MJO Propagation Across the Maritime Continent: Are CMIP6 Models Better Than CMIP5 Models?

Many climate models struggle with a poor simulation of the Madden‐Julian Oscillation (MJO), especially its propagation across the Maritime Continent (MC). This study quantitatively evaluates the robustness of MJO propagation over the MC in climate models that participated in Coupled Model Intercomparison Project Phase 5 (CMIP5) and Phase 6 (CMIP6) with a newly developed MC propagation metric. The results show that the CMIP6 models simulate MJO propagation over the MC more realistically than the CMIP5 models. Lower free‐tropospheric moisture budget analysis highlights that the greater horizontal moisture advection is responsible for the enhanced MJO propagation over the MC. The increase in horizontal moisture advection in the CMIP6 models is mainly attributed to the steeper horizontal mean state moisture gradient around the MC, which is associated with the reduction of the equatorial dry bias.


Introduction
The Madden-Julian Oscillation (MJO, Madden & Julian, 1971, 1972) is a planetary-scale, eastward propagating envelop of tropical convection that is tightly coupled with large-scale circulation. The MJO influences a wide range of weather and climate phenomena not only in the tropics but also in the midlatitude and high-latitude regions by its teleconnections (see a review by Zhang, 2013). For example, when the MJO convection is located over the Western Pacific, the frequency of flood events increases over the Philippines and the West Coast of North America (Bond & Vecchi, 2003;Zhang, 2013), tropical cyclones occur more frequently over the Western Pacific (Klotzbach, 2014;Zhang, 2013), and more frequent westerly wind burst events occur in the Western Pacific that can trigger El Niño development (Hendon et al., 2007;Zhang, 2013).
The Indo-Pacific Maritime Continent (MC), the largest archipelago on Earth, resides between the Indian Ocean and the Western Pacific. This is an important region regarding the MJO's life cycle and its teleconnections. Because more than one half of all MJO events initiate over the Indian Ocean (Zhang & Ling, 2017), whether an MJO event successfully passes through the MC determines the longevity and zonal extent of the event. Also, MJO teleconnections to the extratropics have been shown to intensify while the MJO convection is propagating over the MC (Adames & Wallace, 2014;Bao & Hartmann, 2014). Therefore, for a climate model to accurately simulate the impacts of the MJO on the global weather-climate system, it must realistically represent MJO propagation across the MC.
Unfortunately, however, many contemporary climate models fail to simulate realistic MJO propagation across the MC (Ahn et al., 2017;Hung et al., 2013;Jiang et al., 2015;Kim et al., 2009;Lin et al., 2006;Ling et al., 2019) and this bias has been pervasive over recent generations of climate models participating in the Coupled Model Intercomparison Project (CMIP). Lin et al. (2006) and Hung et al. (2013) analyzed CMIP3 and CMIP5 models, respectively, using the same lag-regression diagnostic of precipitation anomalies to examine the MJO propagation. When considering propagation through 150°E longitude as a criterion of MJO fidelity over the MC in the lag-longitude diagram, only 4-5 out of 14 (28-36%) CMIP3 models show realistic MJO propagation across the MC (Lin et al., 2006), and only 4-7 out of 20 (20-35%) CMIP5 models satisfy this criterion (Hung et al., 2013). As the CMIP6 models are newly released, there is a critical need to analyze the CMIP6 models to examine whether they are better than the CMIP5 models in the simulation of the MJO propagation across the MC.
In support of community efforts to establish objective tests to gauge how well climate models represent various observed characteristics (e.g., Baker & Taylor, 2016;Flato et al., 2013;Gleckler et al., 2008;Gleckler et al., 2016;Lee et al., 2019), a diverse collection of community-based MJO simulation diagnostics and metrics has been developed to capture the prominent characteristics of the MJO (Kiladis et al., 2014;MJOWG, 2009;Sperber & Kim, 2012;Wheeler & Hendon, 2004;Wheeler & Kiladis, 1999;Zhang & Ling, 2017). However, to date, little attention has been given to quantifying the robustness of MJO propagation over a specific region. We propose a new metric that focuses on the MJO's behavior over the MC, which will then be utilized to quantitatively evaluate the CMIP5 and CMIP6 models.
As it will be shown that there is a robust improvement in the representation of MJO propagation over the MC in the CMIP6 models, another goal of the present study is to understand the difference between the two model generations (CMIP5 vs. CMIP6) in the context of the moisture mode framework. In the moisture mode framework, the propagation and maintenance of the MJO are understood by diagnosing the physical factors that give rise to the moisture anomalies (Adames et al., 2020;Adames & Kim, 2016;Fuchs & Raymond, 2017;Raymond & Fuchs, 2009;Sobel & Maloney, 2013). We will analyze the moisture budget of the MJO in CMIP5 and CMIP6 models to identify the processes responsible for the differences in MJO propagation between the two model groups.

