bluuebunny/crossref_metadata_2025 huggingface dataset:
An eigenvalue numerical technique for solving unsteady linear groundwater models continuously in time
Authors: Sahuquillo Andrés
Published: February 2008

A procedure for solving the differential groundwater flow equation is presented herein. Using a finite difference or finite element discretization scheme, a set of simultaneous linear equations is obtained. The eigenvalues and eigenvectors of a matrix, which is a function of the coefficients of the set, are the key to the solution. A vector L is obtained straightforwardly by combining the eigenvector matrix A, the eigenvalue vector α, the pumping vector P, and the initial head vector H. Vector L, which depends on time, can be expressed simply and explicitly as a function of the eigenvalues. Piezometric heads can be obtained by combining A and L. L is the only vector that needs to be computed as P changes with time. In this way, influence functions of a piezometric head, flow velocity and flow depletion of a stream connected with the aquifer under a unit stress, can be obtained explicitly and continuously in time. The method can be applied to confined as well as to leaky aquifers and to one‐, two‐, or three‐ dimensional linear models. Its main advantage lies in the fact that it is unnecessary to repeatedly solve a matrix for every time increment. The method is particularly useful for groundwater management problems in which a large number of alternatives have to be evaluated.
Heat transfer in fractured geothermal reservoirs with boiling
Authors: Pruess Karsten
Published: February 2008

Analytical and numerical techniques are used to study nonisothermal flow of water and steam in idealized fractured porous media. We find that heat conduction in the rock matrix can substantially alter the flowing enthalpy in the fractures. Effects of matrix permeability and fracture spacing are demonstrated for production from and injection into vapor‐dominated and liquid‐dominated geothermal reservoirs.
Aquifer parameter identification with kriging and optimum parameterization
Authors: Yeh William W‐G. , Yoon Young S. , Lee K. S.
Published: February 2008

A new parameter identification method is developed for a two‐dimensional, unsteady state groundwater flow model. The method is a direct approach, as it requires no iterative searching of parameters. The unknown functional coefficients (parameters) are optimally determined by a generalized matrix inversion scheme. Kriging, an unbiased minimum variance estimator, is used as a presampling filter to reconstruct the head distribution for the entire flow domain. The ill‐posedness of the inverse problem as characterized by instability and nonuniqueness is controlled by reparameterization utilizing the technique of finite elements. A set of statistics are developed to quantify explicitly the tradeoff between the system modeling error and the error associated with the parameter uncertainty. These two types of errors are shown to be a function of the parameter dimension. Residual mean square and trace of the covariance matrix of the estimated parameters serve as good indicators for the determination of the optimum parameter dimension. A set of numerical experiments are conducted to illustrate the methodology.
Temperature distribution around a well during thermal injection and a graphical technique for evaluating aquifer thermal properties
Authors: Chen Chia‐Shyun , Reddell Donald L.
Published: February 2008

Analytical solutions of temperature distribution are developed for the problem of thermal injection into a confined aquifer with a caprock of finite thickness. Heat transfer by horizontal conduction and convection within the aquifer and by vertical conduction in the caprock and bedrock is considered. Steady state and two asymptotic unsteady state solutions of temperature distribution around a thermal injection well are determined. One unsteady state solution is for short time periods and the other is for long time periods. The caprock thickness is only important in the long time period solution. A graphical technique is presented using hypothetical data for evaluationg four pertinent aquifer thermal properties: (1) the horizontal thermal conductivity of the aquifer, (2) the thermal capacity of the aquifer, (3) the vertical thermal conductivity of the caprock, and (4) the thermal capacity of the caprock. Field measurements of aquifer temperatures near the steady state condition are theoretically needed to utilize the graphical technique. In many practical situations a long time period is required to achieve a steady state condition. Therefore, a modified graphical technique employing an unsteady temperature distribution is illustrated and can be used to estimate the horizontal thermal conductivity and aquifer thermal capacity.
A simplified semiempirical approach to probabilities of extreme hydrologic droughts
Authors: Güven Oktay
Published: February 2008

