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Although the moisture feedback has been well known to be essential in the Madden–Julian Oscillation (MJO) dynamics, whether its pre-moistening effect plays a key role in exciting the onset of primary MJO events, as has been confirmed in the successive initiation, remains elusive. In this study, using a hybrid coupled climate model that has a good fidelity in simulating the intraseasonal variability, we develop a new framework of methodology to investigate the nonlinear excitation of primary MJO event, of which the key achievement is the successful implementation of the conditional nonlinear optimal perturbation (CNOP). In an application of this new framework, the CNOP-type moisture perturbations are calculated for the pre-chosen non-MJO reference states and generally favor a moistening in the equatorial region while drying in the poleward. Comparisons of the model simulation with observation give credibility to the existence of moisture signals several weeks before some primary MJO events. A suite of numerical experiments confirms that the CNOPs of moisture can contribute to the excitation and propagation of strong primary MJO events while random perturbations cannot. The moisture budget analysis further reveals the central importance of the horizontal moisture advection, especially the nonlinearly upscaled moisture transports associated with the high-frequency disturbances on the quasi-3–4-day and 6–8-day synoptic time scales, in supporting the nonlinear excitation of the primary MJO events. The subgrid-scale processes of evaporation, condensation and eddy transport of moisture are found to be critical for the pre-moistening effect in the boundary layer as well. This study directly supports the vital importance of the moisture perturbations, which are characterized by a particular pattern concentrated at low levels, to the nonlinear growth and propagation of the primary MJO events.

This study investigates modulation of El Niño–Southern Oscillation (ENSO) on the Madden–Julian oscillation (MJO) propagation during boreal winter. Results show that the spatiotemporal evolution of MJO manifests as a fast equatorially symmetric propagation from the Indian Ocean to the equatorial western Pacific (EWP) during El Niño, whereas the MJO during La Niña is very slow and tends to frequently “detour” via the southern Maritime Continent (MC). The westward group velocity of the MJO is also more significant during El Niño. Based on the dynamics-oriented diagnostics, it is found that, during El Niño, the much stronger leading suppressed convection over the EWP excites a significant front Walker cell, which further triggers a larger Kelvin wave easterly wind anomaly and premoistening and heating effects to the east. However, the equatorial Rossby wave to the west tends to decouple with the MJO convection. Both effects can result in fast MJO propagation. The opposite holds during La Niña. A column-integrated moisture budget analysis reveals that the sea surface temperature anomaly driving both the eastward and equatorward gradients of the low-frequency moisture anomaly during El Niño, as opposed to the westward and poleward gradients during La Niña, induces moist advection over the equatorial eastern MC–EWP region due to the intraseasonal wind anomaly and therefore enhances the zonal asymmetry of the moisture tendency, supporting fast propagation. The role of nonlinear advection by synoptic-scale Kelvin waves is also nonnegligible in distinguishing fast and slow MJO modes. This study emphasizes the crucial roles of dynamical wave feedback and moisture–convection feedback in modulating the MJO propagation by ENSO.

Westerly Wind Events (WWEs) over the tropical Pacific are characterized by their spatiotemporal diversity and classified into six types based on their different locations and durations. Various types of WWEs exhibit quite different characteristics in terms of their amplitudes. The long events with a 10–30-day duration are stronger than the short events with a 6–10-day duration, and the maximum amplitudes of the Central-Pacific (C) type and Eastern-Pacific (E) type of long events are larger than the Western-Pacific (W) type of long ones. The evolutions of these six types of WWEs are also quite different. The W-type short and long events and the C-type long events show a distinct eastward propagation, whereas the C-type short events and the E-type short and long events have no apparent propagation direction. We demonstrate that such a difference in the eastward propagation of WWEs can be significantly associated with the Madden-Julian Oscillation (MJO). The W-type events are more influenced heavily by the MJO, as indicated by their more distinct eastward propagation patterns, than the two other types of WWEs. In addition to the MJO, the convectively coupled Kelvin waves are also associated with the WWEs, especially for the short events.

