Evaluating EOF modes against a stochastic null hypothesis
In this paper it is suggested that a stochastic isotropic diffusive process, representing a spatial first order auto regressive process (AR(1)-process), can be used as a null hypothesis for the spatial structure of climate variability. By comparing the leading empirical orthogonal functions (EOFs) of a fitted null hypothesis with EOF modes of an observed data set, inferences about the nature of the observed modes can be made. The concept and procedure of fitting the null hypothesis to the observed EOFs is in analogy to time analysis, where an AR(1)-process is fitted to the statistics of the time series in order to evaluate the nature of the time scale behavior of the time series. The formulation of a stochastic null hypothesis allows one to define teleconnection patterns as those modes that are most distinguished from the stochastic null hypothesis. The method is applied to several artificial and real data sets including the sea surface temperature of the tropical Pacific and Indian Ocean and the Northern Hemisphere wintertime and tropical sea level pressure.
This work was motivated by fruitful and inspiring discussions with Alexander Gershunov and Thomas Reichler. Comments from Ian Jolliffe and the anonymous reviewers helped to improve this analysis significantly. Furthermore, I like to thank Noel Keenlyside, Mojib Latif, Katja Lorbacher, Oliver Timm, Jörg Wegener and Jürgen Willebrand for comments and proof reading.
- Folland CK, Parker DE, Colman AW, Washington R (1999) Large scale modes of ocean surface temperature since the late nineteenth century. In: Navarra A (ed) Beyond El Nino. Springer, Berlin Heidelberg New York, pp 73–102Google Scholar
- Jolliffe IT (2002) Principal component analysis, 2nd edn. Springer, Berlin Heidelberg New York, pp 150–166Google Scholar
- Kalnay E, Kanamitsu M, Kistler M, Collins R, Deaven W, Gandin D, Iredell L, Saha M, White S, Woollen G, Zhu J, Chelliah Y, Ebisuzaki M, Higgins W, Janowiak W, Mo J, Ropelewski KC, Wang C, Leetmaa J, Reynolds A, Jenne R, Joseph R, Dennis R (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteor Soc 77(3):437–471CrossRefGoogle Scholar
- North GR, Cahalan RF, Coakley JA (1981) Energy-balance climate models. Rev Geophys Sp Phys 19:91–121Google Scholar
- Saji NH, Goswami BN, Vinayachandran PN, Yamagata T (1999) A dipole mode in the tropical Indian Ocean. Nature 401:360–363Google Scholar
- von Storch H, Zwiers FW (1999) Statistical analysis in climate research. Cambridge University Press, Cambridge. ISBN 0 521 45071 3, 494 ppGoogle Scholar