Skip to main content

Non-random correlation structures and dimensionality reduction in multivariate climate data

Abstract

It is well established that the global climate is a complex phenomenon with dynamics driven by the interaction of a multitude of identifiable but intertwined subsystems. The identification, at some level, of these subsystems is an important step towards understanding climate dynamics. We present a method to determine the number of principal components representing non-random correlation structures in climate data, or components that cannot be generated by a surrogate model of independent stochastic processes replicating the auto-correlation structure of each time series. The purpose of the method is to automatically reduce the dimensionality of large climate datasets into spatially localised components suitable for further interpretation or, for example, for use as nodes in a complex network analysis of large-scale climate dynamics. We apply the method to two 2.5° resolution NCEP/NCAR reanalysis global datasets of monthly means: the sea level pressure (SLP) and the surface air temperature (SAT), and extract 60 components explaining 87 % variance and 68 components explaining 72 % variance, respectively. The obtained components are in agreement with previous results in that they recover many well-known climate modes previously identified using other approaches including regionally constrained principal component analysis. Selected SLP components are discussed in more detail with respect to their correlation with important climate indices and their relationship to other SLP and SAT components. Finally, we consider a subset of the obtained components that have not yet been explicitly identified by other authors but seem plausible in the context of regional climate observations discussed in literature.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

References

  • (AMO) Atlantic Multidecadal Oscillation index. http://esrl.noaa.gov/psd/data/correlation/amon.us.data. Accessed 9/2013

  • (EA) East Atlantic teleconnection index. ftp://ftp.cpc.ncep.noaa.gov/wd52dg/data/indices/ea_index.tim. Accessed: 9/2013

  • (NAO-pc) North Atlantic Oscillation index: PC-based, updated regularly. http://climatedataguide.ucar.edu/sites/default/files/cas_data_files/asphilli/nao_pc_monthly_8.txt. Accessed: 9/2013

  • (NAO-station) North Atlantic Oscillation index: station-based, updated regularly. http://climatedataguide.ucar.edu/sites/default/files/cas_data_files/asphilli/nao_station_monthly_4.txt. Accessed 9/2013

  • (NINO3.4) Niño 3.4 SST index. http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Nino34/. Accessed 9/2013

  • (NPO) The North Pacific Oscillation index, updated regularly. https://climatedataguide.ucar.edu/sites/default/files/climate_index_files/npindex_monthly_0.txt. Accessed 9/2013

  • (PDO) Pacific Decadal Oscillation index. http://jisao.washington.edu/pdo/PDO.latest. Accessed 9/2013

  • (PNA) Pacific/North American index. http://jisao.washington.edu/data/pna/#digital_values. Accessed 9/2013

  • (PNA-pc) Pacific/North American PC-based index. http://www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/norm.pna.monthly.b5001.current.ascii. Accessed 9/2013

  • (SAM-obs) Southern Hemisphere Annular Mode index: observation-based. http://www.nerc-bas.ac.uk/public/icd/gjma/newsam.1957.2007.txt. Accessed 9/2013

  • (SAM-pc) Southern Hemisphere Annular Mode index: PC-based. http://www.lasg.ac.cn/staff/ljp/data-NAM-SAM-NAO/Monthly.SAMI.index.1948-2011.ascii. Accessed 9/2013

  • (SCAN) Scandinavia teleconnection index. ftp://ftp.cpc.ncep.noaa.gov/wd52dg/data/indices/scand_index.tim. Accessed 9/2013

  • (SOI) Southern Oscillation Index. http://www.cgd.ucar.edu/cas/catalog/climind/SOI.signal.ascii. Accessed 9/2013

  • (TNA) Tropical North Atlantic Pattern index. http://www.esrl.noaa.gov/psd/data/correlation/tna.data. Accessed 9/2013

  • (TPI) Trans Polar Index. http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/tpi.long.data. Accessed 9/2013

  • (WPO) West Pacific Oscillation index. ftp://ftp.cpc.ncep.noaa.gov/wd52dg/data/indices/wp_index.tim. Accessed 9/2013

  • Barnston A, Livezey R (1987) Classification, seasonality and persistence of low-frequency atmospheric circulation patterns. Mon Weather Rev 115:1083–1126

