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Hannah D.M.,Earth and Environmental SciencesUniversity of BirminghamBirmingham | Blume T.,Helmholtz Center Potsdam | Blaen P.J.,Earth and Environmental SciencesUniversity of BirminghamBirmingham | Knapp J.L.,Center for Applied Geoscience | And 5 more authors.
Water Resources Research | Year: 2016

Improved understanding of stream solute transport requires meaningful comparison of processes across a wide range of discharge conditions and spatial scales. At reach scales where solute tracer tests are commonly used to assess transport behavior, such comparison is still confounded due to the challenge of separating dispersive and transient storage processes from the influence of the advective timescale that varies with discharge and reach length. To better resolve interpretation of these processes from field-based tracer observations, we conducted recurrent conservative solute tracer tests along a 1 km study reach during a storm discharge period and further discretized the study reach into six segments of similar length but different channel morphologies. The resulting suite of data, spanning an order of magnitude in advective timescales, enabled us to (1) characterize relationships between tracer response and discharge in individual segments and (2) determine how combining the segments into longer reaches influences interpretation of dispersion and transient storage from tracer tests. We found that the advective timescale was the primary control on the shape of the observed tracer response. Most segments responded similarly to discharge, implying that the influence of morphologic heterogeneity was muted relative to advection. Comparison of tracer data across combined segments demonstrated that increased advective timescales could be misinterpreted as a change in dispersion or transient storage. Taken together, our results stress the importance of characterizing the influence of changing advective timescales on solute tracer responses before such reach-scale observations can be used to infer solute transport at larger network scales. © 2016. American Geophysical Union. All Rights Reserved.


Scho niger A.,Center for Applied Geoscience | Wo hling T.,Lincoln University at Christchurch | Nowak W.,Institute for Modelling Hydraulic and Environmental Systems LS3 SimTech
Water Resources Research | Year: 2014

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. © 2014. The Authors.


Cirpka O.A.,Center for Applied Geoscience | Chiogna G.,Center for Applied Geoscience | Rolle M.,University of TubingenTubingen Germany
Water Resources Research | Year: 2015

Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two-dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady-state flows. In three-dimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady-state groundwater whirls. We analyze steady-state solute transport in three-dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse-dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log-hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two-point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two-particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux-related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy. © 2014. American Geophysical Union.


Loschko M.,Center for Applied Geoscience | Cirpka O.A.,Center for Applied Geoscience
Water Resources Research | Year: 2016

We simulate aquifer-scale reactive transport using an approach based on travel times and relative reactivity. The latter quantifies the intensity of the chemical reaction relative to a reference reaction rate with identical concentrations and can be interpreted as the strength of electron-donor (or electron-acceptor) release by the matrix, scaled by a reference release. In general, the relative reactivity is a spatially variable property reflecting the geology of the formation. In the proposed approach, we track the path of individual water parcels through the aquifer and evaluate the age of the water parcels and the relative reactivity integrated along their trajectories. By switching from spatial discretization to cumulative relative reactivity, advective-reactive transport can be simulated by solving a single system of ordinary differential equations for each combination of concentrations in the inflow. We test the validity of the approach in a two-dimensional test case of steady state groundwater flow and reactive transport involving aerobic respiration and denitrification. Here we compare steady state concentration distributions of the spatially explicit virtual truth, accounting for dispersive mixing, with the approximation based on cumulative relative reactivity and show that the errors introduced by neglecting dispersive mixing are minor if the target quantities are the mass fluxes crossing a control plane or being collected by a well. We further demonstrate the efficiency of the approach in a synthetic three-dimensional case study. The proposed approach is computationally so efficient that ensemble runs to assess statistical distributions of concentration time series of reactive solutes become feasible, which is not practical with a spatially explicit model. © 2016. American Geophysical Union. All Rights Reserved.


