Modeling and inverting reactive stream tracers undergoing two-site sorption and decay in the hyporheic zone

Abstract

[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.

Hyporheic flow and transport processes: Mechanisms, models, and biogeochemical implications

“…Transient storage in both surface and subsurface (i.e., hyporheic) zones leaves a peculiar signature in the shape of in‐stream solute concentration curves, and recent studies have aimed to separate these two contributions to obtain information on hyporheic exchange processes. To face this problem, it has been stressed that residence times of solutes in different TS zones can be properly inferred by collecting concentration time series both from the main channel and from surface [ Briggs et al ., ] and subsurface TS zones [ Harvey and Fuller , ] or by using additional tracers such as temperature [ Neilson et al ., , ] or reactive solute tracers which are subject to different chemical transformations in surface and subsurface storage zones [ Haggerty et al ., ; Liao and Cirpka , ; Liao et al ., ]. Regardless of the adopted method, particular attention should be paid when using any stream transport model to discriminate between water and solute exchange with the hyporheic zone and with slow, stagnant zones of the stream channel.…”

Determination of hyporheic travel time distributions and other parameters from concurrent conservative and reactive tracer tests by local‐in‐global optimization

“…Conversely, Liao and Cirpka [] and Liao et al . [] used a shape‐free approach to infer hyporheic travel time distributions from conservative and reactive tracer breakthrough curves. In the latter approach, the only constraints on the continuous hyporheic travel time distributions are that they must be nonnegative and exhibit a certain smoothness (for details see Cirpka et al .…”

“…The higher flexibility of the shape‐free approach calls even more for global‐search methods, but the associated computational costs have so far been considered unacceptable so that Liao et al . [] used a gradient‐based method to estimate the hyporheic travel time distribution and other parameters of stream‐tracer transport coupled to hyporheic exchange.…”

Non-stationary nonparametric inference of river-to-groundwater travel-time distributions

“…However, the complexity of riverbed morphology and sediments could facilitate such transfer functions. To overcome this difficulty, our workgroup has developed non-parametric methods of estimating non-negative, smooth transfer functions and applied them to bank-filtration problems (Cirpka et al, 2007;Vogt et al, 2010), stream-to-stream tracer tests (Payn et al, 2008), and the identification of hyporheic travel-time distributions (Liao and Cirpka, 2011;Liao et al, 2013). Recently, McCallum et al (2014b) suggested a similar method in which the smoothness regularization of Cirpka et al (2007) has been replaced by applying the singular-valuedecomposition based pseudo-inverse in the solution of the resulting close-to-singular system of linear equations.…”