What controls phase-locking of ENSO to boreal winter in coupled GCMs?

Abstract

In this study, the phase-locking of El Nino Southern Oscillation (ENSO) in a coupled model with different physical parameter values is investigated. It is found that there is a dramatic change in ENSO phase-locking in response to a slight change in the Tokioka parameter, which is a minimum entrainment rate threshold in the cumulus parameterization. With a smaller Tokioka parameter, the model simulates ENSO peak in the boreal summer season rather than in the winter season as observed. It is revealed that the differences in climatological zonal sea surface temperature (SST) gradient and its associated mean state changes are crucial to determine the phase-locking of ENSO. In the simulations with smaller Tokioka parameter values, climatological zonal SST gradient during the boreal summer is excessively large, because the zonally-asymmetric SST change (i.e., SST increase is relatively smaller over the eastern Pacific) is maximum during the boreal summer when the eastern Pacific SST is the coolest of the year. The enhanced climatological zonal SST gradient in boreal summer reduces the convection over the eastern Pacific, which leads to a weakening of air–sea coupling strength. The minimum coupling strength during summer prevents SST anomalies from further development in the following season, which favors SST maximum during summer. In addition, enhanced zonal SST gradient and resultant thermocline shoaling over the eastern Pacific lead to excessive zonal advective feedback and thermocline feedback. Atmospheric damping is also weakened during boreal summer season. These changes due to feedback processes allow an excessive development of SST anomalies during the summer time, and lead to a summer peak of ENSO. The importance of basic state change for the ENSO phase-locking is also validated in a multi-model framework using the Coupled Model Intercomparison Project phase-3 archive. It is found that several of the climate models have the same problem in producing a summer peak of ENSO. Consistent with the simulations with different physical parameter values, these models have minimum air–sea coupling strength during the boreal summer season. Also, they have stronger climatological zonal SST gradient and shallower climatological thermocline depth over the eastern Pacific during the boreal summer season.

1 Introduction

The phase-locking of El Nino or La Nina peak to the boreal winter season is one of the most robust features of El Nino Souther Oscillation (ENSO) evolution (Rasmusson and Carpenter 1982; Jin et al. 1994; Tziperman et al. 1995, 1998; Galanti and Tziperman 2000; An and Wang 2001). To investigate the possible reason for the phase-locking of ENSO, various studies focused on the interaction between seasonal cycle and the ENSO (e.g., Philander 1983; Philander et al. 1984; Zebiak and Cane 1987; Cane et al. 1990). Among them, several studies emphasized on the role of seasonal modulation of the strength of coupled ocean–atmosphere instability (Battisti 1988; Chang et al. 1994; Tziperman et al. 1997, 1998; Harrison and Vecchi 1999; Neelin et al. 2000; Galanti and Tziperman 2000; An and Wang 2001). For example, Tziperman et al. (1998) argued that the seasonally varying amplification of Rossby and Kelvin waves due to coupled instability forces an ENSO event to mature during the boreal winter season when this coupled instability is at its minimum strength. Due to the weak air–sea coupling strength during the boreal winter season, the generation of Kelvin waves is damped out by that of the reflected Rossby waves that were generated with stronger amplitude during the previous season. They validated this theory using the intermediate coupled model, called the Cane-Zebiak (CZ) model (Zebiak and Cane 1987). In addition, Harrison and Vecchi (1999) argued that seasonally-varying meridional migration of ENSO-related surface wind anomalies is an important factor in determining the season of ENSO phase-locking, which is also linked to the seasonal modulation of air–sea coupling. Similarly, An and Wang (2001) showed that the seasonal variation of ENSO-related wind anomalies in the western Pacific is important for simulating realistic phase-locking in the CZ model. They also emphasized the role of seasonal variation of mean tropical convergence zone, especially for La Nina phase-locking, which regulates anomalous convective heating through atmospheric convergence feedback. The authors also argued the anomalous atmospheric cooling related to La Nina is confined over the region with climatological low-level convergence due to the nonlinear relationship between low-level divergence and atmospheric cooling.

As the seasonal variation in the atmosphere, the seasonal variation in the ocean also plays an important role in ENSO phase-locking (Battisti 1988; An and Wang 2001). For example, An and Wang (2001) mentioned that the seasonal variation in the mean thermocline depth over the eastern Pacific can affect the ENSO phase-locking. They showed that the relatively deeper thermocline depth during the boreal summer season than the other seasons regulates the local air–sea interaction during the boreal summer.

Even though these hypotheses are widely accepted, there are limitations that most of them are only validated by intermediate models. The fact is that ENSO phase-locking is not properly simulated by some global climate models (Wittenberg et al. 2006), which either show little seasonal modulation or has phase-locking to a wrong season. Furthermore, it is unclear why some models fail to simulate phase-locking of ENSO to boreal winter. Therefore, in this study we will evaluate some current coupled general circulation models (CGCMs) in terms of their ability to reproduce the ENSO phase-locking. Especially, we integrate the GFDL CM2.1 with different convective parameter value; the parameter is called “Tokioka parameter” (Tokioka et al. 1988; Kim et al. 2011). We will show that the ENSO phase-locking changes dramatically with small change of this convective parameter, in addition to the change of the ENSO magnitude to this parameter as shown in Kim et al. (2011). In addition to examining whether the existing hypotheses (i.e., role of air–sea coupling strength and tropical climatological states on the ENSO phase-locking) about the ENSO phase-locking exist in these CGCMs, we will investigate possible impacts of other ENSO feedbacks on the ENSO phase-locking.

