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

Abstract

Abstract. 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.

Quantifying phosphorus uptake using pulse and steady‐state approaches in streams

“…Pulse releases can increase the uncertainty of conservative transport parameters (Wagner and Harvey 1997), in part because they do not integrate hydrologic variability over a very long period (Gooseff et al 2008). Gooseff et al (2008) also demonstrated that residence time distributions for conservative tracers in transient storage zones differed between pulse and continuous releases.…”

“…However, because continuous injections integrate tracer movements over a longer period than pulses (Gooseff et al 2008), it is possible that differences in conservative transport parameters could sometimes arise. Further, Wagner and Harvey (1997) found that continuous injections yielded a lower coefficient of variation (CV) for each conservative transport parameter than pulses. However, the pulse approach still yielded CV < 0.2 for D, A, A s , and α in more than 80% of the situations modeled in that work.…”

Investigating the spatio-temporal variability in groundwater and surface water interactions: a multi-technique approach

“…While c h is simple to measure in the field, calculating q h has historically been solved by conducting in-stream tracer injections and modelling breakthrough curves (Runkel, 1998;Wagner and Harvey, 1997), which can be logistically difficult in large river systems. The flux of 222 Rn from the hyporheic zone can alternatively be estimated from river stretches that are not receiving groundwater input where there is little change in 222 Rn activity .…”

A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations

“…Despite the relative ease of the combined tracer test-OTIS-P approach, many investigators have concluded that particular data sets and stream conditions may yield substantial uncertainty in the inferred values of transientstorage parameters (Wagner and Gorelick 1986, Wagner and Harvey 1997, Wagener et al 2002, Kelleher et al 2013, Mueller Price et al 2015. The limited power of transientstorage parameter estimates can be problematic because even the most basic statistical methods would emphasize that useful results from inverse modeling require an objective and rigorous consideration of uncertainty in parameter estimates.…”