Analysis of key parameters in a diffusion type beach profile evolution model

Abstract

Diffusion type formulations are commonly used in beach profile evolution models. The practical idea behind that is to map the behaviour of the beach profile onto a simple mathematical model that exhibits the same behaviour under defined operating conditions. The success of this approach is based on the accurate determination of key parameters in the diffusion model that govern its behaviour, using observed beach behaviour in the field. In order to determine these parameters, i.e. diffusion coefficient and a time and space varying source function, we used observations of historic beach profiles at Milford-on-Sea beach in Christchurch Bay, Dorset, United Kingdom. The relationship between the diffusion coefficient and Dean's equilibrium profile was investigated, leading to a new interpretation of the diffusion coefficient in terms of the sediment characteristics. The analysis also shows the significance of the diffusion process in the medium to long term evolution of the beach profile. A canonical correlation analysis (CCA) was undertaken in order to identify patterns of behaviour between wave conditions and source terms, and the possible correlations between them. The analysis provides strong evidence of a useful link between the source term in the simple dynamical equation and the distribution of wave steepness.