On the basis of an available theory approximately valid for stationary first‐order two‐state Markovian processes and an assumption that the distribution of drought severity is approximately two‐parameter gamma, a semiempirical method is proposed for the estimation of the probabilities of extreme drought durations and severities which may occur in the annual flow sequence of a stream during a period of finite length. The method is applied to the annual flows of eight streams in various parts of the world, and the semiempirical probability distributions obtained using this method are compared with experimental distributions obtained using synthetic streamflows generated with a lag one Markov model as well as a long‐memory broken line model. The comparisons suggest that considerable insight into the extreme drought probabilities can be gained by the use of the simple semiempirical method introduced here.
Wave speed–discharge relations in natural channels
Authors: Wong Tony H. F. , Laurenson Eric M.
Published: February 2008

Empirical studies of wave speed for six Australian river reaches show that wave speed at first increases quickly with discharge, then decreases quickly, and finally increases slowly. The increasing parts of the relation can be fitted by power functions with exponents less than unity. Minimum wave speed occurs close to bank‐full discharge. These results have a direct application to storage‐discharge relations and important implications in flood routing and runoff routing.

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An efficient finite element technique for modeling transport in fractured porous media: 1. Single species transport
Authors: Huyakorn Peter S. , Lester Barry H. , Mercer James W.
Published: February 2008

A mathematical model is presented for numerical simulation of solute transport in naturally fractured porous media. The model is based on the dual‐porosity conceptual approach and is capable of simulating interactions between porous rock matrix and fractures. Unlike earlier dual‐porosity transport models, which rely on parallel fracture assumptions, the present model is a unified model that is also able to represent blocky fractured systems (i.e., systems with suborthogonal fractures) by using a spherical idealization of matrix blocks. Two governing, partial differential equations are written for solute transport in the fractures and diffusion in the porous matrix blocks. These equations are coupled by mass flux terms (leakages). An efficient numerical scheme is presented for approximating the governing transport equations. The scheme effectively combines a two‐dimensional, upstream‐weighted, finite‐element approximation for transport in the fractures with a one‐dimensional Galerkin approximation for diffusion within the individual matrix blocks. Coupling of the two approximations is performed implicitly. The systems of algebraic equations resulting from both finite‐element approximations are solved by using sequential solution algorithms designed especially for this type of problem. Stability and accuracy of the numerical scheme are checked by applying the model to a number of test problems and comparing results with available analytical solutions. In all cases the numerical scheme is found to be highly stable and capable of producing reliable results with the use of relatively coarse spatial and temporal discretizations. Finally, the utility of the model is demonstrated by applying it to a hypothetical, yet realistic, problem.
Finite element techniques for modeling groundwater flow in fractured aquifers
Authors: Huyakorn Peter S. , Lester Barry H. , Faust Charles R.
Published: February 2008

A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual‐porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual‐porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one‐dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element‐convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture‐matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models.
A Bayesian Markov Model of the flood forecast process
Authors: Krzysztofowicz Roman
Published: February 2008

A flood forecast process with a discrete time index k is defined as {i(k), h(k)}, where i denotes the current flood level and h denotes the forecasted flood crest. It is a finite, random duration process with the actual flood crest hh being its terminal state: {hh | i(k) h(k)}. This process is modeled as a two‐branch Markov chain. Nonstationary transition probability functions are obtained from a Bayesian information processor which can be imbedded in a dynamic programing algorithm that solves an ensuing Markovian decision problem. The lead time and the processing time of the forecasts are represented by their certainty equivalents. The structure of the model is motivated by an analysis of historical flood forecast records. Methods of estimation of the prior probability and likelihood functions are described. The model is intended primarily as a component of a decision methodology for determining the economic value of and the optimal decisions in response to riverine flood forecasts.
Cascade Model of Monthly Municipal Water Use
Authors: Maidment David R. , Parzen Emanuel
Published: February 2008

