EXPERIMENTAL-DESIGN FOR ESTIMATING PARAMETERS OF RATE-LIMITED MASS-TRANSFER - ANALYSIS OF STREAM TRACER STUDIES

Tracer experiments are Valuable tools for analyzing the transport char acteristics of streams and their interactions with shallow groundwater . The focus of this work is the design of tracer studies in high-gradi ent stream systems subject to advection, dispersion, groundwater inflo w, and exchange between the active channel and zones in surface or sub surface water where flow is stagnant or slow moving. We present a meth odology for (1) evaluating and comparing alternative stream tracer exp eriment designs and (2) identifying those combinations of stream trans port properties that pose limitations to parameter estimation and ther efore a challenge to tracer test design. The methodology uses the conc ept of global parameter uncertainty analysis, which couples solute tra nsport simulation with parameter uncertainty analysis in a Monte Carlo framework. Two general conclusions resulted from this work. First, th e solute injection and sampling strategy has an important effect on th e reliability of transport parameter estimates. We found that constant injection with sampling through concentration rise, plateau, and fall provided considerably more reliable parameter estimates than a pulse injection across the spectrum of transport scenarios likely encountere d in high-gradient streams. Second, for a given tracer test design, th e uncertainties in mass transfer and storage-zone parameter estimates are strongly dependent on the experimental Damkohler number, DaI, whic h is a dimensionless combination of the rates of exchange between the stream and storage zones, the stream-water velocity, and the stream re ach length of the experiment. Parameter uncertainties are lowest at Da I values on the order of 1.0. When DaI values are much less than 1.0 ( owing to high velocity, long exchange timescale, and/or short reach le ngth), parameter uncertainties are high because only a small amount of tracer interacts with storage zones in the reach. For the opposite co nditions (DaI much greater than 1.0), solute exchange rates are fast r elative to stream-water velocity and all solute is exchanged with the storage zone over the experimental reach. As DaI increases, tracer dis persion caused by hyporheic exchange eventually reaches an equilibrium condition and storage-zone exchange parameters become essentially non identifiable.