The Influence of ENSO on the Generation of Decadal ...

The Influence of ENSO on the Generation of Decadal Variability in the North Pacific*

SOON-IL AN

Department of Atmospheric Sciences/Global Environmental Laboratory, Yonsei University, Seoul, South Korea

JONG-SEONG KUG

School of Earth and Environmental Science, Seoul National University, Seoul, South Korea

AXEL TIMMERMANN

International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii

IN-SIK KANG

School of Earth and Environmental Science, Seoul National University, Seoul, South Korea

OLIVER TIMM

International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii

(Manuscript received 20 September 2005, in final form 16 June 2006)

ABSTRACT

This diagnostic study explores the generation of decadal variability in the North Pacific resulting from theasymmetry of the El Niño–Southern Oscillation phenomenon and the nonlinearity of the atmospherictropical–extratropical teleconnection. Nonlinear regression analysis of the North Pacific sea surface tem-peratures and atmospheric fields with respect to the ENSO index reveals that the main teleconnectioncenters shift between El Niño and La Niña years. This asymmetry in the ENSO response, together with theskewed probabilistic distribution of ENSO itself, may contribute to the generation of the long-term decadalvariability of sea surface temperatures in the extratropical North Pacific. It is argued that this hypothesismay explain the significant variance of the observed Pacific decadal oscillation in the extratropics.

1. Introduction

The pattern of the Pacific decadal oscillation (PDO)has both tropical and extratropical loadings in bothhemispheres. Still unresolved is the debate whether thismode of Pacific climate variability originates from thetropical Pacific or whether it is created by atmosphere–ocean instability in the extratropics.

Based on a coupled general circulation model

(CGCM) simulation, Latif and Barnett (1996) pro-posed that positive air–sea interactions in conjunctionwith the propagation of oceanic midlatitude Rossbywaves could give rise to a delayed-action oscillator typeof decadal North Pacific (NP) coupled mode that bearssome similarities with the observed PDO. In later mod-eling studies (Schneider et al. 1999), the importance ofcoupled air–sea interactions for this mode was relaxedand the importance of stochastic forcing and the spatialresonance mechanism (Saravanan and McWilliams1997) was highlighted. Several possibilities exist tocommunicate the extratropical decadal signals into theTropics. Among these possibilities is the Gu and Phi-lander (1997) hypothesis of advecting extratropicaltemperature anomalies on the isopycnal surfaces intothe tropical Pacific, which has received a great deal ofattention. However, further quantitative estimates(Schneider et al. 1999; Nonaka et al. 2002) revealed that

* School of Ocean and Earth Science and Technology Contri-bution Number 6985 and International Pacific Research CenterContribution Number 417.

Corresponding author address: Dr. Soon-Il An, Department ofAtmospheric Sciences, Yonsei University, Shinchon-Dong 134,Seodaemun-ku, Seoul 120-749, South Korea.E-mail: [email protected]

15 FEBRUARY 2007 A N E T A L . 667

DOI: 10.1175/JCLI4017.1

© 2007 American Meteorological Society

JCLI4017

this pathway is rather inefficient for the generation ofdecadal variability in the tropical Pacific. The footprint-ing mechanism (Vimont et al. 2003) may also help tocommunicate extratropical signals into the tropical Pa-cific as well as decadal transport changes of the sub-tropical cells (Kleeman et al. 1999; Nonaka et al. 2002).Alternatively, Bratcher and Giese (2002), Giese et al.(2002), and Luo et al. (2003) suggested that the decadalsignals in the tropical Pacific originate from the SouthPacific.

In addition to the extratropical forcing mechanisms,several tropical mechanisms have been suggested,which may explain the presence of decadal variability inthe tropical and extratropical Pacific. Neglecting oceandynamics, even the mixed layer has the ability to inte-grate the stochastic momentum and heat fluxes, yield-ing a red-noise spectrum (Hasselmann 1976) and,hence, enhanced variance on decadal time scales.

Another source for ENSO irregularity (chaos), andhence decadal variability in the tropical Pacific, is thenonlinear interaction between ENSO and the annualcycle (Jin et al. 1994; Tziperman et al. 1994). For certaincoupling strengths the annually varying backgroundstate in the tropical Pacific can trigger low-dimensionalENSO chaos as a result of nonlinear resonances and thedevil’s staircase. Timmermann and Jin (2002), Timmer-mann et al. (2003), and Timmermann (2003) hypoth-esize that ENSO chaos as well as the emergence ofdecadal El Niño bursting can be generated without in-voking extratropical processes or the tropical annualcycle or stochastic forcing.

