ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab ocean

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1 Clim Dyn (2016) 46: DOI /s ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab ocean Yanshan Yu 1 Dietmar Dommenget 1 Claudia Frauen 1 Gang Wang 1 Scott Wales 2 Received: 3 November 2014 / Accepted: 16 May 2015 / Published online: 28 May 2015 Springer-Verlag Berlin Heidelberg 2015 Abstract El Nino-Southern Oscillation (ENSO) is the leading mode of interannual global climate variability, which in its essence is often described by the equatorial dynamics of the recharge oscillator with a fixed pattern. Here we explore the idea that ENSO can be simulated in a model with a fixed pattern of sea surface temperature variability following the recharge oscillator mechanism, which interacts with the thermodynamic red noise of a slab ocean. This model is capable of simulating the leading modes of sea surface temperature variability in the tropical Pacific in good agreement with the observations and most coupled general circulation models. ENSO dynamics, amplitude, seasonality, the structure of the leading patterns, its meridional extension, its variations in an eastern and central Pacific pattern and associated positive feedbacks are all influenced and simulated well by including the interaction of recharge oscillator and the thermodynamic coupling to the slab ocean model. We further point out that much of the ENSO diversity in the spatial structure is a reflection of this interaction. However, it also has to be noted that some equatorial dynamics are missing in this model and in coupled general circulation models that are important for the ENSO diversity. Keywords ENSO dynamics Slab ocean ENSO diversity Tropical climate variability Climate model * Dietmar Dommenget dietmar.dommenget@monash.edu Yanshan Yu yanshan.yu@monash.edu 1 2 School of Earth, Atmosphere and Environment, Monash University, Clayton, VIC 3800, Australia The University of Melbourne, Parkville, VIC, Australia 1 Introduction The El Nino-Southern Oscillation (ENSO) mode is the leading mode of interannual climate variability. Theoretical studies describe a number of physical mechanisms and models for the variability generally summarized as ENSO (Wyrtki 1975, 1985; Suarez and Schopf 1988; Battisti and Hirst 1989; Jin 1997; Picaut et al. 1997; Weisberg and Wang 1997; Neelin et al. 1998; Wang et al. 1999). The widely accepted recharge oscillator mechanism is a zero order fast wave approximation of ENSO with only two scalar variables: the east Pacific sea surface temperature (SST) anomaly and mean equatorial Pacific thermocline depth anomaly (Burgers et al. 2005). It describes phase transitions of ENSO by recharge and discharge of heat content over the equatorial Pacific and the SST in the NINO3 region (5 S 5 N, 150 W 90 W). This simple form of the recharge oscillator with a fixed pattern of SST anomalies (the first empirical orthogonal function, EOF-1, of SST anomalies over the tropical Pacific domain) in the tropical Pacific, coupled to an atmospheric general circulation model (AGCM), is able to simulate the main statistical features of ENSO including period, seasonality and skewness (Frauen and Dommenget 2010). However, in their simulation there is only one mode of SST variability in the tropical Pacific by construction, i.e., the fixed pattern. Accordingly, thermodynamic coupling in the tropical Pacific is absent, albeit averaged heat flux anomaly in a much smaller NINO3 region is employed in the recharge oscillator. Dommenget (2010) pointed out that the atmospheric processes without ocean dynamics in his simulation, considered as slab ocean noise, may play an important role in some El Nino events over some time period in the past or future. Other studies also employed an AGCM coupled with a slab ocean to investigate tropical Pacific SST variability (Kitoh

2 1666 Y. Yu et al. et al. 1999; Chang et al. 2007; Dommenget and Latif 2008; Clement et al. 2011; Dommenget et al. 2014). The aim of this study is to see how the thermodynamic coupling, i.e. slab ocean noise, interacts with recharge oscillator to influence the ENSO variability and dynamics. The diversity in the patterns of ENSO events, with more El Nino events occurring in the central Pacific [CP El Nino, or El Nino Modoki (Ashok et al. 2007)] in recent decades rather than the traditional El Nino events in the eastern Pacific (EP El Nino), is of particular interest in recent studies. There is currently a debate on whether El Nino events with distinct locations of maximal SST anomalies differ in their underlying dynamics. Kug et al. (2009) identified stronger zonal advection feedback in CP El Nino events. Kao and Yu (2009) argued that only local SST-atmosphere interactions are involved in CP El Nino events. Singh and Delcroix (2013) found that the poleward discharge of warm water from equatorial band during CP El Nino events is not as pronounced as during EP El Nino events. By contrast, Ashok et al. (2007) stressed the thermocline variations induced by wind stress anomalies are as important to the development of CP El Nino. Ren and Jin (2013) suggested that both types of El Nino events can be understood to a large extent by the recharge oscillator mechanism. Some studies suggested the central and western Pacific is a source of alternative ENSO variability (Rasmusson et al. 1990; van Oldenborgh et al. 2005). Some studies disputed the reality of the statistical distinction between EP and CP. Giese and Ray (2011) indicated, by analyzing the SODA reanalysis data sets, that the peak positions of El Nino events along the equator are following a continuous distribution with no indication of a bimodal structure, which could be interpreted as a spatial red noise null hypothesis. The null hypothesis of red noise suggests that the diversity of ENSO pattern is a reflection of atmospheric noise integrated by the ocean in the absence of any ocean dynamics, solely by the thermodynamic coupling (Hasselmann 1976; Dommenget 2007). This suggests that slab ocean thermodynamics may play a role in observed ENSO diversity. In this study we