Showing papers in "Water Resources Research in 1985"

Reservoir Management and Operations Models: A State‐of‐the‐Art Review

Abstract: The objective of this paper is to review the state-of-the-art of mathematical models developed for reservoir operations, including simulation. Algorithms and methods surveyed include linear programming (LP), dynamic programming (DP), nonliner programming (NLP), and simulation. A general overview is first presented. The historical development of each key model is critically reviewed. Conclusions and recommendations for future research are presented.

Modeling the Effects of Acid Deposition: Assessment of a Lumped Parameter Model of Soil Water and Streamwater Chemistry

Abstract: Quantitative predictions of the effects of acid deposition onterrestrial and aquatic systems require physically based, process-oriented models of catchment soil water and streamwater chemistry. A desirable characteristic of such models is that they include terms to describe the important phenomena controlling a system's chemical response to acidic deposition, yet be restricted in complexity so that they can be implemented on diverse systems with a minimum of a priori data. We present an assessment of a conceptual model of soil water and streamwater chemistry based on soil cation exchange, dissolution of aluminum hydroxide, and solution of carbon dioxide, all processes that occur in catchment soils and that have rapid equilibration times. The model is constructed using an “average” or lumped representation of these spatially distributed catchment processes. The adequacy of the model is assessed by applying it to 3 years of soil water and streamwater chemistry data from White Oak Run, Virginia, a second-order stream in the Shenandoah National Park. Soil properties predicted by the model are in good agreement with presently available measurements of those soil properties. The success of the model suggests that lumped representations of complex and spatially distributed chemical reactions in soils can efficiently describe the gross chemical behavior of whole catchments (e.g., pH, alkalinity, and major ionic concentrations in surface waters). Further assessment of the adequacy of this conceptual approach will require more detailed empirical knowledge of the soil processes being modeled, particularly soil cation exchange and the variability of soil CO2 partial pressures.

Validity of the local equilibrium assumption for modeling sorbing solute transport through homogeneous soils

Abstract: Sorption processes that occur during reactive solute movement through porous media can be modeled using either an equilibrium or kinetic approach. Because of the resulting conceptual and mathematical simplification, many transport models assume local chemical equilibrium is valid for describing sorption reactions. This paper presents quantitative criteria to assess the validity of the local equilibrium assumption for one-dimensional, steady flow through homogeneous soils. A method is described whereby formulas for solute breakthrough curve time moments can be determined without knowledge of the nalytical solution to the mass transport model. This method is applied to several commonly used nonequilibrium formulations as well as the standard linear equilibrium model. The formulations considered include both the physical nonequilibrium models where the sorption rate is controlled by diffusive solute transfer between mobile and stagnant fluid zones and the chemical nonequilibrium models where the overall sorption rate is governed by the rate of reaction at the soil-solution interfaces. Criteria for local equilibrium to be valid are derived by comparing the time moment formulas for the nonequilibrium and equilibrium models. These criteria explicitly show that basic system parameters (e.g., seepage velocity, dispersion coefficient, distribution coefficient, sorption rate, boundary conditions) have a significant influence on the attainment of local equilibrium.

Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 1. Statistically Isotropic Media

Abstract: Steady unsaturated flow with vertical mean infiltration through unbounded heterogeneous porous media is analyzed using a perturbation approximation of the stochastic flow equation which is solved by spectral representation techniques. The hydraulic conductivity K is related to the capillary pressure head ψ by K = Ks exp (−αψ), where Ks is the saturated conductivity, and α is a soil parameter. A general formulation is presented for the case with Ks and α represented as statistically homogeneous spatial random fields. In part 1, solutions are developed assuming α is constant and representing Ks variability by one-dimensional and three-dimensional isotropic random fields. Results are obtained for head variances and covariance functions, effective hydraulic conductivities, variances of the unsaturated hydraulic conductivity, flux variances, and variance of pressure gradient. When the parameter α is relatively large, corresponding to coarse textured soils, the head variance decreases and all of the results demonstrate a trend toward gravitationally dominated one-dimensional vertical flow. The effective conductivity is dependent on the correlation scale of ln Ks and the mean hydraulic gradient.