Timmermann et al. (2003) argued that a heteroclinicconnection in phase space between a saddle node(weak La Niño state) and the saddle point (radiative–convective equilibrium) organizes ENSO dynamics in aparticular way: ENSO variations grow until they reachthe maximum intensity El Niño, then a quick resettakes place and the small ENSO variations grow again.Because of the skewness of El Niño and La Niña in thismodel, the decadal growth of the ENSO amplitude isimmediately translated into decadal background statechanges. Hence, decadal tropical variability is a re-siduum of the skewed ENSO amplitude modulations.This idea had been supported by Timmermann (2003)using a CGCM simulation and by Rodgers et al. (2004).Given the strong atmospheric teleconnection from thetropical Pacific to the extratropical North and SouthPacific, decadal variability in the extratropical Pacificcan be easily triggered from decadal changes of ENSOand the associated changes of the climate backgroundcondition. This scenario may also explain why the PDOexhibits such a strong equatorial symmetry. Further-more, additional persistence of the teleconnections and

extratropical SST anomalies may originate from dy-namical changes in the extratropical ocean or the re-emergence mechanism (Alexander et al. 1999).

Our study addresses the following questions: Is theextratropical component of the PDO just the residuumof very strong El Niño events? How much of the dec-adal North Pacific SST variability can be explained interms of the decadal modulations of ENSO and atmo-spheric teleconnections? In the following, section 2 de-scribes two processes that generate the skewed NorthPacific interannual SST variation. In section 3, we showhow the skewed interannual SST variations are recti-fied into the background state, thus generating the dec-adal variation over the North Pacific. In section 4, themain factors to generate the nonlinear teleconnectionare discussed. The concluding remarks are given in sec-tion 5.

2. Asymmetric interannual SSTA variation in theNorth Pacific

The anomalous tropical heating associated withENSO perturbs the large-scale atmospheric circulationresulting from Rossby wave propagation into the Northand South Pacific sector (Hoskins and Karoly 1981),thereby altering also extratropical SST via heat fluxanomalies. Interestingly, this teleconnection is not sim-ply linear; teleconnections during La Niña have a largermagnitude than those during similarly strong El Niñoevents (Hoerling et al. 1997). This asymmetric (i.e.,nonlinear) teleconnection can be extracted by a projec-tion method using nonlinear regression analysis (Wuand Hsieh 2004). Nonlinear regression and composites(Hoerling et al. 1997, 2001) yield similar results for theasymmetry of the ENSO teleconnection. Using the Na-tional Centers for Environmental Prediction–NationalCenter for Atmospheric Research (NCEP–NCAR) re-analysis (Kalnay et al. 1996) and the Extended Recon-structed Sea Surface Temperature, version 2 (ERSST.v2)(Smith and Reynolds 2004), we compare the nonlinearregression between Niño-3 SST anomalies (SSTAs)(area-averaged SST over 5°S–5°N, 150°–90°W) and the500-hPa geopotential height (GPH) anomalies and theSSTA field in the North Pacific, respectively.

Figure 1 shows the nonlinear response pattern of 500-hPa GPH and SSTA over the North Pacific during theboreal wintertime to SSTA in the Niño-3 area. Thenonlinear response function is defined as follows:

��x, Nino� � �i�1

N

Ei�x� · Ci�Nino�, �1�

where x is the state vector, Ei is the eigenvector ob-tained by the empirical orthogonal function (EOF) of

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GPH or SST over the North Pacific, and Ci is the non-linear regression function, which represents the nonlin-ear fitting curve between the EOF principal component(PC) time series and Niño-3 index. We use the fiveleading EOF modes; thus, N � 5. The nonlinear func-tion (C) has been obtained by using the artificial neuralnetwork (NN). In the present NN approach, we useonly one input variable (Niño-3 SST) and five outputvariables (EOF PCs). This approach is very similar tothat used by Wu and Hsieh (2004). The input variable

is first nonlinearly mapped to two intermediate vari-ables (i.e., hidden neurons), which are linearly mappedto five output variables. The NN model parameters areoptimized in order to minimize the mean square errorbetween the output variables and the observed EOFPCs. We repeated the above calculation with a boot-strap approach by randomly selecting data samples.Bootstrapping reveals that the present results are in-sensitive to the data sampling (not shown here).

As shown in Fig. 1, during weak ENSO events (�1°C

FIG. 1. Nonlinear regression pattern of SST anomaly (shading) and 500-hPa geopotential height (contour) in the North Pacific withrespect to the Niño-3 SSTA. Nonlinear regression has been obtained from the neural network technique.


