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Nonlinear atmospheric variability in the winter northeast Pacific associated with the Madden-Julian oscillation Jamet, Cedric; Hsieh, William W. 2005-07-13

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Nonlinear atmospheric variability in the winter northeast Pacificassociated with the Madden-Julian oscillationCe´dric Jamet and William W. HsiehDepartment of Earth and Ocean Sciences, University of British Columbia, Vancouver, British Columbia, CanadaReceived 17 May 2005; accepted 13 June 2005; published 13 July 2005.[1] The Madden-Julian Oscillation (MJO), the primarymode of large-scale intraseasonal variability in the tropics,is known to relate to the mid-latitude atmosphericvariability. Using neural network techniques, a nonlinearprojection of the MJO onto the precipitation and 200-hPawind anomalies in the northeast Pacific during January–March shows asymmetric atmospheric patterns associatedwith different phases of the MJO. For precipitation, thestrength of the nonlinear effect to the linear effect was 0.94(in terms of the squared anomalies and averaged over allphases of the MJO), indicating strong nonlinearity, while forthe 200-hPa wind, the ratio was 0.55, indicating moderatenonlinearity. In general, anomalous winds blowing from thenorth or from land were associated with negativeprecipitation anomalies, while winds from the south orfrom the open ocean, with positive precipitation anomalies.The nonlinear effects generally induced positiveprecipitation anomalies during all phases of the MJO.Citation: Jamet, C., and W. W. Hsieh (2005), Nonlinearatmospheric variability in the winter northeast Pacific associatedwith the Madden-Julian oscillation, Geophys. Res. Lett., 32,L13820, doi:10.1029/2005GL023533.1. Introduction[2] The Madden-Julian Oscillation (MJO) is the domi-nant mode of the subseasonal tropospheric variability overthe tropical Indian and Pacific Oceans. The MJO wasoriginally identified as a coherent, eastward-propagatingperturbation in the tropical sea level pressure, upper levelzonal wind and atmospheric convection, with a relativelybroad spectral peak of 30–90 days [Madden and Julian,1994]. The impact of the MJO on the atmospheric circula-tion outside of the tropics has been of considerable interest.There is evidence that deep tropical convection forces themid-latitude flow both directly [Hoskins and Karoly, 1981;Horel and Wallace, 1981] and indirectly [Schubert andPark, 1991]. Connections have been found between mid-latitude weather variations and the MJO [Higgins and Mo,1997; Mo and Higgins, 1998; Jones, 2000; Bond andVecchi, 2003, hereinafter referred to as BV]. Most of thestudies on the MJO used an index to present and explain theMJO life cycle in the tropics and extratropics. These studiesworked with linear methods, e.g. phase sum composite,correlation, regression [Hendon and Salby, 1994; Knutsonand Weickmann, 1987; Rui and Wang, 1990; Maloney andHartmann, 1998; BV]. Recently, a multiple linear regres-sion model has been used to analyse the relationshipsbetween eastward- and westward-moving intraseasonalmodes by Roundy and Frank [2004], who concluded thatthe regression model produced physically valid analysesthat revealed processes of partly nonlinear wave interactionsin the tropical atmosphere.[3] In recent years, neural network (NN) methods havebeen increasingly applied to nonlinearly study the atmo-sphere and oceans, with reviews given by Hsieh and Tang[1998] and Hsieh [2004]. In this study, we apply fullynonlinear NN techniques to create a nonlinear compositelife cycle and try to separate the linear and nonlinearresponses of the atmosphere to the MJO. The associationbetween the MJO and the climate in the northeast Pacific isinvestigated by applying a nonlinear projection (i.e. nonli-near regression) of the BV MJO index onto the 200-hPawind and precipitation anomalies during winter (January–March). If x denotes the MJO index and y, the atmosphericresponse to MJO, the nonlinear response function y = f(x)can be obtained via NN [Wu and Hsieh, 2004] (thenonlinear projection by NN is simply called an NNprojection thereafter). In contrast to the linear projection,the NN projection detects the fully nonlinear atmosphericvariability associated with MJO. As the effects of theMJO over northeast Pacific and the northwestern part ofNorth America (esp. western Canada) is not well docu-mented, the purpose of this study is to reveal thenonlinear association between the winter precipitationand 200 hPa wind anomalies in the northeast Pacificand the tropical MJO.2. Data and Methods[4] To characterize the state of the MJO, we used theMJO index developed by Bond and Vecchi [2003], availablefor the period from January 1, 1980 to December 31, 2003.This index is composed of an amplitude A and a phase Fbased on the two leading principal components of theintraseasonal 850-hPa zonal wind in the 5C176S–5C176N band.An MJO event is defined as a period of 30 or more daysduring which A exceeds 0.7 standard deviation and duringwhich F corresponds to eastward propagation for the entireperiod. In the A and F time series, values are only definedduring MJO events.