Relationship between beach profiles and waves at Duck, North Carolina, determined by canonical correlation analysis

Abstract

Abstract An 11-year long measurement time series of waves and profiles from Duck, North Carolina, was analyzed using canonical correlation analysis (CCA) in order to determine the covariability between waves and profile response. The main objectives of this analysis were (1) to detect simultaneously occurring patterns in the wave and profile data and, if possible, give such patterns a physical interpretation to increase the insight into the governing processes, and (2) to investigate the possibility to use CCA in a predictive mode with the aim to calculate the profile response from the waves. The profile shape itself and the change between consecutively surveyed profiles were correlated with both the offshore (deep-water) and nearshore wave conditions. In the offshore, the waves were described by composite probability density functions (pdf) derived based on the measured wave conditions prior to a profile survey. Nearshore wave conditions were calculated using a random breaker decay model and averaged local wave properties were used as input to the CCA. The profile response displayed significantly higher correlation with the nearshore wave properties as compared to the offshore waves, and the highest correlation was found between the profile shape and the mean ratio of breaking waves for the time period preceding the profile survey. The CCA using nearshore wave properties indicates a potential for predicting the profile response with an acceptable degree of accuracy once a regression matrix relating the profiles to the waves has been established that represents the typical variability at the site.