investigate the effect of both slab ocean noise and recharge oscillator mechanism on the ENSO variability, dynamics and its diversity. We address the questions of how the dynamics of ENSO vary after the slab ocean noise is coupled with the recharge oscillator and how the interaction between these two processes affects the dominant EOF modes of SST variability and the consequent occurrences of El Nino events with different locations of maxima in SST anomalies. To answer these questions, we develop three models, each of which focuses on slab ocean noise, recharge oscillator, and their combined effect respectively. By comparing these models and analyzing the ENSO diversity in the simulation that consider both processes, we try to shed some light on these questions. The remainder of this paper is organized as follows. In Sect. 2 we describe the data, models and methods used for this study. In Sect. 3 we investigate the ENSO SST variability in the model simulations and in Sect. 4 we focus on the ENSO dynamics in the interaction of the recharge oscillator and the slab ocean model. In Sect. 5 the ENSO diversity is analyzed. Here we in particular look at how the interactions between SST, wind stress and the thermocline depth change for different SST patterns. We conclude this study with a brief summary and discussion in Sect Data, models and methods The observed monthly mean SSTs are taken from the Hadley Centre Sea Ice and SST data set (HadISST) from 1950 to 2009 (Rayner et al. 2003). Potential temperature from Global Ocean Data Assimilation System from 1980 to 2009 is used to calculate observed thermocline depth defined as 20 C isotherm depth (Behringer and Xue 2004). The observed monthly mean zonal wind stresses and heat fluxes are from NCEP reanalysis data from 1950 to 2009 (Kalnay et al. 1996). All available coupled general circulation model (CGCM) simulations for the 20c3m scenario in the CMIP3 (Meehl et al. 2007) and for the historical run scenario in the CMIP5 (Taylor et al. 2012) database from 1900 to 1999, are used for comparison with our models (see Table 1). The SST and potential temperature from these simulations are interpolated to a common grid and linearly detrended to remove the global warming signal prior to the analysis. A series of four different 500 years long simulations is based on a full complexity AGCM, which is a low-resolution version ( ) of the UK Meteorological Office Unified Model AGCM with HadGEM2 physics (Davies et al. 2005; Martin et al. 2010, 2011). The simulations differ only in the formulation of the ocean model simulation of the SST variability, while the mean SST climatology is the same in all simulations. The time step of all ocean components and the coupling frequency to the AGCM is the same as the time step in the AGCM (40 min). The first model (Slab) is a slab ocean component describing variation of SST at each grid point in the ocean: γ dsst( x, t) dt = F atmos ( x, t) + F Q ( x, tj ), where γ is the heat capacity of the 50 m mixed layer, F atmos is the net heat flux into the ocean provided by the atmosphere model and F Q is a heat flux correction to maintain a mean SST climatology close to the observed HadISST SST climatology. Both SST and F atmos are functions of location, x, and time, t, and F Q is a function of location and calendar day of the year, t j. Thus F Q is a state independent constant for each x and t j. The second model (ReOsc) is the same as (1)

3 ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab 1667 Table 1 CMIP3 and CMIP5 simulations used in this study ranked by their RMSE EOF value CMIP3 models RMSE EOF (%) CMIP5 models RMSE EOF (%) CMIP5 models RMSE EOF (%) CNRM-CM FIO-ESM 5.02 IPSL-CM5A-MR MPI-ECHAM CESM1-CAM FGOALS-s GFDL-CM CESM1-WACCM MPI-ESM-P ReOsc Slab GFDL-ESM2M GISS-E2-R IAP-FGOALS1-0-G GFDL-CM2p ACCESS CSIRO-MK CESM1-BGC HadGEM2-CC INGV-ECHAM CESM1-FASTCHEM GISS-E2-R-CC IPSL-CM CCSM IPSL-CM5A-LR GFDL-CM ReOsc Slab GISS-E2-H UKMO-HADCM NorESM1-ME IPSL-CM5B-LR CSIRO-MK NorESM1-M HadCM MRI-CGCM2-3-2A CanESM HadGEM2-ES MIROC3-2-MEDRES GFDL-CM MPI-ESM-MR BCCR-BCM BCC-CSM1-1-M GFDL-ESM2G CCCMA-CGCM3-1-T FGOALS-g CMCC-CM NCAR-PCM CMCC-CESM MRI-CGCM CCCMA-CGCM GISS-E2-H-CC BCC-CSM MIROC3-2-HIRES ACCESS CSIRO-Mk GISS-MODEL-E-H CNRM-CM BNU-ESM GISS-MODEL-E-R CMCC-CMS GISS-AOM MPI-ESM-LR Bold values indicate the ReOsc-Slab model s performance among 59 CMIP models Smallest (best) to highest (worst) the Slab simulation except the slab ocean component in the tropical Pacific (20 S 20 N, 130 E 70 W) is replaced by a low order 2-dimensional recharge oscillator model (Burgers et al. 2005) as in Frauen and Dommenget (2010). The original recharge oscillator consists of two scalar equations: dt(t) = a 11 T(t) + a 12 h(t) + ζ 1 dt dh(t) = a 21 T(t) + a 22 h(t) + ζ 2 dt with T representing the SST anomalies in the NINO3 region, h representing the mean equatorial Pacific thermocline depth anomaly and ζ 1 and ζ 2 some stochastic anomaly forcings. Here parameters a 11 and a 22 represent the linear damping of SST and thermocline depth. The coupling parameter a 12 (a 21 ) represent the effect of thermocline depth anomaly (SST) on the time tendency of SST (thermocline depth anomaly). Note, that all parameters here effectively present both atmospheric and oceanic feedbacks and processes. In the ReOsc simulation Eq. (2) are coupled to the atmosphere model leading to the equations: dt(t) = a 11O T(t) + a 12 h(t) + a 12 λτ(t) + f (t) dt γ dh(t) = a 21O T(t) + a 22 h(t) + λ dt 2 a 22τ(t), (2) (3) where f is the averaged F atmos anomaly in NINO3 region and τ is averaged zonal wind stress anomaly in the central Pacific (6 S 6 N, 160 E 140 W), both of which are provided by the atmospheric model; λ is a free coupling parameter. Both f and τ have a relation to T, which in Eq. (2) is modelled by a 11 and a 21. Thus we have to exclude the linear regressions of f and τ with NINO3 index, C τt (C ft ), to avoid a double accounting of the atmospheric relation to T and define the residual oceanic feedback parameters a 11O and a 21O, as in Frauen and Dommenget (2010): a 11O = a 11 a 12 λc τt C ft γ ; a 21O = a 21 a 22 2 λc τt, The regression values C τt (C ft ) are estimated from a 200 years long simulation with an oscillating ENSO pattern as in Frauen and Dommenget (2010). To get basin-wide temperatures, the anomaly T value multiplied with the pattern of the recharge oscillator component, P ReOsc ( x), (Fig. 1g) is added to the SST climatology of the Slab model, SST clim ( x, tj ) : SST( x, t) = SST clim ( x, tj ) + T(t) PReOsc ( x) The calculation of P ReOsc ( x) will be discussed further below in context with the third model. The third model (ReOsc Slab) considers both slab (Eq. 1) and recharge oscillator (Eq. 4) in the tropical Pacific: (4)