[5] For the variability in northeast Pacific, we examinedthe daily 200-hPa wind from the NCEP-NCAR extendedreanalysis product [Kalnay et al., 1996] and the dailyMSU precipitation (both downloadable from http://www.cdc.noaa.gov). The precipitation data, availableduring 1979–1995, were derived from channel 1 of themicrowave sounding unit, which is sensitive to emission bycloud water and rainfall in the lowest few kilometers of theGEOPHYSICAL RESEARCH LETTERS, VOL. 32, L13820, doi:10.1029/2005GL023533, 2005Copyright 2005 by the American Geophysical Union.0094-8276/05/2005GL023533$05.00L13820 1of4atmosphere [Spencer, 1993]. The MSU precipitation prod-uct is only usable over the ocean. For both datasets, thedaily climatological means were subtracted from the dailyvalues to yield the anomalies. To obtain intraseasonalanomalies, a Lanczos response bandpass filter with 240weights and cutoff periods at 35 and 120 days was appliedto the wind and precipitation anomalies [Duchon, 1979]. Westudied the period 1980–1995 during the months January,February and March for both datasets and the MJO index.The analysis was performed only when MJO events werepresent, thus shrinking the data record to 968 days. Ourstudy is focused on the northeast Pacific area, between30C176N–60C176N and 150C176W–112.5C176W.[6] After removing the linear trend, a combined prin-cipal component analysis (PCA) was used to compressthe meridional and zonal wind anomalies, with the8 leading principal components (PC) (accounting for95.2% of the variance) retained. For the precipitationanomalies, the 8 leading PCs, accounting for 64.4% ofthe variance, were retained. Analysis using differentnumber of PCs showed that our results were not sensitiveto the number of modes retained as long as 8 or morePCs were used.[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 byour group [Hsieh and Tang, 1998]. Here, the NN model hastwo inputs (predictors) A cos F and A sin F (from the MJOindex) and 8 output variables (the 8 leading PCs of the200-hPa wind anomalies or precipitation anomalies). Theinputs were first nonlinearly mapped to intermediate vari-ables hj(called hidden neurons), which were then linearlymapped to the 8 output variables pk, i.e.hj¼ tanh wjAcosFþ ^wjAsinFþbjC0C1;pk¼Xj~wjkhjþ~bk;where wˆj, wj, ~wjk, bjand~bkare the model parameters. Withenough hidden neurons, the NN model is capable ofmodeling any nonlinear continuous function to arbitraryaccuracy. Starting from random initial values, the NNmodel parameters were optimized so that the mean squareerror (MSE) between the 8 model outputs and the8 observed PCs was minimized. To avoid local minimaduring optimization [Hsieh and Tang, 1998], the NNmodel was trained repeatedly 25 times from random initialparameters and the solution with the smallest MSE waschosen.[8] To reduce the possible sampling dependence ofa single NN solution, we repeated the above calculation100 times with a bootstrap approach. A bootstrap samplewas obtained by randomly selecting data (with replacement)968 times from the original record of 968 days, so that onaverage about 63% of the original record was chosen in abootstrap sample [Efron and Tibshirani, 1993]. The ensem-ble mean of the resulting 100 NN models was used as thefinal NN solution, found to be insensitive to the number ofhidden neurons, which was varied from 2 to 10 in asensitivity test. Results from using 4 hidden neurons arepresented. For comparison, the linear regression (LR) modelis simplypk¼ wkAcosFþ ^wkAsinFþbk:3. Results[9] The output signal from the NN projection is man-ifested by a surface in the 8 dimensional space spanned bythe PCs; in contrast, the linear projection from LR ismanifested by a plane in the same 8-D space (not shown).The phase of the MJO was binned into eight equal parts asin BV, phase 1 (C0p C20 F < C03p/4), ..., phase 8 (3p/4 C20F < p). The model outputs were computed for each phasebin by averaging all data with F falling within a given bin.Also by combining the PCs with their corresponding spatialpatterns (the empirical orthogonal functions) yielded thespatial anomalies during each phase of the MJO. Thecomposite spatial anomalies of the 200-hPa wind andprecipitation are shown during the 8MJO phases in Figure 1,where the top two rows are the LR results, the middle tworows, the NN results, and the bottom two rows, the nonlin-ear residual (i.e. the NN projection minus the LR projec-tion). The corresponding tropical behaviour of the MJOduring the 8 phases are shown in Figure 1 of BV.