Showing papers in "Water Resources Research in 1995"

Artificial Neural Network Modeling of the Rainfall‐Runoff Process

Abstract: An artificial neural network (ANN) is a flexible mathematical structure which is capable of identifying complex nonlinear relationships between input and output data sets. ANN models have been found useful and efficient, particularly in problems for which the characteristics of the processes are difficult to describe using physical equations. This study presents a new procedure (entitled linear least squares simplex, or LLSSIM) for identifying the structure and parameters of three-layer feed forward ANN models and demonstrates the potential of such models for simulating the nonlinear hydrologic behavior of watersheds. The nonlinear ANN model approach is shown to provide a better representation of the rainfall-runoff relationship of the medium-size Leaf River basin near Collins, Mississippi, than the linear ARMAX (autoregressive moving average with exogenous inputs) time series approach or the conceptual SAC-SMA (Sacramento soil moisture accounting) model. Because the ANN approach presented here does not provide models that have physically realistic components and parameters, it is by no means a substitute for conceptual watershed modeling. However, the ANN approach does provide a viable and effective alternative to the ARMAX time series approach for developing input-output simulation and forecasting models in situations that do not require modeling of the internal structure of the watershed.

Multiple‐Rate Mass Transfer for Modeling Diffusion and Surface Reactions in Media with Pore‐Scale Heterogeneity

Abstract: Mass transfer between immobile and mobile zones is a consequence of simultaneous processes. We develop a “multirate” model that allows modeling of small-scale variation in rates and types of mass transfer by using a series of first-order equations to represent each of the mass transfer processes. The multirate model is incorporated into the advective-dispersive equation. First, we compare the multirate model to the standard first-order and diffusion models of mass transfer. The spherical, cylindrical, and layered diffusion models are all shown to be specific cases of the multirate model. Mixtures of diffusion from different geometries and first-order rate-limited mass transfer can be combined and represented exactly with the multirate model. Second, we develop solutions to the multirate equations under conditions of no flow, fast flow, and radial flow to a pumping well. Third, using the multirate model, it is possible to accurately predict rates of mass transfer in a bulk sample of the Borden sand containing a mixture of different grain sizes and diffusion rates. Fourth, we investigate the effects on aquifer remediation of having a heterogeneous mixture of types and rates of mass transfer. Under some circumstances, even in a relatively homogeneous aquifer such as at Borden, the mass transfer process is best modeled by a mixture of diffusion rates.

Combined Use of Groundwater Dating, Chemical, and Isotopic Analyses to Resolve the History and Fate of Nitrate Contamination in Two Agricultural Watersheds, Atlantic Coastal Plain, Maryland

Abstract: The history and fate of groundwater nitrate (NO3−) contamination were compared in 2 small adjacent agricultural watersheds in the Atlantic coastal plain by combined use of chronologic (CCl2F2, 3H), chemical (dissolved solids, gases), and isotopic (δ15N,δ13C, δ34S) analyses of recharging groundwaters, discharging groundwaters, and surface waters. The results demonstrate the interactive effects of changing agricultural practices, groundwater residence times, and local geologic features on the transfer of NO3− through local flow systems. Recharge dates of groundwaters taken in 1990–1992 from the surficial aquifer in the Chesterville Branch and Morgan Creek watersheds near Locust Grove, Maryland, ranged from pre-1940 to the late 1980’s. When corrected for localized denitrification by use of dissolved gas concentrations, the dated waters provide a 40-year record of the recharge rate of NO3−, which increased in both watersheds by a factor of 3–6, most rapidly in the 1970's. The increase in groundwater NO3− over time was approximately proportional to the documented increase in regional N fertilizer use, and could be accounted for by oxidation and leaching of about 20–35% of the fertilizer N. Groundwaters discharging upward beneath streams in both watersheds had measured recharge dates from pre-1940 to 1975, while chemical data for second-order reaches of the streams indicated average groundwater residence times in the order of 20+ years. At the time of the study, NO3− discharge rates were less than NO3− recharge rates for at least two reasons: (1) discharge of relatively old waters with low initial NO3− concentrations, and (2) local denitrification. In the Chesterville Branch watershed, groundwaters remained oxic throughout much of the surficial aquifer and discharged relatively unaltered to the stream, which had a relatively high NO3− concentration (9–10 mg/L as N). In the Morgan Creek watershed, groundwaters were largely reduced and denitrified before discharging to the stream, which had a relatively low NO3− concentration (2–3 mg/L as N). Chemical and isotopic data indicate that quantitative denitrification occurred within buried calcareous glauconitic marine sediments that are present at relatively shallow depths beneath the Morgan Creek watershed. NO3− removal by forests, wetlands, and shallow organic-rich soils in near-stream environments was largely avoided by groundwaters that followed relatively deep flow paths before converging and discharging rapidly upward to the streams.

