The quantitative description of beach cycles

A quantitative method is developed to describe sequential changes in beach profile morphology. Dominant cycles in temporal eigenfunctions (computed by empirical eigenfunction analysis and rotary component analysis) are defined and used to construct a sequence of profiles representing the energetic portions of beach cycles. Five sets of beach profile data from Torrey Pines Beach in southern California were analyzed with these techniques. Because the first and second eigenfunctions account for between 65 and 90% of the variability of the data, the beach profiles are accurately described with only these two variables and the mean profile. Using rotary component analysis, beach changes represented by the two dominant eigenfunctions can be separated into many elliptical components, each representing a particular frequency associated with cycles in beach state. Profiles are reconstructed using points from the perimeter (latera recta) of these beach state ellipses. A frequency of 1 cpy is the most energetic frequency in the first and second eigenfunctions, corresponding to the cyclic onshore—offshore sediment movement associated with “bar” and “berm” profiles. Profiles constructed from points on the elliptical path associated with annual cycles graphically depict the sequential development of bar and berm during the beach cycle. Beach cycles corresponding to a frequency of 2 cpy are also significant, primarily due to the energy of the second eigenfunction. No other frequencies are consistently found to be as significant as the annual and semi-annual cycles at this beach. In particular, monthly beach cycles have little energy associated with them. The method described provides a uniform way to objectively discriminate energetic beach cycles, and yields a concise representation for beach modeling and prediction. It should be a valuable tool for uniform, quantitative intercomparison of beaches and beach cycles.