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Changes in the Arctic Oscillation under increased atmospheric greenhouse gases Boer, George J.; Hsieh, William W.; Wu, Aiming; Zwiers, Francis W. 2007

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Changes in the Arctic Oscillation under increased atmosphericgreenhouse gasesAiming Wu,1William W. Hsieh,1George J. Boer,2and Francis W. Zwiers2Received 14 January 2007; revised 2 April 2007; accepted 16 May 2007; published 16 June 2007.[1] The Arctic Oscillation (AO) under increasedatmospheric concentration of greenhouse gases (GHG)was studied by comparing an ensemble of simulationsfrom 13 coupled general circulation models with GHG atthe pre-industrial level and at the late 20th century level, forNovember to March. The change in the linear AO pattern asGHG increased reveals positive sea level pressure (SLP)anomalies centered over the Gulf of Alaska, and weakernegative SLP anomalies over eastern Canada and NorthAtlantic – a pattern resembling the nonlinear AO patternarising from a quadratic relation to the AO index. Thisquadratic AO pattern itself has positive SLP anomaliesreceding from Europe but strengthening over the Gulf ofAlaska and surrounding areas as GHG increased. This studypoints to the importance of the nonlinear structure indetermining how the linear oscillatory pattern changes whenthere is a change in the mean climate. Citation: Wu, A.,W. W. Hsieh, G. J. Boer, and F. W. Zwiers (2007), Changes in theArctic Oscillation under increased atmospheric greenhouse gases,Geophys. Res. Lett., 34, L12701, doi:10.1029/2007GL029344.1. Introduction[2] The Arctic Oscillation (AO) is the leading mode ofatmospheric variability over the extratropical NorthernHemisphere [Thompson and Wallace, 1998, 2001]. Throughprincipal component analysis (PCA), the spatial AO patternis commonly obtained from the first empirical orthogonalfunction (EOF) of the mean sea level pressure (SLP)anomaly field, while the associated principal component(PC) time series serves as an AO index.[3] The AO index has gradually risen since the 1960swith historic highs in the early 1990s. It has been suggestedthat this positive trend in the AO index significantlycontributed to the observed warming trend over Eurasiaand North America, accounting for as much as 50% of thewinter warming over Eurasia [Thompson et al., 2000]. It isalso notable that the AO index has been decreasing in recentyears; with these recent data included, Cohen and Barlow[2005] found that the overall trends for the past 30 yearswere weak to nonexistent.[4] Most climate models under increasing greenhousegases (GHG) forcing showed a positive trend in the AOindex [Gillett et al., 2002]. Comparing the observed SLPtrends with those simulated in response to natural andanthropogenic influence in a suite of coupled generalcirculation models (CGCM), Gillett et al. [2005] found thatwhile the simulated Southern Hemisphere SLP trends wereconsistent with observations, the simulated Northern Hemi-sphere SLP trends were far too weak. Some authors [e.g.,Scaife et al., 2005] suggested that a well-resolved strato-sphere in the model could be important for simulating theAO trend.[5] Besides trends in the AO index, the AO spatialanomaly pattern may also respond to changes in naturaland anthropogenic forcing. Analyzing the data from anensemble of 201-year simulations by the Canadian Centrefor Climate Modelling and Analysis (CCCma) coupledclimate model forced by changing GHG concentrationsand aerosol loading [Flato and Boer, 2001], Fyfe et al.[1999] found that the model simulated an essentially un-changed AO spatial pattern superimposed on a forcedclimate pattern. AO also has nonlinear structure. For exam-ple, composite analyses reveal that during positive andnegative AO phases, the associated atmospheric anomalypatterns are not simply anti-symmetric to each other [Pozo-Va´zquez et al., 2001; Wu et al., 2006]. Using nonlinearprojection via a neural network (NN) approach to studynonlinear atmospheric teleconnections, Hsieh et al. [2006]found that, in addition to the classic (i.e. linear) AO spatialpattern, there is significant variability that is associatedquadratically with the AO index.