A time series model of monthly municipal water use is formulated as a set of equations representing the effects of four factors on water use: trend, seasonality, autocorrelation, and climatic correlation. The parameters of these equations are found by passing the water use time series through a cascade of four transformations; in each transformation the parameters of an equation associated with one factor are statistically determined and the series transformed to remove the effects of this factor. After the last transformation, only a random error series remains. Monthly municipal water use at Canyon, Texas, from 1961–1978 is modeled as an example. The model explains 86% of the variance of this series, divided among the four factors as trend (29%), seasonality (44%), autocorrelation (2%), and climatic correlation (11%). The random error is shown to be normally distributed by a nonparametric procedure characterizing probability families by their density quantile functions.
Extremal Hypotheses for River Regime: An Illusion of Progress
Authors: Griffiths George A.
Published: February 2008

The extremal hypotheses of minimum stream power, minimum unit stream power, minimum energy dissipation rate, and maximum sediment transport rate, when combined with conventional sediment transport and flow resistance equations, lead to conclusions incompatible with observations. For wide, straight, unconstrained alluvial reaches in equilibrium, these conclusions include that the Einstein sediment discharge and Shields entrainment function are nearly constant, the magnitude of the particular constants depending only on the hypothesis and equations used, whereas data from flumes and natural rivers show that both expressions are highly variable in stable channels. Constancy of the Einstein and Shields expressions provides, in fact, a sufficient but unnecessary condition for channel stability. In the maximum friction factor hypothesis there is no maximum for friction factor when channel width, depth, and slope are dependent variables. Variational principles may one day supply a solution to the problem of alluvial channel stability, but current formulations of the mentioned hypotheses require redefinition.
Acid Mine Drainage From Reclaimed Coal Strip Mines 1. Model Description
Authors: Jaynes D. B. , Rogowski A. S. , Pionke H. B.
Published: February 2008

A model describing the long‐term oxidation of pyrite and the removal of reaction products from reclaimed coal strip mines is presented. Both direct‐oxygen and ferric iron oxidation of pyrite are considered. The pyrite oxidation rate is assumed to be controlled by first‐order, solid‐liquid kinetics and the rate of simple diffusion of oxidant into reactive, coarse, stone fragments. The oxygen supply into the reclaimed profile is considered to be governed by one‐dimensional gas diffusion. Ferric iron is produced by both purely chemical and bacterial oxidation of ferrous iron. Activity of the iron‐oxidizing bacteria is controlled by the energy available from ferrous oxidation, as measured by the ferric/ferrous ratio, and from a combination of potentially inhibiting factors: the oxygen concentration in the spoil air, the hydrogen ion concentration in solution, and the spoil temperature. Bacterial activity and pyrite oxidation are linked through a shared environment. The side reactions considered include the complexation and precipitation of ferric iron and the interaction between hydrogen ion in solution and the spoil matrix. Soluble reaction products are removed from the reclaimed profile by percolating water.
Guidelines for Improved Institutional Analysis in Water Resources Planning
Authors: Ingram Helen M. , Mann Dean E. , Weatherford Gary D. , Cortner Hanna J.
Published: February 2008

Institutional factors are often among the most formidable obstacles to the development and implementation of feasible water resource programs. Guidelines for gathering and analyzing information on institutional factors as part of water resource planning and evaluation activities are presented. In approaching the analysis of current institutional arrangements, analysts should pay particular attention to (1) the actors and their stakes in the decision‐making process; (2) the political and decision making resources actors have available to pursue their interests and (3) the biases of the alternative decision‐making structures through which various water resource decisions are made. While institutional analysis can pinpoint important barriers and constraints to plan implementation, it is of most use when it goes beyond a description and analysis of current institutional arrangements to assess possible strategies and solutions that can be applied to the problems identified.
Describing the Transport of Ion‐Exchanging Contaminants Using an Effective Kd Approach
Authors: Valocchi Albert J.
Published: February 2008

