Showing papers in "Water Resources Research in 1989"

Source areas, drainage density, and channel initiation

Abstract: An analysis of channel head locations provides insight into controls on drainage density, the response of landscapes to climatic change, and the delineation of source areas for channel network simulations. Channel heads and colluvial deposits were mapped in a roughly 2 km2 area near San Francisco, California, and, although channel heads are located within colluvial deposits in hollows, many such deposits do not support channel heads. Channel heads were classified as either gradual or abrupt. For either type of channel head, the channel reach immediately downslope may be contiguous with the channel network or may consist of a series of short discontinuous channel segments. The local valley slope at the channel head is inversely related to both source area and source-basin length as well as to the contributing area per unit contour length at the channel head. In contrast, valley slope does not vary with drainage area upslope of channel heads. Field observations and a similarity between predicted and observed area-slope relations suggest that the location of channel heads on steep slopes may be controlled by subsurface flow-induced instability of the colluvial fill. Preliminary field observations also suggest that abrupt channel heads on gentle slopes are controlled by seepage erosion, whereas gradual channel head locations appear to be governed by saturation overland flow. Consideration of the geometric relationship between source areas and the first-order drainages that contain them results in an inverse relation between mean source-basin length and drainage density.

An assessment of bed load sediment transport formulae for gravel bed rivers

Abstract: The performance is tested of 12 bed load sediment transport formulae developed for use in gravel bed channels. The formulae are applied in the manner intended by the original authors. To this end, the test data are restricted to ones obtained in approximately steady flow when the material in motion was similar to that present on the bed; that is, transport was not size selective. This represents the nearest approach to “equilibrium sediment transport” that can be realized with available data. Four sets of river data and three sets of flume data were chosen for the test, covering a range of eight orders of magnitude in unit bed load transport rate. The test data were not used in the development of the formulae. The analysis separates mean bias and local bias. No formula performs consistently well. Limitations of the test data, the constraints imposed by an operationally realistic test, and reasons based upon the physics of the transport phenomenon all may be adduced for this. To estimate the magnitude of transport with limited hydraulic information, stream power equations should be used because they provide the most straightforward scale correlation of the phenomenon. In particular, the approach of Bagnold deserves further study. When local hydraulic information is available, a formula should be selected that is sensitive to bed state or grain size distribution and, in this context, the formulae of Einstein, Parker, and Ackers-White-Day bear continued examination.

A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components

Abstract: Many hydrogeochemical models have appeared in recent years for simulating subsurface solute transport. The hydrological transport of solutes can be described by a set of linear partial differential equations, and the chemical equilibria are described by a set of nonlinear algebraic equations. Three approaches are currently used to formulate the problem: (1) the mixed differential and algebraic equation (DAE) approach, (2) the direct substitution approach (DSA), and (3) the sequential iteration approach (SIA). An extremely important consideration in any approach is the choice of primary dependent variables (PDVs). Six types of PDVs have been employed in the existing models: (1) concentrations of all species, (2) concentrations of all component species and precipitated species, (3) total analytical concentrations of aqueous components, (4) total dissolved concentrations of aqueous components, (5) concentrations of aqueous component species, and (6) hybrid concentrations. Because of many possible combinations of PDVs and approaches, many hydrogeochemical transport models for multicomponent systems have been developed. This paper critically evaluates and discusses these models. The discussion and evaluation are conducted in terms of (1) how severe can the constraints be that a model imposes on computer resources, (2) which equilibrium geochemical processes can a model include, and (3) how easily can a model be modified to deal with mixed kinetic and equilibrium reactions. The use of SIA models leads to the fewest constraints on computer resources in terms of central processing unit (CPU) memory and CPU time; both DAE and DSA models require excessive CPU memory and CPU time for realistic two- and three-dimensional problems. Only those models that use the first three types of PDVs can treat the full complement of equilibrium reactions simultaneously. DAE and SIA models can be modified with reasonable ease to handle mixed chemical kinetics and equilibria. DSA models require strenuous efforts to modify for treating mixed chemical kinetics and equilibria. Therefore SIA models using the third type of PDVs are recommended for their practicality and flexibility. DSA and DAE models should remain research tools for one-dimensional investigations.

