The Analysis of Exponential Beach Profiles
Keywords:Beaches, beach profiles, equilibrium profiles, beach profile models
The overall form of many beach profiles has an exponential shape where the depth h is given by h = S0 / k) (1-e-kx) with S0 the beach-face slope at x = 0 and k is an adjustable coefficient that determines the degree of concavity. The cross-shore variation in beach slope is then S = S0e–kx or S = S0 - kh. Beach profiles can be analyzed in terms of both the cross-shore variations in hand S. Based on previous studies, the beach-face slope S0 is predictable as a function of the sediment grain size and wave parameters. The evaluation of k can be based on best-fit comparisons with the measured profile depths or from bottom slope variations across the profile. Equations are derived for the evaluation of k from the offshore closure depth of the envelope of profile changes, or from some arbitrarily selected coordinate of the profile. An example of the analysis approach is provided by a beach profile from the Nile Delta coast of Egypt. This measured profile shows good agreement with the exponential form for cross-shore variations in both the absolute depth h and local bottom slope S. There is poor agreement with the h = Ax2/3 profile relationship, in part because this Nile Delta profile is more reflective and has a greater concavity than allowed by the x2/3 dependence. The failure of the x2/3 profile form is still more evident in analyzing the beach-slope variations since it predicts an infinite slope at the shoreline. The exponential beach profile is a convenient mathematical relationship that should be useful in many applications.