Abstract. In environmental applications it is often of interest to predict the rates at which contaminant mass is discharged at a given cross section of streams and rivers. We present a Lagrangian methodology for evaluating tracer discharge (mass per unit time) at specified control cross sections (CCS) of streams. The key transport processes included in the analysis are advection, degradation/decay, and kinetically controlled mass transfer in storage zones and in bed sediment. The transport in the bed sediment is described as a diffusion process, where the tracer may sorb onto the sediment. We have derived a general solution for tracer discharge in the Laplace domain wherefrom temporal moments are computed. The derived solutions may account for deterministic changes in morphological characteristics along stretches of streams. The results are illustrated for zeroth and first two moments where we show the combined effect of advection, degradation, physicochemical mass transfer, and morphology. For illustrative purposes, we assume morphology to change downstream following power laws suggested by Langbein [1947] and Leopold and Maddock [1953]. The moments depend nonlinearly on the downstream distance, following power laws that reflect the power laws for the hydraulic geometry. We define two main dimensionless parameters, namely, kinetic storage parameter a* and bed parameter M, that control the amount of tracer mass eventually discharged at any given CCS. For M •-• 0.3 the most dominant mechanism that controls the amount of ultimately discharged tracer mass is the exchange with the bed sediment. Once estimated from field data for stretches of specified streams, the dimensionless parameters can be used in the derived expressions for predictive purposes.

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[1] A probabilistic model for material transport in a stream network is developed based on geomorphology of the subcatchment and water transit time distribution. A tracer may be a point source or a source distributed over the entire catchment. The tracer particles are transported by advection through streams of different order and also diffuse and react chemically with the sediments lying at the bottom of the streams. Stochastic analysis of travel time is complicated by microscopic exchange processes, which act to retain the tracer in the surrounding medium. These include kinetically controlled exchange with the storage zones, diffusion into the bed sediment, and linear equilibrium sorption. In addition, degradation delays the downstream tracer movement. The sensitivity analysis indicates that for 50% mass arrival the mean arrival time is increased by 3 times for a change in mass transfer parameter, c*, by 10 times. This increase is further pronounced for higher mass arrivals and higher c*. The results on a specific application example show that a mere doubling of the uncertain value of diffusive mass transfer rate in the bed sediment reduces the probability that 25% of solute mass arrives at the outlet by %90%. The high sensitivity of the probability of the solute mass arrival at the outlet to the uncertain diffusive mass transfer rate implies uncertainty also in predictions of the solute transport process. Thus it can be concluded that the correct estimation of mass transfer rate in the bed sediments within a catchment plays an important role in field-scale estimation of transport parameters.

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