1. Introduction
El Niño–Southern Oscillation (ENSO) is the dominant source of interannual variability in the tropical Pacific. While it has long been established that ENSO is governed by basinwide ocean–atmosphere feedbacks (Bjerknes 1969), the origin of its variability and irregularity has yet to be completely understood. It has been argued that ENSO irregularity results from an internal chaotic interaction between the annual cycle and slowly evolving ocean modes (Zebiak and Cane 1987; Jin et al. 1994; Tziperman et al. 1994). The leading contrary hypothesis is that atmospheric variability uncoupled to the ocean, acting as external stochastic forcing (SF), can at least partially drive irregular ENSO (Chang et al. 1996; Kleeman and Moore 1997; Eckert and Latif 1997; Blanke et al. 1997; Moore and Kleeman 1999; Penland et al. 2000; Zavala-Garay et al. 2003). One of the major sources of SF for ENSO is the Madden–Julian oscillation (MJO; Madden and Julian 1971)—a series of large-scale eastward-propagating disturbances in the tropical atmosphere separated by a month or more (Rui and Wang 1990; Yano et al. 2004). Surface westerly anomalies of the MJO can force downwelling oceanic Kelvin waves and influence ENSO evolution (McPhaden and Taft 1988; Kessler et al. 1995). MJO forcing extracted from surface wind data can reasonably reproduce ENSO in coupled ocean–atmosphere models of intermediate complexity (Zavala-Garay et al. 2005, 2008; Kapur et al. 2012, hereafter K12).
While studies have largely focused on the influence of MJO on ENSO, the fact that sea surface temperatures (SSTs) associated with ENSO can heavily modulate the MJO itself has yet to be fully considered. It is well known that the MJO convection occurs more favorably over warm than cold waters, and that it extends eastward with the expansion of the western Pacific warm pool (McPhaden and Picaut 1990). Gutzler (1991) showed that during El Niño events the intraseasonal variance enhances on the eastern side of the date line. This was corroborated by Fink and Speth (1997), who noted that the MJO events tend to propagate farther toward the east when ENSO-related warm SST anomalies lie underneath. McPhaden (1999) analyzed the 1997/98 El Niño and showed that an envelope of strong MJO surface signals shifted eastward in tandem with the 29°C isotherm. Kessler (2001) quantified the east–west meandering of the MJO envelope and found that it is correlated to ENSO indices. Not only are the MJO strength and location impacted by warm SSTs, but its speed also reduces because of the lowering of moist static stability (Davey 1989; Wang and Xie 1998). Westerly wind bursts (WWBs), found in all MJO events, grow in strength, expand, and move eastward during the warming of the central eastern Pacific (Eisenman et al. 2005; Tziperman and Yu 2007; Gebbie and Tziperman 2009a). In essence, MJO—an influence on ENSO—is itself influenced by ENSO. This is noticeable in Fig. 1a, which superimposes MJO surface zonal wind anomalies on observed total and anomalous SSTs. Thus, the MJO likely acts as multiplicative as opposed to additive SF.
Hovmöller diagram of positive MJO surface zonal winds (magenta contours) averaged over 5°S–5°N and derived from the National Centers for Environmental Prediction (NCEP)–Department of Energy Global Reanalysis 2 (NCEP2). The contour interval is 1 m s−1. Superimposed are the SST anomalies (color shading) and total SST (black contours) from (a) NCEP2 and (b) the ZC model driven by MJO derived from the NCEP2 data, and averaged over 10°S to 10°N. In each panel, the dotted line shows the climatological annual mean location of the 28°C isotherm at the equator. The vertical graphs in the middle depict the simultaneous Niño-3 index and the warm-pool index ω [defined in Eq. (2)].
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
Theories of SF postulate that the introduction of multiplicative noise fundamentally changes the characteristics of a physical system (Hasselmann 1976; Horsthemke and Lefever 1984). Using an analytic recharge oscillator framework, Jin et al. (2007) demonstrated that the state dependence of SF might impart instability and mean-state biases to the ENSO system.
Modeling studies with realistic SF structure have reached similar conclusions. Perez et al. (2005) introduced SST feedback in an intermediately complex coupled model by linearly amplifying SF by Niño-3 SST. They found an improvement in the reproduction of enhanced likelihood of warm events when the model was tuned to a neutral or slightly unstable regime. Since their SF was derived from observed surface winds as a residual of linear regression with SST, it might already be biased with nonlinear SF modulation associated with ENSO (such as slowing down of MJO over warm water). Moreover, their SF easterlies are unrealistically amplified by the same factor as westerlies. Eisenman et al. (2005) introduced multiplicative SF in an intermediately complex coupled model by adding idealized WWBs with occurrences dependent on the extent of the western Pacific warm pool. They noted an enhancement in the interannual component of WWBs, with a simultaneous doubling of ENSO amplitude. They also postulated that introducing multiplicative noise is equivalent to enhancing the coupled instability. Gebbie et al. (2007) implemented SST modulation of WWBs in hybrid coupled models and found that it affects the strength, period, and asymmetry of ENSO events. Gebbie and Tziperman (2009b) found that doing so might also improve the skill to predict an El Niño.
The role of SST feedback to the MJO, as opposed to WWB or generalized SF, has never been studied in the context of its influence on ENSO. The hurdle is to represent the MJO in a manner that allows control of its individual events while preserving its characteristics that are essential over larger time scales. For instance, the linear theory of SF (Hasselmann 1976) and modeling studies (e.g., Roulston and Neelin 2000; Zavala-Garay et al. 2008; K12) require that the low-frequency tail of the MJO must be retained in order to generate ENSO. Thus, one requirement of a study of multiplicative MJO forcing is that the control of individual MJO events must lead to indirect control over its interannual variability.
