Author(s): H. F. P. Van Den Boogaard; H. Gerritsen; A. E. Mynett
Linked Author(s):
Keywords: Basis Function Models; Tidal Analysis; Model and Data Uncertainties; Confidence Intervals; Parameter Identification; Calibration; Cost Functions; Maximum Likelihood
Abstract: In tidal analysis a time series of observed water levels or currents is often modelled as a superposition of harmonic components. The number of tidal constituents and their radial frequencies are prescribed beforehand while the amplitudes and phases form the model's unknown parameters and must be estimated from the observed time series. In this way a tidal analysis forms a special case of the calibration of a basis function model. In this paper we will in particular deal with uncertainties in linear basis function models, and how these uncertainties can appropriately be included in the model's calibration. The calibration procedure is based on the Maximum Likelihood principle and as a result it will be possible to find measures for the uncertainties of the identified model parameters (e.g. spreads and/or confidence intervals), and the uncertainties that are subsequently involved in model predictions after calibration. When amplitudes and phases are used for the representation of a tidal time series, the actual basis function model is not linear in these parameters, and the uncertainties of the identified amplitudes and phases cannot be expressed anymore in ‘simple' analytical forms. In this case resampling techniques such as a Bootstrap or a Jack Knife algorithm provide important new opportunities to obtain the desired uncertainties after all. In the main text the mathematical background of uncertainty assessment in basis function models is worked out, and as an illustrative application the tidal analysis of a two years record of observed water levels at Flushing (The Netherlands) is presented.
Year: 2003