GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 1–6, doi:10.1002/grl.50264, 2013

The 1970’s shift in ENSO dynamics: A linear inversemodel perspectiveChristopher M. Aiken,1 Agus Santoso,1 Shayne McGregor,1 and Matthew H. England1

Received 26 December 2012; accepted 15 February 2013.

[1] Inverse methods are used to investigate whether theobserved changes in El Niño–Southern Oscillation (ENSO)character since the 1970’s climate shift are consistent with achange in the linear ENSO dynamics. Linear Inverse Models(LIMs) are constructed from tropical sea surface temperature(SST), thermocline depth, and zonal wind stress anoma-lies from the periods 1958–1977 and 1978–1997. EachLIM possesses a single eigenmode that strongly resemblesthe observed ENSO in frequency and phase propagationcharacter over the respective periods. Extended stochas-tically forced simulations using these and the LIM fromthe combined period are then used to test the hypothesisthat differences in observed ENSO character can be repro-duced without changes in the linear ENSO dynamics.The frequency and amplitude variations of ENSO seen ineach period can be reproduced by any of the three LIMs.However, changes in the direction of zonal SST anomalypropagation in the equatorial Pacific cannot be explainedwithin the paradigm of a single autonomous stochasticallyforced linear system. This result is suggestive of a possiblefundamental change in the dynamical operator governingENSO and supports the utility of zonal phase propagation,rather than ENSO frequency or amplitude, for diagnos-ing changes in ENSO dynamics. Citation: Aiken, C. M., A.Santoso, and M. H. England (2013), The 1970’s shift in ENSOdynamics: A linear inverse model perspective, Geophys. Res. Lett.,40, doi:10.1002/grl.50264.

1. Introduction[2] The observational record of tropical sea surface tem-

perature (SST) is suggestive of a significant change in thecharacter of El Niño–Southern Oscillation (ENSO) since thelate 1970s. The following decades saw a decrease in the fre-quency of ENSO events and an increase in their intensity,plus a change in the predominant direction of ENSO SSTanomaly phase propagation along the equator [e.g., An andWang, 2001; Wang and An, 2002]. During the 1960s and1970s warm anomalies appeared first in the eastern Pacificand expanded westward, but since then they have developedin the central Pacific either prior to or concurrently with theeastern Pacific [Fedorov and Philander, 2000; Wang and An,2002; Trenberth et al., 2002].

1Climate Change Research Center (CCRC), University of New SouthWales, Sydney, New South Wales, Australia.

Corresponding author: C. M. Aiken, Climate Change Research Center(CCRC), University of New South Wales, Sydney, NSW 2052, Australia.(cm.aiken@yahoo.com)

©2013. American Geophysical Union. All Rights Reserved.0094-8276/13/10.1002/grl.50264

[3] It has been demonstrated that such changes may beconsistent with a change in the mean state of the coupledtropical ocean-atmosphere and hence in the stability of thesystem’s coupled modes [An and Jin, 2000; Fedorov andPhilander, 2001]. In particular, the deepening of the easternPacific thermocline, resulting from the mean weakening ofthe trades, favors the longer period delayed oscillator modeand decreases the growth rate of the shorter period SSTmode. However, while the observations appear to be con-sistent with a significant change in the underlying dynamicsof coupled modes in the tropics, the possibility still existsthat at least some of the observed alteration in ENSO char-acter may result from either trends in the forcing [An andWang, 2000; Wang and An, 2001] or noise-induced vari-ability [Kirtman and Schopf, 1998; Thompson and Battisti,2001; McPhaden et al., 2011; Newman et al., 2011]. Thereis also evidence to suggest that there has been no statisti-cally significant changes in ENSO frequency and intensity[Mendelssohn et al., 2005; Douglass, 2010].

