Big trouble in a little box: Can we distinguish groundwater transport hypotheses given observational uncertainties?

This study explores the difficulties associated with inferring heterogeneity and transport processes given observational uncertainties. A well-characterized laboratory experiment consisting of a small laboratory sand tank with dimensions of 73 cm x 71 cm x 70 cm serves as the basis for our study. The tank is packed with a coarse outer sand (K=0.005 m/s) around a centralized 20 cm cube of fine sand (K=0.00014 m/s). Our goal is to infer the low conductivity cube, without making any assumptions as to its presence within the tank. Using time series breakthrough curves of water wells as well as geophysical probes within the sand (collected via electrical resistivity tomography), we monitor the flow (steady state) and transport of a 6,000 s step-pulse injection of NaCl across six experimental configurations with three replicates each (18 total tests). Experiments were grouped into three classifications: (1) lateral extent- how does the lateral extent of the injection plane affect our ability to infer hydrologic properties? (2) concentration - how does the injected concentration affect our ability to infer hydrologic properties? (3) sampling configuration - for the geophysical data, how important is frequency of data vs. number of sampling points? Replicate tracer tests show strong variability across for the highly controlled replicate experiments. Particularly, tracer signal to background conditions strongly influences the identification of heterogeneity and perceived transport processes. The experiments, designed to be controlled by advection-dispersion, show far more complex and potentially difficult to replicate behavior. Contrary to intuition, plume variability (calculated via temporal moments) is highest near the point of solute injection and decreases as the plume becomes more developed downstream. While temporal moments serve as a way to track the variability of measurements across experiments, they fail to convincingly distinguish the low conductivity cube, especially in experiments with truncated tails. Given that many field scale experiments have tailing due to time constraints or system heterogeneity, care should be taken to account for moment truncation as well as measures that consider the characteristic shape of the breakthrough curve to infer system heterogeneities. This study should serve as a cautionary tale to field scientists interested in site characterization. For robust field site characterization, it is essential to: (1) have a strong control on solute tracer variables with a clear understanding of background conditions, and (2) perform replicate experiments where possible, to quantify observational uncertainty.