David L. Freyberg

Use of sedimentological information for geometric simulation of natural porous media structure

A geometric simulation method was used to develop a three-dimensional, highly detailed synthetic representation of point bar sediments in the Wabash River system. Geometric simulation methods, in comparison to well-known second-order stochastic methods, offer the advantage of being more closely related to depositional processes, which are often similarly conceptualized (i.e., described in terms of shapes of discrete bed forms, trends in grain size, and spatial relationships of defined geologic facies). Multiple scales of geometric variation were defined within a sedimentologically prescribed framework, and shapes of discrete geometric elements were established at each scale. The selected shapes were based on published field studies including sedimentological bed form studies and trench studies in active point bar sediments. The parameterization of the shapes allowed for random variability of the shape descriptors; discrete shapes were then generated and assimilated by computer. Hydraulic conductivity values were assigned to the discrete elements based on reports of observed variations in grain size and field measurements of hydraulic conductivity. The synthetic model, referred to as a numerical aquifer, is being used as the basis for extensive numerical experimentation to study the relationship between natural spatial structure and subsurface flow and transport.

Slow advection and diffusion through low permeability inclusions

Abstract Heterogeneous porous media with low permeability lenses can produce contaminant plumes with extended tails. Highly asymmetric breakthrough curves cannot be described well by an advection–dispersion equation (ADE) with a uniform velocity and dispersion coefficient. The character of such a solute plume depends on many factors, including plume size, the geometry and arrangement of the low permeability inclusions, and the transport through such regions. We develop an inclusion Peclet number that effectively characterizes the relative importance of advection and diffusion for transport within a low permeability lens. This inclusion Peclet number is a function of the far-field velocity, the effective diffusion coefficient, the length scale of the inclusion, and the ratio of the permeability of the lens to that of the surrounding matrix. We investigate the effects of a single, elliptical inclusion on the arrival of a solute at a downgradient control plane with numerical particle tracking. Effects specific to advection or diffusion dominance within the inclusion are subtle: diffusion gives rise to more distributed tailing whereas advection produces behavior that is more abrupt. These slight differences are not enough to allow one to determine the dominant process within the inclusion by observing the first three temporal moments alone. The time scale for the dominant transport process within the inclusion is the primary factor affecting the contaminant tailing. For high inclusion Peclet numbers (when advection dominates), the characteristic time varies with the permeability contrast, the far-field velocity, and the size and geometry of the inclusion. For low inclusion Peclet numbers (when diffusion dominates), the characteristic time varies with the size of the inclusion and the effective diffusion coefficient.

State‐Dependent Anisotropy: Comparisons of Quasi‐Analytical Solutions with Stochastic Results for Steady Gravity Drainage

Anisotropy in large-scale unsaturated hydraulic conductivity of layered soils changes with the moisture state. Here, state-dependent anisotropy is computed under conditions of large-scale gravity drainage. Soils represented by Gardners exponential function are perfectly stratified, periodic, and inclined. Analytical integration of Darcy’s law across each layer results in a system of nonlinear equations that is solved iteratively for capillary suction at layer interfaces and for the Darcy flux normal to layering. Computed fluxes and suction profiles are used to determine both upscaled hydraulic conductivity in the principal directions and the corresponding “state-dependent” anisotropy ratio as functions of the mean suction. Three groups of layered soils are analyzed and compared with independent predictions from the stochastic results of Yeh et al. (1985b). The small-perturbation approach predicts appropriate behaviors for anisotropy under nonarid conditions. However, the stochastic results are limited to moderate values of mean suction; this limitation is linked to a Taylor series approximation in terms of a group of statistical and geometric parameters. Two alternative forms of the Taylor series provide upper and lower bounds for the state-dependent anisotropy of relatively dry soils.

Implementing hydrologic boundary conditions in a multiphysics model

Modeling of hydrologic processes using multiphysics modeling packages shows significant promise in a number of applications. However, these packages have not yet developed a complete set of implementations for boundary conditions important in hydrologic modeling. Three such boundary conditions—rainfall infiltration, seepage faces, and evapotranspiration fluxes—are implemented using the generic boundary condition and internal sink routines provided in one multiphysics package, COMSOL multiphysics. Comparison with results from previous simulations using dedicated hydrologic models demonstrates that with care and creativity these boundary conditions can be implemented accurately and efficiently. Boundary condition implementation should not limit the applicability of multiphysics models to a broad set of problems of interest to the hydrologic community.

Assessing the Scale of Resource Recovery for Centralized and Satellite Wastewater Treatment

Wastewater treatment to recover water, energy, and other resources is largely carried out at centralized treatment facilities. An alternative is local treatment at satellite facilities where wastewater is removed from a collection system, resources are recovered locally, and the residuals are returned to the collection system. Satellite systems decrease the pipe and energy required for delivery of treated water and may decrease cost. But decisions regarding the geographic scale of resource recovery require consideration of many criteria. In this study, we rank water and energy recovery options for a simplified test case at three scale configurations: a centralized configuration and two hybrid configurations. We first choose criteria for decision-making. Quantitative performance metrics are defined for each criterion, weighted, and computed for each configuration. We then rank configurations. Rankings depend upon the decision-making strategy. For our test case, though, several strategies yield the same top-ranked configuration: a hybrid where communities close to the centralized facility use centralized resource recovery; communities far from the centralized facility use satellite resource recovery. Our ranking is sensitive to initial investment cost for satellite treatment. The results underscore the importance of cost-effective treatment systems and of an accurate and comprehensive analysis of design components.