Fig 1 live 4/C

of Niño-3), both GPH and SSTA in the North Pacificrespond linearly in their amplitude. However, as theENSO forcing becomes larger (e.g., �2°C for Niño-3SSTA), both the GPH and SSTA response patternsexhibit asymmetries in the extratropics. The maximumSSTAs in the North Pacific associated with El Niño andLa Niña anomalies are located east of the date linearound 40 °N, but the associated GPH amplitude for aLa Niña event (�2°C) is almost twice as large as thatfor an El Niño event (�2°C), thereby corroborating theconclusions of Hoerling et al. (1997). The GPH re-sponse to ENSO shows that not only the amplitude butalso the location exhibits asymmetric features. In com-parison with the weak SSTA forcing case, the GPHpattern associated with El Niño is shifted more south-eastward (around 40°N, 150°W), whereas that associ-ated with a strong La Niña shifts to the northwest(around the date line, 50°N). This zonal shift of theGPH pattern can be attributed to the difference in thelocation of the tropical heat source for El Niño and LaNiña events (Hoerling et al. 1997; Kang and Kug 2002).The anomalous atmospheric circulation induces theanomalous latent heat fluxes and anomalous oceanicvertical mixing, with a direct impact on the generationof the SST anomaly in Fig. 1. Comparing the anomalousheat fluxes associated with the eastward shift of thestrong La Niña teleconnection with the mean circula-tion, it becomes apparent that the eastward shift of thecenter of action is accompanied by relatively large SSTresponses. As expected, the nonlinear regression pat-tern of the latent heat flux to the Niño-3 SSTA alsoshows asymmetric features with respect to Niño-3SSTA. The warming (cooling) resulting from the latentheat flux anomalies during strong La Niña (El Niño)events is strongly contributing to the generation of apositive (negative) SSTA in the Fig. 1. We will discussthis point further in section 4.

In addition to the nonlinear response of the NorthPacific SSTA anomalies to ENSO as shown in Fig. 1,the asymmetry of ENSO (Burgers and Stephenson1999; Timmermann 1999; An 2004a) may also influencethe asymmetric behavior of North Pacific SST varia-tions.

A very suitable way to identify the asymmetric char-acter of ENSO is the independent component analysis(ICA) (Comon 1994; Hyvärinen and Oja 2000). In con-trast to correlation-based transformations, such as EOFanalysis, ICA decorrelates the signals (second-orderstatistics) and efficiently reduces higher-order statisticaldependencies, thus making the signals as independentfrom each other as possible. This allows the ICA todetect skewed and non-Gaussian signals in multivariatesignals.

A fast fixed-point algorithm for the ICA (Hyvärinenand Oja 1997) was applied to the observed SSTA datafrom 1950–2000 in the tropical band from 20°S to 20°N.The projection pattern of ICA mode 1 (2) is similar tothat of EOF mode 2 (1). However, ICA mode 1 local-izes the regions where the asymmetry between El Niñoand La Niña is most pronounced (Fig. 2a). It explains33% of the variance in the SST anomaly fields. A veryinteresting result is that the locally explained varianceof this mode is confined to the eastern part of the tropi-cal Pacific. In the easternmost part of the tropical Pa-cific nonlinear terms play a dominant role in the heatbudget of the mixed layer. The second ICA projectionpattern explains 19% of the total variance in the field.It is similar to the leading EOF mode, but more con-strained to the equator. The pattern of locally ex-plained variability (not shown) highlights a dipolestructure with maxima over the central equatorial Pa-cific and the warm pool region. These results highlightthe nonlinear processes causing the asymmetry in theeastern basin, which are decoupled from the warm poolregion. The EOF analysis cannot fully decouple theseprocesses in the variance maximization projection pur-suit.

The independent components are plotted againsteach other for the pre-1976 and post-1976 periods (Fig.2). As shown in Fig. 2, El Niño is typically stronger thanLa Niña. As shown previously (An 2004a), the El Niño–La Niña asymmetry has become more dominant sincethe late 1970s (e.g., An 2004a; An et al. 2005), which isa feature clearly captured by the ICA. The differencebetween the two panels in Fig. 2b shows that the ElNiño–La Niña asymmetry undergoes interdecadalchanges. In the following section, we will show how thisdecadal change in the El Niño–La Niña asymmetry andthe teleconnection can be a contributor to the genera-tion of the decadal variability of the North Pacific SST.

3. Nonlinear rectification

In this section we describe a simple experiment thathelps to quantify the effects of the nonlinear telecon-nection and ENSO asymmetry on North Pacific SSTAvariability. We use the nonlinear regression functiondefined in Eq. (1), �(x,Nino), for the total response,including both the linear and nonlinear responses. Forthe idealized experiment, we calculate the residualbetween the NP SST/GPH responses to El Niño andLa Niña for the nonlinear response (�(x,Nino) ��(x,-Nino); NON), and that for the linear response([�(x,Nino) � �(x,-Nino)]/2; LIN) to a given forcing(i.e., Niño-3 index). Note that the “linear response”used here may contain the effects associated with the


higher-order odd functions that are usually treated asthe nonlinear function; nevertheless, these odd func-tions cannot generate the asymmetry so that their ef-fects are neglected in this study.