    Article  Google Scholar 

  • Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57(1):289–300

    Google Scholar 

  • Beranová R, Huth R (2008) Time variations of the effects of circulation variability modes on European temperature and precipitation in winter. Int J Climatol 28(2):139–158

    Article  Google Scholar 

  • Boccaletti S, Latora V, Morenod Y, Chavez M, Hwang D (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–300

    Article  Google Scholar 

  • Bueh C, Nakamura H (2007) Scandinavian pattern and its climatic impact. Q J R Meteorol Soc 133(629):2117–2131

    Article  Google Scholar 

  • Cheng X, Nitsche G, Wallace J (1995) Robustness of low-frequency circulation patterns derived from EOF and rotated EOF analyses. J Clim 8:1709–1713

    Article  Google Scholar 

  • Clinet S, Martin S (1992) 700-hPa geopotential height anomalies from a statistical analysis of the French Hemis data set. Int J Climatol 12:229–256

    Article  Google Scholar 

  • Deser C, Alexander MA, Xie SP, Phillips AS (2010) Sea surface temperature variability: patterns and mechanisms. Annu Rev Mar Sci 2:115–143

    Article  Google Scholar 

  • Dommenget D (2007) Evaluating EOF modes against a stochastic null hypothesis. Clim Dyn 28:517–531

    Article  Google Scholar 

  • Dray S (2008) On the number of principal components: a test of dimensionality based on measurements of similarity between matrices. Comput Stat Data Anal 52:2228–2237

    Article  Google Scholar 

  • Dyson F (1971) Distribution of eigenvalues for a class of real symmetric matrices. Rev Mex Fís 20:231–237

    Google Scholar 

  • Enfield DB, Mestas-Nuñez AM, Mayer DA, Cid-Serrano L (1999) How ubiquitous is the dipole relationship in tropical Atlantic sea surface temperatures? J Geophys Res Ocean (1978–2012) 104(C4):7841–7848

    Article  Google Scholar 

  • Enfield DB, Mestas-Nuñez AM, Trimble PJ (2001) The Atlantic multidecadal oscillation and its relation to rainfall and river flows in the continental US. Geophys Res Lett 28(10):2077–2080

    Article  Google Scholar 

  • Fountalis I, Bracco A, Dovrolis C (2013) Spatio-temporal network analysis for studying climate patterns. Clim Dyn

  • Gong D, Wang S (1999) Definition of Antarctic oscillation index. Geophys Res Lett 26(4):459–462

    Article  Google Scholar 

  • Hannachi A, Jolliffe I, Stephenson D (2007) Empirical orthogonal functions and related techniques in atmospheric science: a review. Int J Climatol 27(9):1119–1152

    Article  Google Scholar 

  • Hasselmann K (1988) PIPs and POPs: the reduction of complex dynamical systems using principal interaction and oscillation patterns. J Geophys Res Atmos 93(D9):11015–11021

    Article  Google Scholar 

  • Hatzaki M, Flocas HA, Asimakopoulos DN, Maheras P (2007) The eastern Mediterranean teleconnection pattern: identification and definition. Int J Climatol 27(6):727–737

    Article  Google Scholar 

  • Hlinka J, Hartman D, Vejmelka M, Novotná D, Paluš M (2013) Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity. Clim Dyn May 2013:1–14

  • Horel J, Wallace J (1981) Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon Weather Rev 109:813–829

    Article  Google Scholar 

  • Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24:417–444

    Article  Google Scholar 

  • Hurrell J (1995) Decadal trends in the North-Atlantic Oscillation—regional temperatures and precipitation. Science 269(5224):676–679

    Article  Google Scholar 

  • Huth R (2006) The effect of various methodological options on the detection of leading modes of sea level pressure variability. Tellus 58A:121–130

    Article  Google Scholar 

  • Jacobeit J (2010) Classifications in climate research. Phys Chem Earth 35(9–12):411–421

    Article  Google Scholar 

  • Jolliffe IT (1987) Rotation of principal components: some comments. Int J Climatol 7:507–510

    Article  Google Scholar 

  • Jolliffe IT (2002) Principal component analysis, 2nd edn. Springer, New York

    Google Scholar 

  • Jones PD, Salinger MJ, Mullan AB (1999) Extratropical circulation indices in the Southern Hemisphere based on station data. Int J Climatol 19(12):1301–1317

