1 Introduction

The main features of the Madden–Julian Oscillation (MJO; Madden and Julian, 1971, 1972) include an eastward-/northward-propagating wave and planetary-scale circulation, with an eastward propagation speed of 5 m s⁻¹ and a dominant period of 30–80 days. As the strongest low-frequency signal in the tropics, MJO has a significant impact on global weather and climate. For example, precipitation (Paegle et al., 2000; Bond and Vecchi, 2003; Barlow et al., 2005; Wheeler et al., 2009; Zhang et al., 2009), temperature (Jeong et al., 2005; Lin, 2015), the global monsoon system (Yasunari, 1979, 1980; Hendon and Liebmann, 1990; Sultan et al., 2003; Lorenz and Hartmann, 2006), tropical cyclone activity (Liebmann et al., 1994; Maloney and Hartmann, 2000; Bessafi and Wheeler, 2006; Klotzbach, 2010; Diamond and Renwick, 2015), and extreme weather events (Jones, 2000; Jones et al., 2004; Xavier et al., 2014; Hsu et al., 2016; Lee et al., 2017; Ren and Ren, 2017; Ren et al., 2018) in different regions and different seasons are all strongly modulated by MJO. As a bridge between deterministic weather forecasting and climate prediction, the MJO’s dominant low-frequency characteristics are considered to be a predictability resource at sub-seasonal timescales (Zhang, 2013), which is an important basis for the concept of “seamless prediction” (Hurrell et al., 2009; Brown et al., 2012).

A realistic MJO simulation is essential for the prediction at the sub-seasonal scale. There has been a significant improvement in the MJO prediction skill during the past decade by using more advanced, fully coupled dynamic climate models (Ren et al., 2015, 2016, 2017; Wu et al., 2016). However, the MJO prediction is still a challenge due to the elusive dynamic mechanisms behind its features (Jiang et al., 2015; Majda and Yang, 2016; Jiang, 2017). In general, the unrealistic features of MJO simulation are mainly reflected in its amplitude (Zhang et al., 2006; Hung et al., 2013; Zhao et al., 2014; Jiang et al., 2015; Ahn et al., 2017), dominant period (Zhang et al., 2006; Kim et al., 2009), eastward propagation (Zhao et al., 2014; Jiang et al., 2015; Jiang, 2017), and vertical tilting structure (Jiang et al., 2015). These MJO simulation biases are usually attributable to the resolution of the model (Hayashi and Golder, 1986; Slingo et al., 1996; Gualdi et al., 1997; Inness et al., 2001; Jia et al., 2008), convective parameterization (Slingo et al., 1996; Wang and Schlesinger, 1999; Maloney and Hartmann, 2001; Zhang and Mu, 2005), diabatic heating (Li et al., 2009), mean state (Slingo et al., 1996; Inness et al., 2003; Sperber et al., 2005; Ajayamohan and Goswami, 2007), and air–sea coupling (Wang and Xie, 1998; Kemball-Cook et al., 2002; Fu and Wang, 2004; Zheng et al., 2004; Sperber et al., 2005; Watterson and Syktus, 2007).

The US Climate Variability and Predictability Program (CLIVAR) developed a standardized diagnosis for MJO to compare simulation capabilities of different models (Waliser et al., 2009). We use this standard diagnosis to evaluate the performance of the Chinese Academy of Meteorological Sciences Climate System Model (CAMS-CSM) in simulating MJO, including the seasonality characteristics, geographical distribution of MJO in winter/summer, dominant wavenumber–frequency, propagation features, and coupling characteristics. The low-level convergence of moisture also plays an important part in the life cycle of MJO and generally promotes the growth of positive moisture anomalies east of the convection, thereby slowly moistening the atmosphere until it reaches a state that is again conducive to the development of convection (Maloney and Hartmann, 1998). The low-level convergence of moisture can therefore be considered as a prerequisite for deep convection in the troposphere (Kikuchi and Takayabu, 2004). The zonal asymmetry of this moisture anomaly mainly occurs in the planetary boundary layer (PBL; 1000–700 hPa), which destabilizes MJO convection and facilitates its eastward propagation (Hsu and Li, 2012; Jiang et al., 2015). Recent studies have shown that the northward propagation of MJO is accompanied by the low-level convergence of moisture ahead of the convection (Jiang et al., 2011; Neena et al., 2017). We also examine several key factors related to the eastward/northward propagation of MJO—including the vertical tilting structure of both moisture and wind and the PBL integral moisture budget—and suggest possible reasons for the detour of MJO over the Maritime Continent.

The paper is organized as follows. An introduction to the model simulations and validation data is given in Section 2. Section 3 presents the strategies and basic results of the MJO simulation. The possible effects of moisture processes on the eastward/northward propagation of MJO are described in Section 4. The summary and discussion are provided in Section 5.

2 Model simulations and validation data 2.1 CAMS-CSM

We evaluate the MJO simulation by using CAMS-CSM, which is a fully coupled model combining atmosphere, ocean, land, and sea ice components. The atmospheric component is ECHAM5 (version 5.4; Roeckner et al., 2003), which has a horizontal resolution of T106 (approximately 1.125°) and 31 vertical layers from the surface to 10 hPa. The oceanic component is the fourth edition of the Modular Ocean Model from Geophysical Fluid Dynamics Laboratory (Griffies et al., 2004). This model has 50 vertical levels with a global zonal resolution of 1°. The meridional resolution is 1/3° within the 10°S–10°N equatorial band, ranging to 1° at 30°S (30°N) with a nominal 1° resolution poleward of 60°N. The sea ice component is the Geophysical Fluid Dynamics Laboratory Sea Ice Simulator, and the land component is the Common Land Model (Dai et al., 2003). A detailed description of the CAMS-CSM model is given by Rong et al. (2018).

