Stochastic Dynamics of Barrier Island Elevation

Barrier islands are ubiquitous coastal features that create low-energy environments where salt marshes, oyster reefs and mangroves can develop and survive external stresses. Barrier systems also protect interior coastal communities from storm surges and wave-driven erosion. These functions depend on the existence of a slowly migrating, vertically stable barrier, a condition tied to the frequency of storm-driven overwashes and thus barrier elevation at the moment of the storm impact. The balance between erosional and accretional processes behind barrier dynamics is stochastic in nature and cannot be properly understood with traditional continuous models. Here we develop a master equation describing the stochastic dynamics of the probability density function (PDF) of barrier elevation at a point. The dynamics is controlled by two dimensionless numbers relating the average intensity and frequency of high water events (HWEs) to the maximum dune height and dune formation time, which are in turn function of the rate of sea level rise, sand availability and stress of the plant ecosystem anchoring dune formation. Depending on the control parameters, the transient solution converges towards a high-elevation barrier, a low-elevation barrier or a mixed, bimodal, state. We find the average after-storm recovery time---a relaxation time characterizing barrier's resiliency to storm impacts---changes rapidly with the control parameters suggesting a tipping point in barrier response to external drivers. We finally present some preliminary field data validating model predictions.