Shape‐free inference of hyporheic traveltime distributions from synthetic conservative and “smart” tracer tests in streams

Abstract

[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,

Concurrent conservative and reactive tracer tests in a stream undergoing hyporheic exchange

“…For the analysis of the acquired data, we adopt a simplified version of the conceptual model for streams undergoing hyporheic exchange described by Liao and Cirpka [], among others. In the model, solutes are assumed to undergo one‐dimensional advection and dispersion in the main channel, supplemented by storage within the hyporheic zone, which is described as a specific volume flux of river water entering the hyporheic zone, staying there over a distribution of times and reentering the stream at the same point.…”

“…The reason for this is to retain comparability with previous studies and to quantify the structural model error associated with this type of model approach. In a companion paper [ Liao et al ., 2013], we present a more elaborate analysis that does not rely on a specific parametric shape of the hyporheic travel‐time distribution (see also Liao and Cirpka []) and considers two‐site sorption of the reactive tracer and its daughter compound within the hyporheic zone. The latter approach, however, is not accessible to the comprehensive MCMC‐based uncertainty analysis applied in the present contribution.…”

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.…”

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.…”