bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical study of the hydromechanical behavior of two rough fracture surfaces in contact
Authors: Unger A. J. A. , Mase C. W.
Published: February 2004

Flow in fractures is traditionally modeled by characterizing the aperture distribution with some deterministic function or set of stochastic parameters. Other models generate the aperture distribution by the closure of two stochastic surfaces. The objective of this research is to develop a model where the aperture distribution is determined during the closure of two random elastic surfaces with complete hydromechanical interaction. Because stress and strain conditions required to generate a given aperture distribution are calculated during closure, the model is used to couple the mechanical and hydraulic characteristics of the fracture. Stochastic realizations of clay fracture surfaces are generated by measuring one‐dimensional profiles of a fracture surface. Next, the spectral representation of the profile is related to the fractal dimension of the fracture. Using the fractal dimension determined from one‐dimensional clay profiles, an equivalent two‐dimensional fractal surface is generated. Conceptually, each surface consists of linear elastic rectangular asperities resting upon a linear elastic half‐space. During closure, asperities that come into contact deform and punch into the half space creating mechanical interaction between all the asperities on the grid. Once we determine the aperture distribution at an applied stress level, a hydraulic gradient is applied across the fracture and fluid flow is determined. Nodal pressures created by flow deform the aperture distribution coupling hydraulic to mechanical behavior. Stress versus relative closure results indicate that stress increases nonlinearly with relative closure. Fluid pressures in the aperture distribution exert a significant influence on the mechanical characteristics of a fracture. Fluid discharge through the fracture decreases exponentially with an increase in relative closure. Flow calculated in the rough walled aperture distribution deviates increasingly from the parallel plate model with the geometric mean aperture as the percent contact area increases. The deviation results from an increase in tortuosity and channelling of the flow field in the aperture distribution. We can use this model to develop stress and flow versus relative closure constitutive relationships for a single fracture as a function of fracture surface geometry.
A stochastic model of dimensionless hyetograph
Authors: Garcia‐Guzman A. , Aranda‐Oliver E.
Published: February 2004

A very simple statistical model is proposed to describe the time distribution of rainfall within a rainy event. The modeled process is the dimensionless hyetograph H(tj) that represents the fraction of rainfall accumulated over the time interval (0, tj), where tj is a fraction of the total duration. In any rainy episode lasting n+1 units of time, the sequence H(t1), …, H(tn) is described as an ordered sample from the beta distribution. Dimensionless rainfall from hourly data at three stations in Southern Spain show little dependence on rainfall duration, amount of precipitation, or period of the year. These results, though not essential to the model structure, simplify its formulation, reducing the number of parameters. Other features of the historical records, such as correlations, maximum dimensionless hourly precipitation, or frequency curves, are reasonably well reproduced by the model.
Development of split‐operator, Petrov‐Galerkin Methods to simulate transport and diffusion problems
Authors: Miller Cass T. , Rabideau Alan J.
Published: February 2004

The rate at which contaminants in groundwater undergo sorption and desorption is routinely described using diffusion models. Such approaches, when incorporated into transport models, lead to large systems of coupled equations, often nonlinear. This has restricted applications of coupled transport and diffusion models to one‐dimensional systems. Further, numerical difficulties inherent in many common solution formulations to coupled transport and diffusion problems result in inaccurate and unreliable solutions to problems of common interest. The objective of this work was to develop methods that provide accurate and robust solutions to coupled transport and diffusion problems for single and multicomponent solute systems in both one and two spatial dimensions. Problems involving pore, surface, and combined pore and surface diffusion into spherical particles are considered. A split‐operator formulation is proposed in which the reaction operator is separated from the transport operator and solved independently. Models derived from such split‐operator formulations to selected coupled transport and diffusion problems are shown to be robust, accurate, and computationally efficient. The developed split‐operator approaches are also amenable to solution using parallel, or for some problems massively parallel, processing methods.
On the use of digital elevation model data for Hortonian and fractal analyses of channel networks
Authors: Helmlinger Keith R. , Kumar Praveen , Foufoula‐Georgiou Efi
Published: February 2004