We will analyze the GFDL CM2.1 archives, and evaluate the ability of reproducing ENSO phase-locking by the models that participated in the Coupled Model Intercomparison Project phase-3 (CMIP3). This is to examine whether the key processes responsible to the ENSO phase-locking in the GFDL CM2.1 simulations are also present in different CGCMs. By understanding the mechanism of ENSO phase-locking in a multi-model framework, we may find future direction on improving CGCMs.

This paper is organized as follows. In Sect. 2, descriptions of the models and observational data used in this study are provided. Critical factors for the ENSO phase-locking in the simulations of GFDL CM2.1, and CMIP3 models are shown in Sects. 3, and 4, respectively. A summary and conclusions are presented in Sect. 5.

2 Model and data

2.1 GFDL CM 2.1 simulations with different Tokioka parameter

Here, a series of 100-year-long simulations of GFDL CM2.1 with different Tokioka parameter values are analyzed. The oceanic component of GFDL CM2.1 is the Modular Ocean Model version 4.1p1 (MOM4.1p1; Griffies et al. 2005; Gnanadesikan et al. 2006). MOM4.1p1 has 1° × 1° horizontal resolution, telescoping to 1/3° meridional spacing near the equator, and 50 vertical levels. The atmospheric component is the GFDL Atmospheric Model version 2p13 (AM2p13; Delworth et al. 2006), with a 2° (latitude) by 2.5° (longitude) grid spacing and 24 vertical levels. A diffusion-type of Convective Momentum Transport (CMT) parameterization is included in AM2p13 (Delworth et al. 2006).

A total of five GFDL CM2.1 simulations are performed with different Tokioka parameter values. The Tokioka modification (Tokioka et al. 1988) is designed to suppress convective plumes when the entrainment rate in a cumulus parameterization is less than a threshold function of the planetary boundary layer (PBL) depth, defined as μ_min = α/D, where D is the PBL depth and α, the Tokioka parameter, is a non-negative constant (Kim et al. 2011). The use of large α-value enhances entrainment rate simulated in the model, by suppressing convective plumes with small entrainment rates. The selected magnitude of Tokioka parameter is slightly different from Kim et al. (2011), which used irregular intervals between 0.002 and 0.04. Instead, we redo 100-year-long integrations with the Tokioka parameter of 0.005–0.045 with a fixed interval of 0.01. Hereafter, Tok005 denotes the simulation with α = 0.005. Likewise, we use Tok015, Tok025, Tok035, and Tok045 for the simulations with α = 0.015 0.025, 0.035 and 0.045, respectively. Note that Tok025 is the simulation that uses the same value as given in the standard version of GFDL CM2.1, which participated in the CMIP3.

2.2 CMIP3 models

We analyze pre-industrial runs of the climate model integrations in the CMIP3 archive. The CO₂ concentration of the pre-industrial run is fixed as 280 ppm for the whole integration period. We exclude the models with small sea surface temperature (SST) variability over the tropical eastern Pacific (i.e., having too weak ENSO variability). After that, 14 CGCM simulations from the CMIP3 archive are remained. Descriptions on each of the 14 model simulations are summarized in Table 1.

Table 1 Description of CGCMs used in this study based on the CMIP3 archive

2.3 Observational data

To verify the model outputs, we use the observed atmospheric and oceanic data. The SST data is the improved Extended Reconstructed Sea Surface Temperature version 2 (ERSST V.2; Smith and Reynolds 2004) from the National Climate Data Center. The monthly-mean data of surface wind, zonal wind stress, surface net heat flux are from the ECMWF 40 Year Re-analysis (ERA-40) reanalysis (Uppala et al. 2005). The periods of ERSST V.2 and ERA40 data are 52 and 43 years from 1959 to 2010 and from 1959 to 2001, respectively. The monthly-mean precipitation is the Modern ERa Retrospective-analysis for Research and Applications (MERRA; Rienecker et al. 2011) from 1980 to 2010. For sub-surface temperature, we use the NCEP Global Ocean Data Assimilation System (GODAS; Behringer and Xue 2004) from 1981 to 2010.

3 ENSO phase-locking in GFDL CM2.1 simulations

In this section, we analyze the GFDL CM2.1 simulations with different Tokioka parameter values. Prior to investigating the phase-locking of ENSO, we firstly examine the overall ENSO magnitude in response to the change of Tokioka parameter. Figure 1 shows the regressed SST and precipitation anomalies onto NINO3.4 SST anomaly (SSTA) index using the whole 100-year integration. In the observation, the regressed SST magnitude is about 1 °C, and the precipitation anomaly is located over the central Pacific. In the model simulations, the ENSO-related SSTA is relatively stronger and is shifted to the west compared to the observed. As the Tokioka parameter value is increased, the ENSO-related SSTA tends to be stronger though the change is not quite linear. Kim et al. (2011) showed that as the Tokioka parameter value increases, the atmospheric responses to ENSO-related SST forcing are shifted eastward because the simulations with larger Tokioka parameter values show more precipitation and weaker descending motion over the eastern Pacific. Then, the eastward shift of atmospheric responses induces effective deepening of the thermocline over the eastern Pacific, which leads to stronger ENSO variability (Kang and Kug 2002; Watanabe et al. 2011). As shown in Fig. 1, the eastward shift of precipitation response is consistent with Kim et al. (2011).

Fig. 1

Regressed precipitation (shaded) and SSTA (contour) onto the NINO3.4 index in a the observation and b–f GFDL CM2.1 simulations with different Tokioka parameter values using the whole 100-year integration

In addition to the overall ENSO variability, Fig. 2 shows the standard deviation of equatorially-averaged (5°S–5°N) SSTAs in the observation and GFDL CM2.1 simulations with different Tokioka parameter values for each calendar month, in order to evaluate the model’s ability of reproducing the ENSO phase-locking. The observed SST variability is robust over the eastern Pacific, with peak variability appearing during the boreal winter season and the minimum of the SST variability appearing between March and May depending on the longitude.

