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Nonlinear Analysis of the ENSO Cycle and Its Interdecadal Changes. An, Soon-Il; Hsieh, William W.; Jin, Fei-Fei 2005

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A Nonlinear Analysis of the ENSO Cycle and Its Interdecadal Changes*SOON-IL ANInternational Pacific Research Center, University of Hawaii at Manoa, Honolulu, HawaiiWILLIAM W. HSIEHDepartment of Earth and Ocean Sciences, University of British Columbia, Vancouver, British Columbia, CanadaFEI-FEI JINDepartment of Meteorology, The Florida State University, Tallahassee, Florida(Manuscript received 27 May 2004, in final form 21 January 2005)ABSTRACTThe nonlinear principal component analysis (NLPCA), via a neural network approach, was applied tothermocline anomalies in the tropical Pacific. While the tropical sea surface temperature (SST) anomalieshad been nonlinearly mapped by the NLPCA mode 1 onto an open curve in the data space, the thermoclineanomalies were mapped to a closed curve, suggesting that ENSO is a cyclic phenomenon. The NLPCAmode 1 of the thermocline anomalies reveals the nonlinear evolution of the ENSO cycle with muchasymmetry for the different phases: The weak heat accumulation in the whole equatorial Pacific is followedby the strong El Niño, and the subsequent strong drain of equatorial heat content toward the off-equatorialregion precedes a weak La Niña. This asymmetric ENSO evolution implies that the nonlinear instabilityenhances the growth of El Niño, but dwarfs the growth of La Niña. The nonlinear ENSO cycle was foundto have changed since the late 1970s. For the pre-1980s the ENSO cycle associated with the thermocline isless asymmetrical than that during the post-1980s, indicating that the nonlinearity of the ENSO cycle hasbecome stronger since the late 1970s.1. IntroductionDespite numerous investigations into the mechanismof the El Niño–Southern Oscillation (ENSO) [see, e.g.,“Reviewing the progress of El Niño research and pre-diction” in J. Geophys. Res., 103, Anderson et al.(1998)], the climate study community still does not havea consensus on some intrinsic questions: the first ques-tion is whether ENSO is a large-scale deterministic sys-tem, the apparently random behavior of which can beexplained by nonlinear dynamics (Jin et al. 1994;Tziperman et al. 1994) or whether ENSO is linear, theerratic behavior of which is caused by stochastic forcing(Penland and Sardeshmukh 1995; Chang et al. 1996;Moore and Kleeman 1999; Thompson and Battisti 2000,2001); the second question is whether ENSO is cyclic orsporadic (e.g., Kessler 2002; Philander and Fedorov2003). These two questions are not simply independentbut should be considered in parallel. This is because thelinear system subjected to stochastic forcing is morelikely to produce a sporadic ENSO, while the determin-istic system with the strong nonlinearity is more likelyto produce a cyclic ENSO.Thompson and Battisti (2001) stochastically forced alinear model that originally does not sustain internallygenerated variability and found that it reproduces all ofthe basic features of ENSO, suggesting that the essen-tial characteristics of ENSO appear to be governed bylinear processes, but it failed to produce the significantpositive skewness of the ENSO index. On the contrary,several observational studies point out that the prob-* School of Ocean and Earth Science and Technology Contri-bution Number 6548 and International Pacific Research CenterContribution Number 313.Corresponding author address: Dr. Soon-Il An, InternationalPacific Research Center, SOEST, University of Hawaii at Manoa,Honolulu, HI 96822.E-mail: sian@hawaii.edu15 AUGUST 2005 A N E T A L . 3229© 2005 American Meteorological SocietyJCLI3466ability density function of ENSO indices (i.e., Niño-1,-2, -3, and -3.4) are distinguishable from a Gaussiandistribution, and the positively skewed SST anomaliesover the eastern Pacific are caused by the nonlinearity(Burgers and Stephenson 1999; Hannachi et al. 2003;Jin et al. 2003; An and Jin 2004). In particular, Jin et al.