Pattern hunting in climate: a new method for finding trends in gridded climate data

Trends are very important in climate research and are ubiquitous in the climate system. Trends are usually estimated using simple linear regression. Given the complexity of the system, trends are expected to have various features such as global and local characters. It is therefore important to develop methods that permit a systematic decomposition of climate data into different trend patterns and remaining no-trend patterns. Empirical orthogonal functions and closely related methods, widely used in atmospheric science, are unable in general to capture trends because they are not devised for that purpose. The present paper presents a novel method capable of systematically capturing trend patterns from gridded data. The method is based on an eigenanalysis of the covariance/correlation matrix obtained using correlations between time positions of the sorted data, and trends are associated with the leading nondegenerate eigenvalues. Application to simple low-dimensional time series models and reanalyses data are presented and discussed. Copyright © 2006 Royal Meteorological Society.

[1]  H. B. Mann.  Nonparametric Tests Against Trend , 1945 .

[2]  ATesting for the Onset of Trend, Using Wavelets , 1999 .

[3]  J. Wallace,et al.  The Arctic oscillation signature in the wintertime geopotential height and temperature fields , 1998 .

[4]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[5]  John R. Lanzante,et al.  Resistant, Robust and Non-Parametric Techniques for the Analysis of Climate Data: Theory and Examples, Including Applications to Historical Radiosonde Station Data , 1996 .

[6]  R. Preisendorfer,et al.  Principal Component Analysis in Meteorology and Oceanography , 1988 .

[7]  K. Fang,et al.  Generalized Multivariate Analysis , 1990 .

[8]  A. O'Neill,et al.  Atmospheric multiple equilibria and non‐Gaussian behaviour in model simulations , 2001 .

[9]  D. Stephenson,et al.  Observed Trends and Teleconnections of the Siberian High: A Recently Declining Center of Action , 2005 .

[10]  John D. Horel,et al.  A Rotated Principal Component Analysis of the Interannual Variability of the Northern Hemisphere 500 mb Height Field , 1981 .

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

[12]  P. Jones,et al.  Asymmetric trends of daily maximum and minimum temperature: Empirical evidence and possible causes , 1993 .

[13]  Ian T. Jolliffe,et al.  A Cautionary Note on Artificial Examples of EOFs , 2003 .

[14]  Aapo Hyvärinen,et al.  Survey on Independent Component Analysis , 1999 .

[15]  N. Lau,et al.  The Cold Ocean-Warm Land Pattern: Model Simulation and Relevance to Climate Change Detection , 1998 .

[16]  Gene H. Golub,et al.  Matrix computations , 1983 .

[17]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[18]  Robert F. Cahalan,et al.  Sampling Errors in the Estimation of Empirical Orthogonal Functions , 1982 .

[19]  Detectability of step trends in the rate of atmospheric deposition of sulfate , 1985 .

[20]  Dennis P. Lettenmaier,et al.  Multivariate nonparametric tests for trend in water quality , 1988 .

[21]  M. Kendall.  Rank Correlation Methods , 1949 .

[22]  Michael B. Richman,et al.  Obliquely Rotated Principal Components: An Improved Meteorological Map Typing Technique? , 1981 .

[23]  David B. Stephenson,et al.  Probability-based methods for quantifying nonlinearity in the ENSO , 2003 .

[24]  I. Jolliffe,et al.  In search of simple structures in climate: simplifying EOFs , 2006 .

[25]  E. Oja,et al.  Independent Component Analysis , 2013 .

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

[27]  Stéphane Champely,et al.  How to separate long-term trends from periodic variation in water quality monitoring , 1997 .

[28]  G. C. Tiao,et al.  A canonical analysis of multiple time series , 1977 .

[29]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[30]  P. Guttorp,et al.  Trend assessment in a long memory dependence model using the discrete wavelet transform , 2004 .

[31]  J. M. Craddock,et al.  Problems and Prospects for Eigenvector Analysis in Meteorology , 1973 .

[32]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[33]  J. L. Hodges,et al.  Estimates of Location Based on Rank Tests , 1963 .

[34]  J. Wallace,et al.  Annular Modes in the Extratropical Circulation. Part I: Month-to-Month Variability* , 2000 .

[35]  John M. Wallace,et al.  The Pacific Center of Action of the Northern Hemisphere Annular Mode: Real or Artifact? , 2001 .

[36]  S. Yue,et al.  Power of the Mann–Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series , 2002 .

[37]  A. J. Collins,et al.  Introduction To Multivariate Analysis , 1981 .

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

[39]  Paul E. Lydolph,et al.  Climates of the Soviet Union , 1977 .

[40]  J. Wallace,et al.  Dynamic Contribution to Hemispheric Mean Temperature Trends , 1995, Science.

[41]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[42]  H. Storch,et al.  Statistical Analysis in Climate Research , 2000 .

[43]  A. Antoniadis,et al.  Wavelet Methods for Curve Estimation , 1994 .

[44]  David B. Stephenson,et al.  On the existence of multiple climate regimes , 2004 .

[45]  John M. Wallace,et al.  North atlantic oscillatiodannular mode: Two paradigms—one phenomenon , 2000 .

[46]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

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

[48]  Francis W. Zwiers,et al.  Climate change in recurrent regimes and modes of northern hemisphere atmospheric variability , 2001 .

[49]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[50]  S. Laughlin.  A Simple Coding Procedure Enhances a Neuron's Information Capacity , 1981, Zeitschrift fur Naturforschung. Section C, Biosciences.

[51]  Kevin P. Gallo,et al.  A new perspective on recent global warming: asymmetric trends of daily maximum and minimum temperature , 1993 .

[52]  A. Solow.  Detecting change in the composition of multispecies community. , 1994, Biometrics.

[53]  M. Latif,et al.  A Cautionary Note on the Interpretation of EOFs , 2002 .

[54]  T. DelSole.  Optimally Persistent Patterns in Time-Varying Fields , 2001 .