJO-related precipitation whiplash

Precipitation whiplash refers to a sudden transition between wet and dry extremes22,23,24,25,26. Previous studies defined precipitation whiplash on a year-to-year basis, but none have examined its connection to the MJO on the S2S timescale. Here, we identify a wet-to-dry event when 20–70-day precipitation exceeds the 99th percentile of the historical values (1979–2014), followed by a dry event below the 1st percentile value, and vice versa for a dry-to-wet event. These wet-to-dry and dry-to-wet events collectively constitute precipitation whiplashes. A subseasonal precipitation whiplash event is considered MJO-related if it takes place from day −15 to day 15 of an MJO event.

Moist GW speed diagnosis

The source of contributions to the convectively coupled, moist GW wave speed can be diagnosed and quantified using a simple two-layer model40. Assuming a trivial effect of evaporation on the GW, ignoring Newtonian cooling and the boundary-layer terms and restoring the dimensions, the combined thermodynamic and moisture equation can be simplified as

$$\frac{\partial \phi }{\partial t}+{C}_{0}^{2}\left(1-I\right)\left(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}\right)=0,$$
(2)

where \(\phi\), \(u\), \(v\) denote the baroclinic component of geopotential, zonal wind, and meridional wind; \({C}_{0}\) denotes the dry GW speed, and the dimensionless parameter \(I\) refers to the coefficient of heating contributed by the wave convergence. The moist GW speed \({C}_{1}\) is then measured by

$${C}_{1}^{2}={C}_{0}^{2}\left(1-I\right),$$
(3)

where the dimensionless parameter \(I\) is given by

$$I=\frac{\bar{q}}{\alpha },$$
(4)

where \(\bar{q}\) is the difference between the vertical mean of specific humidity in the lower atmosphere (500–1000 hPa; \({\bar{q}}_{3}\)) and the upper atmosphere (0–500 hPa; \({\bar{q}}_{1}\)), namely,

$$\bar{q}\equiv {\bar{q}}_{3}-{\bar{q}}_{1}.$$
(5)

In a completely dry atmosphere, the GW speed would reduce to \({C}_{0}\). The non-dimensional measure of dry static stability \(\alpha\) writes

$$\alpha=\frac{2{C}_{p}{p}_{2}{C}_{0}^{2}}{{Rb}{L}_{c}{{{\rm{\delta }}}}p},$$
(6)

where \(R\) is the specific gas constant for dry air (287 J kg−1 K−1), \({L}_{c}\) is the latent heat of condensation (2.26 × 106 J kg−1), \(b\) is the fractional conversion coefficient of moisture into rainfall (taken as 0.9), \({{{\rm{\delta }}}}p\) is the half-depth of the atmosphere (500 hPa), \({C}_{p}\) is the specific heat at constant pressure (1004 J kg−1 K−1), and \({p}_{2}\) is the pressure in the middle of the free atmosphere (500 hPa). Our sensitivity test showed that the choice of \(b\) does not affect the result of a stronger effect of dry static stability than moisture destabilization in future GW speed. The dry GW speed of the gravest baroclinic mode can be measured by

$${C}_{0}={\left(\frac{{S}_{2}{{{\rm{\delta }}}}{p}^{2}}{2}\right)}^{1/2},$$
(7)

where \({S}_{2}\) refers to the 500-hPa static stability parameter (units: m2 s−2 Pa−2) estimated by \(\frac{1}{{\theta }_{2}{\rho }_{2}}\frac{{\theta }_{1}-{\theta }_{3}}{{p}_{1}-{p}_{3}}\), with \({\rho }_{2}\) being the basic-state air density at 500 hPa. Since CMIP6 output does not contain data at 750 hPa, potential temperatures \({\theta }_{1}\), \({\theta }_{2}\) and \({\theta }_{3}\) are taken as those at 250, 500, and 700 hPa, respectively.

Differentiating both sides of Eq. (3) between two periods of time, the future change of the dimensionless parameter \(I\) can be expressed as

$$\Delta {C}_{1}=\frac{1}{2{\left({C}_{1}\right)}_{h}}\left[\Delta {C}_{0}^{2}\left(1-{I}_{h}\right)-{\left({C}_{0}^{2}\right)}_{h}\Delta I\right],$$
(8)

Where \(\Delta \equiv {\left(\cdot \right)}_{f}-{\left(\cdot \right)}_{h}\), with the subscript \(f\) and \(h\) denote the mean quantity in the future and historical periods, respectively.

Dropping the subscript \(h\) for simplicity and differentiating Eq. (7) gives

$$\Delta {C}_{0}^{2}=\frac{\delta {p}^{2}}{2}\Delta {S}_{2}.$$
(9)

Similarly, the future change of \(I\) writes

$$\Delta I=A\left({S}_{2}^{-1}\Delta \bar{q}-\bar{q}{S}_{2}^{-2}\Delta {S}_{2}\right),$$
(10)

where \(A=\frac{{Rb}{L}_{c}}{{C}_{p}{p}_{2}\delta p}\). Substituting Eqs. (9) and (10) into Eq. (8) gives the budgets from the future change in the moist GW speed:

$$\Delta {C}_{1}=\frac{\delta {p}^{2}}{4{C}_{1}}\left[\left(1-I+A\bar{q}{S}_{2}^{-1}\right)\Delta {S}_{2}-A\Delta \bar{q}\right],$$
(11)

The first and second terms on the right-hand side of Eq. (11) represent the effects of static stability and moisture destabilization, respectively. Equation (11) provides useful physical insights into the competition between the dry static stability and the moisture effect on the moist GW speed.