The outputs of 23 models from the CMIP5 used for the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) has been analysed (see model list in Table 1). The 250-year long simulations of the pre-industrial (hereafter PI) experiment (Taylor et al., 2012) are used for the evaluation of ENSO types, while a selected 20 years among these simulations are used to diagnose the ITV characteristics. The motivation for focusing on the PI experiment and not on the historical simulations as it is commonly done for model evaluation stands in the fact that it eases the interpretation of the results since there is no external forcing in the PI experiments, which provides a benchmark for further assessment of the sensitivity of the ENSO / ITV relationship to climate change in the CMIP5 models. Monthly-mean sea surface temperature (SST) over a 250-year period and daily-mean zonal wind at 850 hPa over selected chunks of 20 years with daily data are used. Taking into account the decadal modulation of the ITV / ENSO relationship, the data of the historical simulations were used for the statistical analysis of the ITV / ENSO relationship, which presents data with daily resolution over a longer period than 20 years. A total of 66 years were used for the analysis (1950–2005). For comparison of the results with observations, the Hadley Centre Global Sea Ice and Sea Surface Temperature (HadISST, Rayner et al., 2003) archive and the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) Reanalysis (Kalnay et al., 1996) zonal wind at 850 hPa are used.

To document the ITV properties, we use the technique proposed by Wheeler and Kiladis (1999). This method is identical to those used in previous studies evaluating the realism of MJO and CCEW in CMIP3 (Lin et al., 2006) and CMIP5 (Hung et al., 2013) models. It is based on the decomposition of the symmetric and antisymmetric components relative to the Equator components of the field in the frequency–wavenumber space. Inversed Fourier transform is then used to recompose the signal in the desired frequency and wavenumber bands. The frequency and wavenumber intervals were derived from the normalised space–time spectrum for U850 and are centred on the spectral maximum of U850 (see Gushchina and Dewitte, 2011). In the models, the localisation of spectral maximum may differ from the reanalysis. However, sensitivity tests show that slight changes in the frequency–wavenumber interval do not significantly change the characteristics of the recomposed signal; therefore, fixed boundaries in the frequency and zonal wavenumber domain were used. These are, for MJO, zonal wavenumbers 1–3 and a period of 30–96 days; for equatorial Rossby waves, zonal wavenumbers -1…-8 and a period of 10–50 days, with negative (positive) zonal wavenumbers corresponding to the westward-propagating (eastward-propagating) waves. For Rossby waves, the frequency–wavenumber bands are also limited by the dispersion curves corresponding to values of the atmosphere equivalent depth ranging from 8 to 90 m, which follows Wheeler and Kiladis (1999).

Following Hayashi (1979), only the part of the eastward power that is incoherent with its equivalent westward power represents the true eastward-propagating signal. Moreover, the results of Jiang et al. (2015) emphasise the dominant stationary signals in many model simulations. To verify if the westward counterpart is present in the models, we recomposed the signal in the same frequency intervals as for MJO and Rossby waves but for the opposite sign of zonal wavenumbers: -1…-3 for MJO and +1…+8 for Rossby waves. Insignificant correlation between westward and eastward signals confirms that westward and eastward parts are incoherent, validating a posteriori our decomposition approach of the model outputs.

The amplitude of ER and MJO was calculated by taking the root mean square (rms) of the recomposed signal in a running window whose span depends on the wave's type (90 and 48 days for MJO and equatorial Rossby waves, respectively). Then, the running rms was considered as monthly averaged. To calculate the anomalies, the mean climatology over the investigated period was removed.

We use here U850 field for ITV filtering instead of outgoing longwave radiation (OLR) or brightness temperature signals from satellite data that are commonly used to derive the frequency–wavenumber of ITV, noting that the filter bands are similar for OLR and U850 as predicted by a simple dynamical model of ITV (Thual et al., 2014). Moreover, the use of zonal wind field eases the interpretation of the results since it is the westerly wind anomalies that serve as a physical conduit from the ITV to the ENSO dynamics. This approach follows previous relevant studies (McPhaden et al., 2006; Hendon et al., 2007).

