Analysis of the Non-linearity in the Pattern and Time Evolution of El Niño Southern Oscillation!

Transcription

1 2 3 Analysis of the Non-linearity in the Pattern and Time Evolution of El Niño Southern Oscillation! 4 DietmarDommenget *,TobiasBayr 2 andclaudiafrauen SchoolofMathematicalSciences,MonashUniversity,Clayton,Victoria, 6 7 Australia. 2 HelmholtzCentreforOceanResearchKiel(GEOMAR), Kiel,Germany; * Correspondingauthor(dietmar.dommenget@monash.edu) 2 3 ClimateDynamics,accepted2July22 4!

2 Abstract! InthisstudytheobservednonZlinearityinthespatialpatternandtimeevolution ofelniñosouthernoscillation(enso)eventsisanalyzed.itisshownthatenso skewnessisnotonlyacharacteristicoftheamplitudeofevents(elniñosbeing stronger than La Niñas) but also of the spatial pattern and time evolution. It is demonstrated that these nonzlinearities can be related to the nonzlinear responseofthezonalwindstoseasurfacetemperature(sst)anomalies. It is shown in observations as well as in coupled model simulations that significant differences in the spatial pattern between positive (El Niño) vs. negative(laniña)andstrongvs.weakeventsexist,whichismostlydescribing thedifferencebetweencentralandeastpacific events. Central Pacific events tendtobeweakelniñoorstronglaniñaevents.inturneastpacificeventstend to be strong El Niño or weak La Niña events. A rotation of the two leading empiricalorthogonalfunction(eof)modesillustratesthatforbothelniñoand La Niña extreme events are more likely than expected from a normal distribution. The Bjerknes feedbacks and time evolution of strong ENSO events in observations as well as in coupled model simulations also show strong asymmetries, with strong ElNiños being forced more strongly by zonal wind stressthanbythermoclinedepthanomaliesandarefollowedbylaniñaevents. In turn strong La Niña events are preceded by El Niño events and are more stronglyforcedbythermoclinedepthanomaliesthanbywindstressanomalies. Further, thezonalwindstressresponseto sea surface temperature anomalies duringstrongelniñoeventsisstrongerandshiftedtotheeastrelativetostrong La Niña events, supporting the eastward shifted El Niño pattern and the asymmetrictimeevolution. BasedonthesimplifiedhybridcoupledRECHOZmodelofENSOitcanbeshown that the nonzlinear zonal wind stress response to SST anomalies causes the asymmetric forcings of ENSO events. This also implies that strong El Niños are mostly wind driven and less predictable and strong La Niñas are mostly thermoclinedepthdrivenandbetterpredictable,whichisdemonstratedbyaset ofperfectmodelforecastensembles.

3 Introduction! TheElNiñoSouthernOscillation(ENSO)modecantofirstorderbedescribedby onestandingseasurfacetemperature(sst)patternwhoseamplitudeincreases or decreases over time(e.g. empirical orthogonal function(eof), see Fig. ). However, it has also been noted that observed and simulated ENSO events can havedifferentpatterns,inparticularithasbeenpointedoutthatelniñoevents aredifferentinpatternfromlaniñaevents[e.g.hoerlingetal.,997,monahan, 2,Rodgersetal.,24,SchopfandBurgman,26,SunandYu,29,Yuand Kim, 2, Takahashi et al., 2 and Choi et al., 2]. Further, it has been notedthatthetimeevolutionsofstrongelniñoeventsaredifferentfromthose ofstronglaniñaevents[larkinandharrison,22,ohbaandueda,29and Okumura and Deser, 2]. These differences in the shape of the patterns and theasymmetryinthetimeevolutionrepresentanonzlinearityofenso.thefact thatnonzlinearitiesintheensomodeareimportanthasintheliteraturemostly been noted in the context of the amplitude of El Niño or La Niña events, reflectingtheskewnessoftheprobabilitydistributionofnino3sstanomalies. Processes that could cause nonzlinearities in the ENSOZmode include oceanic, biologicalandatmosphericprocesses.thelaterhasbeenthefocusofaseriesof recentpublications[kangandkug,22,philipandvanoldenborgh,29and Frauen and Dommenget, 2]. The studies found thattheskewness of NINO3 SSTanomaliescanbeexplainedbythenonZlinearresponseofthezonalwindsin the central Pacific to SST anomalies. The aim of the study presented hereis to illustrate that the skewness of the probability distribution of ENSO events also reflectsitselfinthepatternshapeandinthetimeevolutionofensoeventsand thatthesenonzlinearitiesorasymmetriesareatleastpartiallycausedbyanonz linearresponseofthecentralpacificzonalwindstresstosstanomalies. The different shape of ENSO events has in recent years caught quite some attention,withseveralstudiesfocusingonelniñoeventsthatarecenteredinthe central Pacific [e.g. Larkin and Harrison, 2 Ashok et al., 27, Kao and Yu, 29, Yeh et al., 29, Takahashi et al., 2 or McPhaden et al., 2].These typeofeventsarenamedelniñomodokibyashoketal.[27].theyarguethat El Niño Modoki events are independent of the canonical El Niño events, controlledbydifferentdynamics.theanalysispresentedhereaimstoillustrate thatthesedifferentensotypesareatleastpartiallyrelatedtononzlinearitiesof theensomode. Thearticleisorganizedasfollows:Insection2wewillpresenttheobservational data sets and model simulations used. In the first analysis section, 3, we will presenttheobservednonzlinearityintheensoeventpatternsandquantifyitin terms of simplified indices. In section 4 we analyze thenonzlinearities in the Bjerknes feedbacks and the time evolution of the ENSO events to explore the causesofthedifferencesintheensopatterns.theobservationalevidencesare thenfurtherbackedupinsectionbystateoftheartcoupledmodelsimulations showing the same nonzlinearity characteristics. In section 6 we will use the strongly simplified hybrid coupled model of Frauen and Dommenget[2] to illustrate how the nonzlinearities in the feedbacks and time evolution relate to thenonzlinearresponseofthezonalwindstresstosstanomalies.theanalysis partiscompletedwithsomediscussiononhowthesenonzlinearitiesintheenso

