Abstract

Coupled dynamics between westerly wind events (WWEs) and the El Niño–Southern Oscillation (ENSO) is examined using an atmosphere–ocean coupled model with intermediate complexity. The model incorporates state-dependent stochastic noise that mimics observed WWEs, which occur at the edge of the Pacific warm pool when the Niño-4 sea surface temperature (SST) anomaly increases positively. The model parameter that controls the efficiency of the thermocline feedback, γ, is perturbed to elaborate the sensitivity of the results to the system’s stability. Without the noise (experiment NO), the model produces an ENSO-like regular oscillation with a 6-yr period, the variance of which increases with γ. When additive noise is introduced over the western Pacific (experiment AD), the oscillations become irregular with a dominant period of 4–6 years and the increase in the variance relative to the NO experiment depends on γ. When state-dependent noise is included (experiment SD), the oscillatory solution is also irregular, and its variance and asymmetry are increased irrespective of the value of γ. Both the additive and state-dependent noise contribute to the occurrence of two types of variability, corresponding to the eastern Pacific (EP) and central Pacific (CP) El Niños. In SD, the state dependence of the stochastic noise guarantees the existence of CP El Niño regardless of γ since the increased likelihood of WWE occurrence with Niño-4 SSTs results in a positive feedback in the central Pacific. The above results suggest that the state dependence of WWEs plays a crucial role in the asymmetry and diversity of ENSO.

1. Introduction

The El Niño–Southern Oscillation (ENSO) phenomenon is a mode of interannual variability in the equatorial Pacific, distinguished by its irregularity, asymmetry, and structural diversity. Its quasi-periodic nature arises from a delayed feedback in the slow atmosphere–ocean coupled process (Schopf and Suarez 1988; Battisti and Hirst 1989; Jin 1997a,b), but a possible interaction of ENSO with high-frequency atmospheric disturbances may also play a role in the ENSO dynamics. Westerly wind events (WWEs) or westerly bursts are sporadic surface wind anomalies that persist for a few days to weeks with a large magnitude over the western and central Pacific (Luther et al. 1983; Hartten 1996; Harrison and Vecchi 1997; Seiki and Takayabu 2007a). The eastward wind stress anomaly associated with WWEs increases the sea surface temperature (SST) in the eastern equatorial Pacific through deepening of the thermocline and zonal advection (Vecchi and Harrison 2000; Lengaigne et al. 2002; Belamari et al. 2003; Karnauskas 2013; Chiodi et al. 2014), while the occurrence of WWEs is more frequent with the SST anomalies associated with El Niño and corresponding eastward expansion of the western Pacific warm pool (Vecchi and Harrison 2000; Eisenman et al. 2005; Seiki and Takayabu 2007a; Hendon et al. 2007; Tziperman and Yu 2007; Gushchina and Dewitte 2012; Puy et al. 2016; Hayashi and Watanabe 2016; Levine and Jin 2017). This indicates that WWEs are not purely stochastic (additive) but also state dependent (multiplicative). Despite the short duration of each WWE episode, frequent WWEs induced anomalous oceanic variations and caused discernible warming in the eastern Pacific during the developing phase of extremely large El Niños in the boreal winters of 1982, 1997, and 2015 (Wyrtki 1985; McPhaden 1999; Jin et al. 2003; Lengaigne et al. 2004).

The modulation of ENSO by WWEs has been examined using various atmosphere–ocean coupled models. Overall, the state dependence of noise mimicking WWEs increases the ENSO instability in intermediate coupled models (Eisenman et al. 2005; Perez et al. 2005), an ocean general circulation model (OGCM) coupled with a statistical atmospheric model (Gebbie et al. 2007), coupled general circulation models (CGCMs) (Lopez et al. 2013), and a simple recharge oscillator model (Jin et al. 2007; Levine and Jin 2010). It has also been shown that the low-frequency tail, or envelope of high-frequency variations, of the state-dependent noise plays a crucial role in the ENSO modulation (Eisenman et al. 2005; Zavala-Garay et al. 2005; Gebbie et al. 2007; Levine and Jin 2010; Kapur and Zhang 2012; Lopez et al. 2013). Some studies have demonstrated that the state dependence increased the positive skewness of the SST anomaly in the eastern equatorial Pacific (Perez et al. 2005; Gebbie et al. 2007; Jin et al. 2007; Levine and Jin 2010; Levine et al. 2016).

However, the contribution of WWEs may depend on the inherent ENSO stability and their state dependence. For instance, additive noise reduced the variance of the ENSO in Lopez et al. (2013), amplified the variance in Perez et al. (2005) and Gebbie et al. (2007), and had little effect in other studies (Eisenman et al. 2005; Jin et al. 2007; Levine and Jin 2010). While the variance of noise was amplified during the El Niño developing phase, thus increasing the magnitude of the El Niño event (Perez et al. 2005; Jin et al. 2007; Levine and Jin 2010; Lopez et al. 2013), Gebbie et al. (2007) showed that the eastward shift of WWEs was also crucial to the amplification of El Niño (see also Lengaigne et al. 2004). Therefore, the role of state-dependent noise should be investigated further across a wide range of the inherent ENSO stability.

Recent studies have suggested that WWEs are important for two types of El Niño that are distinguished by differences in the structure of their SST anomalies, called the El Niño flavor or diversity (e.g., Yeh et al. 2014; Capotondi et al. 2015). One type has a maximum in the SST anomaly in the eastern Pacific similar to the conventional El Niño (EP El Niño), and the other has a peak in the central Pacific (CP El Niño) (Larkin and Harrison 2005; Ashok et al. 2007; Kug et al. 2009; Kao and Yu 2009). In observations, the thermocline feedback is dominant in the development of EP El Niño, while CP El Niño is mainly driven by zonal advective feedback (Kug et al. 2009; Kao and Yu 2009). Lian et al. (2014) and Chen et al. (2015) showed that CP El Niño and extremely strong EP El Niño can be produced by the state-dependent WWEs in a coupled model with intermediate complexity. However, the contribution of the state dependence is still unclear since they did not conduct experiments with additive WWEs. Since the impact of WWEs on the El Niño flavor may depend on the ENSO behavior in CGCMs (Lopez and Kirtman 2013), the sensitivity to the inherent stability should also be elaborated.