[6] In this study, using data from 13 CGCMs, we foundthat despite the general similarity between the spatial AOpattern in the pre-industrial and in the current period, thereare subtle changes which can be explained by nonlinear(mainly quadratic) AO behavior.2. Data and Methodology2.1. Data[7] We studied simulations produced with 13 CGCMs forthe Intergovernmental Panel on Climate Change (IPCC)Fourth Assessment Report, namely CCCma-CGCM3.1,CNRM-CM3, CSIRO-Mk3.0, GFDL-CM2.0, GISS-ER,IAP-FGOALS-g1.0, INM-CM3.0, IPSL-CM4, MIROC3.2,MIUB-ECHO-G, MRI-CGCM2.3.2, NCAR-CCSM3.0 andUKMO-HadCM3. See for details.We used two simulations from each model, one from theintegration with the GHG concentrations fixed at the pre-industrial (PI) level, and the other from the committedclimate change experiments (CMT) where the GHG andaerosols were fixed at the level of the late 20th century. Thevarious model runs ranged in length from 100 to 500 years.[8] The observed monthly SLP data from NCAR[Trenberth and Paolino, 1980] during January 1950 toGEOPHYSICAL RESEARCH LETTERS, VOL. 34, L12701, doi:10.1029/2007GL029344, 2007ClickHereforFullArticle1Department of Earth and Ocean Sciences, University of BritishColumbia, Vancouver, British Columbia, Canada.2Canadian Centre for Climate Modelling and Analysis, University ofVictoria, Victoria, British Columbia, Canada.Copyright 2007 by the American Geophysical Union.0094-8276/07/2007GL029344$05.00L12701 1of4December 2005 were also used, with SLP anomalies cal-culated by subtracting the monthly climatological meansfrom 1950–2005. After weighting the anomalies by thesquare root of the cosine of the latitude, PCAwas performedon the November to March monthly anomaly data over theN. Hemisphere from 20C176Nto90C176N, with the standardizedfirst PC defined as the AO index. A longer record ofmonthly SLP data from 1850 to 2004, namely the HadleyCenter SLP Version 2 (HadSLP2) [Allan and Ansell, 2006],was also used.[9] For the model SLP data from each CGCM, theclimatological monthly mean from the PI run was sub-tracted to give the anomalies both for the PI run and for theCMT run. For each CGCM, PCA was performed on theNovember to March monthly SLP anomalies in the PI run,with the standardized first PC taken to be the AO index. Tokeep a consistent definition of the AO index between the PIand CMTexperiments for each CGCM, the CMT anomalieswere projected to the first EOF from the PI experiment, thenstandardized (using the mean and standard deviation fromthe PI experiment) to obtain the AO index. The mean of theAO index in each of the 13 model CMT runs are 0.13, 0.08,0.05, 0.11, 0.07, C00.02, 0.10, 0.36, 0.03, 0.33, 0.07, 0.14and C00.07, respectively. The average over the 13 values is0.11, compared to 0.16, the change in the mean AO indexover the period 1950–2004 relative to that over the period1850–1900 (from the HadSLP2 data). We acknowledge thatit is only a rough comparison, as forcing is constant in theCMT runs (although the climate is not in equilibrium),while forcing is not constant in the real world especiallyduring the latter half of the 20th century.2.2. Quadratic Polynomial Fit[10] In the work by Hsieh et al. [2006], the nonlinearrelation between the N. Hemisphere winter SLP anomaliesand the AO index was found be basically quadratic. Hencewe will fit a quadratic polynomial between the gridded SLPanomalies (y) and the AO index (x) (with no time lagbetween x and y),y ¼ ax þ bx2þ c; ð1Þwhere a gives the classic linear AO pattern, while b givesthe quadratic response pattern.[11] For each CGCM, a quadratic polynomial leastsquares fit was performed separately for the PI and CMTruns, and the linear and quadratic patterns were thenensemble averaged over the 13 CGCMs. For the shorterobservational record, bootstrap resampling [Efron andTibshirani, 1993] was performed 400 times, where eachbootstrap sample was obtained by randomly selecting (withreplacement) one winter’s data N times from the originalrecord of N years. The linear and quadratic patterns werethen ensemble averaged over the 400 quadratic polynomialfits.3. Results[12] Figures 1a and 1b show the ensemble mean of thelinear AO pattern for the PI and CMT model runs, respec-tively, while Figure 1c shows the corresponding resultsfrom observations for the period 1950–2005. The SLPanomaly patterns are visually quite similar to each otherin Figures 1a, 1b and 1c, except that in the model results theAO SLP anomalies are too strong over N. Pacific comparedto the observations, where the AO is weaker over N. Pacificthan over N. Atlantic and Europe.