[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.

[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.

[1] The hyporheic zone has been identified as important for river ecology, natural biogeochemical turnover, filtration of particles, degradation of dissolved pollutants-and thus for the self-cleaning capacity of streams, and for groundwater quality. Good estimation of the traveltime distribution in the hyporheic zone is required to achieve a better understanding of transport in the river system. The transient-storage model has been accepted as an appropriate tool for reach-scale transport in rivers undergoing hyporheic exchange, but the choice of the best parametric function for the hyporheic traveltime distribution has remained unclear. We present an approach to obtaining hyporheic traveltime distributions from synchronous conservative and ''smart'' tracer experiments that does not rely on a particular functional form of the hyporheic traveltime distribution, but treats the latter as a continuous function. Nonnegativity of the hyporheic traveltime distribution is enforced by the application of Lagrange multipliers. A smoothness parameter, needed for regularization, and uncertainty bounds are obtained by the expectation-maximization method relying on conditional realizations. The shape-free inference provides the opportunity for capturing unconventional shapes, e.g., multiple peaks, in the estimation. We test the approach by applying it to a virtual test case with a bimodal hyporheic traveltime distribution, which is recaptured in the inversion of noisy data.Citation: Liao, Z., and O. A. Cirpka (2011), Shape-free inference of hyporheic traveltime distributions from synthetic conservative and ''smart'' tracer tests in streams, Water Resour. Res., 47, W07510,

Abstract. Resazurin (Raz) and its reaction product resorufin (Rru) have increasingly been used as reactive tracers to quantify metabolic activity and hyporheic exchange in streams. Previous work has indicated that these compounds undergo sorption in stream sediments. We present laboratory experiments on Raz and Rru transport, sorption, and transformation, consisting of 4 column and 72 batch tests using 2 sediments with different physicochemical properties under neutral (pH = 7) and alkaline (pH = 9) conditions. The study aimed at identifying the key processes of reactive transport of Raz and Rru in streambed sediments and the experimental setup best suited for their determination. Data from column experiments were simulated by a travel-time-based model accounting for physical transport, equilibrium and kinetic sorption, and three first-order reactions. We derived the travel-time distributions directly from the breakthrough curve (BTC) of the conservative tracer, fluorescein, rather than from fitting an advective-dispersive transport model, and inferred from those distributions the transfer functions of Raz and Rru, which provided conclusive approximations of the measured BTCs. The most likely reactive transport parameters and their uncertainty were determined by a Markov chain–Monte Carlo approach. Sorption isotherms of both compounds were obtained from batch experiments. We found that kinetic sorption dominates sorption of both Raz and Rru, with characteristic timescales of sorption in the order of 12 to 298 min. Linear sorption models for both Raz and Rru appeared adequate for concentrations that are typically applied in field tracer tests. The proposed two-site sorption model helps to interpret transient tracer tests using the Raz–Rru system.

Tracheal cartilage has been widely regarded as a linear elastic material either in experimental studies or in analytic and numerical models. However, it has been recently demonstrated that, like other fiber-oriented biological tissues, tracheal cartilage is a nonlinear material, which displays higher strength in compression than in extension. Considering the nonlinearity requires a more complex theoretical frame work and costs more to simulate. This study aims to quantify the deviation due to the simplified treatment of the tracheal cartilage as a linear material. It also evaluates the improved accuracy gained by considering the nonlinearity. Pig tracheal rings were used to exam the mechanical properties of cartilage and muscular membrane. By taking into account the asymmetric shape of tracheal cartilage, the collapse behavior of complete rings was simulated, and the compliance of airway and stress in the muscular membrane were discussed. The results obtained were compared with those assuming linear mechanical properties. The following results were found: (1) Models based on both types of material properties give a small difference in representing collapse behavior; (2) regarding compliance, the relative difference is big, ranging from 10 to 40% under negative pressure conditions; and (3) the difference in determining stress in the muscular membrane is small too: <5%. In conclusion, treating tracheal cartilage as a linear material will not cause big deviations in representing the collapse behavior, and mechanical stress in the muscular part, but it will induce a big deviation in predicting the compliance, particularly when the transmural pressure is lower than -0.5 kPa. The results obtained in this study may be useful in both understanding the collapse behavior of trachea and in evaluating the error induced by the simplification of treating the tracheal cartilage as a linear elastic material.