4 96 97 patternrelatetothedifferentdefinitionsofensotypes(section7).finally,we summarizeanddiscussthemainfindingsofthisstudyinsection Data!and!Models! The analysis presented here is based on observed linear detrended SST anomaliesfortheperiod9 2takenfromtheHADISSTdataset[Rayneret al., 23]. Additional analysis with the ERSST data set [Smith et al., 28] are donetosupporttheresultswiththehadisstdataset. The observed sea level pressure (SLP) and m zonal wind is taken from the NCEP reanalysis data from 9Z28 [Kalnayetal.,996]. Since subsurface ocean observations are rare prior to the midz98s, the observed equatorial Pacific thermocline depths are estimated by the Max Planck Institute Ocean Model(MPIZOM)oceangeneralcirculationmodel[Marslandetal.,23]forced withthencepzreanalysisfrom948to2.datafromthissimulationwasused alsoinpreviousstudiesoftropicalcoupleddynamics[e.g.keenlysideandlatif, 27andJansenetal.,29]. The coupled general circulation model simulations analyzed in this study are taken from the CMIP3 database 2th century control simulations[meehletal., 27]. All models in the database that have a 2th century control simulation availablearetakenintoaccountforthisstudy.forallfollowinganalysesthe24 modelsimulationshavebeeninterpolatedontoaregular2. x2. globalgrid. The hybrid coupled RECHOZ model is a yrs long simulation with simplified linear ocean dynamics in the tropical Pacific, a single column ocean model outside the tropical Pacific and a fully complex atmosphere model (ECHAM), seefrauenanddommenget[2]fordetails.therechozmodelisalsoused for a sensitivity study in which the tropical SST variability outside the tropical Pacificisremoved. 3. Observed!El!Niño!pattern!non=linearity! The nonzlinearityoftheensopattern can in a first attempt be summarized by splittingthesstanomaliesintofourcategories,definedbytwocharacteristicsof NINO3.4SSTanomalies:thesignandthestrength.Theaveragepatternsforeach of the fourcategoriesareshowninfig.2. Each of these four mean composite patterns has been normalized by the mean NINO3.4 SST anomalies of each composite, which allows comparing the relative shape of each pattern against the shapes of the other patterns. Subsequently, the composites for negative events have been presented with revised signs for better comparison with the patterns of positive events. Note, that notalldatais represented bythefour categories, as data points with the SST anomaly of NINO3.4 near zero are not consideredinanyofthefourcategories.severalcombinationsofthedifferences between the mean patterns are shown as well to highlight the differences between positive vs. negative and strong vs. weak events. The following mean featuresshouldbepointedouthere: FollowingastudentsTZtestassumingevery2monthsareindependent, theeasternpolealongtheequatorissignificantly(9%confidencelevel) differentfromthezeronullhypothesisinallfourdifferencepatterns.the most significant differences are seen in Fig. 2c with all of the contoured

5 regions passing the 9% confidence level and the least significant differences are seen in Fig. 2h with only the eastern pole around the equatorpassingthe9%confidencelevel. Strong El Niño events are significantly shifted to the east and are more closelyconfinedtotheequatorthanstronglaniñaevents. Almost the exact opposite is true for weak events: weak El Niño events are significantly shifted to the west and have larger meridional extend thanweaklaniñaevents. The difference between strong and weak El Niño events is almost the sameasthedifferencebetweenstrongelniñoandstronglaniñaevents. The same holds for the difference between strong and weak La Niña events. Subsequently,themeanpatternofastrongElNiñoeventissimilartothe mean pattern of a weak La Niña event with the opposite sign, and the meanpatternofaweakelniñoeventissimilartothemeanpatternofa stronglaniñaeventwiththeoppositesign. All difference patterns have basically the same equatorial shifts and all strongly project onto the pattern of EOFZ2 (see Fig. b or Fig.2i and patterncorrelationvaluesinheadingsoffig.2). AsimilarselectionofENSOeventshasbeenmadebySunandYu[29],Yuand Kim [2] and Choi et al. [2]. Those results largely agree with those presentedhere,buttheirdiscussionfocusesondecadalensomodulations,while hereweliketofocusonthenonzlinearityoftheinterannualensovariability. The significant differences in the ENSO event types (e.g. strength or sign) basicallymeanthattheycannotbedescribedcompletelybytheevolutionofone pattern(e.g.eofz).astrongelniñoevent,forinstance,isasuperpositionofthe EOFZ pattern plus the EOFZ2 pattern and a strong La Niña event is a superposition of the EOFZ pattern with negative sign and the EOFZ2 pattern withpositivesign.thus,theeofz2hasanonzlinearcozvariabilitywiththeeofz :whenevertheeofzisinanextremephase(strongelniñoorstronglaniña) theneofz2ispositive.thisbehaviorcanbeseeninthetimeseriesofpczand PCZ2,seeFig.3.AllmajorstrongElNiñoevents(e.g.years973,983or997) have also positive PCZ2 values, mostly with relatively strong magnitudes. The sameholdsforallmajorstronglaniñaevents(e.g.years974,989or999). InturnthePCZ2tendstohavenegativevalueswhenthePCZisclosetoneutral values(z<pcz<).toquantifythiswecanbuildcompositesofthesixstrongest El Niño events and the six strongest La Niña events and look at the time evolution of the composite mean values of PCZ and PCZ2 relative to the Decemberoftheevents,seeFig.3bandc.WecanquiteclearlyseethatbothPCZ andpcz2peakduringstrongelniñoevents.thiscanalsobeseenforstrongla Niña events, but we can further notice that the strong La Niña events are precededbyelniñoeventsaboutayearearlier,whichwillbediscussedfurther insection4. ThisnonZlinearrelationbetweenthePCZandPCZ2canbestbeillustratedbya scatter plot of the time series of PCZ versus that of PCZ2; see Fig. 4a. Ifwe assume that the EOFZ and EOFZ2 modes represent independent modes of variability (as often done in the interpretation of EOFZmodes; e.g. Ashok et al. [27])withnearnormaldistributions,thenthescatterplotshouldbeacircular shapeclusterthatpeaksattheoriginofthecoordinatesystem.however,wecan