In this paper, we present a parameterization scheme capable of controlling the characteristics of MJO, including its modulation by ENSO SST, but with realistic structure and propagation (as opposed to stationary WWBs). Our study employs a coupled ocean–atmosphere model of intermediate complexity, which is described in section 2. The MJO parameterization and the procedure to incorporate SST feedback are explained in section 3. Our design allows us to systematically test the sensitivity of various ENSO characteristics to the statistics (section 4a) and SST modulation (section 4b) of various MJO parameters. Based on the results, we construct an ensemble of simulations using fully multiplicative forcing (i.e., with feedbacks implemented in parameters that exhibit sensitivity) and compare it to an ensemble of fully additive simulations (i.e., with stochasticity in all parameters but no SST feedback). Comparisons are drawn in terms of ENSO variance (section 4c) and interdecadal variability of ENSO (section 4d). Conclusions are made in section 5.
2. Model
The intermediately complex coupled ocean–atmosphere model employed in this study is a slightly modified version of the Zebiak and Cane (1987) model, which is described in detail in K12. To avoid confusion, this model is hereafter referred to as the “ZC model,” while the original model of Zebiak and Cane is referred to as the “ZC87 model.” The modifications by K12 include eliminating the ENSO irregularity arising from the chaotic interaction among lower-order ocean modes. This suits well with the current study because it is based on the premise of stochastically driven ENSO. The modification would remain valid even if nonlinear chaos exists in ENSO because we seek to understand whether and how SST feedback to the MJO may influence ENSO, instead of whether such feedback is the only or even the dominant influence. While the ZC87 model always produces irregular ENSO, the ZC model can only produce irregularity in the presence of external forcing (see K12 for details). The ZC model allows daily SF, as opposed to minimum 10-day SF in ZC87. This is important because the MJO events can fully grow or decay, or propagate up to 15° of longitude within 8 days. The zonal and meridional resolutions are 5.625° and 2°, respectively, fine enough to capture the surface signature and propagation characteristics of the MJO.
The MJO is introduced in the model by converting the MJO surface winds to wind stress anomalies and adding them to those internally produced by the atmospheric model. For simplicity, we tailor the forcing to have a Gaussian shape in the meridional direction with a width of 10°, which is approximately equal to the Rossby radius of deformation in the tropics.
An important variable in the model is the air–sea coupling coefficient, which appears in the bulk formula for wind stress as a multiplier to the drag coefficient. A value of the coupling coefficient below a certain threshold produces damped oscillations in unforced runs, representing stable regime. We can safely choose this range for our study because K12 demonstrated that it is in this regime that the model produces most realistic Niño-3 SST anomalies, in terms of its time series, power spectrum, seasonality, and seasonal autocorrelation, when forced by the MJO derived from observations. The simulated anomalous and total SST for the 1997/98 El Niño is compared to the observed SST in Fig. 1.
3. MJO parameterization
MJO primarily influences ENSO through surface westerlies, which are led and followed by relatively weak easterlies (Rui and Wang 1990). The westerlies propagate eastward at about 5 m s−1 near the equator like a pulse (Yano et al. 2004; Hendon and Salby 1994). The meridional winds associated with the MJO are too weak to significantly influence the ocean (Zhang 1996). Taking all these characteristics into account, we construct our parameterized MJO as pulses of anomalous eastward-propagating surface westerly wind interspersed with a background of constant easterly anomalies. We enforce the long-term mean of the MJO surface zonal wind anomalies to be zero so that there is no net momentum or energy transfer to the ocean.
a. Definitions of parameters
The main simplification in our MJO parameterization is that the spatial structure of westerly anomalies of a parameterized MJO event is Gaussian in both zonal and meridional directions. The meridional Gaussian shape is tailored by the coupled model (section 2). Each individual MJO westerly event is parameterized in terms of its zonal width (W), amplitude (A), terminal decay rate (D2), terminal longitudinal (L2), eastward propagation speed (C), and time interval between two adjacent events (I). The assumption is that the quantities represented by these parameters remain constant during the lifetime of an MJO event. This implies that some observed features, such as the gradual weakening, fastening, and off-equatorial drifting of the MJO signals in the central/eastern Pacific (over colder waters), are ignored in the design of the parameterization. In addition to these parameters, five others describe the seasonal cycle of the MJO. All parameters are formally defined below. Wherever possible, their physical correspondence is illustrated in Figs. 2a and 2b, which show a Hovmöller diagram and fixed-longitude amplitude evolution, respectively, labeled with variables representing MJO parameters.
Speed (C) represents the zonal propagation speed of an MJO event.
Zonal width (W) represents the zonal scale of the surface westerlies of an MJO event. It is quantified as the spacing between the two half-maxima of the Gaussian describing MJO zonal wind along the equator. Consequently, the time evolution of zonal wind during the passage of an MJO event is also a Gaussian, with temporal width C−1W (Fig. 2b).
Amplitude (A) represents the westerly strength of an MJO event. It is defined as the magnitude difference between the peak and asymptotical base of the Gaussian describing zonal wind temporal evolution (Fig. 2b). This nontrivial definition makes it easier to compute the constant easterlies (uE in Fig. 2b) that must be subtracted from surface wind anomalies to obtain zero long-term mean. The peak westerly strength of an MJO event remains constant until the terminal decay sets in.
Terminal longitude (L2) represents the zonal propagation extent of an MJO event. It is defined as the longitude where the MJO westerlies begin to decay (Fig. 2a). Its counterpart L1, the longitude where an MJO event is initiated, is not required here because the domain of our ENSO model is the tropical Pacific. All MJO events are assumed to arrive at the western boundary from the Indian Ocean.
Terminal decay time (D2) represents the time scale of the weakening of MJO westerlies, which kicks in at L2. It is defined as the time elapsed between the onset of decay and the half-weakening of MJO westerlies (Fig. 2a). Its counterpart, the growth time (D1), can be similarly defined corresponding to L1, but is irrelevant in this study because L1 is always over the Indian Ocean.