A common method of channel network extraction from digital elevation model (DEM) data is based on specification of a threshold area Ath, that is, the minimum support area required to drain to a point for a channel to form. Current efforts to predict Ath from DEM data are inconclusive, and usually an arbitrary constant Ath value is chosen for channel network extraction. In this paper, we study the effects of threshold area selection on the morphometric properties (such as drainage density, length of drainage paths, and external and internal links) and scaling properties (such as Horton's laws and fractal dimension) of a channel network. We also study the related problem of DEM data resolution and its effect on estimation of scaling properties. The results indicate that morphometric properties vary considerably with Ath, and thus values reported without their associated Ath are meaningless and should be used in hydrologic analysis with caution. Also, the “completeness” of a channel network (in terms of having the outlet stream flowing directly into a higher‐order stream) is found to depend on Ath in a random unpredictable way. Even if only the complete channel networks are used in the analysis, the statistical variability of scaling properties estimates due to Ath selection is significant and can be of comparable size to the variability due to DEM resolution and variability between estimates of different river networks. Our analysis highlights the need to carefully study the problem of network source representation or channel initiation scale from DEMs which will point to an appropriate Ath for channel network extraction and estimation of morphometric properties.
Analysis of uncertainty in optimal groundwater contaminant capture design
Authors: Tiedeman Claire , Gorelick Steven M.
Published: February 2004

A three‐dimensional groundwater management model is developed for a shallow, unconfined sandy aquifer at a Superfund site at which a vinyl chloride plume is migrating toward Lake Michigan. We use nonlinear simulation‐regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants. Parameter uncertainty is translated into flow model prediction uncertainty using a first‐order Taylor series approximation. Optimal minimum‐pumping strategies for steady state hydraulic containment of the plume are designed, and model prediction uncertainty is accounted for with stochastic programming. It is impossible to achieve a reliability level higher than 60% using only two pumping wells. For the 10‐well case, pumping rates must increase about 40% to extend reliability from 50 to 90%. Monte Carlo analyses indicate that for the 10‐well 90% reliability formulation, the first‐order method of propagating uncertainty results in a solution with accurate performance reliabilities. We find that the coefficient of variation in hydraulic gradient dictates whether the probabilistic constraints are obeyed. Comparison of the probabilistic constraint and “safety factor” approaches to overcoming model uncertainty reveals that the ability of probabilistic constraints to accommodate local variations in model prediction uncertainty is highly important. Postoptimization solute transport studies show that increased reliability levels for hydraulic containment do not necessarily translate into faster plume cleanup times.
The worth of data in predicting aquitard continuity in hydrogeological design
Authors: James Bruce R. , Freeze R. Allan
Published: February 2004

A Bayesian decision framework is developed for addressing questions of hydrogeological data worth associated with engineering design at sites in heterogeneous geological environments. The specific case investigated is one of remedial contaminant containment in an aquifer underlain by an aquitard of uncertain continuity. The framework is used to evaluate the worth of hard and soft data in investigating the aquitard's continuity. The analysis consists of four modules: (1) an aquitard realization generator based on indicator kriging, (2) a procedure for the Bayesian updating of the uncertainty with respect to aquitard windows, (3) a Monte Carlo simulation model for advective contaminant transport, and (4) an economic decision model. A sensitivity analysis for a generic design example involving a design decision between a no‐action alternative and a containment alternative indicates that the data worth of a single borehole providing a hard point datum was more sensitive to economic parameters than to hydrogeological or geostatistical parameters. For this case, data worth is very sensitive to the projected cost of containment, the discount rate, and the estimated cost of failure. When it comes to hydrogeological parameters, such as the representative hydraulic conductivity of the aquitard or underlying aquifer, the sensitivity analysis indicates that it is more important to know whether the field value is above or below some threshold value than it is to know its actual numerical value. A good conceptual understanding of the site geology is important in estimating prior uncertainties. The framework was applied in a retrospective fashion to the design of a remediation program for soil contaminated by radioactive waste disposal at the Savannah River site in South Carolina. The cost‐effectiveness of different patterns of boreholes was studied. A contour map is presented for the net expected value of sample information (EVSI) for a single borehole. The net EVSI of patterns of precise point measurements is also compared to that of an imprecise seismic survey.
A multicomponent decomposition of spatial rainfall fields: 1. Segregation of large‐ and small‐scale features using wavelet transforms
Authors: Kumar Praveen , Foufoula‐Georgiou Efi
Published: February 2004

Issues of scaling characteristics in spatial rainfall have attracted increasing attention over the last decade. Several methods based on simple and multiscaling and multifractal ideas have been proposed and parameter estimation techniques developed for the hypothesized models. Simulations based on these models have realistic resemblance to “generic rainfall fields.” In this research we analyze rainfall data for scaling characteristics without an a priori assumed model. We look at the behavior of rainfall fluctuations obtained at several scales, via orthogonal wavelet transform of the data, to infer the precise nature of scaling exhibited by spatial rainfall. The essential idea behind the analysis is to segregate large‐scale (long wavelength) features from small‐scale features and study each of them independently. The hypothesis is set forward that rainfall might exhibit scaling in small‐scale fluctuations, if at all, and at large scale this behavior will break down to accommodate the effects of external factors affecting the particular rain‐producing mechanism. The validity of this hypothesis is examined. In the first of these papers we develop the methodology for the segregation of large‐ and small‐scale features and apply it to a severe spring time midlatitude squall line storm. The second paper (Kumar and Foufoula‐Georgiou, this issue) develops a framework for testing the presence and studying the nature of self‐similarity in the fluctuations.
A multicomponent decomposition of spatial rainfall fields: 2. Self‐similarity in fluctuations
Authors: Kumar Praveen , Foufoula‐Georgiou Efi
Published: February 2004

