This study examines the roles of shallow convection in the eastward propagation of the Madden–Julian oscillation (MJO) using new and old versions of the Model for Interdisciplinary Research on Climate, versions 6 and 5 (MIROC6 and MIROC5), respectively. A major modification of MIROC6 from its previous version, MIROC5, is the implementation of the shallow convection scheme following Park and Bretherton. The MJO representation in MIROC6 is improved compared to MIROC5. The MJO convective envelopes that occur over the Indian Ocean, which decay too early over the western Pacific in MIROC5, propagate farther into the eastern Pacific in MIROC6. In the initial stage of the MJO development, the shallow convection transports boundary layer moisture upward forming an important moisture source for the lower free troposphere in MIROC6. In the mature stage of the MJO, the deep convection becomes increasingly active with the large amount of moisture in the free troposphere. Accordingly, the moisture anomalies associated with the MJO show an upward- and westward-tilted structure, as in the observations. Conversely, MIROC5 exhibits a dry bias in the lower free troposphere, suggesting that the shallow convective activity is underestimated. A parameter perturbation experiment, modifying the intensity of shallow convection, confirms that enhanced shallow convection reduces the moisture bias in the lower free troposphere and improves the simulation of the MJO in MIROC6.
The Madden–Julian oscillation (MJO) is the dominant atmospheric variability of convective envelopes that are propagating eastward along the equator (Madden and Julian 1972). It exerts a strong influence on many climate phenomena, such as tropical cyclones, El Niño–Southern Oscillation, monsoons, and precipitation extremes [see reviews by Lau and Waliser (2012)]. A realistic MJO representation in a climate model is crucial for seasonal predictions and future climate projections of these phenomena (e.g., Vitart et al. 2012).
The MJO structure has been extensively examined in many previous studies (e.g., Kikuchi and Takayabu 2004; Del Genio et al. 2012). In front of the eastward-propagating MJO envelope (or in the developing stage of the MJO), the free atmosphere is relatively dry and shallow convection (a cloud-top height of approximately 800 hPa) is dominant. In the MJO envelope, deep convection (a cloud top near the tropopause) is very active and stratiform anvils spread behind the envelope, forming an organized convective system. Accordingly, the moisture anomalies associated with the MJO show an upward- and westward-tilted structure (Kikuchi and Takayabu 2004; Del Genio et al. 2012). MJO convection is strongly coupled with large-scale circulations. The convective heating forces a Rossby wave response to the west and a Kelvin wave response to the east (Gill 1980). The associated moisture convergence in the lower troposphere occurs slightly to the east of the MJO convective center, which is thought to be important for the eastward propagation (Kim et al. 2009; Kiranmayi and Maloney 2011; Hung et al. 2013). An important next step is to identify the moisture source of the free troposphere.
Despite the efforts of previous studies, the MJO remains poorly represented in climate models (Lin et al. 2006; Kim et al. 2009; Jiang et al. 2015). For example, Hung et al. (2013) examined 20 state-of-the-art climate models from phase 5 of the Climate Model Intercomparison Project (CMIP5) and demonstrated that approximately one-third of the models show a spectral peak period of approximately 20–90 days corresponding to the MJO. However, even in these relatively good models, the MJO amplitude is largely underestimated compared to observations and its eastward propagation is not well reproduced. Some studies suggest representations of shallow convection are important for realistic MJO simulations (e.g., Zhang and Song 2009; Del Genio et al. 2012; Jiang et al. 2015; Plant and Yano 2015; Pilon et al. 2016; Cao and Zhang 2017). In models with better MJO, the shallow convection transports boundary layer moisture upward to the free troposphere. This serves to precondition the troposphere by providing moisture for deep convection. The transition from shallow to deep convection with the upward- and westward-tilted moisture structure is thought to be a key factor for realistic MJO simulations (Zhang and Song 2009; Pilon et al. 2016; Cao and Zhang 2017).
Recently, a new version of the atmosphere–ocean general circulation model, known as the Model for Interdisciplinary Research on Climate, version 6 (MIROC6), has been cooperatively produced by the Japanese research community (H. Tatebe et al. 2017, unpublished manuscript). One of the major modifications from its previous version, MIROC5 (Watanabe et al. 2010), is the implementation of a shallow convection scheme. MIROC5 was categorized as one of the good CMIP5 models in the MJO evaluation of Hung et al. (2013); however, some deficiencies remain: the MJO amplitude is underestimated and its eastward propagation from the Indian Ocean decays too early in the western Pacific. In this study, we examine the roles of shallow convection in the MJO by comparing MIROC5 and MIROC6. In particular, we focus on the MJO eastward propagation over the Indian Ocean and across the Pacific. The model and the data used in this study are described in section 2, the results are provided in section 3, and a summary and discussion are presented in section 4.