Time interval (I) represents the time between the initiations of two adjacent events (Fig. 2a) at L1 assumed to be 80°E.
- Seasonal cycle of the MJO is described by five parameters that define a factor S that is multiplied by the amplitude of MJO surface winds:where t is the calendar day, H1 and H2 represent the specified annual and subannual strengths, respectively, of the MJO in a particular year, tφ and tτ represent their corresponding temporal phases, and F is subannual harmonic mode (equal to the number of peaks of S in that year), and 360 is the number of days in a ZC model year.
(a) Hovmöller diagram of surface zonal winds for idealized (additive) MJO. The contour interval is 1 m s−1 with positive (negative) values represented by solid (dotted) contours. (b) Surface winds during the passage of an MJO event at a fixed longitude [along the dark solid line shown in (a)]. See text for definitions of the labeled MJO parameters.
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
b. Prescription of parameter values
We prescribe the parameter values for MJO events based on the statistics of the observed MJO. No event-to-event correspondence is sought between the parameterized and observed MJO. Parameter W is kept equal to 60° for all MJO events in all simulations based on the robustness of the horizontal structure and scale of the MJO surface winds (Rui and Wang 1990; Zhang and Dong 2004). Parameter D2 is set equal to W/C on the assumption that an MJO event decays by smashing into an unfavorable environment (such as the equatorial cold tongue). The five seasonal-cycle parameters are also kept fixed because the only known sources of MJO’s deviations from its seasonal cycle are the stochasticity and SST modulation of individual MJO events. Unless specified otherwise, their values are H1 = 0.2 and H2 = 0.1 based on maximum and minimum MJO seasonal amplitude1 over the central western Pacific (K12); F = 2 based on the biannual transit of the MJO between the two hemispheres (Zhang and Dong 2004); and tφ = tτ = 110 days to place the first peak in mid-April. Figure 3 shows the resulting multiplication factor S as a function of calendar day t. Also superimposed are the equivalent seasonal amplitude derived from the observed MJO and its 5th–95th percentile range and 50th percentile values derived from the ensemble additive and multiplicative cases (described in section 4c).
Ensemble spread (5th–95th percentiles) of seasonal amplitude of the MJO from simulations using additive (shaded patch) and multiplicative (stippled patch) forcing. Also superimposed are the corresponding 50th-percentile curves (thin lines), prescribed seasonal-influence multiplication factor S (circles), and seasonal amplitude derived from the MJO obtained from NCEP2 reanalysis (thick line).
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
Unless a sensitivity experiment requires its fixation, any other parameter X (which could be A, C, L2, or I) is varied from one MJO event to another either independently of the evolving ENSO state, in the case of additive MJO forcing, or as a function of SST in the case of multiplicative MJO forcing. It is randomly selected from a Gaussian probability distribution defined by five metaparameters: the most probable value X*, the standard deviation ΔX, the SST modulation φ, and truncations Xmin and Xmax. In the additive case, φ is zero.
Table 1 lists the default values of X*, ΔX, and φ for various MJO parameters. The justification and details of how these values are prescribed in the additive and multiplicative cases can be found in appendixes A and B, respectively. In either case, our choices are based on approximate information from observational studies to get the MJO statistics qualitatively, if not quantitatively, right.
Default values for statistics of MJO parameters.
The MJO surface westerly wind uW(t) is reconstructed based on the prescribed metaparameter values. Constant background easterly wind (uE), equal in magnitude to the mean MJO westerly wind, is added over the Pacific between the western boundary and the terminal longitude L2. Based on the values in Table 1 for MJO parameters, uE is −0.82 m s−1 (Fig. 2b).

Figure 4 depicts the prescribed Gaussian probability distributions for A, C, L2, and I based on the Table 1 values of their X* and ΔX, superimposed by the 50th-percentile curve and the 5th to 95th percentile interval from histograms computed from ensemble additive and multiplicative cases (described in section 4c). As expected, the 50th percentiles curve closely follows the prescribed probability distribution but the ensemble spread is relatively large. While the multiplicative MJO parameters have different histograms than the additive MJO, their values are still realistic.
Ensemble spread (5th–95th percentiles) of histograms of the MJO (a) amplitude, (b) time interval, (c) propagation speed, and (d) terminal longitude obtained from simulations using additive (shaded patch) and multiplicative (stippled patch) MJO forcing. Also superimposed, in each panel, are the corresponding 50th-percentile curves (thin lines) and the prescribed truncated Gaussian PDFs (dashed line). In each case, the most probable value X*, stochasticity ΔX, and the special truncations (if any) were taken from Table 1.
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
Magenta contours in Fig. 5 depict additive and multiplicative MJO uW over a 3-yr span. Although the temporal behavior is similar to the observed MJO in Fig. 1, the spatial variability is somewhat different. The variations of amplitude and zonal extent with underlying SST (Fig. 5b) are similar to Fig. 1.
Hovmöller diagram of positive surface zonal winds (magenta contours) averaged over 5°S–5°N for (a) additive and (b) multiplicative MJO forcing. The contour interval is 1 m s−1. Superimposed are the corresponding SST anomalies (color shading) and total SST (black contours) reproduced by the ZC model and averaged over 10°S–10°N. In each panel, the dotted line shows the climatological annual mean location of the 28°C isotherm at the equator. The vertical graphs in the middle depict the simultaneous Niño-3 index and the warm-pool index ω.
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
Ensemble spread (5th–95th percentiles) of multitaper power spectra of the Kelvin wave forcing index in the east Pacific from simulations using additive (shaded patch) and multiplicative (stippled patch) MJO forcing. Also superimposed are the corresponding 50th-percentile curves (thin lines) and the spectrum derived from the MJO obtained from NCEP2 data (thick line).
