Equilibrium Beach Profile Concept for Delaware Beaches

We utilize beach profile data from 37 profile locations on the Atlantic coast of Delaware that were surveyed an average of 12 times between 1964 and 1993 to assess the validity of several equilibrium beach profile (EBP) formulations. Under consideration are (1) a power law formulation; (2) a formulation including the effects of downslope transport; and (3) a modified form of the latter model suggested herein. We perform a least-square fit of these models to the individual observed profiles, the mean profiles at the 37 locations, as well as regionally averaged profiles over eight geographically distinct regions. The analysis results in best-fit values for the model coefficients. The results indicate that the first model is robust and predicts observed mean and regionally averaged profiles with an estimated normalized error of 26 and 15%, respectively. However, the predicted beach slopes near the shoreline are infinite and, hence, unphysical. The second model includes the effects of downslope transport and remedies this shortcoming. Predictions are drastically improved (15 and 6% relative errors for mean and regionally averaged profiles, respectively), but the coefficient values required for these predictions are outside of the physically justifiable range for beaches with an average slope that is of comparable magnitude to the foreshore slope. When physically realizable coefficient values are used the predictive skill of this model is low (with relative errors up to 50% for the regionally averaged profiles). We find that the problem arises because of the dominance of the gravity-related term over much of the profile and suggest a heuristic remedy that restricts the effect of the gravity term to a region close to the shoreline. This modified model has a high skill (15 and 6% relative errors for mean and regionally averaged profiles, respectively) while still retaining robust and reasonable values for the model coefficients.