The left panel of Fig. 3 shows the nonlinear NP SSTresponse to symmetric ENSO forcing (NON-SYM).Here, the symmetric ENSO forcing (SYM) means thatthe amplitude of El Niño and La Niña are the same,while the asymmetric ENSO forcing (ASYM) indicatesthat the amplitudes of El Nino and La Niña are differ-ent. When the ENSO amplitude is 2° or 3°,1 the North

Pacific SSTA exhibits a horseshoe-like pattern with aSST anomaly of 0.5°–1.5° amplitude. Note that theincrease of the forcing amplitude results in an increaseof the response of NP SST, but the relationship be-tween the forcing and response is not simply linear. Fora small-amplitude forcing of 1°, the response of NorthPacific SSTA is very weak, indicating the neither thenonlinear teleconnection nor the rectification effect aresignificant.

In the center panels of Fig. 3, we show the linear NPSST response to the asymmetric ENSO forcing by con-sidering only the linear teleconnection effect. We con-sider the case of a positively skewed ENSO, similar tothe observations. As expected, when El Niño events arestronger than La Niña events, the central NP SST be-

1 It should be noted that the �3° of Niño-3 is an idealized butunrealistic setting.

FIG. 2. Results of the ICA: (a) the (top) first and (bottom) second inde-pendent components of the monthly mean SST anomalies for 1950–99; (b)projection patterns of the (top) first and (bottom) second independent com-ponents; (c) scatter (dots) and probability density estimates (PDF) of theindependent components. Blue (red) dots denote months 1950–75 (1976–99).The contour lines show the kernel estimates of the PDF.


Fig 2 live 4/C

comes negative, and the large difference in amplitudebetween El Niño and La Niña results in a large re-sponse of NP SST.

Finally, we consider the nonlinear teleconnectionand asymmetric ENSO forcing effects at the same time(right panel of Fig. 3). By considering the nonlinearteleconnection, the residual of NP SST is reduced com-pared with the counterpart of the linear teleconnection.This is due to the relatively strong La Niña influencethrough the nonlinear teleconnection (lower left). Forthe �2° and 3° ENSO forcing (the right-lower panel),the NP SST shows the positive response in the centralNP, in which the nonlinear teleconnection effect some-how overwhelms the asymmetric forcing effect. In thepre-1980s ENSO variations were quite symmetric,whereas in the post-1980s ENSO variations were posi-tively skewed, as shown in Fig. 2. Obviously the factthat the central Pacific SSTA was positive during thepre-1980s and negative during the post-1980s (Zhang etal. 1997) corresponds to our simple statistical modelexperiment (see the middle panels of the first and thirdcolumn, respectively).

For the transient experiment, we adopt Newman etal.’s (2003) method. They proposed a simple model forthe hindcast of the annually averaged PDO index. Theidea is based on the fact that the North Pacific acts toredden not only atmospheric noise, but also the ENSOsignal. Based on their idea, we propose a simple alter-native model for the NP SSTA that is utilizing the non-linear concepts described here. We choose

Pn�x, t� � �Pn�1�x, t� � ��En, t�, �2�

where P is the NP SST, E is the ENSO index (here,Niño-3 index), and � is the nonlinear function definedat (1). The represents the reddening factor (An andWang 2005), or physically “the re-emergence effect”(Alexander et al. 1999). The results are sensitive to thevalue of in the sense that smaller values for domi-nate the shorter time-scale variability. However, thelow-frequency behavior is rather insensitive to . Here,we choose � 0.7, which is similar to the choice inNewman et al.’s model. The main difference of ourmodel from that of the Newman et al. (2003) model isto consider the nonlinearity and to also forecast thespatial pattern. It should be mentioned, however, thatbecause the response function has been obtained byusing five leading EOF modes for the boreal wintermean data, the prediction skill of this model may not bebetter than Newman et al.’s model.

