Modelling the Influence of Vegetation on the Stochastic Dynamics of Coastal Dunes

Coastal dunes are the highest natural features on a barrier island, where they protect beach communities, infrastructure and low-energy back-barrier ecosystems from flooding and erosion during storms and other high-water events. Their formation, and poststorm recovery, is a result of a subtle competition between the physical and biological processes controlling the initial stages of dune growth. Vegetation colonises a barren back-beach and traps wind-driven (aeolian) sand to form dunes, but at low enough elevation, plants can be eroded by water-driven transport during random flooding events, which slows down or prevents dune formation. This competition has been previously investigated using both process-based and analytical models. However, the effect of finite vegetation recovery times together with the precise stochastic nature of flooding events has not been taken into account before. A recent stochastic dune model assumed that vegetation grows and recovers instantaneously, whereas an existing process-based dune model, the Coastal Dune Model (CDM), did not properly resolve the stochastic flooding events. Here, we address this knowledge gap by adding a much more realistic description of high-water events of the stochastic model to CDM and investigate the role of vegetation growth and recovery times in dune formation. We first replicate the stochastic model predictions assuming instantaneous vegetation growth. We then define the vegetation colonisation time and relate it to the initial dune formation time. Since dune formation requires the presence of vegetation, a finite colonisation time leads to an expected lag in dune formation and recovery. Depending on the competition between vegetation growth and aeolian erosion, we find that dune dynamics can be divided into two regimes: one with a stable (static) vegetated dune and another one with a mobile, partially vegetated, dune propagating landward. Within the stable dune regime, the influence of vegetation on dune recovery is solely controlled by the relation between the vegetation colonisation time, the dune growth time after plant colonisation and the return period of high-water events flooding the back-beach. We introduce two control parameters based on these times and use them to describe a simplified phase space of the dune state. We then find a simple analytical expression for the transition from a ‘high’ state with mature dunes to a ‘low’ state devoid of dunes based on the competition between dune recovery time controlled by vegetation and the flooding frequency. Finally, we use the transition threshold to propose a vulnerability indicator for dune recovery as the minimum elevation after an overwash required for vegetation to recover.