Fig. 2

Standard deviation of equatorially-averaged (5°S–5°N) SST anomalies for each calendar month in a the observation and b–f GFDL CM2.1 simulations with different Tokioka parameter values

In the model simulations, it is obvious that there is dramatic change of ENSO phase-locking with different Tokioka parameter values. For example, in the simulations with small Tokioka parameter value, the simulated SST variability is strongest during the boreal summer season, which is quite different from the observed. On the other hand, the simulations with larger Tokioka parameter values, such as Tok035 and Tok045, show smaller SST variability during the boreal summer season; so the unrealistic summer peak disappears. Also, it is interesting that the larger variance of SST during the boreal summer season is slightly shifted to the east as the Tokioka parameter value increases. For example, the maximum SST variability in July is located over 120°W in the simulations with small Tokioka parameter values, while it is located around 110°W in the simulations with large Tokioka parameter values.

In order to show the seasonality of ENSO amplitude, Fig. 3 shows the standard deviation of NINO3.4 SSTAs (i.e., SSTAs averaged over 170–120°W, 5°S–5°N) in the observation and model simulations for each calendar month. Note that the standard deviation in each calendar month is normalized by the standard deviation using all the seasons, in order to focus on the seasonal change of NINO3.4 variability. In the observation, the peak of NINO3.4 standard deviation is in December, while the minimum of NINO3.4 standard deviation is between April and May. However, in Tok005 and Tok015 the ENSO peak is during the boreal summer season, in July. The minimum of ENSO variability in Tok005 or Tok015 is between April and May. As Tokioka parameter value increases, this unrealistic summer ENSO peak is no longer there. For example, in Tok035 and Tok045 the peak of ENSO variability is during the boreal winter season (i.e., between November and January), while the minimum is between April and May in spite of relatively small range of ENSO amplitude. Clearly, the ENSO phase-locking is quite sensitive to the change of this convective parameter. Hereafter, we will analyze the model simulations to investigate the possible mechanism that results in the dramatic change of ENSO phase-locking.

Fig. 3

Standard deviation of NINO3.4 SST anomalies in the observation and GFDL CM2.1 simulations for each calendar month. Note that the standard deviation for each calendar month is normalized by the standard deviation for all months to focus on the seasonal change of NINO3.4 variability

3.1 Atmospheric feedback

As mentioned earlier, Tziperman et al. (1998) argued that the air–sea coupling strength, which is an index to measure how strongly surface wind stress responds to the unit change of eastern-Pacific SST, is at its minimum during the boreal winter season when the ENSO tends to be at its peak. According to the delayed oscillator theory, it takes the downwelling Kelvin waves, which are generated by surface wind forcing to amplify El Nino-related SSTA, about 1 month to travel from the central to the eastern Pacific (Tziperman et al. 1998). On the other hand, it takes the reflected upwelling-favorable Rossby waves, which damp El Nino-related SSTA, 6 months to reach the eastern Pacific (Graham and White 1988; Suarez and Schopf 1988). It means Kelvin waves over the eastern Pacific are immediately affected by central-Pacific air–sea coupling strength with 1 or 2 months of time delay, while it has 6 months of time delay between the magnitude of the air–sea coupling strength and that of Rossby waves over the eastern Pacific. In other words, when the air–sea coupling strength is at its minimum, the magnitude of the Kelvin waves also becomes minimum with short delays, while that of Rossby waves is maintained until about 6 months later. Therefore, the generation of downwelling Kelvin waves is compensated by that of the reflected upwelling Rossby waves, and there is no more ENSO growth after the season when the air–sea coupling strength is at its minimum.

Figure 4 shows the air–sea coupling strength, which is measured by linear regression of zonal wind stress anomalies with respect to the NINO3.4 index for each calendar month using the observation and GFDL CM2.1 simulations. This quantity represents the strength and spatial pattern of atmospheric response to the ENSO-related SSTAs. Note that it is one of conventional methods to measure the air–sea coupling strength in climate models (Jin 1997; Lloyd et al. 2009; An et al. 2010; Choi et al. 2011). The westerly (easterly) anomalies associated with the El Nino are related to positive (negative) atmospheric feedback; therefore, the air–sea coupling strength is stronger when zonally-integrated wind stress anomaly is larger. In the observation, there is an anomalous westerly over the central Pacific around the dateline, while weak anomalous easterly is located over the western Pacific. Over the central Pacific, the anomalous westerlies are the strongest in the boreal fall season between August and October, and are the weakest between December and January, which is possibly related to the southward shift of equatorial zonal wind anomalies (Harrison and Vecchi 1999; Vecchi and Harrison 2000). Even though there is a local minimum in May over the central Pacific, the westerly wind stress anomaly over 140–120°W would enhance the air–sea coupling strength related to the ENSO. In addition, the anomalous easterlies over the western Pacific are stronger during winter and early spring. By combining the wind anomalies over the central and eastern Pacific, the zonally-integrated air–sea coupling strength over the Pacific (120°E–90°W) is minimal during the boreal winter season in January when the ENSO tends to be at its peak in the observation (not shown).

