MECHANISM FOR GLOBAL OPTIMIZATION OF RIVER NETWORKS FROM LOCAL EROSION RULES

We show that landscapes and their drainage networks evolve under erosi on rules to obey a variational principle. Starting from hydrodynamics we first find by separation of variables a general relationship betwee n erosion and a modified slope-area law. This law encompasses previous work and observations, and we confirm it by simulation. Secondly we s how that this corresponds to a solution of a variational minimization model, generalized from Rodriguez-Iturbe et al. Thus a mechanism by wh ich the local process of erosion acts to globally optimize a river net work is produced.