2. Models and data
The models used in this study are MIROC5 (Watanabe et al. 2010) and MIROC6 (H. Tatebe et al. 2017, unpublished manuscript), which were developed jointly at the University of Tokyo, the National Institute for Environmental Studies, and the Japan Agency for Marine-Earth Science and Technology. The horizontal resolution of the atmosphere is T85 spectral truncation (~1.4°) in both models. The vertical resolution in MIROC6 is increased to 81 levels with the model top of 0.004 hPa compared to the 40 levels with the model top of 3 hPa in MIROC5.
In MIROC5, the cumulus ensemble including shallow convection, midheight convection (a cloud top near 600 hPa), and deep convection is calculated based on Chikira and Sugiyama (2010). In this scheme, the tendency of the convective activity is proportional to the cloud work function, which is a measure of the atmospheric instability. While this scheme represents deep convection reasonably well, it underestimates shallow convection (Chikira and Sugiyama 2013). In addition to the Chikira and Sugiyama scheme, the shallow convection scheme following Park and Bretherton (2009) is implemented in MIROC6. In this scheme, the cloud-base mass flux is dependent on the turbulent kinetic energy in the subcloud mixed layer. In MIROC6, shallow convection associated with the atmospheric instability is calculated in the Chikira and Sugiyama scheme, and that associated with the turbulent energy is represented in the Park and Bretherton scheme. The low-top cloud distribution is significantly improved in MIROC6 compared to MIROC5 (H. Tatebe et al. 2017, unpublished manuscript). The differences between MIROC5 and MIROC6 described above are summarized in Table 1. This study compares the MJO in the standard climate (preindustrial control) simulations of MIROC5 and MIROC6 (H. Tatebe et al. 2017, unpublished manuscript). We analyze 30-yr data from each experiment to examine the MJO features in the annual mean climatology.
The observational reference of outgoing longwave radiation (OLR) used in this study is the daily product from the Advanced Very High Resolution Radiometer (AVHRR; Liebmann and Smith 1996). The OLR is a measure of the deep convective activities. The zonal wind, vertical pressure velocity, temperature, specific humidity, and relative humidity are obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-I; Dee et al. 2011) and the Japanese 55-year Reanalysis (JRA-55; Kobayashi et al. 2015). The results using ERA-I and JRA-55 are qualitatively similar; thus, only figures using ERA-I are shown here. We analyze the datasets of AVHRR and the reanalysis during the period of 1980–2009. All data used are linearly interpolated onto spectral T85 horizontal Gaussian grids to allow comparisons to be made.
We first investigated various equatorial waves in the atmosphere by calculating the zonal wavenumber–frequency power spectra of the OLR following Wheeler and Kiladis (1999) (H. Tatebe et al. 2017, unpublished manuscript). The signals corresponding to the MJO, equatorial Kelvin (EK), and equatorial Rossby (ER) waves stand out from the background spectra in the observations. MIROC5 qualitatively reproduces these spectral maxima; however, the amplitudes of the MJO and the EK waves are underestimated. These underestimations are partially mitigated in MIROC6. The power summed over the eastward wavenumbers 1–3 and the periods of 30–60 days corresponding to the MJO are increased by 20%.
Next, we examined the MJO, which was defined using a combined empirical orthogonal function (CEOF) analysis of the OLR and the zonal wind at 200 and 850 hPa around the equator (15°S–15°N) based on Wheeler and Hendon (2004). We applied a 20–100-day bandpass filter to each variable to extract the intraseasonal variabilities prior to the CEOF analyses. The first and second modes of the CEOF for AVHRR and ERA-I, MIROC5, and MIROC6 are shown in Fig. 1. One of the two modes shows negative OLR (enhanced convection) with lower-level convergence and upper-level divergence around the Maritime Continent (~120°E), and the other mode shows positive OLR with lower-level divergence and upper-level convergence over the Indian Ocean (~90°E). The principal component (PC) of one mode leads the other mode by a one-quarter cycle (not shown) indicating that these modes constitute the eastward-propagating MJO. The variance explained by these MJO modes is 44% in AVHRR and ERA-I, 26% in MIROC5, and 32.2% in MIROC6. The amount of underestimated explained variance of the MJO modes accounted for in MIROC5 is slightly enhanced in MIROC6. The enhanced spectral power corresponding to the MJO, the larger explained variance of the MJO modes, and the following analyses of the MJO events suggest that the MJO representations in MIROC6 are improved compared to MIROC5.