MC Propagation Metric
We propose a new metric that is designed to indicate the robustness of MJO propagation over the MC. The metric, which will be called the "MC propagation metric," is obtained from one of the popular MJO simulation diagnostics: the lag-regression diagnostic. To yield a diagram that shows the behaviors of anomalous convection before and after it peaks over the Indian Ocean, 10°S to 10°N averaged intraseasonal (i.e., 20-100days band-pass filtered) precipitation anomalies are regressed against a reference Indian Ocean (85-95°E and 5°S to 5°N) intraseasonal precipitation time series and the results are plotted in a lag-longitude diagram ( Figure 1). From the lag-longitude diagram, the positive regression coefficients over the MC area (100-150°E) and over 0-25 lag days are summed. The sum is then normalized by the TRMM observed value to yield the MC propagation metric (Figure 2).

Moisture Budget Analysis
The moisture budget of the MJO is analyzed to understand the moisture evolution associated with the MJO. Two vertical levels in the low free troposphere-850 and 700 hPa-are used. The low free-tropospheric moisture is tightly coupled to MJO convection in the intraseasonal time scales and the MJO-associated moisture anomaly peaks around 700 hPa (Adames & Wallace, 2015;Kiladis et al., 2005;Sperber, 2003). The low free-tropospheric moisture equation for MJO anomalies is written as follows: where q, u, v, and ω are the specific humidity, zonal velocity, meridional velocity, and vertical pressure velocity, respectively. C and E are the condensation and evaporation. The angled bracket indicates a mass weighed integral from 850 to 700 hPa, and the prime indicates MJO anomalies. The MJO anomalies are obtained from the lag-regression analysis of each intraseasonal moisture budget term against the same Indian Ocean reference time series that is used for the lag-regression diagnostic in Figure 1. The tendency, zonal and meridional advection terms are calculated using available model output variables, and the sum of the other terms is obtained as a residual. Figure 1 shows the lag-longitude diagrams for TRMM, and for 30 CMIP5 and 34 CMIP6 models. Also shown in Figure 1 are the multimodel mean of the diagrams for the two model groups (Figures 1b and 1c). In the TRMM observations the MJO's eastward propagation is clearly seen from the Indian Ocean to the Western Pacific with a propagation speed of about 5 m/s. Over the MC region and for the positive lag days, the regression coefficients are greater than 0.2 in many longitude points over several days.
When averaged over the two model groups, the CMIP5 multimodel mean shows weaker eastward propagation over the MC region in the positive lag days, with the regression coefficients showing values near 0.1. The lag-longitude diagram for the CMIP6 multimodel mean is much closer to the observations in its pattern and 10.1029/2020GL087250
The multimodel mean values of the MC propagation metric show significant improvement in the CMIP6 models over the CMIP5 models. The multimodel mean value of the CMIP6 models is 0.85, while that of the CMIP5 models is 0.69. The difference between the two mean values is statistically significant at the 90% confidence level, but not at the 95% confidence level (p value~0.06). Also, the intermodel spread is reduced by about 23% in CMIP6 (0.30) compared to CMIP5 (0.39) although the number of CMIP6 ensemble is larger. These results indicate that the representation of MJO propagation is notably improved over the MC area in the CMIP6 models compared to the CMIP5 models.

Geophysical Research Letters
The low free-tropospheric moisture budget analysis is performed as described in section 2.3 to understand the improved simulation of MJO propagation in CMIP6 models from a moisture mode framework point of view. Figures 3a and 3b show intraseasonal precipitation (shading) and low free-tropospheric moisture tendency (contours) anomalies that are associated with MJO. When the center of enhanced MJO convection is located over the eastern Indian Ocean, positive low free-tropospheric moisture tendencies (solid contours) appear over the southern MC and the Western Pacific in both model generations. However, the moisture tendency to the south of Sumatra and Java Islands is much greater in the CMIP6 models than in the CMIP5 models. The difference between the two model groups in that area is statistically significant at the 95% confidence level (Figure 3c). The greater amount of moisture recharging over the southern MC area would provide a favorable condition for MJO propagation over the MC region in the CMIP6 models.
In Figure 3d, we compare the moisture budget terms over the southern MC area (95-120°E and 15-7.5°S, red box in Figures 3a-3c) between the two model groups. In the CMIP6 models, the total moisture tendency is about 2 times larger than that in the CMIP5 models, consistent with the above results. The zonal and meridional advection terms show positive values, indicating that horizontal moisture advection is the main recharging mechanism in this region before the onset of MJO convection. They also exhibit a larger value in the CMIP6 models, suggesting that the horizontal advection process is responsible for the difference in total moisture tendency. The sum of other terms and residual (right most bars in Figure 3d) is similar in the two model groups; thus, it is unable to explain the difference in the total moisture tendency. The results of the moisture budget analysis strongly suggest that MJO propagation in the MC area is more realistic in the CMIP6 models due to the greater rate of moisture recharging from the zonal and meridional advection processes. Figure S1 shows that in both model groups the horizontal advection is mainly determined by the advection of mean state moisture by MJO perturbation wind, which is consistent with previous studies (e.g., Ahn et al., 2020;Kim et al., 2017;Jiang, 2017;Kim et al., 2014;Kim, 2017;Kiranmayi & Maloney, 2011). This suggests that the difference in the horizontal advection terms between the CMIP5 mean and the CMIP6 mean is likely due to the difference in the mean state moisture gradient. We show in Figures 4a-4c the low free-tropospheric mean state moisture from ERA5 and from the simulations. Compared to ERA5, the CMIP5 multimodel mean exhibits a notable dry bias over the Indo-Pacific Warm Pool region, especially near the equator. The dry bias in the CMIP5 models has been reported in previous studies (e.g., Takahashi, 2018). The dry bias is remarkably improved in the CMIP6 multimodel mean. The root-mean-square error (RMSE) of the mean state moisture over the Indo-Pacific area (60-180°E and 20°S to 20°N) is also about 34% lower in CMIP6 (1.13) than in CMIP5 (1.72). The mean moisture difference between CMIP5 and CMIP6 models is statistically significant at the 95% confidence level over most of the Indo-Pacific Warm Pool region (Figure 4d).
The increase in the mean state moisture has direct implications for the gradient of the mean state moisture; a dry bias peaking near the equatorial MC would weaken the horizontal gradient, while removing the bias would steepen it. Figure 4e shows the difference in the zonal moisture gradient between the two model groups. The differences that are statistically significant are located south of Sumatra and Java Islands, with the gradient being larger in the CMIP6 models. The southern MC is the area where the rate of moisture recharging before the onset of MJO convection is greater in the CMIP6 models. The difference in the meridional moisture gradient (Figure 4f) is also statistically significant over the southern MC area. With the steeper mean state moisture gradient, all other conditions being equal, the same MJO wind anomaly would result in a greater moistening in the CMIP6 models than in the CMIP5 models. The results of our mean state analysis, when considered with the moisture budget analysis above, strongly suggests that the reduction of the dry bias in the MC region in the CMIP6 models helps them to better represent MJO propagation more realistically compared to the CMIP5 models.