[4] While a range of studies have investigated the naturalmodes of the coupled tropics via reduced-physics analyticalor numerical models, in which the governing physics wereassumed a priori and the choice of parameter values wasto some extent arbitrary, it has also been shown that ENSOdynamics can be inferred to a surprisingly good degree usinginverse methods. In particular, skillful models have beenconstructed under the sole a priori assumption that ENSOis governed by a stochastically forced dissipative linearsystem that obeys a fluctuation-dissipation relationship[Penland and Magorian, 1993; Penland and Matrosova,1994; Penland and Sardeshmukh, 1995; Newman et al.,2009; Newman et al., 2011]. Thus, the empirical estimationof ENSO dynamics via Linear Inverse Models (LIMs) offersan alternative with which to investigate causes of the shift inENSO character.

[5] In order to minimize the uncertainty in the inferreddynamical system, previous LIM-based studies of ENSOhave commonly used the entire data record since the 1950sfor building the model, with the implicit assumption that theunderlying dynamics of ENSO have not changed over thisperiod. Here, we investigate whether the LIM based on theentire period can plausibly explain the climate shift, or alter-natively whether the observed differences in ENSO implya fundamental change in ENSO dynamics. It is found that,while the observed change in ENSO frequency and ampli-tude does not necessarily require altered linear dynamics,the change in the direction of propagation of SST in theequatorial Pacific does.

2. Linear Inverse Models of ENSO[6] The theory of linear inverse models and their appli-

cation to ENSO is thoroughly developed in Penland and

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Matrosova [1994] and Penland and Sardeshmukh [1995].The method used to generate LIMs here follows closely thatdescribed in Newman et al. [2011a]. The principal assump-tion made is that ENSO variability may be modeled as alinear system driven by additive Gaussian white noise ofthe form

dx/dt = Bx + �(t), (1)

where x is the state vector, B is an autonomous linear oper-ator, and � is a Gaussian white noise process. Knowledgeof the covariance properties of the observations of x allowsthe best fit estimate of B in the least squares sense to bedetermined as follows:

B = �–10 ln

�C(�0)C(0)–1� , (2)

where C(�0) and C(0) are the covariance matrices at lags of�0 and zero, respectively. Following Newman et al. [2011a],the 23 element state vector

x = [T0 Z20 �x] (3)

contains the projections of the anomalies onto the first 13empirical orthogonal functions (EOFs) of sea surface tem-perature (T0), the first 7 EOFs of 20ıC isotherm depth (Z20),and the first 3 EOFs of zonal wind stress (�x). T0 was takenfrom the International Comprehensive Ocean-AtmosphereData Set Project (ICOADS) [Woodruff et al., 2011], Z20from the Simple Ocean Data Assimilation 2.2.4 globalocean reanalysis [Carton and Giese, 2008; Giese et al.,2011], and �x from ERA-40 [Uppala et al. 2005]. LIMswere generated corresponding to the periods 1958–1977,1978–1997, and 1958–1997 (referred to hereafter as LIM1,LIM2, and LIM0, respectively). In order to address the pos-sible high sensitivity of the results to individual features inthe short records, an ensemble of estimates of each LIMwas constructed using a jackknife technique in which eachconsecutive 2-year period was removed sequentially fromthe analysis. All results that follow are based on these jack-knife estimates of each LIM. All data were subjected to a3-month running mean prior to removing the seasonal cycleand linear trend. These filtered anomalies were then consol-idated into bins of 2ı latitude by 5ı longitude within theregion between the 25ıN and 25ıS parallels. The resultingbinned anomalies were then projected onto the state vector(3) and used to generate the linear inverse model B via (2).The covariance timescale � used for calculating the LIMswas 3 months in each case. The results that follow are notsensitive to this choice.

[7] A significant degree of uncertainty exists in the trendspresent in historical observational data sets due to sparsesampling and changes in observational methods over time.In particular, the apparent change in ENSO character coin-cides roughly with the availability of satellite SST, produc-ing a sudden increase in the quantity and quality of SSTobservations from the tropics. By removing the mean andseasonal cycle independently from each period, the follow-ing analysis is less sensitive to any such artifacts in theobservational record. Only observational errors that affectthe covariance will degrade the LIM.

