Suspended sediment and contaminant routing with alluvial storage: New theory and applications

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In large watersheds, sediment storage imposes geologic timescales on the downstream movement of suspended sediment and associated contaminants. Modeling these processes requires temporal and spatial averaging, a task often accomplished using concepts derived from reservoir theory, where residence times and age and storage time distributions of stored sediment are treated as constants, even though all of these quantities should be time-variable under conditions of unsteady sediment transport. Here, concepts from reservoir theory are replaced by deposition and erosion laws to develop a parsimonious quantitative framework for watershed-scale routing of sediment and contaminants that explicitly accounts for time-dependent alluvial storage. Solution of the new equations, combined with appropriate initial and boundary conditions, predicts the age and storage time distributions of stored sediment, the sediment residence time, the mass of stored sediment, and the variations in all of these quantities through time. Model calibration is illustrated by reinterpreting previously published data from the Little Missouri River in North Dakota to create a 3-dimensional chronostratigraphic model of stored sediment, supplemented by observations of contemporary patterns of erosion. Model parameters from the Little Missouri River are then used to demonstrate that approximately 750 yr will be required to remove arsenic-contaminated alluvium supplied by a century of mine tailings discharges to a 112-km reach of the Belle Fourche River in South Dakota. The new approach described here requires very modest computing resources to simulate long timescales across large watersheds, and the fidelity of storage parameters, which ultimately control the timing of sediment delivery, is supported by site-specific stratigraphic observations and sediment dating.