Assessment of the Madden‐Julian Oscillation in CMIP6 Models Based on Moisture Mode Theory

The moist processes of the Madden‐Julian Oscillation (MJO) in the Coupled Model Intercomparison Project Phase 6 models are assessed using moisture mode theory‐based diagnostics over the Indian Ocean (10°S–10°N, 75°E–100°E). Results show that no model can capture all the moisture mode properties relative to the reanalysis. Most models satisfy weak temperature gradient balance but have unrealistically fast MJO propagation and a lower moisture‐precipitation correlation. Models that satisfy the most moisture mode criteria reliably simulate a stronger MJO. The background moist static energy (MSE) and low‐level zonal winds are more realistic in the models that satisfy the most criteria. The MSE budget associated with the MJO is also well‐represented in the good models. Capturing the MJO's moisture mode properties over the Indian Ocean is associated with a more realistic representation of the MJO and thus can be employed to diagnose MJO performance.

Numerous studies have observed that the growth of MJO convection is associated with feedbacks that increase moisture anomalies (Del Genio & Chen, 2015;Sobel et al., 2014;B. Zhang et al., 2019).Moreover, the eastward propagation of MJO is predominantly governed by horizontal and vertical moisture advection (Adames & Wallace, 2015;Hung & Sui, 2018;Kim, Kug, & Sobel, 2014;Kiranmayi & Maloney, 2011;K.-C. Tseng et al., 2015).These features have led to a view of MJO that is known as moisture mode theory.Moisture mode theory posits that the MJO precipitation is tightly modulated and organized by moisture fluctuations, while temperature anomalies play a minor role because of weak temperature gradient (WTG) balance (Adames, 2017;Adames & Kim, 2016;Adames & Maloney, 2021;Ahmed et al., 2021;Emanuel et al., 1994;Mayta & Adames Corraliza, 2023;Raymond & Fuchs, 2009;Sobel et al., 2014, among others).The processes that lead to evolution of the moisture fluctuations also lead to the evolution of moisture mode.These features led Ahmed et al. (2021) to propose three criteria to assess whether a wave is a moisture mode.Mayta et al. (2022) modified these criteria in order to apply them diagnostically to observations, reanalysis, and model output.The first criterion emphasizes a high correlation between precipitation and column moisture.The second criterion describes that the wave behavior should satisfy WTG balance.The third criterion assures the dominance of moisture in the evolution of anomalous column moist static energy (MSE).Mayta et al. (2022) also included a fourth criterion based on the scale analysis of Adames et al. (2019) and Adames (2022).By using these criteria, Mayta and Adames Corraliza (2023) found that the MJO behaves as a moisture mode only over the Indian Ocean.Outside this region, temperature fluctuations are as influential as moisture anomalies in MJO's thermodynamics because its faster propagation prevents WTG balance.
Although our understanding of the MJO has significantly improved, accurate representation of MJO variability remains a major challenge in global climate models (GCMs; Ahn et al., 2017Ahn et al., , 2020;;Kim et al., 2009).It is welldocumented that the failure of models to simulate the MJO is largely a result of inadequate treatment of deep cumulus convection, particularly its insufficient sensitivity to free tropospheric water vapor (e.g., Holloway et al., 2013;Kim, Lee, et al., 2014;M.-I. Lee et al., 2003;Maloney & Hartmann, 2001).Models in which convection is sensitive to water vapor fluctuations produce regions of precipitation that persist at the intraseasonal timescale, hence producing MJO activity.From this, models that have a strong coupling of precipitation with moisture can simulate more realistic MJO convection (Ahn et al., 2017;Holloway et al., 2013).Furthermore, a strong horizontal gradient of mean state moisture can drive robust MJO propagation (Ahn et al., 2020;Jiang, 2017).All of these features are consistent with the MJO being at least partially explained as a moisture mode.
Based on these previous results, we hypothesize that the moisture mode properties of the MJO are essential for its realistic simulation.To this end, we seek to examine the MJO simulation in the Coupled Model Intercomparison Project Phase 6 (CMIP6) models based on the moisture mode framework (Ahmed et al., 2021;Mayta et al., 2022;Mayta & Adames, 2023).Specifically, we seek to answer the following questions Q1: Can the global climate models reproduce the MJO moisture mode properties over the Indian Ocean?Q2: If a model can capture the moisture mode behaviors, does it mean that the model has better skills in the MJO simulation than others?
The structure of this paper is as follows.Section 2 describes the datasets and methods.Section 3 diagnoses MJO simulation by the moisture mode theory.In Section 4, we compare the good and poor simulations in the moisture mode behaviors against the observations.Section 5 discusses the relationship between the moisture mode criteria and MJO strength.Major findings are summarized in Section 6.
Observation and reanalysis data are used as a reference for model simulations.We use the moisture, precipitation, temperature, horizontal winds, vertical velocity, geopotential height, radiation, and surface fluxes from the fifth generation of the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5; Hersbach et al., 2019).The outgoing longwave radiation (OLR) from NOAA Physical Sciences Laboratory (Liebmann & Smith, 1996) is used to calculate the MJO index.The precipitation from Tropical Rainfall Measuring Mission (TRMM; Kummerow et al., 2000) product is applied to compute the realistic wave responses by the space-time power spectra.All data are interpolated into a uniform horizontal resolution of 2.5°longitude × 2.5°latitude.We discuss the MJO activity during the extended boreal winter (November-April) when the MJO is more active (X.Li et al., 2020;Q. Zhang et al., 2019).