(2003) introduced a dynamical measure of ENSO non-linearity [i.e., nonlinear dynamical heating (NDH)]along with a statistical measure such as skewness. Theyconcluded that the NDH could cause the positivelyskewed SST anomalies over the eastern Pacific.To identify the principal mode associated with tropi-cal Pacific interannual variability, traditional statisticalmethods such as the principal component analysis[PCA, a.k.a. empirical orthogonal function analysis(EOF)] or the maximum covariance analysis [MCA,a.k.a. singular value decomposition (SVD)] werewidely used. These linear methods obviously identifythe most dominant pattern associated with ENSO inwhich the spatial pattern associated with El Niñoisexactly the same as that associated with La Niña but ofan opposite sign. However, in reality the spatial pat-terns associated with El Niño and La Niña are not iden-tical due to the nonlinearity (Hoerling et al. 1997;Monahan 2001). Recently, using nonlinear principalcomponent analysis (NLPCA), which detects a low-dimensional nonlinear structure in multivariate data-sets, Hsieh (2001, 2004) objectively characterized theasymmetric features between El Niño and La Niña. Thenonlinear principal mode showed that not only is theamplitude of El Niño larger than that of La Niña, butalso the maximum sea surface temperature (SST) of ElNiño is confined to the eastern equatorial Pacific, whilethe minimum of La Niña is located at the central equa-torial Pacific.While PCA finds a straight line that passes throughthe “middle” of a data cluster, a nonlinear mapping ofNLPCA possibly replaces the straight line by a continu-ous open or closed curve for approximating the data(Hsieh 2004). As an open-curve solution, for example,a U-shaped curve solution nonlinearly connects two ex-treme states. On the other hand, a quasi-periodic geo-physical phenomenon may call for the closed-curve so-lution. For example, Hamilton and Hsieh (2002) ap-plied the NLPCA to the stratospheric equatorial zonalwind data to study the quasi-biennial oscillation andfound a closed-curve solution.Monahan (2001) and Hsieh (2001) applied theNLPCA to tropical Pacific SST anomalies to reveal thenonlinear principal mode of ENSO. Despite ENSO’squasi-oscillatory behavior, the mapped curve turnedout to be a U-shaped curve, which links La Niña statesat one end to the El Niño states at the other end. Inother words, the pathway from El NiñotoLaNiñaissimilar to that from La NiñatoElNiño. This is becausethe SST patterns during the transition phase do notchange much depending on whether El Niño proceedsto La Niña or the other way around. On the other hand,the oceanic heat content (with the thermocline as aproxy) clearly shows a complete cyclic feature forENSO, shown in observations (Jin and An 1999;Meinen and McPhaden 2000) and the ocean–atmos-phere coupled general circulation model (CGCM)(Mechoso et al. 2003), because the thermocline depthduring the transition phase from El NiñotoLaNiñaisshallow over the entire equatorial Pacific, while thatduring the transition phase from La NiñatoElNiñoisdeeper. Thus, in this study, by using NLPCA, we willidentify the cyclic feature of ENSO, and also explorethe nonlinearity of ENSO.In section 2, we describe the data and the analysismethod. Section 3 presents the NLPCA modes of thethermocline anomalies to reveal the ENSO cycle with anonlinear behavior. In section 4, we compare theNLPCA modes of the thermocline before and after a“climate regime” shift since the late 1970s to explorethe nonlinear interdecadal changes in the ENSO cycle.Summary and discussion are given in section 5.2. Data and methodThe data utilized are the National Centers for Envi-ronmental Prediction (NCEP) ocean assimilation datafor January 1980–October 2000 (Ji et al. 1995;Behringer et al. 1998; Vossepoel and Behringer 2000).Observed surface and subsurface ocean temperaturesas well as satellite altimetry sea level data fromTOPEX/Poseidon were assimilated into a PacificOcean general circulation model. The model wasforced with weekly mean surface winds and heat fluxesof NCEP operational atmospheric analyses. Thisdataset has 16 levels in the upper 200 m, where theinterval between levels is around 10–30 m. From thetemperature data, the depth of the 20°C isotherm hasbeen calculated. This isotherm is used as a proxy for thetotal heat content.We also used the simple ocean data assimilation(SODA) set (Carton et al. 2000) for investigating thelong-term change and comparing with the NCEP data.The SODA data (January 1950–December 2001) werebuilt by interpolating unevenly distributed ocean mea-surements into three-dimensional global fields of tem-perature, salinity, and current velocity using an oceangeneral circulation model. The Tropical Ocean GlobalAtmosphere (TOGA) Tropical Atmosphere Ocean3230 JOURNAL OF CLIMATE VOLUME 18(TAO) data and TOPEX/Poseidon data were used forchecking the quality of the SODA dataset (e.g., Cartonet al. 2000; Xie et