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Nonlinear Northern Hemisphere winter atmospheric response to ENSO Wu, Aiming; Hsieh, William W. 2004-01-16

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The nonlinear Northern Hemisphere winter atmospheric response toENSOAiming Wu and William W. HsiehDept. of Earth and Ocean Sciences, University of British Columbia, Vancouver, B.C., CanadaReceived 21 October 2003; revised 5 December 2003; accepted 17 December 2003; published 16 January 2004.[1] A nonlinear projection of the tropical Pacific seasurface temperature anomalies (SSTA) onto the NorthernHemisphere winter 500-mbar geopotential height (Z500)by a neural network reveals asymmetric atmosphericpatterns associated with El Nin˜o and La Nin˜a. While thelinear response of Z500 to tropical Pacific SSTA islargely confined over North Pacific and North America,the nonlinear response, mainly a quadratic response to theSSTA, reveals that regardless of the sign of the SSTA,positive Z500 anomalies are found over the central-eastern North America, North Atlantic and westernEurope, and negative Z500 anomalies over the westcoast of North America, Scandinavia and easternEurope—consistent with the positive Pacific-NorthAmerica (PNA) teleconnection pattern and the positiveNorth Atlantic Oscillation (NAO) pattern beingexcited. INDEX TERMS: 1620 Global Change: Climatedynamics (3309); 3339 Meteorology and AtmosphericDynamics: Ocean/atmosphere interactions (0312, 4504); 3309Meteorology and Atmospheric Dynamics: Climatology (1620).Citation: Wu, A., and W. W. Hsieh (2004), The nonlinearNorthern Hemisphere winter atmospheric response to ENSO,Geophys. Res. Lett., 31, L02203, doi:10.1029/2003GL018885.1. Introduction[2] The climate of the tropical Pacific is dominated by anirregular interannual fluctuation known as the El Nin˜o-Southern Oscillation (ENSO), where a warm episode iscalledanElNin˜o, and a cold episode, a La Nin˜a. Theclassicalparadigmthattheextratropicalatmosphererespondslinearly to opposite phases of ENSO via teleconnection[Wallace and Gutzler, 1981] has been questioned by recentevidence from climate statistics and numerical models,suggesting that the global atmospheric response to thetropical Pacific sea surface temperature (SST) anomalousforcing is inherently nonlinear [Hoerling et al., 1997, 2001;Sardeshmukh et al., 2000; Hannachi, 2001; Wu et al., 2003].The North America winter climate response to ENSO showsaneastwardphaseshiftofthecirculationanomalies(byabout35C176) between the composites of warm ENSO episodes andthe composites of cold episodes, with the two wave trainsmanifesting different tropical origins [Hoerling et al., 1997].Composites of observed surface air temperature and precip-itationanomalyoverNorthAmericaduringElNin˜oyearsarealso not exactly anti-symmetrical to those during La Nin˜ayears [Shabbar et al., 1997; Montroy et al., 1998]. Pozo-Va´zquez et al. [2001] mentioned that, in the North Atlanticarea, no statistically significant sea level pressure (SLP)anomalypatterns werefoundassociated withwarm episodes,while during cold episodes a statistically significant SLPanomaly pattern resembling the positive phase of the NorthAtlantic Oscillation (NAO) [Hurrel, 1995] was found, sug-gesting a nonlinear association between the Euro-Atlanticclimate and ENSO.[3]IfxdenotesanENSOindex,andifyistheextratropicalatmospheric response to ENSO, how does one derive thenonlinear response function y = f(x)? A linear f is easilyobtained by regressing the atmospheric variables upon anENSO SST index, yielding atmospheric spatial patternsassociated with the SSTA [e.g., Deser and Blackmon,1995]. In this linear projection of the ENSO index to theatmospheric variables, the atmospheric patterns during ElNin˜o are by definition strictly anti-symmetrical to thoseduring La Nin˜a. Composite analysis computes the atmo-spheric patterns by averaging the data over the years whenwarm episodes occurred, and averaging over cold episodes.While the patterns during warm and cold episodes are notforced to be anti-symmetrical, composite analysis does notyield a nonlinear response function. ‘‘One-sided