Filtering, EOF Analysis, and Regressions
The dominant mode of the MJO convection is derived through empirical orthogonal function (EOF) analysis of 20-96-day bandpass filtered OLR over the equatorial belt (15°S-15°N).The first EOF mode (EOF1) has the largest amplitude around 90°E (Figure S1 in Supporting Information S1).The field variables are lag regressed onto the first principal component (PC1) time series to obtain a composite of the MJO evolution from 30 to 30 days, following the same process as previous studies (e.g., Adames et al., 2021;Mayta & Adames Corraliza, 2023;Mayta et al., 2021).These perturbations are then scaled to one standard deviation (SD) of PC1.To make the peak MJO convection near 90°E occur at lag 0 day in all data, we refer to the basis function approach (J. Lee et al., 2019;Orbe et al., 2020, among others) to project simulated OLR anomalies onto the observed EOF1 and hence obtain the PC1 time series of each model.

Diagnostic Criteria
In order to evaluate the moist thermodynamics of simulated MJO, we apply the moisture mode criteria over the Indian Ocean (10°S-10°N, 75°E-100°E) region, where the MJO shows characteristics of a moisture mode (Mayta & Adames Corraliza, 2023).The criteria are (Ahmed et al., 2021;Mayta et al., 2022): 1. Wave must exhibit a large moisture signature that is highly correlated with the precipitation anomalies To be considered a moisture mode, the MJO's precipitation anomalies P′ should be sensitive to column water vapor variations 〈q〉′.In other words, it must exhibit a high linear correlation between 〈q〉′ and P′ (R P,q ) as follows, where 〈 ⋅ 〉 ≡ 1 g ∫ 1000 100 ( ⋅ )dp is vertical integration from 1,000 to 100 hPa, and primes (′) represent the regressed anomalies.The correlation coefficient between 〈q〉′ and P′ should be higher than 0.9, indicating that the moisture fluctuations significantly modulate the precipitation evolution, at least 81% of the variance.The slope of 〈q〉′ to P′ is the convective moisture adjustment time scale (τ c ≡ 〈q〉′ P′ ) , defined as the time to remove column moisture through rainfall (Bretherton et al., 2004).The τ c of MJO convection should be about 1 day over the Indian Ocean (Mayta & Adames Corraliza, 2023).

The system must be in the WTG balance
The WTG approximation states that the vertical advection of dry static energy (DSE) 〈ω∂ p s〉′ must approximate balance the apparent heat source 〈Q 1 〉′: where s=C p T + gz is DSE.To satisfy this second criterion, the slope of 〈Q 1 〉′ to 〈ω∂ p s〉′ should be close to 1 in linear least-squares fitting, and their correlation must also be higher than 0.9.
However, the second criterion might not confirm that temperature fluctuations are negligibly small.It could mean that apparent heat source is very large compared to the temperature tendency.To rigorously verify that moisture anomalies play a key role in modulating the system, the following third criterion is necessary.

