[1] Knowledge about the strength and travel times of hyporheic exchange is vital to predict reactive transport and biogeochemical cycling in streams. In this study, we outline how to perform and analyze stream tracer tests using pulse injections of fluorescein as conservative and resazurin as reactive tracer, which is selectively transformed to resorufin when exposed to metabolically active zones, presumably located in the hyporheic zone. We present steps of preliminary data analysis and apply a conceptually simple mathematical model of the tracer tests to separate effects of in-stream transport from hyporheic exchange processes. To overcome the dependence of common parameter estimation schemes on the initial guess, we derive posterior parameter probability density functions using an adaptive Markov chain Monte Carlo scheme. By this, we can identify maximum-likelihood parameter values of instream transport, strength of hyporheic exchange, distribution of hyporheic travel times as well as sorption and reactivity coefficients of the hyporheic zone. We demonstrate the approach by a tracer experiment at River Goldersbach in southern Germany (60 L/s discharge). In-stream breakthrough curves were recorded with online fluorometers and jointly fitted to simulations of a one-dimensional reactive transport model assuming an exponential hyporheic travel-time distribution. The findings show that the additional analysis of resazurin not only improved the physical basis of the modeling, but was crucial to differentiate between surface transport and hyporheic transient storage of stream solutes. Parameter uncertainties were usually small and could not explain parameter variability between adjacent monitoring stations. The latter as well as a systematic underestimation of the tailing are due to structural errors of the model, particularly the exponential hyporheic travel-time distribution. Mean hyporheic travel times were in the range of 12 min, suggesting that small streambed structures dominate hyporheic exchange at the study site.

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[1] Performing stream-tracer experiments is an accepted technique to assess transport characteristics of streams undergoing hyporheic exchange. Recently, combining conservative and reactive tracers, in which the latter presumably undergoes degradation exclusively within the hyporheic zone, has been suggested to study in-stream transport, hyporheic exchange, and the metabolic activity of the hyporheic zone. The combined quantitative analysis to adequately describe such tests, however, has been missing. In this paper, we present mathematical methods to jointly analyze breakthrough curves of a conservative tracer (fluorescein), a linearly degrading tracer (resazurin), and its daughter compound (resorufin), which are synchronously introduced into the stream as pulses. Instream transport is described by the one-dimensional advection-dispersion equation, amended with a convolution term to account for transient storage within the hyporheic zone over a distribution of travel times, transformation of the reactive tracer in the hyporheic zone, and two-site sorption of the parent and daughter compounds therein. We use a shapefree approach of describing the hyporheic travel-time distribution, overcoming the difficulty of identifying the best functional parameterization for transient storage. We discuss how this model can be fitted to the breakthrough curves of all three compounds and demonstrate the method by an application to a tracer test in the third-order stream Goldersbach in Southern Germany. The entire river water passes once through the hyporheic zone over a travel distance of about 200 m with mean hyporheic residence times ranging between 16 and 23 min. We also observed a secondary peak in the transfer functions at about 1 h indicating a second hyporheic flow path. We could jointly fit the breakthrough curves of all compounds in three monitoring stations and evaluated the parameter uncertainty of the individual and joint fits by a method based on conditional realizations of the hyporheic travel-time distribution. The approach gives insight into in-stream transport, hyporheic exchange, metabolic activity, and river-bed sorption of the stream under investigation.