In the first paper (Kumar and Foufoula‐Georgiou, this issue) we developed a methodology for the segregation of large‐ and small‐scale features (fluctuations) of spatial rainfall fields. In this paper we develop a framework for testing the presence and studying the nature of self‐similarity in the fluctuations. It is found that rainfall fluctuations may be approximated by stable distributions and show scaling up to a certain scale. We define and estimate parameters that characterize the scaling and spatial dependence of the rainfall fluctuations and we use these parameters, estimated for several radar rainfall frames (in time), to relate to and identify the evolutionary nature of rainfall. Two radar depicted rainfall fields have been extensively analyzed: a severe spring time midlatitude squall line storm and a mild midlatitude winter type storm. The type of scaling in rainfall fluctuations shows significant variation from one rainfall field to another.
Conceptual‐stochastic modeling of seasonal runoff using autoregressive moving average models and different scales of aggregation
Authors: Claps Pierluigi , Rossi Fabio , Vitale Cosimo
Published: February 2004

The statistical and phenomenological aspects of the runoff process observed on different scales of aggregation are taken as a priori information for the conceptually based stochastic modeling of seasonal runoff. Runoff is considered as the sum of two groundwater components, with over‐year and subannual response lag, and of a purely random component representing the direct runoff. This scheme is equivalent to a linear system, with two parallel linear reservoirs plus a zero lag linear channel. The system output is the runoff, and the input is the effective rainfall, considered proportional to the direct runoff. Assuming the effective rainfall as a non‐Gaussian periodic independent process and considering nonseasonal groundwater parameters, this conceptualization leads to an autoregressive and moving average (2, 2) stochastic process with periodic independent residual. Stochastic model parameters are directly related to the linear system coefficients, and the effective rainfall structure can be determined from the estimated model residual. In order to obtain parameter estimates consistent with the conceptual constraints, two estimation stages, on an annual and a seasonal basis, and an iterative procedure are needed. The model was applied to a number of time series of monthly streamflows in the Apennine regions of Italy with promising results.
Effects of an index of atmospheric circulation on stochastic properties of precipitation
Authors: Katz Richard W. , Parlange Marc B.
Published: February 2004

Conditional chain‐dependent processes are fit to time series of daily precipitation amounts given an index of large‐scale atmospheric circulation (i.e., either below or above normal monthly mean sea level pressure). Precipitation data for January at several locations in California are analyzed. The two conditional daily models differ both in terms of the parameters of the occurrence process and of the intensity process. Each of these daily effects contributes to changes in the distribution of monthly total precipitation associated with the circulation index. The process induced by combining the conditional daily models produces a variance for monthly total precipitation much closer to the observed value than that for the corresponding unconditional chain‐dependent model.
Simulation of field measurement of hydraulic conductivity in unsaturated heterogeneous soil
Authors: Tseng Peng‐Hsiang , Jury William A.
Published: February 2004

In this study, the procedures used in common methods for field measurement of unsaturated hydraulic conductivity in heterogeneous soil were simulated through numerical experiments. It was assumed that the heterogeneity of the field soil can be described by a scaling factor δ which is treated as a lognormally distributed, second‐order stationary random variable in space. After the hypothetical random field was generated using property variability and correlation length scales typical of those observed in field measurements, it was used to test various field measurement methods currently in practice. One detailed and three simplified unsteady drainage flux methods were used to estimate the hydraulic conductivity under plausible field measurement conditions. In addition, the soil water retention data were used to predict hydraulic conductivity from a pore‐size distribution model. It was found that even under the assumption that there were no reading or instrument errors, other sources of errors can still be created due to the limitations of the observation techniques. These error sources include limited number of readings in space and time, separation distances between the readings of water content and pressure head, and volume‐averaged readings rather than point estimates with common instrumentation. Under the conditions studied in the simulations, the detailed method of estimation produced reasonable estimates of hydraulic conductivity, but only when very dense measurements of water content and matric potential were used in the estimation. None of the approximate methods yielded accurate measurements of the true hydraulic conductivity of the field region measured.
Application of a land class hydrological model to climatic change
Authors: Kite G. W.
Published: February 2004

