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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