6 clearly see a skewed distribution. For extreme values of PCZ PCZ2 tends to be positiveandforpcz near zero PCZ2 tends to be negative, which is consistent withtheabovediscussionofthenonzlinear pattern and time series behavior. ThisnonZlinearrelationbetweenPCZandPCZ2canberelativelywellmodeled byaquadraticrelationship:!2!!!!#$%& (!) =! (!(!))! [] A fit of PCZ2 to this model is shown in Fig. 4a. The PCZ time series correlates with this nonzlinear model of PCZ2 relatively well (correlation.) and is clearly significantly different from the null hypothesis of zero correlation assumingastudentstztestwith6(eachyear)independentvalues(resultingtz value = 4.6 corresponding to the % value of the distribution). This quadratic relationship basically describes the results of Fig. 2, where we found that the difference between strong events of opposing signs is exactly the opposite of those of the weak events and the difference between strong and weakelniñoeventsisexactlytheoppositetothoseofthelaniñaevents.pcz2is positiveifpcztakeslargeabsolutevaluesanditisnegativeifpcztakessmall absolutevalues.thesuperpositionofpcz and PCZ2 then gives the effect of shiftedpeaksbetweenchangesofsignorchangesinmagnitude. We can test if this nonzlinear relationship between PCZ and PCZ2 can account for the nonzlinearity seen in the ENSO event composites in Fig. 2 by excluding this nonzlinear relationship from the data. To do so, we reconstruct the SST variabilitywiththe2leadingeofzmodes,butexcludethenonzlinearpartofpcz 2,!2!!!!#$%&, from the PCZ2 time series, resulting into a residual PCZ2 time series,!2!#$%&'(,definedas:!2!#$%&'(! =!2!!2!!!!#!# (!) [2] IfweapplythecompositeanalysisofFig.2tothereconstructeddata,usingthe!2!#$%&'(,wefindthemeanpatternsshowninFig..Wenowseethatallfour mean patterns are quite similar and the difference patterns are mostly insignificant,indicatingthatthenonzlinearrelationshipbetweenpczandpcz2, as formulated in eq.[], does indeed describe the nonzlinear patterns of ENSO events relatively well andthathigherordereofzmodes are to first order not neededtodescribethisphenomenon. ThedistributionofdatapointsinFig.4amainlyscattersaroundthenonZlinear function!2!!!!#$%&. It therefore seems reasonable to select ENSO events relative to!2!!!!#$%& (e.g. strong El Niño events are at the right end of the curve).however,westartedtheanalysisofthespatialpatternnonzlinearityby selectingensoeventsbynino3.4sstanomalyvalues(fig.2).thenino3.4sst indexisbasicallythesameasthepcz(seealsotakahashietal.[2])andthus follows the PCZ axis. Therefore, a selection of positive or negative, strong or weakensoeventswasdonebysplittingthedistributionalongconstantlinesof the PCZ axis in Fig. 4a (e.g. strong ElNiño events infig. 2a are essentiallyall values with PCZ>.), which cuts through the line of!2!!!!#$%& at a nonz orthogonal angle. This is not the optimal way to select the events, as the distribution is relatively wide in this direction. If we rotate thedistributionof Fig.4aby4 o counterclockwisewefindapresentationinwhichwecanselect

7 strongelniño(>onthenewyzaxis)andstronglaniñaevents(<zonthenew xzaxis) with lines of constant values of the new main axes and roughly orthogonaltothe!2!!!!#$%& curve,seefig.4b.thenewrotatedaxespcelzniño andpclazniñaareanorthogonalrotationofthepczandpcz2: PC!!!ñ$ = (PC + PC2)/ 2!;!!!!!PC!!!ñ$ = (PC PC2)/ 2 [3] Takahashietal.[2]definedthesamerotationbaseonsimilararguments.The patternscorrespondingtothepcelzniñoandpclazniñaareshowninfig.4candd. Due to the 4 o rotation both modes explain equal amounts (27%) of the total variance.theelniñopatternisclearlyshiftedtotheeastandmoreconfinedto theequatorthaneofz,whichisconsistentwiththediscussionofthecomposite nonzlinearityinfig.2.inturnthelaniñapatternisclearlyshiftedtothewest and much wider in its meridional extent than EOFZ. These patterns basically presentthenonzlinearspatialstructureofensoeventsinanoptimalway. ItisinterestingtocomparetheprobabilitydistributionsofPCElZNiño andpclazniña withthoseofpczandpcz2,seefig.4eandfandfig.candd.thefollowing pointsshouldbenotedhere: The PCZ and PCZ2 are both much closer to a normal distribution than PCElZNiño and PCLaZNiña, which is illustrated by the skewness and kurtosis values. Thecentrallimittheoremsuggeststhatdistributionsthatfollowanormal distribution are a sum of many processes adding up to the distribution. ThisinturnwouldsuggestthattheEOFZmodesaremorelikelytopresent some superposition of several processes than the PCElZNiño and PCLaZNiña modes as they are more normally distributed. The characteristic that EOFZmodestendtobesuperpositionsofmany physical modeshasbeen discussedinsomemoredetailindommengetandlatif[22]. InturnthestrongernonZnormalitypresentinthedistributionsofthePCElZ NiñoandPCLaZNiñamodesindicatesthatthesemodesaremorelikelytofocus onlowzorderspecificphysicalprocessesthantheeofzmodes. TheskewnessandkurtosisofthePCElZNiñoislargerthanthatoftheEOFZ andnino3sstanomalies.thusthepcelzniñoindexidentifiesmuchmore extremepositiveelniñoevents,thanthepczandnino3sstindices. The PCLaZNiña has a strong negative skewness, suggesting a strong nonz linearity towards extreme La Niña events that is not reflected in any of theconventionallarge scaleindicesofenso. In summary, we find that the nonzlinear spatial pattern of ENSO events is relativelywelldescribedbytherotationofthefirsttwopcsintothepcelzniñoand PCLaZNiña modes. This presentation gives a very good separation of extreme El Niño or La Niña events from moderate events or neutral conditions. For the subsequentanalysiswewillinmostcasesusethetworotatedmodestodefine extreme events, as they are the dynamically better presentations. Note, that weakeventscannotbeselectedbytherotatedmodesverywell,astheywouldbe mixed up between the PCElZNiño and PCLaZNiña modes (compare Fig.4 a and b). However,mostofthefollowingcompositeswillonlyshowminorchangesifthe selectionsarebasedonnino3.4sstorpczindices.