4 1668 Y. Yu et al. Fig. 1 Comparison between modeled and observed SST variability modes. The first three dominant EOF patterns of SST in the tropical Pacific with explained variance from the observation (a c), the ReOsc Slab model (d f), and the Slab model (h j). g The recharge oscillator pattern P ReOsc of the ReOsc and ReOsc Slab model HadISST (a) 1stEOF 51.4% (b) 2ndEOF 11.6% (c) 3rdEOF 4.7% ReOsc-Slab (d) 1stEOF 51.8% (e) 2ndEOF 6.9% (f) 3rdEOF 5.2% ReOsc (g) PReOsc Slab (h) 1stEOF 19.5% (i) 2ndEOF 14.2% (j) 3rdEOF 8.9% Table 2 Parameters of the recharge oscillator equations as estimated from observations and 500 years model simulations, and as chosen in the model Eqs. (3) and (5) a 11 (month 1 ) a 12 (K month 1 m 1 ) a 21 (m month 1 K 1 ) a 22 (month 1 ) amp. of ζ τ (Nm 2 ) amp. of ζ f (Wm 2 ) Estimated from observations Model parameter in Eqs. (3) and (5) for ReOsc and ReOsc Slab Model parameter in Eq. (3) for ReOsc Obs Estimated from ReOsc Slab Estimated from ReOsc Estimated from ReOsc Obs The amplitudes of wind noise, ζ τ, and heat flux noise, ζ f, are defined as standard deviation of residual term in the linear regression of wind stress and heat flux against NINO3 index respectively in 500 years model simulations dsst( x, t) ( ) γ = F atmos ( x, t) + F Q x, tj + PReOsc ( x) [a 11O T(t) + a 12 h(t) + a 12 λτ(t)] γ dt dh(t) = a 21O T(t) + a 22 h(t) + λ dt 2 a 22τ(t) (5) The tendencies of the SST in the tropical Pacific are determined by two processes: one is the slab ocean process F atmos ( x, t) + F Q ( x, tj ) and the other is the recharge oscillator Eq. (3) in which the heat flux term was excluded, as it is already represented by the slab ocean process. The model parameters a 11O, a 21O, a 12, a 22 and λ have been estimated in an indirect and iterative way to force the ReOsc Slab model simulation statistics to have effective the observed recharge oscillator parameters a 11, a 21, a 12, a 22 similar to the approach in Frauen and Dommenget (2010). They are estimated by linear regressing the monthly mean tendencies of T and h against monthly mean T and h. See Table 2 for model parameters in Eq. (5) and the statistical values estimated from the model simulations.

5 ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab 1669 Unlike Frauen and Dommenget (2010) the recharge oscillator pattern P ReOsc ( x) is now not the leading EOF-1 mode in the tropical Pacific SST as observed (Fig. 1a), but it is assumed that the combined variability of the Slab Ocean and the recharge oscillator with P ReOsc ( x) leads to the observed EOF-1. The effective P ReOsc ( x) is again estimated in an indirect and iterative way to force the ReOsc Slab model simulation to be close to the observed EOF-1. At first P ReOsc ( x) was set to be the observed EOF-1 and the simulation was run for 200 years. The discrepancy between simulated EOF-1 and observed EOF-1 was subtracted from the observed EOF-1 to obtain the effective P ReOsc ( x). The resulting P ReOsc ( x) pattern is a much narrower pattern than the observed EOF-1, confined mostly to the equatorial region (Fig. 1g). Based on this pattern, the ReOsc Slab model was run for 500 years, and the EOF-1 in this simulation is similar to observed EOF-1, as a result of interaction between recharge oscillator and slab process (Fig. 1d). The ReOsc Slab thus assumes that the effective parameters of the recharge oscillator model and the leading mode of SST variability in the tropical Pacific are the combined effect of the recharge oscillator and slab ocean component. The same model parameters a 11, a 21, a 12, a 22 and λ, and recharge oscillator pattern P ReOsc ( x) are prescribed in the ReOsc model for convenient comparison with ReOsc Slab. For comparison to the model developed in Frauen and Dommenget (2010) we further build a recharge oscillator only model (no slab ocean model in the tropical Pacific), ReOsc Obs, in which we adjust the ReOsc model by changing the prescribed parameters a 11, a 21, a 12, a 22 and λ to make the effective statistics of the ReOsc Obs ENSO amplitude similar to observed parameters, and prescribing recharge oscillator pattern as the observed EOF-1, as done in Frauen and Dommenget (2010). For all parameters see Table 2. Thus in total we have four different simulations with the initial condition for all simulations as SST climatology (no initial anomalies) and h = 0. It should be noted here again that in the following analysis we have two different types of recharge oscillator parameter sets (see Table 2): First we have a set of model parameters that define the Eqs. (3) and (5), which are integrated with a time step of 40 min. Second we have the sets of statistical parameters estimated for the observed or simulated monthly mean statistics of the topical Pacific SST and thermocline variability as done in other previous studies (e.g. Burgers et al or Jansen et al. 2009). The model and statistical sets of the parameter do not need to be the same, and in general will not be the same, due to the interaction of different processes (slab ocean and recharge oscillator) and due to the atmospheric forcings not just being a linear relation to the NINO3 SST with additional normally distributed white noise. The skill of the models in simulating the observed modal structure can be quantified on the basis of the EOF-modes by a root-mean-square error (RMSE EOF ) relative to the observations (Wang et al. 2015). The difference in EOFmodes between the observed and the simulated SST variability is based