A new method for estimating extreme sea levels from short sea-level records in a tide-dominated environment is presented. A short sea-level record is first decomposed into its constituent components such as tide, mean level of the sea, and storm surge. Monte Carlo simulations are then incorporated into an empirical simulation technique to randomly recombine the components to produce an annual series of sea levels at high tide from which the annual maximum is selected. The yearly simulation is repeated many thousands of times to yield robust statistics on extreme values. Comparison of the method with the traditional extreme-value analysis of annual maximum sea levels for a 33-year record shows that the methods give similar results. The method is likely to be most useful for estimation of extreme sea levels at locations where the available sea-level record is short (<15 years) and where the various sea-level components can be assumed to be largely independent.

The data processing required to extract long waves from tide-gauge data is described and applied to three diverse but typical examples: meteorologically generated long waves (rissaga), far infragravity waves, and tsunami. The steps are: detiding, despiking, degapping, high-pass filtering, and denoising. Orthogonal wavelet decomposition is used for despiking, high-pass filtering, and denoising. This has the advantage that it can be used for nonstationary data such as rissaga and tsunami because the basis function (the mother wavelet) is localized. The long-wave extraction method has evolved from development of real-time systems for monitoring long waves for navigation purposes. Using the technique, there are hundreds of modern tide gauges around the world (every major port has one) whose data could be used to monitor long waves that affect navigation and cause a hazard.