Text of Complex EOF - Jackson School of · PDF file 2015-03-31 · Complex EOF !...
Conventional EOF analysis allows the detection of standing oscillation.
For propagating oscillation, such as waves, they often show up as 2 or
more separate EOFs, instead of one mode of variation.
For large data with unknown dominant frequency and spatial scales,
cross-spectral analysis is less informative, especially for regional, non-
stationary phenomena characterized by short lived, irregularly
occurring and episodes or propagating wave signals. CEOF is more
A scalar field x j,t can be represented by
x j,t = aj
∑ (ω)cos ωt( )+ bj (ω)sin(ωt)
A propagating feature can be described by
∑ aj (ω)cos ωt( )+ bj (ω)sin(ωt)
+ i bj (ω)cos ωt( )− aj (ω)sin(ωt)
=x j,t + ix̂ j,t where x j,t is the original data, x̂ j,k is the quadrature function
or Hilbert transform. It's amplitude is the same as x j,t, but phase is advanced by π /2.
Examples of Hilbert transformation: Hilbert transforms
does not act as a low-pass filter upon the data It contains
as much energy due to noise as original data and it may
redistribute the noise to different part of the time series.
Vector form of the
Complex time series
One can use apply eigen-analysis to the correlation
between the jth and kth location to [X*j(t)] in a
similar way of conventional EOF, namely,
After subtract mean and normalize by standard deviation, we obtain