al. 2002). Both NCEP and SODAdatasets contain monthly mean data.In principal component analysis (PCA), also knownas empirical orthogonal function analysis, a straightlineapproximation to the dataset is sought that accounts forthe maximum amount of variance in the data. There arenow several types of neural network (NN) models thatuse, instead of the straight line, a continuous curve toapproximate the data (Hsieh 2004). Using a multilayerperceptron NN formulation, the nonlinear PCA(NLPCA) method of Kramer (1991) is capable of find-ing an open curve to approximate the data. However,for periodic or quasiperiodic phenomena, it would bemore appropriate to fit the data with a closed curveinstead of an open curve. Kirby and Miranda (1996)introduced a NLPCA variant, which has a circularbottleneck node, thereby allowing the extraction ofclosed-curve solutions. This variant of NLPCA, used byHsieh (2001) and Hamilton and Hsieh (2002) to studytropical climate variability, is the one used in this paper.For more details of the method, see the review paper byHsieh (2004).The input data are in the form x(t) H11005 [x1(t), ...,xl(t)], where each variable xi(i H11005 1, ..., l), is a timeseries containing n observations. To perform NLPCA(Fig. 1), the information is mapped forward through abottleneck to the output xH11541. The parameters of the net-work are solved by minimizing the cost function, whichis basically the mean-square error (MSE) of x relativeto xH11541. Because of local minima in the cost function, anensemble of 30 NNs with random initial weights andbias parameters was run. Also, 15% of the data wererandomly selected as test data and withheld from thetraining of the NNs. Runs where the MSE was largerfor the test dataset than for the training dataset wererejected to avoid overfitted solutions. Then the NNwith the smallest MSE was selected as the solution.The gridded 20°C thermocline data were linearly de-trended, then reduced by PCA to five leading principalcomponent (PC) time series. These five PCs then be-come the input x(t) H11005 [x1(t),...,x5(t)] of the NLPCAnetwork. The number of model parameters (i.e.,weights) is controlled by m, the number of nodes in theencoding layer (and in the decoding layer). Excessive mand excessively large weights can lead to overfitting. Aweight penalty term is added to the cost function toavoid excessively large weights (see Hsieh 2001, 2004,with the weight penalty parameter being 1). Also, mwas varied between 2 and 8, and the one giving thelowest MSE was selected.3. NLPCA mode of tropical Pacific thermoclineWe have applied PCA to the 21-yr monthly mean20°C isotherm depth anomalies (a proxy of the ther-mocline depth) obtained from NCEP ocean assimila-tion data (Ji et al. 1995), where to determine theanomalies the 21-yr climatological monthly mean andthe linear trend were removed. In Fig. 2, the dominantfeature of the thermocline anomaly is summarized bythe two leading PCA modes: the first mode is a zonalcontrast mode and the second mode has a strong zonal-symmetric component. Two leading PCA modes ex-plain 31% and 22% of total variance, respectively. Thefirst mode varies in phase with ENSO (where ENSO isrepresented by the Niño-3 index), and its amplitude isFIG. 1. A schematic diagram illustrating the neural networkmodel used for performing NLPCA. The model is a feed-forwardmultilayer perceptron neural network, with three “hidden” layersof variables or “neurons” (denoted by circles) sandwiched be-tween the input layer x on the left and the output layer xH11541 on theright. Next to the input layer is the “encoding” layer, followed bythe narrow “bottleneck” layer, then the “decoding” layer, andfinally the output layer, i.e., a total of four layers of transfer func-tions are needed to map from the inputs to the outputs. A neuronH9271iat the ith layer receives its value from the neurons vi-1in thepreceding layer, i.e., H9271iH11005 fi(wi· vi-1H11001 b), where wiis a vector ofweight parameters and b a bias parameter, and the transfer func-tions f1and f3are the hyperbolic tangent functions, while f2and f4are simply the identity functions. The bottleneck contains twoneurons p and q constrained to lie on a unit circle, i.e., only onedegree of freedom as represented by the angle H9258. Effectively, anonlinear function H9258H11005 f(x) maps from the higher-dimension inputspace to the lower-dimension bottleneck space, followed by aninverse transform xH11541 H11005 G(H9258) mapping from the bottleneck spaceback to the original space, as represented by the outputs. To makethe outputs as close to the inputs as possible, the cost function J H11005H20855|x – xH11541|2H20856, i.e., the MSE is minimized (where H20855...H20856 denotes asample or time mean). By minimizing J, the optimal values of theweight and bias parameters are solved. Data compression isachieved by the bottleneck, yielding the nonlinear principal com-ponent H9258.15 AUGUST 2005 A N E T A L . 