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
4. Results
We first determine the sensitivity of model ENSO to the distribution parameters (i.e., X* and ΔX; see section 4a) and the SST feedback (i.e., φ; section 4b). Then, we compare additive and multiplicative cases in terms of ENSO strength, period, regularity, annularity, warmest month, tendency for extreme warm events (section 4c), and eventually ENSO interdecadal variability (section 4d). In each experiment, ENSO is diagnosed in terms of Niño-3 SST (averaged over 5°S–5°N, 90°–150°W). The strength is measured as variance; period and regularity as the frequency and full-width at half-maximum (FWHM), respectively, of the dominant spectral peak; annularity and warmest month as the amplitude and phase, respectively, of a sinusoidal curve least squares fitted to the seasonally segregated variance; and tendency for extreme warm events as the kurtosis. The sensitivity is summarized in Table 2.
Sensitivity of ENSO to MJO characteristics. A plus sign (+) means that the measure of ENSO characteristic (columns) increases with positive increments in the corresponding MJO parameter (rows). The minus sign (−), zero (0), and tilde (~) represent decrease, no variation, and erratic variation, respectively.
a. Sensitivity to additive MJO
The first 10 rows of Table 2 list the sensitivity of ENSO to the most probable value (X*) and stochasticity (ΔX) for different additive MJO parameters, as well as to seasonal cycle parameters H1 and tφ. The simulations leading to these results span 150 years each and had a common initial SST, although the first 30 years were excluded to account for the initialization shock. If the sensitivity to a given X* is tested, all other X* and seasonal-cycle parameters are set to their Table 1 values. To avoid variations from stochasticity and SST feedback, all ΔX and φ are set to zero. The exception is ΔI, which is set to its Table 1 value because setting it to zero makes ENSO completely disappear regardless of the values of other parameters (discussed below in detail). The sequence of I’s generated using this nonzero ΔI is prescribed identically to all simulations so that the random differences in timings of MJO events do not contaminate the comparison. The exceptions, of course, are the experiments in which the sensitivity to I* or ΔI is being tested.
Figure 7a shows the ENSO variance as a function of X*. ENSO strength grows almost linearly with increasing A* and
Variance of Niño-3 in sensitivity simulations as a function of (a) most probable value, (b) stochasticity, and (c) coefficient of SST feedback of the MJO amplitude A (dark solid), terminal longitude L2 (solid), speed C (dark dashed), and interval I (dashed).
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
ENSO strength enhances with ΔA and ΔI, but is insensitive to ΔL2 and ΔC (Fig. 7b). The sensitivity to ΔI is expected because a larger ΔI corresponds to a larger projection on interannual frequencies. ENSO almost entirely disappears if ΔI is zero, or if the sequence of MJO events is made the same during each year. This is consistent with the linear theory (Hasselmann 1976) and modeling studies that found that the low-frequency tail of stochastic forcing is required to generate ENSO (Roulston and Neelin 2000; Zavala-Garay et al. 2008; K12). ENSO is sensitive to ΔA more than ΔL2 and ΔC likely because ΔA imparts more irregularity on the MJO. ENSO completely vanishes if the signal becomes stationary (C = 0), as in cases of WWBs not associated with the MJO. This result differs from previous studies that show sensitivity to WWB (Gebbie and Tziperman 2009b; Eisenman et al. 2005), likely because their surface westerlies often had much larger zonal width2 (up to 100°) than the width W of our MJO (fixed at 60°), and were not interspersed by anomalous easterlies (thus adding net zonal momentum to the ocean).
The simulated ENSO variance is used only to estimate the sensitivity; it is unreliable for quantitative analysis despite the realism of individual parameter statistics (Fig. 4) because of unrealistically large integrated zonal wind.
The sensitivity to the rest of the parameters is also listed in Table 2, but without the aid of figures. The table reveals that ENSO period is sensitive to
b. Sensitivity to SST feedback
The last three rows of Table 2 list the sensitivity of ENSO to the SST feedback coefficients (φ) for different MJO parameters. As in section 4a, the simulations span 150 years and have a common initial condition. In each experiment, all X* are set to their default values (Table 1). The φ to which the sensitivity is studied is incremented from simulation to simulation, while all other φ and ΔX are set to zero to eliminate their influence. ENSO sensitivity is tested to all three φ (i.e., α, κ, and λ).
Figure 7c shows that ENSO strength enhances with α. This might be explained by the argument of Eisenman et al. (2005) that enhancements in the amplitude feedback are equivalent to the enhancements in ENSO coupling strength—the latter being shown by K12 to produce linear increases in ENSO strength. However, the equivalence is not evident for λ, sensitivity to which is nonmonotonous. The ENSO variance is insensitive to κ.
Table 2 reveals that ENSO becomes more frequent and irregular with increases in λ and κ, but its spectrum is unaffected by α. The shift is toward observed values, indicating that feedback in these parameters improves ENSO spectrum. Analysis analogous to that of Fig. 7c reveals that λ has a larger contribution in the improvement than κ. Seasonal variance of ENSO is sensitive to all φ. Although the ENSO annularity grows and moves closer to observed annularity with all three φ, the timing of its warming becomes unrealistic because of the emergence and strengthening of aberrational boreal fall peak for both α and κ. The likelihood of extreme events is insensitive to κ, but increases with increments in α or λ—the parameters with the largest influence on MJO variance. The increase is consistent with the findings of Perez et al. (2005), who did not explicitly use MJO as stochastic forcing, as well as with theory of multiplicative forcing (Horsthemke and Lefever 1984). It is expected because strengthening of MJO forcing during an El Niño leads to stronger forcing of oceanic Kelvin waves that further strengthen the El Niño (vice versa for La Niña). The same reasoning does not explain the insensitivity to κ because the integrated wind stress has an inverse nonlinear relationship with C: the feedback is significant only when El Niño warming is strong enough to reduce C to the range of oceanic Kelvin wave phase speed, whereas La Niña cooling produces little effect on the MJO forcing because C faster than normal makes little difference to the wind stress forcing.
c. Ensemble comparison: Additive versus multiplicative
Two 100-member ensembles are generated each for additive and multiplicative cases. Each member is comprised of a 30-yr segment split from a continuous 3000-yr simulation. This assumes that ergodicity holds (i.e., the ENSO state at the beginning of each 30-yr segment does not influence its evolution beyond a few years)—an assumption justified by K12 for the ZC model tuned in a stable regime. Within each ensemble (additive or multiplicative), the members differ from each other solely by virtue of the prescribed stochasticity in MJO parameters. The multiplicative ensemble is generated using all default values from Table 1. The additive ensemble is generated using the same values, except with all φ set to 0.
