R. Allan Freeze

Bio: R. Allan Freeze is an academic researcher from University of British Columbia. The author has contributed to research in topics: Groundwater flow & Subsurface flow. The author has an hindex of 29, co-authored 53 publications receiving 6092 citations.

A Stochastic-Conceptual Analysis of One-Dimensional Groundwater Flow in Nonuniform Homogeneous Media

Abstract: The most realistic representation of a naturally occurring porous medium is a stochastic set of macroscopic elements in which the values of the three basic hydrogeologic parameters (hydraulic conductivity K, compressibility α, and porosity n) are defined by frequency distributions. A homogeneous formation under this representation is one in which the frequency distributions do not change through space. All soils and geologic formations, even the ones that are homogeneous, show random variations in the values of the hydrogeological parameters through space; that is, they are nonuniform, and a measure of the nonuniformity is provided by the standard deviation of the frequency distributions. If K and α are log normally distributed and n is normally distributed, and if we define Y = log K and C = log α, then the parameters Y, C, and n can be generated from a multivariate normal density function with means μy, μc, and μn, standard deviations σy, σc, and σn, and correlation coefficients ρyc, ρyn, and ρcn The analysis of groundwater flow in nonuniform media requires a stochastic-conceptual approach in which the effects of stochastic parameter distributions on predicted hydraulic heads are analyzed with the aid of a set of Monte Carlo solutions to the pertinent boundary value problems. In this study, two one-dimensional saturated flow problems are analyzed: steady state flow between two specified heads and transient consolidation of a clay layer. The primary output is the statistical distribution of hydraulic head ϕ, through space and time, as indicated by the mean values and their standard deviations Sϕ¯(x, t) Results show that the standard deviations of the input hydrogeologic parameters, particularly σy and σc, are important index properties; changes in their values lead to different responses for even when the means μy, μc, and μn are fixed. The degree of uncertainty associated with hydraulic head predictions increases as the degree of nonuniformity of the porous medium increases. For large values of σy and σc it becomes virtually impossible to obtain meaningful hydraulic head predictions. For transient flow the output distribution of hydraulic head values is almost never normal; in some cases it approaches a uniform distribution. The results of this study throw into question the validity of the hidden assumption that underlies all deterministic groundwater modeling; namely, that it is possible to select a single value for each flow parameter in a homogeneous but nonuniform medium that is somehow representative and hence define an ‘equivalent’ uniform porous medium. For transient flow there may be no way to define an equivalent medium. The fact that nine index parameters rather than three are required to describe a nonuniform geologic formation, the large uncertainties in predicted hydraulic heads for relatively simple flow problems in nonuniform soils, and the contention that there may be no simple way to define an equivalent uniform porous medium all have important implications in the development of groundwater flow theory and in its most fundamental applications.

Theoretical analysis of regional groundwater flow: 2. Effect of water-table configuration and subsurface permeability variation

Abstract: Details of steady-state flow in regional groundwater basins can be investigated using digital computer solutions of appropriately designed mathematical models. The factors that must be considered are: (1) ratio of depth to lateral extent of the basin; (2) Watertable configuration; and (3) stratigraphy and resulting subsurface variations in permeability. The results of this study provide a theoretical basis for the following properties of regional flow systems: (1) groundwater discharge will tend to be concentrated in major valleys; (2) recharge areas are invariably larger than discharge areas; (3) in hummocky terrain, numerous sub-basins are superposed on the regional system; (4) buried aquifers tend to concentrate flow toward the principal discharge area, have a limiting effect on sub-basins, and need not outcrop to produce artesian flow conditions; (5), stratigraphic discontinuities can lead to distributions of recharge and discharge areas that are difficult to anticipate and that are largely independent of the water-table configuration. (Key words: Groundwater; computers, digital; drainage basin characteristics)

Three-Dimensional, Transient, Saturated-Unsaturated Flow in a Groundwater Basin

Abstract: A three-dimensional finite difference model has been developed for the treatment of saturated-unsaturated transient flow in small nonhomogeneous, anisotropic geologic basins. The uniqueness of the model lies in its inclusion of the unsaturated zone in a basin wide model that can also handle both confined and unconfined saturated aquifers, under both natural and developed conditions. The integrated equation of flow is solved by the line successive overrelaxation technique. The model allows any generalized region shape and any configuration of time variant boundary conditions. When applied to natural flow systems, the model provides quantitative hydrographs of surface infiltration, groundwater recharge, water table depth, and stream base flow. Results of simulations for hypothetical basins provide insight into the mechanisms involved in the development of perched water tables. The unsaturated basin response is identified as the controlling factor in determining the nature of the base flow hydrograph. Application of the model to developed basins allows one to simulate not only the manner in which groundwater withdrawals are transmitted through the aquifers, but also the changes in the rates of groundwater recharge and discharge induced by the withdrawals. For any proposed pumping pattern, it is possible to predict the maximum basin yield that can be sustained by a flow system in equilibrium with the recharge-discharge characteristics of the basin.