A distributed slope stability model for steep forested basins

Abstract: A distributed, physically based slope stability model (dSLAM), based on an infinite slope model, a kinematic wave groundwater model, and a continuous change vegetation root strength model, is presented. It is integrated with a contour line-based topographic analysis and a geographic information system (GIS) for spatial data extraction and display. The model can be run with either individual rainfall events or long-term sequences of storms. These inputs can be either actual storm records or synthesized random events based on Monte Carlo simulation. The model is designed to analyze rapid, shallow landslides and the spatial distribution of safety factor (FS) in steep, forested areas. It can investigate the slope stability problem in both temporal and spatial dimensions, for example, the impact of timber harvesting on slope stability either at a given time or through an extended management period, the probability of landslide occurrence for a given year, and the delivery of landslide sediments to headwater streams. The dSLAM model was applied in a steep, forested drainage of Cedar Creek in the Oregon Coast Ranges using actual spatial patterns of timber harvesting and measured rainfall during a major storm which triggered widespread landslides in that area in 1975. Simulated volume and number of failures were 733 m3 and 4, respectively. These values agreed closely with field measurements following the 1975 storm. However, the effect of parameter uncertainty may complicate this comparison. For example, when soil cohesion values of 2.0 and 3.0 kPa were used, the failure volume changed by factors of 2.04 and 0.41, respectively, compared with the average condition of 2.5 kPa used in the simulation. For soil depths 30% higher and lower than the standard condition, the failure volume changed by factors of 2.0 and 0.27, respectively. When maximum root cohesion changed from 12.5 kPa (average condition) to 10 kPa, the failure volume increased 1.73-fold; for the case of 15 kPa, the failure volume changed by a factor of 0.55. The simulated failures caused by the storm were mostly in hollows. The simulations show that the spatial distribution of FS is controlled mainly by topography and timber-harvesting patterns and is greatly affected by groundwater flow patterns during major rainstorms. Most areas with FS < 3.0 corresponded with the distribution of blocks clear-cut in 1968, and all elements with FS < 2.0 were in areas clear-cut in 1968. Areas with low FS (1.0–1.6) expanded dramatically during the rainstorm and decreased at a slow rate after the storm. Factors of safety in hollows declined sharply during the storm.

Role of Near-Bed Turbulence Structure in Bed Load Transport and Bed Form Mechanics

Abstract: The interactions between turbulence events and sediment motions during bed load transport were studied by means of laser-Doppler velocimetry and high-speed cinematography. Sweeps (u′ > 0, w′ 0 w′ > 0) which contribute negatively to the bed shear stress and are relatively rare, individually move as much sediment as sweeps of comparable magnitude and duration, however, and much more than bursts (u′ 0) and inward interactions (u′ < 0, w′ < 0). When the magnitude of the outward interactions increases relative to the other events, therefore, the sediment flux increases even though the bed shear stress decreases. Thus, although bed shear stress can be used to estimate bed load transport by flows with well-developed boundary layers, in which the flow is steady and uniform and the turbulence statistics all scale with the shear velocity, it is not accurate for flows with developing boundary layers, such as those over sufficiently nonuniform topography or roughness, in which significant spatial variations in the magnitudes and durations of the sweeps, bursts, outward interactions, and inward interactions occur. These variations produce significant peaks in bed load transport downstream of separation points, thus supporting the hypothesis that flow separation plays a significant role in the development of bed forms.

Quasi‐Linear Geostatistical Theory for Inversing

Abstract: A quasi-linear theory is presented for the geostatistical solution to the inverse problem. The archetypal problem is to estimate the log transmissivity function from observations of head and log transmissivity at selected locations. The unknown is parameterized as a realization of a random field, and the estimation problem is solved in two phases: structural analysis, where the random field is characterized, followed by estimation of the log transmissivity conditional on all observations. The proposed method generalizes the linear approach of Kitanidis and Vomvoris (1983). The generalized method is superior to the linear method in cases of large contrast in formation properties but informative measurements, i.e., there are enough observations that the variance of estimation error of the log transmissivity is small. The methodology deals rigorously with unknown drift coefficients and yields estimates of covariance parameters that are unbiased and grid independent. The applicability of the methodology is demonstrated through an example that includes structural analysis, determination of best estimates, and conditional simulations.

Pool Spacing in Forest Channels

Abstract: Field surveys of stream channels in forested mountain drainage basins in southeast Alaska and Washington reveal that pool spacing depends on large woody debris (LWD) loading and channel type, slope, and width. Mean pool spacing in pool-riffle, plane-bed, and forced pool-riffle channels systematically decreases from greater than 13 channel widths per pool to less than 1 channel width with increasing LWD loading, whereas pool spacing in generally steeper, step-pool channels is independent of LWD loading. Although plane-bed and pool-riffle channels occur at similar low LWD loading, they exhibit typical pool spacings of greater than 9 and 2–4 channel widths, respectively. Forced pool-riffle channels have high LWD loading, typical pool spacing of <2 channel widths, and slopes that overlap the ranges of free-formed pool-riffle and plane-bed channel types. While a forced pool-riffle morphology may mask either of these low-LWD-loading morphologies, channel slope provides an indicator of probable morphologic response to wood loss in forced pool-riffle reaches. At all study sites, less than 40% of the LWD pieces force the formation of a pool. We also find that channel width strongly influences pool spacing in forest streams with similar debris loading and that reaches flowing through previously clear-cut forests have lower LWD loading and hence fewer pools than reaches in pristine forests.

Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments

Abstract: A new methodology for solution of the inverse problem in groundwater hydrology is proposed and applied to a site in southeastern New Mexico with extensive hydrogeologic data. The methodology addresses the issue of nonuniqueness of the inverse solutions by generating an ensemble of transmissivity fields considered to be equally likely, each of which is in agreement with the measured transmissivity and pressure data. It consists of generating a selected number of conditionally simulated transmissivity fields and then calibrating each of the fields to match the measured steady state or transient pressures, in a least squares sense. The calibration phase involves an iterative implementation of an automated pilot point approach coupled with conditional simulations. Pilot points are the parameters of calibration. They are synthetic transmissivity data which are added to the transmissivity database to produce a revised conditional simulation during calibration. Coupled kriging and adjoint sensitivity analysis is employed for the optimal location of pilot points, and gradient search methods are used to derive their optimal transmissivities. The pilot point methodology is well suited for characterizing the spatial variability of the transmissivity field in contrast to methods using zonation. Pilot points are located where their potential for minimizing the objective function is the highest. This minimizes the perturbations in the transmissivities which are optimally assigned to the pilot point and results in minimal changes to the covariance structure of the transmissivity field. The calibrated fields honor the transmissivity measurements at their locations, preserve the variogram, and match the measured pressures in a least squares sense. Since there are numerous options in the execution of this methodology, computational experiments have been conducted to identify the most efficient among them. The method has been applied to the Waste Isolation Pilot Plant (WIPP) site, in southeastern New Mexico, where the U.S. Department of Energy is conducting probabilistic system assessment for the permanent disposal of transuranic nuclear waste. The resulting calibrated transmissivity fields are input to a Monte Carlo analysis of the total system performance. The present paper, paper 1 of a two-paper presentation, describes the methodology. Paper 2, a companion paper, presents the methodology's application to the WIPP site.

Using Genetic Algorithms to Solve a Multiobjective Groundwater Monitoring Problem

Abstract: This paper builds on the work of Meyer and Brill (1988) and subsequent work by Meyer et al. (1990, 1992) on the optimal location of a network of groundwater monitoring wells under conditions of uncertainty. We investigate a method of optimization using genetic algorithms (GAs) which allows us to consider the two objectives of Meyer et al. (1992), maximizing reliability and minimizing contaminated area at the time of first detection, separately yet simultaneously. The GA-based solution method has the advantage of being able to generate both convex and nonconvex points of the trade-off curve, accommodate nonlinearities in the two objective functions, and not be restricted by the peculiarities of a weighted objective function. Furthermore, GAs have the ability to generate large portions of the trade-off curve in a single iteration and may be more efficient than methods that generate only a single point at a time. Four different codings of genetic algorithms are investigated, and their performance in generating the multiobjective trade-off curve is evaluated for the groundwater monitoring problem using an example data set. The GA formulations are compared with each other and also with simulated annealing on both performance and computational intensity. Simulated annealing relies on a weighted objective function which can find only a single point along the trade-off curve for each iteration, while all of the multiple-objective GA formulations are able to find a larger number of convex and nonconvex points of trade-off curve in a single iteration. Each iteration of simulated annealing is approximately five times faster than an iteration of the genetic algorithm, but several simulated annealing iterations are required to generate a trade-off curve. GAs are able to find a larger number of nondominated points on the trade-off curve, while simulated annealing finds fewer points but with a wider range of objective function values. None of the GA formulations demonstrated the ability to generate the entire trade-off curve in a single iteration. Through manipulation of GA parameters certain sections of the trade-off curve can be targeted for better performance, but as performance improves at one section it suffers at another. Run times for all GA formulations were similar in magnitude.

Noninvasive Soil Water Content Measurement Using Electromagnetic Induction

Abstract: The feasibility of soil water content measurement using electromagnetic induction was investigated in an arid region of southern New Mexico. Soil water measurements were taken monthly with a neutron probe at 65 equally spaced stations along a 1950-m transect. At the same time, noninvasive electrical conductivity measurements of the soil were taken with a Geonics EM-31 ground conductivity meter. Using 16 months of measurements, we found a linear relationship exists between bulk soil electrical conductivity and total soil water content in the top 1.5 m of the profile. A simple linear regression model was developed to describe the relationship between soil water content and bulk soil electrical conductivity. The spatial and temporal accuracy of the regression model is addressed as well as the total number of neutron access tubes needed to accurately calibrate the model. By comparison with the neutron scattering method the electromagnetic induction method is quite accurate for the prediction of water content changes over time. The speed and ease of use combined with the accuracy of the measurements make the ground conductivity meter a valuable tool for rapid, noninvasive soil water measurements.

