Stochastic Dynamics of Barrier Island Elevation
Stochastic dynamics of barrier island elevation Orencio Duran´ Vinenta,1 , Benjamin E. Schafferb, and Ignacio Rodriguez-Iturbea,1 aDepartment of Ocean Engineering, Texas A&M University, College Station, TX 77843-3136; and bDepartment of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08540 Contributed by Ignacio Rodriguez-Iturbe, November 11, 2020 (sent for review June 29, 2020; reviewed by Carlo Camporeale and A. Brad Murray) Barrier islands are ubiquitous coastal features that create low- a marked Poisson process with exponentially distributed marks. energy environments where salt marshes, oyster reefs, and man- The mark of a HWE is defined as the maximum water level groves can develop and survive external stresses. Barrier systems above the beach during the duration of the event and charac- also protect interior coastal communities from storm surges and terizes its size and intensity. This result opens the way for a wave-driven erosion. These functions depend on the existence of probabilistic model of the temporal evolution of the barrier/dune a slowly migrating, vertically stable barrier, a condition tied to elevation, along the lines of the stochastic model of soil moisture the frequency of storm-driven overwashes and thus barrier ele- dynamics (4). The knowledge of the transient probability dis- vation during the storm impact. The balance between erosional tribution function of barrier elevation allows the calculation of and accretional processes behind barrier dynamics is stochastic in after-storm recovery times, overwash probability and frequency, nature and cannot be properly understood with traditional con- and the average overwash transport rate driving the landward tinuous models. Here we develop a master equation describing migration of barriers.
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