Maxwell R.M.,Colorado School of Mines | Putti M.,University of Padua | Meyerhoff S.,Colorado School of Mines | Delfs J.-O.,Helmholtz Center for Environmental Research | And 17 more authors.
Water Resources Research | Year: 2014

There are a growing number of large-scale, complex hydrologic models that are capable of simulating integrated surface and subsurface flow. Many are coupled to land-surface energy balance models, biogeochemical and ecological process models, and atmospheric models. Although they are being increasingly applied for hydrologic prediction and environmental understanding, very little formal verification and/or benchmarking of these models has been performed. Here we present the results of an intercomparison study of seven coupled surface-subsurface models based on a series of benchmark problems. All the models simultaneously solve adapted forms of the Richards and shallow water equations, based on fully 3-D or mixed (1-D vadose zone and 2-D groundwater) formulations for subsurface flow and 1-D (rill flow) or 2-D (sheet flow) conceptualizations for surface routing. A range of approaches is used for the solution of the coupled equations, including global implicit, sequential iterative, and asynchronous linking, and various strategies are used to enforce flux and pressure continuity at the surface-subsurface interface. The simulation results show good agreement for the simpler test cases, while the more complicated test cases bring out some of the differences in physical process representations and numerical solution approaches between the models. Benchmarks with more traditional runoff generating mechanisms, such as excess infiltration and saturation, demonstrate more agreement between models, while benchmarks with heterogeneity and complex water table dynamics highlight differences in model formulation. In general, all the models demonstrate the same qualitative behavior, thus building confidence in their use for hydrologic applications. Key Points Seven hydrologic models were intercompared on standard benchmark problems In general, though there are differences in approach, these models agree Model differences can be attributed to solution technique and coupling strategy © 2014. The Authors.


Schoniger A.,Center for Applied Geoscience | Wohling T.,Water and Earth System Science Competence ClusterUniversity of TubingenTubingen Germany | Nowak W.,Institute for Modelling Hydraulic and Environmental Systems LS 3 SimTech
Water Resources Research | Year: 2015

Bayesian model averaging (BMA) ranks the plausibility of alternative conceptual models according to Bayes' theorem. A prior belief about each model's adequacy is updated to a posterior model probability based on the skill to reproduce observed data and on the principle of parsimony. The posterior model probabilities are then used as model weights for model ranking, selection, or averaging. Despite the statistically rigorous BMA procedure, model weights can become uncertain quantities due to measurement noise in the calibration data set or due to uncertainty in model input. Uncertain weights may in turn compromise the reliability of BMA results. We present a new statistical concept to investigate this weighting uncertainty, and thus, to assess the significance of model weights and the confidence in model ranking. Our concept is to resample the uncertain input or output data and then to analyze the induced variability in model weights. In the special case of weighting uncertainty due to measurement noise in the calibration data set, we interpret statistics of Bayesian model evidence to assess the distance of a model's performance from the theoretical upper limit. To illustrate our suggested approach, we investigate the reliability of soil-plant model selection following up on a study by Wöhling et al. (2015). Results show that the BMA routine should be equipped with our suggested upgrade to (1) reveal the significant but otherwise undetected impact of measurement noise on model ranking results and (2) to decide whether the considered set of models should be extended with better performing alternatives. © 2015. American Geophysical Union. All Rights Reserved.


Lutzenkirchen J.,Karlsruhe Institute of Technology | Marsac R.,Karlsruhe Institute of Technology | Kulik D.A.,Paul Scherrer Institute | Payne T.E.,Australian Nuclear Science and Technology Organisation | And 3 more authors.
Applied Geochemistry | Year: 2014

Spectroscopic studies and atomistic simulations of (hydr)oxide surfaces show that ionic aqueous adsorbates can bind to one, two, three, or four surface oxygen atoms (sites), forming multi-dentate species in surface complexation reactions. The law of mass action (LMA) for such reactions can be expressed in several alternative scales of surface concentration (activity). Unlike for mono-dentate surface complexes, the numerical value of the equilibrium constant is not independent of the choice of the surface concentration scale. Here, we show in a number of examples that the different formalisms implemented in popular speciation codes (MINEQL, MINTEQ, PHREEQC, and ECOSAT) yield different results for the same systems when the same parameters are used. We conclude that it is very important to generate general equations to easily transfer stability constants between the different concentration scales. It is of utmost importance for application of these models to reactive transport that the implementation in both the model fitting and speciation codes, and in the transport codes, is transparent to users. We also point to the problem that the implementation of the diffuse layer formalism in the various codes is not necessarily generally applicable. Thus, codes like VisualMinteq or MINEQL involve the Gouy-Chapman equation, which is limited to symmetrical (z:z) electrolytes, while PHREEQC and ECOSAT use general equations. Application of the former two to environmental problems with mixed electrolytes will therefore involve an inconsistency. © 2014 Elsevier Ltd. All rights reserved.