Hydrogeologists have traditionally used distribution coefficients Kd to describe the rate of migration of sorbing contaminants. Recent investigations have questioned the validity of the Kd approach for contaminants governed by multicomponent ion exchange and have noted that computed Kd values in such cases are not constant across an advancing solute front. This report demonstrates that mass balance arguments can nevertheless be utilized to define a constant “effective” Kd which may then be used to calculate the contaminant front velocity. For selected cases of one‐dimensional binary and ternary exchange, front locations calculated using the effective Kd approach agree closely with concentration profiles calculated using a general numerical simulation model of ion‐exchanging solute transport. The effective Kd approach is also applied to a field problem involving the injection of advanced‐treated municipal effluent into a shallow confined aquifer. Although the effective Kd approach is sometimes a practically useful tool, it is shown to be limited to situations where dispersion can be neglected.
Stratigraphic Evidence of Eutrophication in an Estuary
Authors: Brush Grace S.
Published: February 2008

Vertical changes in chlorophyll degradation products preserved in sediments deposited in an urban estuary show a significant increase in algal productivity with the introduction of sewage effluent into the river. By comparison, algal production during intensive agriculture of the watershed, including heavy applications of fertilizers, was less by an order of magnitude where there was no sewage discharge from a point source. Concentrations of orthophosphorus correspond with concentrations of algal cells and chlorophyll in the water column and are greater by an order of magnitude where sewage is discharged into an estuary draining an urban‐agricultural watershed than where there is no sewage. The response of the estuary to short‐ and long‐term changes in the amount of sewage discharged is reflected by similar changes in chlorophyll production. However, chlorophyll production does not correspond with increases in the amount of fertilizers used in recent years over the amount used in the middle to late nineteenth century.
Wetting Front Analysis of the Nonlinear Diffusion Equation
Authors: Parlange J.‐Y. , Lisle I. G. , Prasad S. N. , Römkens M. J. M.
Published: February 2008

A perturbation procedure for the solution of the nonlinear diffusion equation is presented, which yields water content as a function of the distance to the wetting front. The result is in agreement with earlier predictions of wetting front position and sorptivity using an optimal technique.
Buoyant Contaminant Plumes in Groundwater
Authors: Paschke Ned W. , Hoopes John A.
Published: February 2008

Buoyant contaminant groundwater plumes occur when liquid wastes which have densities different from groundwater are released from various land disposal activities (e.g., landfills, infiltration lagoons, injection wells). By using mass and momentum conservation equations, an analytical model for plume characteristics and behavior (namely, trajectory, concentration, and boundary) is developed for steady flow in a homogeneous, isotropic aquifer. The model predicts that plume behavior and characteristics are different close to the source from those far from the source. Solutions of the model yield dimensionless relations for the plume characteristics and behavior in each region in terms of length and concentration scales representing the combined effects of the source buoyancy flux and size and the ambient groundwater flow and dispersion. Experimental results, from a series of tests in a homogeneous, isotropic sand medium with a salt water discharge, are in reasonable agreement with model predictions. The model results have application to field problems under similar conditions.
Scales for Double‐Diffusive Fingering in Porous Media
Authors: Green Theodore
Published: February 2008

The influence of the double‐diffusive process of fingering on vertical transport in a porous medium is examined, using a very successful model borrowed from oceanic salt finger theory. The results suggest that fluxes associated with double‐diffusive fingering may well be important, at least in regions where the porous medium is saturated. The effect of horizontal dispersion remains to be accounted for and will probably place limits on the efficiency of the process.
Unsteady Shallow Groundwater Flow Over a Curved Impermeable Boundary
Authors: Chapman Tom G. , Dressler Robert F.
Published: February 2008

