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.

This work introduces a physically-based modeling framework 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 robustness and accuracy of the proposed approach. The results enhance understanding of dune vegetation dynamics and offer a framework for coastal restoration strategies.

Vegetation is crucial for stabilizing and developing coastal dunes. Different plant species exhibit different spatial distributions which reflect their environmental role and adaptation strategy. This study aims to provide a fine-scale species-by-species analysis of vegetation spatial patterns on coastal dunes within the San Rossore – Migliarino – Massacciuccoli Regional Park (Tuscany, Italy). A comprehensive vegetation dataset generated by an Object-Based Image Analysis (OBIA) algorithm applied to high-resolution ortho-images has been utilized. A Digital Terrain Model (DTM) of the study area was created to assess the impact of dune morphology on plant distribution. Moreover, a wave runup analysis was also conducted to understand the interaction between vegetation and hydrodynamic forces. The research highlights how the vegetation threshold distance from the coastline, L_veg, is superimposed by the reaching distance of wave runup during extreme events. Terrain morphology significantly affects the vegetation zonation: on taller and undisturbed dunefields, species zonation is clearer and more defined, whereas, on flatter and disturbed ones, spatial distribution is significantly fuzzier. A positive correlation emerges between the abundance of a species and its degree of spatial clustering, indicating that less abundant species show more tightly clustered spatial patterns. Modified Ripley’s L-function analysis revealed a multi-scale clustered pattern for most species under examination. The present results may provide a solid benchmark in coastal ecology research for supporting natural-based conservation plans and eco-morphodynamic modeling.

Incipient channelization in mountainous landscapes is often associated with the presence of first-order valleys at a regular wavelength under diverse hydroclimatic forcings. Here we provide a formal linear stability analysis of a landscape evolution model in detachment-limited erosion conditions to quantify the impact of the erosion law on the regular valley formation. The linear stability analysis is conducted for the unchannelized hillslope solutions along a long mountain ridge, where the perturbed equations constitute a third-order differential eigenvalue problem. The solutions to the posed eigenvalue problem are obtained by a spectral Galerkin technique with numerical quadrature. Results reveal the dependence of the erosion threshold and the emergent ridge/valley wavelength on the exponents in the power-law scaling coupling fluvial erosion with specific drainage area (m) and local slope (n). As the exponent m increases for a fixed n, the emergent valley spacing expands and the erosion limit for the first channel instability declines. Conversely, the erosion threshold for the first channelization rises with an increase in n at a particular value of m. We also show that predictions of the stability analysis conform with numerical simulations for different degrees of nonlinearity in the erosion mechanism and agree well with topographic data of a natural landscape.

In this comment, we clarify that the specific contributing area is defined in the limit of an infinitesimal contour length. We also confirm that not all solutions obtained from the minimalist landscape evolution model of Bonetti et al. (2020) are rescaled copies of each other because of the crucial role of the boundary conditions. We use dimensional analysis and numerical simulations for a case where only one horizontal length scale enters the physical law to establish this point.