Composites of the MJO events extracted from the 30-yr data were examined. The MJO events were selected as days when the amplitude defined as (PC12 + PC22)1/2 was greater than 1.5 standard deviations and was maximum during the previous seven days and the following seven days. We further classified these events into eight phases with different locations of the MJO convection depending on the sign and magnitude of PC1 and PC2 (Wheeler and Hendon 2004). For example, phase 3 is when PC1 > 0, PC2 < 0, |PC1| < |PC2|, and the MJO convection is located near the eastern Indian Ocean (Figs. 2 and 3). The number of events for each phase is approximately 30–40, which is sufficient to analyze the climatological features of the MJO.
Figures 2a,d show the anomalies of the OLR and the zonal wind at 850 hPa associated with the composite of the MJO events for AVHRR and ERA-I. In phase 1, the anomalies of the negative OLR are identified over the Indian Ocean and these convective signals propagate eastward over the Indian Ocean and the Pacific Ocean with the phase (time). Corresponding westerly and easterly anomalies are located to the west and the east of the convective center, respectively. MIROC5 shows similar eastward propagation of the MJO over the Indian Ocean to the Maritime Continent; however, the OLR anomalies are positive near 180° longitude for phases 6–7 (Fig. 2e). This early dissipation of the MJO signals is a common problem for many CMIP5 models (Hung et al. 2013). Conversely, the MJO signals in MIROC6 continue to propagate across the Pacific (Fig. 2f), as in the observations.
The life cycles of the MJO events were examined via the PC1 and PC2 phase space diagram, as shown in Fig. 3. Each trajectory starts when the MJO amplitude is maximum and shows the time evolution of the PCs for the subsequent 40 days. For all the phases, AVHRR and ERA-I and the models show counterclockwise trajectories toward the center indicating that the MJO propagates eastward as its amplitude decays. For phase 1, the trajectories of AVHRR and ERA-I and MIROC6 are very similar whereas that of MIROC5 decays too early. A lifetime, defined as the time for the MJO amplitude to be one standard deviation, is 19.6 days in AVHRR and ERA-I, 15.9 days in MIROC5, and 19.4 days in MIROC6. In addition, for the other phases, MIROC5 generally shows dissipation that occurs too early and MIROC6 shows outer trajectories that are more like the observations.
The vertical structure of the MJO events was investigated by examining the pressure–phase diagram of the specific humidity and the apparent heat source (Q1) averaged over the Maritime Continent and the western Pacific (15°S–15°N, 130°–170°E). Q1 is defined as
where u is horizontal wind vector, ω is vertical velocity, T is temperature, and Sp is a static stability parameter (Yanai et al. 1973). It includes latent heating associated with convection, turbulent heat transport, and the radiative heating. As shown in Fig. 4, ERA-I shows gradual moistening in the lower troposphere around 800 hPa from phases 2 to 4, and the maxima of Q1 in the boundary layers suggests active shallow convection. When the free troposphere is sufficiently moist near phase 5, deep convection with large Q1 near 500 hPa occurs. Because the MJO propagates eastward, this upward- and backward-tilted vertical structure corresponds to the upward- and westward-tilted structure (not shown) that was considered important for the MJO representations in previous studies (e.g., Del Genio et al. 2012; Jiang et al. 2015).
MIROC5 reproduces the tilted vertical structure to some extent with a deepening of the moist free troposphere from phases 2 to 5. However, the moistening starts near 700 hPa in MIROC5 and 900–750 hPa is dry compared to the reanalysis. The midheight convection seems to be active instead of the shallow convection in the initial developing stage of the MJO. These biases are consistent with Chikira and Sugiyama (2013) who saw overestimated midheight convection and underestimated shallow convection in their scheme. In MIROC6, the dry bias around 900–750 hPa is partially mitigated and the tilted moisture structure becomes more realistic. The moist bias near 700 hPa in MIROC5 is also somewhat alleviated but remains in MIROC6. This issue will be discussed in section 4.
The moisture budget analyses associated with the MJO events were performed over the Maritime Continent and the western Pacific as shown in Fig. 5. Apparent moisture source (Q2) including moistening (and evaporation) associated with convection, cloud, and turbulent processes is calculated as
where q is specific humidity (Yanai et al. 1973). The moisture anomalies shown in Fig. 4 generally correspond to the vertical advection in ERA-I, MIROC5, and MIROC6. Although horizontal wind converges in the lower troposphere near the MJO convective center (Fig. 2), the horizontal advection is not positive because the moisture gradient is positive along the wind direction (). Q2 is negative near the convective center mainly because of condensation processes associated with deep convective activities. These results do not mean that the horizontal moisture transport and the convective activities are not important because they are closely related with the vertical advection. The moisture transported horizontally in the lower troposphere is vertically transported resulting in the positive vertical advection. The vertical motions causing the vertical advection are largely driven by the convective heating.