Comparison of Single and Multiple Flow Direction Algorithms for Computing Topographic Parameters in TOPMODEL

Abstract: Single flow direction (sfd) and multiple flow direction (mfd) algorithms were used to compute the spatial and statistical distributions of the topographic index used in the watershed model TOPMODEL. An sfd algorithm assumes that subsurface flow occurs only in the steepest downslope direction from any given point; an mfd algorithm assumes that subsurface flow occurs in all downslope directions from any given point. The topographic index in TOPMODEL is In (a/tan/3), where In is the Napierian logarithm, a is the upslope area per unit contour length, and tan/3 is the slope gradient. The In (a/tan /3) distributions were computed from digital elevation model (DEM) data for locations with diverse topography in Arizona, Colorado, Louisiana, Nebraska, North Carolina, Oregon, Pennsylvania, Tennessee, Vermont, and Virginia. The means of the In (a/tan/3) distributions were higher when the mfd algorithm was used for computation compared to when the sfd algorithm was used. The variances and skews of the distributions were lower for the mfd algorithm compared to the sfd algorithm. The differences between the mfd and sfd algorithms in the mean, variance, and skew of the In (a/tan/3) distribution were almost identical for the various DEMs and were not affected by DEM resolution or watershed size. TOPMODEL model efficiency and simulated flow paths were affected only slightly when the In (a/tan/3) distribution was computed with the sfd algorithm instead of the mfd algorithm. Any difference in the model efficiency and simulated flow paths between the sfd and mfd algorithms essentially disappeared when the model was calibrated by adjusting subsurface hydraulic parameters.

Deducing the Distribution of Terminal Electron‐Accepting Processes in Hydrologically Diverse Groundwater Systems

Abstract: The distribution of microbially mediated terminal electron-accepting processes (TEAPs) was investigated in four hydrologically diverse groundwater systems by considering patterns of electron acceptor (nitrate, sulfate) consumption, intermediate product (hydrogen (H{sub 2})) concentrations, and final product (ferrous ion, sulfide, and methane) production. In each hydrologic system a determination of predominant TEAPs could be arrived at, but the level of confidence appropriate for each determination differed. In a portion of the lacustrine aquifer of the San Joaquin Valley, for example, all three indicators (sulfate concentrations decreasing, H{sub 2} concentrations in the 1-2 nmol range, and sulfide concentrations increasing along flow paths) identified sulfate reduction as the predominant TEAP, leading to a high degree of confidence in the determination. In portions of the Floridan aquifer and a petroleum hydrocarbon-contaminated aquifer, sulfate reduction and methanogenesis are indicated by production of sulfide and methane, and hydrogen concentrations in the 1-4 nmol and 5-14 nmol range, respectively. However, because electron acceptor consumption could not be documented in these systems, less confidence is warranted in the TEAP determination. In the Black Creek aquifer, no pattern of sulfate consumption and sulfide production were observed, but H{sub 2} concentrations indicated sulfate reduction as the predominant TEAP. In this case,more » where just a single line of evidence is available, the least confidence in the TEAP diagnosis is justified. Because this methodology is based on measurable water chemistry parameters and upon the physiology of microbial electron transfer processes, it provides a better description of predominant redox processes in groundwater systems than more traditional Eh-based methods.« less

Scale and the Nature of Spatial Variability: Field Examples Having Implications for Hydrologic Modeling

Abstract: In this paper we examine how the nature of spatial variability affects hydrologic response over a range of scales using five field studies as examples. The nature of variability was characterized as either stochastic, when random, or deterministic, when due to known, nonrandom sources. We have emphasized how that characterization may change with the scale of hydrologic model. The five field examples, along with corresponding sources of variability, were (1) infiltration and surface runoff affected by shrub canopy, (2) groundwater recharge affected by soil depth, (3) groundwater recharge and streamflow affected by small-scale topography, (4) frozen soil runoff affected by elevation, and (5) snowfall distribution affected by large-scale topography. In each example there was a scale, the deterministic length scale, over which the hydrologic response was strongly dependent upon the specific, location-dependent ecosystem properties. Smaller-scale variability may be represented as either stochastic or homogeneous with nonspatial data. In addition, changes in scale or location sometimes resulted in the introduction of larger-scale sources of variability that subsume smaller-scale sources. Thus recognition of the nature and sources of variability can reduce data requirements by focusing on important sources of variability and using nonspatial data to characterize variability at scales smaller than the deterministic length scale. All the sources of variability described are present in the same watershed and affect hydrologic response simultaneously. Physically based models should therefore utilize both spatial and stochastic data where scale appropriate. Other implications for physically based modeling are that modeling algorithms should reflect larger-scale variability which generally has greater impact and that model and measurement grids should be consistent with the nature of variability.

