Transport and Feedback in Models of Self-Organizing Vegetation Patterns in Dryland Ecosystems: Some Comparisons with Satellite Images

Bands of vegetation alternating periodically with bare soil have been observed in many dryland environments since their discovery in the Horn of Africa in the 1950s. Mathematical modeling efforts over the past two decades have sought to account for these bands via a self-organizing interaction between vegetation and water resources. Understanding the processes underlying vegetation patterns in arid and semi-arid regions is important to predict desertification risk under increasing anthropogenic pressure. Various modeling frameworks have been proposed that are capable of generating similar patterns through self-organizing mechanisms which stem from key assumptions regarding plant feedbacks on surface/subsurface water transport. We discuss a hierarchy of hydrology-vegetation models for the coupled dynamics of surface water, soil moisture, and vegetation biomass on a hillslope. We identify distinguishing features and trends for the periodic traveling wave solutions when there is an imposed idealized topography and make some comparisons to satellite images of large-scale banded vegetation patterns in drylands of Africa, Australia and North America.