    Article  Google Scholar 

  • Kaiser HF (1958) The Varimax criterion for analytic rotation in factor analysis. Psychometrika 23(3):187–200

  • Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo K, Ropelewski C, Wang J, Leetmaa A, Reynolds R, Jenne R, Joseph D (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77(3):437–471

    Article  Google Scholar 

  • Kidson JW (1975) Tropical eigenvector analysis and the Southern Oscillation. Mon Weather Rev 103(3):187–196

    Article  Google Scholar 

  • Kimoto M (2005) Simulated change of the East Asian circulation under global warming scenario. Geophys Res Lett 32(16):L16701

  • Kistler R, Kalnay E, Collins W, Saha S, White G, Woollen J, Chelliah M, Ebisuzaki W, Kanamitsu M, Kousky V, van den Dool H, Jenne R, Fiorino M (2001) The NCEP-NCAR 50-year reanalysis: monthly means CD-ROM and documentation. Bull Am Meteorol Soc 82:247–268

    Article  Google Scholar 

  • Kutzbach J (1967) Empirical eigenvectors of sea-Level pressure, surface temperature and precipitation complexes over North America. J Appl Meteorol 6:891–802

    Article  Google Scholar 

  • Kutzbach J (1970) Large-scale features of monthly mean northern hemisphere anomaly maps of sea-level pressure. Mon Weather Rev 98(9):708–716

    Article  Google Scholar 

  • Laloux L, Cizeau P, Bouchaud JP, Potters M (1999) Noise dressing of financial correlation matrices. Phys Rev Lett 83:1467–1470

    Article  Google Scholar 

  • Lau K, Sheu P, Kang IS (1994) Multiscale low-frequency circulation modes in the global atmosphere. J Atmos Sci 51(9):1169–1193

    Article  Google Scholar 

  • Leathers DJ, Yarnal B, Palecki MA (1991) The Pacific/North American teleconnection pattern and United States climate. Part I: regional temperature and precipitation associations. J Clim 4(5):517–528

    Article  Google Scholar 

  • Mantua N, Hare S, Zhang Y, Wallace J, Francis R (1997) A Pacific interdecadal climate oscillation with impacts on salmon production. Bull Am Meteorol Soc 78(6):1069–1079

    Article  Google Scholar 

  • Marshall G (2003) Trends in the southern annular mode from observations and reanalyses. J Clim 16(24):4134–4143

    Article  Google Scholar 

  • Marshall GJ (2007) Half-century seasonal relationships between the southern annular mode and Antarctic temperatures. Int J Climatol 27(3):373–383

    Article  Google Scholar 

  • Miller R (1981) Simultaneous statistical inference. Springer, Berlin

    Book  Google Scholar 

  • Mo KC (2000) Relationships between low-frequency variability in the Southern Hemisphere and sea surface temperature anomalies. J Clim 13(20):3599–3610

    Article  Google Scholar 

  • Mo KC, Higgins RW (1998) The Pacific-South American modes and tropical convection during the Southern Hemisphere winter. Mon Weather Rev 126:1581–1596

    Article  Google Scholar 

  • Müller M, Baier G, Galka A, Stephani U, Muhle H (2005) Detection and characterization of changes of the correlation structure in multivariate time series. Phys Rev E 71(046):116

    Google Scholar 

  • O’Lenic E, Livezey R (1988) Practical considerations in the use of rotated principal component analysis (RPCA) in diagnostic studies of upper-air height fields. Mon Weather Rev 116:1682–1689

    Article  Google Scholar 

  • Osborn T, Briffa K, Tett S, Jones P, Trigo R (1999) Evaluation of the North Atlantic Oscillation as simulated by a coupled climate model. Clim Dyn 15(9):685–702

    Article  Google Scholar 

  • Paluš M, Hartman D, Hlinka J, Vejmelka M (2011) Discerning connectivity from dynamics in climate networks. Nonlinear Process Geophys 18(5):751–763

    Article  Google Scholar 

  • Pittock AB (1984) On the reality, stability and usefulness of Southern Hemisphere teleconnections. Aust Meteorol Mag 32(2):75–82

  • Plerou V, Gopikrishnan P, Rosenow B, Amaral LN, Stanley HE (1999) Universal and nonuniversal properties of cross correlations in financial time series. Phys Rev Letters 83:1471–1474

