A ray tracing model that includes the effects of refraction in shallow water has been developed to allow the evaluation of a set of empirical formulae for the prediction of directional wave spectra. The formulae have been tested by hindcasting the waves at eight offshore sites in the North Sea during WHIST storms 3, 5 and 6. At the peak of a storm the model predicted significant wave heights that agreed with observed values to within the ±10% accuracy suggested by the Department of Energy. Although the model is first-generation and cannot resolve non-linear interactions, it is computationally efficient and may be suitable for many engineering applications. In particular, it could be used in sensitivity tests for determining the grid spacing and coastal wind correction factors that should be applied during the use of second-and third-generation wave models. The good results obtained during high wave conditions are the result of the high directional resolution of the model coupled with the use of a realistic formula for the energy in the saturated wave spectrum.


Hydrodynamic models of the currents and surface elevations associated with tides and surges can give results of high accuracy (e.g. Heaps and Jones, 1979). This is because the physics of the problem is well understood, and the equations that describe the motion contain only a relatively small amount of empiricism (with empirical formulae being used to represent the surface and bottom stresses, and the vertical eddy viscosity in the case of a three-dimensional model), in contrast wave models contain a fair degree of empiricism. For example, the BMO model (Gloding 1983), which is a second-generation model, attempts to take account of the effect of the non-linear interactions by replacing the wind-sea part of the spectrum by a JONSWAP spectrum with the same energy. Consequently, the model results depend not only on the empirical formulae used to describe the wave growth, but also on the empirical constants that appear in the JONSWAP spectrum. The lack of our understanding of the true physics of wave generation is reflected in the predictions made by wave models which can show appreciable errors. The Department of Energy has suggested that a wave model should be accurate to±10% of peak wave height, and existing second-generation models have been evaluated by applying them to the WHIST storms (Department of Energy, 1986).

Recent wave models (the third-generation models) are becoming even more complex as they attempt to solve explicitly the non-linear interactions, thus necessitating the use of high-powered computers. Ultimately, this may lead to a better understanding of the physics of wave generation, but it limits the work to those researchers who have access to parallel processing computers, and the computational costs are likely to be high. An alternative approach is to accept the empirical nature of much wave modelling, and to investigate the use of purely empirical methods for the practical prediction of wave spectra. This may not advance our understanding of wave dynamics, but may produce practical models that will be suitable for many engineering problems.

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