Fig. 4

Regressed zonal wind stress over the equatorial region (5°S–5°N) onto the NINO3.4 index (units: N/m²/°C) for each calendar month in a the observation, b Tok005, c Tok015, d Tok025, e Tok035, and f Tok045

On the other hand, in the GFDL CM2.1 simulations, the seasonality of air–sea coupling strength is distinguishably different from that in the observation. For example, all model runs show an increase of SST variance from May to July, which is not seen in observations. This feature corresponds quite well to the air–sea coupling strength, which shows a large increase from March to May (i.e., about 2 months earlier than the increase in SST variance). In addition, the differences among the five simulations are also large. In Tok005, there is an abrupt decrease in coupling strength from May to July, which might be associated with a decrease of in SST variance from July. In addition, it is obvious that the air–sea coupling strength is at its minimum during the boreal summer season and at its maximum during the boreal winter season around 150°E. However, as the Tokioka parameter value increases, the air–sea coupling strength during the boreal summer season is gradually increased, and the decrease of the coupling strength is shown from December to January. It means that the minimum of the air–sea coupling strength is at the boreal winter season between January and April. For example, in Tok045 the air–sea coupling strength during the boreal summer season (i.e., June–August) is as strong as that during the fall season (i.e., September–November), and the minimum is between February and April. This result is consistent with the argument of Tziperman et al. (1998) that the season with the minimum air–sea coupling strength is the ENSO peak season. In Tok005 and Tok015, the air–sea coupling strength is minimum during the boreal summer season between June and August, which might generate the peculiar summer peak of ENSO. When the air–sea coupling strength is minimum between June and August, the SST amplification due to the Kelvin waves is weakened 1 or 2 months later, while the magnitude of SST damping due to the Rossby waves is still strong. Therefore, the SST damping due to the Rossby waves overwhelms in the boreal fall season, which means El Nino-related SST shows no further growth; therefore, the ENSO peaks during the boreal summer season. In contrast, the coupling strength in Tok035 and Tok045 is relatively larger during the boreal summer, so the SSTA can develop further in the following season. This can restrain the summer peak of SSTA, and therefore favors a winter peak.

One may ask whether the arguments (Tziperman et al. 1998) can be applicable to the climate model, because the maximum ENSO-related wind forcing tends to be shifted to the west than the observed. In GFDL CM2.1 simulations, the ENSO-related wind stress anomaly is shifted to the west about 20° than the observed (not shown). This might change the travel time of oceanic waves to eastern Pacific and relationship between the seasonal evolution of air–sea coupling strength and that of ENSO phase-locking from the observed. However, based on the simple calculation using theoretical speed of oceanic waves, it is found that the time lag between Kelvin and Rossby wave is roughly shorted about 1 month with 20° westward shift of wind stress forcing. It implies that arguments in Tziperman et al. (1998) which argue about the ENSO peak time is still applicable in the model, because it originally designed to explain why ENSO events shows peak during the winter and not during summer. Tziperman et al. (1998) already mentioned that it does not explain why the ENSO peak in November, December, or January.

3.2 Climatological thermocline depth in boreal summer season

In the previous sub-section, we showed that the air-sea coupling strength is important to determine the turnabout season of ENSO. In addition to the positive atmospheric feedback, it is worthwhile to investigate oceanic factors that are responsible for the excessive ENSO growth during the boreal summer season in the simulations with small Tokioka parameter values. This will provide more insights how the ENSO phase-locking is controlled in complex CGCM.

First, we investigate the climatological thermocline depth that determines the strength of thermocline feedback according to An and Wang (2001). They argued that the deepening of the eastern Pacific seasonal-mean thermocline depth in the boreal summer and shoaling in the boreal fall favor ENSO turnaround in late fall through regulating local air–sea interaction. That is to say the deepening (shoaling) of seasonal-mean thermocline depth in the boreal summer season prevents (amplifies) the growth of ENSO, because SST response to an anomaly in the thermocline depth is decreased when the seasonal-mean thermocline depth is deepened (Bejarano and Jin 2008; Collins et al. 2010). This is related to the weakening of thermocline feedback, which denotes the vertical advection of anomalous sub-surface temperature due to seasonal-mean upwelling.

To investigate how seasonal-mean thermocline depth is changed in the GFDL CM2.1 simulations, Fig. 5 shows the seasonal-mean thermocline depth (defined by the 20 °C isotherm depth) relative to annual mean values in the observation and GFDL CM2.1 simulations. To investigate the difference among the GFDL CM2.1 simulations with different Tokioka parameter values, deviation in each simulation from the ensemble mean of the five simulations is denoted as shading, which can be denoted as $V^{*} \left( {x,m;p} \right) = V\left( {x,m;p} \right) - \left\langle {V\left( {x,m} \right)} \right\rangle$, where $\left\langle {V\left( {x,m} \right)} \right\rangle = \frac{1}{5}\sum\nolimits_{{p = 1}}^{5} {V(x,m;p)}$, when x, m denotes longitudes, and calendar month, respectively, and p = 1, 2, 3, 4, and 5 is Tok005, Tok015, Tok025, Tok035, and Tok045, respectively. In the observation, the semi-annual component is robust (Fig. 5a). For example, over the eastern Pacific there are negative anomalies of seasonal-mean thermocline depth during March–May and during August–October, and positive anomalies during May–July and during October–January. This semi-annual cycle is also clear over both central and western Pacific. Consistent with An and Wang (2001), the seasonal cycle of the seasonal-mean thermocline depth over the eastern Pacific is positive during the boreal summer season and negative during the fall season.

Fig. 5

Seasonal cycle of thermocline depth (units: m; contour) for each calendar month in a the observation, b Tok005, c Tok015, d Tok025, e Tok035, and f Tok045. The shading in the model simulations denotes the deviation of values from the averaged-value of all the simulations. Note that the shading is deviation of the total annual-mean value, not just a deviation of the seasonal-mean value. The thermocline depth in this study is defined by the 20 °C isotherm depth

However, in the model simulations the annual component is dominant rather than the semi-annual component; especially in the simulations with small Tokioka parameter values, which show a single cycle of thermocline depth over the eastern Pacific, which is the deepest during the boreal winter time and shallowest during the boreal summer time. This means the thermocline deepening during the boreal summer season is not reproduced in the simulations with small Tokioka parameter values. However, in Tok035 and Tok045 the semi-annual component of the seasonal-mean thermocline depth appears over the eastern Pacific to some extent, with a positive anomaly during the boreal summer season (i.e., May–July).

