STOCHASTIC THEORY OF PARTICLE TRAJECTORIES THROUGH ALLUVIAL VALLEY FLOORS

Abstract

Temporary storage of sediment within alluvial valley floors modulates the long-term transport of sediment through landscapes. The fate of weathering minerals or sediment-bound constituents in fluvial environments depends on the relative time scales of constituent degradation and particle residence time within valleys. Particles follow a set of trajectories through valley floors: some particles pass directly through the channel, reaching the basin outlet rapidly after being introduced to the fluvial system; others remain for long periods in deposits such as flood plains. Traditional sediment routing theory, based on the principle of sediment mass conservation along reaches of channel, does not account for exchanges of sediment with temporary sediment storage reservoirs outside the channel, such as flood plains, deltas, and alluvial fans. This article formalizes a theory that incorporates the role of such exchanges in the migration of sediment through river systems, by computing the probabilistic structure of particle trajectories through alluvial valley floors. Equations are developed for computing these trajectories from the sediment budget of a valley floor in steady state. Mathematical strategies for using such relationships to model transient storage conditions are proposed, and other potential model enhancements are discussed. The approach is illustrated using a hypothetical valley floor as an example. The theory can be used to examine rates of sediment overturn in valleys, map particle residence times, and account for the redistribution and decomposition of weathering minerals and particle-bound constituents. The theory has numerous potential management applications, some of which are discussed herein. The hypothetical example demonstrates that the probability distribution of particle residence times in the valleys of most alluvial rivers should be strongly right skewed. [PUBLICATION ABSTRACT]