Vegetation in arid riparian zones heavily depends on groundwater, meanwhile the distribution of vegetation impacts the groundwater flow in the area. This study describes a methodology to characterize groundwater-vegetation dynamics using a spatial evolutionary algorithm (SEA). It incorporates spatial knowledge of groundwater and vegetation to facilitate the optimal search of vegetation distribution compatible to groundwater flow. Unlike a regular EA for spatial models, the SEA employs a hierarchical tree structure to represent spatial variables in a more efficient way. Furthermore, special crossover and mutation operators are designed in accordance with the tree representation. In this paper, the SEA is applied to searching for the maximum vegetation coverage associated with a distributed groundwater system in an arid region. The results of computational experiments demonstrate the efficiency of SEA for large-scale spatial optimization problems. Extension of the algorithm for other water resources management problems is discussed.