Brian J. Wagner

Evaluating the Reliability of the Stream Tracer Approach to Characterize Stream‐Subsurface Water Exchange

Stream water was locally recharged into shallow groundwater flow paths that returned to the stream (hyporheic exchange) in St. Kevin Gulch, a Rocky Mountain stream in Colorado contaminated by acid mine drainage. Two approaches were used to characterize hyporheic exchange: sub-reach-scale measurement of hydraulic heads and hydraulic conductivity to compute streambed fluxes (hydrometric approach) and reachscale modeling of in-stream solute tracer injections to determine characteristic length and timescales of exchange with storage zones (stream tracer approach). Subsurface data were the standard of comparison used to evaluate the reliability of the stream tracer approach to characterize hyporheic exchange. The reach-averaged hyporheic exchange flux (1.5 mL s−1 m−1), determined by hydrometric methods, was largest when stream base flow was low (10 L s−1); hyporheic exchange persisted when base flow was 10-fold higher, decreasing by approximately 30%. Reliability of the stream tracer approach to detect hyporheic exchange was assessed using first-order uncertainty analysis that considered model parameter sensitivity. The stream tracer approach did not reliably characterize hyporheic exchange at high base flow: the model was apparently more sensitive to exchange with surface water storage zones than with the hyporheic zone. At low base flow the stream tracer approach reliably characterized exchange between the stream and gravel streambed (timescale of hours) but was relatively insensitive to slower exchange with deeper alluvium (timescale of tens of hours) that was detected by subsurface measurements. The stream tracer approach was therefore not equally sensitive to all timescales of hyporheic exchange. We conclude that while the stream tracer approach is an efficient means to characterize surface-subsurface exchange, future studies will need to more routinely consider decreasing sensitivities of tracer methods at higher base flow and a potential bias toward characterizing only a fast component of hyporheic exchange. Stream tracer models with multiple rate constants to consider both fast exchange with streambed gravel and slower exchange with deeper alluvium appear to be warranted.

Experimental design for estimating parameters of rate-limited mass transfer: Analysis of stream tracer studies

Tracer experiments are valuable tools for analyzing the transport characteristics of streams and their interactions with shallow groundwater. The focus of this work is the design of tracer studies in high-gradient stream systems subject to advection, dispersion, groundwater inflow, and exchange between the active channel and zones in surface or subsurface water where flow is stagnant or slow moving. We present a methodology for (1) evaluating and comparing alternative stream tracer experiment designs and (2) identifying those combinations of stream transport properties that pose limitations to parameter estimation and therefore a challenge to tracer test design. The methodology uses the concept of global parameter uncertainty analysis, which couples solute transport simulation with parameter uncertainty analysis in a Monte Carlo framework. Two general conclusions resulted from this work. First, the solute injection and sampling strategy has an important effect on the 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 encountered in high-gradient streams. Second, for a given tracer test design, the uncertainties in mass transfer and storage-zone parameter estimates are strongly dependent on the experimental Damkohler number, DaI, which is a dimensionless combination of the rates of exchange between the stream and storage zones, the stream-water velocity, and the stream reach length of the experiment. Parameter uncertainties are lowest at DaI 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 length), parameter uncertainties are high because only a small amount of tracer interacts with storage zones in the reach. For the opposite conditions (DaI .. 1.0), solute exchange rates are fast relative to stream-water velocity and all solute is exchanged with the storage zone over the experimental reach. As DaI increases, tracer dispersion caused by hyporheic exchange eventually reaches an equilibrium condition and storage-zone exchange parameters become essentially nonidentifiable.

Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling

Abstract Parameter estimation and contaminant source characterization are key steps in the development of a coupled groundwater flow and contaminant transport simulation model. Here a methodologyfor simultaneous model parameter estimation and source characterization is presented. The parameter estimation/source characterization inverse model combines groundwater flow and contaminant transport simulation with non-linear maximum likelihood estimation to determine optimal estimates of the unknown model parameters and source characteristics based on measurements of hydraulic head and contaminant concentration. First-order uncertainty analysis provides a means for assessing the reliability of the maximum likelihood estimates and evaluating the accuracy and reliability of the flow and transport model predictions. A series of hypothetical examples is presented to demonstrate the ability of the inverse model to solve the combined parameter estimation/source characterization inverse problem. Hydraulic conductivities, effective porosity, longitudinal and transverse dispersivities, boundary flux, and contaminant flux at the source are estimated for a two-dimensional groundwater system. In addition, characterization of the history of contaminant disposal or location of the contaminant source is demonstrated. Finally, the problem of estimating the statistical parameters that describe the errors associated with the head and concentration data is addressed. A stage-wise estimation procedure is used to jointly estimate these statistical parameters along with the unknown model parameters and source characteristics.

Sampling Design Methods For Groundwater Modeling Under Uncertainty

A sampling network design model is presented that evaluates the trade-off between the varying costs of different types of data and the contribution of those data to improving model reliability. The methodology couples parameter-estimate and model-prediction uncertainty analyses with optimization to identify the mix of hydrogeologic information (e.g., head, concentration, and/or hydraulic conductivity measurement locations) that will minimize model prediction uncertainty for a given data collection budget. Two alternative optimization algorithms are presented and compared: a branch-and-bound algorithm and a genetic algorithm. A series of synthetic examples are presented to demonstrate the adaptability of the methodology to different sampling scenarios. The examples reveal two important properties of this network design problem. First, model-parameter and model-prediction uncertainty analyses are important components of the network design methodology because they provide a natural framework for evaluating the cost/information trade-off for different types of data and different sampling network designs. Second, the genetic algorithm can identify near-optimal solutions for a small fraction of the computational effort needed to determine the globally optimal solutions of the branch-and-bound algorithm.