Donald M. Reeves

A Model-Averaging Method for Assessing Groundwater Conceptual Model Uncertainty

This study evaluates alternative groundwater models with different recharge and geologic components at the northern Yucca Flat area of the Death Valley Regional Flow System (DVRFS), USA. Recharge over the DVRFS has been estimated using five methods, and five geological interpretations are available at the northern Yucca Flat area. Combining the recharge and geological components together with additional modeling components that represent other hydrogeological conditions yields a total of 25 groundwater flow models. As all the models are plausible given available data and information, evaluating model uncertainty becomes inevitable. On the other hand, hydraulic parameters (e.g., hydraulic conductivity) are uncertain in each model, giving rise to parametric uncertainty. Propagation of the uncertainty in the models and model parameters through groundwater modeling causes predictive uncertainty in model predictions (e.g., hydraulic head and flow). Parametric uncertainty within each model is assessed using Monte Carlo simulation, and model uncertainty is evaluated using the model averaging method. Two model-averaging techniques (on the basis of information criteria and GLUE) are discussed. This study shows that contribution of model uncertainty to predictive uncertainty is significantly larger than that of parametric uncertainty. For the recharge and geological components, uncertainty in the geological interpretations has more significant effect on model predictions than uncertainty in the recharge estimates. In addition, weighted residuals vary more for the different geological models than for different recharge models. Most of the calibrated observations are not important for discriminating between the alternative models, because their weighted residuals vary only slightly from one model to another.

Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation

[1] This paper investigates whether particle ensembles in a fractured rock domain may be adequately modeled as an operator-stable plume. If this statistical model applies to transport in fractured media, then an ensemble plume in a fractured rock domain may be modeled using the novel Fokker-Planck evolution equation of the operator-stable plume. These plumes (which include the classical multi-Gaussian as a subset) are typically characterized by power law leading-edge concentration profiles and super-Fickian growth rates. To investigate the possible correspondence of ensemble plumes to operator-stable densities, we use numerical simulations of fluid flow and solute transport through largescale (2.5 km by 2.5 km), randomly generated fracture networks. These two-dimensional networks are generated according to fracture statistics obtained from field studies that describe fracture length, transmissivity, density, and orientation. A fracture continuum approach using MODFLOW is developed for the solution of fluid flow within the fracture network and low-permeability rock matrix, while a particle-tracking code, random walk particle method for simulating transport in heterogeneous permeable media (RWHet), is used to simulate the advective motion of conservative solutes through the model domain. By deterministically mapping individual fractures onto a highly discretized finite difference grid (1 m � 1m � 1 m here), the MODFLOW ‘‘continuum’’ simulations can faithfully preserve details of the generated network and can approximate fluid flow in a discrete fracture network model. An advantage of the MODFLOW approach is that matrix permeability can be made nonzero to account for any degree of matrix flow and/or transport.

On iterative techniques for computing flow in large two-dimensional discrete fracture networks

Computation of flow in discrete fracture networks often involves solving for hydraulic head values at all intersection points of a large number of stochastically generated fractures inside a bounded domain. For large systems, this approach leads to the generation of problems involving highly sparse matrices which must be solved iteratively. Distributions of fracture lengths spanning over several orders of magnitude, and the randomness of fracture orientations and locations, lead to coefficient matrices that are devoid of any regular structure in the sparsity pattern. In addition to the rapid increase in computational effort with increase in the size of the fracture network, the spread in the distribution of fracture parameters, such as length and transmissivity, dramatically influences the convergence behavior of the system of linear equations. An overview of the discrete fracture network (DFN) methodology for computation of flow is presented along with a comparative study of various Krylov subspace iterative methods for the resulting class of sparse matrices. The rate of convergence of the iterative techniques is found to exhibit a systematic pattern with respect to changes in statistical parameters of the stochastically generated fracture networks. Salient features of the observed trends in the convergence pattern are discussed and guidelines for design of DFN algorithms are provided.

A fractional-order tempered-stable continuity model to capture surface water runoff

The dynamics of surface runoff exhibits scale-dependent anomalous behavior due to heterogeneity present within natural systems, including spatial variations in surface topography and soil hydraulic properties which may not be efficiently captured by traditional modeling approaches. This study proposes a fractional-order continuity equation to quantify the scale-dependent anomalous behavior of overland flow, where the influence of sub-scale heterogeneity on flow dynamics can be characterized using spatiotemporally nonlocal terms built upon fractional derivatives. Both Eulerian and Lagrangian solvers are developed and cross-verified to approximate the proposed physical model. Numerical experiments further show that, on one hand, the space-fractional diffusive term in the flow model does not lead to apparent early arrivals in the steep rising limb of a hydrograph. This is likely caused by the combined effects of uniformly distributed precipitation over the entire hillslope and the immediate arrival of surface runoff at the downslope portion of the hillslope, both of which can overshadow the leading front of superdiffusion. The time-fractional term in the model, on the other hand, can 1) distinguish mobile and immobile water packets, 2) account for the strong time-nonlocal influence of net recharge on the receding limb of a hydrograph, and 3) efficiently characterize a wide range of late-time behavior of flow according to the tempered stable law. The applicability of the physical model is tested using two local-scale surface runoff data sets. The fractional-order tempered-stable flow model therefore may capture the complex hydrological response to precipitation in the real-world land surface.

Fractional dynamics of tracer transport in fractured media from local to regional scales

Tracer transport through fractured media exhibits concurrent direction-dependent super-diffusive spreading along high-permeability fractures and sub-diffusion caused by mass transfer between fractures and the rock matrix. The resultant complex dynamics challenge the applicability of conventional physical models based on Fick’s law. This study proposes a multi-scaling tempered fractional-derivative (TFD) model to explore fractional dynamics for tracer transport in fractured media. Applications show that the TFD model can capture anomalous transport observed in small-scale single fractures, intermediate-scale fractured aquifers, and two-dimensional large-scale discrete fracture networks. Tracer transport in fractured media from local (0.255-meter long) to regional (400-meter long) scales therefore can be quantified by a general fractional-derivative model. Fractional dynamics in fractured media can be scale dependent, owning to 1) the finite length of fractures that constrains the large displacement of tracers, and 2) the increasing mass exchange capacity along the travel path that enhances sub-diffusion.

Hydrogeologic Characterization of Fractured Rock Masses Intended for Disposal of Radioactive Waste

There are currently 441 nuclear power reactors in operation or under construction distributed over 30 countries (International Atomic Energy Agency, 2011). The global radioactive waste inventory reported as storage in 2008 was approximately 17.6 million cubic meters: 21% short-lived, lowand intermediate-level waste, 77% long-lived, lowand intermediate-level waste and 2% high-level waste (International Atomic Energy Agency, 2011). There is a consensus among most of the scientific community that geologic repositories offer the best solution for the long-term disposal of radioactive waste. In the United States, for example, geologic disposal is considered the only technically feasible, long-term strategy for isolating radioactive waste from the biosphere without active management (Long & Ewing, 2004; National Research Council, 2001; Nuclear Energy Agency, 1999).