A simple model for interannual sandbar behavior

Time and length scales of beach variability have been quantified using 16 y ears of beach surveys sampled at the Army Corps of Engineers' Field Researc h Facility, located on the U.S. Atlantic coast. Between 50% and 90% of the bathymetric variability at this site was explained by alongshore-uniform re sponse over the approximately 1 km alongshore span of the surveys. Although the incident wave height variance was dominated by frequencies at or highe r than 1 cycle/yr, more than 80% of the bathymetric variance at all cross-s hore locations was explained by frequencies <1 cycle/yr. Interannual cycles consisting of sandbar formation, migration, and decay contributed to the l ow-frequency variability. The observed behavior can be explained by a simpl e, heuristic model. The model assumes that bars migrate toward a wave heigh t dependent equilibrium position. This position was shown to coincide with the wave "breakpoint." Additionally, the rate of bar response is taken to b e variable and was empirically determined to be proportional to the wave he ight cubed. The net effect of a variable response rate is to shift the expe cted long-term mean sandbar position offshore, toward the equilibrium posit ion associated with the largest waves. The model explained up to 80% of the observed bar position time series variance and up to 70% of the variance o f bar crest velocity time series, which were extracted from three different sandbars. Characteristic bar response times (related to the inverse of the response rate) were found to be long relative to the characteristic timesc ale of the forcing (1 year in our case). As a result, transient response (i .e., bar position far from equilibrium) tended to persist for many cycles o f the forcing. Transient bar behavior appears in the observations when bars formed near the shoreline or when outer bars decayed and inner bars faced a changed wave climate. While the present model is able to explain the evol ution of these transients, it does not contain a mechanism for their introd uction.