A stochastic approach to modeling the role of rainfall variability in drainage basin evolution

We develop a simple stochastic theory for erosion and sediment transport, b ased on the Poisson pulse rainfall model, in order to analyze how variabili ty in rainfall and runoff influences drainage basin evolution. Two cases ar e considered: sediment transport by runoff in rills and channels and partic le detachment from bedrock or cohesive soils. Analytical and numerical resu lts show that under some circumstances, rainfall variability can have an im pact equal to or greater than that of mean rainfall amount. The predicted s ensitivity to rainfall variability is greatest when (1) thresholds for runo ff generation and/or particle detachment are significant and/or (2) erosion and transport are strong nonlinear functions of discharge. In general, sed iment transport capacity is predicted to increase with increasing rainfall variability. Depending on the degree of nonlinearity, particle detachment c apacity may either increase or decrease with increasing rainfall variabilit y. These findings underscore the critical importance of hydrogeomorphic thr esholds and other sources of nonlinearity in process dynamics. The morpholo gic consequences of rainfall variability are illustrated by incorporating t he pulse rainfall theory into a landscape simulation model. The simulation results imply that, all else being equal, catchments experiencing a shift t oward greater climate variability will tend to have (1) higher erosion rate s, (2) higher drainage density (because of increased runoff erosion efficie ncy), and ultimately (3) reduced relief. The stochastic approach provides a useful method for incorporating physically meaningful climate data within the current generation of landscape evolution models.