Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity

Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The choice of dependence measure is key for the results of the subsequent analysis and interpretation. The use of linear Pearson’s correlation coefficient is widespread and convenient. On the other side, as the climate is widely acknowledged to be a nonlinear system, nonlinear dependence quantification methods, such as those based on information-theoretical concepts, are increasingly used for this purpose. In this paper we outline an approach that enables well informed choice of dependence measure for a given type of data, improving the subsequent interpretation of the results. The presented multi-step approach includes statistical testing, quantification of the specific non-linear contribution to the interaction information, localization of areas with strongest nonlinear contribution and assessment of the role of specific temporal patterns, including signal nonstationarities. In detail we study the consequences of the choice of a general nonlinear dependence measure, namely mutual information, focusing on its relevance and potential alterations in the discovered dependence structure. We document the method by applying it to monthly mean temperature data from the NCEP/NCAR reanalysis dataset as well as the ERA dataset. We have been able to identify main sources of observed non-linearity in inter-node couplings. Detailed analysis suggested an important role of several sources of nonstationarity within the climate data. The quantitative role of genuine nonlinear coupling at monthly scale has proven to be almost negligible, providing quantitative support for the use of linear methods for monthly temperature data.

[1]  M. Paluš,et al.  Nonlinear Processes in Geophysics , 2000 .

[2]  M. Paluš,et al.  Information theoretic test for nonlinearity in time series , 1993 .

[3]  Norbert Marwan,et al.  The backbone of the climate network , 2009, 1002.2100.

[4]  Maurizio Corbetta,et al.  Functional connectivity in resting-state fMRI: Is linear correlation sufficient? , 2011, NeuroImage.

[5]  Milan Paluš,et al.  Testing for Nonlinearity in Weather Records , 1994 .

[6]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[7]  Milan Paluš,et al.  Phase-coherent Oscillatory Modes in Solar and Geomagnetic Activity and Climate Variability , 2022 .

[8]  M. Paluš.  Detecting phase synchronization in noisy systems , 1997 .

[9]  M. Paluš,et al.  Directionality of coupling from bivariate time series: how to avoid false causalities and missed connections. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  Sang-Wook Yeh,et al.  ENSO nonlinearity in a warming climate , 2011 .

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

[13]  Dimitris Kugiumtzis,et al.  Evaluation of Mutual Information estimators for Time Series , 2009, Int. J. Bifurc. Chaos.

[14]  Michael Ghil,et al.  Oscillatory Climate Modes in the Eastern Mediterranean and Their Synchronization with the North Atlantic Oscillation , 2010 .

[15]  M. Paluš.  Testing for nonlinearity using redundancies: quantitative and qualitative aspects , 1994, comp-gas/9406002.

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

[17]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

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

[19]  D. Stephenson,et al.  Probability-based methods for quantifying nonlinearity in the ENSO , 2003 .

[20]  Jürgen Kurths,et al.  Investigating the topology of interacting networks , 2011, 1102.3067.

[21]  M. Paluš,et al.  Nonlinear Processes in Geophysics Northern Hemisphere patterns of phase coherence between solar / geomagnetic activity and NCEP / NCAR and ERA 40 near-surface air temperature in period 7 – 8 years oscillatory modes , 2011 .

[22]  Theiler,et al.  Generating surrogate data for time series with several simultaneously measured variables. , 1994, Physical review letters.

[23]  A. Kraskov,et al.  Estimating mutual information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Fei-Fei Jin,et al.  Nonlinearity and Asymmetry of ENSO(. , 2004 .

[25]  J. Thepaut,et al.  The ERA‐Interim reanalysis: configuration and performance of the data assimilation system , 2011 .

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

[27]  Milan Palus,et al.  Small-world topology of functional connectivity in randomly connected dynamical systems , 2012, Chaos.

[28]  William W. Hsieh,et al.  Nonlinear atmospheric teleconnections , 2006 .

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

[30]  Jürgen Kurths,et al.  Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks , 2011, ArXiv.

[31]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[32]  C. Spearman.  The proof and measurement of association between two things. , 2015, International journal of epidemiology.

[33]  S. Saigal,et al.  Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  P. Rapp,et al.  Statistical validation of mutual information calculations: comparison of alternative numerical algorithms. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Milan Paluš,et al.  Quasi-biennial oscillations extracted from the monthly NAO index and temperature records are phase-synchronized , 2006 .

[36]  A. Sterl,et al.  The ERA‐40 re‐analysis , 2005 .

[37]  C. Simmer,et al.  Statistical characteristics of surrogate data based on geophysical measurements , 2006 .

[38]  Cees Diks,et al.  Redundancies in the Earth's climatological time series , 2000 .

[39]  L. D. Costa,et al.  Community structure and dynamics in climate networks , 2011 .

[40]  M. Paluš,et al.  The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks. , 2011, Chaos.

[41]  M. Kendall.  A NEW MEASURE OF RANK CORRELATION , 1938 .

[42]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.