Beach memory and ensemble prediction of shoreline evolution near a groyne

In this paper we address the question of estimating the average position of a beach and its inherent variability about this mean. It is demonstrated how, even in a much simplified situation, the ensemble average of beach plan shape involves cross-correlation of the beach position and wave conditions. This renders the governing equations inimical to analytical treatment. A new analytical expression for the mean beach plan shape and its variation are derived for the case of a single groyne exposed to waves varying in direction only. This demonstrates that ‘beach memory’ is directly related to the autocorrelation of wave direction. For more general conditions a semi-analytical expression for the ensemble average of the shoreline position is derived. This solution is estimated with site specific wave conditions using Monte Carlo simulations. The characteristics of the solution are investigated and it is demonstrated that, for this case at least, the terms involving the wave direction are virtually uncorrelated with the terms that do not. It is concluded that, in an ensemble sense, the morphodynamic impact of wave direction is decoupled from that due to wave height and period.