Using this model, we perform a series of idealizedexperiments as well as the hindcast experiments. As thefirst idealized experiment, we choose a symmetricENSO forcing of the model with the maximum ampli-tude of 2° and the period of 5 yr. The response of thecentral North Pacific SST at 30°N and 160°W (the re-sults are insensitive to other choices of central NP in-dices) (first panel of Fig. 4) shows asymmetric interan-nual fluctuations. The low-frequency variations ob-tained by taking a 15-yr running mean show a constantpositive value of 0.5°. For the second experiment, weselect the same time series as in the first experiment butmodulate its amplitude with a 20-yr decadal time scale.The decadal ENSO envelope period generates decadal

FIG. 3. Residual patterns in North Pacific SSTA obtained from the nonlinear regression. The Niño-3 as a modelforcing is shown the upper-right corner of each panel. The response of the nonlinear model with (left) symmetricforcing (NON-SYM), that of (middle) the linear model with asymmetric forcing (LIN-ASYM), and that of (right)the nonlinear model with asymmetric forcing (NON-ASYM) are shown. The contour intervals are 0.3°C. Thenegative values are shaded.


variability in the NP resulting from the nonlinearity ofthe teleconnections. This result indicates that the dec-adal modulations of ENSO amplitude alone withoutdecadal mean variations in the forcing can induce thedecadal variation of NP SST. As a further experiment,the asymmetric ENSO forcing is given with an ampli-tude modulation with a 20-yr period. Local mean valuesare zero (i.e., nondecadal variation), but the skewness ispositive. Resulting from the skewed ENSO forcing, thelong-term variation of NP SST becomes negative for acertain period. Again, decadal variation emerges.

Finally, the observed Niño-3 index is given as a forc-ing. The correlation between the simulated NP SST andthe observed NP SST for the recent 50 yr is 0.38, whichis exceeds the 95% significance level. However, for theearly century the correlation is insignificant at thislevel. In addition to interannual ENSO-forced variabil-ity, the NP SST variations are also characterized byinterdecadal time scales. The decadal variation of theNiño-3 index is observed, and thus the forcing itselfexhibits decadal variations of the background state asshown in the figure. This decadal variation of theNiño-3 forcing could also directly generate decadalvariations of NP SST, even via linear teleconnections.After taking out the local mean (i.e., 15-yr runningmean) from the original Niño-3 time series, the Niño-3time series that has no decadal mean variations stillgenerates decadal variations of NP SST with reduced

amplitude (50%), through the nonlinear teleconnectionand asymmetric ENSO forcing. Without decadal meanvariations of ENSO forcing, the model-simulated NPSSTA hardly drops below zero in this hindcast experi-ment. This might be due to the competition betweenthe nonlinear teleconnection and the skewed ENSOforcing. Thus, we suggest that observed NP SSTA ob-tains an important contribution from a combination ofthe direct influence by the decadal tropical forcing andthe nonlinearly rectified influence resulting from thedecadal modulation of ENSO. It should also be men-tioned that the decadal SST variations in the tropicalPacific might be partly due to the nonlinear rectifica-tion of decadal amplitude modulations of ENSO (Jin etal. 2003; Rodgers et al. 2004). Therefore, the decadalchanges in the North Pacific SST contain significantcontributions from the decadal modulation of ENSO inboth direct and indirect ways.

To compare the spatial distributions of the decadalchange of North Pacific SSTA between those observedand simulated, we calculated the difference betweenthe averaged North Pacific SSTA for 1956–75 and thatfor 1980–99. The ERSST data are used for the observedchange, and the previous model results are used for thesimulated decadal change. The results are shown in Fig.5. Because the model is composed by a statistical rela-tionship under the first-order approximation, we wouldnot expect that the simulated SSTA is so realistic. In

FIG. 4. Time series of (left) the Niño-3 index as a model forcing, and the corresponding response of (right) thecentral North Pacific SST obtained from the simple statistical model. The details in the model are shown in the text.


this sense, rather than the comparison in the quantity,the comparison in quality is appropriate. The recon-structed and observed patterns generally are quite simi-lar. Particularly, the simulated SSTA pattern to the eastof the date line, where ENSO has a strong influence, isquite similar to that observed. On the other hand,SSTA over the west of the date line, including theKuroshio extension, possibly resulting from the oceaniczonal advection or the local atmospheric stochasticforcing (Schneider and Cornuelle 2005) is less similar tothe observation.

4. Discussion on the main factor driving thenonlinear teleconnection

The mechanism on the dynamical linkage betweenENSO and North Pacific atmospheric circulationthrough the atmospheric teleconnection (e.g., Hoskinsand Karoly 1981) is well known. Obviously, changes inthe atmospheric circulation induce changes in the seasurface temperature over the North Pacific by modify-ing the surface heat fluxes and thermal dynamical ad-

vection in the ocean. Because our aim is to address therole of ENSO in the generation of the decadal variationof SST over the North Pacific a question we have tofurther address is what factors drive the nonlinear SSTresponse in the North Pacific. In this section, we focusin particular on the surface heat flux (especially, latentheat flux).