3231linearly proportional to the ENSO amplitude. The sec-ond mode leads ENSO by a quarter cycle. Those fea-tures are similar to that described by a recharge para-digm under the linear dynamical framework (Jin1997a,b). However, the amplitude of the second modeis not simply proportional to the amplitude of the fol-lowing ENSO, indicating that the linear mechanismmay not be enough to explain this thoroughly. In thissection, we identify the principal patterns of the ther-mocline variation by using NLPCA, which provides amuch clearer idea about the nonlinearly related pat-terns.From the first five leading PCA modes of the ther-mocline anomalies, we extracted the NLPCA mode.Here, the first NLPCA explains 48% of total variance.In Fig. 3, NLPCA gives a continuous closed-curve so-lution in the five-dimensional space (here, we onlydraw the curve in the three-dimensional space as shownin Fig. 3b), as the nonlinear principal component H9258(t)isan angular variable. The system generally progressesclockwise along the closed curve in Fig. 3a with theupper- and lowermost points of the curve correspond-ing to the transition phase from La NiñatoElNiño andthat from El NiñotoLaNiña, respectively. Since thedata are approximated by a closed continuous curve,the thermocline anomalies are dominated by a quasi-periodic fluctuation, and thus ENSO may be consid-ered as an oscillatory mode. However, the amplitudemoving from one phase of the cycle to another is asym-metric. Likewise, the center of the closed curve in Fig.3a is not located at the center of the diagram. Theamplitude of the recharge (top of curve) associatedwith a subsequent El Niño (right side of curve, with alarge amplitude) is smaller than that of the discharge(bottom of curve) associated with a subsequent La Niña(left side of curve, with a small amplitude). This asym-metry was also mentioned by Meinen and McPhaden(2000), who examined 18 years of surface temperaturedata. Note that the data points are strongly scatteredabout the curve in Fig. 3a during the transition from LaNiñatoElNiño (associated with the recharge period oftotal heat content), while they fit closely to the curveduring the transition from El NiñotoLaNiño (associ-ated with the discharge period of total heat content),suggesting that stochastic variability may be more ac-tive for the La Niña–El Niño transition.To show the spatial distribution of the thermoclineassociated with the ENSO cycle, we draw the NLPCAmode 1 with a quarter cycle interval in Fig. 4: the ma-ture phase of El Niño (Fig. 4a), transition phase from ElNiñotoLaNiña (Fig. 4b), mature phase of La Niña(Fig. 4c), and transition phase from La NiñatoElNiñoFIG. 2. The 20°C isotherm depth patterns of (a) EOF1 and (b) EOF2, and the corresponding PC time series. The redsolid line in each panel indicates the Niño-3 SST anomalies.3232 JOURNAL OF CLIMATE VOLUME 18Fig 2 live 4/C(Fig. 4d). For the mature phase of El Niño, there arelarge positive anomalies over the eastern tropical Pa-cific centered near the eastern boundary and largenegative anomalies over the western tropical Pacificcentered near the western boundary. This zonal con-trast pattern of the thermocline obviously leads tostrong poleward geostrophic transport, resulting in thestrong discharge of the equatorial total heat content.Consequently, for the transition phase from El NiñotoLa Niña, the thermocline depth becomes considerablyshallower over the whole equatorial Pacific. This shoal-ing thermocline presumably leads to the La Niña. Dur-ing La Niña, the zonal contrast of the thermocline hasan opposite sign to that during El Niño, and its strengthis about half of that during El Niño. This results in theweak equatorward heat transport. Thus, the recharge ofFIG. 4. Thermocline field for the (a) mature phase of El Niño, (b) transition phase from El NiñotoLaNiña, (c)mature phase of La Niña, and (d) transition phase from La NiñatoElNiño. Contour interval is 10 m. Positivevalues are shaded.FIG. 3. Scatterplot of the thermocline anomaly data (dots) and the NLPCA mode 1 in the (a) PC1–PC2 planeand (b) three-dimensional PC1–PC2–PC3 space. The NLPCA mode-1 approximation to the data is shown by thesmall circles, which traced out a closed curve. The progression of the system with time is primarily clockwise alongthe curve.15 AUGUST 2005 A N E T A L . 