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

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.

[1]  M. Kimoto.  Simulated change of the east Asian circulation under global warming scenario , 2005 .

[2]  P. Jones,et al.  Extratropical circulation indices in the Southern Hemisphere based on station data , 1999 .

[3]  Paul J. Roebber,et al.  What Do Networks Have to Do with Climate , 2006 .

[4]  X. Cheng,et al.  Robustness of Low-Frequency Circulation Patterns Derived from EOF and Rotated EOF Analyses , 1995 .

[5]  K. Hasselmann.  PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patterns , 1988 .

[6]  J. Hurrell.  Decadal Trends in the North Atlantic Oscillation: Regional Temperatures and Precipitation , 1995, Science.

[7]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[8]  Alberto M. Mestas-Nuñez,et al.  How ubiquitous is the dipole relationship in tropical Atlantic sea surface temperatures , 1999 .

[9]  Milan Paluš,et al.  Discerning connectivity from dynamics in climate networks , 2011 .

[10]  K. Mo,et al.  Relationships between Low-Frequency Variability in the Southern Hemisphere and Sea Surface Temperature Anomalies , 2000 .

[11]  M. Paluš,et al.  Partitioning networks into clusters and residuals with average association. , 2010, Chaos.

[12]  Michael A. Palecki,et al.  The Pacific/North American teleconnection pattern and United States climate , 1991 .

[13]  In-Sik Kang,et al.  Multiscale low-frequency circulation modes in the global atmosphere , 1994 .

[14]  J. Wallace,et al.  A Pacific Interdecadal Climate Oscillation with Impacts on Salmon Production , 1997 .

[15]  J. Wallace,et al.  Teleconnections in the Geopotential Height Field during the Northern Hemisphere Winter , 1981 .

[16]  R. Reynolds,et al.  The NCEP/NCAR 40-Year Reanalysis Project , 1996, Renewable Energy.

[17]  Clara Deser,et al.  Sea surface temperature variability: patterns and mechanisms. , 2010, Annual review of marine science.

[18]  Robert E. Livezey,et al.  Practical Considerations in the Use of Rotated Principal Component Analysis (RPCA)in Diagnostic Studies of Upper-Air Height Fields , 1988 .

[19]  Jeffery C. Rogers,et al.  Patterns of Low-Frequency Monthly Sea Level Pressure Variability (1899–1986) and Associated Wave Cyclone Frequencies , 1990 .

[20]  Anirvan M. Sengupta,et al.  Distributions of singular values for some random matrices. , 1997, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  M. Richman,et al.  Rotation of principal components , 1986 .

[22]  Ian T. Jolliffe,et al.  Rotation of principal components: Some comments , 1987 .

[23]  Freeman J. Dyson,et al.  DISTRIBUTION OF EIGENVALUES FOR A CLASS OF REAL SYMMETRIC MATRICES. , 1971 .

[24]  GILBERT WALKER,et al.  World Weather , 1928, Nature.

[25]  Trevor D. Davies,et al.  Instrumental pressure observations and atmospheric circulation from the 17th and 18th centuries: London and Paris , 2001 .

[26]  Nitesh V. Chawla,et al.  Multivariate and multiscale dependence in the global climate system revealed through complex networks , 2012, Climate Dynamics.

[27]  W. Collins,et al.  The NCEP–NCAR 50-Year Reanalysis: Monthly Means CD-ROM and Documentation , 2001 .

[28]  Jucundus Jacobeit,et al.  Classifications in climate research , 2010 .

[29]  Jeffery C. Rogers,et al.  Spatial Variability of Sea Level Pressure and 500 mb Height Anomalies over the Southern Hemisphere , 1982 .

[30]  John E. Kutzbach,et al.  LARGE-SCALE FEATURES OF MONTHLY MEAN NORTHERN HEMISPHERE ANOMALY MAPS OF SEA-LEVEL PRESSURE , 1970 .

[31]  Kevin E. Trenberth,et al.  The Definition of El Niño. , 1997 .

[32]  D. Dommenget.  Evaluating EOF modes against a stochastic null hypothesis , 2007 .