Summary and Discussion
Many climate models share a common bias that the simulated MJO terminates over the MC too often, and this bias has persisted over the previous generations of CMIP models (Hung et al., 2013;Lin et al., 2006). In the current study, we developed a metric that indicates the robustness of MJO propagation over the MC and we applied it to 30 CMIP5 and 34 CMIP6 models to quantitatively evaluate whether the CMIP6 models are better than the CMIP5 models in simulating MJO propagation over the MC.
Our results showed that the MJO propagation skill over the MC is significantly improved in CMIP6 models compared to CMIP5 models. Using the MC propagation metric, 20 out of 34 (59%) CMIP6 models have values close to that observed (0.75-1.25), while only 7 out of 30 (23%) CMIP5 models exhibit such fidelity.
In terms of the multimodel mean value of the MC propagation metric, the CMIP5 mean is about 69% of the observed value, whereas for CMIP6 it is about 85% of the observed value. This CMIP6 improvement is statistically significant at the 90% confidence level, but not at the 95% confidence level with a p value of about 0.06. Tables S2 and S3 compare the MC propagation index between two generations-CMIP5 and CMIP6of models from the same institute. In 15 out of 16 model pairs, CMIP6 models show improvement (i.e., becomes closer to 1) over their CMIP5 versions. Although the CMIP6 models show robust improvement in the simulation of MJO propagation across the MC, many models still underestimate the observed metric.
Our process diagnosis indicates that the improvement in the MC propagation metric is related to the better representation of the mean state moisture around the MC. Probing deeper, the moisture budget analysis revealed that the improved MJO propagation over the MC in the CMIP6 mean is mainly attributed to the larger zonal and meridional moisture advection over the southern MC. The larger zonal and meridional moisture advection in CMIP6 mean are associated with the steepened horizontal gradient of mean state moisture over the southern MC. A dry bias over the Indo-Pacific Warm Pool region, which is pronounced in the CMIP5 models, almost disappears in the CMIP6 models, steepening the horizontal gradient of the mean state moisture over the southern MC area.
Our conclusion that the better MJO simulation in CMIP6 models is mainly due to the reduction of the dry bias is supported by the recent model intercomparison studies conducted by Gonzalez and Jiang (2017) and Jiang (2017). They also showed a systematic difference in the mean state moisture between relatively good-and poor-MJO models using climate models participating in the MJOTF/GASS MJO model intercomparison project. They showed that the models with robust MJO propagation tended to exhibit a wetter mean state over the tropics with a steeper horizontal moisture gradient over the MC area.
While this study highlights the role of the basic state moisture in the simulation of the MJO, our understanding of the processes that control the mean state moisture around the MC is still limited. Jiang et al. (2019) suggested that the MC diurnal cycle and topography play an important role on the formation of the mean state moisture around the MC. The improvement in the mean state moisture around MC in CMIP6 models is possibly due to the increased horizontal resolution, thus a better representation of MC island effects. Ahn et al. (2020) suggested that the intensity and convective top height of the MC land convection could modulate the mean state moisture around the MC with idealized model experiments in which the MC land convection is controlled to be shallower or deeper. More work is needed to better understand the processes that modulate the mean state moisture around the MC in a wide range of weather and climate systems.

Disclaimer
This document was prepared as an account of work sponsored by an agency of the U.S. government. Neither the U.S. government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.