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

Abstract

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 14C) 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 14C 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., 10Be, 210Pb, or 7Be) or organic 14C.