Stochastic dynamics of barrier island elevation

Abstract

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 during 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 are 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 a 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 toward 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 derive explicit expressions for the overwash probability and average overwash frequency and transport rate characterizing the landward migration of barriers.

Dune Dynamics Drive Discontinuous Barrier Retreat

“…Here, dunes are more likely to exhibit bistable behavior (Figure 2d), transitioning between stable states of tall, overwash-resistant dunes and low, overwash-vulnerable dunes. This dune behavior is consistent with previous models of dune-storm interactions (Durán Vinent & Moore, 2015;Durán Vinent et al, 2021;Goldstein & Moore, 2016). The bistability of dunes directly impacts overwash flux and, consequently, barrier migration, evidenced by instances of taller dunes occurring predominantly within periods of immobility and shorter dunes within periods of transgression (Figure 2d).…”

“…When storm processes dominate, dunes cannot recover before the next storm and become trapped in a perpetual state of low elevation. However, when the time scales of dune recovery and storm occurrence are similar, foredune height becomes bistable (Durán Vinent & Moore, 2015;Durán Vinent et al, 2021;Goldstein & Moore, 2016). In this bistable regime, foredune systems respond nonlinearly to environmental drivers and are prone to abrupt shifts from one state to the other as the result of only small changes in environmental forcing.…”

“…Here, we suggest that discontinuous retreat can also arise from dune dynamics, a suite of processes internal to barrier systems. Barrier dune systems tend to exist in one of two stable states as a result of feedbacks between dune recovery and storm erosion processes: a high-elevation, overwash-resistant state; or a low-elevation, overwash-vulnerable state (Durán Vinent & Moore, 2015;Durán Vinent et al, 2021;Goldstein & Moore, 2016). When biophysical dune recovery processes dominate, dunes tend to recover quickly if knocked down, remaining at or near their maximum height (Durán & Moore, 2013) and withstanding all but the largest of storms.…”

Probabilistic structure of events controlling the after-storm recovery of coastal dunes

“…Although we currently lack a simple explanation for this homogeneity, it seems to be related to the distribution of the extreme values of a runup parameter HR defined in terms of deep-water wave height and wavelength. As shown in a companion paper (12), our results are crucial for the development of a relatively simple analytical stochastic model of dune dynamics in barrier islands that can shed light on their response to external drivers.…”

Textbook dune: Is there a representative and scale‐invariant beach‐dune profile?

“…While results of these previously published field‐based studies suggest that beach‐dune profiles are not scale‐invariant, the CDM model continues to be used in studies on the controls of foredune ridge development (Moore et al 2016), post‐storm foredune recovery (Vinent and Moore 2015), foredune hummockiness (Goldstein et al 2017), coupled marine and aeolian controls on foredune growth (Cohn et al 2019), and barrier island elevation (Vinent et al 2021). Using a combination of previously published and remotely sensed data, this short communication formally tests for scale‐invariance of beach‐dune profiles within and between sites as is assumed in the CDM.…”