Partitioning Tracer Test for Detection, Estimation, and Remediation Performance Assessment of Subsurface Nonaqueous Phase Liquids

Abstract: In this paper we present a partitioning interwell tracer test (PITT) technique for the detection, estimation, and remediation performance assessment of the subsurface contaminated by nonaqueous phase liquids (NAPLs). We demonstrate the effectiveness of this technique by examples of experimental and simulation results. The experimental results are from partitioning tracer experiments in columns packed with Ottawa sand. Both the method of moments and inverse modeling techniques for estimating NAPL saturation in the sand packs are demonstrated. In the simulation examples we use UTCHEM, a comprehensive three-dimensional, chemical flood compositional simulator developed at the University of Texas, to simulate a hypothetical two-dimensional aquifer with properties similar to the Borden site contaminated by tetrachloroethylene (PCE), and we show how partitioning interwell tracer tests can be used to estimate the amount of PCE contaminant before remedial action and as the remediation process proceeds. Tracer tests results from different stages of remediation are compared to determine the quantity of PCE removed and the amount remaining. Both the experimental (small-scale) and simulation (large-scale) results demonstrate that PITT can be used as an innovative and effective technique to detect and estimate the amount of residual NAPL and for remediation performance assessment in subsurface formations.

Grain Size Patchiness as a Cause of Selective Deposition and Downstream Fining

Abstract: One facet of the debate about the hypothesis of equal mobility of all grain sizes in a mixture is that equal mobility seems contrary to field evidence for selective deposition as an important mechanism of downstream fining. We argue that regardless of the ultimate outcome of the equal mobility debate, variability in local mean grain size across a reach can give rise to strong selective deposition even if locally equal mobility is satisfied exactly. We consider a system in which the sediment is arranged into locally well mixed zones (“patches”) whose mean grain size varies randomly across the reach. We assume that the shear stress is randomly distributed with a mean value near the critical value for the reach-averaged median size, that the variance in stress scales with the variance in grain size, and that the development of fine patches in areas of high shear stress is supply limited. The main controls on fining rate are then the ratio of mean stress to critical stress for the section-averaged mean grain size and the ratio of the patch standard deviation (assumed constant) to the standard deviation of patch means. In addition, in any system in which fining occurs by selective transport and deposition, the fining rate is strongly influenced by the spatial distribution of deposition rate.

Step-Pool Streams: Adjustment to Maximum Flow Resistance

Abstract: Steep headwater streams are often characterized by alternating steps and pools, which may be described by mean step height and mean step length . A conceptual model is developed based on the notion that the largest floods are just capable of moving the largest debris in the channel. The model suggests that step pools evolve toward a condition of maximum flow resistance because maximum resistance implies maximum stability and that this condition is achieved when steps are regularly spaced and the mean step steepness is slightly greater than the channel slope S. To test this conceptual model, four series of flume experiments were performed. These experiments show that the relation between resistance to flow and is convex upward with maximum flow resistance occurring when steps are regularly spaced and have values between 1 and 2. Field measurements reveal that 18 natural step-pool streams also satisfy the inequality , strongly suggesting that the form of such streams is adjusted to maximize resistance to flow. The results of the flume experiments are inconsistent with the proposition that step pools form as antidunes, as Froude numbers for the flume step pools at which flow resistance was maximized fall well below those values usually associated with these bed forms.

Two‐Phase Flow Visualization and Relative Permeability Measurement in Natural Rough‐Walled Rock Fractures

Abstract: A laboratory flow apparatus was used to visualize and measure two-phase gas-liquid flows in natural rough-walled rock fractures. Experiments at carefully controlled flow rate and pressure conditions have been performed using a natural fracture and three transparent fracture replicas. Two-phase flow exhibited persistent instabilities with cyclic pressure and flow rate variations even under conditions of constant applied boundary conditions. Visual observations of changes in pore occupancy showed that the instabilities could be explained as resulting from an interplay between capillary effects and pressure drop due to viscous flow. Measurements of relative permeabilities indicated strong phase interference, with relative permeabilities reduced to very small values at intermediate saturations for both wetting and nonwetting phases. These results run counter to a conventional view of fracture relative permeabilities that assumes that the relative permeability of each phase is equal to its saturation, but the results are consistent with recent models that view fractures as two-dimensional heterogeneous porous media. 35 refs., 10 figs., 1 tab.

Spatial Prediction of Soil Salinity Using Electromagnetic Induction Techniques: 1. Statistical Prediction Models: A Comparison of Multiple Linear Regression and Cokriging

Abstract: We describe a regression-based statistical methodology suitable for predicting field scale spatial salinity (EC,) conditions from rapidly acquired electromagnetic induction (EC,) data. This technique uses multiple linear regression (MLR) models to estimate soil salinity from EC, survey data. The MLR models incorporate multiple EC, measurements and trend surface parameters to increase the prediction accuracy and can be fitted from limited amounts of EC, calibration data. This estimation technique is compared to some commonly recommended cokriging techniques, with respect to statistical modeling assumptions, calibration sample size requirements, and prediction capabilities. We show that MLR models are theoretically equivalent to and cost-effective relative to cokriging for estimating a spatially distributed random variable when the residuals from the regression model are spatially uncorrelated. MLR modeling and prediction techniques are demonstrated with data from three salinity surveys.