The Madden-Julian Oscillation (MJO) is a dominant intraseasonal variability originating in the tropics and influencing global weather and climate. Despite this dominance, we still lack reliable precursor signals triggering nonlinear initiation of primary MJO events. Here for the first time, we deal with this question from the point of view of nonlinearity, with successful implementation of conditional nonlinear optimal perturbation (CNOP). Our results show that relative to random perturbations, CNOPs of moisture have the most potential to trigger the strongest primary MJO events more than 15-20 days in advance from the given non-MJO reference states. The CNOPs manifest as a moist equator and aggregate in the lower troposphere, with stronger signals over the western Indian Ocean than over the eastern one. These CNOPs can also capture the observational moist precursor conditions of primary MJO events. This work also implies the necessity of utilizing nonlinear optimal moist initialization in subseasonal predictions. Plain Language Summary As a dominant intraseasonal (20-90 days) variability prevailing in the tropics, the Madden-Julian Oscillation (MJO) casts significant impacts on global weather and climate. However, we still lack reliable precursor signals for MJOs initiating over the western Indian Ocean, especially for primary events, that is, those without an immediately preceding MJO event. Here for the first time, we deal with this topic from the point of view of nonlinearity, with the successful implementation of conditional nonlinear optimal perturbation (CNOP). In particular, we find that our CNOPs can identify the optimal precursors of primary MJO initiation. We examined four non-MJO reference states, selected based on both circulation- and convection-based MJO indices. Although different reference states produce different CNOPs, all tend to manifest as a moist equator and aggregate in the lower troposphere, with stronger signals over the western Indian Ocean than over the eastern Indian Ocean. These CNOP-type moist precursor conditions are also found preceding the onset of observed primary events. We find that, relative to random perturbations, CNOPs of moisture have the most potential to trigger the strongest MJO event more than 15-20 days in advance. This work implies the necessity of utilizing nonlinear optimal moist initialization to improve subseasonal (15-60 days) predictions.

The authors present an air–sea coupled dynamic moisture (ASDM) model to explore the mechanism of preferred planetary scale of the Madden–Julian Oscillation (MJO). This ASDM model, extended from the original frictionally coupled dynamic moisture model and a mixed layer model, can present a good simulation of planetary-scale characteristics of the MJO, including a slow eastward propagation of 5 m s−1, coupled Rossby–Kelvin wave-like structure, and phase leading of convective center by warm sea surface temperature (SST). It is interesting that the planetary-scale selection in terms of instability is only found in the nonlinear ASDM model with the assumption of positive-only heating. Such a scale selection, however, cannot be found in the ASDM model with linear heating or in an uncoupled atmosphere model. The essential mechanism for the scale selection is nonlinear positive-only heating, and the air-sea interaction primarily provides an instability source to support this scale selection. This scale selection is attributed to different phase speeds of coupled moist Rossby–Kelvin waves and dry Kelvin waves. From short-wave initial perturbations, the easterly wind anomalies of eastward-propagating dry Kelvin waves from a stronger wave component will catch up with other weaker moist components and suppress their westerly wind anomalies, resulting in weak SST gradient as well as reduced moisture convergence and precipitation for these suppressed components. As a result, the wavenumber-one structure is selected. The Warm Pool-like mean state will select the stronger component among the initial short-wave perturbations and accelerate this scale selection process. These results provide new insight into MJO mechanism in terms of air-sea interaction.

To reveal key parameter-related physical mechanisms in simulating Madden-Julian Oscillation (MJO), seven physical parameters in the convection and cloud parameterization schemes of Beijing Climate Center Climate System Model (BCC_CSM1.2) are perturbed with Latin hypercube sampling method. A new strategy is proposed to select runs with good and poor MJO simulations among 85 generated ones. Outputs and parameter values from good and poor simulations are composited separately for comparison. Among the seven chosen parameters, a decreased value of precipitation efficiency for shallow convection, higher values of relative humidity threshold for low stable clouds and evaporation efficiency for deep convective precipitation are crucial to simulate a better MJO. Changes of the three parameters act together to suppress heavy precipitation and increase the frequency of light rainfall over the Indo-Pacific region, supplying more moisture in low and middle troposphere. As a result of a wetter lower troposphere ahead of the MJO main convection, the low-level moisture preconditioning along with the leading shallow convection tends to be enhanced, favorable for MJO&rsquo, s further development and eastward propagation. The MJO&rsquo, s further propagation across the Maritime Continent (MC) in good simulations is accompanied with more land precipitation dominated by shallow convection. Therefore, the above-mentioned three parameters are found to be crucial parameters out of the seven ones for MJO simulation, providing an inspiration for better MJO simulation and prediction with this model. This work is valuable as it highlights the key role of moisture-shallow convection feedback in the MJO dynamics.

The observed convective adjustment time (CAT) associated with Madden–Julian Oscillation (MJO) precipitation is found to vary significantly in space. Here, we investigate the effect of different spatial distributions of CAT on MJO precipitation based on the frictional coupled dynamics moisture (FCDM) model. The results show that a large value of CAT tends to decrease the frequency and growth rate of eastward-propagating MJO-like mode in the FCDM model, delaying the occurrence of MJO deep convection and slowing down its eastward propagation. A large phase lag between circulation and convection decreases convective available potential energy (CAPE). In the observations, a small background vertical moisture gradient (BVMG) tends to increase the frequency associated with cold sea surface temperature (SST), while a large value of CAT tends to decrease the frequency. Due to their competing effect, the simulated frequency and phase speed remain the same when the convection moves from a warm to a cold SST region. The convection is heavily suppressed over the cold SST region due to the decreasing growth rate of unstable wavenumber-one mode with smaller BVMG and longer CAT. This theoretical finding should improve our understanding of MJO dynamics and simulation.