Catchment Power and the Joint Distribution of Elevation and Travel Distance to the Outlet

Abstract:

The delivery of water, sediment and solutes by catchments is influenced by the distribution of source elevations and their travel distances to the outlet. For example, elevation affects the magnitude and phase of precipitation, as well as the climatic factors that govern rock weathering, which influences the particle size and production rate of sediment from slopes. Travel distance, in turn, affects the timing of flood peaks at the outlet and the degree of sediment size reduction by wear, which affect particle size distributions at the outlet. The distributions of elevation and travel distance have been studied extensively but separately, as the hypsometric curve and width function. Yet a catchment can be considered as a collection of points, each with paired values of elevation and travel distance. We refer to the joint distribution of these two fundamental catchment attributes as “catchment power,” recognizing that the ratio of elevation to travel distance is proportional to the average rate of loss of the potential energy provided by source elevation, as water or sediment travel to the outlet. We explore patterns in catchment power across a suite of catchments spanning a range of relief, drainage area and channel network geometry. We also develop an empirical algorithm for generating synthetic catchment power distributions, which can be parameterized with data from natural catchments, and used to explore the effects of varying the shape of the distribution on fluxes of water, sediment, isotopes and other landscape products passing through catchment outlets. Ultimately, our goal is to understand how catchment power distributions arise from the branching properties of networks and the relief structure of landscapes. This new way of quantifying catchment geometry may provide a fresh perspective on problems of both practical and theoretical interest.