The analysis of contaminated tidal data

David Gamble

In this thesis we consider analysis of tidal data contaminated by secondary effects. These effects occur because of the tide, but do not have direct astronomical origin. Examples resulting from problems with instrument deployment and the presence of bores or solitons are discussed. We begin with a description of the physical forcing responsible for the generation of tides. The response and harmonic analysis methods are presented although we concentrate on the harmonic method. Parameter estimation is typically performed with least squares. We illustrate how methods such as the EM-algorithm and robust statistical methods may be applied to the analysis of tidal data. Problems associated with the direct application of robust techniques are discussed. A technique, with modifications to suit the large data sets, for identification of contamination using least trimmed squares is presented. Of particular importance to any analysis is the validity of the model. The analysis of tides relies heavily on an assumption of time invariance. We present a technique which may be used to test the assumption of time invariance for tidal models. High power against an alternative hypothesis of a phase shift in the tidal signal is demonstrated. The test is designed to indicate situations in which the tidal model is not appropriate. This may be due to time invariance of the tidal signal or to a combination of multiple signals with significant energy at tidal frequencies. Data in which soliton-like activity is known to occur are shown to fail the test for time invariance and hence model suitability. Given that the tidal model may not be suitable, we explore techniques which may be used to directly determine tidal extremes. We find that even here, innovations in analysis methods require a valid tidal model.

The analysis of contaminated tidal data

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