In this study, an intermediate coupled model is constructed to examine the coupling between WWEs and ENSO. We couple the ocean component of the Zebiak–Cane (ZC) model (Zebiak and Cane 1987) and a linearized global atmospheric model (Watanabe and Jin 2003). The WWEs are parameterized based on an observational analysis of the relationship between WWEs and the SST (Hayashi and Watanabe 2016). By perturbing the parameter controlling the model’s ENSO stability, we quantify the proportion of ENSO modulation due to additive and state-dependent WWEs in stable and unstable regimes to clarify the role of the state dependence.

The rest of this paper is structured as follows. An intermediate atmosphere–ocean coupled model and WWE parameterization are explained in section 2. In section 3, an overview of ENSO in the model is given. The statistics of the model’s ENSO are examined in section 4, and the impact of WWEs on the El Niño flavor is considered in section 5. A summary and discussion are given in section 6.

2. Method

a. Model

An intermediate atmosphere–ocean coupled model is used. The atmospheric component consists of a moist linear baroclinic model (mLBM), which is based on primitive equations linearized about a basic state (Watanabe and Jin 2003). This calculates the atmospheric steady response to SST anomalies (T) under the seasonally varying basic state, symbolically written as

 
formula

where is a state vector containing atmospheric variables (perturbations of vorticity, divergence, temperature, logarithm of surface pressure, and specific humidity), is a linear dynamical operator associated with the basic state, and is a forcing vector containing T. We use a low-resolution version of T21 and 11 vertical levels, and the basic state is derived from the monthly climatology from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996). The mLBM has been used to examine the linear dynamical response of the atmospheric general circulation to observed or idealized SST anomalies (e.g., Watanabe and Jin 2003).

The ocean component is a prognostic anomaly model for the equatorial Pacific (29°S–29°N, 124°E–80°W), comprising the shallow-water equations and a thermodynamic model for the mixed layer temperature. This model was adopted from the ZC coupled atmosphere–ocean model (Zebiak and Cane 1987). The zonal and meridional resolutions are 2° and 0.5° for the ocean dynamics, respectively, and the time step is 10 days. In the thermodynamic equation, T is formulated as

 
formula

where and w are the anomalies of the horizontal surface currents and upwelling, respectively; overbars indicate the basic states prescribed from observations; α ( day−1) is the coefficient for linear damping; Q is the surface heat flux calculated in the mLBM; and for and for so that the SST is affected by vertical advection only in the presence of upwelling. The anomalous vertical temperature gradient is defined by

 
formula

where is the mixed layer depth (50 m), and is the temperature anomaly entrained into the surface layer having the following form:

 
formula

The ratio between the subsurface temperature anomaly and T is defined as γ, and is prescribed as a function of h:

 
formula

where h and are the anomaly and prescribed mean of the thermocline depth, respectively. Parameter values were estimated from the observations, as in Zebiak and Cane (1987). To calculate T, the ocean variables are interpolated onto a 5.625° and 2° grid in the zonal and meridional directions. The total SST is limited not to be greater than 30°C assuming the radiative-convective equilibrium (e.g., Jin et al. 2003). The ocean model can reproduce the observed interannual SST anomalies in the equatorial Pacific when forced by the observed wind stress anomalies (e.g., Kang and Kug 2000), and the ZC coupled model has been used to predict El Niño events (e.g., Chen et al. 1995).

The atmospheric response to T is calculated at each time step. The ocean component of the model is forced by the wind stress anomalies (τ) using a linearized standard bulk formula:

 
formula

where is the air density, is a bulk transfer coefficient (Louis 1979), and and are the anomalous and climatological surface winds, respectively. The magnitude of τ is reduced to 70% under the assumption of a large damping effect in the planetary boundary layer of the mLBM, based on previous studies for stabilizing a coupled model (e.g., Perez et al. 2005; Eisenman et al. 2005; Kapur et al. 2012).

b. Observational data

The long-term SST data for 1850–2014 [the Centennial in situ Observation-Based Estimates (COBE-SST) dataset; Ishii et al. 2005] is used. The monthly SST anomaly is defined as the deviation from the 1981–2010 average. We also use the daily surface wind anomaly derived from the Japanese 55-year Reanalysis Project (JRA-55; Kobayashi et al. 2015) from 1 January 1982 to 31 December 2013. To extract the observed WWEs to be used as the basis of the WWE parameterization, the zonal wind anomaly is averaged over 2.5°S–2.5°N after subtracting its interannual component defined as the 91-day running mean of the anomaly. The minimum thresholds for the magnitude, duration, and zonal extent are 5 m s−1, 2 days, and 10° in longitude, respectively. An event is required to satisfy these three thresholds at each grid point over the equatorial Pacific (120°E–80°W). See Hayashi and Watanabe (2016) for more details on the extraction of WWEs. According to their analysis, WWEs are observed frequently at the eastern edge of the western Pacific warm pool when the Niño-4 (5°S–5°N, 160°E–150°W) SST anomaly is positively large (see Figs. 1a,c), consistent with dynamical amplification of high-frequency surface westerlies by low-level westerly (Seiki and Takayabu 2007b; Sooraj et al. 2009) and anomalous zonal contrasts in the SST and sea level pressure (Lengaigne et al. 2003; Yu et al. 2003).

Fig. 1.

WWEs in the (a) observations and (b) parameterizations applied to the observed SST anomaly (shade, K) with and corresponding to SD. Black bars indicate the timing and location of WWEs. The green contour indicates the 3-month running mean of the 28.5°C SST isotherm averaged for 2°S–2°N. The date line is represented by the black dashed line. (c) PDF for WWE occurrences with respect to the Niño-4 SST anomaly in SD (red solid) and the observation (black dotted) for 1982–2013. The PDF for AD (green solid) is also shown for comparison.

Fig. 1.