    Article  Google Scholar 

  • Rayner N, Parker D, Horton E, Folland C, Alexander L, Rowell D, Kent E, Kaplan A (2003) Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J Geophys Res Atmos 108(D14):4407

  • Richman M (1986) Rotation of principal components. Int J Climatol 6:293–335

    Article  Google Scholar 

  • Richman M (1987) Rotation of principal components: a reply. Int J Climatol 7:511–520

    Article  Google Scholar 

  • Rogers J (1990) Patterns of low-frequency monthly sea level pressure variability (1899–1986) and associated wave cyclone frequencies. J Clim 3:1364–1379

    Article  Google Scholar 

  • Rogers JC, van Loon H (1982) Spatial variability of sea level pressure and 500 mb height anomalies over the Southern Hemisphere. Mon Weather Rev 110(10):1375–1392

    Article  Google Scholar 

  • Sáenz J, Zubillaga J, Rodríguez-Puebla C (2001) Interannual winter temperature variability in the north of the Iberian Peninsula. Clim Res 16(3):169–179

    Article  Google Scholar 

  • Schlesinger M, Ramankutty N (1994) An Oscillation in the global climate system of period 65–70 years. Nature 367(6465):723–726

    Article  Google Scholar 

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  Google Scholar 

  • Sengupta A, Mitra P (1999) Distributions of singular values for some random matrices. Phys Rev E 60:3389–3392

    Article  Google Scholar 

  • Slonosky VC, Jones PD, Davies TD (2001) Instrumental pressure observations and atmospheric circulation from the 17th and 18th centuries: London and Paris. Int J Climatol 21:285–298

    Article  Google Scholar 

  • Steinhaeuser K, Tsonis A (2013) A climate model intercomparison at the dynamics level. Clim Dyn 1–6. doi:10.1007/s00382-013-1761-5

  • Steinhaeuser K, Ganguly A, Chawla N (2011) Multivariate and multiscale dependence in the global climate system revealed through complex networks. Clim Dyn 39:889–895

    Article  Google Scholar 

  • Trenberth K (1997) The definition of El Niňo. Bull Am Meteorol Soc 78(12):2771–2777

    Article  Google Scholar 

  • Tsonis A, Roebber P (2004) The architecture of the climate network. Phys A 333:497–504

    Article  Google Scholar 

  • Tsonis A, Swanson K, Roebber P (2006) What do networks have to do with climate? Bull Am Meteorol Soc 87:585

    Article  Google Scholar 

  • Vejmelka M, Paluš M (2010) Partitioning networks into clusters and residuals with average association. Chaos 20(033):103

    Google Scholar 

  • Walker G, Bliss E (1932) World Weather. V Mem R Meteorol Soc 4(36):53–84

    Google Scholar 

  • Wallace J, Gutzler D (1981) Teleconnections in the geopotential height field during the Northern Hemisphere winter. Mon Weather Rev 109:784–812

    Article  Google Scholar 

  • Wang C, Kucharski F, Barimalala R, Bracco A (2009) Teleconnections of the tropical Atlantic to the tropical Indian and Pacific Oceans: a review of recent findings. Meteorol Z 18(4):445–454

    Article  Google Scholar 

  • Werner PC, von Storch H (1993) Interannual variability of Central European mean temperature in January/February and its relation to large-scale circulation. Clim Res 3:195–207

    Article  Google Scholar 

  • Wu B, Zhang R, D’Arrigo R (2006) Distinct modes of the East Asian winter monsoon. Mon Weather Rev 134(8):2165–2179

    Article  Google Scholar 

Download references

Acknowledgments

This study was supported by the Czech Science Foundation, Project No. P103/11/J068. The work of J. Hlinka and D. Hartman was also partially supported by Grant 13-17187S of the Czech Science Foundation.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin Vejmelka.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (ZIP 5616 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vejmelka, M., Pokorná, L., Hlinka, J. et al. Non-random correlation structures and dimensionality reduction in multivariate climate data. Clim Dyn 44, 2663–2682 (2015). https://doi.org/10.1007/s00382-014-2244-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00382-014-2244-z

Keywords

  • Climate dynamics
  • Sea level pressure
  • Surface air temperature
  • Principal component analysis
  • Varimax
  • Complex networks
  • Modes of variability