Interestingly, the most robust model difference over the eastern Pacific is during the boreal summer season. It is evident that the simulations with smaller Tokioka parameter values exhibit shallower thermocline depth, particularly during the boreal summer time. Because the shallow (deep) thermocline depth during the boreal summer season strengthens (weakens) the thermocline feedback (An and Jin 2001), the SST variability during the boreal summer can be intensified (reduced) in the simulations with small (large) Tokioka parameter values.

3.3 Climatological zonal SST gradient in boreal summer season

In addition to the thermocline feedback, the zonal advective feedback is also a critical component in enhancing SST variability associated with ENSO (An and Jin 2001). The zonal advective feedback is proportional to the zonal gradient of climatological SST, which is seasonally varying. To investigate the seasonal SST changes, Fig. 6 shows the seasonal-mean SST. In the observation, there are positive SSTAs during the boreal spring season, and negative SSTAs during the boreal fall season (Xie 1994). Overall, this feature is well simulated in all the GFDL CM2.1 simulations. However, the magnitude of the seasonal cycle in the simulations is stronger than that in the observation, especially in the simulations with small Tokioka parameter values.

Fig. 6

Same as Fig. 5, except for the SST (units: °C)

The difference of SST among the simulations denoted in shading shows that the climatological SST is generally cooler as the Tokioka parameter value is increased. For example, the SST in Tok005 and Tok015 is warmer than that in Tok035 and Tok045 in general. Kim et al. (2011) argued that the high cloud, which is maintained by deep convection, is reduced when the deep convection is suppressed by a larger Tokioka parameter value. Then, the associated cloud feedback, particularly related to longwave radiation, results in SST cooling.

However, the degree of SST change also exhibits strong locality and seasonality. For example, the SST warming is relatively weak over the eastern Pacific, and it is weakest during the boreal summer. Therefore, it seems that the eastern Pacific seasonal-mean SST during the boreal summer is not much affected by the change in Tokioka parameter. This is related to the degree of convective activity in this region. We will return to discuss this issue later in this section.

This seasonal dependency of SST difference leads to a change in seasonal-mean zonal SST gradient. During the boreal summer season, it is striking that the zonal SST gradient over the tropical Pacific is stronger when Tokioka parameter is smaller. This difference in seasonal-mean SST would lead to several changes in ENSO feedback during the boreal summer season. First, the change in the mean zonal SST gradient leads to different strength of zonal advective feedback (An et al. 1999; Jin and An 1999; An and Jin 2001). Since the zonal advective feedback represents the zonal advection of the climatological temperature due to anomalous zonal currents, the strength of the climatological zonal SST gradient is a critical factor in determining the strength of the zonal advective feedback. Based on the strong seasonal-mean zonal SST gradient during the boreal summer season, the zonal advective feedback in the simulations with small Tokioka parameter values is expected to be the strongest, which leads to excessive SST variability during the boreal summer season. As shown in Fig. 2, the westward shift of maximum SST variability during the boreal summer in the simulations with small Tokioka parameter is also conceived that stronger zonal advective feedback can be responsible for the westward shift of the maximum SST variability.

3.4 Atmospheric damping

In addition to the zonal advective feedback, the change of the seasonal-mean SST can affect the atmospheric damping during ENSO events. To quantify the strength of ENSO-related atmospheric damping, Fig. 7 shows the regressed atmospheric heat flux anomalies averaged over the NINO3.4 region onto the NINO3.4 SSTA index during JJA. Note that the positive sign denotes that the anomalous heat flux enters the ocean; therefore, it acts to warm the ocean temperature. The total heat flux is between −3 and −4 W/m² in Tok005, Tok015, and Tok025, and is around −5 W/m² in Tok035 and Tok045, indicating that the surface heat flux further damps the ENSO SSTAs in the simulations with large Tokioka parameter values during the boreal summer season. Among the surface flux terms, it is found that the latent heat flux is responsible for this change among the GFDL CM2.1 simulations, while the other heat flux terms do not show any systematic changes (not shown). Consistent with the net heat flux, the latent heat flux regressed onto the NINO3.4 index gradually increases in the simulations with smaller Tokioka parameter, which means there is less latent heat loss during the boreal summer season to amplify ENSO-related SSTAs. It implies that the latent heat flux plays some role in generating strong summer ENSO variability in the simulations with small Tokioka parameter.

Fig. 7

Regressed net surface heat flux (black) and latent heat flux (red) anomalies averaged over the NINO3.4 region onto the NINO3.4 SSTA index (units: W/m²/°C) from the averaged value of all GFDL CM2.1 simulations during the JJA season. The positive sign denotes that the anomalous heat flux goes into the ocean; therefore, it acts to warm the ocean temperature