2.2 Observational data

We use various observational data to evaluate the MJO simulation in the 23-yr run of CAMS-CSM, including the outgoing longwave radiation (OLR) from NOAA satellites (Liebmann and Smith, 1996) and daily reanalysis data from ERA-Interim (Dee et al., 2011) of wind speed and specific humidity. The pentad-mean Climate Prediction Center (CPC) Merged Analysis of Precipitation dataset (CMAP; Xie and Arkin, 1997) is also used.

All these observational datasets have a horizontal resolution of 2.5° × 2.5°. To facilitate the comparison of the model results with the observational data, corresponding data for the model were interpolated to obtain a resolution consistent with the observational data. The common period for all the observational datasets is 1981–2003. The summer season is defined as 1 May to 31 October and the winter season is from 1 November to 30 April of the following year.

3 Diagnostic strategy and basic results

Our goal is to examine the primary features of MJO by using the two-level diagnostic strategies proposed by the CLIVAR MJOWG (MJO Working Group) (Waliser et al., 2009). When verifying the ability of CAMS-CSM to simulate MJO, the intraseasonal variability (ISV) signal is obtained by filtering out days 20–100 by using the Lanczos filter (Duchon, 1979). The daily climatological mean and seasonal cycle (first three annual harmonics) are subtracted before filtering.

3.1 Simulation of ISV characteristics

We examine the ability of CAMS-CSM to simulate 20–100-day ISVs, including the seasonality characteristics, winter/summer regional dependence, dominant wavenumber–frequency, and propagation characteristics.

3.1.1 Examination of the seasonality of ISV

It is well known that the spatial distribution of ISVs shows a significant seasonality, that is, the winter ISV is mainly concentrated in the equatorial Indian Ocean and western Pacific and its positions are south of the equator, whereas the summer ISVs are mainly concentrated to the north of the equator, showing a clear tendency to migrate northward. This seasonal migration is not well represented in some models (Sperber, 2004; Zhang et al., 2006). Therefore, we first examine the ability of CAMS-CSM to simulate the seasonality of ISVs. The intraseasonal variance of precipitation and U850 of each calendar month averaged over the Indian Ocean (60°–130°E) and western Pacific (130°E–180°) show the seasonal variations in ISV as a function of time and latitude. The most salient feature in the observed seasonal cycle is the south–north migration of the ISV activity, which is reflected in the transitions between boreal winter and summer over both regions (Figs. 1a, c). Here, the ISV variance of precipitation and U850 is centered south of the equator in winter and moves northward to north of the equator in summer. Such a seasonal shift in the ISV variance can be well represented by the model (Figs. 1b, d), suggesting that the model gives a good simulation of the seasonality of ISVs. Given the clear seasonal difference in the distribution of ISVs, it is necessary to assess the ability of the model to simulate MJO signals in each season. We therefore evaluate the capability of the model to simulate MJO signals in both winter (November–April) and summer (May–October).

3.1.2 Distribution of ISV and its relationship with the mean state

The spatial distribution and amplitude of the ISV activity are described by the ISV variances of precipitation and U850 during boreal winter (Fig. 2; contours) and summer (Fig. 3; contours). To relate the ISV activity to the corresponding background state, we also give the mean field distribution of precipitation and U850 (Figs. 2, 3; shading).

The strongest ISV of U850 in the observations is located in the south of the Maritime Continent, whereas the second value is located in the tropical western central Pacific and eastern Indian Ocean during boreal winter. Similarly, ISV of precipitation is concentrated in the equatorial eastern Indian Ocean and western Pacific. CAMS-CSM shows a good performance in representing the ISV variance of both U850 and precipitation, performing well for both the intensity center and amplitude. The model bias in ISV of precipitation is featured by a separation in western Pacific, with two centers on both sides of the equator. The model clearly simulates U850 better than precipitation during boreal winter, indicating that the coherence of precipitation and wind field in the model is slightly weaker than in the observations. No strong ISV signal was found over the Maritime Continent, tropical South America nor Africa, despite of the strong mean precipitation and U850 in these regions. Many previous studies have attempted to explain these features (Salby et al., 1994; Wang and Li, 1994; Maloney and Sobel, 2004; Zhang et al., 2006). It is probable that the land surface, especially complex terrains, affects the amount of energy absorbed by MJO from surface evaporation and moisture convergence. Locations of the largest ISV variance of U850 and precipitation move northward in boreal summer and these migrations are well captured by CAMS-CSM. Similarly, The model simulates U850 better than precipitation in boreal summer, and the main bias of precipitation is located in western Pacific, where the model overestimates ISV of precipitation in the North and South Pacific convergence zones.

