We compared simulated MJO characteristics using three coupled and uncoupled AGCMs. Figure 1 shows the wavenumber–frequency spectra of simulated 850 hPa zonal wind (shading) and precipitation (contours). All three uncoupled AGCMs (hereafter referred to as AGCMs) simulated intraseasonal signals with a lower frequency than was observed and overestimated the westward propagation with periods greater than 80 d (Fig. 1e–g). ECHAM5 and HiRAM simulated signals of wavenumbers 1–3 instead of the observed wavenumber 1 in 850 hPa zonal wind. These results show that all three AGCMs simulated stationary fluctuations with low frequency that were not consistent with the observations. In contrast, coupled AGCMs realistically reproduce the observed spectral characteristics and strength of the eastward propagation at wavenumbers 1 to 2 in 850 hPa zonal wind (Fig. 1b–d). Although HiRAM simulated eastward propagation in a wider frequency spectrum than observed, the coupled model clearly displays improvements in the MJO simulation compared with the stationary intraseasonal fluctuation in the uncoupled simulation. Hovmöller diagrams presented in Fig. 2 illustrate the temporal evolution of 850 hPa zonal wind and precipitation in the tropics in both observations and simulations. All three models simulated either stationary (CAM5 and HiRAM) or weak eastward-propagating (ECHAM5) signals in AGCMs, but they more realistically simulated the eastward propagation of the MJO in the coupled models. However, the propagation in the ECHAM5-SIT is still slightly slower than was observed. The improvement obtained in coupled models suggests that active ocean–atmosphere interaction is crucial for successful MJO simulation.

The composite MJO life cycle, featuring intraseasonal OLR and 10 m surface wind anomalies for boreal winter in eight phases (following Wheeler and Hendon , 2004), is displayed in Fig. 3. All three coupled models simulated realistic MJO with enhanced circulations and propagation tendency compared to the uncoupled models. The MJO in phase 4, when deep convection is the strongest over the Maritime Continent (MC), demonstrates the large-scale zonally overturning circulation coupling with the convection (Fig. 4). The positive heating region in the coupled experiment is significantly enlarged, deepened, and tilted westward with increasing height compared to those in the uncoupled experiment. Correspondingly, the convective circulation envelope of the MJO is thicker and longitudinally wider in coupled experiments. The strong convection is associated with much enhanced low-level moisture convergence (green contours). Furthermore, the area of positive rainfall anomaly in the coupled experiment becomes larger, and the sea level pressure anomaly is meridionally more confined, exhibiting the characteristics of intensified Kelvin-wave-like perturbations to the east of the deep convection. This enhancement of low-level moisture convergence is consistent with the frictional wave-conditional instability of the second kind of mechanism (Frictional wave CISK; Wang and Rui, 1990; Kang et al., 2013). The enhancement of the Kelvin wave can be observed in the symmetric wavenumber–frequency spectra (Fig. 5). The spectra between 0 and 0.35 d-1 are presented to highlight the MJO and equatorial Kelvin waves. The coherence at wavenumbers of 2–4 for the 10–20 d period is simulated to be stronger in the three coupled models than in the uncoupled models.

In addition to the atmospheric structure, the SST (Fig. S1) and vertical profile of ocean temperature examined are presented in Fig. 6. The observed SST variation in MJO variability is reproduced well in all three coupled models (Fig. S1). The warm SST leads the main MJO convection by approximately 5–10 d, followed by the cold SST approximately 5–10 d later (Flatau et al., 1997; DeMott et al., 2015; Tseng et al., 2015). Moreover, the observed amplitude fluctuation (approximately 0.5 to 1 ∘C) is realistically simulated. The observed ocean temperature profiles, characterized by the warm layer, along the Equator from the Indian Ocean to the western Pacific are simulated well in the three coupled models (Fig. 6). Meanwhile, simulated temperature anomalies are larger in ECHAM5-SIT than in CAM5-SIT and HiRAM-SIT. Figure S2 shows the fluctuations of observed SST and simulated SST in three sets of coupled and uncoupled models. There is no fluctuation (as expected) in uncoupled simulations, whereas the simulated SST fluctuates with phases similar to those observed at different locations. The amplitudes in ECHAM5-SIT and CAM5-SIT are similar to the observed values, whereas those in HiRAM-SIT seem to be smaller in the western Pacific. The differences between models are likely due to the different atmospheric model configurations because they were otherwise coupled to the same 1-D ocean model. Since the atmosphere is the main driver to extract heat from the ocean, different responses of atmospheric models likely have different effects on SST. Pinpointing the cause of quantitative differences between models will require further detailed analysis. The consistent results in all three coupled models support the conclusion of Tseng et al. (2015) that resolving fine vertical resolution in the upper ocean improves the simulation of the warm layer and MJO propagation and variability. Our results further demonstrate that the effect of atmosphere–ocean coupling on the MJO could be independent of AGCMs with different configurations and atmospheric physical parameterizations and that coupling seems to be a more fundamental approach.

