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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

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. Source

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

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. Source

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

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. Source

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

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. Source

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

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. Source

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