Estimating constituent loads

Abstract: Several recent articles have called attention to the problem of retransformation bias, which can arise when log linear regression models are used to estimate sediment or other constituent loads. In some cases the bias can lead to underestimation of constituent loads by as much as 50%, and several procedures have been suggested for reducing or eliminating it. However, some of the procedures recommended for reducing the bias can actually increase it. This paper compares the bias and variance of three procedures that can be used with log linear regression models: the traditional rating curve estimator, a modified rating curve method, and a minimum variance unbiased estimator (MVUE). Analytical derivations of the bias and efficiency of all three estimators are presented. It is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates. However, other conditions exist where they have substantial bias and a large mean square error. These conditions commonly occur when sample sizes are small, or when loads are estimated during high-flow conditions. The MVUE, however, is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct. Since an efficient unbiased estimator is available, there seems to be no reason to employ biased estimators.

A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface

Abstract: Accurate estimates of the unsaturated hydraulic properties are needed for any quantitative description of multiphase flow in porous media. This paper presents a consistent set of parametric models for the isothermal, hysteretic unsaturated fluid phase content (retention) and hydraulic conductivity functions of typical two-phase systems like water and air, or water and hydrocarbons. The equations are obtained by combining expressions for the hysteretic fluid retention curves with the statistical pore size distribution model of Mualem (1976) which predicts the hydraulic conductivity from more easily measured fluid retention data. Hysteresis is described using the model of Scott et al. (1983). The existence of residual fluid saturations for both the wetting and non wetting fluids is justified. Theoretical and experimental considerations indicate a need to match predicted and observed hydraulic conductivities at fluid phase contents less than full saturation.

Improved field probes for soil water content and electrical conductivity measurement using time domain reflectometry

Abstract: Volumetric water content θ and soil electrical conductivity σ may be measured in situ using time domain reflectometry (TDR). The parallel-wire or two-wire transmission line TDR probes currently in field use suffer from unwanted noise and information loss due to impedance mismatch between the probe and the coaxial connecting cable. Here we describe symmetric, multiwire probes designed to minimize these problems and eliminate the need for a balancing transformer between probe and TDR device. Analysis of the electric field distributions around these new probes shows that they emulate a coaxial transmission line, and their measured characteristic probe impedances approach that of coaxial probes. Signals from the new probes permit more reliable and accurate θ and σ measurement and are superior to those of two-wire probes with balancing transformer. The enhanced signal clarity of the new probes extends to sample diameters of at least 0.2 m. We show that electrical conductivity determined with the new probes is identical to that found with a coaxial cell and substantially different from that measured by a two-wire probe. Our results indicate that values of σ, determined using the Giese-Tiemann thin sample approach and measured characteristic probe impedances of coaxial or multiwire probes, agree with values of σ measured using an ac bridge for both electrolyte solutions and soil samples to within ±10%, provided σ exceeds 10 mS m−1. Finally, we give an example of the use of multiplexed three-wire probes in following rainfall infiltration and redistribution during and after a simulated rainfall event in the field. Infiltrated quantities of water estimated from the TDR water content profiles agreed within ±10% with the amount applied.

Implementation of the three-dimensional turning bands random field generator

Abstract: Numerical techniques to generate replicates of spatially correlated random fields are often used to synthesize sets of highly variable physical quantities in stochastic models of naturally heterogeneous systems. Within the realm of hydrologic research, for example, such tools are widely used to develop hypothetical rainfall distributions, hydraulic conductivity fields, fracture set properties, and other surface or subsurface flow parameters. The turning bands method is one such algorithm which generates two- and three-dimensional fields by combining values found from a series of one-dimensional simulations along lines radiating outward from a coordinate origin. Previous work with two-dimensional algorithms indicates that radial lines evenly spaced about the unit circle lead to enhanced convergence properties. The same can be said for the three-dimensional models, but it is more difficult to choose an arbitrary number of evenly spaced lines about the unit sphere. The current investigation shows that the use of larger numbers of randomly oriented lines (100) can enhance the performance of the three-dimensional algorithm. This improved performance is needed to effectively simulate problems characterized by full three dimensionality and/or anisotropy in either Monte Carlo or single-realization applications. Use of a large number of lines will also reduce the presence of a distortion effect manifested as linelike patterns in the field. Increased computational costs can be reduced by employing a fast Fourier transform technique to generate the line processes.