Figure 6 shows the moistening by the shallow convection scheme, the Chikira and Sugiyama (2010) convection scheme, the turbulent mixing scheme, and the cloud physics scheme in MIROC6. In the developing stage of the MJO (phases 2– 4), the turbulent mixing scheme provides the moisture around 1000–750 hPa. The moistening by shallow convection shows negative values in the boundary layers and positive values around 900–600 hPa indicating that the shallow convection transports boundary layer moisture upward to the lower free troposphere. Note that the shallow convection also contributes to the lower-tropospheric moisture indirectly by influencing the vertical advection and the turbulent mixing processes as will be discussed later in this section (e.g., see Fig. 12).
Figure 7 shows the vertical structure of the specific humidity and Q1 over the Indian Ocean (10°S–10°N, 70°–120°E), where the MJO propagates eastward in both MIROC5 and MIROC6. These vertical structures are qualitatively similar to those over the Maritime Continent and the western Pacific described above (Fig. 4). The dry bias around 900–750 hPa in MIROC5 is mitigated in MIROC6, although the maximum in the humidity anomalies extend too high near 650 hPa in the initial stage of the MJO development in both models. It is interesting that the MJO in MIROC5 propagates eastward over the Indian Ocean despite the dry bias around 850 hPa. This may occur because the roles of moisture in the MJO propagation are somewhat different over the Indian Ocean and the western Pacific. These regional dependencies of the MJO will be explored in future studies.
We further verified that the shallow convective moistening alleviates the dry bias in the lower free troposphere by examining the climatological mean state. Figure 8 shows the specific humidity bias relative to ERA-I in the annual mean climatology. The dry bias is located over the Indian Ocean to the western Pacific around 900–750 hPa in MIROC5 and is largely reduced in MIROC6. The moisture budget of the climatological mean state for the difference between MIROC5 and MIROC6 is examined in Fig. 9. Note that MIROC5 does not have the shallow convection scheme of Park and Bretherton (2009); thus, the shallow convective heating shown here is that for MIROC6. The moistening by the shallow convection scheme shows negative values below 850 hPa and positive values around 850–600 hPa (Fig. 9c) indicating that the shallow convection transports the boundary layer moisture upward to the lower free troposphere. The anomalous drying of the boundary layers is counteracted by the moistening by the turbulent mixing scheme around 950 hPa (Fig. 9e) and the Chikira and Sugiyama (2010) convection scheme below 800 hPa (Fig. 9d). These results suggest that the shallow convection scheme is responsible for the reduced dry bias in the lower free troposphere in MIROC6 compared to MIROC5.
Finally, we perform sensitivity experiments, in which intensity of shallow convection is artificially controlled by modifying specified values for parameter “kfp” in the shallow convection scheme. The kfp is an empirical parameter describing the partitioning of TKE between horizontal and vertical motions (Bretherton et al. 2004). The larger kfp increases the cloud-base mass flux and its moisture transport. Figure 10 shows annual mean heating (temperature tendency) by the shallow convection scheme around the equator (15°S–15°N, all longitudes) for the kfp values of 0.2, 0.3, 0.5, 0.7, and 0.8. The shallow convective heating is evident around 950–800 hPa, and its magnitude increases with the kfp value. Here, we show results of sensitivity experiments with kfp values of 0.3 (kfp03) and 0.7 (kfp07) in comparison with the MIROC6 standard experiment with kfp value of 0.5. Because these sensitivity experiments and the MIROC6 standard experiment are identical except for the kfp parameter in the shallow convection scheme, anomalies of kfp03 and kfp07 relative to MIROC6 indicate the impacts of the weakened and strengthened shallow convective activities, respectively.
Figures 11a and 11b show the longitude–phase diagrams of the OLR and the zonal wind at 850 hPa for kfp03 and kfp07, respectively. The OLR signals of the MJO events in kfp03 dissipate in the western Pacific as in MIROC5, whereas those in kfp07 continue to propagate over the Pacific as in MIROC6. The results clearly demonstrate that intensity of shallow convection controls the MJO propagation in this model. Figures 11c and 11d show the specific humidity bias relative to ERA-I. The humidity in the troposphere is generally underestimated in kfp03 and overestimated in kfp07.