linearregression’’, which calculates the linear regression betweenall occurrences of one sign of the SST index and thecorresponding response variable [Hoerling et al., 2001], fitsto an f(x) forced to be linear for x > 0 and for x < 0 —a veryrestrictive class of nonlinear functions. Nonlinear canonicalcorrelation analysis (NLCCA), a newly developed techniqueusing neural networks (NN) [Hsieh, 2001], has been appliedto the observed SSTand an ensemble of atmospheric generalcirculation model (AGCM) simulations [Wu et al., 2003],whereasymmetriesoccurredbetweenElNin˜oandLaNin˜ainthe nonlinear mode for both the SST and atmosphericanomaly fields. The disadvantage of the NLCCA is that ittrains three NNs separately and has a rather large number ofmodel parameters, which requires many samples to obtainrobust results when trying to extract weak signals. In short,extracting the general nonlinear response function of theatmosphere to ENSO has so far been elusive.[4] Inthepresentwork,anonlinearprojectionoftheENSOSST index to the Northern Hemisphere winter (November toMarch) 500-mbar geopotential height (Z500), via a NN, isused to obtain the nonlinear response function f(x), and thenonlinearZ500anomalypatternsassociatedwithENSO.TheSST index used is the leading principal component (PC) ofthe winter SSTA over the tropical Pacific.2. Data and Methodology[5] The monthly Z500 data from January 1950 to March2003 with 2.5C176 by 2.5C176 resolution were obtained from theNational Centers for Environmental Prediction (NCEP)GEOPHYSICAL RESEARCH LETTERS, VOL. 31, L02203, doi:10.1029/2003GL018885, 2004Copyright 2004 by the American Geophysical Union.0094-8276/04/2003GL018885$05.00L02203 1of4reanalysis datasets at the NOAA-Cooperative Institute forResearch in Environmental Sciences (NOAA-CIRES) Cli-mate Diagnostic Center [Kalnay et al., 1996]. Anomalieswere calculated by subtracting the monthly climatologybased on 1950–2002 period. Data over the NorthernHemisphere (20C176N to the North Pole) and during the winterseason (November–March) were used, thus the total num-ber of months was 268. After removing the linear trend andweighing the anomalies by the square root of the cosine ofthe latitude, principal component analysis (PCA) was usedto compress the data, with the 10 leading principal compo-nents (accounting for 76% of the variance) retained.[6] The SST index is the standardized first PC of thewinter (November–March) SSTA over the tropical Pacific(122C176E–72C176W, 22C176S–22C176N with a resolution of 2C176 C2 2C176).The monthly Extended Reconstructed Sea Surface Temper-atures (ERSST) were downloaded from the National Cli-mate Data Center (NCDC), National Oceanic andAtmospheric Administration (NOAA, ftp.ncdc.noaa.gov/pub/data/ersst). Anomalies were calculated by subtractingthe monthly climatology, and linear trend removal wasperformed prior to PCA.[7] The multi-layer perceptron NN model with 1-hiddenlayer used here has a similar structure to the multivariatenonlinear regression model used for ENSO prediction by ourgroup [Hsieh and Tang, 1998], except that it has only onepredictor (the SST index) and multiple response variables(the 10 leading PCs of the Z500 anomalies). The input SSTindex is first nonlinearly mapped to four intermediate vari-ables (called hidden neurons), which are then linearlymapped to 10 output variables. With enough hidden neurons,the NN is capable of modeling any nonlinear continuousfunction to arbitrary accuracy. Starting from random initialvalues, the NN model parameters are optimized so that themean square error (MSE) between the 10 model outputs andthe 10 leading PCs of the Z500 anomalies is minimized. Toavoid local minima during optimization [Hsieh and Tang,1998], the NN model was trained repeatedly 30 times fromrandom initial conditions and the solution with the smallestMSE was chosen and the other 29 rejected.