In order to depict ENSO variability in terms of its two flavours (or regimes), we used the indices defined by Takahashi et al. (2011), the so-called E and C indices, that consist in the linear combination (through rotation) of the first two EOFs of the SST anomalies over the tropical Pacific (20∘ S–20∘ N; 120∘ E–80∘ W). Whereas the E index accounts for the extreme El Niño events that are of EP type, the C index grasps the variability associated with the CP El Niño and La Niña events. These indices, independent by construction (i.e. their correlation is zero), can be conveniently used for correlation or regression analyses. In particular, we infer the mode patterns associated with the two types of El Niño by bilinearly regressing the SST anomalies over the tropical Pacific onto the E and C indices. These mode patterns have a more consistent physical interpretation than the mode patterns associated with the first two EOF modes of SST anomalies over the tropical Pacific (see Takahashi et al., 2011 for details).

The CP and EP events were selected using the time series of E and C indices. The E/C index above 0.75 times their standard deviation during at least 3 consecutive months of the winter period (October–March) defines EP/CP El Niño events.

As a first step, the models' skill in simulating ENSO diversity is assessed based on the comparison of the E and C modes with those of observations. The E and C patterns for the ensemble mean of the 23 CMIP5 models (see Table 1 for the list of models) and for the observations (HadISST dataset) are presented in Fig. 1. As a metric of the skill of the model in accounting for the amplitude and pattern of the modes, we estimate the projection of model pattern onto the observed one within 10∘ S–10∘ N (bottom panel of Fig. 1). Figure 1 indicates that the model ensemble is quite realistic in accounting for the two types of El Niño in terms of their spatial pattern. The ensemble mean hides however some dispersion among models that is illustrated in Fig. 1e. The discrepancy between the models and observation in terms of the X value (see formula in the caption) is due to the model's tendency to have a SST anomaly pattern shifted to the west compared to the observations (Kim and You, 2012; Ham and Kug, 2012) but also due to the differences in the amplitude of the mode patterns, which is related to the deficiency of the models in accounting realistically for the ENSO asymmetry (Zhang and Sun, 2014) and non-linearity (Karamperidou et al., 2017). In general, though, the models simulate a reasonable ENSO period (not shown), in particular, with a shorter period of the E index (∼ 3–6 years) than the C index (∼ 5–8 years), in agreement with the observations. The objective classification of the models is difficult considering the number of other important ENSO properties to consider (e.g. seasonal phase locking, asymmetry, amplitude modulation, relative contribution of feedbacks) than just its diversity. We have also to consider a compromise between the model skill in realistically simulating ENSO properties and ITV (see next section). For simplicity, and considering the dispersion in ENSO amplitude among models, we thus decide to quantify the model skill in simulating ENSO diversity based on a simple metric consisting in the spatial correlation of the E and C patterns between the observations and models within 5∘ S–5∘ N (Table 2) and consider that the model is “realistic” enough if the value of this metric is above 50 %. This excludes three models from the subsequent analyses: GFDL-CM3, GFDL-ESM2M and CSIRO-Mk3. We will see hereafter that the evaluation of ITV in the models yields a more stringent test of the model realism, which will reduce drastically the number of models for the assessment of the ENSO / ITV relationship (Sect. 3.3).

The characteristics of ITV are documented here with the focus on its intensity, seasonality and propagating features. Earlier studies have evidenced biases in the simulation of MJO and CCEW in CMIP models (Guo et al., 2015; Jiang et al., 2015; Klingaman et al., 2015; Xavier et al., 2015), however, with the CMIP5 models being more realistic (Hung et al., 2013) than the CMIP3 models (Lin et al., 2006). Our analysis here is based on the most realistic models in terms of their skill in simulating the two types of El Niño. Some modes are not considered in the analyses because the daily data of U850 were not available in open access. We thus retain 16 models: ACCESS1-3, BNU-ESM, CanESM2, CCSM4, CMCC-CM, CNRM-CM5, EC-EARTH, HadGEM2-CC, HadGEM2-ES, INMCM4, IPSL-CM5A-MR, MIROC5, MPI-ESM-LR, MPI-ESM-P, MRI-CGCM3 and NorESM1-M. The 20 years of the PI experiment for each model are analysed, the results of which are compared to the NCEP/NCAR Reanalysis data over the period 1980–1999.