Further investigation of the relationship between the ISV and background state indicated that there is a close relationship between the ISV variance and mean fields, that is, the ISV signal has a tendency to appear in the strong (weak) westerly (easterly) belts and in ocean areas with abundant precipitation. Both the observational data and model simulation have these characteristics, indicating that ISV has a strong dependence on the corresponding background, confirming the link between them (Slingo et al., 1996; Inness and Slingo, 2003). In other words, if a model does not simulate the distribution of climatic mean states well, its ability to simulate ISV signals may be weakened. Such a close relationship between the ISV and climatic mean state is highlighted in Fig. 4, which shows the difference between the model simulations and observations in Figs. 2, 3. The ISV signal is more likely to occur in the area of the westerly anomaly and for large values of precipitation. The CAMS-CSM simulation gives values for precipitation in the Northern Hemisphere intertropical convergence zone (ITCZ) and South Pacific convergence zone that are larger than the observational data, referred to as the double ITCZ phenomenon. The excessive precipitation in the model also leads to an overestimation of the amplitude of ISV, further confirming the dependence of ISV on the mean state.

3.1.3 Wavenumber–frequency characteristics

The spatiotemporal spectrum (Hayashi, 1979; Wheeler and Kiladis, 1999) emphasizes the existence of eastward-propagating signals on intraseasonal and planetary scales, which are fundamental features of MJO within the equatorial belt. Because the MJO signal is usually stronger and shows a more significant eastward propagation in boreal winter than in other seasons, our assessment focused on this period. Figure 5 shows the wavenumber–frequency spectra of the equatorial precipitation (Figs. 5a, b), OLR (Figs. 5c, d), and U850 (Figs. 5e, f) anomalies in boreal winter.

The east/west (E/W) ratio obtained by dividing the eastward-propagating component of the MJO band (days 30–80 and wavenumbers 1–3) by its westward-propagating component has been widely used in both observational (Zhang and Hendon, 1997) and modeling studies (Lin et al., 2006; Kim et al., 2009; Li et al., 2016; Ahn et al., 2017) to examine the robustness of the eastward propa-gation of MJO. It is applied in this study to test the performance and to give a quantitative evaluation of the model simulations.

In the observations, the spectral peaks of precipitation and OLR are concentrated in zonal wavenumbers 1–3 and timescale of the 30–80-day period, whereas the peak U850 is concentrated in wavenumber 1—that is, the zonal scale of U850 is larger than those of precipitation and OLR, which is in agreement with previous results (Zhang et al., 2006; Waliser et al., 2009; Li et al., 2016). In general, the model gives a reasonable simulation of the MJO spectrum band, on which the eastward-propagating power of precipitation, OLR, and U850 are much greater than that of the westward-propagating power. Compared with previous studies, this model gives an encouraging simulation of the spatiotemporal scale of MJO (Kim et al., 2009; Li et al., 2016; Ahn et al., 2017). However, although the model can simulate the main features of the MJO scale, such as the intraseasonal signal and eastward-propagating direction, there are still some systematic deviations. The model bias includes the following features. (1) The E/W ratio is weakened, and the precipitation, OLR, and U850 show a slight decrease in the ratio of eastward- to westward-propagating power, indicating that the MJO eastward-propagating features in the model are slightly weaker than those in the observational data. (2) Unrealistic low-frequency timescales with spectral peaks in the model shift to a lower frequency than the observed 30–80-day timescale. (3) There is more spreading of spectral peaks on the spatial scale. For example, the spectral peaks of precipitation and OLR are concentrated in wavenumbers 1–3 in the observational data, but extend to wavenumbers 4 and 5 in the model simulations. For U850, spectral peaks in the observation data are mainly concentrated in wavenumber 1, but the counterparts of the model can extend to wavenumbers 2 and 3.

3.1.4 Propagation characteristics

One of the notable characteristics of MJO that is distinguished from other variabilities lies in its propagation features. During winter, this is mainly the eastward propagation, described in the spatiotemporal analysis of the spectrum, whereas in summer there is also significant northward propagation. This section presents the ability of CAMS-CSM to simulate the propagation characteristics of ISVs based on a lagged regression analysis. The spatial distributions of the regression coefficients are obtained by using filtered values for OLR and U850, and the OLR anomaly averaged over the Indian Ocean (5°S–5°N, 75°–85°E) and western Pacific (5°S–5°N, 130°–150°E). Figure 6 shows the time evolution of OLR and U850 along the equator for both observations and model simulations against the Indian Ocean and western Pacific base points in boreal winter. The main observational features show the eastward propagation in both OLR and U850, in which OLR is mainly confined to the Eastern Hemisphere with a propagation speed of 5–6 m s⁻¹. In the Eastern Hemisphere, the propagation speed between U850 and OLR is equivalent, but after crossing the dateline, the eastward transmission of U850 is clearly accelerated. Signals of OLR and U850 show a 90° phase shift in the Indian Ocean, with the anomalous westerly wind lagging behind a negative OLR anomaly by about 5–7 days. When MJO enters the western Pacific region, the negative OLR anomaly is almost synchronized with U850, and the strongest convection is mainly controlled by westerly winds (Hendon and Salby, 1994; Zhang et al., 2006).

CAMS-CSM can reproduce the typical features of the observed MJO propagation well. In the model, the eastward propagation of OLR and U850 in the Eastern Hemisphere are clear and the only difference is seen in the propagation speed. CAMS-CSM tends to produce a slower speed than the observational data, which is consistent with the results of the wavenumber–frequency spectrum in Fig. 5. The coherence of U850 and OLR is also simulated reasonably well in the model, where the lag effect in the Indian Ocean region and asymptotic synchronization in western Pacific between the westerly winds and OLR are captured well by the model.