[33]  Ian T. Jolliffe,et al.  Empirical orthogonal functions and related techniques in atmospheric science: A review , 2007 .

[34]  Radan Huth,et al.  The effect of various methodological options on the detection of leading modes of sea level pressure variability , 2006 .

[35]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[36]  Annalisa Bracco,et al.  Teleconnections of the tropical Atlantic to the tropical Indian and Pacific Oceans: A review of recent findings , 2009 .

[37]  I. Jolliffe.  Principal Component Analysis , 2002 .

[38]  A. Barnston,et al.  Classification, seasonality and persistence of low-frequency atmospheric circulation patterns , 1987 .

[39]  Hisashi Nakamura,et al.  Scandinavian pattern and its climatic impact , 2007 .

[40]  Radan Huth,et al.  Time variations of the effects of circulation variability modes on European temperature and precipitation in winter , 2008 .

[41]  John M. Wallace,et al.  Planetary-Scale Atmospheric Phenomena Associated with the Southern Oscillation , 1981 .

[42]  H. Kaiser.  The varimax criterion for analytic rotation in factor analysis , 1958 .

[43]  J. W. Kidson,et al.  Tropical Eigenvector Analysis and the Southern Oscillation , 1975 .

[44]  P. Jones,et al.  Evaluation of the North Atlantic Oscillation as simulated by a coupled climate model , 1999 .

[45]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[46]  H. Storch,et al.  Interannual variability of Central European mean temperature in January-February and its relation to large-scale circulation , 1993 .

[47]  Karsten Steinhaeuser,et al.  A climate model intercomparison at the dynamics level , 2012, Climate Dynamics.

[48]  Jon Sáenz,et al.  Interannual winter temperature variability in the north of the Iberian Peninsula , 2001 .

[49]  Serge. Martin,et al.  700‐HPA geopotential height anomalies from a statistical analysis of the French Hemis data set , 1992 .

[50]  Ilias Fountalis,et al.  Spatio-temporal network analysis for studying climate patterns , 2014, Climate Dynamics.

[51]  Stéphane Dray,et al.  On the number of principal components: A test of dimensionality based on measurements of similarity between matrices , 2008, Comput. Stat. Data Anal..

[52]  Michael E. Schlesinger,et al.  An oscillation in the global climate system of period 65–70 years , 1994, Nature.

[53]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[54]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[55]  R. Wayne Higgins,et al.  The Pacific–South American Modes and Tropical Convection during the Southern Hemisphere Winter , 1998 .

[56]  D. N. Asimakopoulos,et al.  The eastern Mediterranean teleconnection pattern: identification and definition , 2007 .

[57]  G. Marshall.  Trends in the Southern Annular Mode from Observations and Reanalyses , 2003 .

[58]  Milan Paluš,et al.  Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity , 2012, Climate Dynamics.

[59]  Paul J. Roebber,et al.  The architecture of the climate network , 2004 .

[60]  D. Gong,et al.  Definition of Antarctic Oscillation index , 1999 .

[61]  Gareth J. Marshall,et al.  Half‐century seasonal relationships between the Southern Annular mode and Antarctic temperatures , 2007 .

[62]  John E. Kutzbach,et al.  Empirical Eigenvectors of Sea-Level Pressure, Surface Temperature and Precipitation Complexes over North America , 1967 .

[63]  Michaf. L. B. Richman.  Rotation of principal components: a reply , 1987 .

[64]  Elizabeth C. Kent,et al.  Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century , 2003 .

[65]  Thorsten Dickhaus,et al.  Simultaneous Statistical Inference , 2014, Springer Berlin Heidelberg.

[66]  Yihui Ding,et al.  Distinct Modes of the East Asian Winter Monsoon , 2006 .

[67]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[68]  Alberto M. Mestas-Nuñez,et al.  The Atlantic Multidecadal Oscillation and its relation to rainfall and river flows in the continental U.S. , 2001 .

[69]  U. Stephani,et al.  Detection and characterization of changes of the correlation structure in multivariate time series. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.