Figure 2 presents the space–time spectra normalised above the background spectra for the symmetric component of U850 wind for the observations (Fig. 2, upper panel) and for the CMIP5 models. Superimposed upon these plots are the dispersion curves for the odd meridional mode number of equatorial waves for various equivalent depths (h=12, 25 and 50 m). A total of 11 models out of 16 are capable of simulating the eastward-propagating MJO signal with maximum at zonal wavenumber 1 in relatively good agreement with the observations. However, the intensity of the MJO-associated spectral maximum differs among the models. A total of five models out of 16 simulate unrealistic westward-propagating disturbances with zonal wavenumbers 1–3. Seven models (BNU-ESM, CCSM4,3 CMCC-CM, INM-CM4, MIROC5, MPI-ESM_P and Nor ESM1-M) simulate a realistic ER spectral maximum (Fig. 2).

The distribution of the variance of the MJO and ER along the equatorial band is also key to accounting for the relationship between ENSO and ITV considering that the balance between oceanic feedbacks which depends on the sloping mean thermocline determines the nature of the coupled instability during ENSO (An and Jin, 2001). The rms values of the ITV components over 20 years averaged between 15∘ N and 15∘ S were plotted as a function of longitude for the models and the NCEP/NCAR Reanalysis (Fig. 3a, b, e, f). The location of the MJO maximum in the eastern Indian Ocean and western Pacific is relatively realistically simulated by ACCESS1-3, BNU-ESM, CCSM4, CMCC-CM, EC-EARTH, HadGEM2-CC, HadGEM2-ES, MIROC5, MPI-ESM-P and NorESM1-M models. In particular, these models have a root mean square error (RMSE) that is ∼ 50 % of the variance of the NCEP/NCAR data in the tropical Pacific region (Fig. 3c, d). However, in CMCC-CM and NorESM1-M, the maximum is shifted toward the central Pacific, while ACCESS1-3, HadGEM2-CC, HadGEM2-ES and EC-EARTH underestimate the total MJO variance in the eastern Indian and western Pacific oceans. CanESM2, CNRM-CM5, IPSL–CM5A–MR, MPI-ESM-LR and MRI–CGCM3 do not exhibit a significant peak in the eastern Indian and western Pacific oceans which may be critical for the proper simulation of the relationship between ITV and oceanic Kelvin wave activity. Nine models out of 16 models simulate a relatively realistic magnitude and longitudinal distribution of ER variance (Fig. 3e, f) associated with a relatively weak RMSE (Fig. 3g, h). It is noteworthy that the ER variance maximum in the central Pacific is correctly simulated by ACCESS1-3, CMCC-CM, HadGEM2-CC and HadGEM2-ES. As a summary of the results, Table 3 synthesises the models' skill in the various diagnostics carried out in this study. Since it is mainly based on the visual appreciation of the figures and thus somehow subjective, Table 3 is mostly provided for clarity and readability.

In the following, the seasonality of the ITV is assessed considering the focus of this study on the seasonal dependence of the ENSO / ITV relationship.

The MJO has a maximum intensity in the summer hemisphere (i.e. in the Northern Hemisphere in July and in the Southern Hemisphere in January), which implies that the MJO variance peaks along the Equator in boreal spring (Zhang and Dong, 2004) when it may act efficiently as an ENSO trigger. Therefore, the MJO cross-equatorial seasonal migration is a key feature that needs to be realistically simulated in the models. The MJO seasonal variability is thus estimated over the three latitudinal belts: 10–15∘ N, 5∘ N–5∘ S and 10–15∘ S (Fig. 4). For ER, since its variance remains confined to the equatorial band all year long, its seasonal cycle is estimated in the 5∘ N–5∘ S belt only (Fig. 5). In the NCEP/NCAR Reanalysis, the MJO exhibits a larger variability in the summer hemisphere with a higher amplitude in the Southern Hemisphere than in the Northern Hemisphere. In the northern tropical Pacific (10–15∘ N), the MJO activity peaks from June to September (Fig. 4a, b), while in the southern tropical Pacific (15–10∘ S), it peaks from November to March (Fig. 4e, f). In the near-equatorial area, there is no marked seasonal peak, but a slight intensification from November to April and a relaxation from May to October are observed (Fig. 4c, d). The seasonal shift of the MJO maximum drastically differs among the models. The comparison of the models to the observations indicates that HadGEM2-CC, ACCESS1-3, MPI-ESM-P, CMCC-CM, BNU-ESM and MIROC5 are the models that simulate the MJO seasonal cycle the most realistically since they have the smallest values of RMSE along the Equator (Fig. 6a). The CCSM4, NorESM1-M and INM-CM4 models simulate the correct timing of the seasonal maximum but with lower MJO amplitude for INM-CM4 and larger amplitude for CCSM4 and NorESM1-M as compared to the observations. The seasonal cycle of ER is reasonably simulated by BNU-ESM, CCSM4, CMCC-CM, HadGEM2-CC, HadGEM2-ES, INMCM4, MIROC5 and NorESM1-M (Figs. 5a, b and 6). The reader is invited to refer to Table 3 for a summary of the models' skill in simulating ITV seasonality.