WWEs in the (a) observations and (b) parameterizations applied to the observed SST anomaly (shade, K) with and corresponding to SD. Black bars indicate the timing and location of WWEs. The green contour indicates the 3-month running mean of the 28.5°C SST isotherm averaged for 2°S–2°N. The date line is represented by the black dashed line. (c) PDF for WWE occurrences with respect to the Niño-4 SST anomaly in SD (red solid) and the observation (black dotted) for 1982–2013. The PDF for AD (green solid) is also shown for comparison.

c. WWE parameterization

WWEs are parameterized as noise in the wind stress in the coupled model (mLBM-ZC) constrained by the observational fact shown by Hayashi and Watanabe (2016) (see section 2b). We fix the spatial pattern of zonal wind stress anomalies by

 
formula

Here, x and y indicate longitude and latitude, respectively; N m−2 is the (constant) amplitude of the WWEs; is the central longitude of the WWEs; and and are 20° and 6°, respectively. In some experiments described below, we set , where is the longitude of the eastern edge of the western Pacific warm pool defined by the longitude of the 28.5°C SST isotherm along the equator (cf. Gebbie et al. 2007; Puy et al. 2016). We impose in the model with probability P at each time step:

 
formula

where [ (10 day)−1] is the base probability of WWE occurrence, (K) is the Niño-4 SST anomaly, and G (K−1) is a constant to control the state dependence of WWE occurrence. That is, the probability of WWE occurrence becomes higher (lower) for warmer (colder) . A WWE occurs centered at when a random number between 0 and 1, generated at each time step, is less than P, and persists for 20 days. The minimum recurrence interval between WWEs is 30 days.

The state-dependent noise should be modeled in line with the observational characteristics of WWEs. In previous studies, the state dependence of WWEs has been assumed without evidence. The variance of the noise is often assumed to increase with the SST in the eastern Pacific (e.g., Perez et al. 2005), although such a relationship has not actually been observed in terms of the occurrences of WWEs (see the supplementary material of Hayashi and Watanabe 2016). The increased likelihood of WWE occurrences with the extension of the warm pool (Eisenman et al. 2005; Gebbie et al. 2007; Kapur and Zhang 2012; Lian et al. 2014; Chen et al. 2015) is also unrealistic since WWEs rarely appear along the equator after the mature phase of El Niño.

d. Numerical experiments

The settings for the numerical experiments are summarized in Table 1. A reference case (referred to as NO) is conducted without external forcing (i.e., ), which produces ENSO-like interannual oscillations (see section 3). In the purely additive or stochastic case (referred to as AD), we set and x0 = 168.75°E so that the WWEs are introduced at the western Pacific independently of the SST. In the state-dependent or multiplicative case (referred to as SD), we set and x0 = xpool − 10°. In addition to AD and SD, the -dependent and -dependent cases are considered (referred to as N4 and WP, respectively). In N4, is used but the occurrence of WWEs is centered at x0 = 168.75°E. In WP, the occurrence of WWEs is centered at x0 = xpool − 10° but . Assuming the association of WWEs with deep cumulus convection, the WWEs appear only when the SST at along the equator is greater than 28.5°C in SD, N4, and WP. To examine the dependence of results on the strength of the state dependence, we also conduct the same experiments with SD except for , 1.0, and 2.0.

Table 1.

List of the names of experiments, experimental designs, and values of the dependence on the Niño-4 SST anomaly (G), and central longitude of WWEs . The eastern edge of the western Pacific warm pool is indicated by .

List of the names of experiments, experimental designs, and values of the dependence on the Niño-4 SST anomaly (G), and central longitude of WWEs . The eastern edge of the western Pacific warm pool is indicated by .
List of the names of experiments, experimental designs, and values of the dependence on the Niño-4 SST anomaly (G), and central longitude of WWEs . The eastern edge of the western Pacific warm pool is indicated by .

Figure 1b shows an example of parameterized WWEs calculated with the observed SST anomaly from 1996 to 2005. Here, we set in SD since the variance of is larger in the observations than the model. The timings and locations of parameterized WWEs are comparable to those in the observations. For instance, WWEs frequently occur prior to the 1997 El Niño and migrate eastward, associated with the warm pool expansion, while they are less frequent during La Niña from mid-1998 to late-2000. In addition, the frequent occurrence of WWEs between 2002 and 2005 is reproduced well by the model. The probability density function (PDF) for the occurrence of WWEs for 1982–2013, calculated using the Epanechnikov kernel (Kimoto and Ghil 1993), has a peak at positive (Fig. 1c), similar to the observations.

The mLBM-ZC is initially forced by the westerly wind stress patch along the equator (Zebiak and Cane 1987). The WWE parameterization is switched on after 10-yr integrations. To calculate anomalous values of in Eq. (5) during the experiments, we removed the climatology derived from the 10 daily model output for 30 years prior to each time step. We analyzed the model output after the 51st year in model integrations, where the climatology for the entire period (300 years in NO, and 1000 years in the others) is removed. Hereafter, “year N” indicates the Nth year of the model output used in the analysis.

3. ENSO-like oscillations in NO and SD

The mechanism for the oscillatory solutions in NO and SD is examined. Figure 2 shows the anomalies in the SST, zonal wind stress, thermocline depth, and surface zonal current along the equator in NO for . The edge of the warm pool (i.e., the 28.5°C SST isotherm) is also shown in Fig. 2a. The ENSO-like oscillation has a period of 6 years, with peaks in the SST anomaly in the eastern Pacific. The anomalies of the westerly (easterly) wind stress and eastward (westward) current have peaks to the west of the warm (cold) SST anomaly. The thermocline depth anomaly is out of phase with the wind stress anomaly and slightly leads the SST anomaly. Although the wind stress anomaly still locates to the east of the observed anomaly, which may increase the eastern Pacific SST variance, a common bias in the easternmost Pacific is significantly reduced (cf. Gebbie et al. 2007; Xie et al. 2015).

Fig. 2.

Time–longitudinal plots averaged between 1°S and 1°N for 10 years in NO with . (a) 3-month running averaged SST anomaly (K), (b) zonal wind stress anomaly associated with ENSO (N m−2, shade), (c) thermocline depth anomaly (m), and (d) zonal surface current anomaly (cm s−1). The green contour in (a) indicates the 3-month running mean of 28.5°C SST isotherm.

Fig. 2.