Wohling T.,Lincoln University at Christchurch | Schoniger A.,Center for Applied Geoscience | Gayler S.,Institute for Geoscience | Nowak W.,Institute for Modelling Hydraulic and Environmental Systems LH3 SimTech
Water Resources Research | Year: 2015

A Bayesian model averaging (BMA) framework is presented to evaluate the worth of different observation types and experimental design options for (1) more confidence in model selection and (2) for increased predictive reliability. These two modeling tasks are handled separately because model selection aims at identifying the most appropriate model with respect to a given calibration data set, while predictive reliability aims at reducing uncertainty in model predictions through constraining the plausible range of both models and model parameters. For that purpose, we pursue an optimal design of measurement framework that is based on BMA and that considers uncertainty in parameters, measurements, and model structures. We apply this framework to select between four crop models (the vegetation components of CERES, SUCROS, GECROS, and SPASS), which are coupled to identical routines for simulating soil carbon and nitrogen turnover, soil heat and nitrogen transport, and soil water movement. An ensemble of parameter realizations was generated for each model using Monte-Carlo simulation. We assess each model's plausibility by determining its posterior weight, which signifies the probability to have generated a given experimental data set. Several BMA analyses were conducted for different data packages with measurements of soil moisture, evapotranspiration (ETa), and leaf area index (LAI). The posterior weights resulting from the different BMA runs were compared to the weight distribution of a reference run with all data types to investigate the utility of different data packages and monitoring design options in identifying the most appropriate model in the ensemble. We found that different (combinations of) data types support different models and none of the four crop models outperforms all others under all data scenarios. The best model discrimination was observed for those data where the competing models disagree the most. The data worth for reducing prediction uncertainty depends on the prediction to be made. LAI data have the highest utility for predicting ETa, while soil moisture data are better for predicting soil water drainage. Our study illustrates, that BMA provides an objective framework for data worth analysis with respect to both model discrimination and model calibration for a wide range of applications. © 2015. American Geophysical Union. All Rights Reserved.


Chiogna G.,Center for Applied Geoscience | Cirpka O.A.,Center for Applied Geoscience | Rolle M.,University of TubingenTubingen Germany | Bellin A.,Environmental and Mechanical EngineeringUniversity of TrentoTrento Itlay
Water Resources Research | Year: 2015

Characterizing the topology of three-dimensional steady-state flow fields is useful to describe the physical processes controlling the deformation of solute plumes and, consequently, obtain helpful information on mixing processes without solving the transport equation. In this work, we study the topology of flow in three-dimensional nonstationary anisotropic heterogeneous porous media. In particular, we apply a topological metric, i.e., the helicity density, and two complementary kinematic descriptors of mixing, i.e., stretching and folding, to investigate: (i) the flow field resulting from applying a uniform-in-the-average hydraulic gradient within a fully resolved heterogeneous three-dimensional porous medium with a nonstationary anisotropic covariance function of the locally isotropic hydraulic log conductivity; (ii) the flow field obtained by averaging a set of Monte Carlo realizations of the former field; (iii) the flow field obtained considering the blockwise uniform anisotropic effective conductivity tensor computed for the fully resolved case. While in the fully resolved case, the local helicity density is zero as a consequence of the local isotropy of hydraulic conductivity, it differs from zero in the other two cases. We show, therefore, that this topological metric is scale dependent and should be computed at the appropriate scale to be informative about the leading patterns of plume deformation. Indeed, streamlines are helical in all three cases at scales larger than the characteristic scale of spatial variability. We apply stretching and folding metrics to investigate the scales at which plume deformation is more influenced by helical motion than by the effect of small-scale spatial heterogeneity in the hydraulic-conductivity field. Under steady-state flow conditions, stretching, which quantifies the increasing length of an interface, dominates at short distances from a given starting plane, while folding, which describes how this interface is bent to fill a finite volume of space, dominates further downstream and can be correlated with the appearance of large-scale secondary motion. We conclude that three-dimensional flows in porous media may show a complex topology whose analysis is relevant for the description of plume deformation. These results have important implications for the understanding of mixing processes, as shown in detail in the companion paper focusing on solute transport. © 2014. American Geophysical Union. All Rights Reserved.

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