on projecting the leading EOF-modes of the simulations onto the observed EOF-modes in a multivariate approach (Dommenget 2007; Wang et al. 2015; Bayr and Dommenget 2014). This allows defining a root mean square error between the two sets of EOF-modes, RMSE EOF : Ne ( ) pe Obs M 2 RMSE EOF (Obs, M) = with the explained variance of the observed ith EOF mode, e Obs i, and the variance that the observed ith EOF mode can explain in the model s data matrix, pe Obs M i, which is calculated by pe Obs M i = N j=1 c 2 ije M j. Here e M j is the explained variance of model s jth EOF mode and c ij is the correlation coefficient between the observed ith EOF mode and model s jth EOF mode (Dommenget 2007). Here N is the number of EOF modes considered in computing pe Obs M i and is set to be 60 within this study. N e is the effective number degrees of freedom in the tropical Pacific, also know as the number of independent modes in this region after Bretherton et al. (1999). In our analysis, we choose N e equal to 4, which means the first four dominant EOF modes are considered. In parts of the analysis section we analysis the spatial diversity of the ENSO pattern by different indices for CP and EP ENSO events. The CP and EP definitions are an effective way of presenting variations of the ENSO pattern amplitudes along the equator. Having said this, we believe that they do not as much imply any different physical mechanisms, but simply statistically describe the geographical location of the maxima in SST anomalies. 3 ENSO SST variability i=1 i Ne i=1 ( e Obs i e Obs i ) 2 We start our analysis with comparing the patterns of observed SST variability with the ReOsc, Slab and ReOsc Slab simulations. In Fig. 2 we show standard deviations of SSTA in the tropical Pacific for observation in comparison with the three simulations and a linear combination of ReOsc and Slab simulations, assuming a summation of two independent sources of variability (variance is e 2 = b 2 + c 2 ). Here we can note a number of points: first the equatorial enhanced variability typical for the ENSO dynamics is present in both the ReOsc and the ReOsc Slab, but it is much stronger and closer to the observed in the ReOsc Slab simulations. The more realistic amplitude

6 1670 Y. Yu et al. Fig. 2 Standard deviations of SSTA in the tropical Pacific in a the observation, b the ReOsc model, c the Slab model, d the ReOsc Slab model, e is a combination of b and c as (b) 2 + (c) 2. (a) HadISST (b) ReOsc (c) Slab (d) ReOsc-Slab (e) combined (b)and (c) in the ReOsc Slab is a result of the above assumptions that the effective parameters of the recharge oscillator model and the leading mode of SST variability in the tropical Pacific are the combined effect of the recharge oscillator and slab ocean component. Subsequently, the ReOsc model variability without the interaction with the slab ocean dynamics has much weaker amplitudes and is more strongly confined to the equator. Secondly, the slab ocean simulation has no enhanced SST variability at the equator, but has the largest amplitudes in the subtropical regions. It should be noted here that Slab Ocean models can also produce equatorial oscillating dynamics with patterns that have largest amplitudes at the equator due to positive cloud feedbacks (Dommenget 2010; Clement et al. 2011; Dommenget et al. 2014). However, these modes of variability requires strong mean cold tongue biases that are not present in the observed SST nor in the Slab Ocean simulation discussed here. The Slab Ocean model discussed here has the mean observed SST and does not support the equatorial oscillating dynamics discussed in Dommenget (2010) and Dommenget et al. (2014). It has the classical red noise behavior with larger amplitudes off the equator. Finally, it is interesting to note that the standard deviation of the combined ReOsc Slab simulation is much larger over most of the equatorial region than the summation of two independent sources of variability (variance is e 2 = b 2 + c 2 ; as shown in Fig. 2e). This suggest that the combination of the ReOsc and Slab alone simulations leads to some amplification of the NINO3 SST variability beyond the linear combination of two independent (not interacting) variability terms. In Fig. 1 we compare the leading modes of SST variability in the different simulations with those observed. The leading modes in the simulation that combines the recharge oscillator and slab ocean model (ReOsc Slab) are quite realistic in shape and relative amplitudes in terms of their explained variances (Fig. 1d f). These modes result from the combination of the slab ocean modes (Fig. 1h j), which are mostly off equatorial, and the equatorial mode of the recharge oscillator model only simulation (ReOsc), which is one fixed pattern along the equator (Fig. 1g). The slab ocean in the ReOsc Slab simulation acts to extend the leading mode of variability further to off-equatorial regions, making it meridionally wider than the variability controlled by the recharge oscillator. Figure 3 shows the differences between the leading mode of ReOsc Slab simulation and the equatorial mode of recharge oscillator model only simulation (ReOsc), which is also prescribed as recharge oscillator pattern in the ReOsc Slab model. The positive values in the off-equatorial areas suggest a meridionally wider structure in the leading mode of ReOsc Slab model. This meridionally wider structure and stronger negative values in the western Pacific than those of the ReOsc model, suggesting that the leading mode is an interaction between the equatorial recharge oscillator dynamics and the mostly offequatorial thermodynamics of the slab ocean. It also somewhat projects onto the CP or Modoki index, with enhanced amplitude in the central Pacific, indicating that the slab ocean dynamics contribute to these. We ranked 59 CMIP3 and CMIP5 5 models and our model ReOsc Slab according to their skill in simulating the observed modal structure on the basis of the root-meansquare error of the EOF-modes (RMSE EOF ; see method