[13] Figures 1d, 1e and 1f show the ensemble averagedquadratic pattern for the PI, CMT and observational data,respectively. Being quadratically associated with the AOindex, these anomalies are excited during both the positiveand negative phase of the AO index. Positive SLP anoma-lies centered over the Gulf of Alaska extended from the N.Pacific to N. America, then through Greenland to Europe,while negative anomalies occurred over the North Atlantic.The magnitudes of the anomalies in these quadratic patternsare much weaker than those in the linear patterns, never-theless, there is considerable similarity among these threequadratic patterns. Although the quadratic anomalies fromobservations have larger magnitude than those from themodels, this could merely be sampling variability as theobserved record is quite short. A similar nonlinear pattern isobtained when using the HadSLP2 data (not shown).[14] The quadratic pattern is also seen changing underincreased GHG (see Figures 1d and 1e): The positiveanomalies receded from Europe but strengthened over theGulf of Alaska and surrounding areas, suggesting that underenhanced GHG, the nonlinear AO behavior tends to occurfarther from the Euro-Atlantic region.[15] The change in the classic linear AO pattern underenhanced GHG (Figure 2) is somewhat similar to thequadratic patterns in Figures 1d, 1e and 1f, especially Figure1e, suggesting that the change in the classic AO pattern isrelated to the nonlinear property of AO itself, as will beinvestigated below.4. Discussion[16] We now examine the quadratic fit (1) to see whathappens when there is a shift in the mean of x under climatechange. Let x = C22x + x0, and y = C22y + y0, where the overbardenotes the mean and the prime denotes the deviation. Themean of (1) givesC22y ¼ aC22x þ bx2þ c; ð2Þhencey0¼ aþ2C22xbðÞx0þ bx02þ c0; ð3Þwhere c0= C0b x02. This implies that if the mean C22x is nonzero,the linear AO pattern given by a +2C22xb would haveimbedded the quadratic pattern b. In the PI runs, C22x =0,sothe linear AO pattern is a; but in the CMT runs, if C22x = D,then the linear pattern becomes a +2bD. The differencebetween the linear patterns in CMT and in PI is thus 2bD,hence the resemblance to the quadratic pattern, as wasindeed found between Figure 2 and Figure 1d or 1e.[17] Our results also imply D to be positive, since if Dwere negative, Figure 2 would have displayed oppositesigned anomalies from Figure 1e. The AO index has indeedbeen found to gradually rise in observations [Wallace andThompson, 2002] and in climate models under increasingGHG forcing [Gillett et al., 2002, 2003]. The change in theL12701 WU ET AL.: AO AND CLIMATE CHANGE L127012of4linear pattern in Figure 2 is manifested most strongly in theGulf of Alaska, where it reaches about 0.4 hPa, whereas thequadratic pattern reaches about 0.4 hPa in the same area inFigure 1e. To account for the change in the linear pattern by2bD requires D C25 0.5. A similar estimate in the Atlanticyields D C25 0.3, hence an average D of about 0.4 is needed.However, in the CMT runs, D averaged only 0.11, a littleless than 30% of the needed value.[18] Therearetwopossibilitiesforthediscrepancy:(a)Theweak D results from the fact that the CGCMs simulate SLPtrends that are too weak in the N. Hemisphere [Gillett et al.,2005], and (b) our assumption that equation (1) is unchangedas GHG increased is not strictly correct. For instance, in theleast squares fit, a is solved for in terms of variances andcovariancesinvolvingy0,x0andx02,whichhavebeenassumedto be unchanged from PI to CMT.5. Summary and Conclusions[19] Data from multiple CGCM simulations with GHGconcentrations at the PI level and at the late 20th centurylevel (CMT) were used to reveal how AO changes underglobal warming. By fitting a quadratic polynomial betweenthe SLP anomalies and the AO index, we obtained theoscillatory patterns in the SLP that are linearly and qua-dratically related to the AO index. The linear pattern is theclassic AO pattern, while the quadratic pattern showsFigure 1. Ensemble averaged linear pattern (top row) and quadratic pattern (bottom row) of the SLP anomalies associatedwith the AO index. The left column shows the ensemble mean from 13 CGCM integrations forced with PI GHGconcentrations, the middle column, from the same models but with the late 20th century (CMT) conditions, and the rightcolumn, the observed data (1950–2005). The shaded areas indicate statistical significance at the 5% level (a, b, d, e) basedon the t-test, and (c, f) based on the bootstrap distribution. The contour interval is 1 hPa for the linear patterns, and 0.1 hPafor the quadratic patterns.Figure 2. Changes in the linear AO pattern underincreased GHG, i.e., Figure 1b minus Figure 1a. Thecontour interval is 0.1 hPa, with shaded areas significant atthe 5% level from the t-test.L12701 WU ET AL.: AO AND CLIMATE CHANGE L127013of4positive SLP anomalies centered over the Gulf of Alaskastretching from northeast Pacific-N. America throughGreenland to Europe, and weaker negative SLP anomaliesover North Atlantic, in general agreement with the quadraticpattern extracted from observed data.