To hypothesize this possible mechanism, we introduce a simple bulk formula for latent heat (LH) flux calculation as follows:

$$ {\text{LH}} \propto {\text{U}}({\text{Q}}_{\text{s}} - {\text{Q}}_{\text{a}} ) $$

where U, Q_s, and Q_a are surface wind speed, specific humidity at the air–sea interface, and specific humidify in the near-surface atmosphere, respectively. After linearizing this expression, we find that the change of El Nino-related LH flux among the model simulations is mainly determined by the change of anomalous wind speed multiplied by climatological humidity difference, or ${\text{U}}^{\prime } \overline{{\left( {{\text{Q}}_{\text{s}} - {\text{Q}}_{\text{a}} } \right)}}$. During the El Nino, the westerly anomaly over the equatorial central-eastern Pacific reduces the wind speed and LF flux anomaly to generate anomalous heat into the ocean (e.g., Kug et al. 2009). We find that this mechanism is intensified in the simulations with small Tokioka parameter. First, the El Nino-related wind speed is further reduced in the simulations with small Tokioka parameter. For example, the wind speed anomaly over the NINO3.4 region regressed onto the NINO3.4 SSTA index is −0.17 and −0.19 m/s in Tok005 and Tok015, respectively, while it is −0.14 and −0.11 m/s in Tok035 and Tok045, respectively. Second, it is expected that the term $\overline{{\left( {{\text{Q}}_{\text{s}} - {\text{Q}}_{\text{a}} } \right)}}$ increases in the simulations with small Tokioka parameter with the aid of high SST, because Q_s is determined by SST and Q_a is nearly constant at the surface. Therefore, it acts to intensify the LH flux increase due to wind speed change in the simulations with small Tokioka parameter.

3.5 Linkage among ENSO feedbacks through mean state change

To summarize, there are several factors that determine the summer ENSO peak in the GFDL CM2.1 simulations with small Tokioka parameter. One of them is the minimum air–sea coupling strength during the boreal summer season. A second factor is one of the strong ENSO feedback processes, such as the strong thermocline feedback and the zonal advective feedback. A third factor is the weak atmospheric damping. Even though these factors are discussed separately, it is shown that the change of seasonal-mean zonal SST gradient is a main factor for change of ENSO phase-locking. This means that all the factors are closely linked to each other via the basic state change, especially the change of seasonal-mean zonal SST gradient. First, the strong seasonal-mean zonal SST gradient in the boreal summer season reduces the convection over the eastern Pacific. If the background descending motion is too strong over the eastern Pacific, warm SSTA hardly produces any positive precipitation anomaly, indicating the weakening of air–sea coupling strength. At the same time, the enhanced zonal SST gradient and co-occurring thermocline shoaling over the eastern Pacific lead to excessive zonal advective feedback and thermocline feedback. In addition, the weak ENSO damping due to increase in LH flux is also hypothesized to be caused by the high SST over the eastern-central Pacific, which is related to the excessive zonal SST gradient.

The question remaining is why the zonal SST gradient increases with small Tokioka parameter, especially during the boreal summer season. To answer this, we first need to understand the characteristics of Tokioka parameter. Because the Tokioka parameter introduces constraints to the convective activity, deep convection is highly suppressed when a large Tokioka parameter value is used. The point is, because the Tokioka parameter is to regulate the strength of convective activity, change in Tokioka parameter can effectively modulate climate state when/where the deep cumulus convection is strongest.

To investigate the strength of the convective activity over the tropical Pacific, Fig. 8a shows the ratio of the monthly-mean cumulus convective precipitation to the monthly-mean total precipitation (sum of precipitation via cumulus convection and large-scale condensation) in Tok025 for each calendar month. Figure 8b shows the standard deviation of SST change among the GFDL CM2.1 simulations. For Fig. 8b, deviation of total SST from the average of all the simulations is obtained, then root-mean-square (RMS) of these deviations from the five GFDL CM2.1 simulations is calculated. That is, the RMS of $V^{*} \left( {x,m;p} \right) = V\left( {x,m;p} \right) - \left\langle {V\left( {x,m} \right)} \right\rangle$ is calculated, where $\left\langle {V\left( {x,m} \right)} \right\rangle = \frac{1}{5}\sum\nolimits_{{p = 1}}^{5} {V(x,m;p)}$, when x, m, and p denotes longitudes, calendar month, and each experiments, respectively. For the convective precipitation ratio, it is obvious that the minimum convective precipitation in the eastern Pacific is during the boreal summer season. This is due to the cold SST during the boreal summer season. Because the convective activity over the eastern Pacific is suppressed due to cold SST, especially during the boreal summer season, the change of SST due to the change of Tokioka parameter is also minimum over the eastern Pacific during boreal summer season. That is to say the SST warming by small Tokioka parameter is the weakest over the eastern Pacific during the boreal summer season as shown in Fig. 6. Therefore, the tropical zonal SST gradient is much increased during the boreal summer season.

Fig. 8

a The ratio of the mean convective precipitation to the mean total precipitation for each calendar month in Tok025 simulation. b The standard deviation of SST change in the GFDL CM2.1 simulations, which means that the RMS of the deviation of total SST from the average of all the simulation is calculated. The shading is a deviation from the annual-mean value over the Pacific (120°E–90°W)

4 ENSO phase-locking in CMIP3 models

Until now, we analyzed only the GFDL CM2.1 simulations with different Tokioka parameter values and investigated the important factors that determine the ENSO phase-locking. One may ask whether or not these factors are also crucial to determine the ENSO phase-locking in other CGCMs. Therefore, we will examine mechanisms for the ENSO phase-locking using the 14 CGCMs participated in the CMIP3. Especially, we will focus on the air–sea coupling strength and the tropical seasonal-mean states that are crucial to determine the ENSO-phase locking in the GFDL CM2.1 simulations.

Prior to investigating the air–sea coupling strength and mean states in the CMIP3 models, we firstly examine the ENSO phase-locking in the 14 CMIP3 models. Figure 9 shows the standard deviation of equatorially-averaged (5°S–5°N) SSTAs in the observation and CMIP3 models for each calendar month. Some models have their peak of SST variability during the boreal winter season, even though the simulated ENSO peak may be 2 or 3 months delayed in several models. For example, the peak of SST variability over the eastern Pacific is between January and February in CNRM_CM3_0, IAP_FGOALS1_0_g, and IPSL_CM4, and is between November and December in MIUB_ECHO_G, INGV_ECHAM4, and MRI_CGCM2_3_2a.