MJO shows northward/northeastward propagation over the Indian summer monsoon region (Yasunari, 1979; Krishnamurti and Subrahmanyam, 1982; Lau and Chan, 1986; Annamalai and Sperber, 2005; Lee et al., 2013) and a northward/northwestward propagation over western North Pacific (Kemball-Cook and Wang, 2001) in boreal summer. Figure 7 shows the ability of the model to simulate the poleward propagation of MJO in these two regions. Using the results for the Indian Ocean base point (0°–10°N, 85°–90°E; Fig. 7a), both OLR and U850 show a significant northward propagation. The enhanced convective anomaly is first formed near the equator on day 0, and then propagates poleward from days 0 to 10 at the speed of 1.98 m s⁻¹, reaching about 20°N. The convection around the equator in the Southern Hemisphere shows a southward trend, although this is not completely clear. Using the results for the western Pacific base point (0°–10°N, 135°–140°E; Fig. 7c), the northward propagation of OLR and U850 is as clear as that in the Indian Ocean, although the southern tropical band does not show any sign of southward propagation. Good coupling can be observed between the U850 and OLR results as the MJO convection propagates from 0° to 10°N. However, the center of U850 gradually detaches from the convection as it is further from the equatorial region. This may be why the MJO propagation slows down in this region and then gradually disappears.

Unfortunately, the poleward propagation of MJO in these two regions is not well represented by the model. However, the simulation of northward propagation in the Indian Ocean is much better than the simulation in the western Pacific region. A more reasonable configuration between U850 and convection in the Indian Ocean may account for the better simulation of northward propagation in this region. The coupling between U850 and convection in the western Pacific region is not captured in the model. However, the ability of CAMS-CSM to simulate the northward propagation of MJO is better than simulations of CESM (Li et al., 2016), CCSM3, CGCM3.1 (T47), CGCM3.1 (T63), FGOALS-g1_0, GIS-AOM, and IPSL-CM4 models (Sperber and Annamalai, 2008), suggesting that the simulation of the northward propagation of MJO during summer is relatively difficult.

In conclusion, CAMS-CSM can successfully simulate the eastward propagation of MJO, but shows a weak simulation of the northward propagation of MJO during boreal summer. Comparing the two areas (the Indian Ocean and western Pacific), CAMS-CSM can simulate the northward propagation of MJO in the Indian Ocean, but the speed of northward propagation is slower than the observed propagation. The simulation of northward propagation of MJO in western Pacific is distorted, indicating that there is still much room for improvement in the model.

3.2 Coherent features of the MJO

Evaluations discussed so far in this paper have focused on univariate ISVs, but classical MJO structures typically appear as interactions between the circulation and convective field, such as the configuration between upper/lower winds and convection. Therefore, this section focuses on these coherent features of MJO, especially the results of the multivariate combined empirical orthogonal function (MCEOF) analysis. The resulting principal components can be used to generate composites during the MJO life cycle, and the unfiltered principal components obtained by projecting the unfiltered anomaly data into the EOF mode can be used to verify whether the extracted MJO modes are physically meaningful and are distinct from noise (Subramanian et al., 2011).

3.2.1 Cross-spectra analysis

Cross-spectra analysis is applied to examine the coherence as well as phase lag between the circulation and convection (Fig. 8), which are presented separately for the symmetrical and asymmetrical components of each field (Wheeler and Kiladis, 1999; Hendon and Wheeler, 2008). We show a magnified display of the spectra of MJO band to highlight details in the MJO space–time scale.

The symmetrical component is the first-order characteristics of the observed MJO. The most prominent feature in the observational data is the peak coherence of the 30–80-day period and wavenumbers 1–3 associated with MJO. For the MJO peak, the southwest-pointing vectors imply that positive westerly (easterly) anomalies lag the suppressed (enhanced) convection by about 235°. Another interpretation is that westerly (easterly) MJO wind anomalies lag the enhanced (suppressed) convection by about 1/8 cycle, or equivalently by about 5 days, which is consistent with previously reported results (Wheeler and Kiladis, 1999; Hendon and Wheeler, 2008; Subramanian et al., 2011; Li et al., 2016). Compared with the observational data, CAMS-CSM produces strong coherence in this low-frequency band and shows a similar phase lag relationship between U850 and OLR signals. However, for wavenumbers 1 and 2, the large value of the simulated peak shifts toward a lower frequency than the observational data with roughly an 80-day period. The coherence at wavenumbers 2 and 3 of the model is stronger than that for the observational data, indicating that the zonal scale is smaller than that for the observational data. However, the symmetrical part of the cross-spectrum may contain the equatorial Kelvin wave signal (Hendon and Wheeler, 2008).

To distinguish the signal of the MJO band from the Kelvin wave, the corresponding asymmetrical part of MJO band can exclude the signal of the linear Kelvin wave (Fig. 8). Both the observational data and model show large coherence values for the MJO band with a wavenumber of 1, indicating that this high coherence is a significant MJO behavior rather than a linear Kelvin wave. Similarly, a shift to a lower frequency of the coherent peak and stronger coherence at wavenumbers 2 and 3 than seen in the observational data also exist in the asymmetrical component. In addition, in the previous analysis of the eastward propagation (Fig. 6), we concluded that the propagation speed is slower in the model than that in the observational data. The cross-spectrum analysis shows that there is a weaker (stronger) Kelvin (Rossby) wave in the model than that in the observational data, which may explain the slower propagation in the model.

To sum up, the model gives a better simulation of the eastward propagation of MJO, and shows strong coherence with observations in the MJO space–time band. However, the simulated propagation is shifted toward a lower frequency, which implies a slower propagation speed than in the observed data, consistent with the results in Figs. 5, 6.