7 ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab 1671 Fig. 3 The difference between the 1st EOF of SST in tropical Pacific from the ReOsc Slab simulation (Fig. 1d) and the embedded recharge oscillator pattern P ReOsc (Fig. 1g) section for details) relative to the observation (see Table 1). The ReOsc Slab model performs better than most CMIP3 and CMIP5 models (ranked 12 out of 60 in RMSE EOF ). It is thus closer to the observed modal structure than most CGCM simulations. It needs to be noted here that the RMSE EOF value is dominated by EOF-1 due to its larger eigenvalue, see definition above. In the ReOsc Slab EOF-1 is tuned to be close to the observed. The RMSE EOF value for the higher order EOF-modes, excluding EOF-1, is larger for the ReOsc Slab simulation and worse than in most CMIP3 and CMIP5 (not shown). However, most CMIP3 and CMIP5 have a similar behavior in the RMSE EOF value with much better agreement in EOF-1 than in the higher order modes. The mismatches in the variability patterns in the ReOsc Slab simulation relative to the observed modes are in particular along the equator. This can be estimated by a rotation of the leading EOF-modes towards the most distinct EOF (DEOF) modes (Bayr and Dommenget 2014). The DEOF method finds the patterns (modes) that show the largest differences in the explained variance between the observational data and the model data. The first three DEOF modes mark modes along the equator that are smaller in spatial scale than the EOF-1 modes (see Fig. 4). In particular the DEOF-1 mode has much more variance in the observations (14.6 %), than in the ReOsc Slab simulation (5.3 %). It looks like observed EOF-2 mode, which means the model have its limitation in simulating the mode similar to EOF-2, which is also a limitation of many CMIP3 models (Roxy et al. 2013). It has strongest amplitudes in the far eastern equatorial cold tongue region and is a mode of variability that is missing in most of the good (RMSE EOF smaller than in ReOsc Slab) CGCM simulations in the CMIP database (see Fig. 5). The large observed variance in the far eastern equatorial cold tongue region has been a long-standing problem in model simulations (Latif et al. 2001). The variability in the far eastern cold tongue and coastal region is dominated by smaller scale turbulent upwelling dynamics. The fact that coarse resolution CGCM models have in general problems with simulating this mode, indicates that the smaller scale dynamics are not well resolved in current CGCMs. The seasonally resolved standard deviation of NINO3 index is in both, the ReOsc and Slab alone simulations, much weaker than the observed and in the combined ReOsc Slab simulation (Fig. 6a). Again we note that the standard deviation of the combined ReOsc Slab simulation is larger in most seasons than the summation of two independent sources of variability, which would roughly amount to only 0.7 K. Further, we can note that both the ReOsc and Slab alone simulation already have the realistic signature of the weaker variability in the boreal spring season and stronger variability in the boreal winter. In particular the realistic seasonality in the Slab alone simulation is interesting, as it indicates that the atmospheric heat fluxes alone and the feedback processes associated with it lead to a realistic seasonal evolution of the NINO3 SST variability. Thus the atmospheric heat fluxes alone lead to growth of SST anomalies in boreal summer and a termination of NINO3 SST anomalies in boreal spring. In the combined ReOsc Slab simulations the spring season minimum gets shifted by 1 2 months earlier in the year and the seasonal contrast comes even more pronounced than the observed. Similarly the power spectrum of the ReOsc Slab simulations is a combination of the interactions of the ReOsc and Slab models, but different from what you would expect if two independent sources of variability are combined (Fig. 6b). For instant, the red noise variance of the Slab only simulation added to the variance of the ReOsc simulation should essentially lead to increase on the decadal timescale variance only. However, the ReOsc Slab simulation has increased variance relative to the ReOsc simulation on all time scales by roughly the same factor. We can further noticed that the largest increase is at the peak oscillation frequency of both the ReOsc Slab and the ReOsc simulation, making the oscillation more dominant over the background red noise spectrum. Finally, we need to note that the overall power spectrum of the ReOsc Slab simulation is shifted towards shorter frequencies compare to what is observed reflecting some limitation in the ReOsc Slab

8 1672 Y. Yu et al. Fig. 4 The three leading distinct EOFs (DEOF) of SST for the ReOsc Slab simulation relative to the observed modes. The two percentages in the heading mark the explained variances by each DEOF in the observations and the ReOsc Slab simulation respectively (a) 1stDEOF 14.6% in observation 5.3% in ReOsc-Slab (b) 2ndDEOF 23.9% in observation 18.7% in ReOsc-Slab (c) 3rd DEOF 5.9% in observation 2.7% in ReOsc-Slab simulation, which is similar to what is found in Frauen and Dommenget (2010) for a similar ReOsc simulation. 4 ENSO dynamics We now focus on how the dynamics of the ENSO mode change due to the interaction between the ReOsc and Slab dynamics. Both, the ReOsc and ReOsc Slab simulations have, by construction, the same four model parameters that define the recharge oscillator model. However, the effective dynamical parameters estimated from the resulting statistics of the simulation are different due to the interaction with the thermodynamics of the slab model and due to the non-linear noise forcing from the atmosphere (Frauen and Dommenget 2010; see Table 2). The SST damping, a 11, becomes smaller in the ReOsc Slab model, which will lead to an increase in SST variability. Table 2 also shows the amplitudes of atmospheric noise in the heat flux and wind stress in these two models. The amplitudes of wind noise, ζ τ, and heat flux noise, ζ f, are defined as standard deviation of residual terms in the linear regression of wind stress and heat flux against NINO3 SST index respectively in 500 years model simulations. Both noises