Figure 8 shows the variance of all 100 members, each for the additive and multiplicative ensembles. The variance for most members of the additive ensemble lies between 0.1°C2 and 0.3°C2. This is obviously weaker than the variance from observations, 0.82°C2 (Hadley SST anomalies), as well as the variance from ZC model forced with the observed MJO, 0.41°C2 (K12). The variance for most members of the multiplicative ensemble lies between 0.15°C2 and 0.75°C2. This is stronger than the variance of most members of the additive ensemble, but still generally weaker than the variance of observed ENSO. Contrary to the additive ensemble, a large percentage of members of the multiplicative ensemble are able to produce variance in the range of ZC model driven by the observed MJO. Figure 8 also shows that in the multiplicative ensemble, the variance of SST strengthens logarithmically with the variance of the MJO.
Scatterplot of variance of MJO Kelvin-wave forcing index (x axis) and variance of corresponding Niño-3 SST anomaly (y axis) from ensemble simulations. The shaded dots are from additive MJO forcing and the circles are from multiplicative MJO forcing. Also included are markers corresponding to the MJO and ENSO from the NCEP2 reanalysis (×) and the ZC model driven by NCEP2 MJO (*).
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
Figure 9 shows the variance-preserving power spectra of normalized Niño-3 SST from the primary additive and multiplicative forcing ensemble runs represented in percentiles (the range from the 5th to 95th percentiles and the curve corresponding to the 50th percentile). The ensemble spread is enormous for the additive run (the ratio of the 95th to 5th percentile power nearly equals 4 around the 4-yr period), but even more so for the multiplicative cases (the 95th to 5th percentile ratio nearly equals 6). The distribution of power matches at all frequencies for observed ENSO and ZC model ENSO driven by the observed MJO. In the multiplicative case, the power is concentrated more in lower (interannual) than higher frequencies, whereas in the additive case, the power is concentrated in annual and biannual frequencies. Neither case fully captures the observed spectrum, although the 50th-percentile curve of the multiplicative ensemble lies closer to the observed spectrum than the additive ensemble, at least in ENSO frequencies.
Ensemble spread (5th–95th percentiles) of variance-preserving multitaper power spectra of normalized Niño-3 SST anomalies from simulations using additive (shaded patch) and multiplicative (stippled patch) MJO forcing. Also superimposed are the corresponding 50th-percentile curves (thin lines), the ENSO spectrum derived from NCEP2 data (thick line), and from the ZC model driven by the NCEP2 MJO (dashed line).
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
Although the annularity, warmest month, and likelihood of warm events all show sensitivity to the feedbacks in various MJO parameters (section 4c), we do not provide figures to aid their ensemble comparison because of the simplicity of interpretation. The warm-phase seasonal variance of ENSO is similar in additive and multiplicative ensembles. In both cases, the ensemble spread is large and engulfs the seasonal variance of the observed ENSO SST, except for a slight departure in December. This suggests that the SST-feedback makes little difference for seasonal variance. The probability of events with Niño-3 SST anomalies larger than 1.5°C is found to be higher in the multiplicative than additive ensemble. In both cases, nearly 95% of members exhibit probability of extreme events higher than the observed. Again, the ensemble spread is larger for the multiplicative than additive case.
d. Comparison of interdecadal variability of ENSO
ZC model simulations of 3000 years are used to compare the effects of additive and multiplicative MJO forcing on the interdecadal variability of ENSO. Continuous wavelet transform (CWT) based on highly regular (“Morlet”) wavelets is computed for normalized Niño-3 SST anomalies. Figure 10 shows smoothed absolute CWT coefficients averaged over ENSO frequencies (3–7 yr) superimposed with running 11-yr variance of Niño-3 SST from both additive and multiplicative cases. The 200-yr viewable timespan is arbitrarily selected from the total 3000-yr timespan. The running variance is a measure of strength, and CWT coefficients at a given pseudofrequency are a measure of regularity at that frequency.3 Temporal variation in smoothed coefficients implies that ENSO is more regular in some epochs than others. The figure reveals that the power and regularity of ENSO vary simultaneously over interdecadal time scales: the correlation is 0.80 for the additive case and 0.92 for the multiplicative case. The standard deviation of absolute ENSO-frequency CWT coefficients and running variance are almost 2 and 3 times greater, respectively, in the multiplicative than in the additive case. This indicates that SST feedback imparts extremely large interdecadal variation in ENSO frequencies. Probability density functions (PDFs) and autocorrelation analysis of CWT coefficients and running variance (not shown) reveal that the multiplicative case has nearly 3 times the number and 1.5-yr longer epochs with relatively strong and regular ENSO activity than the additive case.
Time series of mean absolute CWT coefficients over ENSO frequencies (solid) for the normalized Niño-3 SST anomalies using (a) additive and (b) multiplicative MJO forcing. The series is shown after applying a smoothing window of 5 yr. Also superimposed, in each panel, is the running 11-yr variance (dashed) of normalized Niño-3 SST anomalies.