3.2.2 MJO mode from MCEOF analysis

Wheeler and Hendon (2004) invented the real-time multivariate MJO index by using MCEOF analysis to monitor and predict the MJO activity in real time, which was shown to effectively capture the salient features of MJO and is now widely used in MJO simulations (Kim et al., 2009; Waliser et al., 2009; Li et al., 2016). The index has no filtering variable (only the first three annual harmonics and interannual variability are removed) for real-time monitoring and prediction purposes in the study of Wheeler and Hendon (2004). However, in order to fully highlight the MJO band, we used the 20–100-day bandpass filtered data to facilitate the isolation of MJO modes, as in Waliser et al. (2009).

Figure 9 shows the meridional mean distribution of the 20–100-day OLR and 850- and 200-hPa zonal winds in the first two spatial modes derived from MCEOF analysis by using the observational data during 1981–2003 and performing the 23-yr run of CAMS-CSM over 15°S–15°N. EOF1 captures the enhanced convective activity over the eastern Indian Ocean and Maritime Continent in the observational data, whereas EOF2 captures the enhanced convection in the western/central Pacific Ocean and suppresses convection in the Indian Ocean. The first two modes together account for 43.8% of the filtered variance and are completely separated from the other modes based on criteria of North et al. (1982). The zonal winds in the upper (U200; blue line) and lower (U850; red line) troposphere are out of phase with each other. Specifically, the strong convection of EOF1 is located at 90° E and the corresponding high- and low-level winds are also inversed at the same longitude. For U850, the west (east) side of enhanced convection is the westerly (easterly) anomaly, so the dynamic field converges in the lower troposphere. By contrast, a westerly (easterly) anomaly of U200 occurs to the west (east) of the enhanced convection, accompanied by high-level divergence. As the convection moves eastward to the vicinity of 150°E (EOF2), the associated wind fields also move eastward to the adjacent area and maintain the baroclinic structure. The coupling between OLR and wind fields forms the most classic structure of MJO. Mode 2 from the observational data corresponds to mode 1 of the model.

The fundamental features of MJO, including the location of enhanced convection and the maximum and minimum wind fields, are reasonably captured by CAMS-CSM. For example, convection is mainly confined to the Eastern Hemisphere, while the wind fields in the Western Hemisphere retain a large amplitude. The baroclinic structure between the upper and lower winds and their coupling to the convective field, such as the configuration of the upper and lower winds on both sides of the convection, are well simulated by the model. However, the overall variance accounted for by each EOF in the model is smaller than the variance in the observed fields because many climate models have smaller amounts of variance in the convective field than those in the observed field and calculation of the variance of individual fields occupied by EOF, especially for OLR, is recommended. The diagnosis of the explained variance of OLR in each EOF can provide a quantifiable measure for the ability of the model to faithfully simulate the strength of MJO (Waliser et al., 2009). The variance contribution of the filtered OLR is about 12%–18% in the observations, but only 6%–8% in the model, a significant reduction of about 50%. This means that the amplitude of OLR is greatly weakened in the model.

The lead–lag correlation between the time series of the first two principal components (PC) provides a measure of coherence for the eastward-propagating MJO (Fig. 10a). The lag time is the time that it takes for MJO to transition from the Indian Ocean to western Pacific (EOF1 to EOF2 in the observational data or EOF2 to EOF1 in the model) and it is equal to about one-fourth of the period of MJO. In the observational data, we found that the correlation coefficient of PC1 leading PC2 reached a maximum value of 0.77 on day −10 and reached a minimum value of −0.78 when PC1 lagged PC2 on day 10. This indicates that the dominant period is roughly 40 days in the observational data, which is consistent with previous studies (Sperber et al., 2005; Waliser et al., 2009; Subramanian et al., 2011). The model can grasp the lead–lag correlation between the first two principle components and show a roughly 40-day period similar to the observational data, with the absolute value of peak correlation coefficient > 0.6 occurring at ± 10-day lags in CAMS-CSM, which indicates that the model is good at simulating the eastward-propagating characteristics of MJO.

This MCEOF analysis is based on filtered data, which contains some flaws, for example, it may misinterpret the red or white noise of the intraseasonal period as physically meaningful intraseasonal oscillations with a similar structure to the leading EOFs. Therefore, another crucial test of our results is needed to verify whether the two EOF modes derived from the MCEOF analysis are physically meaningful and distinct from noise. Figure 10b also shows the lead–lag correlation of the first two principle components formulated by projecting the unfiltered anomaly data onto the two leading EOFs. Use of unfiltered data has a benefit over use of filtered data as it examines the model’s ability to simulate intraseasonal signals. If a model simulation has a lower frequency variability than the observational data, as shown in Fig. 8, but with a similar spatial pattern to MJO, then this it will be seen in the lead–lag correlation using unfiltered data (Ahn et al., 2017). We can see that the peak correlation between the two principle components decreases sharply in both the observational data and model simulation relative to the results calculated by the filtered data. The dominant timescale of the intraseasonal signal in the model is also larger than that in the observational data, and the minimum and maximum lag coefficients appear on days 10 and −12, respectively. We can conclude from the lead–lag correlation analysis that the model can simulate the MJO timescale well, but on a lower frequency timescale than the observational data, which is in agreement with the results of Fig. 8.