Fig. 9

Standard deviation of equatorially-averaged (5°S–5°N) SST anomalies in (1) the observation and (2–15) CMIP3 models for each calendar month

Interestingly, we find that some models simulate the ENSO peak at the boreal summer season. In CSIRO_MK3_0, CSIRO_MK3_5, GFDL_CM2_0, GFDL_CM2_1, and INMCM3_0, the peak of SST variability is in July. This implies there may be common problems in these models in terms of simulating the ENSO phase-locking in the boreal summer season. Among the models with summer ENSO peak, CSIRO_MK3_5 and INMCM3_0 simulate stronger SST variability over the central Pacific rather than the eastern Pacific.

To examine whether the ENSO phase-locking in the CMIP3 models is also controlled by the air–sea coupling strength, Fig. 10 shows the air–sea coupling strength averaged over the equatorial Pacific region (120°E–90°W, 5°S–5°N) in the observation and CMIP3 models. We use the Pacific-averaged air–sea coupling strength, because the impact of wind stress forcing can reach the eastern Pacific through the propagation of the oceanic waves. Note that the five models from No. 2 to 6 have their peak of SST variability during the boreal summer season.

Fig. 10

Regressed zonal wind stress averaged over the equatorial Pacific region (120°E–90°W, 5°S–5°N) onto the NINO3.4 index (units: N/m²/°C) for each calendar month in (1) the observation and (2–15) CMIP3 models. Note that the air–sea coupling strength larger (smaller) than the annual mean value is denoted as red (blue) bar

The seasonal evolution of the air–sea coupling strength is well matched to that of ENSO variability with 1–2 month delays. For example, the increase of the air–sea coupling strength is shown between March to Mary in CNRM_CM3_0, MIUB_ECHO_g, and MRI_CGCM2_3_2a, and the ENSO variability shows abruptly increase after 1–2 months during May to July. In addition, the minimum of air–sea coupling strength is also well matched to the ENSO peak month in CMIP3 models. In most of the models with winter peak of SST variability, the minimum of the air–sea coupling strength is between January and March. On the other hand, the models like CSIRO_MK3_5, GFDL_CM2_0, and GFDL_CM2_1, which have summer ENSO peak, has minimum air–sea coupling strength during the boreal summer season. It supports the notion that the air–sea coupling strength is a critical factor in determining ENSO phase-locking in the CMIP3 models.

Next, we check the mean states over the tropical Pacific. Especially, we examine the seasonal-mean thermocline depth and zonal SST gradient during the boreal summer season that determine the strengths of two dominant ENSO feedbacks, namely, the thermocline feedback and zonal advection feedback, respectively. Note that the zonal SST gradient is only an index for the zonal advective feedback, but also a proxy for the air–sea coupling strength as mentioned in Sect. 3.5. Figure 11 shows the scatter diagram between the bias (i.e., model climatology—observed climatology) of seasonal thermocline depth and zonal SST gradient anomaly at June–July season. The zonal SST gradient is defined as the SST difference between the two boxes over the western Pacific (WP) and eastern Pacific (EP). The box for the western Pacific covers 130°E–160°W, 5°S–5°N, and that for the eastern Pacific is over 150–90°W, 5°S–5°N; then, the zonal SST gradient is obtained by calculating SST(WP) minus SST(EP), where SST(WP) and SST(EP) are box-averaged SST. The thermocline depth over the eastern Pacific is the value of 20 °C isotherm depth averaged over the eastern Pacific box. Note that the scatter using GFDL CM2.1 in the CMIP3 archive is replaced by Tok025 in the scatter diagram, because the model configuration of Tok025 is identical to that of the GFDL CM2.1 simulation in the CMIP3 archive. The values using Tok025 and GFDL CM2.1 simulation in the CMIP3 archive were similar (not shown).

Fig. 11

Scatter diagram between the bias of seasonal-mean zonal SST gradient anomaly (x-axis) and thermocline depth (y-axis) in June–July months in the CMIP3 models and GFDL CM2.1 simulations. The models that have summer ENSO peak (CSIRO_MK3_0, CSIRO_MK3_5, GFDL_CM2_0, GFDL_CM2_1, and INMCM3_0) are denoted by green squares, while those that have winter ENSO peak are denoted by black squares. In addition, the GFDL CM2.1 simulations are denoted by red circles with various shades (e.g., Tok005 with light red, and Tok045 with dark red). The zonal SST gradient is defined by the difference of the WP box over 130°E–160°W, 5°S–5°N from the EP box over 150–90°W, 5°S–5°N, and thermocline depth over the eastern Pacific is the value averaged over 180–90°W, 5°S–5°N

In the scatter diagram, there is a linear relation between bias of seasonal-mean thermocline depth over the eastern Pacific and seasonal-mean zonal SST gradient. It means that strong seasonal-mean zonal SST gradient and associated anomalous easterly is related to the shallow seasonal-mean thermocline depth over the eastern Pacific. It also implies that the change of the mean zonal SST gradient due to the change of Tokioka parameter is linked to changes in surface wind and thermocline depth as mentioned earlier. It is also interesting that the models with summer ENSO peak commonly simulate excessive mean zonal SST gradient except for one model (INMCM3_0). Similar to the mean zonal SST gradient, most of the models with summer ENSO peak tend to have shallow mean thermocline depth over the eastern Pacific, even though some models (i.e., CNRM_CM3_0, IPSL_CM4, and MRI_CGCM2_3_2a) with shallow mean thermocline depth do not have summer ENSO peak.