Analysis of the Spatial Structure of Properties of Selected Aquifers

Abstract: Data from 31 regional aquifers are analyzed to identify the horizontal spatial correlation structure of transmissivity, hydraulic conductivity, and storage coefficient. Three parameters are estimated: the variance of small-scale variability (or nugget) and the variance and integral scale (range) of an exponential covariance function. The assumption of normality of the aforementioned geohydrologic parameters and their logarithmic transformations is also examined. Results are obtained which indicate that the logarithms of these properties generally pass normality tests.

Downstream dilution of a lahar : transition from debris flow to hyperconcentrated streamflow.

Abstract: Nearly instantaneous melting of snow and ice by the March 19, 1982, eruption of Mount St. Helens released a 4 × 106 m3 flood of water from the crater that was converted to a lahar (volcanic debris flow) through erosion and incorporation of sediment by the time it reached the base of the volcano. Over the next 81 km that it traveled down the Toutle River, the flood wave was progressively diluted through several mechanisms. A transformation from debris flow to hyperconcentrated streamflow began to occur about 27 km downstream from the crater, when the total sediment concentration had decreased to about 78% by weight (57% by volume). The hyperconcentrated lahar-runout flood wave, transporting immense quantities of sand in suspension, continued to experience progressive downstream dilution. Although turbulence was significantly dampened by the extremely high suspended load, very large standing waves and antidune waves were observed. The hyperconcentrated lahar-runout flow deposited an unusual, faintly stratified, coarse sand which locally contained small, isolated gravel lenses. Very similar deposits in the Quaternary stratigraphy of Mount St. Helens and other Cascades volcanoes suggest that lahars may be more frequent than previously recognized.

Stochastic Optimization of a Multireservoir Hydroelectric System: A Decomposition Approach

Abstract: A computational scheme that is able to determined at each stage the most economical generation decision for each plant of a hydrothermal system is presented. The algorithm is based on the stochastic extension of Benders decomposition and can be implemented from already existing operation models. The results can be used in the weekly or monthly generation scheduling activities in real-time operation. A case study with 37 reservoirs of the Brazilian system is presented and discussed.

Regional Hydrologic Analysis: 1. Ordinary, Weighted, and Generalized Least Squares Compared

Abstract: Streamflow gaging networks provide hydrologic information which is often used to derive relationships between physiographic variables and Streamflow statistics. This paper compares the performance of ordinary, weighted, and generalized least squares estimators of the parameters of such regional hydrologic relationships in situations where the available Streamflow records at gaged sites can be of different and widely varying lengths and concurrent flows at different sites are cross-correlated. A Monte Carlo study illustrates the performance of an ordinary least squares (OLS) procedure and an operational generalized least squares (GLS) procedure which accounts for and directly estimates the precision of the predictive model being fit. The GLS procedure provided (1) more accurate parameter estimates, (2) better estimates of the accuracy with which the regression model's parameters were being estimated, and (3) almost unbiased estimates of the model error. The OLS approach can provide very distorted estimates of the model's predictive precision (model error) and the precision with which the regression model's parameters are being estimated. A weighted least squares procedure which neglects the cross correlations among concurrent flows does as well as the GLS procedure when the cross correlation among concurrent flows is relatively modest. The Monte Carlo examples also explore the value of Streamflow records of different lengths in regionalization studies.

A Multiphase Approach to the Modeling of Porous Media Contamination by Organic Compounds: 1. Equation Development

Abstract: A multiphase approach to the modeling of aquifer contamination by organic compounds is developed. This approach makes it possible to describe the simultaneous transport of a chemical contaminant in three physical forms: as a nonaqueous phase, as a soluble component of an aqueous phase, and as a mobile fraction of a gas phase. The contaminant may be composed of, at most, two distinct components, one of which may be volatile and slightly water soluble and the other of which is both nonvolatile and insoluble in water. Equations which describe this complex system are derived from basic conservation of mass principles by the application of volume averaging techniques and the incorporation of various constitutive relations and approximations. Effects of matrix and fluid compressibilities, gravity, phase composition, interphase mass exchange, capillarity, diffusion, and dispersion are all considered. The resulting mathematical model consists of a system of three nonlinear partial differential equations subject to two equilibrium constraints. These equations relate five unknowns: two capillary pressures and three mass fractions.