Time–longitudinal plots averaged between 1°S and 1°N for 10 years in NO with . (a) 3-month running averaged SST anomaly (K), (b) zonal wind stress anomaly associated with ENSO (N m−2, shade), (c) thermocline depth anomaly (m), and (d) zonal surface current anomaly (cm s−1). The green contour in (a) indicates the 3-month running mean of 28.5°C SST isotherm.

The thermodynamic budget terms for the SST evolution in the eastern equatorial Pacific, calculated directly in the model by Eq. (1), are shown in Fig. 3. In the developing phase of El Niño (e.g., from years 4 to 5), the vertical and zonal advective terms, the thermocline and zonal advective feedbacks, respectively, contribute to increased SSTs. The meridional advective component also warms the SST via the equatorward surface current anomaly balanced with the anomalous equatorial downwelling. The development process for La Niña is the reverse of this. This is a typical ENSO cycle observed in nature and CGCMs (e.g., Jin and An 1999; Huang et al. 2010, 2012) that is described by classical theories (e.g., Jin 1997a), except that El Niño has a slightly larger magnitude than La Niña (Fig. 2a). The asymmetry of ENSO in NO could be caused by the nonlinearity in Eq. (2) and the nonlinear advection (Jin et al. 2003; An and Jin 2004; Duan et al. 2008).

Fig. 3.

Temporal evolutions of the SST anomaly (orange thick, K) and its tendency (gray thick, K month−1) in NO with . The values are averaged over 1°S–1°N, 150°–90°W. The thin red, green, blue, and cyan lines show the zonal, meridional, and vertical advective terms and a damping term including the surface heat flux, respectively, in Eq. (1). The right and left vertical axes indicate the SST anomaly and its tendency terms, respectively.

Fig. 3.

Temporal evolutions of the SST anomaly (orange thick, K) and its tendency (gray thick, K month−1) in NO with . The values are averaged over 1°S–1°N, 150°–90°W. The thin red, green, blue, and cyan lines show the zonal, meridional, and vertical advective terms and a damping term including the surface heat flux, respectively, in Eq. (1). The right and left vertical axes indicate the SST anomaly and its tendency terms, respectively.

State-dependent WWEs modify the ENSO-like oscillation dramatically. Figure 4 shows the anomalies in the SST, zonal wind stress, thermocline depth, and zonal surface current along the equator during a 10-yr period in SD with . The zonal wind stress anomalies are separated into the slow component as calculated with Eq. (3) (denoted as ) and the parameterized component using Eqs. (4) and (5). Unlike the solution in NO, the SST anomaly evolves irregularly in time and has various structures, and the magnitude of El Niño is much larger than that of La Niña. El Niño events have peaks greater than 2 K in the eastern Pacific in 1987/88 and 1991/92, while the positive anomalous SST appears near the date line from 1983 to 1984 (Fig. 4a). As expected from Eq. (5), WWEs occur frequently (rarely) for the positive (negative) Niño-4 SST anomaly (Fig. 4c). They excite the oceanic Kelvin waves as indicated by the eastward-propagating signals of the deepened thermocline and eastward surface current (Figs. 4d,e). The central longitude of WWEs shifts eastward when the warm pool expands to the east during El Niño.

Fig. 4.

As in Fig. 2, but in SD and adding (c) the zonal wind stress associated with WWEs (N m−2) and 28.5°C isotherm. Here (d) and (e) are thermocline depth anomaly and zonal surface current anomaly, respectively. Scales in shadings are different from Fig. 2.

Fig. 4.

As in Fig. 2, but in SD and adding (c) the zonal wind stress associated with WWEs (N m−2) and 28.5°C isotherm. Here (d) and (e) are thermocline depth anomaly and zonal surface current anomaly, respectively. Scales in shadings are different from Fig. 2.

The comparison between NO and SD indicates that the state-dependent WWEs induce the structural diversity of the model’s ENSO and enhance its asymmetry and irregularity. The statistics and diversity of the model’s ENSO will be further discussed in sections 4 and 5, including their dependence on γ and G.

4. Statistics of El Niño indices

a. Time series of Niño-3 index

The time series of the monthly SST anomalies in the Niño-3 region (5°S–5°N, 150°–90°W) are shown for the observations for 1850–2014 (Fig. 5a) and the model experiments (NO, AD, SD, N4, and WP) with for 300 years (Figs. 5b–f). The observed ENSO is irregular and positively skewed, and extremely strong El Niño events appear in 1982/83 and 1997/98. The model’s ENSO in NO is periodic with a small amplitude. In AD, WWEs make the ENSO-like oscillation irregular but the variance is similar to or slightly smaller than that in NO. The model’s ENSO in SD is also irregular, and has a large variance due to extreme El Niños during some epochs. Larger variance is also observed in N4. In WP, strong El Niño events reaching 2 K appear more frequently than in AD.

Fig. 5.

Time series of the monthly Niño-3 SST anomalies (K) in (a) the observations from 1850 to 2014, (b) NO, (c) AD, (d) SD, (e) N4, and (f) WP from years 1 to 300.

Fig. 5.

Time series of the monthly Niño-3 SST anomalies (K) in (a) the observations from 1850 to 2014, (b) NO, (c) AD, (d) SD, (e) N4, and (f) WP from years 1 to 300.

b. Variance

The PDFs for the Niño-3 SST anomalies are compared between the observations and the model experiments for (Fig. 6a). Their standard deviations are shown in Table 2. The PDF for NO is bimodal, as was shown by Perez et al. (2005), while the other PDFs are close to a Gaussian distribution. In SD and N4, is larger than for the other experiments, indicating that the dependence of WWE occurrence on increases the variance of ENSO in the model. The standard deviations of the Niño-4 SST anomalies are increased in SD, N4, and WP (Table 2), although they are much smaller than the observed value due to the limitations of the ocean model (Kang and Kug 2000).

Fig. 6.

(a) PDFs for the Niño-3 SST anomalies (K) in NO (dark-gray solid), AD (green solid), SD (red solid), N4 (orange dotted), WP (blue dotted), and the observation (black dotted). (b) The upper and lower tails of the PDFs. The PDFs are calculated using the Epanechnikov kernel (Kimoto and Ghil 1993).

Fig. 6.