Many climatologists predict major changes in the earth's climate due to an expected doubling of atmospheric greenhouse gases. Global circulation models have been used to derive alternate climate scenarios under such conditions and the effects on water resources have been estimated with hydrological models. The hydrological models have generally assumed that the watershed itself wouid remain unchanged. However, it is more likely that a changing climate would alter the distribution and the transpiration efficiency of vegetation types within a watershed. A new hydrological model in which the parameters are based on land use class (effectively, vegetation type) was calibrated and verified for a watershed in the Rocky Mountains of British Columbia. The changes in land use associated with a doubled carbon dioxide scenario were estimated, and the model was rerun incorporating the changed climate and the changed land use. Details of the effects of this scenario on the hydrology of the watershed are given, but it is emphasized that the purpose of the paper is to develop the methodology and not to endorse any particular scenario of climatic change.
Dissolution and biorestoration of nonaqueous phase hydrocarbons: Model development and laboratory evaluation
Authors: Malone Donald R. , Kao Chih‐Ming , Borden Robert C.
Published: February 2004

A one‐dimensional numerical model is presented for simulating the enhanced biorestoration of aquifer material contaminated with residual nonaqueous phase liquid (NAPL) hydrocarbon. The model simulates the simultaneous dissolution, transport, and biodegradation of individual hydrocarbons under oxygen‐limiting conditions. Partitioning between the NAPL and aqueous phase is modeled as a linear first‐order process where the NAPL is composed of two fractions, a fast oil fraction with a high mass transfer rate and a slow oil fraction with a much lower mass transfer rate. Microorganisms are assumed to be present attached to the soil grains and are assumed to be immobile. Biodegradation of the problem compounds is simulated as a multistep process where the parent compounds are first biotransformed to oxygenated intermediates. These intermediates may then be mineralized to CO2 and H2O. Comparison of model simulations with experimental results from soil columns containing residual hydrocarbon and an active microbial population indicate that the model is capable of simulating the extent of hydrocarbon biodegradation using reasonable model parameters. Model simulations indicate that if benzene, toluene, and xylene are assumed to be completely mineralized, the model will greatly underestimate the extent of biotransformation. The model overestimated the extent of hydrocarbon biotransformation at low substrate concentrations.
Rain‐induced water percolation in snow as detected using heat flux transducers
Authors: Sturm Matthew , Holmgren Jonathan
Published: February 2004

The percolation of water through snow is shown to be detectable with heat flux transducers (HFTs) at the base of, or embedded within, the snow. Theory indicates that the arrival of water at a HFT will result in a rapid drop in heat flow to negative values, followed by an exponential rise. Laboratory and field tests verify that the theory correctly predicts the form of the signal, and consideration of conditions in a snow cover suggest that it is unlikely the signal can be generated in any other way. Large (15×15 cm) HFTs were installed at the snow/ground interface at three locations in Alaska where rain on snow is common. During three winters, heat flux signals indicative of water percolating to the base of the snow were detected 23 times, often simultaneously at two or more sites. All signals were coincident with rain‐on‐snow events, though not all rain‐on‐snow events (there were a total of 27) were associated with distinctive heat flux signals. Signals were observed only when rainfall rates exceeded 1.5 cm d−1, and the character of the signal differed if the snow/ground interface was at or lower than 0°C. Observed delays between the start of rain and the arrival of water at the base of the snow ranged between 2 and 40 hours. A geometric analysis was used to calculate the spacing of percolation fingers or columns necessary to produce the observed number of times that water percolated onto the HFTs. The number of times there were abrupt changes in the temperature of thermistors installed in the snow adjacent to the HFTs was used in a similar manner. Results from both analyses suggest percolation columns with a mean spacing of about 25 cm, which is consistent with observations of these features in snow trenches.
The significance of biofilms in porous media
Authors: Rittmann Bruce E.
Published: February 2004

The recent literature contains conflicting claims about the characteristics of attached bacteria in subsurface porous media and how these characteristics affect permeability reduction. Some claim that the bacteria form continuous biofilms that restrict the pore size, while others claim that bacteria are attached in patchy aggregates that accumulate in pore throats. This contribution applies a recently developed tool from biofilm kinetics, the normalized surface loading, to interpret a wide range of experimental data from porous media experiments and biological filtration. The normalized surface loading is the actual substrate flux (i.e., rate of removal per unit surface area) divided by the minimum flux capable of supporting a deep biofilm. The analyses show that biofilms are continuous for normalized surface loadings greater than 1.0, but appear to become discontinuous for values less than about 0.25. For the low‐load situation, distinguishing between continuous and discontinuous biofilms is not important when the modeling goal is prediction of substrate removal. However, the distinction is more critical when the modeling goal is to describe the spatial distribution of attached biomass and permeability loss.
An inverse technique for developing models for fluid flow in fracture systems using simulated annealing
Authors: Mauldon Amy Davey , Karasaki Kenzi , Martel Stephen J. , Long Jane C. S. , Landsfeld Martin , Mensch Antoine , Vomvoris Stratis
Published: February 2004