8 Observed!Feedbacks! In the following analysis we want to explore the time evolution and feedbacks relatedtoextremeensoeventstogainsomeunderstandingofwhatcausesthe nonzlinearitiesintheevents.themainfeedbacksassociatedwithensoarethe Bjerknesfeedbacks,whichdescribeinteractionsbetweenzonalwindstress,SST andthedepthofthethermocline.sincethefeedbackscontroltheevolutionofthe eventsitisinstructivetoanalyzethelagzleadtimeevolutionofeventcomposites. As a starting point we analyze the lagzlead time evolution of the equatorial Pacific SST for strong and weak ElNiño and La Niña events, see Fig. 6. A few characteristicscanbenotedhere: First of all near lag (in Fig.6aZc) we find the same characteristic eastz westshiftbetweenstrongelniñoandlaniñaeventsasinfig.2.thusat lagzerothisfigureisbasicallyanotherwayofpresentingthesamespatial asymmetryasinfig.2. The same holds for the eastzwest shift of the weak events, but just with theoppositesign.notethattheweakeventsareselectedbypcz,asthe rotatedpcsarenotusefulforselectingweakevents.seediscussionabove. The most interesting aspect in the lagzlead time evolution of the strong eventsisthesignificantnonzlinearityataboutoneyearbeforeandafter theevent(december).thelaniñaeventsataroundoneyearafterstrong ElNiñoeventstendtobestrongerthanthosepreceding.Whereasinturn stronglaniñaeventsarenotfollowedbyelniñoeventsoneyearlater. Further, a strong La Niña event is preceded by a significant El Niño anomalyintheeasternequatorialpacific,whereasstrongelniñoevents do not have such a significant preceding La Niña anomaly. The time evolutiondifferenceinthenino3.4regionbetweenzmonbeforeand after lag is statistically very significant (>>99% value of the tztest distribution). This was also indicated in the PCs mean composite time evolutions shown in Fig. 3b and c. The asymmetric time evolution described here is in good agreement with similar findings of Ohba and Ueda[29]andOkumuraandDeser[2]. Theoppositetimeevolutionwefindfortheweakevents.HereaweakLa Niña event is followed by a significant El Niño anomaly a year later, whereasinturnweakelniñoeventsarenotfollowedbylaniñaevents. Insummary this lagzlead time evolution of the ENSO events suggests that the driving mechanisms for El Niño andla Niña events are different. The fact that strong La Niña events tend to follow an El Niño event, could suggest that the strong La Niña events are triggered partially by the ocean state set by the precedingelniñoevent.inturnnosuchpresetoceanstatemayexistforstrong ElNiñoevents,whichinturnwouldsuggestthatstrongElNiñoeventsmightbe forcedbyrandomatmosphericforcingsthatmaybeunpredictable.theopposite mayholdforweakevents. Before we look at the elements of the Bjerknes feedbacks we first examine the atmosphericevolutionduringstrongevents.themeansealevelpressure(slp) is, to first order, a good estimator of the atmospheric evolution during strong ENSOevents,seeFig.7aZc.WecanroughlyseethatthenonZlinearitiesintheSLP compositesfollowthemainpatternofthesstnonzlinearities:thelowpressure is shifted to the east roughly inlinewiththesstshiftandthestrongelniño events are followed by a positive SLP anomaly about a year later, again in line

9 withthesstevolution.furtherwefindthattheslpanomaliesprecedingstrong El Niño events for a few months are stronger in amplitude than those of the strong La Niña events, again being consistent with the idea that the strong El Niñoeventsmayhavebeenforcedmorestronglybyatmosphericforcingsthan stronglaniñaevents. More important for the understanding of the ENSO forcing is the zonal wind stressrelationtosst,whichisoneelementinthebjerknesfeedbacks.thezonal wind composites again show some significant nonzlinearities, see Fig. 7dZf. The followingshouldbenotedhere: AtaroundlagzerowefindaneastZwestshift,byabout2 o,inthesame direction as the SST peak shifts. During strong El Niño events the westerly zonal wind anomalies are shifted to the east and are more pronouncedoverthewholeoftheequatorialpacificeastofthedateline. ThisbasicstructureofobservednonZlinearityinthezonalwindshasalso beendescribedinkangandkug[22]andohbaandueda[29]. As in the SST and SLP evolution we also find that the zonal wind anomalies priortothepeakofstrongel Niño events are stronger(per NINO3.4 SST anomaly) than in the strong La Niña events. In particular around the dateline and west of it. Indeed the peak of the zonal wind responseisabouttwomonthsearlier. Again the zonal winds show a reversed anomaly about a year after strongelniñoeventsinlinewiththesstanomalies,indicatingachange tolaniñaconditionsafterstrongelniñoevents. WhilethezonalwindsshowaclearnonZlinearitybetweenstrongElNiñoandLa Niña events, we cannot yet conclude whether the zonal winds are a forcing or response to the SST. Thus it is unclear whether the nonzlinearityinthezonal winds is a response to the different SST patterns or whether the zonal winds cause the differences in the SST patterns. However, studies of Zhang and McPhaden[26and2]givesomesupportfortheideathattheshiftsinthe zonalwindresponsewouldsupporttheshiftsinthesstpatterns.theyfindthat thesstintheeasternequatorialpacificissensitivetothelocalwindsaswell, with weakening of the zonal winds leading to warming of the SST, thus supporting the eastward shift during strong El Niño events. Some indications about cause and response will also be discussed later in the analysis of the simplifiedmodelsimulations(section6),butfornowwefocusonpresentingthe nonzlinearitiesintheobservedbjerknesfeedbacks. ThesecondelementoftheBjerknesfeedbackisthethermoclinedepthsensitivity tozonalwindstress;seefig.7gzi.notethatunlikethepreviouscompositesthe composites of thermocline depth anomalies are normalized by the mean zonal windanomaliesinthecentralpacific(6 o Eto2 o W)andnotbytheNINO3.4 SST anomalies, as we are interested in the sensitivity of thermocline depth to zonalwind,notsst.someimportantnonzlinearitiescanbenotedhere: As for the zonal wind, we find a west to east shift in the thermocline anomalies by about 2 o, which is however much further to the eastern side of the Pacific than in the zonal wind, as this is the region with the peakinthethermoclineresponse. Alsoinlinewiththepreviousfindingswefindsomeindicationofachange in sign in the thermocline anomalies following about one year after a