Moisture must govern the evolution of MSE
If the MJO is a moisture mode, the column water vapor must be the main contributor to its MSE (m), To guarantee the approximation in Equation 3, a slope of 〈L v q〉′ to 〈m〉′ must be ∼1 in linear least-squares fitting (S q,m ), with a high correlation between both variables (>0.9).

N mode
The dimensionless N mode parameter is also adopted to quantify the relative importance of column water vapor versus temperature in the evolution of MSE (Adames et al., 2019).N mode is defined as in Adames et al. (2019) and Mayta et al. (2022) as: where c = 50 m s 1 is the phase speed of a first baroclinic free gravity wave, c p is the phase speed of MJO over the warm pool Indian Ocean, τ c is the convective moisture adjustment time scale, and τ is the characteristic temporal scale of MJO (i.e., ∼37 days in the ERA5).The MJO can be classified as a moisture mode when N mode ≪ 1 (i.e., log 10 N mode < 0.5).
Following Mayta et al. (2022), the first three criteria are applied to the reanalysis by constructing scatterplots of regressed field variables (Figure S2 in Supporting Information S1), considering time series from lag day 30 to day +30 and all grid points within the analysis domain (10°S-10°N, 75°E-100°E).Various methods exist to calculate τ c , in addition to the one proposed in this study (e.g., Jiang et al., 2016).However, we have verified that the main findings of this study are not affected by the method used to calculate τ c .For the fourth criterion, the c p is estimated by applying the Radon Transform method (Mayta et al., 2024;Radon, 1917), which is described in Supporting Information S1.The same procedures are repeated for CMIP6 data.

Moist Thermodynamic Diagnostics of MJO Simulation
The moisture mode criteria applied to the reanalysis and models are summarized in Figure 1.Reanalysis, as recently documented in Mayta and Adames Corraliza ( 2023), shows a high correlation between 〈q〉′ and P′ over the Indian Ocean (R P,q = 0.95), whereas the climate models depict an average value of 0.88 ± 0.05.Among them, HadGEM3-GC31-LL, KACE-1-0-G, and TaiESM1 models have the highest correlation (R P,q = 0.94).The remaining 15 models underestimate R P,q (<0.9; black values).The τ c of ERA5 is about 1.02 days.Ten out of 25 models (40% of total) are within ±0.5 model SD relative to the reanalysis (0.93-1.12 days).For the WTG approximation, the slope of 〈Q 1 〉′ versus 〈ω∂ p s〉′ in reanalysis is 0.99 (not shown).The values of the 25 models range from 0.98 to 1.06, and the multi-model mean is 1.01 ± 0.02.The correlation between 〈Q 1 〉′ and 〈ω∂ p s〉′ is higher than 0.99 in ERA5 and all models included.It suggests that these simulations largely satisfy WTG balance over the Indian Ocean, so this criterion is not shown in Figure 1. S q,m in ERA5 is approximately 0.98 (Figure 1).The mean of the 25 models is ∼0.92 ± 0.06, with most models showing values ranging from 0.89 to 1.02 (within 1.5 SD relative to ERA5).However, the S q,m in 11 models is lower than 0.9, particularly the IITM-ESM and MPI-ESM-1-2-HAM models (<0.85).The relatively low S q,m values indicate that the contribution of 〈s〉′ to 〈m〉′ is more significant.All models and reanalysis have a high correlation coefficient (>0.98) between moisture and MSE anomalies (not shown).
The log 10 N mode value of ERA5 is approximately 0.69 (N mode ∼ 0.2), indicating that the MJO exhibits moisture mode behavior over the Indian Ocean, in agreement with Mayta and Adames Corraliza (2023).Eight models depict a log 10 N mode > 0.3 (N mode > 0.5), implying that their behavior is far from a moisture mode.It is worth noting that some models show reasonable results for the first three moisture mode criteria but have log 10 N mode > 0.25 (N mode > 0.56; e.g., ACCESS-CM2, HadGEM3-GC31-MM, and KACE-1-0-G).Adames et al. (2019) and Adames (2022) performed a scale analysis and demonstrated that N mode is largely determined by the phase speed of the wave.These models, as expected, simulate a faster MJO phase speed (c p > 8 m s 1 ) than ERA5 (Figure S3 in Supporting Information S1).A high sensitivity of N mode to c p was found in these 25 CMIP6 models (further discussion in the SI).On the other hand, the log 10 N mode < 0.8 (N mode < 0.16; e.g., AWI-ESM-1-1-LR, IITM-ESM, IPSL-CM6A-LR-INCA, MPI-ESM-1-2-HAM, MPI-ESM1-2-HR, and MPI-ESM1-2-LR) are models with near stationary MJO-like behavior (c p < 2.2 m s 1 ).
For the simulated MJO to satisfy the moisture mode criteria, the model should have R P,q > 0.9, τ c ∼ 1 day (at least within ±0.5 model SD relative to the observation), S q,m > 0.9, and that log 10 N mode ranges within 0.8 to 0.5 (marked by the blue values in Figure 1).The results show that no model accurately captures all the MJO's moisture mode properties seen in reanalysis.However, some models still have values reasonably close to the reanalysis but with a slightly long τ c or small S q,m .