Further, the propagating characteristics of the MJO and ER along the Equator are documented for the most skilful models in terms of the amplitude and seasonal cycle of the ITV. Figures 7 and 8 show the lag correlation of the MJO and ER filtered U850 time series averaged between 5∘ N and 5∘ S with respect to itself at the Equator and 105∘ E for MJO and 150∘ E for ER, respectively. Superimposed upon these plots are the lines corresponding to phase speeds of 5, 7, 10 and 15 m s-1. The observation evidences an eastward-propagating MJO pattern with a phase speed of about 5 m s-1 (Fig. 7). A total of six models out of 11 display propagation characteristics that are consistent with the observations. The MJO phase speed is slightly slower than in observations in CMCC-CM, EC-EARTH, INM-CM4, MIROC5 and MPI-ESM-P. Note that Hung et al. (2013), who documented the MJO signal from precipitation data, found a very slow propagation in most CMIP5 models, which is not the case here for the MJO-associated patterns of the low troposphere winds. The Rossby wave propagates westward with phase speed around 7 m s-1 to the west of the dateline and 5 m s-1 to the east of the dateline in the observations. Eight models simulate a realistic Rossby wave phase speed value, while three models (CMCC-CM, INM-CM4 and NOR-ESM1-M) simulate a too slow phase speed (Fig. 8).

In this section, our objective is to illustrate the large dispersion among models' skill in simulating the ITV / ENSO relationship, despite an overall good skill in simulating ITV and ENSO diversity separately for some of them. We thus arbitrarily select five models among the “good” models (see Table 3). One difficulty for assessing the ITV / ENSO relationship is associated with the fact that it can experience a low-frequency modulation. Gushchina and Dewitte (2018) showed in particular that there is a significant decadal variability of the ITV / ENSO relationship over the observational record (see Fig. S1), which arises either from change in mean state impacting the ENSO dynamics or changes in the properties of ITV itself. Thus, in order to take into account such a decadal modulation, the 11-year running mean of the lagged correlation between the MJO and ER activity indices in the equatorial Pacific and the E and C indices in January is first assessed in order to determine the periods (in the historical runs) when the statistics are robust (see Fig. S2 for an example for the CMCC-CM model). The MJO and ER indices are calculated as the running variance of U850, filtered in the domain of MJO and ER, averaged over the regions where the maximum of the ITV / ENSO relationship is observed in reanalysis (Gushchina and Dewitte 2011): western Pacific (120–180∘ E; 5∘ S–5∘ N) for MJO and central Pacific (140∘ E–160∘ W; 5∘ S–5∘ N) for Rossby waves. In order to select the periods, following Gushchina and Dewitte (2018), we define a measure of the “predictive skill” of either the MJO or ER with respect to ENSO. It is defined as follows: PITVENSOt=∫τ=Mar(-1)τ=Jan(0)corITVENSOτ,tJan(0)-Mar(-1)2.Jan(0)-τ⋅dτ, where corITVENSOτ,t represents the correlation as a function of time (t) and time lag (τ) between the ENSO index (either E or C indices) in Jan(0) (i.e. at the ENSO peak) and the considered month of ITV (either MJO or ER) activity. corITVENSOτ,t within the integral is set to zero when it is not statistically significant at the 95 % confidence level. PITVENSOt is thus the weighted ITV / ENSO correlation between Mar(-1) and Jan(0) which gives larger weight to correlation at large time lags (1 in Mar(-1)) and little at short lags (0 in Jan(0)), and can therefore be interpreted as a measure of the predictive value of either MJO and ER with regards to the E and C indices. The time series of PMJOEt, PMJOCt, PEREt and PERCt for the model and the observations are provided in Fig. 9. For the following diagnostic, we identify the period of a strong MJO / E(C) and ER / E(C) relationship as a period with positive predictive score during at least 16 years (in accordance with the observations where the period of a strong ITV / C relationship is 2000–2015). Note that the mean over the full period was removed in the models for comparison between them but not in the observations (for comparison with Gushchina and Dewitte, 2018). The observations exhibit higher values of the predictive score than the model anyway (see also the Supplement). In some models, there is no extended period of time (i.e. period longer than 16 years) when the value of the predictive score is positive over the whole record. In this case, we choose to consider a 16-year period centred on the peak value of the predictive score. The periods used for the subsequent lag correlation analysis are provided in Table 5. The reference period for the NCEP/NCAR Reanalysis is 1979–1998 for EP El Niño and 2000–2015 for CP El Niño, selected as a period of occurrence of mostly EP or CP El Niño events, respectively. The lagged correlation between the C and E indices with respect to the MJO and ER activity indices is then calculated as a function of calendar month (Figs. 10 and 11).