10 strong El Niño event. Again indicating La Niña conditions following the strongelniñoevents. In contrast to the SLP and zonal wind response, which are weaker for strong La Niña compared to strong El Niño events, wenowfinda weak indication of a stronger thermocline depth anomaly for strong La Niña eventsthanforstrongelniñoevents.averagedoverthewholeeq.pacific thethermoclinedepthanomaliesprecedingthestronglaniñaeventsby aboutuptoayeararemorepronouncedthanforstrongelniñoevents. ThisresultismostlyconsistentwithasimilarfindingbyOhbaandUeda [29] using the SODA ocean reanalysis data for the period 94Z24 [Cartonetal.,2]. Insummary,wefindsomeindicationsthatthezonalwindsprecedingstrongEl Niño events are stronger than during strong La Niña events. Further, we find someweakindicationsthatthethermoclineresponsetozonalwindsinstrongla Niña events is stronger than in strong El Niño events. Both findings are consistentwiththeideathatstronglaniñaeventsaremorestronglyforcedby the ocean state than strong El Niño events, which are more strongly forced by theatmosphere CMIP3!Model!simulations! Theanalysisofobservationsislimitedinquantityandquality.Someoftheabove results are only marginal significant and model simulations can therefore provideadditionalindependentverifications.further, theunderstandingofthe processesinvolvedincomplexinteractionsofensoismucheasierachievedwith modelsimulationsaselementsofthemodelscanbetakenapart.however,ithas tobenotedthatthestateoftheartcoupledgeneralcirculationmodels(cgcms) arefarfrombeingperfectinsimulatingenso.mostcgcmsarequitelimitedin theirskillsofsimulatingmainaspectsoftheensomode.inparticularthenonz linearaspectsofenso(e.g.skewnessandkurtosis)arequitebadlyrepresented in most climate models [e.g. An et al., 2 or van Oldenborgh et al., 2]. Indeed,mostCMIP3modelsarenotcapableofsimulatingthepositiveskewness of ENSO (e.g. NINO3 SST index). Therefore it seems likely that most CMIP3 models will also have problems in simulating the observed nonzlinear ENSO patternevolutionsthatwehavedescribedabove. In order to quantify to what extent the CMIP3 models can simulate the asymmetrybetweenelniñoandlaniñapatternandtimeevolutionwedefined twoindicesbasedonthecompositedifferencesalongtheequator,δeq,$andinthe time evolution, Δtime. The index Δeq is defined as the difference between the eastern equatorial Pacific (22 o EZ28 o E/ o SZ o N) and the western equatorial Pacific(4 o EZ2 o E/ o SZ o N)inthenormalizedcompositedifferenceasshown in Fig. 2c and the index Δtime is defined as the difference between the mean NINO3.4SSTanomaliesforleadtimesof2montomonminusmeanNINO3.4 SST anomalies for lag times of to 2mon as shown in the normalized composite difference Fig. 6c. The events are selected by the NINO3.4 index insteadofvaluesoftherotatedpcs,asthesearenotdefinedforallthemodels. FortheobservationsweusedtheKintheNINO3.4indexforselectionofstrong events in Fig. 2, which corresponds to about.2 standard deviations of NINO3.4. Since the models standard deviations of NINO3.4 index are very

11 differentinthedifferentmodelswealsouse.2standarddeviationsofnino3.4 ofeachmodelasathresholdinsteadofthekthreshold. For the two observational data sets Δeq,$ is about. and Δtime about.4 (both indicesin[k]per[k]inthenino3.4index).infig.8weplottedthevaluesforall 24CMIP3modelsinthe2 th centurysimulationsandtheobservations.wesee that for most models the Δeq value fluctuates around zero, with 8 models even showing negative signs in Δeq, indicating strong El Niño events with larger amplitudes further to the west compared to strong La Niña events. The asymmetryinthetimeevolutionisbetterrepresentedinthemodels,withmost models showing the same behavior (La Niñas following strong El Niños or El Niños preceding strongla Niñas). Overall the distribution of the models tends into the direction of the observed asymmetries, but only 4 models (GFDL 2., GFDL2.,IPSLandtheMPI)aresimulatingbothasymmetriesrelativelywell.Yu andkim[2]didasimilarselectionofthecmip3models(excludingthempi model) based on differences along the equator only. They additionally selected themiubandcnrmmodels,whichinourselectioneitherdidnotpasstheδtime criteria(miub)orweretoosmallintheδeqcriteria(cnrm).thecnrmmodel, however, does show all of the features that we discussed for the observations and the selected models below. Ohba et al. [2] also did analysis of the asymmetric time evolution of the CMIP3 models. They come to similar conclusionsandtheiranalysisalsoshowedthatthegfdl2.,gfdl2.,ipsland thempishowsomeasymmetrictimeevolutionconsistentwiththeobservations. Thefactthatmostmodelsfailourselectioncriteriafirstofallindicatesthatmost modelsarenotcapableofsimulatingtheensopatternandtimeevolutionnonz linearity realistically. However, the set of 4 models seems to have some capability in simulating this characteristic. In the following we will focusthe analysis on these 4 models. We therefore treat the 4 models as one data set: defining anomalies for each of the models individually relative to the 2 th centurysimulationslineardetrendedclimatologicalmeanvaluesandcombining theanomaliesofthe4modelstoonedataset.however,weanalyzedeachofthe 4 models individually and found that the characteristics discussed below are significantinallmodels. The two leading EOFZmodes (not shown) of the combined data set are very similar to those observed (Fig. ). In particular the EOFZ2 mode has a very similareasttowestdipolealongtheequatorwiththewesternpoleextendingto the northern (more pronounced) and southern (less pronounced) subtropics. The EOFZ appears to be slightly more pronounced in the CMIP models (46% explainedvariance)andtheeofz2issignificantlyweaker,withexplainingonly 7%(itwas%intheobservations)ofthetotalvariance. The differences in the strong El Niño vs. La Niña composites(as defined in the analysisforfig.2,butnotshown)arenotaspronouncedasintheobservations (see distribution along the xzaxis of Fig. 8) and are stronger in the western Pacificwarmpoolregionandmuchweakerintheeasternequatorialandcoastal coldtongueregion.thedifferencesalsodoprojectontheeofz2ineachofthe4 models separately, but correlation values are significantly lower than observed (.92) ranging from.2(ipsl) to.64(gfdl 2.) and the combined ensemble datasethasacorrelationvalueof.6. AnalogtotheobservationswecantakeacloserlookatthenonZlinearinteraction betweenthepcz and PCZ2, see Fig. 9a. The distribution is quite similar to the