Comparison Between Observations, Good, and Poor Models
In this section, we further discuss whether the models that capture the highest amount of moisture mode criteria are able to simulate a more realistic MJO.To this end, we consider relaxed standards to select relatively good and poor models.First, the R P,q , τ c , and S q,m of model range within ±1.5 SD relative to the reanalysis.Second, log 10 N mode should be 0.8 to 0.3 because log 10 N mode < 0.3 ensures a higher contribution from the moisture fluctuation than the temperature fluctuation (N mode < 0.5).In addition, we avoid selecting more than one model from the same research institution to prevent multi-model means being dominated by similar simulations.In cases where models originate from the same research center, we choose the model with the best (worst) performance to include in the relatively good (poor) model group.Subsequently, we qualitatively assess the model's proficiency in replicating moisture mode properties using these criteria.For each criterion, the model is assigned a score of Values of criteria R P,q , τ c , S q,m , and log 10 N mode from ERA5 and 25 Coupled Model Intercomparison Project Phase 6 models.Numbers in blue represent values that satisfy the moisture mode criteria: (1) R P,q > 0.9, and τ c within ±0.5 model standard deviations relative to ERA5 (0.93-1.12 days); (2) S q,m > 0.9; and (3) log 10 N mode ranges from 0.8 to 0.5.Green boxes indicate that the model satisfies the moisture mode criteria (R P,q and τ c considered as one) and receive a score of 1. Orange boxes represent that the model only satisfies the criteria for model selection (0.5 score): (1) R P,q , τ c , and S q,m range within ±1.5 model standard deviations relative to the reanalysis; and (2) log 10 N mode ranges from 0.8 to 0.3.Numbers in brackets denote the model's total scores.The relatively good and poor models are marked by the green circles and red crosses, respectively.
one if it successfully fulfills the criteria outlined in the moist thermodynamic diagnostics (green boxes in Figure 1).If the model only satisfies the relaxed criteria (orange boxes), it is assigned a score of 0.5.Models that fail the criteria receive a score of 0. Note that R P,q and τ c are considered together as one criterion.Figure 1 shows the order of models sorted by their total score.

Space-Time Spectrum
First, we compute space-time power spectra, making use of the fast Fourier transform.The calculation procedure is similar to those used by previous studies (e.g., Y. Li et al., 2022;Rushley et al., 2019;Wheeler & Kiladis, 1999, among others).We use precipitation from TRMM, RGMs, and RPMs as an input for the calculation.The results of TRMM and ERA5 are similar (not shown), although ERA5 (1995ERA5 ( -2014) ) has a longer period than TRMM observation (1998-2014).
Figure 2 shows the symmetric power spectra of precipitation in the frequency-wavenumber domain.For the MJO band (wavenumber k = 1 4, and period of 30-90 days), TRMM and ensemble good models show strong spectra (power >1.5), whereas it is relatively weak in the poor model group (power <1.4).While precipitation exhibits a strong Kelvin wave signal in the observation and RGMs, such a signal is largely weak in the RPMs.Overall, the good model group can capture better wave signals and intensities than the poor model group.