One of the characteristics of flow and transport in fractured rock is that the flow may be largely confined to a poorly connected network of fractures. In order to represent this condition, Lawrence Berkeley Laboratory has been developing a new type of fracture hydrology model called an “equivalent discontinuum” model. In this model we represent the discontinuous nature of the problem through flow on a partially filled lattice. This is done through a statistical inverse technique called “simulated annealing.” The fracture network model is “annealed” by continually modifying a base model, or “template,” so that with each modification, the model behaves more and more like the observed system. This template is constructed using geological and geophysical data to identify the regions that possibly conduct fluid and the probable orientations of channels that conduct fluid. In order to see how the simulated annealing algorithm works, we have developed a synthetic case. In this case, the geometry of the fracture network is completely known, so that the results of annealing to steady state data can be evaluated absolutely. We also analyze field data from the Migration Experiment at the Grimsel Rock Laboratory in Switzerland.
Sensitivity of the thermal stratification model eddy diffusion dimension 1 using a factorial experimental design
Authors: Henderson‐Sellers B.
Published: February 2004

Engineering use of ecological models requires, as a precondition, appropriate validation and sensitivity testing. Using one such well‐validated thermal stratification model, the application of an industrial statistical technique for multifactor sensitivity testing is described. This method, of fractional factorial numerical experimentation, permits identification of important model parameters (here wind speed and internal mixing mechanisms), as well as potential interactions between two or more factors.
Evaluation of the Energy Budget Method of determining evaporation at Williams Lake, Minnesota, using alternative instrumentation and study approaches
Authors: Rosenberry D. O. , Sturrock A. M. , Winter T. C.
Published: February 2004

Best estimates of evaporation at Williams Lake, north central Minnesota, were determined by the energy budget method using optimum sensors and optimum placement of sensors. These best estimates are compared with estimates derived from using substitute data to determine the effect of using less accurate sensors, simpler methods, or remotely measured data. Calculations were made for approximately biweekly periods during five open water seasons. For most of the data substitutions that affected the Bowen ratio, new values of evaporation differed little from best estimates. The three data substitution methods that caused the largest deviations from the best evaporation estimates were (1) using changes in the daily average surface water temperature as an indicator of the lake heat storage term, (2) using shortwave radiation, air temperature, and atmospheric vapor pressure data from a site 110 km away, and (3) using an analog surface water temperature probe. Recalculations based on these data substitutions resulted in differences from the best estimates as much as 89%, 21%, and 10%, respectively. The data substitution method that provided evaporation values that most closely matched the best estimates was measurement of the lake heat storage term at one location in the lake, rather than at 16 locations. Evaporation values resulting from this substitution method usually were within 2% of the best estimates.
U.S. streamflow patterns in relation to the El Niño/Southern Oscillation
Authors: Kahya Ercan , Dracup John A.
Published: February 2004

The relationship between the El Niño/Southern Oscillation (ENSO) and unimpaired streamflow over the contiguous United States is studied. The extreme phases of the Southern Oscillation have been linked to fairly persistent classes of atmospheric anomalies over the low and middle latitudes at regional and global scales. Of particular interest in this investigation is the identification of regions of land that appear to have strong and consistent ENSO‐related streamflow signals. The first harmonic extracted from a 24‐month ENSO composite at each station is assumed to be the ENSO‐related signal appearing in streamflow anomalies. These regions were identified by the similarity in phase of the harmonic vectors. The vectorial display of these harmonics over a map of the United States provides the areal extents of ENSO influence on streamflow. Coherent and significant streamflow responses to hypothesized ENSO forcing are found in four regions of the United States: the Gulf of Mexico, the Northeast, the North Central, and the Pacific Northwest. Once an ENSO event sets in, a long‐range forecasting utility may be available for these regions. The results of this analysis, which are consistent with previous studies on precipitation and temperature, demonstrate the mid‐latitude hydrologic response to the tropical ENSO phenomena.
Unit graph estimation and stabilization using quadratic programming and difference norms
Authors: Dietrich C. R. , Chapman T. G.
Published: February 2004

For a rainfall‐runoff event, quadratic programming is particularly suited to the estimation of unit graph as linear and positivity constraints on unit graph ordinates can be naturally implemented. In this paper, the quadratic programming framework is invoked in a novel way to stabilize the unit graph estimation procedure via the use of difference norms. The advantage of the latter over standard ridge regression is that penalties are placed on oscillations of the unit graph rather than on the size of its ordinates, Application of the methodology to real rainfall‐runoff data is provided and comparisons with existing approaches are made. The latter indicate that our approach generally yields unit graph estimates of more realistic shape and smaller variance resulting in a better fit to the runoff data.
Modeling of streamflow processes at different time scales
Authors: Bartolini Paolo , Salas Jose D.
Published: February 2004