3233the equatorial total heat content is relatively weakerthan the discharge (also see Fig. 3a). Observationally,La Niña tends to strictly follow El Niño (e.g., the 1982–83 El Niño is followed by the 1983–84 La Niña, and the1997–98 El Niño is followed by the 1998–99 La Niña),whereas the recharge process that possibly leads to thetransition from La NiñatoElNiño is relative weak.Kessler (2002) even argued for a distinct break in theENSO cycle, especially when it goes from La NiñatoElNiño. We will get to this point in section 5.Figure 5 shows the propagation feature of the ther-mocline anomalies associated with the dominant non-linear ENSO cycle over the equator, as well as the as-sociated surface wind stress anomalies. The surfacewind stress data are obtained from the Florida StateUniversity (Goldenberg and O’Brien 1981). This pat-tern is again obtained from the NLPCA mode 1. Dur-ing El Niño, the positive maximum thermocline ap-pears at the far eastern Pacific near 90°W, while duringthe La Niña the maximum negative thermocline ap-pears at the central-eastern Pacific near 120°W. Inother words, the maximum for the El Niño anomalytends to shift to the east compared to that for the LaNiña. This difference in the zonal location may be re-lated to the difference in the location of the anomalousatmospheric heating—the equatorial central Pacific forEl Niño and the western Pacific for La Niña—causingthe surface wind to be located differently as shown inFig. 5. It is known that the thermocline variation in theequatorial western Pacific is transmitted to the equato-rial eastern Pacific through the equatorial waveguide(Wyrtki 1985). For La Niña, the amplitude of the nega-tive thermocline in the equatorial central-eastern Pa-cific is almost equal to that in the western Pacific duringthe previous El Niño, whereas for the El Niño, thepositive thermocline anomaly in the equatorial easternPacific is 4 times that of the positive anomaly in thewestern Pacific during the previous La Niña. Thus, thethermocline variation during La Niña seems to be to-tally drained from the western Pacific thermoclineanomaly that was built during the previous El Niño. Inother words, the weak preconditioning for El Niñothrough a recharge process and rapid growth of the ElNiño, in contrast to the relative strong preconditioningfor La Niña through a strong discharge process andweak growth of La Niña, indicates that El Niño may beless predictable than La Niña.To examine the evolution of the total heat content,we show the phase–latitude section of the zonal-meanthermocline anomalies associated with the NLPCAmode 1 in Fig. 6. A strong asymmetry between therecharge and discharge is pronounced. The dischargeprocess indicating the loss of the equatorial heat con-tent and the gain of the off-equatorial heat contentseems to agree well with the recharge paradigm (Jin1997a,b), while the recharge process is relatively weakand less obvious. Not only the asymmetry between re-charge and discharge, but also the north–south asym-metry during the discharge is observed such that thereFIG. 5. Phase–longitude section of the thermocline anomaly (incolor: m) and the zonal wind stress anomaly (in contour: H1100310H110021NmH110022) along the equator (5°S–5°N) associated with the first modeNLPCA. Phase in the y axis represents the time sequence. Twocycles are plotted with the phase (in °) increasing with time. Con-tour interval is 0.1 N mH110022.FIG. 6. Phase–latitude section of the zonal-mean thermoclineanomaly associated with the first mode NLPCA. Contour intervalis 4 m. Positive values are shaded.3234 JOURNAL OF CLIMATE VOLUME 18Fig 5 live 4/Cis a large heat content increase in the off-equatorialNorth Pacific but not in the off-equatorial South Pa-cific. Kug et al. (2003) pointed out that the asymmetricpoleward mass transports are due to a southward shiftof the maximum zonal wind stress anomaly during theENSO mature phase associated with the seasonalmarch southward of the intertropical convergencezone. The negative equatorial heat content lives longerthan the positive heat content does, and the off-equatorial heat content is smaller in magnitude than theequatorial heat content for the discharge, while for therecharge, the opposite is true.4. Interdecadal