We also investigated whether the extracted MJO modes are significantly distinct from noise by performing a power spectrum analysis of the unfiltered principle components (Fig. 11). If the power spectra for the unfiltered data exhibit statistically significant peaks on the MJO timescale, then the extracted EOFs can be assumed to represent meaningful MJO modes. For the first two principle components in the observations, the spectrum shows a prominent peak on the MJO timescale of 30–80 day, with the explained variances of about 52% and 46%, respectively. A similar peak at the 30–80-day period is also found in the model simulation, with the explained variances of about 37%–39% in both principle components. We also found that the spectral peaks in the MJO band in the model shift toward lower frequencies than those in the observational data.

3.2.3 MJO life cycle composite

Wheeler and Hendon (2004) showed that the leading EOFs are independent of the season. Therefore the life cycle of MJO can be obtained through composite analysis during boreal summer and winter and compared with the model simulations to assess the ability of the model to simulate the phase propagation structures of ISV (Figs. 12, 13). The composite is constructed by using only the days with (PC1² + PC2²) > 1, when MJO is strongly activated.

Observations in winter show that convection originally forms in the western Indian Ocean and is enhanced during the eastward propagation. Convection is weakened when crossing the Maritime Continent, after which it is strengthened again in the western Pacific region, then gradually weakens during further eastward propagation and disappears near the dateline. In general, the model produces a continuous propagation phase associated with MJO, which is similar to the phase distribution in the observational data. We also found that the model reasonably simulates the clear southward detour (Wu and Hsu, 2009), as documented in the observations when MJO passes through the Maritime Continent. CAMS-CSM shows a more organized pattern for OLR and more realistic detour-propagating components across the Maritime Continent than similar composites reported by Subramanian et al. (2011) for CCSM4 and Li et al. (2016) for CESM. Based on the results in Fig. 6, speed of the eastward propagation of convection in the model is slower than that in the observational data. We found a similar bias in the model simulation during the composite analysis of the MJO life cycle. The eastward propagation of convection in the model is slower than that in the observational data in phases 1–3 and then abruptly accelerates in phases 4–6, resulting in a more non-uniform phase speed in the model.

The eastward propagation of MJO in boreal summer is weakened in both the observational data and model, and is not as clear as in boreal winter. It is characterized by the northward propagation of OLR and U850, consistent with the results shown in Fig. 7. From the perspective of coupling between the wind and OLR, the northeasterly propagation is accompanied by the enhanced convection during phases 1–3 of MJO when it enters India and the Bay of Bengal. The convection and wind then spread to the northeast in the vicinity of the South China Sea and Philippine Sea during MJO phases 3–5. CAMS-CSM generally shows a good simulation of the phase propagation characteristics of MJO in boreal summer. However, similar to that in winter, the model’s bias is mainly reflected in the strength of convection, which is weaker in the model than that in the observational data.

4 Role of low-level moistening ahead of MJO convection

In theoretical studies, the conditional instability of the second kind, namely the wave-CISK is considered to be the most important mechanism for maintaining MJO (Wang, 1988; Salby et al., 1994) and requires the presence of moisture in the PBL converging to the east of the area of deep convection. Many studies have documented the vertical structure of MJO (Sperber, 2003; Kiladis et al., 2005; Sperber et al., 2005; Kim et al., 2009; Jiang et al., 2011, 2015; Li et al., 2016), and the low-level convergence of moisture is considered to be a prerequisite of deep convection (Kikuchi and Takayabu, 2004). We therefore explored the moisture process, to which the propagation of MJO is closely related.

Figure 14 shows the vertical–longitudinal profiles of the zonal wind (U), vertical velocity (W), and specific humidity (Q) onto the 20–100-day filtered OLR averaged over the base points of the Indian Ocean (5°S–5°N, 75°–85°E) and western Pacific (5°S–5°N, 135°–140°E) based on lagged-regression analysis. It reveals the association between the vertical structure of the observed moisture content and MJO from the observational data and CAMS-CSM. Since the eastward propagation of MJO is more dominant in winter than that in summer (Figs. 12, 13), our analysis of the vertical structure for eastward propagation only focuses on boreal winter. Low-level moistening ahead of the convection can be clearly seen in both the observational data and model simulations during the evolution of propagation of MJO from the Indian Ocean to western Pacific based on the Indian Ocean base point (Figs. 14a–h). The vertical tilting structure of the U/W wind and top-heavy profile of Q are also well represented in CAMS-CSM. Correct simulation of the vertical structure of these variables is considered to be a key factor in simulating the eastward propagation of MJO (Jiang et al., 2015), which may explain why the MJO propagation can be simulated well in CAMS-CSM. Similar vertical tilting structures and a good model simulation can also be found for the western Pacific base point during the eastward propagation of MJO from western Pacific to the dateline (Figs. 14i–p).