Size‐selective entrainment of bed load in gravel bed streams

Abstract: Entrainment of mixed size gravel bed material was studied in nine reaches of three high-power streams in Scotland and Norway. Paired measurements of at-a-point shear stress (estimated from velocity profiles) and bed load transport (by hand-held sampler) were made. They extended to very high values (400 N m -2, 3.5 kg m-x s-x). Analyses of maximum bed load diameter, mean bed load diameter, transport rates of individual size fractions, and tracer pebble movements all show some dependence of threshold shear stress for entrainment on absolute particle size, despite strong relative size effects. Precise equal mobility of all sizes was approached in the data set with the highest shear stresses and transport rates. Size-selective transport in the streams studied is also indicated by clear downstream and downbar reductions in surface sediment size over distances too short for abrasion to be significant.

Sediment Transport and Resulting Deposition in Spawning Gravels, North Coastal California

Abstract: Incubating salmonid eggs in streambeds are often threatened by deposition of fine sediment within the gravel. To relate sedimentation of spawning gravel beds to sediment transport, infiltration of fine sediment (<2 mm in diameter) into clean gravel beds, bed material size distributions, scour-fill depths, and sediment transport during 10 storm flow events were measured in three streams of north coastal California. Although suspended sediment comprised most (75–94%) of the clastic load during storm flows, bed load material (0.25–2 mm) accounted for most (70–78%) of the fine sediment accumulated in experimental gravel implanted in the streambeds. Sand trapped in the interstices of the top several centimeters formed a seal that impeded deeper deposition of very fine sand and finer material. The seal was responsible at least in part for a decrease in the rate of fine-sediment accumulation with increasing cumulative bed load transport. Areas of the streambeds commonly scoured or filled 0.1 m or more during storm flows, and thus scour and fill commonly created a sandy layer at least as thick as the seal formed by sediment infiltration. Scour could erode eggs laid in the bed and expose deeper levels of the bed to infiltration by fine sediment, but at the same time could allow fine sediment to be winnowed away. Great temporal and spatial variation in sedimentation in these streams suggests that individual storms of moderate size pose a threat to eggs in many but not all areas selected by fish for spawning.

Modeling the transport of volatile organics in variably saturated media

Abstract: The understanding of the processes of dissolution, volatilization, and gas-liquid partitioning in porous media is very limited. The few models which attempt to characterize the transport of volatile organics such as petroleum products and halogenated hydrocarbon solvents in variably saturated media all assume that mass transfer processes are at equilibrium. In addition, gas phase advection is neglected by assuming that gas phase pressures are uniformly atmospheric and that density gradients are negligible. In this study a model was developed to solve for water phase flow and transport and density dependent gas phase flow and transport. Simple expressions for dissolution, volatilization, and gas-liquid partitioning, employing the concept of an overall mass transfer coefficient, were incorporated into the model. The transport of trichloroethylene in a variably saturated vertical cross section, under a variety of conditions, was simulated. Results of the simulations appeared qualitatively correct. The importance of gas phase processes in increasing subsurface contamination from volatile organics, and in dissipating residual amounts of these substances, was demonstrated. The lack of similar analytical and/or numerical models, or suitable experimental studies, excluded the possibility of validating, or verifying, the model.

Modeling the transport of solutes influenced by multiprocess nonequilibrium

Abstract: A model that explicitly accounts for multiple sources of nonequilibrium is presented. The multiprocess nonequilibrium (MPNE) model is specifically formulated for cases where nonequilibrium is caused by a combination of transport- and sorption-related processes. Sensitivity analyses were performed to delineate the conditions under which the MPNE model reduces to the bicontinuum and to the local equilibrium models. These conditions are strongly controlled by the magnitude of the dimensionless rate parameters. Performance of the MPNE model was evaluated with several published data sets. An empirical regression equation was successfully used to estimate values for sorption rate constants required in the MPNE model. The MPNE model, with values for all parameters obtained from independent sources, predicted behavior exhibited by the data. This provides support for the validity of the conceptualization upon which the model is based.

