A simple model for interannual sandbar behavior

Abstract

Abstract. Time and length scales of beach variability have been quantified using 16 years of beach surveys sampled at the Army Corps of Engineers' Field Research Facility, located on the U.S. Atlantic coast. Between 50% and 90% of the bathymetric variability at this site was explained by alongshore-uniform response over the approximately 1 km alongshore span of the surveys. Although the incident wave height variance was dominated by frequencies at or higher than 1 cycle/yr, more than 80% of the bathymetric variance at all cross-shore locations was explained by frequencies <1 cycle/yr. Interannual cycles consisting of sandbar formation, migration, and decay contributed to the lowfrequency variability. The observed behavior can be explained by a simple, heuristic model. The model assumes that bars migrate toward a wave height dependent equilibrium position. This position was shown to coincide with the wave "breakpoint." Additionally, the rate of bar response is taken to be variable and was empirically determined to be proportional to the wave height cubed. The net effect of a variable response rate is to shift the expected long-term mean sandbar position offshore, toward the equilibrium position 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 of 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 timescale 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 of 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 evolution of these transients, it does not contain a mechanism for their introduction.

Recurrent neural network modeling of nearshore sandbar behavior

“…To reduce the number of inputs for the models, these variables are combined into the wave height at breaking (Plant et al, 1999):…”

“…Existing analyses of time-series of cross-shore sandbar position have suggested a nonlinear dependence of sandbar migration on various environmental factors, such as the height of the incident waves at breaking, see, for instance, Plant et al (1999). Furthermore, 'memory' is sometimes suggested to be present in time-series of sandbar position, meaning dependencies in sandbar position spanning longer time periods which might even exceed the duration of individual storms.…”

“…The most obvious example thereof is the organization of sandy bed material in spatially quasi-periodic patterns known as alongshore sandbars, 0.5-3 m high submarine ridges of sand located approximately parallel to shore and occurring singularly or in multiples of up to four or five bars. The crossshore oriented dynamics of sandbars constitutes an important part of the morphological dynamics of the entire nearshore zone and comprises variability on timescales of a few days to years (e.g., Gallagher, Elgar, and Guza (1998), Plant, Holman, Freilich, and Birkemeier (1999), Ruessink, Wijnberg, Holman, Kuriyama, and Van Enckevort (2003)). …”

Morphologic properties derived from a simple cross‐shore sediment transport model

“…Part of the difficulty is that the relevant scales span a very broad range, from millimeters (individual sand grains) to kilometers (the cross-shore width of the surfzone) and tens of kilometers (alongshore extent of littoral cells). The largest spatial scales are particularly important because they contain the majority of the spatial and temporal variability of nearshore bathymetric change [Lippmann and Holman, 1990;Plant et al, 1999]. These are also the spatial and temporal scales that characterize human interactions with the coast.…”

Nonlinear transfer function modelling of beach morphology at Duck, North Carolina

“…As seen in Figure 2 of the revised manuscript, alongshore volume differences between northerly and southerly profiles occur, particularly post 1991. Reversed migration directions of the nearshore sand bars on either side of the FRF pier (Plant et al, 1999), longshore rhythmic sand bars and sand waves (Lippmann and Holman, 1990;Plant and Holman, 1996; Miller and Dean, 2007a,b), and extended periods of shore-oblique waves generating unidirectional longshore sediment transport (Miller et al, 1983; Keen et al, 2003) have been observed to contribute to the alongshore variability at Duck. Furthermore, as the beach profile data used in the present study extend beyond the average position of the depth of closure, gains/losses in beach volume (Figure 2) are expected to be predominantly influenced by longshore processes as cross-shore processes would mainly influence the redistribution of sediment within the profile.…”