Mean State
Previous studies have found that a realistic representation of the background MSE is critical for MJO simulation because the advection of mean-state MSE by the MJO winds dominates the MJO propagation (e.g., Ahn et al., 2020;Jiang, 2017;Ren et al., 2021, and others).On the other hand, the mean low-level easterlies in the western Pacific can be a barrier to eastward propagating MJO in the model simulation (Inness & Slingo, 2003;Inness et al., 2003).Thus, it is worthwhile to compare the mean-state column-integrated MSE and 850-hPa zonal The functional form of the tapering window is the same as described in Wheeler and Kiladis (1999).
winds between the reanalysis, RGM, and RPM (Figure 3).The pattern correlation and root mean square deviation between the individual model group and the reanalysis are also shown in the upper right corner of each panel in Figure 3.
For ERA5, the relatively high column MSE is concentrated over the Indo-Pacific warm pool and decreases with increasing latitude (Figure 3a).Most models simulate a similar but underestimated column MSE distribution compared with the reanalysis (not shown).The RGM has a higher column MSE over the equatorial warm pool relative to the RPM, especially in the western Pacific with the MSE extreme.This leads to stronger background zonal and meridional gradients of MSE in the good model group than in the poor model group.The observed westerlies cover the tropical warm pool from 60°E to 165°E, while the maximum wind speed occurs in the Indian Ocean (Figure 3b).For the RGM, the peak of zonal winds appears near the Maritime Continent, resulting in weaker westerlies over the Indian Ocean than reanalysis.In addition, the RGM simulates weaker (stronger) westerlies than the poor model group in the Indian Ocean (western Pacific) region.The westerlies can extend toward 150°E in the RGM; however, they are replaced by the easterly winds at 140°E in the RPM, especially for AWI-ESM-1-1-LR, INM-CM4-8 and IPSL-CM6A-LR-INCA (not shown), where the strong mean low-level easterlies might partially explain why their MJO convection cannot propagate across the Maritime Continent (Figure S3 in Supporting Information S1).

MSE Budget Analysis
The column-integrated MSE budget is widely used to investigate the moist energy recharging and discharging associated with MJO convection (Inoue & Back, 2015;Ren et al., 2021;W.-L. Tseng et al., 2022, and others).It is written as: Figure 4 shows the Hovm öller diagram of the regressed MSE budget terms in Equation 5for the ERA5 and model groups.〈 v ⋅ ∇m〉′ varies in phase with 〈∂ t m〉′ (Figure 4a).RGM simulations reproduce the eastward MJO convection with strong 〈 v ⋅ ∇m〉′ and 〈∂ t m〉′.The RPM exhibits weak and nearly non-propagating convection.
Compared with ERA5, 〈 ω∂ p m〉′ has a stronger drying effect (〈 ω∂ p m〉′ < 0) in the RGM and an underestimated amplitude in the RPM.The observed Source′ exhibits a lagged evolution with 〈∂ t m〉′ (Figure 4c).This feature implies that Source′ is in phase with the column MSE anomalies rather than 〈∂ t m〉′ and thus mainly contributes to the MJO maintenance.The simulated Source′ of RGM is weaker than the reanalysis, whereas the Source′ in the RPM does not show clear eastward propagation.