Exploration of a Rigid Ice Model of Frost Heave

Abstract: A numerical model is explored which simulates frost heave in saturated, granular, air-free, solute-free soil. It is based on equations developed from fundamental thermomechanical considerations and previous laboratory investigations. Although adequate data are lacking for strict experimental verification of the model, we note that simulations produce an overall course of events together with significant specific features which are familiar from laboratory experience. Simulated heave histories show proper sensitivities in the shapes and orders of magnitude of output responses and in the relations between crucial factors such as heave rate, freezing rate, and overburden.

A Comparison of Rainfall-Runoff Modeling Techniques on Small Upland Catchments

Abstract: This paper reports a set of model performance calculations for three event-based rainfall-runoff models on three data sets involving 269 events from small upland catchments. The models include a regression model, a unit hydrograph model, and a quasi-physically based model. The catchments are from the Washita River Experimental Watershed, Oklahoma; the Mahantango Creek Experimental Watershed, Pennsylvania; and the Hubbard Brook Experimental Forest, New Hampshire. Model performance was assessed for a verification period that is carefully distinguished from the calibration period. Performance assessment was carried out both in forecasting mode and in prediction mode. The results show surprisingly poor forecasting efficiencies for all models on all data sets. The unit hydrograph model and the quasi-physically based model have little forecasting power; the regression model is marginally better. The performance of the models in prediction mode is better. The regression model and the unit hydrograph model showed acceptable predictive power, but the quasi-physically based model produced acceptable predictions on only one of the three catchments. We believe that the primary barrier to the successful application of physically based models in the field lies in the scale problems that are associated with the unmeasurable spatial variability of rainfall and soil hydraulic properties. The fact that simpler, less data intensive models provided as good or better predictions than a physically based model is food for thought.

Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 2. Statistically Anisotropic Media With Variable α

Abstract: Steady unsaturated flow in heterogeneous soil with an arbitrarily oriented mean hydraulic gradient is analyzed using spectral solutions of the stochastic perturbation equation which describes the capillary pressure head ψ. The unsaturated hydraulic conductivity is related to ψ by K = Ks exp (−αψ), where Ks is the saturated hydraulic conductivity and α is a soil parameter, and both Ks and α are treated as three-dimensional statistically homogeneous, anisotropic random fields. Analytical results are obtained for the capillary pressure head variance and the effective (mean) unsaturated hydraulic conductivity. The head variance depends upon the degree of anisotropy of the ln Ks covariance; when α is random, the head variance increases with mean capillary pressure head. The effective hydraulic conductivity for arbitrary orientation of the mean hydraulic gradient J is shown to have tensorial properties, but its components depend on the magnitude and direction of J and the orientation of the stratification in the soil. When α is random, the degree of anisotropy of the effective conductivity depends strongly on mean capillary pressure.

Modeling the Effects of Acid Deposition: Estimation of Long‐Term Water Quality Responses in a Small Forested Catchment

Abstract: Research in recent years has led to conceptualizations of the long-term responses of catchment surface water quality to acidic deposition. That research has focused attention on certain soil processes as likely keys to catchment responses (anion retention, cation exchange, primary mineral weathering, aluminum dissolution, and CO2 solubility). We present a mathematical model which uses quantitative descriptions of these soil chemical processes to estimate the long-term chemical changes that occur in the soil, soil water, and surface waters of catchments in response to changes in atmospheric deposition. The model is applied to a small forested catchment in the Shenandoah National Park, Virginia. Historical changes in surface water quality are reconstructed for the catchment for the last 140 years. The model indicates that alkalinity of surface waters in the catchment may have been reduced by as much as 50%. Water quality is forecast for the catchment under three different scenarios of future changes in atmospheric deposition. The model indicates that all but very large reductions in deposition will result in further deterioration of the catchment water quality. The process-oriented, lumped-parameter approach used is consistent with all currently available observations of water quality in the catchment. Due to the lack of long-term records of catchment water quality, strict verification of the model estimates and an assessment of the model validity is problematic. This is the case for all models of long-terrn catchment chemical responses to acid deposition. Nonetheless, the model provides a means of integrating the results of individual process level laboratory and field studies. Used this way, the model becomes a vehicle for examining the interactions and long-term implications of our conceptualization of the acidification process.