Northward propagation is also noticeable in MJO, especially during boreal summer (Fig. 7). CAMS-CSM shows the northward propagation of MJO based on the Indian Ocean base point, but has difficulty in simulating the slow and continuous propagation of the western Pacific base point. Different capabilities in simulating the northward propagation between the Indian Ocean and western Pacific base points provide an opportunity to illustrate the key physical processes associated with MJO. Figure 15 shows the vertical structures of MJO during its northward propagation. A low-level moistening ahead of convection occurs when MJO propagates north from the equator to near 20°N based on the Indian Ocean base point during lag days 0–15 (Figs. 15a–h). In addition, a clear southward tilt with height is observed in the U/W wind with a westerly (easterly) anomaly on the south (north) side of the convective center. Meridional shear of the zonal wind produces a positive vorticity in front of the convection, resulting in the low-level convergence of moisture, which in turn provides favorable conditions for the northward propagation of MJO. Comparing the simulation results of CAMS-CSM with the observational data, we find that the vertical structures of Q and U/W winds are well represented in the model. A previously reported study has shown that the exact representation of vertical structures in the Q field plays a key part in the ability of the model to simulate the northward propagation of MJO (Neena et al., 2017). In view of the successful simulation of the vertical structure of MJO by using the Indian Ocean base point of CAMS-CSM, the model also shows a good performance in simulating the northward propagation of MJO in the Indian Ocean region (Figs. 7a, b). A much poorer structure is simulated in CAMS-CSM for the western Pacific base point (Figs. 15i–p). Specifically, the simulated Q and U/W winds in the model precede convection much more than those in the observational data during the lag days 0–5, which agrees well with the faster propagation seen in Figs. 7c, d. After lag day 10, the near-disappearance of the convergence of moisture in the model is not conducive to the further northward propagation of MJO, which leads to the poor simulation of northward propagation in western Pacific (Figs. 7c, d).

Figure 14 shows that low-level moisture anomalies usually precede convection in the Indian Ocean and western Pacific, but are usually in phase in the mid- to upper-troposphere. Therefore, the preceding effect of low-level moisture anomalies provides a potential instability layer on the east side of convection, which in turn promotes the eastward propagation of MJO (Hsu and Li, 2012, Adames et al., 2016). We can find the phenomenon known as the MJO detour (Kim et al., 2017) in the life cycle of MJO (Fig. 12), which is characterized by stronger convection in Sumatra, Java, and southern Timor Sea than elsewhere in Indonesia. Successful simulation of the MJO detour in CAMS-CSM provides a good opportunity for us to understand the interaction between the MJO and Maritime Continent. We analyzed the budget of the integral moisture in PBL of the observational data and model to further examine the physical processes of moistening ahead of convection, which is of great significance in understanding the eastward propagation, especially the detour characteristics of MJO, and in improving the model capability to simulate MJO.

The intraseasonal, vertically integrated specific humidity budget can be expressed as

$ \frac{{\partial {{\left\langle q \right\rangle }^\prime }}}{{\partial t}} = - {\left\langle { { V} \cdot \nabla q} \right\rangle ^\prime } - {\left\langle {\omega \frac{{\partial q}}{{\partial p}}} \right\rangle ^\prime } - \frac{{{{Q}_2}'}}{L}, $

where q (g kg⁻¹) is the specific humidity; $ V$ represents the horizontal wind vector (m s⁻¹); p is the pressure level; $\omega $ (Pa s⁻¹) is the vertical pressure velocity; ${Q_2}$ (J kg⁻¹ s⁻¹) is the apparent atmospheric moisture sink; and L (J kg⁻¹) is the latent heat of condensation. The prime symbol (′) indicates an intraseasonal anomaly and the angled brackets denote the vertical integral ( $\left\langle A \right\rangle = 1/g \displaystyle\int_{{p_{\rm t}}}^{{p_{\rm{b}}}} {A{\rm d}p} $ , where p_b = 1000 hPa and p_t = 700 hPa).

Figure 16 shows the lagged regression of the convection and PBL integral (1000–700 hPa) moisture anomalies based on PC1 (model PC2) calculated from Fig. 9. Good coupling between OLR and moisture can be found in both the model and observational data, with the low-level moisture converging ahead of the convection by 0–10 days. As the enhanced convective anomaly propagates toward the Maritime Continent, these areas experience a transition to an enhanced condition in both latitude bands (lag days −15 to 5). Amplitude of the shift is markedly different between the two latitude bands and shows a much stronger transition in the southern Maritime Continent (sMC; 15°–5°S) than that in the central Maritime Continent (cMC; 5°S–5°N). A much slower eastward propagation was found in CAMS-CSM than that in the observational data, with the transition from abnormally dry to wet conditions lasting for about 30 days (lag days −20 to 10). Similar to the observational data, the charging process for PBL moisture in CAMS-CSM is also stronger in sMC than that in cMC, corresponding to a more favorable conditions for development of deep convection in sMC than in cMC. The Maritime Continent therefore undergoes a charging process ahead of convection in both the observational data (lag days −15 to 5) and CAMS-CSM (lag days −20 to 10), and the transition in sMC is stronger than that in cMC.

To address the question of what processes are responsible for the marked contrast during the suppressed–active transition over the Maritime Continent, we examine the PBL integrated moisture budget of MJO during the charging period (Fig. 17). The total tendency of moistening in the observational data and model is greater in sMC than that in cMC, and the largest positive contribution of the difference in moistening comes from the zonal advection of moisture convergence. This is the same as the results from the model. Our budget analysis shows that the zonal moisture advection plays a primary part in the MJO detour. The largest positive contribution of the moistening ahead of convection in the cMC region is the vertical advection of moisture. CAMS-CSM is unable to simulate this factor, and the maximum positive contribution is the meridional advection of moisture. The largest difference between sMC and cMC is the relative contribution of the vertical advection of moisture, which tends to contribute negatively to the low-level moistening in both the observational data and model over the sMC region. In general, the model successfully shows the moistening ahead of the MJO convection, which is reflected in the total tendency of the PBL integral moisture anomalies and relative contribution of each term, especially the zonal advection of moisture convergence, which is related to the MJO detour. Based on the results of the PBL integrated moisture budget of MJO in both the observational data and model, we conclude that the advection of low-level zonal moisture makes the dominant contribution to the difference in moistening between sMC and cMC regions, which may result in the MJO detour over the Maritime Continent.