First, we calculate the composite maps for El Niñoand La Niña events separately. For the composite, fiveEl Niño and five La Niña events were selected. Toobtain the asymmetric component (which can be re-ferred as the nonlinear component), we simply add theEl Niño and La Niña composites as in Hoerling et al.(1997). Figure 6a shows the asymmetric component ofSST anomalies over the North Pacific. Because of thedominance of the La Niña effect, the positive SSTanomaly over the central area of North Pacific and thenegative SST anomaly in the eastern side of the NorthPacific are observed. This feature can be also easilyexpected from the NN pattern of SSTA in Fig. 1.

The asymmetric component of the SST anomaliesover the North Pacific could be related to the nonlin-

FIG. 5. (top) Observed and simulated North Pacific SSTA difference between 1956–75 and1980–99. The simulated SSTA has been obtained from the statistical model defined by Eq. (2).


earity of the surface heat flux and also that of the ther-mal advection in the ocean surface layer. This is be-cause the changes in the atmospheric circulation mightmodify the heat budget of the ocean surface layer bychanging either the surface heat flux or thermal advec-

tion by modifying the ocean surface current. Becausethe role of the thermal advection is beyond our scope,we concentrate on the change in the surface heat flux.In particular, we examine the latent heat flux by sepa-rately considering wind speed effect and the moisture

FIG. 6. (a) Asymmetric component of the sea surface temperature anomalies estimated bythe sum of two composites of the seasonally averaged DJF observed sea surface temperatureanomalies for El Niño and La Niña states. Contour interval is 0.1°C. Dark (light) shadingindicates positive (negative) values. (b) Same as in (a), except for the latent heat flux anoma-lies associated with the changes in the wind speed. (c) Same as in (a), except for the latent heatflux anomalies associated with the changes in the moisture. Units for (b) and (c): W m�2.


effect on the latent heat flux. The conventional latentheat flux is written as following:

Q � L�CE |V � V | ��qs � qs� � �qa � qa��

� L�CE |V |�qs � qa�, �3�

where the overbar indicates the climatological mean; qs

and qa indicate the mixing ratio at surface and the mix-ing ration of the surface air, respectively; and the sur-face wind at 2 m is used for this calculation. Now, ap-proximately the change of the latent heat flux associ-ated with the wind speed and with the moisture can berepresented as

Q�wind� � L�CE� |V � V | � |V | ��qs � qa�

Q�moisture� � L�CE |V |�qs � qa�. �4�

Assuming that surface air over the cool ocean surface isnearly saturated and using the Clausius–Clapeyronequation, Eq. (4) is approximated as follows:

Q�wind� � L�CE�|V � V| � |V|�qs�T�L

R�Ts2 �Ts � Ta�

Q�moisture� � L�CE|V|qs�Ts�L

R�Ts2 �Ts � Ta�. �5�

Using Eq. (5) and in the same way as for Fig. 6a, theasymmetric component of the latent heat flux anoma-lies associated with the wind speed change is calculatedand shown in Fig. 6b. The negative (positive) fluxanomaly indicates the warming (cooling) tendency ofSST. The negative asymmetric component of the fluxanomaly in the central North Pacific and the positiveasymmetric component of the flux anomaly are overallwell matched with the positive and the negative asym-metric components of the SST anomaly, respectively.On the other hand, the asymmetric component of thelatent heat flux anomaly associated with the moisturechange (shown in Fig. 6c) in the central North Pacific,which is calculated by using Eq. (5), is very weak andnot well organized. The negative asymmetric compo-nent is pronounced over the Kuroshio region, wherethe weak asymmetric component of SST anomaly isobserved. Thus, the nonlinear teleconnection may beattributed to the nonlinearity of the latent heat fluxresulting from the changes in the wind speed.

Another possible cause of the nonlinear teleconnec-tion is related to the change in the mixed layer depth.The deep (shallow) mixed layer is related to cold(warm) SST anomaly by more (less) turbulent verticalmixing under stratified ocean. Figures 7a and b showthe mixed layer depth anomalies associated with ElNiño and La Niña composites, respectively. The theUniversity of Maryland Simple Ocean Data Assimila-

tion (SODA) data are utilized for January 1958–December 2001 (Carton et al. 2000). Mixed layer depthwas defined as a level where the temperature differencefrom SST is less than 0.5 K. As shown in Figs. 7a and 7b,during the El Niño (La Niña) events, the deep (shal-low) mixed layer depth is observed over the centralNorth Pacific. Because the mixed layer depth is roughlyproportional to the wind speed, the response of themixed layer depth can be expected from Fig. 1. Thedeep (shallow) mixed layer is linked to the cooling(warming) SST tendency, referring to the fact that theanomalous oceanic mixing process is also another fac-tor to induce the NP SST responses associated withENSO. Figure 7c shows the asymmetric component ofthe mixed layer depth. Over the west of the date line,the asymmetric component of the mixed layer is nega-tive, possibly related to the negative asymmetric SSTcomponent (as shown in Fig. 6a), while it seems that themixed layer depth response on ENSO forcing itself hasno significant asymmetric component over the centralNorth Pacific, indicating that the mixed layer responseis quite linear.

