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ABSTRACT
New computer software that permits more versatility in the harmonic analysis of tidal time series is described and tested. Specific improvements to traditional methods include the analysis of randomly sampled and/or multiyear data; more accurate nodal correction, inference, and astronomical argument adjustments through direct incorporation in the least squares matrix; multiconstituent inferences from a single reference constituent; correlation matrices and error estimates that facilitate decisions on the selection of constituents for the analysis; and a single program that analyzes one- or two-dimensional time series. This new methodology is evaluated through comparisons with results from old techniques and then applied to two problems that could not have been accurately solved with older software. They are (i) the analysis of ocean station temperature time series spanning 25 yr, and (ii) the analysis of satellite altimetry from a ground track whose proximity to land has led to significant data dropout. This new software is free as part of the Institute of Ocean Sciences (IOS) Tidal Package and can be downloaded, along with sample input data and an explanatory readme file.
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1. Introduction
There have been many advances in tidal analysis and prediction since the earliest documented predictions for the bore on the Chhien-Thang River in China and flood tide at London Bridge in the eleventh and thirteenth centuries, respectively (Cartwright 1999). Parker (2007) has recently published a guide on the various considerations that are needed, and contemporary approaches that can be used, to carry out accurate tidal analyses and predictions. One of the most successful and widely used approaches has been, and continues to be, harmonic analysis wherein the energy at specific tidal frequencies is determined by a mathematical fitting procedure, usually least squares. Though computer software that performs harmonic tidal analysis of one- and twodimensional time series has been are available for more than 40 yr (links to software packages are available online at http://www.pol.ac.uk/psmsl/training/analysis.html), many of these codes are restrictive in both the form of the input time series (e.g., regularly sampled, albeit with gaps) and the manner in which nodal correction, astronomical argument, and inference calculations are made (e.g., as adjustments to results from a least squares fit). In the early days of harmonic analysis, these restrictions arose...