To investigate the relationship between zonal SST gradient (or thermocline depth) and summer ENSO variability further, we calculate the correlation between summer NINO3.4 variability and bias of seasonal-mean zonal SST gradient (or thermocline depth) using all 18 climate models (i.e., 13 CMIP3 models plus 5 GFDL CM2.1 simulations because one of the CMIP3 is the same as GFDL CM2.1). To focus on the phase-locking of ENSO among climate models, the standard deviation of the NINO3.4 index during JJA season is divided by that during the whole period. The correlation coefficient between zonal SST gradient and normalized summer NINO3.4 standard deviation is 0.4 at 95 % confidence level, while the correlation between thermocline depth and normalized summer NINO3 standard deviation is 0.1 only. This implies that the zonal SST gradient will be a relatively more important component in generating summer ENSO peak in the climate models. Or, this emphasizes the relative important role of the air–sea coupling strength in ENSO phase-locking in CMIP3 models.

5 Summary and conclusions

In this study, the ENSO phase-locking in five GFDL CM2.1 simulations with different Tokioka parameter values and 14 CMIP3 models is examined to understand what the critical factors are in reproducing the observed phase-locking in winter. In the model sensitivity experiments using the GFDL CM2.1 model, the simulations with smaller Tokioka parameter values have ENSO peak during the boreal summer season. From these sensitivity experiments, we have revealed a major problem in simulating unrealistic summer ENSO peak, namely, the differences in climatological zonal SST gradient and its related mean state change that lead to the change in phase-locking of the ENSO. Figure 12 is a conceptual diagram about the changes in the mean state and their linkage to the ENSO phase-locking during the boreal summer season for small Tokioka parameter. When the Tokioka parameter is small, deep convection is easily generated. The increase of high cloud amount leads to the increase of downward longwave radiation; in turn, it leads to SST warming. This process is especially robust over the western Pacific where mean convection is active. On the contrary, eastern Pacific SST is insensitive to the change of Tokioka parameter because of the weak climatological convective activity there. Therefore, the SST warming due to change in Tokioka parameter is also relatively weak over the eastern Pacific. This zonally-asymmetric SST change is maximum during the boreal summer season when the convective activity over the eastern Pacific is minimum due to the coolest SST of the year. It means, during the boreal summer season, the SST warming with smaller Tokioka parameter takes place only over the western Pacific; as a result, the seasonal-mean zonal SST gradient is stronger. In turn, it enhances the zonal advective feedback. At the same time, due to the enhanced mean zonal SST gradient, low-level easterly wind is also strengthened. Then, the resultant shoaling of seasonal-mean thermocline depth enhances the thermocline feedback to increase the SST variability during the boreal summer season.

Fig. 12

The conceptual diagram about the change in the mean state and ENSO feedback by decreasing Tokioka parameter in the GFDL CM2.1 simulations

On the atmospheric side, enhanced zonal SST gradient reduces the convection over the eastern Pacific, which weakens atmospheric response to the ENSO-related SSTAs (Ham and Kug 2011; Watanabe et al. 2011). The weakened atmospheric response leads to weakening of the air–sea coupling strength; therefore, the air–sea coupling strength and boundary layer circulation becomes minimum during the boreal summer season. Therefore, it results in weak ENSO variability with 1–2 month delay in the boreal fall season, which is why the ENSO peaks during the boreal summer season. In addition, ENSO damping due to latent heat flux is also weakened by warmer SST over the eastern-central Pacific, which is related to the excessive zonal SST gradient. It implies that zonal SST gradient and its related changes in the thermocline depth, low-level wind, and convective activity lead to a stronger ENSO variability during the boreal summer season.

We also investigate the ENSO phase-locking in the CMIP3 models. Many of these models still have a serious problem in reproducing the phase-locking in winter. In particular, several models give a unrealistic summer peak. By examining the air–sea coupling strength and bias of seasonal-mean oceanic states over the tropical Pacific, it is found that the models, which have a summer ENSO peak, have similar bias to the simulations with smaller Tokioka parameter. That is to say they tend to have weaker air–sea coupling strength and stronger zonal SST gradient during the boreal summer time. These models also have shallower eastern Pacific thermocline than the other models that have a winter ENSO peak. This supports the notion that such biases are quite critical in simulating the phase-locking of ENSO in CGCMs.

This study emphasizes that the mean zonal SST gradient and related changes in basic states are crucial factors to control the ENSO phase-locking through modulating both atmospheric and oceanic feedbacks. The key is that both atmospheric and oceanic feedback changes act in same direction to modulate ENSO phase-locking, does not cancel out each other. Therefore, the quantitative comparisons between factors which might provide more precise insights about the ENSO phase-locking are not given in this study. In addition, it is difficult to separate the role of the single factor in long-term simulation of CGCM, because it is tightly coupled to the other factors. This quantitative comparison might be archived through the additional experiment using simple model whose coupled feedback strength can be easily controlled by changing parameters or prescribed basic states, however, the results from this model can be also different from the result in complex CGCM. Therefore, more dedicated efforts are required for the quantitative comparisons of ENSO-related atmospheric and oceanic feedbacks in complex CGCM, and we leave it as a future work.

To have realistic ENSO phase-locking in climate models is an important issue for a successful ENSO simulation. With these motivations, this study examines the simulations results using various CGCMs to understand the mechanism of ENSO phase-locking in climate model simulations. Failing to phase-lock ENSO in winter would also affect the ENSO prediction skill using climate models, because a unrealistic ENSO phase-locking will cause a different ENSO evolution from the observed. Therefore, it is essential to understand what determines the ENSO phase-locking in climate models. We have shown that a reasonable simulation of ENSO phase-locking is still challenging in some climate models, and there exist common biases in mean states of climate models, which make summer ENSO peak. It gives good clues that the improvement of mean states would lead to a realistic ENSO phase-locking in climate models. In addition, by understanding how the one convective parameter (i.e., Tokioka parameter) dramatically changes the ENSO phase-locking, this study also provides some means to improve climate models.