The analysis and modeling of streamflow processes has attracted the attention of water resources specialists for several decades. A number of models have been suggested in the past for representing seasonal and annual streamflow processes. The topic addressed in this paper centers around the compatibility of stochastic models of streamflow at different time scales. More specifically, given a model for monthly flows, the models for the processes obtained by aggregation, i.e., models for bimonthly, quarterly, etc., time scales, are derived. Likewise, parameter space and covariance properties of such derived processes as well as the relationship of such properties of different time scales are given. These concepts are applied to modeling streamflow of the Niger River. The developments are restricted to the family of periodic autoregressive moving average (PARMA) processes. For instance, it was found that monthly flows based on the PARMA(2, 1) process leads to PARMA(2, 2) bimonthly flows and stationary ARMA(2, 2) annual flows. Furthermore, applications to modeling the Niger River flows suggest that one can reproduce the seasonal and annual second‐order statistics without using disaggregation if PARMA models are used for modeling the seasonal flows.
Multilayered leaky aquifer systems: 2. Boundary element solutions
Authors: Cheng A. H.‐D. , Morohunfola O. K.
Published: February 2004

The boundary element algorithm for the multilayered leaky aquifer system of Neuman‐Witherspoon and Herrera is presented. By applying the Laplace transform to the integrodifferential equations of Herrera, a set of coupled two‐dimensional elliptic equations results. The boundary integral representation is derived from Green's theorem. Green's functions governed by an adjoint system of the original governing equations are found from the pumping well solutions given in part 1 by a coefficient exchange. The resultant numerical system requires a discretization only at the boundaries of the planar aquifers and is free from aquitard unknowns. Several numerical examples, including one‐dimensional flow, pumping well problems, and two‐dimensional problems are provided for the purpose of validation and demonstration.
Flume simulation of recirculating flow and sedimentation
Authors: Schmidt John C. , Rubin David M. , Ikeda Hiroshi
Published: February 2004

Experiments were conducted in a 4‐m‐wide flume to simulate recirculating flow and sedimentation in a lateral eddy within a channel expansion. The percentage of main stem sediment that was captured by the eddy decreased from 37% (when the eddy was empty) to 24% (when sand filled approximately 32% of the eddy volume). The reattachment bar within the eddy grew in an upstream direction, and the finest size sediment was deposited in the lee of the obstruction; both observations are consistent with field observations. Measurements of reattachment length during sediment transport (0.5–1.0 kg/s) at constant discharge (0.60 m3/s) show that reattachment length depends not only on characteristics of the expanding jet, but also on the topography of the channel bed downstream; reattachment length decreased when part of the channel expansion was filled by an aggrading midchannel bar. Comparison of these results with measurements in the Colorado River in Grand Canyon suggests that downstream channel irregularities play a large role in controlling the length of eddies in natural rivers.
Relation between grain velocity and sediment concentration in overland flow
Authors: Abrahams Athol D. , Atkinson Joseph F.
Published: February 2004

Previous flume studies of the velocity of saltating grains have almost all measured single grains traveling in otherwise clear water. However, such measurements disregard the likelihood that grain velocities are affected by the presence of other grains. In this laboratory study of overland flow we show that grain velocity is negatively related to sediment concentration. This negative relation is attributed to two mechanisms. The first mechanism is a decrease in water velocity as sediment concentration increases. Water velocity decreases because an increasing proportion of potential energy is dissipated in transporting sediment rather than being converted to kinetic energy. The second mechanism is an increase in the dispersion of the normal component of grain momentum as grain collisions increase with sediment concentration. The dispersive stress so created opposes bed load movement and causes grain velocity to decrease. Multiple regression analyses reveal relations in the experimental data that are consistent with these two mechanisms.
Heterogeneity of unsaturated, gravitational flow of water through beds of large particles
Authors: Dexter A. R.
Published: February 2004

Water was applied uniformly as a fine spray onto the surface of beds of nonabsorbing particles. The outflow at the base of the bed was collected separately from 74 equal, small collecting areas. The spatial heterogeneity of the outflow was determined as a function of bed height, particle diameter, and the size of the collection areas. The results show that spatial heterogeneity develops with increasing bed depth and decreases with increasing area of the collectors. Particle diameter has only a small effect on flow heterogeneity. It is hypothesized that spatial heterogeneity develops because individual flow pathways, or rivulets, take a “random walk” downward through the particles in the bed. When two flows meet by chance, they combine and stay combined. In this way, the number of rivulets per unit cross‐sectional area of bed decreases with increasing depth, and the spatial flow heterogeneity increases. It is proposed that this process may occur in the tilled layer of soil.
Economic and environmental impacts of water quality protection policies: 1. Framework for regional analysis
Authors: Bernardo D. J. , Mapp H. P. , Sabbagh G. J. , Geleta S. , Watkins K. B. , Elliott R. L. , Stone J. F.
Published: February 2004

