State‐space discrimination and clustering of atmospheric time series data based on Kullback information measures

Statistical problems in atmospheric science are frequently characterized by large spatio-temporal data sets and pose difficult challenges in classification and pattern recognition. Here, we consider the problem of identifying geographically homogeneous regions based on similarities in the temporal dynamics of weather patterns. Two disparity measures are proposed and applied to cluster time series of observed monthly temperatures from locations across Colorado, U.S.A. The two disparity measures are based on state-space models, where the monthly temperature anomaly dynamics and seasonal variation are represented by latent processes. Our disparity measures produce clusters consistent with known atmospheric flow structures. In particular, the temporal anomaly pattern is related to the topography of Colorado, where, separated by the Continental Divide, the flow structures in the western and eastern parts of the state have different dynamics. The results further suggest that seasonal variation may be affected by locally changing solar radiation levels primarily associated with elevation variations across the Rocky Mountains. The general methodology is outlined and developed in the Appendix. We conclude with a discussion of extensions to time varying and non-stationary systems. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Michael B. Richman,et al.  On the Application of Cluster Analysis to Growing Season Precipitation Data in North America East of the Rockies , 1995 .

[2]  P. Laycock,et al.  SPECTRAL RATIO DISCRIMINANTS AND INFORMATION THEORY , 1981 .

[3]  Jun S. Liu,et al.  Mixture Kalman filters , 2000 .

[4]  Richard A. Davis,et al.  Time Series: Theory and Methods (2Nd Edn) , 1993 .

[5]  Michael Ghil,et al.  Advanced data assimilation in strongly nonlinear dynamical systems , 1994 .

[6]  J. Cavanaugh,et al.  Assessing the predictive influence of cases in a state space process , 1999 .

[7]  P. Houtekamer,et al.  A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation , 2001 .

[8]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[9]  G. Burroughs,et al.  THE ROTATION OF PRINCIPAL COMPONENTS , 1961 .

[10]  W. Liggett.  On the Asymptotic Optimality of Spectral Analysis for Testing Hypotheses About Time Series , 1971 .

[11]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[12]  J. Alagón.  SPECTRAL DISCRIMINATION FOR TWO GROUPS OF TIME SERIES , 1989 .

[13]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[14]  P. J. Diggle,et al.  TESTS FOR COMPARING TWO ESTIMATED SPECTRAL DENSITIES , 1986 .

[15]  Robert H. Shumway,et al.  Discrimination and Clustering for Multivariate Time Series , 1998 .

[16]  R. Stone.  Weather types at Brisbane, Queensland: An example of the use of principal components and cluster analysis , 1989 .

[17]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[18]  M. A. Wincek.  Applied Statistical Time Series Analysis , 1990 .

[19]  R. Fovell,et al.  Climate zones of the conterminous United States defined using cluster analysis , 1993 .

[20]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[21]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[22]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.

[23]  N. Cressie,et al.  A dimension-reduced approach to space-time Kalman filtering , 1999 .

[24]  Linear discriminant function for complex normal time series , 1992 .

[25]  Charles E. Heckler,et al.  Applied Multivariate Statistical Analysis , 2005, Technometrics.

[26]  Richard A. Davis,et al.  Time Series: Theory and Methods (2nd ed.). , 1992 .

[27]  T. J. Alsop.  The Natural Seasons of Western Oregon and Washington , 1989 .

[28]  J. William Ahwood,et al.  CLASSIFICATION , 1931, Foundations of Familiar Language.

[29]  Richard G. Derwent,et al.  Radiative forcing in the 21st century due to ozone changes in the troposphere and the lower stratosphere , 2003 .

[30]  kwang-yul kim,et al.  EOF-Based Linear Prediction Algorithm: Examples , 1999 .

[31]  R. Shumway,et al.  Linear Discriminant Functions for Stationary Time Series , 1974 .

[32]  David F. Findley,et al.  Time Series: Forecasting, Simulation, Applications (Gareth Janacek and Louise Swift) , 1995, SIAM Rev..

[33]  Chris Snyder,et al.  Toward a nonlinear ensemble filter for high‐dimensional systems , 2003 .

[34]  K. Mo,et al.  Cluster analysis of multiple planetary flow regimes , 1988 .

[35]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[36]  P. Houtekamer,et al.  Data Assimilation Using an Ensemble Kalman Filter Technique , 1998 .

[37]  Solomon Kullback,et al.  Information Theory and Statistics , 1970, The Mathematical Gazette.

[38]  Rahim Chinipardaz,et al.  Discrimination of AR, MA and ARMA time series models , 1996 .

[39]  竹安 数博,et al.  Time series analysis and its applications , 2007 .

[40]  Michael B. Richman,et al.  Climatic Pattern Analysis of Three- and Seven-Day Summer Rainfall in the Central United States: Some Methodological Considerations and a Regionalization , 1985 .

[41]  kwang-yul kim,et al.  A Comparison Study of EOF Techniques: Analysis of Nonstationary Data with Periodic Statistics , 1999 .

[42]  Vincent Kanade,et al.  Clustering Algorithms , 2021, Wireless RF Energy Transfer in the Massive IoT Era.

[43]  Guy Melard,et al.  Testing for homogeneity and stability of time series , 1983 .

[44]  Will Gersch,et al.  NEAREST NEIGHBOR RULE CLASSIFICATION OF STATIONARY AND NONSTATIONARY TIME SERIES , 1981 .

[45]  Richard H. Jones,et al.  Longitudinal Data with Serial Correlation : A State-Space Approach , 1994 .