(a) PDFs for the Niño-3 SST anomalies (K) in NO (dark-gray solid), AD (green solid), SD (red solid), N4 (orange dotted), WP (blue dotted), and the observation (black dotted). (b) The upper and lower tails of the PDFs. The PDFs are calculated using the Epanechnikov kernel (Kimoto and Ghil 1993).

Table 2.

Standard deviations of the Niño-3 and Niño-4 SST anomalies ( and , respectively) and asymmetricities of the Niño-3 and Niño-4 SST anomalies ( and , respectively) in the experiments with and observations for 1850–2014 (denoted as OBS) and 1981–2014 (denoted as OBS81).

Standard deviations of the Niño-3 and Niño-4 SST anomalies ( and , respectively) and asymmetricities of the Niño-3 and Niño-4 SST anomalies ( and , respectively) in the experiments with  and observations for 1850–2014 (denoted as OBS) and 1981–2014 (denoted as OBS81).
Standard deviations of the Niño-3 and Niño-4 SST anomalies ( and , respectively) and asymmetricities of the Niño-3 and Niño-4 SST anomalies ( and , respectively) in the experiments with  and observations for 1850–2014 (denoted as OBS) and 1981–2014 (denoted as OBS81).

The values of and depend on both γ and G (Figs. 7a,b). The standard deviations increase monotonically for G for the entire range of γ, consistent with Levine and Jin (2010). That is, the state dependence of WWEs acts to destabilize ENSO regardless of the inherent model’s stability. By comparing AD with NO, the additive WWEs are found to increase and for , and suppress them for . This suggests that the additive WWEs damp the model’s ENSO cycle in the unstable oscillatory regime, but intensify it in the stable regime.

Fig. 7.

Dependence of standard deviations (K) and asymmetricities (K2) of the Niño-3 and Niño-4 SST anomalies on γ and G in the experiments with the noise. SD and AD are corresponding to and , respectively, and the cross marks indicate the main experiment with and . The values in NO are also depicted in the upper boxes, but for since ENSO-like oscillations are damped.

Fig. 7.

Dependence of standard deviations (K) and asymmetricities (K2) of the Niño-3 and Niño-4 SST anomalies on γ and G in the experiments with the noise. SD and AD are corresponding to and , respectively, and the cross marks indicate the main experiment with and . The values in NO are also depicted in the upper boxes, but for since ENSO-like oscillations are damped.

c. Asymmetry

Figure 6b shows the upper and lower tails of the PDF in Fig. 6a. The Niño-3 SST anomaly greater than 2 K, which is not observed in NO, is more frequent in SD and WP than in AD and N4. The number of occurrences during the 1000 simulated years is 0 in AD, 29 in SD, 1 in N4, and 12 in WP. This indicates that the occurrence of WWEs at the warm pool edge favors stronger El Niño events. On the other hand, the probability of values less than −2 K is almost zero in all of the model experiments.

The dependence of the ENSO asymmetry on γ and G is shown in Figs. 7c and 7d in the same manner as in Figs. 7a and 7b. Here, we define a parameter to measure the asymmetricity, b, which is the variance-weighted skewness suggested by An et al. (2005):

 
formula

where is the kth moment and (where is the ith data point, is the mean, and N is the number of observations). The asymmetricity is used instead of skewness [the normalized third statistical moment, ] to avoid causing the larger skewness originating from the smaller standard deviation in the denominator. Values of b for the Niño-3 and Niño-4 SST anomalies ( and , respectively) are shown in Table 2 for the observation and experiments with . In the observations for 1850–2014, and , although these values vary on interdecadal time scales and are of a larger magnitude after the 1980s [ and for 1981–2014; cf. An (2004)]. In NO, increases and decreases with γ. For any value of γ, is smaller than NO regardless of G. This may be caused by the climatology of the thermocline depth induced by the WWE forcing, which is positive in the eastern Pacific, so that the nonlinearity in Eq. (2) is reduced. The value of increases with respect to G in the greater part of Fig. 7c, consistent with previous numerical studies (Perez et al. 2005; Gebbie et al. 2007; Jin et al. 2007; Levine and Jin 2010; Lopez et al. 2013; Levine et al. 2016). This indicates that the state dependence of WWEs, especially the dependence on the warm pool expansion (Fig. 6b), is responsible for the ENSO asymmetry in the model. However, decreases for both G and γ when exceeds 1 K. This is caused by the upper limit of the total SST in this model (see section 2a): while the growth of El Niños is limited, La Niñas can be stronger for larger γ due to the increased thermocline feedback. Values of also decrease with respect to G regardless of γ. Thus, the state dependence also enhances the negative asymmetricity in the western and central Pacific. The above results suggest that the state-dependent WWEs help to produce the asymmetry in SSTs as in the observations (cf. An and Jin 2004).

d. Periodicity

The power spectrum of the monthly Niño-3 SST anomalies is shown in Figs. 8a–c for NO, AD, and SD as a function of γ, calculated by Welch’s overlapped segment averaging with 50-yr windows using Hamming’s taper and zero padding. In NO, the power is concentrated with a period of 6 years, with a secondary peak with a period of 3 years. These two peaks may correspond to the two inherent modes in the linearized ZC model (Bejarano and Jin 2008). In the other experiments forced by noise, the spectra are widened and have broad peaks with a period of 4–6 years (cf. Blanke et al. 1997). The dominant peaks in AD and SD shift toward a higher frequency than that in NO regardless of γ, as observed in CGCMs with a WWE parameterization (Lopez et al. 2013). This originates from the nonlinearity in Eq. (2) that causes La Niña events to terminate rapidly, rather than a lengthening of El Niño events, since the shallower thermocline in the eastern Pacific is more sensitive to the thermocline deepening associated with WWEs (figure not shown).

Fig. 8.

Power spectral density in (a) NO, (b) AD, and (c) SD as a function of γ, and (d) the difference between SD and AD. In (a), the value for is not depicted since the model’s ENSO cycle is damped in NO. Vertical dashed lines denote .

Fig. 8.

Power spectral density in (a) NO, (b) AD, and (c) SD as a function of γ, and (d) the difference between SD and AD. In (a), the value for is not depicted since the model’s ENSO cycle is damped in NO. Vertical dashed lines denote .