12 observed,withasimilarsignificantnonzlinearrelationbetweenpczandpcz2. ForextremevaluesofPCZPCZ2tendstobepositiveandforPCZnearzeroPCZ2 tends to be negative, which is consistent with the observations. Again the nonz linearmodelofeq.[]describesthisnonzlinearityrelativelywell(correlationof.3), but not as good as in the observations. Overall the set of 4 models remarkably reproduces the observed nonzlinearinteractionbetweenpcz and PCZ2,whichisastrongsupportforadynamicalcauseforthisrelationship. AgainwecanrotatethedistributionofFig.9aby4 o counterclockwise,asfor theobservationsinfig.4b,tobetterhighlighttheextremeelniñoandlaniña events(fig.9b).thefollowingcanbenotedhere: As in the observations the models find very strong nonznormal distributions for both PCElZNiño and PCLaZNiña, which is illustrated by the skewnessandkurtosisvaluesshown(fig.9ezf). The PCElZNiño has a quite significant positive skewness, but an even more significant kurtosis, highlighting the much larger probability of extreme eventsthanexpectedfromanormaldistribution. ThePCLaZNiñadistributionhasagainaquitesignificantnegativeskewness, suggestingastrongnonzlinearitytowardsextremelaniñaeventsthatis notreflectedinanyoftheconventionallargezscaleindicesofenso. ThepatternsassociatedwiththePCElZNiñoandPCLaZNiña(Fig.9cZd)showthe sameeasttowestshiftalongtheequatorasobserved;againsupporting theideathatstrongel Niño events are further to the east and more confinedtotheequator,andstronglaniñaeventsarefurthertothewest andhavealargerlatitudinalextent. BasedontherotatedPCElZNiñoandPCLaZNiñawecandefinethemeantimeevolution ofcompositesofstrongelniñoandlaniñaeventsinanalogtotheanalysisof the observations (Fig. 6aZc). Themodel results shown in Fig. azc are quite similar to those of the observations: again at lag zero we find the equatorial dipole, but as mentioned above more pronounced in the western part. Even morepronouncedthanintheobservationswefindthatstrongelniñoeventsare followedbylaniñaeventsandstronglaniñaeventsareprecededbyelniño events.thisagainindicatessomeasymmetryinthedrivingforcingofstrongel NiñoandLaNiñaeventsinthesefourmodels. The asymmetry in the Bjerknes feedbacks in the four models is shown in Fig. dzi.asintheobservationswefindtheasymmetriesinthezonalwindresponse to SST anomalies and in the relationship between zonal wind and thermocline depthanomalies.thelaterisinparticularmorepronouncedinthemodelsand marksaverystrongnonzlinearityinthefeedbacksofstrongelniñoandlaniña events. In summary the set of four CMIP3 models finds nonzlinear dynamics between strongelniñoandlaniñaevents,thatareverysimilartothoseobserved.this supports the observed findings and suggests that the main processes causing thesenonzlinearitiesaresimulatedinthosefourmodels ENSO!in!a!simplified!model:!The!RECHOZ!model!! Simplified models of ENSO help to deconstruct the elements of the ENSO dynamics and therefore help to better understand the interactions. In the following we use the ENSO recharge oscillator model after Burger et al.[2]

13 coupled to a fully complex atmospheric GCM from Frauen and Dommenget [2]inayrslongsimulation(herenamedRECHOZ).TheRECHOZmodel simplifies the ocean dynamics to a2zdimensional linear interaction between NINO3 SST and equatorial Pacific mean thermocline depth anomalies. The SST patterninthetropicalpacificisbyconstructionthefixedpatternoftheobserved EOFZ.ItthushasonlyonedegreeoffreedominthetropicalPacificSSTandno spatial pattern asymmetry (e.g. eastztozwest)ofensoeventscanexistinthis model.theanalysisoffrauenanddommenget[2]showedthattherechoz model,despiteitssimplicity,hasrealisticskewnessandseasonalityofensoand arealisticstandarddeviationandpowerspectruminthenino3sstindex.the factthattheoceandynamicsarelinear,ofveryloworderandwithoutanyspatial degreesoffreedomsimplifiesallnonzlinearitiesthatthismodelproducestononz linearities caused by the atmospheric heat fluxes and zonal wind stress. Therefore,themodelhelpstoexplorehowtheatmosphericnonZlinearfeedbacks contributetotheensopatternandevolutionnonzlinearities. Further, the model is coupled to a simple single column mixed layer ocean outsidethetropicalpacifictoallowforsstvariabilityindependentofensoand also in response to ENSO dynamics. We will analyze an additional yrs sensitivityexperiment,inwhichwesetthesstinthetropicalindianandatlantic OceanstoclimatologytoexploretheinfluencethatSSTforcingfromoutsidethe tropicalpacificmayhaveontheensononzlinearity. The simplicity of the model further allows us to compute a very large set of perfectmodelforecastensembles.wethereforerestartedthecoupledmodelat thefirstofjanuaryatdifferentyears,eachstartdateyearsapartfromeach other. For each restart we computed a set of four ensemble members for a 2 monthslongforecast,witheachmemberstartingfromslightlyperturbedinitial SSTconditions. First,wetakealookatthenonZlinearityinthetimeevolutionofENSOeventsin the RECHOZ control simulation. The time evolutions of strong El Niño and La NiñaeventsintheRECHOZmodelareshowninFig.aZc.Sincethepatternof ENSOeventsintheRECHOZmodelisbyconstructionfixed,thedifferenceinthe SST composites is by construction zero along the equator at lag zero. So by constructionnoeastztozwestasymmetryofensoeventscanexistinthismodel. TheonlynonZlinearityintheSSTthatcouldexistintheRECHOZmodelisinthe time evolution of the events. Indeed we can see that some significant nonz linearitybetweenthetimeevolutionofstrongelniñoandlaniñaeventsexist: As in the observations a strong El Niño event is followed by a La Niña event aboutoneyearlaterandastronglaniñaeventisprecededbyanelniñoevent. Since the RECHOZ model has by construction no nonzlinearitiesintheocean dynamics, the results suggest that the asymmetric time evolution of the strong ENSOevents is at least partially caused by nonzlinearities in the atmospheric forcings. TheSLPanomaliesperunitSSTNINO3anomalyinthestrongElNiñoevents(not shown) are much stronger than those of the strong La Niña events, which is in the overall tendency similar to the observations (Fig. 7aZc). The zonal wind evolution shows a similar nonzlinearitybetweenstrongel Niño andla Niña events.sincethesstpatternisbyconstructionalwaysthesameintherechoz model, we can from this shift in the zonal winds clearly conclude that the atmosphererespondstothepositivesstpatternmorestronglyandmoreshifted