Figure 12 shows anomalies of the moisture budget for kfp03 relative to MIROC6 (kfp05). Consistent with the less active shallow convection in kfp03, the anomalies of moistening by the shallow convection scheme are smaller at 750–600 and 900–850 hPa. The moistening anomalies by the Chikira and Sugiyama (2010) scheme, the turbulent scheme, and cloud physics scheme also show large value, and balance with the horizontal and vertical advection anomalies. Since the kfp value is used only in the shallow convection scheme, these differences in the other schemes and the advection are induced by the modified shallow convection. The moisture budget anomalies for kfp07 relative to MIROC6 are essentially opposite of the kfp03 anomalies discussed above (Fig. 13). These results demonstrate that the lower-tropospheric moisture is largely controlled by the parameter in the shallow convection scheme in MIROC6.
4. Summary and discussion
A new version of the Model for Interdisciplinary Research on Climate, version 6 (MIROC6) has recently been developed (H. Tatebe et al. 2017, unpublished manuscript). A major modification from the previous version, MIROC5, is the implementation of a shallow convection scheme based on Park and Bretherton (2009). This study investigated the role of moistening by shallow convection in the improved model representation and eastward propagation of the MJO by comparing results from MIROC5 to those from MIROC6. In addition, two sensitivity experiments, where the activities of shallow convection are reduced (kfp03) and enhanced (kfp07), were performed to further examine the impacts of shallow convection.
The representations of the MJO are improved in MIROC6. The MJO convective envelopes that occur over the Indian Ocean, which decay too early over the western Pacific in MIROC5, propagate farther into the eastern Pacific. In the initial stage of MJO development, the shallow convection transports boundary layer moisture upward and is an important moisture source for the lower free troposphere. In the mature stage of the MJO, the deep convection becomes more active with the large amount of moisture in the free troposphere. Accordingly, the moisture anomalies associated with the eastward-propagating MJO show an upward- and westward-tilted structure similar to the reanalysis. Conversely, MIROC5 underestimates shallow convective activity with a dry bias in the lower free troposphere, which presumably cause the early dissipation of the MJO in the western Pacific. The shallow convection in MIROC6 also removes the dry bias in the climatological mean field over the Indian Ocean and the western Pacific.
Previous studies have suggested that the model’s ability to simulate the MJO is closely related to the coupling strength of the convection and the tropospheric moisture (e.g., Kim et al. 2014; Hirota et al. 2014). Following Kim et al. (2014), we examined vertical profiles of the relative humidity stratified against the daily precipitation intensity, as shown in Fig. 14. Strong precipitation occurs when the troposphere is very moist, while weak precipitation dominates when the free troposphere is dry. These general features are common in ERA-I, MIROC5, and MIROC6. However, the humidity profiles for strong precipitation in MIROC5 are very dry near 750–850 hPa and very moist near 700–650 hPa compared to ERA-I, consistent with the previous results in Figs. 4 and 7. The shallow convection in MIROC6 reduces the dry bias in the lower free troposphere and the humidity profiles for strong precipitation are more realistic. We suggest that not only the coupling strength but also the moisture profiles with realistic convection heights are important for improving the MJO simulations. Even though previous studies showed that the coupling strength can be tuned in many ways (e.g., changing the convective entrainment rate or the raindrop evaporation; Kim et al. 2011), we see that the MJO improvements in MIROC6 are achieved via the shallow convection scheme, which was well documented in previous studies (Park and Bretherton 2009).
MIROC6 shows overestimated moisture anomalies near 700 hPa (Figs. 4, 7, and 14). This bias is produced by the overestimated midheight convection in the convection scheme of Chikira and Sugiyama (2010). This is likely because our model calculates the Chikira and Sugiyama scheme before the shallow convection scheme of Park and Bretherton (2009). The atmospheric instability that should be reduced by shallow convective mixing causes an overestimation of the midheight convection. Note that the convective activity of the Chikira and Sugiyama scheme is related to the cloud work function, whereas that in the Park and Bretherton scheme is dependent on the turbulent kinetic energy in the subcloud mixed layers. The convective triggering conditions and/or the order of the calculations will be examined in future developments of the model.
The authors thank Dr. Takahito Kataoka for conducting the sensitivity experiments of MIROC6. This study was supported by the Integrated Research Program for Advancing Climate Models and KAKENHI (15H02132) of the Ministry of Education, Culture, Sports, Science, and Technology, Japan, and by the Environment Research and Technology Development Fund (2-1503) of the Environmental Restoration and Conservation Agency, Japan. The Earth Simulator at JAMSTEC and NEC SX-ACE at NIES were used to perform the model simulations. The Grid Analysis and Display System was used to plot the figures.