changes in the tropical Pacificthermocline evolutionConcurrent with the well-known climate shift, notonly the general characteristics of ENSO such as theperiod, intensity, spatial pattern, propagating feature,and onset (Wang 1995; An and Jin 2000; An and Wang2000; Wang and An 2001), but also the nonlinearity ofENSO has changed during the late 1970s (Jin et al.2003; Wu and Hsieh 2003; An 2004; An and Jin 2004).After the 1980s, the skewness of the ENSO index (e.g.,Niño-3 index) increased to being more positive so thatthe asymmetry between El Niño and La Niña also in-creased (Wu and Hsieh 2003; An 2004). An and Jin(2004) pointed out that the asymmetry of ENSO wasdue to the nonlinear dynamical heating, which also in-creased after the late 1970s. Naturally, this inspires usto explore the interdecadal change in the nonlinearENSO cycle.The NCEP ocean assimilation data only cover therecent 20 years, too short for the interdecadal study.Instead, we use the SODA data, which cover over 50years. A cross check between two datasets for the re-cent 20 years also gives us confidence in our results.Again, PCA was applied to the 20°C isotherm anoma-lies, and the PCs of the first five leading modes wereused for the further application. The leading PCA pat-terns are in general similar to those obtained fromNCEP ocean assimilation data (not shown here). Next,we divided the whole period into two parts—one for1950–75 and the other for 1980–2001—and calculatedthe NLPCA mode of the thermocline anomalies foreach period and for the whole period as well.Figure 7 shows a scatterplot in the PC1–PC2 planefor NLPCA mode 1 for each different period. First ofall, we found that the scatterplot for SODA data (Fig.7c) is similar to that for NCEP data (Fig. 3), whichverifies the robustness of the result. The closed curvefor the pre-1980s (Fig. 7b) is less asymmetrical than thatfor the post-1980s (Fig. 7c). For the pre-1980s (Fig. 7b),the recharged total heat content (lowermost part) isslightly larger than the discharged total heat content(uppermost part), and the La Niña pattern (left end) isalso slightly stronger than the El Niño pattern (rightend). These decadal changes are consistent with thechanges in the skewness and nonlinearity of ENSO,which has increased since the late 1970s. For the totalperiod, the closed curve in the PC1–PC2 plane (Fig. 7a)shows a rather symmetrical circle, indicating that thecanonical feature of ENSO is quite symmetrical. Inother words, the canonical ENSO resembles the re-charge paradigm, but ENSO in each interdecadal pe-riod has its own characteristics, mainly due to the in-terdecadal changes in the nonlinearity of ENSO.We show the evolution feature of the thermoclineanomalies obtained from the NLPCA mode 1 along theequator and associated surface wind stress anomalies inFig. 8. Again, for the post-1980s, the result of SODA(Fig. 8c) and that of NCEP (Fig. 5) data are similar inquality. The difference in quantity is presumably due toa difference in the assimilation method or difference inthe climatological mean used for the anomaly calcula-tion. Interestingly, the negative center of the ther-mocline anomaly for the post-1980s is confined over thecentral equatorial Pacific, which is stronger than thepositive thermocline anomaly over the eastern Pacific,whereas for the pre-1980s there are two negative ther-mocline anomaly centers (in the western equatorial Pa-cific and the eastern Pacific) of which the amplitudesare slightly smaller than the positive thermoclineanomalies. Also the positive and negative centers arelocated at the same longitude in the eastern and west-ern Pacific for the pre-1980s.The interdecadal change in the thermocline observedhere is dynamically consistent with the interdecadalchanges in the surface wind. As shown in Fig. 8, as wellas in Wu and Hsieh (2003), for the pre-1980s the surfacewind stress anomaly for El Niño is slightly smaller thanthat for La Niña with the opposite sign, while for thepost-1980s the surface wind anomaly for El Niño has alarger amplitude and its zonal location is shifted east-ward relative to that for La Niña. Since the surface windstress patterns for El Niño and La Niña are more or lesssymmetrical in their longitudes for the pre-1980s, thethermocline patterns for El Niño and La Niña are alsosimilar. On the other hand, for the post-1980s, the lon-gitudinal distribution of the thermocline shifts to theeast and the zonal contrast becomes stronger during ElNiño because of the stronger surface wind stress andthe eastward shift of the surface wind stress patternduring El Niño. The eastward shift in the dominantpattern of surface wind stress anomalies associated withENSO since the late 1970s, as shown in An and Wang15 AUGUST 2005 A N E T A L . 