However, the change of the mixed layer depth itselfhas a crucial nonlinear effect on the SST change indi-rectly. That is, the deep (shallow) mixed layer depthmakes SST to be less (more) sensitive to a given surfaceheat flux. In this regard, even the response of the mixedlayer depth on ENSO forcing is linear; the net effect ofthe mixed layer change can induce the nonlinear re-sponse in the SST anomaly. During the El Niño eventsthe mixed layer depth is deepened, which is supposedto act as the smaller cooling effect, while the shoaling ofthe mixed layer depth during La Niña acts as the inten-sification of the warming effect. Therefore, the mixedlayer depth change associated with ENSO plays an im-portant role in the intensification of the asymmetriccomponent induced by the surface heat flux. It shouldbe noted that changes in the mixed layer depth areinduced by the ENSO teleconnection, and thus the at-mospheric teleconnection is considered as the main fac-tor used to generate the asymmetric component of theSST over the central North Pacific through the com-bined effect of the latent heat flux and the mixed layerdepth.

5. Concluding remarks

The midlatitude atmospheric circulation patternssuch as the Pacific–North America (PNA) pattern areinternal modes of atmospheric variability, which can befurther excited by external forcing such as by tropicalSST anomaly forcing associated with ENSO (An andWang 2005). For our purposes the internal variability ofthe atmospheric modes can be considered as a noise


source, whereas the teleconnection contribution fromENSO is regarded as the signal. Our analysis has fo-cused on this signal component and it was shown thateven symmetric ENSO forcing could generate an asym-metric response in the atmospheric teleconnections,asymmetric North Pacific heat flux anomalies, and sub-sequently asymmetric North Pacific SST anomaly. As

shown in idealized experiments resulting from this non-linear teleconnection, decadal/interdecadal changes inthe amplitude of ENSO can generate decadal/inter-decadal variations in the mean of North Pacific SSTanomaly. In addition, ENSO itself has asymmetric com-ponents that modulate the strength of the teleconnec-tions.

FIG. 7. Composites of the seasonally averaged December–February (DJF)-observed mixedlayer depth anomalies in the North Pacific for (a) El Niño and (b) La Niña states. (c)Asymmetric component of the mixed layer depth anomalies, as estimated by the sum (a) plus(b). Contour interval is 5 m. Dark (light) shading indicates positive (negative) values.


Many studies offered generation mechanisms of thePacific decadal oscillation (PDO)/variability. One ofthem stressed the local deterministic instability (e.g.,Latif and Barnett 1996), and the other the stochasticresponse of the ocean (e.g., Saravanan and McWilliams1997). The remote effect rather than the local processhas been argued by other studies (e.g., Gu and Philan-der 1997; Newman et al. 2003). Our work adds moreweight to the remote route from the tropical (especiallyEl Niño) to the midlatitude Pacific. Furthermore, wedemonstrated here that the remote route is nonlinear.

The nonlinear rectification resulting from the asym-metric ENSO forcing and the nonlinear teleconnectionmay not be limited to the North Pacific only, but also tothe tropical Indian (Klein et al. 1999; Xie et al. 2002)and Atlantic (Lanzante 1996) Oceans. The relationshipbetween the Indian (also the Asian monsoon) and Pa-cific Oceans underwent some interdecadal changes(Ashok et al. 2004), which are, however, weaker thanthose expected just from random processes (Gershunovet al. 2001). Whether the nonlinear rectification effectsdescribed in this paper and those described in Timmer-mann (2003) and Rodgers et al. (2004) have an influ-ence on the Asian monsoons or on the South Pacificclimate or the Indian Ocean zonal mode (An 2004b) isan important question that will be addressed in our nextstudy.

Acknowledgments. Authors appreciate two reviewersand editor’s constructive comments. This work was sup-ported by the SRC program of Korea Science and En-gineering Foundation, and the Brain Korea 21 project.S.-I. An was also supported by Yonsei University Re-search Fund of 2005. J.-S. Kug and I.-S. Kang weresupported by Ministry of Environment as “The Eco-techonopia 21 Project.” A. Timmermann and O. Timmhave been supported by the Japan Agency for Marine-Earth Science and Technology through its sponsorshipof the International Pacific Research Center.