Density-driven flow of gas in the unsaturated zone due to the evaporation of volatile organic compounds

Abstract: A theoretical investigation of factors affecting the gas phase transport of evaporating organic liquids in the unsaturated zone is presented. Estimates of density-driven advective gas flow using a simple analytic expression indicate that significant advective gas flow will result from the evaporation of volatile liquids in soils having a high permeability. Numerical simulations using a two-dimensional cylindrical geometry and including the effects of phase partitioning between the solid, gas, water, and organic liquid phases show that mass transfer due to density-driven flow may dominate the gas phase transport of some organic chemical vapors in the unsaturated zone.

Chaos in rainfall

Abstract: The question is posed regarding possible chaotic dynamics in the temporal rainfall of storm events Chaotic dynamics implies a nonlinear deterministic system very sensitive to initial conditions which yields outputs indistinguishable from a stochastic process by standard techniques The trajectories of these systems in the phase space are characterized by being contained in a strange attractor of fractal dimension A time series of 1990 points of 15-s rainfall for the storm of October 25, 1980, in Boston is analyzed in detail toward this objective It is found that both the characteristics of the correlation integral and the Lyapunov exponents of the historical data give preliminary support to the presence of chaotic dynamics with a strange attractor The implications of these findings for the modeling of storm rainfall and for the limits of predictability of the process are discussed jointly with the research challenges lying ahead in this field

Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments

Abstract: This paper applies stochastic methods to the analysis and prediction of solute transport in heterogeneous saturated porous media. Partial differential equations for three unconditional ensemble moments (the concentration mean, concentration covariance, and velocity concentration cross covariance) are derived by applying perturbation techniques to the governing transport equation for a conservative solute. Concentration uncertainty is assumed to be the result of unmodeled small-scale fluctuations in a steady state velocity field. The moment expressions, which describe how each moment evolves over time and space, resemble the classic deterministic advection-dispersion equation and can be solved using similar methods. A solution procedure based on a Galerkin finite element algorithm is illustrated with a hypothetical two-dimensional example. For this example the required steady state velocity statistics are obtained from an infinite domain spectral solution of the stochastic groundwater flow equation. The perturbation solution is shown to reproduce the statistics obtained from a Monte Carlo simulation quite well for a natural log conductivity standard deviation of 0.5 and moderately well for a natural log conductivity standard deviation of 1.0. The computational effort required for a perturbation solution is significantly less than that required for a Monte Carlo solution of acceptable accuracy. Sensitivity analyses conducted with the perturbation approach provide qualitative confirmation of a number of results obtained by other investigators for more restrictive special cases.

The effect of water-treatment processes on the removal of hepatotoxins from microcystis and oscillatoria cyanobacteria - a laboratory study

Abstract: The behaviour of hepatotoxins fromMicrocystis andOscillatoria cyanobacteria in some common water treatment processes was investigated on the laboratory scale in order to obtain data on their potential transfer to drinking water. Two toxins were separated from both of the freeze-dried cyanobacterial materials used in the experiments, a natural bloom consisting ofM. wesenbergii andM. viridis and a laboratory-grown culture ofO. agardhii. The concentrations of all four toxins before the treatments were between 30 and 60 μg/1. The investigated water treatment processes, selected from among methods applied in Finland, were: (1) Al2(SO4)3 flocculation with sand filtration and chlorination; (2) FeCl3 flocculation with sand filtration and chlorination; (3) addition of activated carbon powder with Al2(SO4)3 flocculation, sand filtration and chlorination; (4) Al2(SO4) flocculation with sand filtration, activated carbon filtration and chlorination; and (5) ozonation with Al2(SO4)3 flocculation, sand filtration and chlorination. The conventional flocculation-filtration-chlorination procedures resulted in a relatively small decrease in the toxin concentrations. Activated carbon powder in low doses did not improve the results, but activated carbon filtration as well as ozonation completely removed the toxins. The toxin concentrations were determined by HPLC. The proper functioning of the treatment processes was monitored by measurement of the KMnO4 value, turbidity and flocculation chemical residues.