14 totheeast.followingthestudiesofzhangandmcphaden[26and2],the shifted wind response would support the nonzlinearity in the observed SST patterns.frauenanddommenget[2]furthershowedthatthisnonzlinearity inthezonalwindresponseisindeedsufficienttoexplaintheskewnessofenso intherechozmodelandisofsimilarstrengththanthatobserved. The thermocline depth in the RECHOZ model is just one scalar number for the whole of the equatorial Pacific. Subsequently, the RECHOZ model equivalent analysis to the observed (Fig. 7gZh) or CMIP model (Fig. gzh) thermocline depth evolution during strong events is not a Hoevmoeller diagram, but is just the equatorial mean thermocline depth evolution as function of different lead times,seefig.2azb.again,wefindthesameasymmetryintherechozmodel as in the observations: strong La Niña events have a much more pronounced thermoclinedepthanomalyprecedingtheevent,whereasstrongelniñoevents developastrongnegativethermoclinedepthanomalyaftertheeventleadingto thefollowinglaniñaconditions. Frauen and Dommenget [2] found that the nonzlinear behavior in the RECHOZ model can essentially be reduced to the nonzlinear response of the zonalwindstresstosstanomalies.theyillustratedthisbyforcingtherecharge oscillator equations with random white noise and by assuming a nonzlinear response of the zonal wind stress to SST anomalies (we refer to this model as REOSCZMC).TherechargeoscillatorequationsofFrauenandDommenget[2] aretwotendencyequations,oneforthenino3sstanomaly,t,andoneforthe meanequatorialthermoclinedepthanomaly,h,givenby:! =!!!!! +!! ℎ +!!! +!!!!!!!!!ℎ =!!!! +!!! ℎ +!!!!!!!! 2! TheforcingsbythenetatmosphericheatfluxovertheNINO3region,f,andthe zonal wind stress over the central Pacific region (6EZ4W, 6SZ6N), τ, are assumed to have one component that is a simple relationship to T$ and the remainingcomponentsarerandomnoiseforcings,ξandξ2:! =!!! +!!!!!!! 3 Forτtheyassumedeitheralinearorquadraticrelationship:! =!!! +!!!!!!! 4!! =!!!! +!!!! +!!!!!!! All parameters of the REOSCZMC model were estimated from observations or modelsimulations,seefrauenanddommenget[2]fordetails.ifthismodel!!!!!!!!!#$!!!,! =!!! =.62!!#$!!,!! =.23!#$!!!!,!! 6.2!!!! 2.2!!#$!!!!!,!!! =.84!!!#$!!,!!! =.2!#$!!,!! 2.9

15 isintegratedwiththelinearrelationbetweensstandzonalwind(eqs.z4)we getalinearmodelwithnoasymmetries,seefig.2czd.however,ifthereoscz MC model assumes the quadratic relationship (eq. ), than we basically reproduce the nonzlinear time evolution between strong El Niño and strong La Niña events in the RECHOZ model, see Fig. 2. Thus the nonzlinear time evolutionintherechozmodelcanbesimplifiedtoanonzlinearresponseofthe zonalwindstresstonino3sstanomalies. IntheanalysissofarwenotedthatstrongLaNiñaeventshavemorepronounced ocean state anomalies and less pronounced atmospheric anomalies preceding the peak phase, indicating that they may be more forced by the ocean. In turn strongelniñoeventsappeartobemoreatmosphericallyforced.sincetheocean state is in general more persistent and therefor more predictable than the atmosphericstate,itseemsreasonabletoassumethatstronglaniñaeventsmay bebetterpredictablethanstrongelniñoevents. We can test this idea with the large set of forecasts in the RECHOZ model simulations.infig.3weseetheanomalycorrelationskillsforthenino3sst anomalies up to a forecast leadztime of 2 months for forecasts starting at the firstofjanuary.firstofallwecannotethattheanomalycorrelationskillofall forecasts drops relatively sharply in April due to the spring predictability barrier. We created two subsets of forecast ensembles to highlight the differencesinpredictabilityforstrongelniñoandlaniñaevents.weselected allthoseforecastsinwhichthecontrolnino3sstanomalyatleadtimesof2 months after the start date of the forecast (December) is larger than one standard deviation (strong El Niños) and smaller than minus one standard deviation(stronglaniñas).theanomalycorrelationskillofthestronglaniña eventforecastsisclearlylargerthantheoneofthestrongelniños,illustrating thatstronglaniñaeventsatleadtimeof2monthsaremuchmorepredictable intherechozmodelthanstrongelniñoevents. ENSO events influence remote regions, such as the tropical Indian or Atlantic Oceans.InturnthetropicalIndianOceanandAtlanticOceanprovideafeedback ontotheensodynamics.itseemsreasonabletoassumethatsuchfeedbacksmay contributetothenonzlineardynamicsofenso.inparticularohbaandwatanabe [22] argue that the asymmetric time evolution of ENSO events is at least partially caused by the interaction with the Indian Ocean. To estimate such feedbacksfromthetropicalindianoceanandatlanticoceanwecanrepeatthe aboveanalysis(fig.)inthesensitivityexperimentwherethetropicalindian andatlanticoceanssstvariabilityisdecoupled(fixedtoclimatologicalvalues), seefig.4.werefertothissimulationasrechozzpaco. FirstofallwecannoteinFig.4aandbthattheeventslastlonger.Thisisin agreement with similar studies that also find that the coupling of the Indian and/or Atlantic Ocean leads to shorter period in ENSO variability and also to a damping of the variability [e.g. Kang and Kug, 22, Dommenget et al., 26, Jansen et al., 29 and Frauen and Dommenget, 22]. IntheRECHOZZPACO simulation the decoupling of the tropical Indian and Atlantic Oceans shifts the period of ENSO from about 3yrs to about 4yrs and increases the NINO3 SST!!!!!!#$!!,!!! =.4!!!,!!#$!!!!! =.!!!!,!!!!#$!!!!!! = 8.!!!,!!!!#$!!!!!! = 9.9!!!!!!#$!!!!