5 Summary and discussion

MJO has an important influence on the global weather and climate. The simulation of MJO is important in helping us to understand the mechanism of this oscillation and to predict its modulation of both the weather and climate. Climate models are continuously increasing in resolution and improving their ability to solve the physical processes that cause and contribute to ISV. However, many climate models are still unable to accurately represent the basic characteristics of MJO. We evaluated the performance of the 23-yr run of CAMS-CSM to reproduce the main features of MJO based on the diagnostic results established by MJOWG.

We examine the ability of CAMS-CSM to simulate the 20–100-day ISVs, including the seasonality characteristics, regional dependence in winter and summer, wavenumber–frequency, and propagation characteristics. It is found that CAMS-CSM can produce a good simulation of the seasonality characteristics of ISV of precipitation and U850. In view of the seasonal differences in the distribution of ISV, we further assess the model’s ability to simulate the regional dependence of ISVs in winter and summer. In general, the regional centers, distribution characteristics, and amplitude of ISV of precipitation and U850 are well represented by the model in both winter and summer. The model simulation of U850 is better than that of precipitation, and the model bias in simulating precipitation is concentrated in western Pacific, showing a double ITCZ structure. ISV signals often occur in a strong westerly wind, a weak easterly wind, and where there is abundant precipitation over the ocean. The double ITCZ bias embodied in the model, which is characterized by excessive precipitation over the Northern Hemisphere ITCZ and South Pacific convergence zone, also leads to overestimate of the amplitude of ISV precipitation in this region, further confirming the dependence of the ISV signal on climatic mean state. Thus a realistic mean state of precipitation in a model is required to give a realistic simulation of MJO.

Wavenumber–frequency spectral analysis is applied to the anomalies in precipitation, OLR, and U850 during boreal winter. The results show that the model gives a good simulation of the dominant frequency (30–80 days) of MJO and wavenumbers 1–3 in the zonal direction. Although the model can show the main characteristics of MJO scales, such as the intraseasonal signals and eastward propagation, there are some systematic deviations. The model bias is mainly manifested in a weaker eastward propagation, lower frequency peak spectra, and smaller zonal scales. Based on the lagged regression method, the ability of the model to simulate the eastward propagation of MJO in winter and its northward propagation in summer is evaluated. The results indicate that the model can simulate the eastward propagation of ISV of OLR and U850 in winter well, but the speed of propagation is slower than that seen in the observational data. The model simulates the northward propagation of MJO in summer moderately well, indicating that there is still room for improvement.

We also evaluate the ability of the model to simulate the coupling feature of MJO and analyze the cross-spectra between OLR and U850 in both the observational dataset and model. The results demonstrate that the model simulation can capture the eastward propagation of MJO, but the spectrum shifts toward lower frequencies and becomes less coherent than the observational data. Furthermore, the MCEOF method is applied to evaluate the ability of the model to simulate MJO. The baroclinic structure of the wind field and coupling characteristics between the wind field and OLR are simulated well in the model, but OLR is weaker than that in the observational data with a smaller explained variance. From the lead–lag correlation analysis of the principle components obtained by MCEOF, we conclude that the model successfully simulates the MJO timescale, proving that it is physically meaningful. In addition, we can obtain the life cycle of MJO through composite analysis by using the principle component obtained by MCEOF. In general, CAMS-CSM generates a realistic succession of MJO phases, close to those from the observational data. However, the eastward propagation of convection is slower during phases 1–3 of MJO than that in the observational data. It then suddenly accelerates in phases 4–6, resulting in a more uneven phase speed in the model.

Moreover, we analyze and evaluate the impact of the moisture process on the eastward/northward propagation of MJO. Through composite analysis of the vertical structure of moisture content, it is found that the low-level moisture anomaly shows a pronounced tilting structure during the life cycle of MJO, which is well represented by the model, again showing the excellent simulation of MJO by the model. Budget analysis of the integral moisture anomaly shows that the dominant contribution of the MJO detour comes from the zonal advection of moisture convergence. CAMS-CSM successfully simulates this moisture charging process and thus can better reproduce the MJO detour during eastward propagation.

As an important factor affecting the global weather and climate, MJO can be considered as a link between weather forecasting and seasonal predictions and can be used as a major resource in extended-range forecasting. Despite of the fact that considerable progress has been achieved in recent decades in the development of climate and weather forecasting models, MJO is still poorly simulated in state-of-art models. Great challenges in the MJO simulation and prediction suggest that our knowledge of the fundamental physics and maintenance mechanism of MJO is still both inadequate and ambiguous. In particular, the propagation of MJO through the Maritime Continent has become a major challenge in current climate models due to its complex topographical distribution. Therefore, a detailed understanding and accurate simulation of the complex processes of interactions between the MJO and Maritime Continent are essential in successful mid-range weather forecasting. More sensitivity experiments are needed to diagnose the connection between the Maritime Continent and MJO to illustrate the influence of the terrain of the Maritime Continent on MJO. This will be the direction explored in our future work.

Acknowledgments. The authors thank the Chinese Academy of Meteorological Sciences for providing the model data. The authors also thank the two reviewers for their constructive comments on this paper.