Convolution Method for Time‐Dependent Beach‐Profile Response

Abstract

A simple analytical solution is presented for approximating the time‐dependent beach‐profile response to severe storms. This solution is in the form of a convolution integral involving a time‐varying erosion‐forcing function and an exponential erosion‐response function. The erosion‐forcing function reflects changes in the nearshore water level and breaking wave height. In this paper, an idealized storm‐surge hydrograph is considered from which an analytic solution is obtained for beach and dune erosion associated with severe storms such as hurricanes or northeasters. It is shown that for a given initial beach geometry and sediment size, the peak water level and the incipient breaking wave height determine the maximum erosion potential that would be achieved if the beach were allowed to respond to equilibrium. Because of the assumed exponential erosion rate, beach response obtained from the convolution method is found to lag the erosion forcing in time, and is damped relative to the maximum erosion potential such that only a fraction of the equilibrium response actually occurs.