3235(2000), might be due to the increase of nonlinearity ofENSO. In particular, the surface wind associated withEl Niño was significantly shifted eastward, while thatassociated with La Niña was not changed much. Notethat the canonical feature of thermocline evolutionshown in Fig. 8a is again more likely symmetric, similarto the pattern shown in the theoretical studies (e.g., Jin1997a,b; Jin and An 1999).To detect interdecadal changes in the evolution ofthe total heat content, we plotted the phase–latitudesection of the zonal-mean thermocline anomalies asso-ciated with the NLPCA mode 1 for the each period inFig. 9. One observes that the SODA result (Fig. 9c) isconsistent with the NCEP result (Fig. 6). In contrast tothe post-1980s, the warm period of the total heat con-tent on the equator during the pre-1980s is relativelylonger than the cold period of the total heat content;the warming of the total heat content is stronger thanthe cooling; and the accumulation of the off-equatorialtotal heat content is weak so that the total heat contentanomalies for the pre-1980s seem to vary only over theequatorial region. The equatorial total heat contentanomalies for the pre-1980s is positively skewed, whilethat for the post-1980s is negatively skewed in terms ofboth the amplitude and duration period. However, thecanonical pattern of the total heat content anomalies(Fig. 9a) shows symmetry in terms of the period and theamplitude due to a linear combination of two inverselyskewed patterns.5. Summary and discussionPCA (and rotated PCA) have been widely used toextract the optimal linear structure from a dataset.When the dataset has an underlying structure that is notlinear, NLPCA may provide a better way to describethe dataset. By applying NLPCA to the thermoclineanomalies in the tropical Pacific, we have identified anENSO cycle with notable nonlinearity. Although pre-vious applications of NLPCA to the SST anomalieshave only found a U-shaped open curve as the best fitto the data, in this study the NLPCA mode of the ther-mocline anomalies reveals a closed curve. In an open-curve solution, the transition from El NiñotoLaNiñaFIG. 7. Scatterplot of the thermocline anomaly data inthe PC1–PC2 plane for (a) the total period, (b) pre-1980sonly, and (c) post-1980s only. The thermocline anomaly isobtained from the SODA data. The system progresses pri-marily clockwise along the curves.3236 JOURNAL OF CLIMATE VOLUME 18is indistinguishable from the reverse transition from LaNiñatoElNiño, whereas in a closed-curve solution, thetwo transitions are distinct. Interestingly, this closedcurve of the NLPCA mode 1 shows an asymmetry fea-ture: A weak recharge of the equatorial zonal-meanthermocline precedes the steep zonal slope of anoma-lous thermocline downward to the east along the equa-tor (strong El Niño), and the subsequent strong dis-charge is followed by a gentle zonal slope of anomalousthermocline downward to the west (weak La Niña).The strong drain of the equatorial total heat content isprobably enough to suppress El Niño, and afterward tolead to La Niña. Since the discharge process drives astrong shoaling of thermocline, one may expect a strongLa Niña in a linear sense. However, the La Niña cannotgrow as much as expected because the nonlinear dy-namical heating dwarfs the growth of La Niña (Jin et al.2003; An and Jin 2004). On the contrary, the increase ofthe total heat content due to the recharge process isweak but the nonlinear dynamic heating intensifies theEl Niño, resulting in the strong El Niño. In particular,the scatter from the regular orbit is more pronouncedduring the transition phase from La NiñatoElNiñosuggesting that other factors—including stochastic forc-ing—strongly agitate the nonlinear ENSO cycle, pre-sumably making the initiation of El Niño due to theheat accumulation over the tropical Pacific less obvi-ous. In other words, there is asymmetry in the precon-ditioning of El Niño and La Niña events due to theasymmetry of recharge and discharge processes associ-ated with nonlinear cycle of the ENSO. A linear sto-chastic forced system normally would not be able toproduce such an asymmetry. In summary, ENSO ap-pears to correspond to a nonlinear cyclic phenomenonand its erratic behavior is caused by the other factorsincluding the stochastic forcing. We also found that theENSO cycle has changed since the late 1970s. For thepre-1980s, the ENSO cycle associated with the ther-mocline is less asymmetric than that during the post-1980s; hence, the nonlinearity of the ENSO cycle hasbecome stronger since the late 1970s.In this study, the nonlinear nature of the ENSO cycleobtained from NLPCA is simply identified as a closedcurve approximating a relatively small amount of datain the linear PC space. Due to the insufficient data, it ishard to ensure that the decadal changes observed areFIG. 