16 standarddeviationbyabout6%.however,moreimportantforthisstudyisthe asymmetryintheevolutionofstrongelniñoversusstronglaniñaevents.this aspectisessentiallyunchanged(comparefig.cwithfig.4c),indicatingthat thenonzlinearevolutionoftheensoeventsistofirstordernotaffectedbythe coupling to the other tropical oceans in the RECHOZ model. This apparent mismatch to the finding Ohba and Watanabe[22] may be related to the fact that the RECHOZ model does not allow for changes in spatial pattern of ENSO events, which may indeed be important to explain the different sensitivities to theindianoceanfeedbacks El!Niño!Modoki! In recent years several publications have argued for different types of El Niño events,callingthemcentralpacificormodokielniño[e.g.ashoketal.,27or Kao and Yu, 29]. The authors basically argue that these different types of ENSO events happen independent of each other (unrelated) and would be controlledbydifferentkindofdynamics.thedefinitionoftheseelniñotypesis projecting on both EOFZ and EOFZ2 and therefore overlaps withdefinitionsof the rotated PCElZNiño and PCLaZNiña introduced in this study. It is therefore instructivetodiscusshowthesedefinitionsofensotypesrelatetothepresent analysis. A similar discussion is also given in Takahashi et al. [2]. A few pointsshouldbenotedheretoputthecentralpacificormodokielniñotypeof definitionsintotheperspectiveonthenonzlinearityofenso: Ashoketal.[27]motivatedthedefinitionoftheElNiñoModokionthe basis of the EOFZ2. They argue that since the eigenvalue of EOFZ2 is statistically well separated from the other eigenvalues it can be considered as a mode of variability independent from EOFZ. This simplistic interpretation of EOF modes is indeed problematic, as discussedindommengetandlatif[22].individualeofmodescannot bediscussedindependentlyoftheothereofmodes,wehavetoconsider that the SST variability is a high dimensional multivariate stochastic process and the EOF modes are a representation of it, see Dommenget [27] for a discussion. In section 3 we have demonstrated that a significantfraction(26%ofthetotalvariance)ofeofz2canbelinkedto the variability of EOFZ. However, it needs to be noted that the largest fraction of EOFZ2 is unrelated to this relationship. This means that a significant part of the variations in the pattern of ENSO events remains. Whether these variations are purely random, following, for instance, a spatial red noise process as described in Dommenget [27], or are linked to another lowzorder mode of variability is unclear from the analysispresenthere,inashoketal.[27]orinkaoandyu[29]. The definition of El Niño Modoki or central Pacific El Niños is roughly identicaltothepclazniña.itthusstronglyprojectsonthelaniñapattern. Since the distribution ofpclazniña is strongly negatively skewed, extreme positive events are essentially not observed. Thus El Niño Modoki or centralpacificelniñoseventswillalwaysfallintothecategoryofweakel Niñoevents.ModokiorcentralPacificElNiñosareunlikelytobestrong events.sincethepclazniña(elniñomodoki)distributionisdominatedby the extreme negative events (La Niñas) and not by positive events (El

17 Niño Modoki), linear regression analysis based on El Niño Modoki or centralpacificelniñosindices(roughlypclazniña)isessentiallyananalysis oflaniñaeventsbutwiththesignreversed. IfwesimplifyENSOtoonefixedpattern(EOFZ),wecanroughlydescribe itbyalinear(normallydistributed)behavior(seefig.c).incontrast,if wefocus on spatial variations of the ENSO patterns, such as the El Niño Modoki, central Pacific El Niño indices (roughly PCLaZNiña) or the discussionwehavepresentedintheaboveanalysis,thennonzlinearities (nonznormaldistribution)becomedominant(asillustratedbyfigs.2,4or )andareindeedcentraltotheunderstandingofthedynamics. Most CMIP3 models are quite bad in simulating the nonzlinearities of ENSO, in particular the pattern and time evolution nonzlinearities. Subsequently, analyses of the CMIP3 models El Niño Modoki or central Pacific El Niño indices for present or future climate change are quit limitedinskill,asitisveryunclearwhetherornotthebulkofthemodels in the CMIP3 database are capable of simulating the appropriate nonz lineardynamicsoftheelniñomodokiorcentralpacificelniñoindices Summary!and!Discussion! In this study we analyzed the observed nonzlinearity in the ENSO SST pattern and time evolution. Some of the observational findings were only marginally significant, but were backed up with additional support from state of the art CGCM simulations. Some insight into the feedbacks causing the observed nonz linearities were based on observational evidence and state of the art CGCM simulations, but most insight were gained by the analysis of the strongly simplifiedhybridcoupledrechozmodeloffrauenanddommenget[2].the main findings of this study can be summarized and discussed by the following points: The observed ENSO events have some significant nonzlinearity in their spatialsstpatternbetweenpositive(elniño)vs.negative(laniña)and strongvs.weakevents.strongelniñoeventsareshiftedtotheeastand are more closely confined to the equator than strong La Niña events, whicharemoreshiftedtothecentralequatorialpacificandarewiderin their meridional extend. The opposite holds for weak El Niño events, which are more shifted to the central equatorial Pacific and are wide in their meridional extend, whereas weak La Niña events are more like strong El Niño events with opposite signs and weaker. Thus they are moreeasterlyandmoreconfinedtotheequator.inturneastpacificenso eventsaremostlystrongelniñoandweaklaniñaeventswhilecentral PacificeventsaremostlystrongLaNiñaandweakElNiñoevents. This has important implications for the teleconnections of ENSO events, whicharelikelytofollowsomeofthesenonzlinearities.hereithastobe notedthatmoststudiesanalyzetheimpactofensoeventsinacanonical way,assumingalinearrelationbetweenpositivevs.negativeandstrong vs. weak events. Thus they describe ENSO by one impact pattern. However, ENSO impact studies should distinguish between the positive vs. negative and strong vs. weak categories and describe the impact of