Evaluating
EOF modes against a stochastic null hypothesis
(DEOF-Analysis)
Abstract
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.
References
Dommenget, D., 2007: Evaluating EOF modes against a stochastic null hypothesis. Climate dynamics, 28, 5, pages 517-531. -> PDF-file
Codes
A MATLAB-script is available to compute the Eigenvalue spectrum comparison and DEOFs as proposed in the Dommenget 2007 paper.
For a start up you can try the DEOF-analysis starter-set, which provides some data and MATLAB scripts to calculate one example. The example is taken from Dommenget (2007) , Fig.4. The tar-file also includes two figures that should be reproduced. Note: numerical differences can result in change of signs in the resulting EOF or DEOF patterns. To do the analysis you only have to run the MATLAB-script deof_analysis_shell.m, which is provided in the tar-file:
In the Bayr and Dommenget [2014] study a MATLAB-script for comparing the EOFs of two data sets is introduced:
Citations
Studies that have applied my DEOF-analysis:
Bayr, T. and D. Dommenget, 2014:
Comparing the spatial structure of variability in two datasets against each other on the basis of EOF modes.
Climate Dynamics, 42, 1631-1648. [pdf-file]
Dommenget, D., 2009:
An Objective Analysis of the Observed Spatial Structure of the Tropical Indian Ocean SST Variability.
Climate Dynamics, in press. DOI 10.1007/s00382-010-0787-1
Cook, E.R., K.J. Anchukaitis, B.M. Buckley, R.D. D'Arrigo, G.C. Jacoby, W.E. Wright, 2010:
Asian Monsoon Failure and Megadrought During the Last Millennium.
Science, 328, 5977, Pages: 486-489.
Suselj K., A. Sood, D. Heinemann, 2009:
North Sea near-surface wind climate and its relation to the large-scale circulation patterns.
THEORETICAL AND APPLIED CLIMATOLOGY, 99, 3-4, Pages: 403-419.
Hannachi A. and D. Dommenget, 2009:
Is the Indian Ocean SST variability a homogeneous diffusion process?
Climate Dynamics, 33, 4, Pages: 535-547.