are stronger in the ReOsc Slab model than in the ReOsc model. This suggests that the stochastic forcing of the recharge oscillator is increased due to the Slab Ocean model, which will lead to an overall increase in the power spectrum. The changes in the dynamics and variance of the recharge oscillator model from the ReOsc alone simulation to the combined ReOsc Slab simulation can best be analyzed on the basis of the two-dimensional recharge oscillator Eq. (2) with the four estimated effective (statistical) parameters and the two parameters that represent the amplitudes of wind noise and heat flux noise of the two different simulations. Similar to how it was done in Frauen and Dommenget (2012). As the wind noise ζ τ and heat flux noise ζ f are assumed to be the parts of τ(t) and f(t) that are linearly independent of NINO3 index T(t), we can replace τ(t) and f(t) in Eq. (3) with τ(t) = ζ τ + C τt T(t) and f (t) = ζ f + C ft T(t), and compare the resulting equations with Eq. (2). Then we find two

9 ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab 1673 (a) CMIP3 CNRM 29.4% -13.9% (b) CMIP3GFDL-CM % -21.5% (c) CMIP3 MIP-ECHAM5 32% % (d) CMIP5FIO-ESM 32.7% -14% (e) CMIP5 CESM1-CAM5 32.6% % (f)cmip5 CESM1-WACCM 25.2% -15.5% (g) CMIP5 GFDL-ESM2M 34.5% -22.4% (h)cmip5 GFDL-CM2p5.6% -22.7% (i) CMIP5 CESM1-BGC 25.9% % (j) CMIP5CESM1-FASTCHEM24.2% - 14% (k) CMIP5 CCSM4 11.8% -4% (l) AverageDEOFpattern Fig. 5 The first DEOF of SST in the tropical Pacific from CMIP models. a k The first DEOF of SST in the tropical Pacific for the CMIP simulations that perform better than the ReOsc Slab model in terms of RMSE EOF. The two percentages in the heading mark the explained variances by each DEOF mode in the observations and in the corresponding CMIP simulation respectively. l Average of the patterns (a k) forcing terms in Eq. (2) ζ 1 and ζ 2 written in the following form: ζ 1 = a 12 λζ τ + ζ f γ 1 and ζ 2 = λ 2 a 22ζ τ. ζ τ and ζ f are assumed to be red noise with e-folding time of 3 days and the amplitudes being estimated from ReOsc Slab or ReOsc simulations shown in Table 2 (Frauen and Dommenget 2012). We analyse the two-dimensional recharge oscillator Eq. (2) with the four estimated effective parameters and the above forcings from either the ReOsc Slab model or the ReOsc model. With each set of parameters the Eq. (2) were integrated in a Monte Carlo (MC) simulation over 10 4 years with a time step of 40 min. MC simulation here means repeated random sampling each time step for the formation of red noise ζ τ and ζ f and the integration of the Eq. (2). In this way, the atmospheric forcing no longer comes from AGCM models, but is simply self-constructed red noise. It provides a simple and instructive method to test the sensitivity of the variables statistics of T and h of the ReOsc model Eq. (2) to individual parameters. Figure 7 shows the power spectra of these 2 simulations with black solid (dash) line representing parameters from the ReOsc Slab (ReOsc) model. It is shown that the main features of power spectra from the ReOsc Slab and the ReOsc model, such as upward shift of spectrum and the stronger peak for the ReOsc Slab model, can be simulated by the two-dimensional recharge oscillator Eq. (2). It should be noted that the peak period from each simulation experiment is around 3 years, which is closer to observed ENSO period than that from either the ReOsc Slab model or the ReOsc model. This is due to the more complex dynamics in the atmospheric forcings than assumed in the simple Monte Carlo simulations. To analyze the effect of changes in the individual effective parameters of the recharge oscillator and atmospheric noise amplitudes on the shift of power spectra between the ReOsc Slab and the ReOsc simulations, we further perform sensitivity experiments by integrating the twodimensional recharge oscillator Eq. (2) with the changes in just one of the statistical parameters as in Frauen and Dommenget (2012). In each sensitivity experiment, we choose one statistical parameter from the ReOsc Slab simulation and take the other five statistical parameters estimated from the ReOsc simulation to investigate the effect of each parameter on the power spectra shift alone. Because there is essentially no difference in estimated parameter a 12 for

10 1674 Y. Yu et al. (a) (b) Fig. 6 ENSO seasonality and power spectra of NINO3 SST index. a Annual cycle of standard deviation and b power spectra of NINO3 SST index from three models and observations Fig. 7 Power spectra of NINO3 SST index from two control Monte Carlo integrations of Eq. (2) with parameters estimated from the ReOsc Slab model and ReOsc model respectively, and five sensitivity experiments these two simulations, a total of five sensitivity experiments are performed. Figure 7 shows the power spectra of these five experiments with colored dash lines. We find that the parameters a 11 (red dash line) and wind noise strength (yellow dash line) contribute most to the upward shifting of the power spectra. The thermodynamic effect of the Slab ocean leads to a reduction in the effective SST damping (a 11 ), which enhances the variance mostly around the peak period, and it enhances the effective random wind stress forcing (wind noise strength), which increases the variance on all frequencies. Changes in the coupling of the SST to the thermocline (a 12 ), the damping of thermocline (a 22 ) and the stochastic heat flux forcing have no significant impact on the over all variance of NINO3 SST. An important discussion point is how the Slab Ocean can enhance the stochastic winds stress forcing and how it can reduce the effective damping of SSTA. First of all, the increased stochastic winds stress forcing from to N m 2 in Table 2 results from the increased SSTA in the equatorial Pacific that does not project onto EOF-1 after the Slab Ocean process is included in the model. These SSTA variability patterns essentially cause winds stress anomalies in the central equatorial Pacific region, which is the wind stress forcing region for the recharge oscillator model Eq. (3). Since these winds stress anomalies are unrelated to the