A numerical model to develop long-term sediment budgets using isotopic sediment fingerprints

Developing accurate long-term, basin-scale sediment budgets using isotopic sediment fingerprints requires a sediment routing model that not only accounts for a range of sediment source terms (e.g. tributaries, surface erosion and erosion of bluffs and terraces) but also considers the variation in time of volume and tracer concentration for the sediment stored in the floodplain. This is accomplished here using a tracer routing model that accounts for production and decay of radioisotopes in the floodplain. The numerical model focuses on the average (i.e. across many hydrographs or years) budget of sediment and tracers at reach scale. To account for storage and remobilization of bulk sediment and/or tracer material, the model represents the floodplain as a system that can gain or lose mass depending on overbank deposition and net bank erosion rates. Isotopic tracers within the floodplain reservoir can be produced as a function of cosmic ray bombardment or atmospheric fallout, and can decay according to a first-order rate equation. Governing equations are derived using a simplified geometry that treats rivers at reach scale: channel sinuosity and migration rates are user-specified parameters, exchange of sediment and tracers between the river and floodplain is modeled at each cross section, and governing equations are derived in a 1D, width-averaged formulation. When the system reaches mobile equilibrium, the sediment deposited on the floodplain through overbank deposition is balanced by the sediment eroded from the floodplain through channel migration and by sediment contributed from external sources. The model is applied to a generic river system and is shown to converge over time to an equilibrium condition that is consistent with an independent analytical solution.