Relationship Between the Moisture Mode Criteria and MJO Strength
From an examination of Figure 2, we see that the RGMs exhibit a stronger MJO signal than the RPMs.Given that none of the four criteria directly diagnose MJO amplitude, this result should be examined in detail.Thus, we further compare the four moisture mode criteria with the east-west power ratio (E/W ratio).
The E/W ratio assesses the MJO intensity by calculating the power ratio of eastward-and westwardpropagating signals (periods of 30-60 days and wavenumbers 1-3) based on the power spectrum of OLR over the tropical region (a detailed explanation is presented in Section S4 of Supporting Information S1).
In Figure 5, R P,q has a high correlation with the E/W ratio, indicating that the models with higher coupling of precipitation and moisture simulate a stronger MJO.In contrast, τ c does not show a significant correlation with the E/W ratio.This result is at odds with Jiang et al. (2016), in which models with a stronger amplitude of MJO precipitation generally have a shorter τ c .This discrepancy may be methodological since Jiang et al. (2016) used rainfall anomalies over the warm pool rather than the E/W ratio to diagnose MJO amplitude.
For S q,m and N mode , we compare the absolute values of the difference between the model value and the reanalysis (e.g., |S q,m (model) S q,m (ERA5)| ), with the E/W ratio.The results reveal a statistically-significant correlation between N mode and the E/W ratio.Since N mode is sensitive to the MJO phase speed (Figure S5 in Supporting Information S1), this result indicates that models with realistic MJO propagation also exhibit a stronger MJO amplitude.We also found that the models that most accurately capture the MJO's moisture mode behavior exhibit more realistic MJO intensity and periodicity (further discussion is presented in Section S4 of Supporting Information S1).

Summary and Conclusions
In this study, we applied the moisture mode theory-based diagnosis proposed by Ahmed et al. (2021), Mayta et al. (2022), and Mayta and Adames Corraliza (2023) to assess the moisture mode properties of MJO over the Indian Ocean (10°S-10°N, 75°E-100°E) in the 25 CMIP6 models.The following are answers to the two questions based on the results in Sections 3 to 4. Inter-model comparison between the E/W ratio and R P,q , τ c , S q,m , and N mode .To calculate the correlation with the E/ W ratio, the model results of R P,q and τ c are used, while the absolute differences (i.e., |model minus observation|) of S q,m and N mode are considered.Blue borders indicate correlations exceeding 95% confidence level ( p-value <0.05).
Q1: Can the global climate models reproduce the MJO moisture mode properties over the Indian Ocean?
Our results demonstrate that none of the models used in this study can reliably reproduce all moist thermodynamic properties of the MJO as observed in Figure 1: (a) Few models showed a high correlation (greater than 0.9) between moisture and precipitation anomalies and exhibited convective adjustment time scale (τ c ) that aligned with the reanalysis; (b) all models can satisfy the criteria for WTG balance; (c) nevertheless, 11 models still exhibited an unrealistically high contribution from temperature fluctuations to the MSE anomalies; and (d) limited number of models showed values of N mode that are close to those of the reanalysis data.High values of N mode (≫0.5; log 10 N mode > 0.3) or low N mode (≪0.16; log 10 N mode < 0.8) imply that many models showed unrealistically fast or nearly non-propagating MJO convection, respectively (Figure S3 in Supporting Information S1).We also considered the analysis and procedures based on the model's EOF (Figure S6 in Supporting Information S1) rather than the observed EOF.However, these 25 models still do not demonstrate the moisture mode properties of the MJO (more details in Figure S7 and Section S3 of Supporting Information S1).
Q2: If a model can capture the moisture mode behaviors, does it mean that the model has better skills in the MJO simulation than others?
While no model fully captures the moisture mode behavior of the MJO, there is a subset that performs reasonably well.These good models (e.g., CESM2-FV2, EC-Earth3, GFDL-CM4, and MIROC6) show a stronger MJO signal than the relatively poor models (Figure 2).The good model group realistically simulates the mean-state column MSE and low-level zonal winds (Figure 3).The MSE budget associated with the MJO is better represented in the good models compared to the poor models, especially in the MSE advection terms (Figure 4).Our results indicate that models accurately capturing the moisture mode behavior of the MJO over the Indian Ocean demonstrate improved simulation of the MJO.
Two of the moisture mode criteria (moisture-rainfall correlation and N mode ) also have a significant correlation with the east-west power ratio (Figure 5), which is commonly used to denote the MJO simulation skill in previous studies (e.g., Ahn et al., 2017;Lan et al., 2022;Y. Li et al., 2022;Orbe et al., 2020).A robust MJO propagation is correlated with a more humid mean state and with stronger horizontal moisture gradients, as well as more robust MJO wind anomalies (Ahn et al., 2020;Y. Li et al., 2022).This consistency is expected since many previous studies have obtained these results under the a-priori assumption that the MJO behaves as a moisture mode.In other words, many previous studies implicitly assume that the moisture mode criteria are always satisfied, and that good MJO models are those that best simulate the processes that lead to the destabilization and propagation of moisture modes.These include having stronger horizontal moisture gradients that lead to more robust propagation via horizontal moisture advection, convection that is more sensitive to moisture variations, and a small effective gross moist stability (e.g., Ahn et al., 2017Ahn et al., , 2020;;Benedict et al., 2014).
Our study extends upon previous work by showing that the expected moisture mode behavior only exists in models that more robustly simulate the MJO.Thus, the relatively good MJO models do not just simulate the processes that lead to the destabilization and propagation of moisture modes, they are also the models that best simulate the moisture mode behavior of the MJO over the Indian Ocean.Poorer models not only have weaker or non-propagating MJO-like variability, but this variability is inconsistent with moisture mode behavior.The models best capturing the MJO's moisture mode behavior over the Indian Ocean also yield more realistic results in previous MJO skill metrics (see Figure S8 and Section S4 in Supporting Information S1 for more details).Thus, simulating a MJO that behaves as a moisture mode over the Indian Ocean may be synonymous with simulating a realistic MJO, and the four criteria used here appear to be useful diagnostic tools for evaluating MJO simulation performance.
In spite of these findings, we cannot say whether simulating the moisture mode behavior is what causes the models to perform better.It may be related to more realistic convection representation, or a combination of other factors.More work is needed to better understand the causality.