Simulation of one-dimensional correlated fields using a matrix-factorization moving average approach

The simulation of one-dimensional stationary correlated fields is of increasing importance in the earth sciences. A new method for repeated generation of independent realizations, which are long and dense relative to the correlation scale of the underlying stochastic process, is examined here. This method is conceptually simple and easy to apply. It consists of a matrix-factorization technique for derivation of moving average coefficients which are used as weights in the construction of successive observations from linear combinations of random normal deviates. The matrix-factorization procedure is fast and need be performed only once for a given correlation function and density of observations. This technique can be used to generate evenly spaced observations in time or a single space dimension for any prescribed correlation function and marginal distribution which is Gaussian with arbitrary mean and variance. Tests of ensemble properties of generation procedures have been developed and results for this method compared with those for a popular generation technique. For correlation functions and generation conditions examined, the matrix-factorization moving average approach more accurately produces ensemble characteristics of the prescribed underlying process. For repeated generation of 2001 observations spaced evenly over realizations with length equal to 100 times the correlation scale, the moving average approach requires only about one fifth the CPU time used by the Shinozuka and Jan method to obtain similar accuracy.

Efficient simulation of single species and multispecies transport in groundwater with local adaptive grid refinement

The computational burden associated with multidimensional, multicomponent, numerical solute transport models can be prohibitive. To solve these CPU intensive problems efficiently and accurately, we have implemented and extended a local adaptive grid refinement method of Berger and Oliger (1984) to track error-prone regions and supply high-resolution subgrids where they are locally needed while maintaining relatively few nodes elsewhere on a coarse, base grid. Novel features include a unique method for detecting a priori where the numerical error is unacceptable, variable time step control which allows smaller time steps on subgrids than on the base grid, and a modular framework which allows easy exchange of partial differential equation solvers to accommodate different problem formulations. Three examples show how the subgrids track the error-prone regions, how multiple subgrids are used for geometrically complex front shapes, and how increased resolution is provided for self-sharpening fronts when multiple reacting species are considered. For all three examples, solutions with accuracies comparable to those achieved with a uniform fine grid are obtained at between 20 and 30% of the computational cost.

Impacts of Land-Use Change on Groundwater Supply: Ecosystem Services Assessment in Kona, Hawaii

AbstractPayments for watershed management link upstream inhabitants whose actions affect water resources with downstream water users. This paper evaluates the effect of plausible shifts in watershed land use on hydrologic services on the Kona coast of Hawai’i Island by measuring vegetation effects on hydrologic fluxes, modeling land-use change impact on the water-supply aquifer, and evaluating the local water department’s associated pumping expenses. Transitions between native and plantation forest will have a 25–40% greater impact on the aquifer than the transition from pasture to either forest type. However, for all transitions, the value to the water department is just 2–5% of the opportunity cost to landowners. To provide context for these findings, the effects of these land transitions on carbon storage, provision of native bird habitat, and land stewardship are assessed. Estimates show that delivery of other services does not always increase when water services increase and suggest that the value of...

Incorporating uncertainty in watershed management decision-making: A mercury TMDL case study

Water quality impairment due to high mercury fish tissue concentrations and high mercury aqueous concentrations is a widespread problem in several sub-watersheds that are major sources of mercury to the San Francisco Bay. Several mercury Total Maximum Daily Load regulations are currently being developed to address this problem. Decisions about control strategies are being made despite very large uncertainties about current mercury loading behavior, relationships between total mercury loading and methyl mercury formation, and relationships between potential controls and mercury fish tissue levels. To deal with the issues of very large uncertainties, data limitations, knowledge gaps, and very limited State agency resources, this work proposes a decision analytical alternative for mercury TMDL decision support. The proposed probabilistic decision model is Bayesian in nature and is fully compatible with a learning while doing adaptive management approach. Strategy evaluation, sensitivity analysis, and information collection prioritization are examples of analyses that can be performed using this approach.

Simulating a Lake as a High-Conductivity Variably Saturated Porous Medium

One approach for simulating ground water-lake interactions is to incorporate the lake into the ground water solution domain as a high-conductivity region. Previous studies have developed this approach using fully saturated models. This study extends this approach to variably saturated models, so that ground water-lake interactions may be more easily simulated with commonly used or public domain variably saturated codes that do not explicitly support coupled lake-water balance modeling. General guidelines are developed for the choices of saturated hydraulic conductivity and moisture retention and relative permeability curves for the lake region. When applied to an example ground water-lake system, model results are very similar to those from a model in which the lake is represented as a specified head boundary continuously updated by a lake mass balance. The high-conductivity region approach is most suitable for relatively simple geometries and lakes with slower and smaller fluctuations when the overall flow pattern and system fluxes, rather than the detailed flow pattern around the intersection of the lake and land surfaces, are of interest.