[10] With the LR projection, the composites for two out-of-phase bins (e.g. bin 1 and 5, 2 and 6, 3 and 7, 4 and 8)gave essentially the same spatial patterns but with oppo-sitely signed anomalies (Figure 1), due to the limitations ofthe LR method. In contrast, for the NN projection, thepatterns and the amplitudes of the 200-hPa wind andprecipitation anomalies changed as the phase of the MJOvaried across the bins, without showing the strict antisym-metry between two out-of-phase bins. For instance, duringphase 1 with LR projection, there is a dipole structure in theprecipitation anomalies, with negative anomalies along thecoast and positive anomalies further west. The superim-posed wind composite shows wind blowing from the landnorth of 40C176N (Figure 1). In the NN projection during phase1, there is no dipole structure in the precipitation anomalies,but only a large tongue of positive anomalies in the openocean with a maximum value of 0.7 mm dayC01, muchgreater than the maximum of 0.4 mm dayC01found in the LRphase 1 projection. In the NN phase 1, there is an anticy-clonic cell over British Columbia, centered just north ofVancouver Island. Generally, over all 8 phases and for boththe NN and LR projections, there is quite good agreementbetween the wind anomalies and the precipitation anomalies(Figure 1), with wind blowing from the north and from landassociated with negative precipitation anomalies, and windblowing from the south and from the open ocean, withpositive precipitation anomalies, as expected.[11] By subtracting the LR projection from the NNprojection, the nonlinear residual (bottom two rows ofFigure 1) represents the purely nonlinear response afterthe removal of the linear response. The nonlinear residualfor precipitation shows weak nonlinearity during phase 2and 3 (with maximum anomalies about 0.1 mm dayC01) andstrong nonlinearity during phase 1, 4 and 5, with anomaliesreaching about 0.3 mm dayC01. The lack of comparablenegative anomalies in the nonlinear residual indicates thatL13820 JAMET AND HSIEH: NONLINEAR ATMOSPHERIC VARIABILITY L138202of4Figure 1. Composites during the 8 phases of the MJO for the LR projection (top two rows), the NN projection (middletwo rows) and the nonlinear residual (NN-LR) (bottom two rows), with precipitation anomalies shown in contour maps and200-hPa wind anomalies by vectors. With negative contours dashed and zero contours thickened, the contour interval is0.1 mm dayC01, and the scale for the wind (5 m sC01) given beside the bottom right panel. The shaded areas indicate statisticalsignificance for the precipitation anomalies at the 5% level based on the bootstrap distribution.L13820 JAMET AND HSIEH: NONLINEAR ATMOSPHERIC VARIABILITY L138203of4the nonlinear effects tend to induce positive precipitationanomalies over all phases of the MJO.[12] We next computed the average of the squaredprecipitation anomalies in each panel in Figure 1, and letr be the ratio between this computed value for the nonlinearresidual and that for the LR projection during a given phase.For phase 1 to phase 8, the values of r are 1.69, 0.25, 0.26,1.18, 1.79, 0.86, 0.56 and 0.96, respectively, which supportsour claim that nonlinearity is weak during phase 2 and 3,but strong during phase 1, 4 and 5, where r actually exceeds1 in all three phases (meaning that the squared anomalies ofthe nonlinear residual averaged over the spatial domainexceeds the corresponding value from the linear projection).