The Impeller Meter for measuring aquifer permeability variations: Evaluation and comparison with other tests

Abstract: A knowledge of the variation of horizontal hydraulic conductivity with vertical position, K(z), is important in understanding the transport and dispersive properties of aquifers. Using an impeller meter to measure the discharge distribution in a screened well while pumping at a constant rate is a promising technique for obtaining the K(z) function. Such an application is described herein, and the resulting K(z) functions are compared with those obtained previously using tracer tests and multilevel slug tests. Impeller meter data were the most convenient to obtain, and tracer data the most difficult. The K(z) functions obtained by the three methods were not identical but quite similar overall. This similarity between both borehole tests and the larger-scale tracer test showed that nonstationary hydraulic conductivity trends, in a stochastic hydrologic sense, exist in the test aquifer. The impeller meter method was better able to detect the higher K layers than was the multilevel slug approach. Overall, the results suggest that a practical strategy for “fitting” impeller meter, tracer, or multilevel slug test data to a given aquifer is to use the selected testing procedure to obtain a dimensionless distribution and then a standard pumping test to measure . Combining both types of information enables dimensional values for K(z) to be calculated. In low permeability aquifers or near the bottom of a test well the fluid velocity due to pumping may be below the stall velocity of an impeller. Thus there is a definite need for the commercial development of more sensitive flow-measuring devices such as heat pulse flowmeters (Hess, 1986), which will extend the resolution of this field method.

Wetting front instability: 2. Experimental determination of relationships between system parameters and two‐dimensional unstable flow field behavior in initially dry porous media

Abstract: This paper describes and interprets experimental studies of wetting front instability guided by the dimensional analysis presented in paper 1 (R.J. Glass et al., this issue). When a wetting front passes from a fine-textured layer of initially dry sand into an underlying coarse layer, the front breaks into fingers. A specially developed vertical slablike chamber and associated techniques were developed for the study of such fingering. The flow rate through the system is systematically varied by using different mean grain size separates for the upper layer (the same coarse separate being used for the bottom layer). Relationships between finger width, propagation velocity, moisture content, and flow rate through individual fingers are experimentally determined and related to the properties of the bottom layer and the flow rate through the system. The results are different than those found in a previous experimental study which used different techniques for sample preparation. Results obtained here agree with a formulation derived earlier by J-Y. Parlange and D.E. Hill (1976) through linear stability analysis.

The common property aquifer as a differential game

Abstract: Open-loop and feedback equilibria are compared using a common property aquifer model. Open-loop solutions correspond to assuming that participants commit themselves in the initial period to pumping rates in all future periods. Feedback solutions represent a more realistic assumption as farm operators adopt pumping strategies that depend on the reserve stock of water. Comparing the two equilibrium concepts reveals two sources of dynamic inefficiency in the common property aquifer: a pumping cost externality and a “strategic externality” that arises from the competition among users to capture the groundwater reserves. The qualitative results show that the open-loop solution captures only the pumping cost externality. The feedback solution captures both externalities and exacerbates the over- exploitation of the commons compared to the open-loop solution. Moreover, the dynamic inefficiency resulting from both externalities increases in the number of independent landowners with access to the aquifer.

Radon in groundwater: A tool to assess infiltration from surface waters to aquifers

Abstract: We measured the concentrations of natural 222Rn (half-life 3.8 days) in groundwater at three sites in Switzerland; here groundwater is recharged mainly by river water. Upon infiltration and movement in the ground, the radon concentration in the water increases by more than two orders of magnitude to reach a steady state. This increase was found at two of the three sites. At the site of main interest, we used the ingrowth of radon between the river and nearby observation wells to estimate groundwater residence times of up to about four half lives. We assumed that the ingrowth of radon can be described by the growth law of radioactivity, that the progenitors of radon (226Ra, 238U) are homogeneously distributed in the aquifer, and that the freshly infiltrated water is not mixed significantly with older groundwater. A linear regression through the data at the site of main interest yielded an average flow velocity of 4.6 m −1, which confirms earlier tracer observations. Radon accumulates to higher concentrations, when the top soil layer is frozen or exhibits a high moisture content. During these conditions the radon data cannot be used for dating purposes.