[8] Each LIM satisfies reasonably well the criteria ofPenland and Sardeshmukh [1995] and reproduces the majorcharacteristics of the corresponding observations, suggest-ing that they capture much of the principal dynamics ofENSO and hence represent useful analogues with which

0 6 12 180

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Figure 1. Mean (solid) and standard deviation (shaded) ofthe RMS error in cross-validated LIM forecasts of Niño3 asa function of lead time for the periods (a) 1958–1977 and(b) 1978–1997. Cross-validation involved performing fore-casts for each two consecutive years using the LIMrecalculated with those years removed from the analysis.The persistence forecast is shown by the dashed line. TheRMS error is normalized by the standard deviation, such thata climatology forecast corresponds to an error of 1 at all lags.

to investigate the real system. The cross-validated skill ofNiño3 forecasts averaged over the jackknife estimates ofeach LIM, shown in Figure 1, reveal that each LIM beatspersistence and climatology forecasts on lead times outto 24 months. In addition, it indicates that LIM1 (LIM2)is more skillful than LIM0 for the former (later) periodon all lead times. As discussed below, the LIMs recoverthe observed spatial structure and frequency of the cou-pled ENSO mode and the propagating character of thecoupled dynamics.

[9] Eigenanalysis of the operator B yields the spectrum(eigenvalues) and modes (eigenvectors) corresponding toeach period. Each of the LIMs possesses one eigenmodethat closely resembles the observed ENSO in both struc-ture and frequency. The quadrature phases of these modesare shown in Figure 2 and are hereafter referred to asthe ENSO modes. The evolution of both ENSO modesis consistent with the classical Bjerknes-type mechanismand the recharge oscillator paradigm [Bjerknes, 1969; Jin,1997; Meinen and McPhaden, 2000]. The basin-wide equa-torial thermocline deepens at the initial state of developingEl Niño (Figures 2a, 2c, and 2e). This is followed by ashoaled and deepened thermocline in the west and east,respectively, enhanced by anomalous westerlies that arefurther reinforced by the eastern Pacific surface warming(Figures 2b, 2d, and 2f). These modes also encapsulatemuch of the lagged correlation structure of the observations(Figures 2g–2l), illustrating the propagating character of thecoupled dynamics. The most notable difference is seen inthe westward and eastward propagating correlation betweenthe zonal wind stress and Niño3 before and after the climateshift, respectively. Although damped, noise forcing sustainsthese ENSO modes through linear interference with othernonorthogonal modes [Penland and Sardeshmukh, 1995;Newman et al., 2011].

3. Can a Single LIM Explain the Observations?[10] Even if the dynamics of ENSO were identical in

both periods and perfectly explained by (1), one would

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1 9 5 8 − 1 9 7 7

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Figure 2. Quadrature phases of the principal ENSO mode of the LIMs corresponding to the periods (a–b) 1958–1977,(c–d) 1978–1997, and (e–f) 1958–1997. SST is shaded, z20 is contoured (with negative contours in green), and �x is indicatedby arrow heads. The spacing in arrow head and contour increments is equivalent to a normalized anomaly of magni-tude 0.2 on the SST scale. The modes evolve as (a), (b), -(a), -(b), (a), etc. Figures 2g–2l display the lagged correlationbetween the Niño3 index and �x (g, i, k) and z20 (h, j, l) as a function of equatorial Pacific longitude. The values deter-mined from the observations are shaded and those corresponding to the the ENSO modes contoured (with negative contoursin green).

still expect our estimates of those dynamics to differ tosome degree due to variations in the applied forcing alone.Thus, the differences between the LIMs may not indicate areal change in dynamics. In the following, we test the nullhypothesis that the observed ENSO frequency and propa-gation character can be reproduced by a single dynamicalsystem and hence that LIM1 and LIM2 represent estimatesof this same unique dynamical operator. For this purpose,a series of 20,000-year simulations of (1) were performedfor each jackknife estimation of each LIM, and the result-ing time series used to generate an ensemble of estimates ofthe dynamical operator by performing the LIM analysis oneach of the 1000 independent 20-year segments. Althougheach time series is generated by a single autonomous dynam-ical operator that obeys (1) exactly, it may be anticipatedthat the properties of each of the estimates of that operatorbased on short records will tend to differ from the origi-nal B. We investigate whether this variability in the inferreddynamics is sufficient to explain the observed changes inENSO character.