Consistently with the results conveyed in Fig. 9, the ITV / ENSO relationships associated with the two types of El Niño events are very diverse among models, and do not compare in a straightforward manner with the observations. In the observations, the MJO activity in March–July is ahead of the peak SST anomalies (correlation greater than 0.6) by 4 to 12 months (3 to 9 months) during the EP (CP) El Niño events (Fig. 10a, g). The significant positive correlation persists up to positive time lags (MJO lags SST) during the CP El Niño event, mirroring the strong MJO after the SST peak. During the EP El Niño event, the MJO precursor signal is present in all models but the correlation is lower in BNU-ESM and INMCM4 as compared to the observations (Fig. 10b, e), while MIROC5 and BNU-ESM simulate shorter time lag between MJO intensification and SST rise (Fig. 10b, f). Note that all models except for MIROC5 exhibit a too strong MJO intensity after the El Niño peak (positive correlation at positive time lags). The MJO intensification prior to the CP El Niño event is also simulated by all models (Fig. 10h–l), however, with a different timing than the observations. In MIROC5, the pattern of the lag correlation is the most realistic amongst the models (correlation in the lag–month space between observations and models reaches 0.45, 0.38, -0.01, -0.06 and -0.06 for MIROC5, BNU-ESM, CCSM4, CMCC-CM and INM-CM4, respectively). Although the precursor signal is simulated by BNU-ESM, the correlation values prior to the ENSO peak are lower than in the observations. In CCSM4 and CMCC-CM, the MJO / C correlation is weak prior to the ENSO peak (Fig. 10i, j). INM-CM4 simulates the strongest simultaneous correlation between the MJO and C indices, while the precursor signal is rather weak (Fig. 10k).

Regarding the Rossby wave, the observations indicate that the ER activity intensifies in February–April and July–September of the year prior to the EP El Niño peak (Fig. 11a). During CP El Niño, the Rossby wave activity also appears to be a good precursor, and the relationship with SST anomalies persists after the peak phase (Fig. 11g). All five models have some skill in simulating the ER / ENSO relationship. However, INM-CM4 does not simulate the peak of ER in February–April (Fig. 11e), MIROC5 has a too strong and persistent correlation between the ER and E indices (Fig. 11f), while BNU-ESM and CCSM4 have differences with the observations in terms of the period of the calendar year when the ITV / ENSO relationship is the strongest (Fig. 11b, c). CMCC-CM exhibits the most realistic features (Fig. 11d). All models simulate the increased ER activity prior to and after the CP El Niño peak but the values of correlation are smaller and the timing of the peak correlation is different from the observations (Fig. 11g–l).