Stochastic analysis of steady state groundwater flow in a bounded domain: 1. One-dimensional simulations

Abstract: A stochastic analysis of two-dimensional steady state groundwater flow in a bounded domain is carried out by using Monte Carlo techniques The flow domain is divided into a set of square blocks A nearest-neighbor stochastic process model is used to generate a multilateral spatial dependence between hydraulic conductivity values in the block system Both statistically isotropic and statistically anisotropic autocorrelation functions are considered This model leads to a realistic representation of the spatial variations in hydraulic conductivity in a discrete block medium Results of the simulations provide estimates of the output distributions in hydraulic head The probability distribution for hydraulic head must be interpreted in terms of the spatial variation of the expected head gradients, the standard deviation in the hydraulic conductivity distribution, the ratio of the integral scales of the autocorrelation function for conductivity to the distance between boundaries on the flow domain, and the arrangement of statistically homogeneous units within the flow domain The standard deviation in hydraulic head increases with an increase in either the standard deviation in hydraulic conductivity or the strength of the correlation between neighboring conductivity values The standard deviations in hydraulic head are approximately halved when a uniform, bounded, two-dimensional flow field is reduced to one-dimensional form The uncertainties in the predicted hydraulic head values are strongly influenced by the presence of a spatial trend in the mean hydraulic conductivity In evaluating the concept of an effective conductivity for a heterogeneous medium, both the nature of the spatial heterogeneities in hydraulic conductivity and the flow system operating within the flow domain must be considered

Role of subsurface flow in generating surface runoff: 2. Upstream source areas

Abstract: Runoff simulation for rainfall events on hypothetical upstream source areas, carried out with a deterministic mathematical model that couples channel flow and saturated-unsaturated subsurface flow, provides theoretical support for the runoff-generating mechanisms observed in the field by Ragan and Dunne. The simulations show that there are stringent limitations on the occurrence of subsurface storm flow as a quantitatively significant runoff component. Only on convex hillslopes that feed deeply incised channels, and then only when saturated soil conductivities are very large, is subsurface storm flow a feasible mechanism. On concave slopes with lower permeabilities, and on all convex slopes, hydrographs are dominated by direct runoff through very short overland flow paths from precipitation on transient near-channel wetlands. On these wetlands surface saturation occurs from below because of rising water tables that are fed by vertical infiltration rather than by lateral subsurface flow. These conclusions, when coupled with field observations that show classic Hortonian overland flow to be a rare occurrence in vegetated humid environments, have implications in the planning of field instrumentation networks, and in the designing of hydrologic response models.

Study and Interpretation of the Chemical Characteristics of Natural Water

Abstract: The chemical composition of natural water is derived from many different sources of solutes, including gases and aerosols from the atmosphere, weathering and erosion of rocks and soil, solution or precipitation reactions occurring below the land surface, and cultural effects resulting from human activities. Broad interrelationships among these processes and their effects can be discerned by application of principles of chemical thermodynamics. Some of the processes of solution or precipitation of minerals can be closely evaluated by means of principles of chemical equilibrium, including the law of mass action and the Nernst equation. Other processes are irreversible and require consideration of reaction mechanisms and rates. The chemical composition of the crustal rocks of the Earth and the composition of the ocean and the atmosphere are significant in evaluating sources of solutes in natural freshwater. The ways in which solutes are taken up or precipitated and the amounts present in solution are influenced by many environmental factors, especially climate, structure and position of rock strata, and biochemical effects associated with life cycles of plants and animals, both microscopic and macroscopic. Taken together and in application with the further influence of the general circulation of all water in the hydrologic cycle, the chemical principles and environmental factors form a basis for the developing science of natural-water chemistry. Fundamental data used in the determination of water quality are obtained by the chemical analysis of water samples in the laboratory or onsite sensing of chemical properties in the field. Sampling is complicated by changes in the composition of moving water and by the effects of particulate suspended material. Some constituents are unstable and require onsite determination or sample preservation. Most of the constituents determined are reported in gravimetric units, usually milligrams per liter or milliequivalents

A physically based, variable contributing area model of basin hydrology

Abstract: A hydrological forecasting model is presented that attempts to combine the important distributed effects of channel network topology and dynamic contributing areas with the advantages of simple lumped parameter basin models. Quick response flow is predicted from a storage/contributing area relationship derived analytically from the topographic structure of a unit within a basin. Average soil water response is represented by a constant leakage infiltration store and an exponential subsurface water store. A simple non-linear routing procedure related to the link frequency distribution of the channel network completes the model and allows distinct basin sub-units, such as headwater and sideslope areas to be modelled separately. The model parameters are physically based in the sense that they may be determined directly by measurement and the model may be used at ungauged sites. Procedures for applying the model and tests with data from the Crimple Beck basin are described. Using only measured and estimated parameter values, without optimization, the model makes satisfactory predictions of basin response. The modular form of the model structure should allow application over a range of small and medium sized basins while retaining the possibility of including more complex model components when suitable data are available.

A physically based, variable contributing area model of basin hydrology / Un modèle à base physique de zone d'appel variable de l'hydrologie du bassin versant

Abstract: A hydrological forecasting model is presented that attempts to combine the important distributed effects of channel network topology and dynamic contributing areas with the advantages of simple lum...

Macropores and water flow in soils

Abstract: This paper reviews the importance of large continuous openings (macropores) on water flow in soils. The presence of macropores may lead to spatial concentrations of water flow through unsaturated soil that will not be described well by a Darcy approach to flow through porous media. This has important implications for the rapid movement of solutes and pollutants through soils. Difficulties in defining what constitutes a macropore and the limitations of current nomenclature are reviewed. The influence of macropores on infiltration and subsurface storm flow is discussed on the basis of both experimental evidence and theoretical studies. The limitations of models that treat macropores and matrix porosity as separate flow domains is stressed. Little-understood areas are discussed as promising lines for future research. In particular, there is a need for a coherent theory of flow through structured soils that would make the macropore domain concept redundant.