A Multiphase Approach to the Modeling of Porous Media Contamination by Organic Compounds: 2. Numerical Simulation

Abstract: A system of equations, derived in part 1 of this paper, which describes the multiphase migration of an organic contaminant in the subsurface is presented. Although this system is not amenable to solution by analytical means, an approximate solution can be sought by a finite difference discretization of the governing equations. A one-dimensional, implicit numerical model is developed in this manner. To handle the solution of the resultant system of nonlinear algebraic equations, a Newton-Raphson iteration scheme is employed. In order to apply the finite difference model to a specific problem a number of parameters must be evaluated. These include three-phase relative permeabilities, saturation-pressure relations, partition coefficients, and mixture densities and viscosities. As a demonstration of the model's applicability, the migration of a two-component hydrocarbon mixture in a soil column is simulated. A mass balance is performed, and convergence of the iteration scheme as well as convergence of the difference scheme in space and time are examined heuristically.

Stochastic Modeling of Groundwater Flow by Unconditional and Conditional Probabilities: The Inverse Problem

Abstract: The inverse problem is defined here as follows: determine the transmissivity at varius points, given the shape and boundary of the aquifer and recharge intensity and given a set of measured log-transmissivity Y and head H values at a few points. The log-transmissivity distribution is regarded as a realization of a random function of normal and stationary unconditional probability density function (pdf). The solution of the inverse problem is the conditional normal pdf of Y, conditioned on measured H and Y, which is expressed in terms of the unconditional joint pdf of Y and H. The problem is reduced to determining the unconditional head-log-transmissivity covariance and head variogram for a selected Y covariance which depends on a few unknown parameters. This is achieved by solving a first-order approximation of the flow equations. The method is illustrated for an exponential Y covariance, and the effect of head and transmissivity measurements upon the reduction of uncertainty of Y is investigated systematically. It is shown that measurement of H has a lesser impact than those of Y, but a judicious combination may lead to significant reduction of the predicted variance of Y. Possible applications to real aquifers are outlined.

Brahmaputra River, Assam, India: Physiography, Basin Denudation, and Channel Aggradation

Abstract: The Brahmaputra River in Assam, India, characterized by high seasonal variability in flow, sediment transport, and channel configuration, experienced a secular period of aggradation from 1971 to 1979. The suspended load budget indicates an overall aggradation of the 607-km Assam reach of the Brahmaputra by about 16 cm during that period, with about 70% of the suspended sediment inflow into the reach being retained in the channel. Expressed as a percentage of the change in storage for the different reaches, computed errors due to sampling variability in sediment discharge generally lie within about 5–15% and do not appear to be large enough to affect the conclusions drawn from the suspended load budget. For a 145-km reach of the Brahmaputra, an alternative method based on measurement of channel cross sections suggests 21 cm of aggradation, somewhat more than estimated by the suspended load budget. Based on the suspended load carried by trans-Himalayan rivers, the present rate of denudation of the eastern Himalayas is estimated to be 73–157 cm/103 years. The average rate for the last 2–3 million years, estimated from the volume of alluvial fill in the Brahmaputra valley in Assam, the sediment yield of the Himalayan rivers, and assuming a total yield to deposition ratio of 1.4 (present study), is 3 cm/103 years. The current high rate of denudation of the Himalayas may be attributed mainly to the rapid uplift of the mountain system, recent earthquake activity, and high susceptibility of geologic formations to erosion by running water coupled with the effectiveness of the monsoon rainfall regime.

Generalized Scale Invariance in the Atmosphere and Fractal Models of Rain

Abstract: In recent years there has been considerable interest in stochastic rain models. By developing new ideas about scale invariance and intermittency we argue that the scope of such models can be greatly extended. The notions of scale invariance, intermittency, and the associated idea of fractal dimension have lately gained considerable ground, particularly in the context of extremely variable phenomena such as those found in the mesoscale and in hydrodynamic turbulence. We review some relevant work and argue that the atmosphere respects a symmetry principle that we call generalized scale invariance in which the statistical properties of the small and large scale are related to each other by a magnification coupled with a differential stratification (due to gravity) and differential rotation (due to the Coriolis force). We further argue that the extremely erratic (intermittent) nature of the atmosphere is characterized by scale invariant (fractal) measures leading to hyperbolic (fat-tailed) probability distributions of the fluctuations. The standard statistical methods based on exponential fall offs in both correlations and probability distributions are inappropriate when the variability is of this type. We show how both the scaling and intermittency may be exploited to develop extremely variable stochastic models of rain. Although the models examined here are the simplest of a family of extremely variable processes (depending on only two radar-determined parameters), they lead to realizations possessing many realistic features of the rainfield including complexity of form, clustering and bands at all scales, as well as differential stratification and rotation. Finally, we point to weaknesses in the models (in particular, their monodimensional nature) and suggest possible improvements.

