Parameter Extraction from Tracer Breakthrough Curves: An Empirical Test of Analytical, Statistical and Analogue Methods

Karst tracer breakthrough curves are usually derived from an in situ filter fluorometer and used to extract hydraulic and form parameters for a tracer route. To date there has been limited evaluation of the parameters resulting from various modes of analysis.

Here, 142 quantitative traces were undertaken in a surface stream using Acid Yellow 73 (Uranine), Acid Red 388 (Rhodamine WT) and Acid Red 52 (Acid Rhodamine B) under a range of steady flows and across varied reaches. The data were calibrated and corrected for temperature, cross fluorescence, background and turbidity and analyzed using advection dispersion retardation modeling (CXTFIT), statistical moments and analogue methods.

Analytical models gave good approximate fits, but showed systematic fitting errors and inconsistent parameters between traces. Statistical moments gave coherent travel times, but dispersivity was very inconsistent with a sensitivity to background correction method. Analogue travel time (time to peak) and dimensionless dispersion (half peak height width/time to peak) were much more coherent.

The poor performance of both analytical and statistical parameters in part arises from sensitivity to the error-prone tail of the breakthrough curve. But the poorest replication was for shorter traces where the tail error should be least. Detailed inspection of high frequency data reveals systematic oscillations in the tracer breakthrough curve, even over 10km. These suggest incomplete mixing, perhaps arising from periodic dead zone exchange with a long enough time constant to modulate in-channel concentrations.

These results indicate that standard parameter extractions are vulnerable to common errors in the tracer breakthrough data. Furthermore, no analytic method can yet deconvolve longitudinal heterogeneity. Low frequency periodic dead zone exchange may prove particularly intractable as it may significantly alter proximal in-stream tracer concentrations. For practical purposes, simple analogue parameters appear to be more stable, sensitive and reliable, and they carry no implicit form implications.