Steady state reach-scale theory for radioactive tracer concentration in a simple channel/floodplain system

A steady state analytical model is presented for reach-scale variation in the concentration of a decaying radioactive tracer associated with sediment particles that regularly pass through an off-channel floodplain. The floodplain is represented as a series of well-mixed sediment reservoirs that continually exchange sediment with the channel. The model allows for tributary input and valley-wide aggradation or degradation. Tracer concentration depends on the upstream boundary concentration, the tracer and sediment load, floodplain geometry, and the rates of in-floodplain tracer production and/or decay. The theory predicts relatively modest down-channel change in the concentration of long-lived isotopes but implies that significant change may occur for (1) tracers with a short-enough half-life (such as C-14) or (2) floodplains with sediment residence times that are large enough for cosmogenic production or meteoric fallout to increase tracer concentration in the down-valley direction. The profiles are shown to be strongly dependent on the grain size distributions of both the sediment load and the floodplain. The results imply that down-channel C-14 profiles have the potential to constrain Holocene bed material loads in systems with sufficient storage. The theory concisely describes the general importance of a floodplain for modifying in situ produced cosmogenic tracer concentration and can also characterize floodplain importance for fallout radioisotopes (i.e., Be-10, Pb-210, or Be-7) or organic C-14.