Citation: Journal of Climate 25, 23; 10.1175/JCLI-D-11-00609.1
5. Conclusions
We have examined the role of SST modulation of the MJO on ENSO variability by introducing an MJO parameterization scheme in a modified Zebiak and Cane (1987) model tuned to be marginally stable. Surface westerlies associated with individual MJO events are described in terms of few basic parameters: the zonal scale, amplitude, propagation speed, zonal propagation extent, time interval between adjacent events, and seasonal strength. The parameter values are prescribed either additively (i.e., randomly within the observed MJO distribution) or multiplicatively (i.e., as a function of the model SST albeit with some stochasticity)—similar to the treatment of WWBs by Gebbie and Tziperman (2009b).
The multiplicative MJO is designed to mimic the observed SST modulation of the MJO in its amplification (McPhaden and Picaut 1990), further eastward penetration (Fink and Speth 1997), and slowing down (Wang and Xie 1998) during an El Niño event (and vice versa). Its stochastic component is constrained to the point where, in conjunction with the SST feedback, the MJO parameter distributions best replicate the additive MJO. However, an analysis of integrated MJO wind spectra (Fig. 6) from 100-member ensembles shows that there is more interannual power in the multiplicative than additive MJO. This is consistent with the theory of multiplicative SF (Hasselmann 1976), which predicts that the strongest variations in SST at interannual frequencies impart a linear feedback to the MJO forcing. A similar relationship between ENSO and interannual characteristics of WWBs was noted by Gebbie and Tziperman (2009a).
Most ENSO characteristics are found to be sensitive to the SST modulation of MJO parameters, but in many cases the nature of that sensitivity is nontrivial. For instance, the sensitivity of ENSO strength to the east–west meandering of MJO with warm waters [noted by McPhaden (1999) and Kessler (2001)] is not linear, but highly erratic (Fig. 7c). Equally nontrivial is that although the propagation of MJO westerlies is important for ENSO (Fig. 7a), its stochasticity or SST feedbacks are not important at all (Figs. 7b,c). For some ENSO characteristics, such as seasonal variance, even though ENSO exhibits no sensitivity to the stochasticity in a given parameter (in this case, zonal extent), it exhibits sensitivity to the feedback in that parameter. Such behavior implies that at least for that parameter, the systematic feedbacks are more important for ENSO than inherent noisiness. The relative importance of MJO stochasticity and SST feedbacks could be tested because our parameterization allows us to independently control these aspects—a feat not possible in frameworks that directly use observed SF (e.g., Perez et al. 2005). The temptation here is to compare the most probable values and feedback coefficients in terms of their relative influences. But the two are incommensurate because the feedback modifies MJO parameters in opposite ways during the warm and cold phases and in no way during the neutral phase; whereas, the most probable values affect ENSO unipolarly and ubiquitously. The diverse degree of ENSO sensitivity to various parameters and feedbacks shows that the structure of MJO is important to its forcing of ENSO. That ENSO strengthens with stronger SST feedback to MJO amplitude, but strengthens or weakens erratically with increments in feedback to the MJO zonal extent, demonstrates that the role of the SST feedback to various MJO parameters in ENSO is often complex and nontrivial. Our parameterization captures the nuances, which would not have been evident had the MJO forcing been replaced with a coherent excitation of the ENSO stochastic optimal (Moore and Kleeman 1999) or had the SST feedback been treated as an equivalent to ocean–atmospheric coupling (suggested by Eisenman et al. 2005). In this regard, MJO parameterization has advantages similar to those noted by Gebbie et al. (2007) in using structured WWBs.
Even though the integrated wind variance of the parameterized MJO is stronger than the observed, the variance of ENSO SST reproduced using additive MJO forcing acting on a marginally stable ZC model is weaker than observed. The same ZC model configuration produces SST variance much closer to the observed value when multiplicative MJO forcing is used. Purely additive MJO does not suffice for ENSO at least when the latter is assumed to reside in a stable regime. This suggests that the source of relatively large ENSO variance in the MJO-driven simulations of Zavala-Garay et al. (2008) and K12 might be the SST modulation inherently contained in their observationally derived MJO. Given that the amplitude is the only parameter for which ENSO is clearly sensitive to the SST feedback, the larger ENSO variance in the multiplicative than additive ensemble in Fig. 8 must be solely due to the SST feedback to MJO amplitude (α).
The ensemble spread is broader in the multiplicative than the additive case for ENSO variance, spectrum, and the likelihood of warm events. The broadening was also noted by Jin et al. (2007) using a conceptual recharge-oscillator model of ENSO. The large ensemble spread within 30-yr ensemble members suggests the presence of interdecadal variability in ENSO, which is indeed corroborated by computing wavelet coefficients and running variance from the continuous 3000-yr run. Our results suggest that the MJO and its SST feedback are important to the interdecadal variability of ENSO.
We have demonstrated that the multiplicative forcing of the MJO to ENSO can be studied by using MJO parameterization. Despite this success, our analysis is limited to sensitivity analysis and the comparison between additive and multiplicative cases. Our framework is not fully capable of quantifying the influences of MJO stochasticity and SST modulation. This is because even though individual MJO parameters lie in a realistic range (section 3b), the MJO and ENSO variances are weaker than the observed (Figs. 6 and 8), implying that quantitative relationships between MJO parameter values and ENSO indices are not being well represented. The discrepancy is likely because the Kelvin wave forcing index [Eq. (5)] taken from Kessler et al. (1995) and Zhang and Gottschalck (2002) does not fully capture the interplay between the MJO and ENSO. Clearly, the influence of SST-modulated MJO on ENSO needs to be further investigated. An obvious way to increase the low ENSO variance would be destabilization of the ZC model. However, previous studies (Zavala-Garay et al. 2008; K12) have found that doing so deteriorates the characteristics of simulated ENSO—which is why we are content with the investigation of a stable regime. Future studies can investigate whether the deterioration occurs even if ENSO produced in unstable regime is forced by parameterized additive or multiplicative MJO. Our results establish, if only in a stable regime, that the SST feedback on the MJO is a significant component of the ENSO puzzle—similar to what Eisenman et al. (2005) speculated for WWBs.