Fractional packing model for hydraulic conductivity derived from sediment mixtures

Abstract: Petrophysical relations are derived to predict porosity and hydraulic conductivity from grain size distributions considering particle packing in sediment mixtures First, we develop a fractional packing model for porosity that considers the fraction of intrapore fines that occur as the fines content increases Then, a fractional packing Kozeny-Carman relation for hydraulic conductivity is developed by examining which particle sizes dominate the pore structure, and which averaging procedure best represents the mean grain diameter in any given sediment mixture The relations developed here perform well for a wide range of sediment mixtures regardless of confining pressure Graphs are presented that show hydraulic conductivity versus weight fraction of fines for mixtures of coarse- and fine-grained sediment commonly observed in the field, such as clayey gravel and silty sand These graphs show that the wide range of hydraulic conductivity values reported for sediment mixtures can display a 5 order of magnitude variation over a few percent fines Finally, a field scale application using grain size distributions from a quantitative depositional model shows that these petrophysical relations successfully predict more than 90% of hydraulic conductivity values to within 1 order of magnitude over 7 orders of magnitude of spatial variability

Runoff Production in a Forested, Shallow Soil, Canadian Shield Basin

Abstract: Storm flow in forested basins on the Canadian Shield is largely supplied by subsurface water; however, mechanisms by which this water reaches the stream remain unclear. Side slope contributions to storm flow were studied using throughflow trenches on slopes in a headwater basin near Dorset, Ontario. Discharge, soil water content, and chemical and isotopic signatures of subsurface water were monitored at each site. Four hypotheses were tested: (1) most flow occurs at the soil-bedrock interface on shield slopes with thin soil; (2) a significant fraction of event water moves vertically to bedrock via preferential flow pathways and laterally over the bedrock surface; (3) relative preevent water contribution to subsurface flow on shield slopes is a function of soil thickness; and (4) a significant portion of event water flux in storm flow from forested basins with shallow soil cover is supplied from side slopes via subsurface flow along the soil-bedrock interface. Hypothesis 1 was confirmed from hydrometric observations during spring and fall rainstorms. Hypotheses 2 and 3 were supported by temporal trends in dissolved organic carbon and 18O in flow at the soil-bedrock interface and by isotopic hydrograph separations (IHSs) of hillslope runoff. Comparison with the streamflow IHS indicated that event water flux from the basin in excess of that attributable to direct precipitation onto near-channel saturated areas could be supplied by flow along the bedrock surface (hypothesis 4). Flow at the soil-bedrock interface on side slopes also contributed ∼25% of preevent water flux from the basin. Much of the event water component of basin storm flow may travel considerable distances via subsurface routes and is not necessarily contributed by surface runoff processes (Horton flow or saturation overland flow). Therefore the assumption that event water undergoes little interaction with the soil during its passage downslope may be unwarranted here.

Bed Load Sediment Transport in an Ephemeral Stream and a Comparison with Seasonal and Perennial Counterparts

Abstract: Bed load sediment flux in an ephemeral channel, the Nahal Yatir, is shown to be a comparatively simple function of stream power and to reach levels that are several orders of magnitude higher than maxima measured at similar levels of stream power in perennial counterparts. Channel average submerged unit flux rates are recorded as high as 4.3 kg s−1 m−1, while at the center of the channel, the highest rate recorded is 6.5 kg s−1m−1. Transport efficiency is at least an order of magnitude higher than in other channels for which there are comparable data and, on average, as much as 400 times that of Oak Creek. These differences are explained by the fact that the bed of the Yatir is not armored. It is surmised that the unvegetated nature of this desert watershed provides ample supplies of sediment of all sizes and that this, together with the rapid recession of the flash flood hydrograph and the extended periods of no flow, discourages the development of an armor layer. The flux rates are not sediment supply-limited, as they are in perennial channels. Nahal Yatir and Oak Creek represent two ends of a spectrum, between which come seasonal and less well armored perennial streams. Transport efficiency is shown to vary considerably for each stream and from one stream to another, suggesting that it may not be possible to incorporate it easily into bed load equations in order to improve levels of prediction.