[11] The simulations of the stochastic differentialequation (1) were performed using the two-step schemeoutlined in Penland and Matrosova [1994], wherein first theintermediate state vector y(t) is generated from

y(t + ı) = y(t) + ıBy + Pr(t)0ı1/2, (4)

where the time step ı = 6 h, P contains the eigenmodesof the forcing covariance matrix multiplied by the squareroot of their corresponding eigenvalues, and r(t) is a vec-tor of independent Gaussian deviates of unit variance. Inorder to remove the effect of differences in the forcing P,the simulations were repeated using a randomly generated Pconstrained to have orthonormal columns. The differencesdue to the form of P were in all cases found to be minor. Thefinal state vector x(t) is then given by

x(t + ı/2) = (y(t) + y(t + ı))/2. (5)

The initial condition for each simulation was determined byspinning up the model from rest for 10 years. All analysis

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60 48 42 36 300

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b) LIM0LIM1LIM2

Figure 3. Probability density functions calculated from theensemble of 20,000-year stochastically forced simulationsfor (a) the period of the ENSO mode, (b) the e-folding decaytime of the ENSO mode, (c) the period of maximum powerspectral density of the Niño3 index, and (d) the standarddeviation of the principal component of the first EOF ofSST, representing the amplitude of ENSO variability. Verti-cal lines in each panel indicate the values derived from theobservations.

that follows was based on the monthly mean values of thestate vector.

[12] Figure 3 presents the probability density func-tions for the estimates of the imaginary and real compo-nents of the eigenvalue corresponding to the ENSO mode(Figures 3c and 3d), together with those for the peak

frequency of Niño3 power spectral density (Figure 3a) andfor the standard deviation of the first principal componentof SST (i.e., of the first element of the state vector; EOF1;Figure 3b). The latter two quantities represent commonlyused metrics of ENSO character (frequency and ampli-tude, respectively) that are determined directly from thetime series. The former two represent indirect, dynamicallybased, estimates of ENSO frequency and amplitude inferredfrom the LIM. Despite the fact that each of the simulationswas generated by a distinct autonomous dynamical opera-tor, there is substantial overlap in the distributions in eachof these measures of ENSO character. The observed fre-quency and decay timescale of the pre-1977 and post-1977ENSO modes (marked by vertical lines in Figures 3c and3d) are located well within the intersection of distributionsof estimates from the extended simulations, such that bothcould plausibly have resulted from a single stochasticallyforced system governed by any of the three LIMs. The dis-tributions of the frequency of peak power spectral densityof Niño3 reflect those for modal frequency, with substantialoverlap between the pre-1977 and post-1977 periods. Simi-larly, there is substantial overlap in the distributions of EOF1amplitude (Figure 3b) and modal decay time (Figure 3d),such that changes in ENSO amplitude also do not neces-sarily indicate changes in the underlying ENSO dynamics.These results suggest that the observed change in ENSOamplitude and frequency could conceivably be explainedby a stochastically forced system with a single dynami-cal operator. Specifically, the hypothesis that the observedENSO frequencies corresponding to the pre-1977 and post-1977 periods resulted from the single dynamical operatorrepresented by LIM0 cannot be rejected.

[13] The inferred direction of propagation of SST anoma-lies in the equatorial Pacific does not, however, vary suf-ficiently during the simulations to explain the observedchange since the 1970s. The propagation direction can bediagnosed by calculating the lagged correlation betweencentral Pacific SST and the difference between eastern andwestern Pacific SST [e.g., Guilyardi, 2006; Santoso et al.,2012 ]. Following Santoso et al. [2012] (see their Figure 7),

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Figure 4. (a) Lagged correlation between Niño3 and the east-west index for the periods 1958–1977 (blue), 1978–1997(red), and 1958–1997 (green). Dashed lines correspond to observations and solid to the average over all 20-year seg-ments from the ensemble of simulations. Shading indicates the correlation within one standard deviation of the mean value.(b) Probability density functions for the gradient of the correlation in Figure 4a evaluated at zero lag from the ensemble of20-year segments, used to quantify the propagation direction. Vertical lines indicate the observed value.