[8] To reduce the possible sampling dependence of asingle NN solution, we repeated the above calculation400 times with a bootstrap approach. A bootstrap samplewas obtained by randomly selecting data (with replacement)268 times from the original record of 268 months, so that onaverage about 63% of the original record was chosen in abootstrap sample [Efron and Tibshirani, 1993]. The ensem-blemeanoftheresulting400NNmodelswasusedasthefinalNN solution, found to be insensitive to the number of hiddenneurons, which was varied from 1 to 5 in a sensitivity test.3. Results[9] The climate signal extracted by the nonlinear projec-tion is manifested by a curve in the 10-dimensional phasespace of the Z500 PCs; in contrast, the linear projectionextracts a straight line in the same 10-D space. This curvewas parabola-like (not shown) when viewed in the PC1-PC2plane and in the PC1-PC3plane, indicating that the Z500response to the SST index is a nonlinear combination ofsome of its leading PC modes. For a specific value of theSST index, the NN solution gives the 10 Z500 PCs, whichwhen combined with the corresponding spatial patterns ofthe PCs (called the empirical orthogonal functions, EOFs),yields the Z500 spatial anomalies associated with the givenSST. As the SST index varies, both the pattern and ampli-tude of the Z500 spatial anomalies change, in contrast to thelinear projection method, which gives a fixed spatial patternand a variable amplitude.[10] When the SST index takes on its minimum value(i.e., strong La Nin˜a), three large anomalies appear in theZ500 anomaly field (Figure 1a) over North Pacific andNorth America, resembling a negative Pacific-NorthAmerica (PNA) teleconnection pattern [Wallace and Gutzler,1981], with negative height anomalies over western Canada.We also see positive anomalies over the North Atlantic andwestern Europe, which are linked to the positive anomaliesover eastern Canada and the United States (US), andFigure 1. The Z500 anomalies associated with (a) theminimum SST index and (d) maximum SST index, and with(b) one half of the minimum SST and (e) one half of themaximum SST. The Z500 anomalies in panel (a) minustwice the anomalies in (b) are shown in panel (c); and theanomalies in panel (d) minus twice the anomalies in (e) areshown in panel (f ). If the Z500 response to the SST index isstrictly linear, then (c) and (f ) will show zero everywhere.Contour interval is 10 meters and the grey areas indicatestatistical significance at the 5% level, based on thedistribution of the results from the 400 bootstrap samples.L02203 WU AND HSIEH: WINTER ATMOSPHERIC RESPONSE TO ENSO L022032of4negative anomalies over Scandinavia and eastern Europe,connected to the negative anomalies over western Canadavia the North Pole. When the SST index takes on itsmaximum value (strong El Nin˜o), the negative PNA patternin Figure 1a has turned into a positive PNA pattern(Figure 1d), with anomaly centers shifted eastward by 30–40C176 and with magnitude approximately doubled over theNorth Pacific and Canada. In both Figures 1a and 1d,negative height anomalies are found over the west coast ofNorth America, and positive anomalies over eastern Canadaand northeastern US. Also, the anomalies over the Atlanticocean and Europe are maintained in Figure 1d, but withabout a 15C176 eastward shift. Clearly, the Z500 anomaliesassociated with strong El Nin˜o are not simply a mirror imageof those associated with strong La Nin˜a.[11] Figures 1b and 1eshowthe anomalies associated withthehalfminimumandhalfmaximumSSTindexrespectively.The Z500 anomalies decrease in magnitude, especiallyovertheNorth AtlanticandEuropeareas.Theanti-symmetrybetween Figures 1b and 1e is much more conspicuous thanthat between Figures 1a and 1d, consistent with the notionthat appreciable SSTA are required for initiating a nonlinearatmospheric response [Hoerling et al., 2001].[12] To reveal the nonlinear response in the Z500 anoma-lies to the tropical SSTA, we plotted in Figure 1c thedifference between the Z500 anomalies in Figure 1a anddouble the anomalies in Figure 1b; and similarly inFigure 1f, the difference between the anomalies inFigure 1d and double the anomalies in Figure 1e. Interest-ingly, despite the large difference between Figures 1aand 1d, and the smaller difference between Figures 1band 1e, the Z500 anomalies in Figures 1c and 1f agree wellwith each other, indicating that regardless of the sign of theSST index, the nonlinear response has positive Z500anomalies appearing over the central-eastern North America,North Atlantic and western Europe, and negative Z500anomaliesoverthewestcoastofNorthAmerica,Scandinaviaand eastern Europe. The anomaly pattern in Figure 1c or 1f isconsistent with the positive phase of the PNA teleconnectionand the positive phase of the NAO being excited.