Our methodology can be advanced in several ways. Improved observations of MJO during ENSO events can lead to more realistic MJO parameterization. Other feedback mechanisms of ENSO to the MJO, such as SST effect on moisture and dependence of MJO initiation on Indian Ocean SST can be considered. Coupled general circulation models (CGCMs) can be used to represent complex and nonlinear processes that might be missing in simple ZC-type models. Experiments could be designed to analyze the implications of SST feedback to the MJO on ENSO predictability—which, we speculate, could be larger than previously envisaged because SST influences narrow the range possible of MJO activity and, by implication, the spread of influenced ENSO.
Acknowledgments
We thank Richard Kleeman for suggesting the use of anomalous warm-pool extent as an index of SST influence for the MJO, and three anonymous reviewers for their constructive comments on early manuscripts of this paper. Our work was supported by a grant from the National Oceanic and Atmospheric Administration (NOAA) Office of Global Programs through the Cooperative Institute for Marine and Atmospheric Studies (CIMAS).
APPENDIX A
Additive Forcing
The additive forcing acquires MJO parameter values in a manner that best mimics the statistical characteristics of observed MJO, including its stochasticity, but not its dependence on the evolving ENSO state. The default value of X* roughly corresponds to the peak of observed PDFs of X. If the Gaussian distribution is truncated equally on both sides (i.e., X* − Xmin = Xmin − X*), then X* is equal to the mean of the distribution. Note that ΔX, representing the stochasticity in X, is by default roughly set equal to the double of the standard deviation of X estimated from observations. For most parameters, Xmin and Xmax are set at X* − 2ΔX and X* + 2ΔX, respectively, beyond which no value is permitted to avoid possible unrealistic characteristics.
The default value of most probable amplitude A* is set to 4 m s−1, consistent with the MJO westerly wind stress used by Kessler and Kleeman (2000). Its default stochasticity ΔA is set at 1.5 m s−1 to account for the variability in the strength of MJO events. The special lower limit of A in Table 1 is different from A* − 2ΔA and contains uE, the background easterlies, which are defined in section 3b. The expression implies that the absolute amplitude is at least 0.5 m s−1, as opposed to A, which is defined in terms of a difference (section 3a). Default I* is set to 70 days, close to the value estimated by Jones (2009), and consistent with the observed frequency of 5 MJO events per year. Default ΔI is set at 50 days so that the range of the interval parameter is close to the “width” of the peak in MJO spectrum; I was assigned a special lower limit of 30 days to represent the observed minimum separation between MJO events. Default C* is set equal to the observed mean MJO propagation speed of 5 m s−1 (Hendon and Salby 1994). Default ΔC is set at 0.6 m s−1—a value heuristically deducible from the longitude–time plot of MJO-related surface wind (Fig. 1), and also close to the estimate by Jones (2009). Default
APPENDIX B
Multiplicative Forcing
The multiplicative MJO is only partially stochastic and mimics the enhancement in MJO strength, slowing down of propagation speed, and extension of eastward propagation with the warming of the central–western Pacific sea surface, and vice versa. The magnitudes of φ in Table 1 are loosely based on a preliminary comparison of features of MJO events during El Niños and La Niñas but are accurate enough in our framework to investigate whether the SST feedback to the MJO has any effect on ENSO.

REFERENCES
Bjerknes, J., 1969: Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev., 97, 163–172.
Blanke, B., J. D. Neelin, and D. Gutzler, 1997: Estimating the effect of stochastic wind stress forcing on ENSO irregularity. J. Climate, 10, 1473–1486.
Chang, P., L. Ji, H. Li, and M. Flügel, 1996: Chaotic dynamics versus stochastic processes in El Nino–Southern Oscillation in coupled ocean–atmosphere models. Physica D, 98, 301–320.
Davey, M. K., 1989: A simple tropical moist model applied to the ‘40-day’ wave. Quart. J. Roy. Meteor. Soc., 115, 1071–1107.
Eckert, C., and M. Latif, 1997: Predictability of a stochastically forced hybrid coupled model of El Niño. J. Climate, 10, 1488–1504.
Eisenman, I., L. Yu, and E. Tziperman, 2005: Westerly wind bursts: ENSO’s tail rather than the dog? J. Climate, 18, 5224–5238.
Fink, A., and P. Speth, 1997: Some potential forcing mechanisms of the year-to-year variability of the tropical convection and its intraseasonal (25–70-day) variability. Int. J. Climatol., 17, 1513–1534.
Gebbie, G., and E. Tziperman, 2009a: Incorporating a semi-stochastic model of ocean-modulated westerly wind bursts into an ENSO prediction model. Theor. Appl. Climatol., 97, 65–73.
Gebbie, G., and E. Tziperman, 2009b: Predictability of SST-modulated westerly wind bursts. J. Climate, 22, 3894–3909.
Gebbie, G., I. Eisenman, A. Wittenberg, and E. Tziperman, 2007: Modulation of westerly wind bursts by sea surface temperature: A semistochastic feedback for ENSO. J. Atmos. Sci., 64, 3281–3295.
Gutzler, D., 1991: Interannual fluctuations of intraseasonal variance of near-equatorial zonal winds. J. Geophys. Res., 96C, 3173–3185.
Hasselmann, K., 1976: Stochastic climate models, Part 1: Theory. Tellus, 28, 473–485.
Hendon, H. H., and M. L. Salby, 1994: The life cycle of the Madden–Julian oscillation. J. Atmos. Sci., 51, 2225–2237.
Horsthemke, W., and R. Lefever, 1984: Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology. Springer Verlag, 318 pp.
