Chapter 13
Spatial Patterns: EOFs
and CCA
by Hans von Storch
13.1 Introd uction
Many analyses of climate data sets suIfer from high dimensions of the variables representing the state of the system at any given time. Often it is
advisable to split the full phase space into two subspaces. The "signal" space
is spanned by few characteristic patterns and is supposed to represent the dynamics of the considered process. The "noise subspace" , on the other hand, is
high-dimensional and contains all processes which are purportedly irrelevant
in their details for the "signal subspace" .
The decision of what to call "signal" and wh at to call "noise" is non-trivial.
The term "signal" is not a weIl-defined expression in this context. In experimental physics, the signal is weIl defined, and the noise is mostly the
uncertainty of the measurement and represents merely a nuisance. In climate research, the signal is defined by the interest of the researcher and the
noise is everything else unrelated to this object of interest. Only in infrequent cases is the noise due to uncertainties of the measurement, sometimes
the noise comprises the errors introduced by deriving "analyses" , i.e., by deriving from many irregularly distributed point observations a complete map.
But in most cases the noise is made up of weIl-organized processes whose
Acknowledgements: I am grateful to Vietor Oeaiia, Gabriele Hegerl, Bob Livezey and
Robert Vautard for their most useful eomments which led to a signifieant (not statistically
meant) improvement of the manuseript. Gerassimos Korres supplied me with Figures 13.1
and 13.2.
Spatial Patterns: EOFs
and CCA
by Hans von Storch
13.1 Introd uction
Many analyses of climate data sets suIfer from high dimensions of the variables representing the state of the system at any given time. Often it is
advisable to split the full phase space into two subspaces. The "signal" space
is spanned by few characteristic patterns and is supposed to represent the dynamics of the considered process. The "noise subspace" , on the other hand, is
high-dimensional and contains all processes which are purportedly irrelevant
in their details for the "signal subspace" .
The decision of what to call "signal" and wh at to call "noise" is non-trivial.
The term "signal" is not a weIl-defined expression in this context. In experimental physics, the signal is weIl defined, and the noise is mostly the
uncertainty of the measurement and represents merely a nuisance. In climate research, the signal is defined by the interest of the researcher and the
noise is everything else unrelated to this object of interest. Only in infrequent cases is the noise due to uncertainties of the measurement, sometimes
the noise comprises the errors introduced by deriving "analyses" , i.e., by deriving from many irregularly distributed point observations a complete map.
But in most cases the noise is made up of weIl-organized processes whose
Acknowledgements: I am grateful to Vietor Oeaiia, Gabriele Hegerl, Bob Livezey and
Robert Vautard for their most useful eomments which led to a signifieant (not statistically
meant) improvement of the manuseript. Gerassimos Korres supplied me with Figures 13.1
and 13.2.