A mathematical model of vegetation-topography feedbacks and their impact on the resilience of arid ecosystems
Tri Juliansyah Muharam Sambas, .
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Vegetation in arid ecosystems is a well-known example of self-organized spatial patterns. The pattern of vegetation bands interspersed with bare soil is explained as a result of positive feedback between infiltration and vegetation. In gently sloped landscapes, vegetation patterns appear as vegetation bands which are perpendicular to the direction of the slope. Moreover, it is widely observed that vegetation bands are found to be arced and convex up-slope. Previous studies suggest that the underlying topography plays a role in shaping the bands as the straight bands are changing to arced when it grows on top of valley-like landscapes. Although it is clear that topography affects the shape of vegetation patterns, it is yet unknown how feedbacks between vegetation and topography influence the resilience of self-organized patterns in arid ecosystems. In this study, we develop a mathematical model based on the interaction between hydrodynamics, vegetation, and topography. We start with modifying the surface water model by Rietkerk et al., 2002 into the shallow water equations and adding a topography dynamics to allow soil erosion. Additionally, we simulate the effect of environmental changes, for example, rainfall pattern to the resilience of vegetation in the presence of topography evolution. The simulation results show that a long dry period could trigger channel formation which then causes an accumulation of water. We also found that as the amount of water increasing in the channels, vegetation begins to inhabit the channels and prevent soil erosion to deepen the channels further. Therefore, we argue that the topographic depression and channels could increase the resilience of vegetation bands in dealing with harsh conditions, by helping the vegetation in concentrating and harvesting water. Finally, our findings suggest that these arced band patterns could be an indicator of a system that is recovering.