Goodness-of-Fit Test for Modeling Tracer Breakthrough Curves in Wetlands

Wetland transport models generally either assume plug flow (with or without dispersion) or conceptualize the wetland as a series of continuously stirred tank reactors (CSTRs). To evaluate the CSTR approach, we present a goodness-of-fit test suitable for evaluating breakthrough curves from tracer experiments. The test, which makes use of confidence intervals associated with the multivariate normal distribution, can be used to test the fit of the breakthrough curve model, but requires sampling across a transect rather than from a single point. To test the CSTR assumption, we conducted a pair of two-dimensional tracer experiments within a $9.9\mathrm{ha}$ wetland constructed to receive effluent from a wastewater treatment plant in San Jacinto, Calif. The wetland operates with five parabolic inlets and a single large parabolic outlet to encourage lateral uniformity. In both experiments tritium oxide (HTO) was used as the tracer. Rhodamine WT dye was also included in the second experiment. Tracer samples were collected along transects installed perpendicular to the direction of flow. Analysis of the results indicates satisfactory lateral mixing and no significant short-circuiting. Rhodamine WT dye performed similarly to HTO when detectable but was too dilute to be observed at the outlet. When tracer movement was modeled as a series of continuously stirred reaction vessels, the parameter associated with the integer number of vessels increased from 2 at the first transect to 8 at the outlet. At each transect, the model was checked with a new goodness-of-fit test. At the $\alpha =0.05$ confidence level, all fitted models were rejected, suggesting that while the CSTR assumption may usefully approximate transport processes, it is not statistically valid for this wetland.