A Model for Steady Fluid Flow in Random Three‐Dimensional Networks of Disc‐Shaped Fractures

Abstract: A model for steady fluid flow in three-dimensional, random networks of fractures has been developed. In this model the fractures are disc shaped discontinuities in an impermeable matrix. The fracture discs can be arbitrarily located within the rock volume and can have any desired distribution of aperture, radius orientation, and density. Thus where the disc model is appropriate it is possible to calculate flow through fracture networks which are statistically similar to those that occur in nature. After the boundary conditions and the desired fractures are specified, the intersections (nodes) between these discs (elements) are identified. Then steady flow through the network is calculated using a mixed analytical-numerical technique. In each fracture, analytic equations for flow into or out of each node as a function of the average head at each node are developed. The equations are based on image theory and the assumption that each node is a source (or sink) of uniform strength. A set of mass balance equations is constructed which equate flow into a node from one of its associated fractures to flow out of the node into the other associated fracture. These equations are solved for the average head at each node, and flux between fractures can then be calculated by substituting the average head values back into the analytical equations. The model has been successfully checked against analytical results for several cases of two and three intersecting fractures. We plan to use these techniques to measure the permeability of fracture networks.

Hydrologic Mechanisms Governing Fluid Flow in a Partially Saturated, Fractured, Porous Medium

Abstract: In contrast to the saturated zone within which fluid moves rapidly along fractures, the fractures (with apertures large relative to the size of matrix pores) will desaturate first during the drainage process, and the bulk of fluid flow would be through interconnected pores in the matrix. Within a partially drained fracture, the presence of a relatively continuous air phase will produce practically an infinite resistance to liquid flow in the direction parallel to the fracture. The residual liquid will be held by capillary force, in regions around fracture contact areas where the apertures are small. Normal to the fracture surfaces, the drained portion of the fractures will reduce the effective area for liquid flow from one matrix block to another matrix block. A general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions. Results are obtained from an aperture distribution model for fracture saturation, hydraulic conductivity, and effective matrix-fracture flow areas as functions of pressure. The effects of distortion of flow paths by the air pockets are taken into account by a phase-separation constriction factor in a generalized cubic law for fracture flow under a partially saturated condition. The reduction of matrix-fracture flow area is taken into account by summing the aperture distribution function to a saturation cutoff aperture, which is inversely proportional to the suction head. Drainage from a column of fractured tuff is simulated using available parameters for the densely welded tuff of the Topopah Spring Member at Yucca Mountain, southern Nevada. The column is bounded by discrete vertical fractures and dissected by horizontal fractures with the fracture spacings determined by the frequencies and orientations of fractured cores. The fraction of fracture surfaces with coatings is assumed to correspond to the fraction of in situ fracture contact area. The characteristic curves for the matrix are based on laboratory measurements of tuff samples. From the cases simulated for the fractured, porous columns with discrete vertical and horizontal fractures and porous matrix blocks explicitly taken into account, it is observed that the highly transient changes from fully saturated conditions to partially saturated conditions are extremely sensitive to the fracture properties. However, the quasi-steady changes of the fluid flow of a partially saturated, fractured, porous system could be approximately simulated without taking the fractures into account.

The Effect of Glaciers on Streamflow Variations

Abstract: The effect of temperate glaciers on runoff variations is examined for the North Cascade Mountains of Washington State. The principal influences of glaciers on streamflow are often unexpected contributions to streamflow volume, a delay of the maximum seasonal flow, and a decrease in annual and monthly variation of runoff. The delay of maximum flow is caused by temporary englacial storage of spring meltwater and by peak meltwater production occurring in midsummer. The englacial storage, for one case, is 54% of the potential May runoff. An algorithm is presented that calculates the coefficient of variation of runoff for any arbitrary glacier cover. The results suggest that a minimum in year-to-year variation occurs for basins about 36% glacierized. On a month-to-month basis, maximum variation occurs in July and August for basins with less than 10% glacier cover but is a minimum for basins with glacier covers greater than 30%.