Agricultural production systems provide some unique challenges for assessing the regional impacts of water quality protection policies. A modeling framework is proposed for assessing the environmental and economic consequences of groundwater quality protection policies at the regional level. The model consists of three components: (1) a crop simulation/chemical transport model, (2) a regional economic optimization model, and (3) an aquifer groundwater flow model. The three submodels are linked and run recursively to simulate producer response to alternative water quality policies over a multiple‐year time horizon. Model solutions provide projections of production practices employed on various resource situations across the region. Economic evaluation of alternative policies may be based upon regional agricultural income, crop production levels, input use, and changes in aquifer water levels over time. Measures of agricultural nonpoint source pollution provided by the model include nitrate, phosphorus and pesticide loadings in deep percolation and runoff water, as well as sediment losses.
A model for the development of marginal water sources in arid zones: The case of the Negev Desert, Israel
Authors: Brimberg Jack , Oron Gideon , Mehrez Abraham
Published: February 2004

A management model is presented for the optimal development of marginal water sources in arid zones in conjunction with minimizing the dependence on high‐quality water. These marginal sources, which may include among others saline groundwater, treated wastewater, and runoff water, are required to augment a limited supply from regional sources. The objective is to minimize operational and capital costs while simultaneously allocating a conventional regional supply in a best way among a set of local sites. A novel aspect is the consideration of water quality as an additional constraint in the decision model. In this way an optimal investment strategy for marginal water source development and use is obtained while satisfying quality requirements at the individual sites. The model formulated takes the form of a mixed binary integer linear problem. The main purpose of the presented model is to delineate a methodology for marginal water considerations and development in arid zones. Water qualities, supply and demand for diverse uses, and related costs are of primary importance. Several simplifying assumptions are made, such as aggregation on an annual basis, in order to cope with the essential features of the problem at a reasonable level of complexity. These assumptions may be relaxed at a later, more detailed stage of analysis. A case study of the Negev Desert in southern Israel is shown. An important conclusion is that saline groundwater production at local demand sites should be increased dramatically. The usefulness of sensitivity analysis in the decision process is also demonstrated.
Nonlinear weighted feedback control of groundwater remediation under uncertainty
Authors: Whiffen Gregory J. , Shoemaker Christine A.
Published: February 2004

Differential dynamic programming is used to compute optimal time‐varying pumping policies for a pump and treat strategy for groundwater remediation. The feedback law generated by a constrained differential dynamic programming algorithm with penalty functions is used as the basis of feedback laws tested in cases where there is uncertainty in the hydraulic conductivity. Confined transient aquifer flow and transport are modeled using a two‐dimensional Galerkin finite element scheme with implicit time differencing. Optimal policies are calculated using a given or “measured” set of hydraulic conductivities and initial conditions. The optimal policies (with and without feedback) are applied using the same finite element model with a second or “true” set of conductivities. The “true” sets of conductivities are generated randomly from an autocorrelated lognormal distribution by the spectral method. The approach used here has an advantage over other uncertainty approaches because it is not necessary to specify precisely which parameters are considered uncertain and which are certain. Also no single probability distribution need be assumed for each uncertain parameter. By adjusting the relative weight assigned each penalty function, robust feedback laws were obtained that perform equally well under nine different assumed error distributions. In our examples, well‐designed feedback policies cost between 4% and 51% less than the cost of applying the calculated optimal policies without using a feedback law.
The Courant and Peclet Number criteria for the numerical solution of the Richards Equation
Authors: El‐Kadi Aly I. , Ling Ge
Published: February 2004

Recent studies indicate that inaccuracies exist in the numerical solutions of the Richards equation. A need exists to examine such inaccuracies and to correlate them, formally, to the soil hydraulic properties and the size of the spatial and temporal mesh. In the absence of criteria for mesh design, mass conservation and the rate of convergence are usually used as bases for acceptance of the solution. It is well documented, however, that neither can guarantee an accurate solution. This paper proposes the Courant and Peclet numbers as criteria for estimating spatial and temporal increments. The study defines upper limits of these numbers for acceptable accuracy of the numerical solutions. For cases that are characterized by decreasing pressure head gradients, although the initial size of the time step may be extremely small, efficient solutions are possible through a careful choice of an expansion factor for such a step.
Mixed finite element simulation of saturated groundwater flow using a multigrid accelerated domain decomposition technique
Authors: Beckie Roger , Wood Eric F. , Aldama Alvaro A.
Published: February 2004