APPENDIX

Independent Component Analysis

A common practice in climate research is to decom-pose spatiotemporal climate variability into spatial pat-terns and associated time indices. The EOF analysis isoften applied to separate the signals (so-called climatemodes) from noise. The underlying assumption is thatthese signals exhibit a large portion of variability in aspatially organized structure. The EOF analysis is seek-ing projection directions (patterns) that maximize thevariance in a multivariate data field. To find these di-

rections, only second-moment statistics are needed. Ifthe multivariate probability density function (PDF) isGaussian, then the projection indices (principal compo-nents) are uncorrelated and are also statistically inde-pendent. However, the variance maximization criteriondoes not take into account higher statistical moments innon-Gaussian multivariate data, such as skewness orkurtosis. In our analysis of the SST we found strongevidence for skewed, non-Gaussian distribution of theSST. In case of non-Gaussianity, the EOF-based indices(and patterns) are uncorrelated but not statistically in-dependent. To separate mutually independent climatemodes in observed SST fields, it is necessary to findprojection patterns that are statistically independent.

The independent component analysis (ICA) is a mul-tivariate statistical method that has the goal of extract-ing statistically independent signals from observed vari-ables. In practical applications it is best applied to cen-tered and whitened multivariate data. Therefore, it canbe understood as a rotation of the leading EOF modes.The rotation of the EOF projection patterns is done ina way that minimizes the statistical dependence of theprojected indices. Also, these directions maximize thenon-Gaussianity in the PDF of the projected data. Interms of information theory, the less Gaussian the PDFthe more information contained in the PDF. Reconsid-ering the central limit theorem—that the sum of inde-pendent random variables generally results in a moreGaussian distribution than any of the individual vari-ables—the maximization of the non-Gaussianity is away to unmix a sum of independent non-Gaussian vari-ables.

Assume a multivariate random variable x (which ann-dimensional column vector). The vector x is the lin-ear combination of n statistically independent signals(represented in a vector s). In matrix notation,

x � As. �A1�

The matrix A is an n n matrix and it is implicitlyassumed to be invertible (i.e., each observable variablein x represents a different linear combination of thesignal processes). Without loss of generality, the obser-vations can be centered and normalized to unit vari-ance. The ICA also assumes unit variance and zeromean for the signals. The ICA is trying to find the linearcombinations of the observations that uncover the un-derlying signal processes as

y � wTx. �A2�

The search algorithm of the ICA tries to find the pro-jection direction wT that maximizes the non-Gaussianity of wTx. We used the “fast ICA” algorithm(Hyvärinen and Oya 1997) in the statistical software


package “R.” The algorithm measures the non-Gaussianity of y in terms of negentropy,

J�y� � ��fg�yg� log�fg�yg�� dyg

� ��f�y� log�f�y�� dy�, �A3�

where fg(yg) represents the Gaussian distribution withthe same variance as y. Several approximations for J(y)are discussed in Hyvärinen and Oja (2000). Instead ofestimating higher statistical moments directly, the fastICA applies nonlinear contrast function of y. By esti-mating the first-moment statistics from such a trans-formed variable the estimation becomes more robust tooutliers.

Starting from an arbitrary projection direction w, anapproximate Newton iteration scheme is applied to findthe w that maximizes J(y), given the observations of x.The signals can be extracted in a step-by-step process orin a parallel multidimensional mode.

To simplify and stabilize the search algorithm anEOF-based prewhitening of the multivariate observa-tions is applied prior to the ICA:

x* � ED��1�2�ETx. �A4�

The matrix E contains the eigenvectors, D is a diagonalmatrix containing the eigenvalues (di)

1/2, i � 1, . . . , n.In this step one can further reduce the dimension of theobservational space by retaining only the leading eigen-modes in the matrix E, D.

It is important to note that the resulting independentcomponents yi are comparable to the principal compo-nents of the EOF analysis, and the projection pattern wi

can be understood as rotated eigenvectors of the EOF.Unlike the EOF, the order of the independent compo-nents is arbitrary. The results of the ICA strongly de-pend on the EOF truncation. In our application wevaried the number of EOFs retained in the prewhiten-ing process. Our prior EOF analysis suggested thatmost of the ENSO-related skewness is distributed onthe three leading EOF modes, and a number of three orfour EOF modes produced robust results in the ICA.However, when the sample size of the observations x isrelatively small (600 month of SST anomalies in ourcase) the inclusion of higher EOF modes increases therisk of being trapped in local maxima, which destabi-lizes the ICA results. It should be noted that the ICAfails in detecting Gaussian signals. Without significantdeviations from the Gaussianity, the optimum projec-tion directions are difficult to detect.

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