Hydraulic Behavior of Quasi‐Saturated Soils in the Presence of Entrapped Air: Laboratory Experiments

Abstract: Entrapped air in soils beneath the water table is one of the key factors controlling the hydraulic behavior under conditions of ponded infiltration, in perched waters, and in unconfined aquifers. The term quasi-saturated soils defines the soils with entrapped air, and the term quasi-saturated hydraulic conductivity defines the relationship between the hydraulic conductivity and entrapped air content. This paper focuses on an investigation of how entrapped air, along with other factors, affects the three-stage temporal behavior of the quasi-saturated hydraulic conductivity of soils. During the first stage the quasi-saturated hydraulic conductivity of soils decreases by as much as 5–8 times, presumably because mobile entrapped air blocks the largest pores. During the second stage, as the mobile entrapped air is discharged from the core, the quasi-saturated hydraulic conductivity of the soils slowly increases. When the mobile air is removed, the remaining immobile entrapped air is discharged as a dissolved phase, and the quasi-saturated hydraulic conductivity increases rapidly by about 1–2 orders of magnitude, essentially reaching the value of the saturated hydraulic conductivity. During the third stage the hydraulic conductivity is decreased to minimum values. The effects of sealing at the soil surface and microbiological activities are assumed to be major factors in the final decrease of the hydraulic conductivity. This three-stage temporal behavior of percolation in loam soils is repeatable. A new power law and an exponential relationship are proposed to describe the quasi-saturated hydraulic conductivity of loams as a function of the entrapped air content.

On Characterization of Anomalous Dispersion in Porous and Fractured Media

Abstract: A key characterization of dispersion in aquifers and other porous media has been to map the effects of inhomogeneous velocity fields onto a Fickian dispersion term (D) within the context of the conventional advection-dispersion equation (ADE). Recent compilations of data have revealed, however, that the effective D coefficient is not constant but varies systematically with the length or timescale over which transport occurs. A natural strategy to encompass this “anomalous” behavior into the context of the conventional ADE is to make D time dependent. This approach, to use D(t) to handle the same anomalous dispersion phenomena, has also been common in the field of electronic transport in disordered materials. In this paper we discuss the intrinsic inadequacy of considering a time-dependent dispersivity in the conventional ADE context, and show that the D = D(t) generalization leads to quantifiably incorrect solutions. In the course of proving this result we discuss the nature of anomalous dispersion and provide physical insight into this important problem in hydrogeology via analysis of a class of kinetic approaches. Particular emphasis is placed on the effects of a distribution of solute “delay times” with a diverging mean time, which we relate to configurations of preferential pathways in heterogeneous media.

Simulation of aerobic and anaerobic biodegradation processes at a crude oil spill site

Abstract: A two-dimensional, multispecies reactive solute transport model with sequential aerobic and anaerobic degradation processes was developed and tested. The model was used to study the field-scale solute transport and degradation processes at the Bemidji, Minnesota, crude oil spill site. The simulations included the biodegradation of volatile and nonvolatile fractions of dissolved organic carbon by aerobic processes, manganese and iron reduction, and methanogenesis. Model parameter estimates were constrained by published Monod kinetic parameters, theoretical yield estimates, and field biomass measurements. Despite the considerable uncertainty in the model parameter estimates, results of simulations reproduced the general features of the observed groundwater plume and the measured bacterial concentrations. In the simulation, 46% of the total dissolved organic carbon (TDOC) introduced into the aquifer was degraded. Aerobic degradation accounted for 40% of the TDOC degraded. Anaerobic processes accounted for the remaining 60% of degradation of TDOC: 5% by Mn reduction, 19% by Fe reduction, and 36% by methanogenesis. Thus anaerobic processes account for more than half of the removal of DOC at this site.

Temporal Moment-Generating Equations: Modeling Transport and Mass Transfer in Heterogeneous Aquifers

Abstract: We present an efficient method for determining temporal moments of concentration for a solute subject to first-order and diffusive mass transfer in steady velocity fields. The differential equations for the moments of all orders have the same form as the steady state nonreactive transport equation. Thus temporal moments can be calculated by a solute transport code that was written to simulate nonreactive steady state transport, even though the actual transport system is reactive and transient. Higher-order moments are found recursively from lower-order moments. For many cases a small number of moments sufficiently describe the movement of a solute plume. The first four moments describe the accumulated mass, mean, spread, and skewness of the concentration histories at all locations. Actual concentration histories at any location can be approximated from the moments by applying the principle of maximum entropy, a constraint consistent with the physical process of dispersion. The forms of the moment-generating equations for different mass transfer models provide insight into reactive transport through heterogeneous aquifers. For the mass transfer models we considered, the zeroth moment in a heterogeneous aquifer is independent of the mass transfer coefficients. Thus, if the velocity field is known, the mass transported past any point, or out any boundary, can be calculated without knowledge of the spatial pattern of mass transfer coefficients and, in fact, without knowledge of whether mass transfer is occurring. Also, for both first-order and diffusive mass transfer models, the mean arrival time depends on the distribution coefficient but is independent of the values of the rate coefficients, regardless of the spatial variability of groundwater velocity and mass transfer coefficients.