A Groundwater Mass Transport and Equilibrium Chemistry Model for Multicomponent Systems

Abstract: A mass transport model, TRANQL, for a multicomponent solution system has been developed. The equilibrium interaction chemistry is posed independently of the mass transport equations which leads to a set of algebraic equations for the chemistry coupled to a set of differential equations for the mass transport. Significant equilibrium chemical reactions such as complexation, ion exchange, competitive adsorption, and dissociation of water may be included in TRANQL. Here, a finite element solution is presented first for cadmium, chloride, and bromide transport in a one-dimensional column where complexation and sorption are considered. Second, binary and ternary ion exchange are modeled and compared to the results of other investigators. Results show TRANQL to be a versatile multicomponent transport model, with potential for extension to a wide range of equilibrium reactions.

Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 3. Observations and Applications

Abstract: Results of stochastic theory for flow in heterogeneous soils are analyzed by comparisons with laboratory experiments and field observations, and through applications examples. The two key theoretical results are (1) the variability of capillary pressure or moisture content increases when mean capillary pressure increases and (2) the anisotropy ratio (horizontal/vertical) of effective (mean) unsaturated hydraulic conductivity increases when mean capillary pressure increases or mean moisture content decreases. Comparisons with the field data on moisture content and capillary pressure variability show trends similar to those predicted by the theory. Calculations of hydraulic conductivity anisotropy based on two actual soils show that the variations in soil texture produce large changes in anisotropy as the mean capillary pressure changes. Several previously reported field observations and laboratory experiments support the theoretical finding of a capillary pressure dependent hydraulic anisotropy for unsaturated flow. The importance of this anisotropy effect in applications involving groundwater recharge, irrigation, surface runoff generation, and waste isolation is discussed.

Kinematic Wave Approximation to Infiltration Into Soils With Sorbing Macropores

Abstract: Infiltration into soils with macropores is treated as two-domain flow The first domain is the soil matrix, in which water is subjected to capillarity, and infiltration is approached by Philip's sorptivity concept The second domain is the soil macropore system in which water moves only under gravity and flow is approached by kinematic wave theory A sink function with respect to flow in the macropore system accounts for water sorption by the soil matrix The two-domain flow model is then applied to infiltration into a block of undisturbed soil containing macropores

Transport of Immiscible Fluids Within and Below the Unsaturated Zone: A Numerical Model

Abstract: A numerical model is developed that describes the simultaneous flow of water and a second immiscible fluid under saturated and unsaturated conditions in porous media. The governing equations are a simplified subset of the three-phase flow equations commonly used in petroleum reservoir simulation. The simplification is analogous to that used to derive the Richard's equation for the flow of water in the unsaturated zone. The assumption that pressure gradients in the air phase are negligible leads to two partial differential equations. The proposed formulation is posed in terms of volumetric water saturation and fluid pressure in the immiscible fluid. The two-dimensional equations for flow in a vertical plane are approximated by finite differences. The fully implicit equations are solved by a direct matrix technique and Newton-Raphson iteration on nonlinear terms. The resulting numerical model is potentially applicable to many problems associated with immiscible contaminants in groundwater. Unfortunately, data such as relative permeabilities and capillary pressures for the types of fluids and porous materials present in hazardous waste sites are not readily available. As this type of data becomes available and field investigation techniques improve, applications of this type of model will become more practical. Examples are used to demonstrate themore » potential application of the model and sensitivity of results to fluid properties.« less

Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators

Abstract: Adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system. For groundwater flow systems, performance measures of interest include piezometric heads in the vicinity of a waste site, velocities or travel time in aquifers, and mass discharge to biosphere points. The parameters include recharge-discharge rates, prescribed boundary heads or fluxes, formation thicknesses, and hydraulic conductivities. The derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity. To calculate sensitivities, adjoint sensitivity equations are formulated from the equations describing the primary problem. The solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients. In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Alternatively, local velocity related performance measures are more sensitive to hydraulic conductivities.