[20] The change of the linear AO pattern under increasedGHG (from PI to CMT) showed a SLP anomaly patternwhich resembled the quadratic pattern. A small change inthe mean of the AO index under increased GHG wouldmodify the linear AO pattern due to the presence of thequadratic pattern. That the underlying nonlinear structurecan alter the classic linear oscillations under changes in themean background state is a new concept which may alsoapply to the other oscillations in our climate system.[21] The quadratic pattern of AO also exhibits changesfrom increased GHG, with the positive SLP anomaliesreceding from Europe while strengthening over the Gulfof Alaska and surrounding areas.[22] Acknowledgments. We acknowledge the modeling groups forproviding their data for analysis, the Program for Climate Model Diagnosisand Intercomparison (PCMDI) for collecting and archiving the modeloutput, and the JSC/CLIVAR Working Group on Coupled Modelling(WGCM) for organizing the model data analysis activity. The multi-modeldata archive is supported by the Office of Science, U.S. Department ofEnergy. We are grateful to the Natural Sciences and Engineering ResearchCouncil of Canada for a strategic project grant, and to Westgrid forcomputational resources. Zhengqing Ye assisted in getting the CGCM datafrom the internet.ReferencesAllan, R. J., and T. J. Ansell (2006), A new globally complete monthlyhistorical gridded mean sea level pressure data set (HadSLP2): 1850–2004, J. Clim., 19, 5816–5842.Cohen, J., and M. Barlow (2005), The NAO, the AO, and global warming:How closely related?, J. Clim., 18, 4498–4513.Efron, B., and R. J. Tibshirani (1993), An Introduction to the Bootstrap,CRC Press, Boca Raton, Fla.Flato, G. M., and G. J. Boer (2001), Warming asymmetry in climate changesimulations, Geophys. Res. Lett., 28, 195–198.Fyfe, J. C., G. J. Boer, and G. M. Flato (1999), The Arctic and Antarcticoscillations and their projected changes under global warming, Geophys.Res. Lett., 26, 1601–1604.Gillett, N. P., M. R. Allen, R. E. McDonald, C. A. Senior, D. T. Shindell,and G. A. Schmidt (2002), How linear is the Arctic Oscillation responseto greenhouse gases?, J. Geophys. Res., 103(D3), 4022, doi:10.1029/2001JD000589.Gillett, N. P., F. W. Zwiers, A. J. Weaver, and P. A. Stott (2003), Detectionof human influence on sea level pressure, Nature, 422, 292–294.Gillett, N. P., R. J. Allan, and T. J. Ansell (2005), Detection of externalinfluence on sea level pressure with a multi-model ensemble, Geophys.Res. Lett., 32, L19714, doi:10.1029/2005GL023640.Hsieh, W. W., A. Wu, and A. Shabbar (2006), Nonlinear atmospheric tele-connections, Geophys. Res. Lett., 33, L07714, doi:10.1029/2005GL025471.Pozo-Va´zquez, D., M. J. Esteban-Parra, F. S. Rodrigo, and Y. Castro-Diez(2001), A study of NAO variability and its possible nonlinear influenceson European surface temperature, Clim. Dyn., 17, 701–715.Scaife, A. A., J. R. Knoght, G. K. Vallis, and C. K. Folland (2005), Astratospheric influence on the winter NAO and North Atlantic surfaceclimate, Geophys. Res. Lett., 32, L18715, doi:10.1029/2005GL023226.Thompson, D. W. J., and J. M. Wallace (1998), The Arctic Oscillationsignature in the wintertime geopotential height and temperature fields,Geophys. Res. Lett., 25, 1297–1300.Thompson, D. W. J., and J. M. Wallace (2001), Regional climate impacts ofthe Northern Hemisphere annular mode, Science, 293, 85–89.Thompson, D. W. J., J. M. Wallace, and G. C. Hegerl (2000), Annularmodes in the extratropical circulation. Part II: Trends, J. Clim., 13,1018–1036.Trenberth, K. E., and D. A. Paolino (1980), The Northern Hemisphere sealevel pressure data set: Trends, errors and discontinuities, Mon. WeatherRev., 108, 855–872.Wallace, J. M., and D. W. J. Thompson (2002), Annular modes and climateprediction, Phys. Today, 55, 28–33.Wu, A., W. W. Hsieh, A. Shabbar, G. J. Boer, and F. W. Zwiers (2006), Thenonlinear association between the Arctic Oscillation and North Americanwinter climate, Clim. Dyn., doi:10.1007/s00382-006-0118-8.C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0G. J. Boer and F. W. Zwiers, Canadian Centre for Climate Modelling andAnalysis, University of Victoria, Victoria, BC, Canada V8W 2Y2.W. W. Hsieh and A. Wu, Department of Earth and Ocean Sciences,University of British Columbia, Vancouver, BC, Canada V6T 1Z4.( WU ET AL.: AO AND CLIMATE CHANGE L127014of4


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