Multivariate analysis of nonlinearity in sandbar behavior

Alongshore sandbars are often present in the nearshore zones of storm-dominated micro- to mesotidal coasts. Sandbar migration is the result of a large num- ber of small-scale physical processes that are generated by the incoming waves and the interaction between the wave- generated processes and the morphology. The presence of nonlinearity in a sandbar system is an important factor de- termining its predictability. However, not all nonlineari- ties in the underlying system are equally expressed in the time-series of sandbar observations. Detecting the presence of nonlinearity in sandbar data is complicated by the de- pendence of sandbar migration on the external wave forc- ings. Here, a method for detecting nonlinearity in multi- variate time-series data is introduced that can reveal the non- linear nature of the dependencies between system state and forcing variables. First, this method is applied to four syn- thetic datasets to demonstrate its ability to qualify nonlin- earity for all possible combinations of linear and nonlinear relations between two variables. Next, the method is applied to three sandbar datasets consisting of daily-observed cross- shore sandbar positions and hydrodynamic forcings, span- ning between 5 and 9 years. Our analysis reveals the presence of nonlinearity in the time-series of sandbar and wave data, and the relative importance of nonlinearity for each variable. The relation between the results of each sandbar case and pat- terns in bar behavior are discussed, together with the effects of noise. The small effect of nonlinearity implies that long- term prediction of sandbar positions based on wave forcings might not require sophisticated nonlinear models.

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