We present strategies to perform large‐scale simulation of saturated groundwater flow using mixed finite element methods. The greatest limitation of these methods is their memory requirements. To overcome the memory limitations of the mixed methods, we use a domain decomposition strategy. We also present a multigrid acceleration for the domain decomposition. For sufficiently small problems, the conventional mixed method is more computationally efficient than the domain decomposition approach. However, the domain decomposition method allows one to simulate larger problems than is possible with the conventional mixed method.
River network fractal geometry and its computer simulation
Authors: Nikora Vladimir I. , Sapozhnikov Victor B.
Published: February 2004

The hierarchical ordinal and statistical models of river networks are proposed. Their investigation has been carried out on the basis of river networks computer simulation as well as on empirical data analysis. The simulated river networks display self‐similar behavior on small scales (the fractal dimension D ≈ 1.52 and Hurst's exponent H = 1.0) and self‐affine behavior on large scales (the lacunary dimension DG ≈ 1.71, H ≈ 0.58). Similar behavior is also qualitatively characteristic for natural river networks (for catchment areas from 142 to 63,700 km2 we obtained DG ≈ 1.87 and H ≈ 0.73). Thus in both cases one finds a region of scales with self‐affine behavior (H < 1) and with DG < 2. Proceeding from fractal properties of the river networks, the theoretical basis of scaling relationships L ∼ Aβ and ℒ ∼ Aε, widely used in hydrology, are given (L, ℒ and A denote the main river length, the total length of the river network, and catchment area, respectively); β = 1/(1+H) and ε=DG/2.
A validation of the 3H/3He method for determining groundwater recharge
Authors: Solomon D. K. , Schiff S. L. , Poreda R. J. , Clarke W. B.
Published: February 2004

Tritium and He isotopes have been measured at a site where groundwater flow is nearly vertical for a travel time of 100 years and where recharge rates are spatially variable. Because the mid‐1960s 3H peak (arising from aboveground testing of thermonuclear devices) is well‐defined, the vertical groundwater velocity is known with unusual accuracy at this site. Utilizing 3H and its stable daughter 3He to determine groundwater ages, we compute a recharge rate of 0.16 m/yr, which agrees to within about 5% of the value based on the depth of the 3H peak (measured both in 1986 and 1991) and two‐dimensional modeling in an area of high recharge. Zero 3H/3He age occurs at a depth that is approximately equal to the average depth of the annual low water table, even though the capillary fringe extends to land surface during most of the year at the study site. In an area of low recharge (0.05 m/yr) where the 3H peak (and hence the vertical velocity) is also well‐defined, the 3H/3He results could not be used to compute recharge because samples were not collected sufficiently far above the 3H peak; however, modeling indicates that the 3H/3He age gradient near the water table is an accurate measure of vertical velocities in the low‐recharge area. Because 3H and 3He have different diffusion coefficients, and because the amount of mechanical mixing is different in the area of high recharge than in the low‐recharge area, we have separated the dispersive effects of mechanical mixing from molecular diffusion. We estimate a longitudinal dispersivity of 0.07 m and effective diffusion coefficients for 3H (3HHO) and 3He of 2.4×10−5 and 1.3×10−4 m2/day, respectively. Although the 3H/3He age gradient is an excellent indicator of vertical groundwater velocities above the mid‐1960s 3H peak, dispersive mixing and diffusive loss of 3He perturb the age gradient near and below the 3H peak.
Groundwater velocity in an unconfined aquifer with rectangular areal recharge
Authors: Zlotnik Vitaly , Ledder Glenn
Published: February 2004

Three‐dimensional solutions for the hydraulic head and velocity components for transient groundwater flow in an unconfined compressible aquifer of finite thickness with a rectangular areal recharge source are analyzed using a linearized mathematical model. The solution generalizes Dagan's (1967) results, which were obtained for an idealized aquifer of infinite thickness, and Hantush's (1967) results, which were derived using the Dupuit assumptions. Hydraulic head and velocity components are estimated by asymptotic methods for large times, which are most appropriate for contaminant transport problems. Numerical analysis of the solution demonstrates spatial features of the velocity components in general and a transient effect of upward flow in particular, similar to that found for circular sources (Zlotnik and Ledder, 1992). Obtained formulas show that applicability of the Dupuit assumption for computation of velocity components in an unconfined aquifer is limited to a far‐field zone given approximately by |x| > 1.5X, |y| > 1.5Y, where X and Y are the half width and half‐length, respectively, of the contaminant source.