NINO3 SSTA they are effectively random wind stress forcings. Secondly the heat flux anomalies tend to reduce the SSTA variability in the tropical Pacific with various damping effect at different locations. Figure 8 shows that in the ReOsc Slab model the regression coefficients of heat flux anomalies against local SSTA attain their largest negative values in the NINO3 region, with smaller values in other areas, which means the damping effect is stronger in the NINO3 region than in other region. The heat flux forcing of the recharge oscillator model Eq. (3) is limited to the NINO3 region. However, the recharge oscillator pattern P ReOsc ( x) covers a much larger region. The coherent variability of the P ReOsc ( x) in the ReOsc model forced by the averaged heat flux anomalies in the NINO3 region, where larger damping occurs, exaggerates damping effect in the other area of the tropical Pacific leading to smaller variability of SSTA in those areas and consequently a weaken ENSO amplitude. This shortage does not exist in the ReOsc Slab model, where the coupling of the atmospheric heat flux forcing is via the Slab Ocean process in Eq. (5) at all covered ocean points. This effectively changes the damping of SST to be a synchronize effect of the recharge oscillator model (acting only via the heat flux in the NINO3 box and the wind stress coupling via the central Pacific region) and the local Slab Ocean thermodynamics acting at all ocean points, and reduces the

11 ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab 1675 Fig. 8 Regression of heat flux against local SSTA in the ReOsc Slab model. Only those values which are over 95 % statistically significant under a student t test are shown damping effect of SST in the whole tropical Pacific area. This further demonstrates that the leading mode of tropical SST variability is a combined effect of the equatorial dynamics of the recharge oscillator and the mostly offequatorial Slab Ocean thermodynamics. The ReOsc model approach here is different from the model developed by Frauen and Dommenget (2010). The latter assumes prescribed parameters estimated from observation and observed EOF-1 is set as the recharge oscillator pattern (see model section for details). The ReOsc Obs simulation uses the same approach. A comparison between the ReOsc Slab and the ReOsc Obs simulations shows some interesting differences. The power spectrum of the ReOsc Slab simulation has more variance on shorter seasonal and on longer decadal time scales, see Fig. 9. It subsequently has a less pronounce interannual peak, which is more realistic than the ReOsc Obs simulation. If we look at the differences in the model parameter (Table 2), we can see that the SST damping is much stronger in the ReOsc Slab simulation than in the ReOsc Obs simulation, supporting a less pronounced peak in power spectrum. Further we can note that the wind noise and heat flux noise is stronger in the ReOsc Slab simulation. The noise generated by Slab Ocean processes plays an important role in generating the larger variance on shorter seasonal and on longer decadal time scales relative to the ReOsc Obs simulation. 5 ENSO diversity We now focus on the ENSO diversity in the spatial patterns of variability. We would like to know whether ReOsc Slab simulation could explain ENSO flavors with different geographical location of maxima in SSTA. Hence, in this section, we evaluate the capability of the ReOsc Slab model in simulating ENSO events with respect to independent evolutions of SSTA in the central and eastern Pacific and Fig. 9 Power spectra of NINO3 SST index from the ReOsc Slab model and the ReOsc Obs model some important coupling relationships in the ENSO development, such as wind-sst and thermocline-sst in this model. 5.1 Independence of SSTA in NINO3 and NINO4 indices In order to see the relationship between the SSTA in the central and eastern Pacific, Fig. 10a shows scatter plots between the normalized seasonal mean NINO3 and NINO4 (averaged SST anomalies over 5 S 5 N, 160 E 150 W) indices during December February when CP or EP El Nino events occur. CP (EP) El Nino events are defined by the normalized seasonal mean NINO4 (NINO3) indices being greater than one and being greater than the seasonal mean normalized NINO3 (NINO4) indices, following the definition of Kug et al. (2009, 2010). According to this definition, the red and blue diamonds in Fig. 10a denote observed CP and EP El Nino, respectively. In the observation, the diversity in the observed CP and EP El Nino events leads to

12 1676 Y. Yu et al. (a) (b) (c) Fig. 10 Normalized seasonal mean NINO3 and NINO4 indices during December February of El Nino events from a the observation, b the ReOsc Slab model and c CMIP models. Red symbols stand for CP El Nino, and blue symbols stand for EP El Nino deviations (scatter away) from a linear one-to-one relationship (Ham and Kug 2012). The simulated El Nino events in CMIP and the ReOsc Slab simulations generally also possess this independent evolution of SSTA in these two regions (Fig. 10b, c). We can quantify the independence of the NINO4 and NINO3 indices by measuring the correlation coefficients between the two indices for the selected El Nino events as shown in Fig. 10, see Fig. 11. The observed correlation coefficient is a small negative value, indicating that mature El Nino events tend to be more EP like events the stronger the amplitude in NINO3 SST is. The bulk of the CMIP and the ReOsc Slab simulations have a weakly positive correlation. Thus most models do have some independence of the NINO3 and NINO4 region, but not as strong as observed. It is in particular interesting to note that the ReOsc Slab simulation can simulate extreme EP El Nino events (points far to the right and below the diagonal in Fig. 10b, normalized seasonal NINO3 > 2.5), but does not simulate extreme CP El Nino events (points above the diagonal and far left in Fig. 10b, normalized seasonal NINO4 > 2.5), which is consistent with previous studies that extreme events tend to be EP like events in the observations (Takahashi et al. 2011; Dommenget et al. 2013). The SSTA differences