Dispersive Transport Dynamics in a Strongly Coupled Groundwater-Brine Flow System

Abstract: Many problems in subsurface hydrology involve the flow and transport of solutes that affect liquid density. When density variations are large (>5%), the flow and transport are strongly coupled. Density variations in excess of 20% occur in salt dome and bedded-salt formations which are currently being considered for radioactive waste repositories. The widely varying results of prior numerical simulation efforts of salt dome groundwater-brine flow problems have underscored the difficulty of solving strongly coupled flow and transport equations. We have implemented a standard model for hydrodynamic dispersion in our general purpose integral finite difference simulator, TOUGH2. The residual formulation used in TOUGH2 is efficient for the strongly coupled flow problem and allows the simulation to reach a verifiable steady state. We use the model to solve two classic coupled flow problems as verification. We then apply the model to a salt dome flow problem patterned after the conditions present at the Gorleben salt dome, Germany, a potential site for high-level nuclear waste disposal. Our transient simulations reveal the presence of two flow regimes: (1) recirculating and (2) swept forward. The flow dynamics are highly sensitive to the strength of molecular diffusion, with recirculating flows arising for large values of molecular diffusivity. For pure hydrodynamic dispersion with parameters approximating those at Gorleben, we find a swept-forward flow field at steady state rather than the recirculating flows found in previous investigations. The time to steady state is very sensitive to the initial conditions, with long time periods required to sweep out an initial brine pool in the lower region of the domain. Dimensional analysis is used to demonstrate the tendency toward brine recirculation. An analysis based on a dispersion timescale explains the observed long time to steady state when the initial condition has a brine pool in the lower part of the system. The nonlinearity of the equations and the competing effects of dispersion and gravity make this variable-density problem a challenge for any numerical simulation method.

Evaluation of 11 Equations for Determining Evaporation for a Small Lake in the North Central United States

Abstract: Eleven equations for calculating evaporation were compared with evaporation determined by the energy budget method for Williams Lake, Minnesota. Data were obtained from instruments on a raft, on land near the lake, and at a weather station 60 km south of the lake. The comparisons were based on monthly values for the open-water periods of 5 years, a total of 22 months. A modified DeBruin-Keijman, Priestley-Taylor, and a modified Penman equation resulted in monthly evaporation values that agreed most closely with energy budget values. To use these equations, net radiation, air temperature, wind speed, and relative humidity need to be measured near the lake. In addition, thermal surveys need to be made to determine change in heat stored in the lake. If data from distant climate stations are the only data available, and they include solar radiation, the Jensen-Haise and Makkink equations resulted in monthly evaporation values that agreed reasonably well with energy budget values.

Fluid Flow in Fault Zones: Analysis of the Interplay of Convective Circulation and Topographically Driven Groundwater Flow

Abstract: High-permeability faults, acting as preferential pathways for fluid migration, are important geological structures for fluid, energy, and solute transport. This paper examines the interaction of thermally driven convective circulation in a steeply dipping fault zone and groundwater flow through the surrounding country rock that is driven by a regional topographic gradient. We consider a geometry where a fault zone with a homogeneous, isotropic permeability is located beneath a narrow valley in a region with substantial topographic relief. System behavior is best characterized in terms of the large-scale permeabilities of the country rock and the fault zone. Using three-dimensional numerical simulations, we map in permeability space four fluid flow and heat transfer regimes within a fault zone: conductive, advective, steady convective, and unsteady convective. The patterns of fluid flow and/or heat transfer are substantially different in each of these regimes. Maximum discharge temperatures can also be plotted in permeability space; the maximum discharge temperature in the advective regime is in general lower than that in the steady convective regime. A higher basal heat flux expands the convective regime in permeability space, as does a greater fault depth. Higher topographic relief on the regional water table compresses the convective regime, with the advective regime suppressing convective circulation at lower country rock permeabilities. If convective cells with aspect ratios close to 1 cannot form, the steady convective regime is smaller in permeability space, and the boundary between steady and unsteady convection occurs at lower values of fault zone permeability. At low country rock permeabilities a water table gradient along the surface trace of the fault of approximately 0.3% suppresses convective cells; at higher country rock permeabilities, convection can be suppressed by smaller gradients on the water table.

New Results for Self-Similar Trees with Applications to River Networks

Abstract: In a little-known series of papers beginning in 1966, Tokunaga introduced an infinite class of tree graphs based on the Strahler ordering scheme. As recognized by Tokunaga (1984), these trees are characterized by a self-similarity property, so we will refer to them as self-similar trees, or SSTs. SSTs are defined in terms of a generator matrix which acts as a “blueprint” for constructing different trees. Many familiar tree constructions are absorbed as special cases. However, in Tokunaga's work an additional assumption is imposed which restricts from SSTs to a much smaller class. We will refer to this subclass as Tokunaga's trees. This paper presents several new and unifying results for SSTs. In particular, the conditions under which SSTs have well-defined Horton-Strahler stream ratios are given, as well as a general method for computing these ratios. It is also shown that the diameters of SSTs grow like mβ, where m is the number of leaves. In contrast to many other tree constructions, here β need not equal 1/2; thus SSTs offer an explanation for Hack's law. Finally, it is demonstrated that large discrepancies exist between the predictions of Shreve's well-known model and detailed measurements for large river networks, while other SSTs fit the data quite well. Other potential applications of the SST framework include diffusion-limited aggregation (DLA), lightning, bronchial passages, neural networks, and botanical trees.