Rewinding the History of Growth of Stream Networks Fed by Groundwater

Abstract:

Previous work on stream networks fed by groundwater has successfully described their geometric aspects as consequences of growth in a Laplacian potential field. This existing work has considered local properties of networks, such as angles of stream bifurcations. We use this same mathematical formalism to give constraints on global properties of networks, examining the shape of the network as a whole. These global constraints allow us to deduce how quickly the network is growing at each spring. We therefore investigate the possibility of rewinding the growth of a network and determining its complete history given only a snapshot of its current shape.