The difference in power between SD and AD is positive for a period of 3–5 years over a wide range of γ (Fig. 8d), which is more robust when G is larger (not shown). That is, the state dependence of WWEs increases the power at higher frequency. This may be related to the modulation in the model’s ENSO flavor, described in the next section.

5. Roles of state-dependent noise in the El Niño flavor

The El Niño flavor (i.e., the coexistence of EP and CP El Niños) is examined in the model. According to Kug et al. (2009), the two types of El Niño events are separated based on the relationship between the magnitudes of the standardized Niño-3 and Niño-4 SST anomalies ( and ) averaged for the boreal winter (December–January–February). To clearly divide these two types, EP El Niño is detected when and , and CP El Niño is detected when and . Using these criteria, 10 EP and 14 CP El Niño events are detected in the observations for 165 years (red and blue circles in Fig. 9a); they include typical EP El Niños in 1972/73, 1982/83, and 1997/98 and CP El Niños in 1994/95, 2002/03, 2004/05, and 2009/10. The composite horizontal structures of the winter SST anomalies are shown in Figs. 10a and 10b for EP and CP El Niños, respectively. The SST maximum of the EP (CP) El Niño is located in the eastern (central) Pacific, consistent with Kug et al. (2009).

Fig. 9.

Scatterplot (gray dots) of the DJF-averaged Niño-3 and Niño-4 SST anomalies standardized by their standard deviations in (a) the observations, (b) NO, (c) AD, and (d) SD with . Note that the plots for 300 years are overlapped in NO. Red and blue dots correspond to CP and EP El Niños, respectively. The thin lines in each panel are related to the conditions to determine CP and EP El Niños. The numbers of CP and EP El Niños for the period of each time series are shown at the bottom of each panel.

Fig. 9.

Scatterplot (gray dots) of the DJF-averaged Niño-3 and Niño-4 SST anomalies standardized by their standard deviations in (a) the observations, (b) NO, (c) AD, and (d) SD with . Note that the plots for 300 years are overlapped in NO. Red and blue dots correspond to CP and EP El Niños, respectively. The thin lines in each panel are related to the conditions to determine CP and EP El Niños. The numbers of CP and EP El Niños for the period of each time series are shown at the bottom of each panel.

Fig. 10.

Composite of DJF-averaged SST anomalies (contour intervals are 0.1 K) for EP and CP El Niños in (a),(b) the observations; (c),(d) AD with ; and (e),(f) SD with . Shaded areas indicate values exceeding the 95% statistical confidence level calculated by a two-tailed Student’s t test.

Fig. 10.

Composite of DJF-averaged SST anomalies (contour intervals are 0.1 K) for EP and CP El Niños in (a),(b) the observations; (c),(d) AD with ; and (e),(f) SD with . Shaded areas indicate values exceeding the 95% statistical confidence level calculated by a two-tailed Student’s t test.

Figures 9b–d show scatter diagrams of and in NO, AD, and SD with . Whereas and are highly correlated and quasi-periodic in NO (plots for 300 years are overlapped in Fig. 9b), their relationship is scattered in AD and SD and indicates that the El Niño flavor appears in these experiments. The numbers of EP and CP El Niños for 1000 years are 92 and 49 in AD, and 76 and 26 in SD, respectively. The composite winter SST anomalies of EP and CP El Niños in AD and SD show similar patterns to the observations (Figs. 10c–f), albeit with smaller magnitudes of CP El Niños.

Temporal evolutions of EP and CP El Niños are obtained from the lagged composites of SST and the related anomaly fields in AD and SD. In AD, EP El Niños develop after the boreal summer and mature in winter, accompanied by the atmospheric response to the SST anomaly (Fig. 11a). Although the occurrence of WWEs is independent of the SSTs in AD due to Eq. (5), the composite of indicates that EP El Niño tends to be triggered by WWEs in early summer through the oceanic response when the anomalous thermocline depth is positive through the Pacific (Fig. 11a). CP El Niño in AD is accompanied by several peaks of WWEs, which induce the eastward surface current, while is weak (Fig. 11b). That is, WWEs stochastically push the warm water eastward and increase the SST in the central Pacific. This triggers CP El Niño when the anomalies of thermocline depth and are still negative in the eastern Pacific, which suppress the growth of SST anomalies by WWE-induced thermocline variations there (e.g., Fedorov 2002; Hu et al. 2014). The zonal advection due to may also contribute to the persistence of the CP El Niño.

Fig. 11.

Lag composite of (a) EP El Niño and (b) CP El Niño for 3 years in AD with , centered at the central day in January. (from left to right) The SST anomaly (K), zonal wind stress anomaly associated with model’s ENSO (N m−2), zonal wind stress of WWEs (N m−2), anomalies of the thermocline depth (m) and surface zonal current (cm s−1) averaged for 1°S–1°N. Hatching indicates values exceeding the 95% statistical confidence level calculated by a two-tailed Student’s t test.

Fig. 11.

Lag composite of (a) EP El Niño and (b) CP El Niño for 3 years in AD with , centered at the central day in January. (from left to right) The SST anomaly (K), zonal wind stress anomaly associated with model’s ENSO (N m−2), zonal wind stress of WWEs (N m−2), anomalies of the thermocline depth (m) and surface zonal current (cm s−1) averaged for 1°S–1°N. Hatching indicates values exceeding the 95% statistical confidence level calculated by a two-tailed Student’s t test.

In SD, WWEs frequently occur during the developing phase of the EP El Niño [i.e., during July(−1) and January(0)], and migrate eastward in association with the warm pool expansion (Fig. 12a). Correspondingly, the thermocline is deepened and the eastward surface current is enhanced, causing EP El Niños to amplify compared with in AD. Similar to AD, CP El Niños are triggered by WWEs in SD when the anomalous thermocline depth and are negative in the eastern Pacific, consistent with previous studies (e.g., Lian et al. 2014). During CP El Niños, successive WWEs in help maintain the eastward current in the central Pacific (Figs. 12b,d). The Niño-4 warming due to increases the probability of occurrence of WWEs, resulting in a further warming. This positive feedback between the SST anomaly and acts to generate CP El Niño in SD. The relationship between WWEs and the SST during EP and CP El Niños in SD is similar to typical events in 1997/98 and 2002/03 (e.g., Fig. 1a).