[13] For the wind speed anomalies, the r values are 0.37,0.52, 0.69, 0.15, 0.19, 1.74, 0.28 and 0.43 during phase 1 tophase 8, respectively. The nonlinear effect is weakest duringphase 4 and 5 and strongest during phase 6, where there is astrong cyclonic cell on the West Coast. Averaged over all8 phases, r is 0.55, versus an average r of 0.94 forprecipitation. Thus the overall nonlinear effect is strongerin the precipitation than in the wind. We expect precipitationto be more nonlinear than wind, as precipitation depends ontemperature and moisture convergence besides wind, andlatent heat, which is governed by a step function, introducesstrong nonlinearity into precipitation.4. Conclusion[14] This study has applied a fully nonlinear technique tostudy the nonlinear association between the MJO and thenortheast Pacific variability of precipitation and 200-hPawind during January–March. By projecting from the MJOindex to the variables in the northeast Pacific, the linear andnonlinear response to MJO were found. For precipitation,the strength of the nonlinear effect to the linear effect was0.94 (in terms of the squared anomalies and averaged overall phases of the MJO). This means the nonlinear effect wasessentially of the same strength as the linear effect. For the200-hPa wind, the ratio was 0.55, indicating moderatenonlinearity. In general, anomalous winds blowing fromthe north or from land were associated with negativeprecipitation anomalies, while winds from the south or fromthe open ocean, with positive precipitation anomalies. Thenonlinear effects generally induced positive precipitationanomalies during all phases of the MJO. Follow-on workcould further explore time lags between MJO and variablesin the northeast Pacific.[15] Acknowledgments. The authors would like to thank Dr. GabrielVecchi for providing his MJO index, and Drs. Phil Austin and Aiming Wufor their useful comments. The authors acknowledge the support from theNatural Sciences and Engineering Research Council of Canada via researchand strategic grants.ReferencesBond, N. A., and G. A. Vecchi (2003), The influence of the Madden-Julianoscillation on precipitation in Oregon and Washington, Weather Fore-casting, 18, 600–613.Duchon, C. E. (1979), Lanczos filter in one and two dimensions, Appl.Meteorol., 18, 1016–1022.Efron, B., and R. J. Tibshirani (1993), An Introduction to the Bootstrap,CRC Press, Boca Raton, Fla.Hendon, H. H., and M. L. Salby (1994), The life cycle of the Madden-Julian oscillation, J. Atmos. Sci., 51, 2227–2240.Higgins, R. W., and K. C. Mo (1997), Persistent North Pacific circulationanomalies and the tropical intraseasonal oscillation, J. Clim., 10, 223–244.Horel, J. H., and J. M. Wallace (1981), Planetary scale atmospheric phe-nomenon associated with the Southern Oscillation, Mon. Weather Rev.,109, 813–829.Hoskins, B. J., and D. J. Karoly (1981), The steady linear response of aspherical atmosphere to thermal and orographic forcing, J. Atmos. Sci.,38, 1179–1196.Hsieh, W. W. (2004), Nonlinear multivariate and time series analysis byneural network methods, Rev. Geophys., 42, RG1003, doi:10.1029/2002RG000112.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.Jones, C. (2000), Occurrence of the extreme precipitation events in Cali-fornia and relationships with the Madden-Julian oscillation, J. Clim., 13,3576–3587.Kalnay, E., et al. (1996), The NCEP/NCAR 40-Year Reanalysis project,Bull. Am. Meteorol. Soc., 77, 437–471.Knutson, T. R., and K. M. Weickmann (1987), 30–60 day atmosphericoscillations: Composite life of convection and circulation anomalies,Mon. Weather Rev., 115, 1407–1436.Madden, R. A., and P. R. Julian (1994), Observations of the 40–50 daytropical oscillation—A review, Mon. Weather Rev., 122, 814–837.Maloney, E. D., and D. L. Hartmann (1998), Frictional moisture in a com-posite life cycle of the Madden-Julian oscillation, J. Clim., 11, 2387–2403.Mo, K. C., and R. W. Higgins (1998), Tropical convection and precipitationregime in the western United States, J. Clim., 11, 2404–2423.Roundy, P. E., and W. M. Frank (2004), Applications of a multiple linearregression model to the analysis of relationships between eastward- andwestward-moving intraseasonal modes, J. Atmos. Sci., 61, 3041–3048.Rui, H., and B. Wang (1990), Development characteristics and dynamicstructure of tropical intraseasonal convection anomalies, J. Atmos. Sci.,47, 357–379.Schubert, S. D., and C.-K. Park (1991), Low-frequency intraseasonal tro-pical extratropical interactions, J. Atmos. Sci., 48, 629–650.Spencer, R. W. (1993), Global ocean precipitation from the MSU during1979–1991 and comparisons to other climatologies, J. Clim., 6, 1301–1326.Wu, A., and W. W. Hsieh (2004), The nonlinear Northern Hemispherewinter atmospheric response to ENSO, Geophys. Res. Lett., 31,L02203, doi:10.1029/2003GL018885.C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0W. W. Hsieh and C. Jamet, Department of Earth and Ocean Sciences,University of British Colombia, 6339 Stores Road, Vancouver, BC, CanadaV6T 1Z4. (whsieh@eos.ubc.ca; cjamet@eos.ubc.ca)L13820 JAMET AND HSIEH: NONLINEAR ATMOSPHERIC VARIABILITY L138204of4

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