[13] Next PCA is used to analyze the field of Z500anomalies resulting from our nonlinear projection of theSST index during Jan. 1950–Mar. 2003. The first PCAmode, explaining 74.8% of the variance of the nonlinearlyprojected Z500 anomalies, gives a typical PNA pattern(Figure 2b) with main variability over the North Pacificand North America. This pattern displays the linear com-ponent of the Z500 signal associated with the SST index, asthe first PC (solid curve in Figure 2a) is correlated at above0.99 with the SST index. The second PCA mode, explaining25.2% of the variance of the nonlinearly projected Z500anomalies, reveals a spatial pattern (Figure 2c) resemblingthe one shown in Figure 1c or 1f. The second PC (dashedcurve in Figure 2a) has positive values not only during theEl Nin˜o years (1958, 1966, 1973, 1983, 1992 and 1998), butalso during La Nin˜a years (1950, 1956, 1971, 1974, 1976,1989, 1999 and 2000). Reversing the sign of the solid curve(PC1) when it is below zero yields a fair approximation tothe dashed curve (PC2)—i.e., PC2 is noticeably positivewhenever PC1 assumes large positive or negative values.Hence, regardless of warm or cold episodes, the Z500 hasthe same response pattern as depicted by Figure 2c. Thisnonlinear component of the Z500 response to ENSO hasabout one third the variance of the linear component;furthermore, this nonlinear component (Figure 2c) spreadsthe ENSO effect well beyond the North Pacific-NorthAmerica domain of the linear component (Figure 2b).[14] To further illuminate the nonlinear response, weconsider a polynomial fit of the SST index to the Z500anomaly at each grid point. Let T be the SST index, andxn= Tn, then z, the Z500 anomaly (reconstructed from the10 leading PCs) at a grid point, was fitted by z = a0+ a1^x1+a2^x2+ ... + aN^xN,where^xnis xnnormalized. For 400bootstrap samples and for each spatial point of the Z500anomaly field, regression coefficients a0,..., aNwere com-puted. After ensemble-averaging over all bootstrap samples,anprovided the spatial pattern associated with the nth orderresponse to the SST index. When tested over independentdata(i.e.,datanotselectedinabootstrapsample),thesmallestMSE (averaged over all bootstrap samples) was found whenN=2,indicatingoverfittedresultswhenN>2.WithN=2,theensemble-averagedvaluesofa1anda2areplottedinFigure3.[15] The linear term (Figure 3a) resembles the first PCAspatial mode of the nonlinear projection (Figure 2b), con-firming that this mode has captured the linear response ofZ500 to ENSO. The quadratic term (Figure 3b) resemblesthe second PCA mode of the nonlinear projection(Figure 2c), as well as Figures 1c and 1f, indicating thatthe nonlinear response of the Z500 anomalies to ENSO ismainly a quadratic response. As adding cubic terms andbeyond to the polynomial fit leads to overfitting, higherorder nonlinear response could not be detected robustly.4. Summary and Discussion[16] A fully nonlinear projection of the ENSO SST indexto the Northern Hemisphere winter (November to March)Z500 monthly anomalies has been achieved using neuralnetworks. During extreme warm and cold episodes, asym-Figure 2. The 2 leading PCs of the Z500 anomaliesassociated with the ENSO SST index as extracted by theNN projection. The solid line in panel (a) represents the firstmode, and the dashed line, the second mode. Thecorresponding 2 PCA spatial modes are shown in panels(b) and (c), respectively. The contour interval is 0.02, andthe spatial modes have been normalized to unit norm.L02203 WU AND HSIEH: WINTER ATMOSPHERIC RESPONSE TO ENSO L022033of4metric Z500 patterns occurred not only over North Americabut also over the Euro-Atlantic region. The Z500 anomaliesfrom the NN projection consist of a linear part, whichresembles the traditional PNA pattern with anomalieslargely confined over North Pacific and North America,and a nonlinear part, which reveals positive Z500 anomaliesover the central-eastern North America, North Atlantic andwestern Europe, and negative Z500 anomalies over the westcoast of North America, Scandinavia and eastern Europeregardless of the sign of the SSTA. The nonlinear compo-nent (with about 1/3 as much variance as the linearcomponent) excites the positive PNA and positive NAOpatterns. A polynomial study further indicates this nonlinearcomponent to be a quadratic response to the SSTA.