Permanent loss of barrier island resilience due to a critical transition in dune ecosystems

Barrier islands are dynamic coastal landforms providing essential protection to coastal infrastructure and diverse ecosystems. Their protective function is significantly influenced by the presence and health of coastal dunes, which mitigate the impact of storms and waves. Dune-less barrier islands are highly susceptible to breaching and potential drowning due to rising sea levels and increased storm frequency. The research focuses on understanding the transition between two stable states of barrier islands: a 'high' state characterized by well-developed, vegetated dunes and a 'barren' state lacking dunes and experiencing frequent flooding. The study uses data from a representative sample of barrier islands in Virginia, USA, to analyze this transition. The central research question is identifying the factors that control the shift from the resilient 'high' state to the vulnerable 'barren' state and the implications of this transition, particularly under the pressure of sea level rise. Understanding this transition is crucial for effective coastal management and predicting the long-term fate of barrier islands under climate change. The transition from a high to a low state is not just about the loss of dunes, but represents a fundamental shift in the island's resilience and its capacity to withstand environmental pressures.

Existing models of barrier island dynamics often simplify dune dynamics, focusing on average planform changes through mass conservation. While some complex, process-based models capture individual storm impacts, large-scale models typically oversimplify dune dynamics, failing to capture the stochastic behavior of barrier elevation. A common approach in many models involves using phenomenological estimations of sand fluxes due to storm overwashes to determine barrier migration rates. However, because the occurrence and intensity of overwash events are closely tied to the island's elevation, a precise description of barrier migration requires a better understanding of dune dynamics. Recent research using a stochastic point model examined barrier island elevation dynamics, focusing on the interplay between dune growth and water-driven erosion. This model provided an analytical description of the barrier elevation state's phase space, expressed as a probability density function (PDF) of barrier elevation based on remotely measurable control parameters. This prior work identified three types of barriers: 'high' (well-developed dunes), 'barren' (no dunes), and 'mixed' (intermediate states). However, further investigation was needed to understand the transition mechanisms between these states and their implications for barrier island resilience.

The study extended a previously developed stochastic point model to describe alongshore variations in barrier elevation. This model incorporated deterministic wind-driven dune growth and stochastic erosion due to high-water events (HWEs), which were modeled as a marked Poisson process. The model simplified dune erosion during overtopping events by assuming complete erosion to a base elevation (h₀). The deterministic dune growth was based on process-based simulations that capture sand transport, wind aerodynamics, vegetation growth, and surface change, resulting in dune growth to a maximum height (H) over a characteristic time (Tₐ). The alongshore extension of the point model accounted for spatial variations in maximum dune height (H(y)) and base elevation (h₀(y)) alongshore (y). The model assumed that wind and water forcing and sand availability were similar alongshore, with spatial variations stemming from pre-existing morphology and vegetation characteristics. The alongshore PDF of barrier elevation f(h) was obtained by integrating the steady-state point PDF fₑ considering normal distributions for H(y) and h₀(y). This process involved simplifying assumptions, such as similar alongshore variations in H and h₀ and the rapid colonization of washovers by dune-building vegetation. Model parameters (Gₐ, h₀, H, and their standard deviations) were estimated from Virginia Barrier Islands (VBI) data. The average size (S) and frequency (λ₁) of HWEs were estimated. The steady-state alongshore elevation distribution was compared to empirical distributions. The mean post-storm dune recovery time (Tᵣ), rescaled by the dune formation time Tₐ, was used to characterize the barrier state and transition between states. The model's robustness was assessed by examining its sensitivity to parameter uncertainty and simplifying assumptions. The effect of sea level rise (SLR) was evaluated by simulating the steady-state stochastic dynamics along a parametric phase curve defined by changing the base elevation (h₀) over time due to SLR while holding other parameters constant (using Hog Island values). The analysis involved assessing the basin of attraction of the high and low elevation equilibrium states using the inverted PDF f(h) as a potential function to characterize the critical transition to a barren state.

The study found that the stochastic model accurately predicted the observed alongshore elevation distributions in the VBI. The model revealed a clear transition from 'high' to 'barren' barrier states primarily driven by a significant increase in the rescaled frequency of HWEs, largely controlled by the mean base elevation (h₀). The analysis showed that a 30-fold increase in the rescaled frequency of HWEs resulted in the transition to a barren state. A parametric phase curve demonstrated a potential transition from a 'high' barrier state (similar to Hog Island) to a barren state, illustrating the impact of increasing base elevation. The model predicted that the transition to a barren state is largely independent of the mean maximum dune height (H), suggesting that the uncertainty in H estimation has minimal impact on the overall results. The study concluded that the barren state is a stable, irreversible state due to the dominance of erosion over dune formation at elevations around the beach berm. Simulations incorporating SLR indicated that a relatively small decrease in h₀, caused by SLR, can lead to a critical transition to a barren state within a few decades. The transition from a 'high' to a 'barren' state exemplifies a critical transition, characterized by critical slowing down, as the system approaches the tipping point. The rescaled dune recovery time (Tᵣ) serves as a useful metric to quantify barrier resilience. The analysis of the average growth rates revealed that barren barrier elevations act as a strong attractor, further supporting the irreversibility of the barren state. The study further found that maximum dune growth rates in the region are relatively uniform (0.2-0.4 m/yr).

The findings highlight the importance of understanding the stochastic nature of barrier island dynamics and the existence of a tipping point leading to an irreversible transition to a barren state. The model successfully captures the complexity of barrier island dynamics using a relatively simple framework. The model's simplicity and ability to predict the transition to a barren state based on readily measurable parameters have significant implications for coastal management. The results emphasize the importance of considering base elevation (h₀) as a primary indicator of barrier island resilience. Sea level rise, by decreasing h₀, accelerates the transition to the irreversible barren state, underscoring the threat posed by climate change. The identification of a change in barrier equilibrium from 'high' to 'barren' could be an early warning sign of broader shifts in the coastal system. These results suggest that current approaches to coastal management which focus on singular factors (such as sea level rise) are insufficient, and a more holistic approach which integrates multiple parameters and considers stochastic variability is necessary.

This research provides a novel stochastic model for predicting the transition of barrier islands from a resilient state with dunes to a vulnerable barren state. This transition is primarily driven by changes in base elevation, strongly influenced by sea level rise. The model uses readily measurable parameters, making it applicable to various coastal settings. Future research could explore incorporating additional factors, such as shoreline changes and vegetation dynamics, to improve model accuracy and applicability to a broader range of barrier island systems. Further investigation into the interplay between barrier island dynamics and carbon cycling in coastal ecosystems is also warranted.

The model simplifies several aspects of barrier island dynamics, such as the assumption of complete dune erosion during overtopping events and the relatively uniform alongshore distribution of wind and water forcing. The model's simplified representation of vegetation dynamics might also limit its accuracy. Additionally, the analysis is based on data from a specific region (Virginia Barrier Islands), and the model's generalizability to other geographical areas with different sediment supplies, vegetation types, and wave climates needs to be further investigated.