Fig. 12.

As in Fig. 11, but for SD with .

Fig. 12.

As in Fig. 11, but for SD with .

The development process of El Niños is quantitatively discussed based on the SST budget analysis. Similar to the prototype oscillation in NO (Fig. 3), all the advective terms act to increase the Niño-3 SST for EP El Niños in AD and SD [Figs. 13a and 13c; cf. Huang et al. (2010)]. While the zonal advective term has only a small peak at June(−1) in AD, it greatly contributes to the warming after the boreal spring in SD, corresponding to the occurrence of WWEs. The vertical and meridional advective terms are also enhanced in SD as compared with AD. Since the state-dependent WWEs force the eastward currents at the warm pool edge, the zonal advection of warm water further strengthens EP El Niños. This is consistent with the increase of the standard deviation and asymmetricity of Niño-3 SST in SD (Figs. 7a,c). In the development of CP El Niños (Figs. 13b,d), the zonal advective term dominates in AD and SD, but it is larger and persists for a longer period in SD (about 10 months). This indicates that the frequent occurrence of WWEs for enhances the zonal advective warming to magnify CP El Niño. The development process of CP El Niño dominated by the zonal advection is consistent with the observed heat budget shown by Kug et al. (2009).

Fig. 13.

Lag composite of the SST anomalies (orange thick, K) and its tendency (gray thick, K month−1) on (left) EP El Niño and (right) CP El Niño for 18 months in (a),(b) AD and (c),(d) SD. For EP (CP) El Niño, the values are averaged over 1°S–1°N and 150°–90°W (160°E–150°W). Thin red, green, blue, and cyan lines show the zonal, meridional, and vertical advective terms and a damping term including the surface heat flux, respectively, in Eq. (1). The right and left vertical axes indicate the SST anomaly and its tendency terms, respectively.

Fig. 13.

Lag composite of the SST anomalies (orange thick, K) and its tendency (gray thick, K month−1) on (left) EP El Niño and (right) CP El Niño for 18 months in (a),(b) AD and (c),(d) SD. For EP (CP) El Niño, the values are averaged over 1°S–1°N and 150°–90°W (160°E–150°W). Thin red, green, blue, and cyan lines show the zonal, meridional, and vertical advective terms and a damping term including the surface heat flux, respectively, in Eq. (1). The right and left vertical axes indicate the SST anomaly and its tendency terms, respectively.

Interestingly, both EP and CP El Niño tend to have their peaks in boreal winter, even though CP El Niño is generated by stochastic additive WWEs in AD. WWEs in winter tend to warm the Niño-4 region due to a seasonal large zonal SST gradient in the basic state, while WWEs in late spring to fall are favorable for triggering and intensifying EP El Niño, owing to the annual cycle of the atmosphere–ocean coupled system (e.g., Harrison and Schopf 1984).

The dependence of the El Niño flavor on the model’s ENSO stability and the strength of the state dependence is examined. The number of occurrences of EP El Niño increases with γ, although this relationship is unclear in a part of the result with (Fig. 14a). Therefore, the frequency of occurrence of EP El Niño is almost independent of the state dependence of WWEs. On the other hand, when γ increases, CP El Niño becomes less frequent for K but more frequent for K, approximately (Figs. 14b and 7b). Consequently, the ratio of CP to EP El Niños declines with γ in AD, whereas it is roughly independent of γ in SD and is about 0.4 (Fig. 14c). In other words, the state dependence of WWEs guarantees the existence of CP El Niño, or the El Niño flavor in the model. Since the period of CP El Niño is shorter than that of EP El Niño, their coexistence is thought to be responsible for the increase of the model’s ENSO power in higher frequencies in SD (Fig. 8d).

Fig. 14.

Dependency of the El Niño flavor on γ and G. The numbers of (a) EP and (b) CP El Niños for 100 years and (c) the ratio of the numbers of CP El Niño to that of EP El Niño. SD and AD are corresponding to and , respectively, and the cross marks indicate the main experiment with and .

Fig. 14.

Dependency of the El Niño flavor on γ and G. The numbers of (a) EP and (b) CP El Niños for 100 years and (c) the ratio of the numbers of CP El Niño to that of EP El Niño. SD and AD are corresponding to and , respectively, and the cross marks indicate the main experiment with and .

The mechanism of CP El Niño may be different between AD and SD since the dependence of its occurrences on γ in Fig. 14b is opposite each other. In AD, it can be understood as a stochastically forced internal mode mainly related with the zonal advective feedback through the atmospheric response (e.g., Bejarano and Jin 2008); thus, its occurrence is suppressed for larger γ ( in Fig. 14b). On the other hand, in SD and the experiments with larger G, CP El Niño appears due to the interaction between the state-dependent noise and SST as shown in Figs. 12b and 13d, and becomes more frequent when γ is increased (Fig. 14b). This dependence on γ comes from Eq. (5) since P varies more largely by the variation of when is larger.

6. Summary and discussion

The role of coupling with WWEs in the complex behavior of ENSO was examined using an intermediate atmosphere–ocean coupled model with a prescribed annual cycle (mLBM-ZC) (Zebiak and Cane 1987; Watanabe and Jin 2003). The model induces a periodic ENSO-like oscillation in the absence of the stochastic noise that represents WWEs. Additive and state-dependent WWEs, having a Gaussian shape in wind stress centered at the equator, are then parameterized in the model based on observations (Hayashi and Watanabe 2016). For the state-dependent noise, the likelihood of occurrence of WWEs increases following positive Niño-4 SST anomalies and the location of WWEs depends on the eastern edge of the warm pool. To elaborate the sensitivity of the results to the inherent stability of the coupled atmosphere–ocean system, a model parameter (γ) that controls the efficiency of the positive thermocline feedback was perturbed over a wide range of values. We summarize the roles of the state dependence of WWEs on the model’s ENSO as follows.

  • Frequent occurrence of WWEs in response to the positive Niño-4 SST anomaly increases the ENSO-related SST variance.

  • Occurrence of WWEs at the warm pool edge increases the asymmetry in ENSO.