The Effect of Timber Harvest on the Fool Creek Watershed, 30 Years Later

Abstract: The Fool Creek watershed at the Fraser Experimental Forest, Colorado was harvested using a pattern of alternating clearcut and forested strips in 1956. Today, with almost 30 years of postharvest record, subtle impacts on the hydrology of the watershed can be detected that were not significant in the past. In addition to the depositional increases in the snowpack in the openings, average peak water equivalent over the entire watershed has been increased (9%). Long-term, postharvest, climatic records now available show a strong correlation between estimated increases in flow and winter and melt period precipitation. Much of the annual variability in increased flow, now explained by precipitation, was formerly attributed to regrowth or time. Peak discharges, advanced 7.5 days following harvest, have also been increased 20%, with the largest effect occurring in the wettest years. Increases in peak water equivalent, annual flow, and date of peak flow occurrence all appear to be returning to preharvest levels at a very slow rate.

Shenandoah Watershed Study: Calibration of a Topography-Based, Variable Contributing Area Hydrological Model to a Small Forested Catchment

Abstract: The topography-based, variable contributing area model of catchment hydrology of K. J. Beven and E. F. Wood (1983) was adapted for continuous simulation and extended to take account of observed processes in White Oak Run, a small forested catchment in Shenandoah National Park, Virginia. Automatic calibration of the model was attempted using eight different objective functions. All objective functions were indifferent to many of the model parameters and thus parameter estimation could not be done reliably. On the basis of results from a regionalized sensitivity analysis, the original model structure was greatly simplified. The parameters of the simplified model, which produced fits to the measured data very nearly as good as did the more complex model, were estimated well using a sum of squared errors criterion.

Optimal urban water distribution design

Abstract: A heuristic linear programming-based procedure has been developed for the least cost layout and design of water distribution networks. The methodology is capable of analyzing a wide range of demand pattern and pipe failure combinations. Hydraulic consistency is ensured throughout the procedure through the use of the Hardy-Cross network solver technique. The procedure can also be extended for use in the expansion or reinforcement of existing network systems. While the techniques used to reduce the size of the constraint set to enable the procedure to handle a wide range of loading conditions do not guarantee global optimality, a pragmatic “reasonable” optimum is achieved. The method is demonstrated by application to the design of a new network and the expansion of an existing network. In the expansion of the existing network problem the solution obtained was less expensive than any previously published solution.

Sorting of Bed Load Sediment by Flow in Meander Bends

Abstract: Equilibrium sorting of coarse mobile bed load sediment in meander bends is considered. A theory of two-dimensional bed load transport of graded material, including the effects of gravity on lateral slopes and secondary currents, is developed. This theory is coupled with a simple treatment of flow in bends, an analytically determined bend shape, and the condition of continuity of each grain size range in transport to describe sorting. The theory indicates that the locus of coarse sediment shifts from the inside bank to the outside bank near the bend apex, as is observed.

Field Determination of the Three-Dimensional Hydraulic Conductivity Tensor of Anisotropic Media: 2. Methodology and Application to Fractured Rocks

Abstract: The analytical solutions developed in the first paper can be used to interpret the results of cross-hole tests conducted in anisotropic porous or fractured media. In the particular case where the injection and monitoring intervals are short relative to the distance between them, the test results can be analyzed graphically. From the transient variation of hydraulic head in a given monitoring interval, one can determine the directional hydraulic diffusivity, Kd(e)/Ss, and the quantity D/Ss, by curve matching. (Here Kd(e) is directional hydraulic conductivity parallel to the unit vector, e, pointing from the injection to the monitoring interval, Ss is specific storage, and D is the determinant of the hydraulic conductivity tensor, K.) The principal values and directions of K, together with Ss, can then be evaluated by fitting an ellipsoid to the square roots of the directional diffusivities. Ideally, six directional measurements are required. In practice, a larger number of measurements is often necessary to enable fitting an ellipsoid to the data by least squares. If the computed [Kd(e)/ss]½ values fluctuate so severely that a meaningful least squares fit is not possible, one has a direct indication that the subsurface does not behave as a uniform anisotropic medium on the scale of the test. Test results from a granitic rock near Oracle in southern Arizona are presented to illustrate how the method works for fractured rocks. At the site, the Oracle granite is shown to respond as a near-uniform, anisotropic medium, the hydraulic conductivity of which is strongly controlled by the orientations of major fracture sets. The cross-hole test results are shown to be consistent with the results of more than 100 single-hole packer tests conducted at the site.