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the former is determined by the Niño3 index, and the latterby the east-west index, defined as the area-averaged SST inthe far eastern Pacific (5ıS–5ıN, 91ıW–80ıW) minus thatin the Niño4 region (5ıS–5ıN, 160ıE–150ıW). Eastward(westward) propagation is indicated by positive correlationsat negative (positive) lags. As is the case for ENSO ampli-tude and frequency, the propagation character of ENSO isencapsulated within the corresponding ENSO mode fromeach LIM. The fact that the ENSO modes mirror the dom-inant phase propagation character of the observations isillustrated in Figures 2g–2l. Figure 4a demonstrates thatthe ensemble average from each LIM agrees closely withthe observations, and hence the LIMs accurately recover thepropagation character of equatorial Pacific SST anomalies:prominent westward propagation in LIM1 and somewhateastward in LIM2. The probability density functions ofthe gradient in the correlation curve evaluated at zero lag,used to quantify phase propagation character, demonstrateno intersection between the distributions of LIM1 and LIM2(Figure 4b). Moreover, even though LIM0 spans periods ofeastward and westward propagation, no 20-year period inthe LIM0 simulations reproduces the propagation charac-teristic of the pre-1977 period. As such, we can reject thehypothesis that the change in propagation characteristic canbe explained by LIM0.

[14] Although the LIMs are contrived to best fit theobserved covariance structure at a given lag, they are notconstrained to reproduce the phase structure at all lags. Infact, it is possible to manipulate the forcing in such a way asto alter the propagation character (such as by removing theprojection of the forcing onto ENSO modes). However, theresults were not altered qualitatively when the spatial forc-ing P was white; in both cases, the estimates of the ENSOmode propagation direction derived from the extended sim-ulations do not vary sufficiently to produce differing ENSOphase propagation characters consistent with the observa-tions. As a result, insofar as the LIM captures the physicsof ENSO phase propagation, the observed change in prop-agation direction demands a fundamental change in theunderlying dynamical operator, such as due to changes in themean state.

4. Conclusions[15] An empirical investigation of ENSO dynamics either

side of the 1970’s shift was performed using linear inversemodels. Consistent with a series of previous studies, ENSOin both periods can be well described as a stochasticallyforced damped linear system, with dominant ENSO modeswhose spatial structure and complex frequencies agreewell with observations. While an altered mean state hasbeen shown to possibly explain the observed differencesin ENSO frequency, here we find that such changes mayalso arise without a change in ENSO dynamics and duesolely to variability in the forcing and to the relatively shortobservational record.

[16] Even though the underlying dynamical operator andstatistics of the forcing were fixed, estimates of the com-plex ENSO mode frequency taken from independent 20-yearsegments of extended stochastically forced simulations varysignificantly. In particular, there was substantial overlapbetween the sets of estimated ENSO complex eigenvaluesfrom the simulations using each LIM. This suggests that the

observational record may be too short to determine whatcomponent of the observed changes in the frequency andamplitude of ENSO can be attributed to dynamical changes(i.e., related to changes in the mean state) and how much issimply a consequence of forcing variability.

[17] In contrast, the observed change in the direction ofzonal SST propagation in the equatorial Pacific does appearto be symptomatic of altered ENSO dynamics. The SSTpropagation character simulated by each LIM varied littleover the course of the stochastically forced simulations, andno single LIM could reproduce the propagation character-istics of both periods. Our study therefore suggests that thedirection of the zonal phase propagation of SST anomaliesmay provide a more useful diagnostic for changes in ENSObehavior, rather than ENSO frequency and amplitude. Theseresults may partially explain the disagreements across Cou-pled Model Intercomparison Project Phase 3models in termsof the response in ENSO frequency and amplitude underglobal warming, despite a more consistent picture in termsof zonal phase propagation [Guilyardi 2006].

[18] Acknowledgment. This study was supported by the AustralianResearch Council.

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