  • State dependence of WWEs guarantees the coexistence of two types of El Niño.

The relationship of additive and state-dependent WWEs with the model’s ENSO is schematically presented in Fig. 15. Without WWEs (Fig. 15a), the thermocline and zonal advective feedbacks drive an ENSO-like oscillation, and Niño-3 and Niño-4 SST anomalies are highly correlated, making it difficult to distinguish between the two types of El Niño. When additive WWEs are incorporated (Fig. 15b), the zonal advection due to WWEs (thick dashed arrow) simultaneously excites the central Pacific warming accompanied by the atmospheric response to the SST; then, the zonal advective feedback between the SST and atmospheric circulation induces CP El Niño when the anomalies of the thermocline depth and zonal wind stress are negative in the eastern Pacific. The additive WWEs also act to trigger EP El Niño through the downwelling Kelvin waves (thick bold arrow), which propagate to the eastern Pacific within a few months. Since the thermocline feedback is effective in the eastern Pacific and increases with γ, the system favors EP El Niño for larger γ. When the WWEs are state dependent (Fig. 15c), the positive Niño-4 SST anomaly increases the probability of occurrence of WWEs (thick gray arrow), enhancing the zonal advective feedback in the western-central Pacific to generate CP El Niño. Although Lopez and Kirtman (2013) showed the robust impact of state-dependent WWEs only on EP El Niño, their result might be affected by filtering the interannual component of surface wind anomalies to construct the statistics of WWEs for their parameterization (cf. Hayashi and Watanabe 2016; Levine and Jin 2017).

Fig. 15.

The main ENSO feedbacks in (a) NO, (b) AD, and (c) SD, updated from Zelle et al. (2004). Here, , h, and T indicate the zonal wind stress associated with ENSO, thermocline depth, and SST anomalies, respectively. and are the SST anomalies in the Niño-3 and Niño-4 region, respectively. indicates the wind stress associated with additive and state-dependent WWEs in (b),(c). Circles with blue and red shadings represent the feedbacks to produce EP and CP El Niños, respectively. All the dashed arrows indicate the zonal advection. Thick black solid and dashed arrows in (b),(c) indicate the roles of , and a thick gray arrow in (c) represent the state dependence. See the text in the figure for the other arrows.

Fig. 15.

The main ENSO feedbacks in (a) NO, (b) AD, and (c) SD, updated from Zelle et al. (2004). Here, , h, and T indicate the zonal wind stress associated with ENSO, thermocline depth, and SST anomalies, respectively. and are the SST anomalies in the Niño-3 and Niño-4 region, respectively. indicates the wind stress associated with additive and state-dependent WWEs in (b),(c). Circles with blue and red shadings represent the feedbacks to produce EP and CP El Niños, respectively. All the dashed arrows indicate the zonal advection. Thick black solid and dashed arrows in (b),(c) indicate the roles of , and a thick gray arrow in (c) represent the state dependence. See the text in the figure for the other arrows.

Since the likelihood of WWE occurrences is controlled by SSTs in the Niño-4 region, remote feedback with Niño-3 SST is required to magnify EP El Niño in the experiments with the state-dependent WWEs. First, WWEs induce the oceanic downwelling Kelvin waves, resulting in subsurface warming in the eastern Pacific where the mean thermocline depth is shallow. Then, the warm water is entrained into the surface layer due to the mean upwelling, and the Niño-3 SST anomaly increases. The atmospheric response to the SST anomaly causes zonal advection to warm the Niño-4 region, which is favorable for the subsequent occurrence of WWEs. In addition, since WWEs rarely emerge during La Niña, the oscillatory system is not suppressed (cf. Fedorov 2002). Therefore, the state-dependent WWEs increase the variance of the Niño-3 SST anomaly. The state-dependent WWEs also strengthen EP El Niño since they migrate to the east in association with the warm pool expansion, where zonal SST contrast is large, so that zonal advective warming is effective (cf. Gebbie et al. 2007). Thus, the ENSO-like oscillation becomes more asymmetric due to the state dependence of WWEs within a limit of the radiative-convective equilibrium.

In the mLBM-ZC, the SST variance in the western-central Pacific is smaller than observed, resulting in a weaker magnitude of CP El Niño. Previous studies attempted to modify the oceanic part of the ZC model, where the focus was on the western Pacific (Kang and Kug 2000; Kug et al. 2005), providing better forecast skill not only in the western Pacific but also in the central-eastern Pacific. Their modifications might improve the performance of the mLBM-ZC as well, although their empirical methods may complicate the physical interpretation. The small SST variance might also result from the atmospheric response locating to the east of the observed variance.

The complex behavior of the model’s ENSO induced by the state-dependent WWEs is consistent with the observations. For instance, the SST anomaly in the eastern Pacific is positively skewed to a great extent when WWEs are energetic (An 2004, 2009; Kug et al. 2008). WWEs are observed frequently during CP El Niño (e.g., McPhaden 2004), but it is still unclear what causes the long-term increase in the occurrence frequency of CP El Niño since 2000 (Yeh et al. 2009; McPhaden et al. 2011; Lee et al. 2016). Although it is possible that other factors for modulating the ENSO cycle have contributed (An 2009), these observational features suggest that the state-dependent WWEs play a crucial role in the ENSO diversity. The relationship between the state dependence of WWEs and ENSO flavor in state-of-the-art CGCMs should be investigated in the future, as well as the asymmetry (Levine et al. 2016).

Acknowledgments

This work was supported by JSPS Grants-in-Aid for Scientific Research 26247079 and 25-5379, and the Program for Risk Information on Climate Change from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. We are grateful to Prof. S.-I. An for kindly providing the ZC model sources and constructive comments. We also would like to thank Profs. F.-F. Jin, M. Kimoto, A. Timmermann, and Dr. R. Xie for helpful discussions, and we appreciate thoughtful suggestions and comments given by three anonymous reviewers. GrADS and gnuplot were used to produce the figures.

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Footnotes

a

Current affiliation: Department of Atmospheric Sciences, School of Ocean and Earth Science and Technology, University of Hawai’i at Mānoa, Honolulu, Hawaii.

Publisher’s Note: This article was revised on 19 April 2017 to correct an error in the authors’ affiliation.

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