Model performance is summarized in Fig. 7. The scatter plot shows the power ratio of east–west-propagating waves (x axis) versus the pattern correlation between the simulated and observed precipitation anomaly in Hovmöller diagrams (Fig. 2; y axis). The east:west ratio was calculated by dividing the eastward-propagating power by the westward-propagating power of 850 hPa zonal wind summed over wavenumbers of 1–2 and a period of 30–80 d. Compared with the observations, coupled simulations (marked by circles) exhibit better simulation than uncoupled simulations (marked by asterisks). A comparison of combined explained variance using real-time multivariate MJO series 1 (RMM1) and 2 (RMM2) (Fig. 7b) based on Wheeler and Hendon (2004) shows marked increases after coupling. The comparison demonstrates that coupling is essential for realistic MJO simulations.

Following the peak MSE tendency over the MC (120–150∘ E) during phase 2 (Fig. 8d, g, and j), values of each term contributing to the column-integrated MSE tendency in Eq. (1) preceding the deep convection over the MC area (10∘ S–0∘ N/S, 120–150∘ E) are shown in Fig. 9. Vertical advection is the dominant term with the major compensation from longwave radiation during phase 2 when convection is still in the eastern Indian Ocean, as identified by Wang and Li (2020). Moreover, the LH term is consistent within all three models and contributes less negative MSE tendency in coupled models than AGCMs. The results show that the contribution comes from the LH term in this early phase stage. The LH effect was overlooked in Tseng et al. (2015) because of the weak MJO variability in coupled simulations. However, this negative LH bias becomes one of the key factors in enhancing the leading MSE tendency during the MJO preconditioning phases. This suggests that the surface latent flux bias in AGCMs can be corrected by involving the coupling process in the preconditioning phase. Generally, coupling improves the budget simulation. The positive contribution of vertical advection and negative contribution of LH in MSE tendency is closer to being realistic in the coupled simulations during the initial phase of the MJO.

We compared the spatial distribution of MSE and precipitation in phase 4 when convection was the strongest in the MC (Fig. 10). In the observations, the main convection occurs in the MC from 90 to 150∘ E. A positive MSE tendency with a maximum value near 10∘ N and 10∘ S is identified in the east of the MJO convection centered near the Equator. Meanwhile, a negative integrated MSE tendency is found in the west of the MJO convection, and the meridionally confined structure near the Equator exhibits the characteristics of the equatorial Kelvin wave embedded in the MJO. Clearly, coupled models outperform uncoupled models in reproducing these signals. To quantify the contribution of coupling to the improvement, we follow Jiang et al. (2018) to project all MSE terms to the observations (Fig. 11). The dominant contribution of horizontal advection to the MSE tendency in the observations (Fig. 11a) is simulated well in the coupled simulations (but not in the uncoupled simulations) of ECHAM5 and CAM5 (Fig. 11b and c). Although a similar dominant effect was observed in both simulation types in HiRAM, it is enhanced in the coupled simulation (Fig. 11d). The horizontal advection term is further decomposed into zonal and meridional components (Fig. 11e–h); both components have a positive contribution, but the meridional component has a larger amplitude. Furthermore, the uncoupled ECHAM5 and CAM5 models simulate unrealistic features: positive contribution from zonal advection but negative contribution from meridional advection. In contrast, coupled models simulate the dominance of meridional advection well. In HiRAM, the uncoupled model simulates almost equally positive contributions from both terms. However, the coupled model simulates a larger contribution from meridional advection. We further decompose the meridional advection to assess the relative contributions of an intraseasonal perturbation and the mean state. Consistent with the observations (Fig. 11i), the meridional advection by intraseasonal flow (-v′∂h‾∂y) is the main factor in improving the simulations in the coupled models (Fig. 11j–l). Our results are consistent with those of Jiang et al. (2018). To evaluate the relative contribution of intraseasonal circulation and background moisture, we further diagnosed changes in Δ(-v′∂h‾∂y) at phase 4. Here the overbar shows that the time mean and prime represents intraseasonal anomaly. Changes in the MJO meridional advection term for coupled experiments relative to uncoupled can be written as follows: 2Δ-v′∂m‾∂y=-Δv′∂m‾∂yuncoupled-v′uncoupledΔ∂m‾∂y(a)(b)-Δv′Δ∂m‾∂y(c), where Δ represents the coupled–uncoupled change. The terms (a)–(c) in Eq. (2) are presented as bar charts in Fig. 12. The change in the intraseasonal circulation in the meridional circulation is the dominant factor in coupled simulations relative to uncoupled experiments. The instantaneous SST horizontal distribution dominates this moisture budget change due to the atmosphere–ocean coupling effect. Therefore, the change of varying moisture induces the intraseasonal circulation change. The results confirm that the dominance of dynamic influence over thermodynamic response to atmosphere–ocean coupling is essential in improving MJO simulations.