8. Phase–longitude section of the thermocline anomaly (in color: m) and the zonal wind stress anomaly (in contour: H1100310H110021NmH110022) along the equator (5°S–5°N) associated with the first mode NLPCA for (a) the total data period, (b) pre-1980s only, and (c)post-1980s only. The phase in the y axis represents the time sequence.15 AUGUST 2005 A N E T A L . 3237Fig 8 live 4/Creal and not due to sampling uncertainty. Nevertheless,first, the NLPCA curves obtained from two differentdatasets (NCEP and SODA) showed a similar obliquepattern and, second, the interdecadal change of ENSOobserved in this study are dynamically consistent withother studies (e.g., Jin et al. 2003; An and Jin 2004, etc.)that took different approaches.Recently some observational studies have pointedout that, while the termination of El Niño has occurredconsistently with a cyclic nature, initiation is less obvi-ous (Kessler and McPhaden 1995; Kessler 2002), andsome studies even concluded that ENSO is most likelya damped linear system subjected to stochastic forcing(Thompson and Battisti 2000, 2001). This linear ap-proach succeeds in producing a sporadic ENSO butfails to produce the asymmetry of ENSO since the non-linear process is not included in the system. Apart fromthe additive stochastic forced system like Thompsonand Battisti’s model, the multiplicative stochasticforced system may induce the asymmetric probabilitydensity function for the ENSO index. However, theasymmetric behaviors in the multiplicative stochasticforced system come from a nonlinear process.A kind of break in the ENSO cycle has been ob-served when La Niña goes to El Niño, during which thecoupled system somehow remains in a weak La Niñastate for a while (Kessler 2002). On one hand, thisbreak in the ENSO cycle may be due to the influence ofa near-annual mode. The near-annual mode is a uniqueair–sea coupled mode with a near-annual time scaleapart from ENSO and is mainly induced by the zonaladvection of mean SST by the anomalous zonal current(Jin et al. 2003; Kang et al. 2004). During La Niña thezonal contrast of equatorial SST becomes larger, whichprovides a favorable condition for generating the near-annual mode, so that the oceanic memory built in asequence of the ENSO cycle is possibly contaminatedby this near-annual mode. Thus, the isolation of thepure ENSO cycle from this near-annual signal shouldgive a clearer picture. On the other hand, Yu et al.(2003) suggested that the westerly wind bursts (WWB)in the western equatorial Pacific, which had been con-sidered as an important trigger of El Niño, could beregulated by ENSO in their generation such that thepre–El Niño state provides a favorable backgroundcondition on which the active WWB are generated, andconsequently the ENSO cycle inherently has an abilityto trigger itself. Their suggestion can be considered as amultiplicative stochastic system, in which the ENSOcycle interacts with the stochastic forcing. Regardingthis topic, further studies need to be pursued.Acknowledgments. This work is supported by Na-tional Science Foundation Grant ATM-0226141 and byNational Oceanographic and Atmospheric Administra-tion Grants GC01-229 and GC01-246. S.-I. An is sup-ported by the Japan Agency for Marine-Earth Scienceand Technology (JAMSTEC) through its sponsorshipof the International Pacific Research Center. W. Hsiehis supported by the Natural Sciences and EngineeringResearch Council of Canada and the Canadian Foun-dation for Climate and Atmospheric Sciences. The au-thors thank Diane Henderson for careful reading andediting of the manuscript.REFERENCESAn, S.-I., 2004: Interdecadal changes in the El Niño–La Niñaasymmetry. Geophys. Res. Lett., 31, L23210, doi:10.1029/2004GL021699.——, and F.-F. Jin, 2000: An eigenanalysis of the interdecadalchanges in the structure and frequency of ENSO mode. Geo-phys. Res. Lett., 27, 1573–1576.FIG. 9. 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