Abstract

This work introduces a physically-based model to capture the spatio-temporal dynamics of dune vegetation under stochastic environmental disturbances. In analogy with other transitional disturbed environments, the model evaluates vegetation cover, within a cross-shore dimensionless framework, in response to random wind speed and runup. The wind speed is modeled as a compound Poisson process with Gamma-distributed properties, facilitating the computation of up-crossing times for various thresholds. The dune topography is represented by a swash zone with a Gaussian shape and a monotonic landward increase, parameterized by slope, wavelength, and height. Key disturbance conditions affecting vegetation---runup-induced flooding in the swash zone and wind-induced scour on the backshore and crest---are addressed through threshold-based analysis. The model uses a state-dependent dichotomic process for vegetation dynamics, where growth and decay are influenced by external forcing and vegetation state. Analytical solutions of the master equation for the vegetation distributions reveal the impact of stochastic factors on vegetation growth and stability. Sensitivity analysis identifies dune steepness, forcing magnitude and variability, and relative roughness as critical parameters. These factors significantly affect vegetation distribution, with increased steepness leading to higher vegetation density at the backshore and reduced density at the shorefront. Also, a Suitability Index to assess analytically dune stability based on disturbance and topographic features is introduced. Validation against satellite imagery and high-resolution real elevation data from the U.S. coastline confirms the model's robustness and accuracy. The results enhance understanding of dune vegetation dynamics and offer a framework for coastal restoration strategies.