A practical method for the estimation of directional wave spectra in reflective wave fields

Abstract

A practical method is presented for the computation of directional spectra in presence of phase locked reflections (e.g., close to coastal structures). Existing modified directional analysis methods (e.g., The Modified Bayesian Method and the Modified Maximum Likelihood Method MMLM) require an input of the effective reflection line distance. In practice the position of the reflection line is often ambiguous leading to large errors in the directional spectrum. This paper presents a refinement of Isobe and Kondo's MMLM [Isobe, Kondo, K., 1984. Methods for estimating directional wave spectrum in incident and reflected wave field. Proc. 19th Conf. on Coastal Eng., Am. Soc. of Civil Eng., New York, pp. 467–483] which includes the reflection line position as an additional free parameter. The method presented here is based on minimising an error function which characterises the difference between the predicted and observed surface elevation variance observed at a number of spatially separated gauges. The new method is tested rigorously with both synthetic time-series and field data. Results indicate that the method is robust in a variety of incident wave conditions, in the presence of added noise and with only four transducers, providing the array is in close proximity to the shore. The new method of directional analysis when applied to field data produced frequency dependent reflection estimates which compared closely to those obtained by using the 2-dimensional approach of Gaillard et al. (1980) [Gaillard, P., Gauthier, M., Holly, F., 1980. Method of analysis of random wave experiments with reflecting coastal structures. Proc. 17th Conf. on Coastal Eng., ASCE, New York, pp. 204–220].