Jin, F.-F., J. D. Neelin, and M. Ghil, 1994: El Niño on the devil’s staircase: Annual subharmonic steps to chaos. Science, 264, 70–72.
Jin, F.-F., L. Lin, A. Timmermann, and J. Zhao, 2007: Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing. Geophys. Res. Lett., 34, L03807, doi:10.1029/2006GL027372.
Jones, C., 2009: A homogeneous stochastic model of the Madden–Julian oscillation. J. Climate, 22, 3270–3288.
Kapur, A., C. Zhang, J. Zavala-Garay, and H. H. Hendon, 2012: Role of stochastic forcing in ENSO in observations and a coupled GCM. Climate Dyn., 38, 87–107.
Kessler, W. S., 2001: EOF representations of the Madden–Julian oscillation and its connection with ENSO. J. Climate, 14, 3055–3061.
Kessler, W. S., and R. Kleeman, 2000: Rectification of the Madden–Julian oscillation into the ENSO cycle. J. Climate, 13, 3560–3575.
Kessler, W. S., M. J. McPhaden, and K. M. Weickmann, 1995: Forcing of intraseasonal Kelvin waves in the equatorial Pacific. J. Geophys. Res., 100 (C6 10 613–10 631.
Kleeman, R., and A. M. Moore, 1997: A theory for the limitation of ENSO predictability due to stochastic atmospheric transients. J. Atmos. Sci., 54, 753–767.
Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28, 702–708.
McPhaden, M. J., 1999: Genesis and evolution of the 1997–98 El Niño. Science, 283, 950–954.
McPhaden, M. J., and B. A. Taft, 1988: Dynamics of seasonal and intraseasonal variability in the eastern equatorial Pacific. J. Phys. Oceanogr., 18, 1713–1732.
McPhaden, M. J., and J. Picaut, 1990: El Niño–Southern Oscillation displacements of the western equatorial Pacific warm pool. Science, 250, 1385–1388.
Moore, A. M., and R. Kleeman, 1999: Stochastic forcing of ENSO by the intraseasonal oscillation. J. Climate, 12, 1199–1220.
Penland, C., M. Flügel, and P. Chang, 2000: Identification of dynamical regimes in an intermediate coupled ocean–atmosphere model. J. Climate, 13, 2105–2115.
Perez, C. L., A. M. Moore, J. Zavala-Garay, and R. Kleeman, 2005: A comparison of the influence of additive and multiplicative stochastic forcing on a coupled model of ENSO. J. Climate, 18, 5066–5085.
Roulston, M. S., and J. D. Neelin, 2000: The response of an ENSO model to climate noise, weather noise and intraseasonal forcing. Geophys. Res. Lett., 27, 3723–3726.
Rui, H., and B. Wang, 1990: Development characteristics and dynamic structure of tropical intraseasonal convection anomalies. J. Atmos. Sci., 47, 357–379.
Sperber, K. R., J. Slingo, P. Inness, and W. K. M. Lau, 1997: On the maintenance and initiation of the intraseasonal oscillation in the NCEP/NCAR reanalysis and in the GLA and UKMO AMIP simulations. Climate Dyn., 13, 769–795.
Tziperman, E., and L. Yu, 2007: Quantifying the dependence of westerly wind bursts on the large-scale tropical Pacific SST. J. Climate, 20, 2760–2768.
Tziperman, E., L. Stone, M. A. Cane, and H. Jarosh, 1994: El Niño chaos: Overlapping of resonances between the seasonal cycle and the Pacific ocean–atmosphere oscillator. Science, 264, 72–74.
Wang, B., and X. Xie, 1998: Coupled modes of the warm pool climate system. Part I: The role of air–sea interaction in maintaining Madden–Julian oscillation. J. Climate, 11, 2116–2135.
Yano, J., R. Blender, C. Zhang, and K. Fraedrich, 2004: 1/f noise and pulse-like events in the tropical atmospheric surface variabilities. Quart. J. Roy. Meteor.Soc., 130, 1697–1721.
Zavala-Garay, J., A. M. Moore, C. L. Perez, and R. Kleeman, 2003: The response of a coupled model of ENSO to observed estimates of stochastic forcing. J. Climate, 16, 2827–2842.
Zavala-Garay, J., C. Zhang, A. M. Moore, and R. Kleeman, 2005: The linear response of ENSO to the Madden–Julian oscillation. J. Climate, 18, 2441–2459.
Zavala-Garay, J., C. Zhang, A. M. Moore, A. T. Wittenberg, M. J. Harrison, A. Rosati, J. Vialard, and R. Kleeman, 2008: Sensitivity of hybrid ENSO models to unresolved atmospheric variability. J. Climate, 21, 3704–3721.
Zebiak, S. E., and M. A. Cane, 1987: A model El Niño–Southern Oscillation. Mon. Wea. Rev., 115, 2262–2278.
Zhang, C., 1996: Atmospheric intraseasonal variability at the surface in the tropical western Pacific Ocean. J. Atmos. Sci., 53, 739–758.
Zhang, C., and J. Gottschalck, 2002: SST anomalies of ENSO and the Madden–Julian oscillation in the equatorial Pacific. J. Climate, 15, 2429–2445.
Zhang, C., and M. Dong, 2004: Seasonality in the Madden–Julian oscillation. J. Climate, 17, 3169–3180.
From Fig. 5 of K12, the ratio of semiannual maximum to minimum variance over western central Pacific is around 2. Ignoring H2, (1 + H1)2/(1 − H1)2 = 2, and thus H1 ≈ 2.
The zonal scale (Lx) in Gebbie and Tziperman (2009b) ranging from 10° to 50° represents the Gaussian half-width, thus corresponding to 20°–100° of W, which is defined as the full width (section 3a).
Wavelet transform, unlike power-spectral density or variance, is a convolution over an oscillatory function.