between normalized composite extreme events (normalized seasonal NINO3 or NINO4 > 2.5) and median events [(i) 1< normalized seasonal NINO3 or NINO4 < 1.5 and (ii) normalized seasonal NINO4 and NINO3 < 2.5] are mainly located in the central Pacific, suggesting extreme El Nino events are more confined in the eastern Pacific and moderate El Nino events are more in the central Pacific (Fig. 12a). This result is consistent with discussion in Dommenget et al. (2013) analysis and also in Giese and Ray (2011). Dommenget et al. (2013) argued that an eastward shift in the wind response for stronger El Nino events should also shift the SST pattern to the east, which they however could not demonstrate in the Frauen and Dommenget (2010) model due to the fix SST-pattern approach in the Frauen and Dommenget (2010) model. The ReOsc Slab model, however, does show this eastward shift in the SST pattern of strong El Nino events, due to the interaction with the slab ocean dynamics. Figure 12b, c shows 2-year evolution of normalized composite extreme and median events. The pronounced westerly wind in the central Pacific preceding the peak phase of extreme event is less obvious in median events. However, the leading thermocline depth is much stronger in median events than in extreme events. Therefore, extreme events tend to be more atmospherically forced, while median events are more likely to be oceanic driven. Note that this discussion is in the context of both median and extreme events being normalized by their respective NINO3 indices. The heat flux anomalies in the NINO3 region generally follow the SST evolution, acting as a damping effect in both conditions. We also find that extreme events are followed by La Nina events in this simulation. These results are again consistent with Dommenget et al. (2013) s analysis. We can conclude that the ReOsc Slab model is capable of simulating independent evolutions of SSTA in the central Pacific and eastern Pacific and El Nino events with different geographical locations of maxima in SSTA, but with similar significant limitations as most of the CMIP3 and CMIP5 simulations. The model can also simulate EP like extreme El Nino events as in observations.

13 ENSO dynamics and diversity resulting from the recharge oscillator interacting with the slab 1677 Fig. 11 Histogram of correlation coefficients between normalized seasonal mean NINO3 and NINO4 indices during December February of El Nino events from individual CMIP model. Each bar represents the number of CMIP models, from which correlation coefficient between the two indices reside in the specified 0.2 interval. The correlation coefficient between indices of El Nino events from all CMIP models (all points in Fig. 10c) is show in red dash line as the mean of CMIP. The correlation coefficients for the ReOsc Slab model (blue line), and the observation (black dash line) are also listed 5.2 Wind SST relationship The response of zonal wind stress to SSTA is an essential part of Bjerkness feedback and critical to the development of El Nino. For observed CP and EP El Nino events, the responses are different (Ashok et al. 2007). Following the approach in Ashok et al Fig. 13a, b shows the observed regression maps of zonal wind stress against NINO3 index and El Nino Modoki index, (EMI), respectively [EMI = (SSTA) A 0.5 (SSTA) B 0.5 (SSTA) C ], the square bracket denotes area over each of the regions A (165 E 140 W, 10 S 10 N), B (110 W 70 W, 15 S 5 N), and C (125 E 145 E, 10 S 20 N); Ashok et al. 2007) to highlight differences in the wind-sst relationship for different ENSO patterns. The EMI index is related to zonal winds that are converging onto the central equatorial Pacific with apparent easterly wind anomalies in the eastern Pacific, which are not as strong for the NINO3 index (Fig. 13a, b). Kug et al. (2009) further pointed out that the easterly wind anomalies in the eastern Pacific are responsible for the suppression of SSTA development in the eastern Pacific due to its enhanced upwelling and surface evaporation, and therefore is also an essential feature for CP El Nino or the EMI index. The ReOsc Slab model appears to have similar regression patterns (Fig. 13c, d): the convergence area of zonal wind stress response is stronger from 140W to 120W for the EMI index than that for the NINO3 index, with apparent easterlies to the east. In the observations we further find that the strongest wind stress response in the western equatorial Pacific is shifted further to the west, from 150 W for the NINO3 index to 180E for the EMI index. This shift is qualitatively similar in the ReOsc Slab model. In the fully coupled climate system and in the studies of Kug et al. (2009) and Ashok et al. (2007) one may argue that the different wind pattern may force the different ENSO-types by ocean dynamic feedbacks to the wind stress forcing. However, in the ReOsc Slab model ocean dynamics responding to wind stress forcing, other than the fixed pattern ReOsc model, do not exist. In the ReOsc Slab simulation the different wind stress patterns are therefore a reflection or response to the different SST patterns resulting from the interaction of the ReOsc and Slab ocean model. 5.3 Thermocline SST relationship Finally, we analyze differences in the thermocline-sst relationship for different types of El Nino events. In the recharge oscillator the thermocline depth anomaly is deeper in the lead up to an El Nino event and is reversing sign after the peak of the event, representing recharge and discharge processes. Figure 14a shows the cross correlation between the thermocline depth anomaly and PC1, i.e. time series of the first EOF pattern of SSTA in the tropical Pacific for the observation, CMIP models and the ReOsc Slab model. Ensemble means of cross correlation coefficients among CMIP3 + 5 models are shown with error bars representing standard deviations of the model ensemble distribution. CMIP models and the ReOsc Slab model have a similar cross correlation to observation, indicating the recharge oscillator mechanism is acting in these models, although the correlation coefficient attains maximum with a shorter