Flow channeling in a single fracture as a two-dimensional strongly heterogeneous permeable medium

Abstract: The void space of a rock fracture is conceptualized as a two-dimensional heterogeneous system with variable apertures as a function of position in the fracture plane. The apertures are generated using geostatistical methods. Fluid flow is simulated with constant head boundary conditions on two opposite sides of the two-dimensional flow region, with closed boundaries on the remaining two sides. The results show that the majority of flow tends to coalesce into certain preferred flow paths (channels) which offer the least resistance. Tracer transport is then simulated using a particle tracking method. The apertures along the paths taken by the tracer particles are found to obey a distribution different from that of all the apertures in the fracture. They obey a distribution with a larger mean and a smaller standard deviation. The shift in the distribution parameters increases with increasing values of variance for the apertures in the two-dimensional fracture. Provided that the correlation length is no greater than one fifth of the scale of measurement, the aperture density distributions of tracer particle paths remain similar for flow in two orthogonal directions, even with anisotropy ratio of spatial correlation up to 5. These results may be applicable in general to flow and transport through a two-dimensional strongly heterogeneous porous medium with a broad permeability distribution, where the dispersion of the system may be related to the parameters of the permeability distribution along preferred flow channels.

An evaluation of methods for the estimation of tributary mass loads

Abstract: Tributary loading estimation methods were evaluated by conducting retrospective studies with comprehensive sets of field data for flow rates, nutrients, heavy metals, and polychlorinated biphenyls. Three broad classes of loading estimation methods were investigated: simple averaging methods, ratio estimation methods, and regression methods. Estimators were evaluated using Monte Carlo sampling studies in which random subsamples of complete loading records were used to estimate annual loadings. These estimates were then compared to “true” loadings determined by calculations using the entire record. No group of estimators were found to be superior for all test cases considered. However, individual estimation approaches within each group often provided low error estimates. Results were inconsistent among test cases and these inconsistencies appeared to be related to specific test case characteristics such as the strength and form of the flow-concentration relationship and the nature of the annual hydrograph. Ratio estimators appeared to be more robust to sources of bias than other estimation approaches.

An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers

Abstract: Three different conceptual frameworks have been adopted in the past for the development of mathematical models of bacterial growth and biologically reacting solute transport in saturated porous media. Two schools of thought are based upon assuming that the pore scale geometrical configuration of the attached bacteria consists of biofilms or microcolonies; the third school of thought represents the traditional approach where pore scale processes are neglected and the bacteria are assumed to respond to the macroscopic bulk fluid substrate concentration. On the basis of a schematic block diagram representation of a saturated porous medium hosting a microbial population, it is shown that these frameworks share a common theoretical foundation, and that they differ only by the choice of particular constitutive equations for several transfer parameters. Using one possible option in this respect, we derive a mathematical model that involves no unwarranted assumption about the distribution of the microorganisms in the pore space. The governing equations of this latter model are shown to be formally identical to those obtained by F.J. Molz et al. (1986), using the concept of microcolony, and to those that would result from adopting a simple form of biofilm model to describe bacterial growth in the pore space. Some of the consequences of this formal similarity between macroscopic transport equations obtained in different conceptual frameworks are discussed from an operational standpoint and in terms of model validation.

Analysis of the linear programming gradient method for optimal design of water supply networks

Abstract: A theoretical analysis of the linear programming (LP) gradient method for optimal design of water distribution networks is presented. The method was first proposed by A. Alperovits and U. Shamir (1977) and has received much attention in the last 10 years. It consists of two stages that are solved in alteration: (1) a LP problem is solved for a given feasible flow distribution and (2) a search is conducted in the space of flow variables, based on the gradient of the objective function (GOF). In this paper a matrix formulation is given for both stages using well-known graph theory matrices. It is proven that the mathematical expression of the GOF is independent of the choice of the sets of loops and paths along which the head constraints are formulated. This is contrary to the claim made by I. C. Goulter et al. (1986). The original GOF expression is shown to have been an approximation of the steepest direction, but still gives good results. Finally, the search procedure is improved by using the projected gradient method.

Contaminant transport and biodegradation: 2. Conceptual model and test simulations

Abstract: A conceptual model of subsurface contaminant transport with biodegradation is presented. This model incorporates both aerobic and anaerobic reactions, with several models of differing complexity presented for the anaerobic case. Nutrient uptake is described using Michaelis-Menten expressions, which are incorporated into a multiple nutrient uptake model. Several uptake inhibition factors are also included in the model. The mathematical model that results takes the form of a series of reactive transport equations. These equations are coupled nonlinearly through the reaction terms, which are themselves coupled to growth equations for subsurface bacterial populations. Example simulations are presented for a variety of cases, ranging from one-substrate, one-population aerobic degradation to multisubstrate, multipopulation anaerobic consortium degradation.

Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: From data to design

Abstract: Most optimization models for groundwater quality management have ignored the effects of uncertainty due to spatial variability of hydraulic conductivity. Here we explicitly incorporate this uncertainty into a procedure for the optimal design of aquifer remediation strategies. Local hydraulic conductivity and head data are used to quantify the uncertainty which is traced through to target a reliable remediation design. The management procedure is based on the stochastic approach to groundwater flow and contaminant transport modeling, in which the log-hydraulic conductivity is represented as a random field. The remediation design procedure has two steps. The first is solution of the stochastic inverse model. Maximum likelihood and Gaussian conditional mean estimation are used to characterize the random conductivity field based on the hydraulic conductivity and hydraulic head measurements. Based on this statistical characterization, conditional simulation is used to generate numerous realizations (maps) of spatially variable hydraulic conductivity that honor the head and conductivity data. The second step is solution of the groundwater quality management model. Two management model formulations are presented. The first, termed the multiple realization management model, simultaneously solves the nonlinear simulation-optimization problem for a sampling of hydraulic conductivity realizations. It is shown that reclamation design based on as few as 30 conductivity realizations can provide reliable (over 90%) remediation strategies. The second model, termed the Monte Carlo management model, solves the nonlinear simulation-optimization problem individually for a sampling of hydraulic conductivity realizations. This provides a relationship between pumping (cost) and reliability. Each of the management models is linked with the stochastic inverse model, and each is demonstrated for two cases: (1) the available data are limited to hydraulic conductivity measurements and (2) both hydraulic conductivity and hydraulic head measurements are used.

Scaling and Elevation in River Networks

Abstract: The analysis of large river networks obtained from digital elevation models has given insight into the variation of channel slope with scale. Investigators have recently suggested that channel slopes are self-similar with magnitude or area as a scaling parameter. Our data indicates otherwise; in particular, the variance of channel slope is larger than that predicted by simple self-similarity. This suggests multiscaling. The scaling exponent for the standard deviation is approximately half the corresponding exponent in the relationship of the slope mean to magnitude or area. A model for channel slopes based on a point process of elevation drops along the channel is presented. The model reproduces observed multiscaling properties when the density of elevation increments is related to area (or magnitude) as A−θ.

The Laplace Transform Galerkin Technique: A time‐continuous finite element theory and application to mass transport in groundwater

Abstract: A time-continuous numerical technique, referred to as the Laplace Transform Galerkin (LTG) method, is developed and applied to the problem of solute transport in porous media. After application of Galerkin's procedure and subdivision of the domain into finite elements, the method involves a simple application of the Laplace transformation to eliminate the temporal derivatives appearing in the space-discretized set of ordinary differential equations. Then, by solving the resulting transformed system of algebraic equations in Laplace p space, numerical inversion of the Laplace-transformed nodal concentration is performed using the robust and accurate Crump (1976) algorithm. The Crump algorithm permits the concentration to be evaluated from a range of time values from a single set of Laplace p space solutions. Because each of the needed p space solutions are independent, the algorithm is well suited for execution on multiprocessor parallel computers. It is demonstrated by means of a series of examples that the LTG scheme is capable of providing highly accurate solutions essentially devoid of numerical dispersion for grid Peclet numbers in excess of 30. Examination of the complex-valued, Laplace-domain concentration profiles reveal that they are generally smooth, well-behaved oscillatory functions compared to the profiles in the time domain, thus permitting the use of a coarse finite element grid. Because of the nature of the Laplace transformation, the LTG method is particularly well suited to the problem of transient groundwater flow and solute transport in fractured porous media or multiple aquifer-aquitard systems based on the dual-porosity integrodifferential equation approach.

Modeling of two‐dimensional overland flow

Abstract: A two-dimensional hydrodynamic and numerical model for overland flow is developed in this paper. The model allows spatial variations in hillslope physical characteristics, including surface roughness, infiltration, and microtopography. The accuracy of the model is tested by comparison with characteristic-based solutions and experimental data. The results of these tests indicate that the model is accurate and has good stability and convergence properties. The application of the model to two-dimensional overland flow on hillslopes is demonstrated by applying it to surfaces with spatially variable roughness, infiltration, and microtopography. These simulations show that microtopography is the dominant factor causing spatial variation in overland flow depth, velocity, and direction.