Hi R folk,
I have a time series of scalar downstream velocity data measured across a tidal
channel. The variables are the locations in bins across the channel, the
samples are over time.
The fluctuation over the tide cycle is an enormous fraction of the time
variation in the data ... 96%. The spectral energy of the tide is concentrated
in a couple bands that make up the major constituents of the tide. Over short
periods, we could pretend there are just two frequencies, though they are
really clusters of nearby frequencies that start to diverge as the record gets
long. Tidal frequencies also beat which causes monthly/14-day "spring-neap"
cycles with greatly accentuated or attenuated inequalities between high tide
and low tide.
Despite the dominance of the tide, there is variation across the channel that
is of interest. A good physical interpretation of what is happening is not just
that amplitude varies across the channel but that the phase on the edge of the
channel gets in and out of shape. So a data description that could characterize
short-medium duration anomalies in relative phase would be really useful and
hints at some sort of complex analysis. These may be excited by the spring-neap
cycle, and my concern with spectral PC analysis that isolates a single band
would be that it might miss that.
Here are the questions:
1. Is there a variant of PC (or other) analysis in R can characterize this type
of variation well?
2. Should I sweat the way a simple time fluctuation dominates the series? I
don't object to having a big PC1, but it doesn't fit the textbook examples very
well. Are there techniques (rotation, normalization) that are designed for this
situation? I seem to run into it in all sorts of applications.
Thanks,
Eli
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