Figure 1 .
Figure 1.Values of criteria R P,q , τ c , S q,m , and log 10 N mode from ERA5 and 25 Coupled Model Intercomparison Project Phase 6 models.Numbers in blue represent values that satisfy the moisture mode criteria: (1) R P,q > 0.9, and τ c within ±0.5 model standard deviations relative to ERA5 (0.93-1.12 days); (2) S q,m > 0.9; and (3) log 10 N mode ranges from 0.8 to 0.5.Green boxes indicate that the model satisfies the moisture mode criteria (R P,q and τ c considered as one) and receive a score of 1. Orange boxes represent that the model only satisfies the criteria for model selection (0.5 score): (1) R P,q , τ c , and S q,m range within ±1.5 model standard deviations relative to the reanalysis; and (2) log 10 N mode ranges from 0.8 to 0.3.Numbers in brackets denote the model's total scores.The relatively good and poor models are marked by the green circles and red crosses, respectively.

Figure 2 .
Figure 2. Space-time spectrum of the precipitation averaged between 10°S and 10°N for (a) Tropical Rainfall Measuring Mission, (b) the RGMs ensemble, and (c) the RPMs ensemble.The solid dispersion curves correspond to 8, 25, and 80 m equivalent depths.Color shading interval is 0.1.The functional form of the tapering window is the same as described in Wheeler and Kiladis (1999).

Figure 3 .
Figure 3. Spatial pattern of mean-state (a) column-integrated moist static energy (10 6 J m 2 ) and (b) 850-hPa zonal wind (m s 1 ) for the boreal winter, derived from (top) the ERA5 (middle top) ensemble good model (middle bottom) ensemble poor model group, and (bottom) the difference between RGM and RPM (RGM minus RPM).The gray dots in the bottom panels indicate statistical significance at the 95% confidence level.The pattern correlation (Cor)/root-mean-square deviation (root mean square deviation) between the model group and reanalysis is presented at the top-right corners, respectively.

Figure 5 .
Figure5.Inter-model comparison between the E/W ratio and R P,q , τ c , S q,m , and N mode .To calculate the correlation with the E/ W ratio, the model results of R P,q and τ c are used, while the absolute differences (i.e., |model minus observation|) of S q,m and N mode are considered.Blue borders indicate correlations exceeding 95% confidence level ( p-value <0.05).