[17] In Figures 2b, 2c, or Figures 3a, and 3b, over theEuro-Atlantic region, the nonlinear part of the Z500 anoma-lies is much stronger than the linear part, indicating that theEuro-Atlantic winter climate mainly responds to ENSOnonlinearly. Thus an implication of this work is that tostatistically predict the North Hemisphere, especially theEuropean, winter climate from the tropical Pacific SSTanomalies, a nonlinear forecast model is needed.[18] Acknowledgments. The authors acknowledge the support fromthe Natural Sciences and Engineering Research Council of Canada viaresearch and strategic grants.ReferencesDeser, C., and M. L. Blackmon (1995), On the relationship between tropicaland North Pacific sea surface temperature variations, J. Clim., 8, 1677–1680.Efron, B., and R. J. Tibshirani (1993), An Introduction to the Bootstrap,CRC, Boca Raton.Hannachi, A. (2001), Toward a nonlinear identification of the atmosphericresponse to ENSO, J. Clim., 14, 2138–2149.Hoerling, M. P., A. Kumar, and M. Zhong (1997), El Nin˜o,LaNin˜a and thenonlinearity of their teleconnections, J. Clim., 10, 1769–1786.Hoerling, M. P., A. Kumar, and T. Xu (2001), Robustness of the nonlinearclimate response to ENSO’s extreme phases, J. Clim., 14, 1277–1293.Hsieh, W. W., and B. Tang (1998), Applying neural network models toprediction and data analysis in meteorology and oceanography, Bull. Am.Meteorol. Soc., 79, 1855–1870.Hsieh, W. W. (2001), Nonlinear canonical correlation analysis of the tropi-cal Pacific climate variability using a neural network approach, J. Clim.,14, 2528–2539.Hurrel, J. W. (1995), Decadal trends in the North Atlantic Oscillation:regionaltemperaturesandprecipitationnetworks,Sciences,269,676–679.Kalnay, E., M. Kanamitsu, R. Kisler, W. Collins, D. Deaven, L. Gandin,M.Iredell,S.Sasha,G.White,J.Woolen,Y.Zhu,M.Chelliah,W. Ebisuzaki, W. Higgins, J. Janowiak, K. C. Mo, C. Ropelewski,J.Wang,A.Leetmaa,R.Reynolds,andR.Jenne(1996),TheNCEP/NCAR40-year reanalysis project, Bull. Am. Meteorol. Soc., 77, 437–471.Montroy, D. L., M. B. Richman, and P. J. Lamb (1998), Observed non-linearities of monthly teleconnections between tropical Pacific sea surfacetemperature anomalies and central and eastern North American precipita-tion, J. Clim., 11, 1812–1835.Pozo-Va´zquez, D., M. J. Esteban-Parra, F. S. Rodrigo, and Y. Castro-Dı´ez(2001),TheassociationbetweenENSOandwinteratmosphericcirculationand temperature in the North Atlantic region, J. Clim., 14, 3408–3420.Sardeshmukh, P. D., G. P. Compo, and C. Penland (2000), Changes ofprobability associated with El Nin˜o, J. Clim., 13, 4268–4286.Shabbar, A., B. Bonsal, and M. Khandekar (1997), Canadian precipitationpatterns associated with Southern Oscillation, J. Clim., 10, 3016–3027.Wallace, J. M., and D. Gutzler (1981), Teleconnection in the geopotentialheight field during the Northern Hemisphere winter, Mon. Wea. Rev., 109,784–812.Wu, A., W. W. Hsieh, and F. W. Zwiers (2003), Nonlinear modes of NorthAmerican winter climate variability derived from a general circulationmodel simulation, J. Clim., 16, 2325–2339.C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0A. Wu and W. W. Hsieh, Dept. of Earth and Ocean Sciences, University ofBritish Columbia, Vancouver, B.C., Canada, V6T 1Z4. (awu@eos.ubc.ca)Figure 3. The Z500 anomaly patterns associated with thelinear and quadratic terms of the tropical Pacific SST index.The contour interval is 5 meters and the shaded areasindicate statistical significance at the 5% level.L02203 WU AND HSIEH: WINTER ATMOSPHERIC RESPONSE TO ENSO L022034of4


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