The asymptotic method which produced the new Dressler equation for curved open channel hydraulic flow is employed here to obtain analogous equations for unsteady, two‐dimensional, free surface groundwater flow over an arbitrarily curved bed. The result is a pair of partial differential equations: the first linear, stemming from Darcy's Law, and the second nonlinear, expressing mass conservation. The hydraulic conductivity and porosity can be functions of position. The flow component above and parallel to the bed behaves as a vortex in the small with centrifugal acceleration but with no centrifugal term in the pressure. For the special case of a plane sloping bed our equations reduce to the Wooding‐Chapman extension of the Dupuit‐Forchheimer equations. Our two‐dimensional flow equations are generalized to a special case of a nonisotropic medium and to include the effect of a variable recharge rate. All the systems are parabolic, thus describing diffusion, and can be integrated numerically as readily as the simpler equations for plane beds.
Scale considerations in the modeling of temporal rainfall
Authors: Rodriguez‐Iturbe Ignacio , Gupta Vijay K. , Waymire Ed
Published: February 2008

Observations on temporal rainfall are invariably taken in cumulative amounts over disjoint intervals representing different time scales such as hours, days, etc. At these scales a mathematical description of the rainfall process is shown to depend on the scale of measurements. This illustration is carried out employing three stochastic models having different dependence structures which range from complete independence and Markovian dependence to non‐Markovian clustering dependence. The problem of estimating the model parameters is also shown to be tied to the scale of measurements. Hourly and daily rainfall data from Denver, Colorado, and daily rainfall data from Agua Fria, Venezuela, are employed for this illustration.
A conceptual model of deep unsaturated zones with negligible recharge
Authors: Ross Benjamin
Published: February 2008

When net recharge is less than about 0.03 mm/yr, moisture movement in deep unsaturated zones at steady state will be dominated by upward movement of vapor driven by the geothermal gradient. With zero net recharge there will be a downward flow of liquid water equal to the upward vapor flux. This will produce a profile of suction potential versus depth qualitatively similar to that expected if recharge is not negligible. Consequently, the existence of a region of uniform potential is not in itself evidence of recharge.
A finite element dual mesh method to calculate Nodal Darcy velocities in nonhomogeneous and anisotropic aquifers
Authors: Batu Vedat
Published: February 2008

A finite element dual mesh method is developed to calculate the horizontal and vertical Darcy velocity components in a highly nonhomogeneous and anisotropic aquifer of constant porosity under steady flow conditions. The finite element method is used to calculate the total head distribution. The finite difference forms of the total head gradients are used to calculate the Darcy velocity components. It is shown that the dual mesh method is suitable for calculating the nodal Darcy velocities with acceptable accuracy. The continuity principle is satisfied to an acceptable degree. The results are compared with an analytical solution, and the agreement is excellent. The results are also compared with another method proposed by Gureghian (1981) and Yeh (1981), and it is observed that the agreement is reasonably good. The dual mesh method can be applied to any nonhomogeneous and anisotropic porous medium to calculate the nodal Darcy velocities.
Interactions of solutes and streambed sediment: 1. An experimental analysis of cation and anion transport in a mountain stream
Authors: Bencala Kenneth E. , Kennedy Vance C. , Zellweger Gary W. , Jackman Alan P. , Avanzino Ronald J.
Published: February 2008

An experimental injection was performed to study the transport of stream water solutes under conditions of significant interaction with streambed sediments in a mountain pool‐and‐riffle stream. Experiments were conducted in Little Lost Man Creek, Humboldt County, California, in a period of low flow duringwhich only a part of the bank‐full channel held active surface flow. The injection of chloride and several trace cations lasted 20 days. In this report we discuss the results of the first 24 hours of the injection and survey the results of the first 10 days. Solute‐streambed interactions of two types were observed. First, the physical transport of the conservative tracer, chloride, was affected by intergravel flow and stagnant watt, zones created by the bed relief. Second, the transport of the cations (strontium, potassium, and lithium) was appreciably modified by sorption onto streambed sediment. In the stream the readily observable consequence of the solute‐streambed interactions was an attenuation of the dissolved concentration of each of the tracers. The attenuation in the stream channel occurred concurrently with the storage of tracers in the streambed via both physical and chemical processes. All tracers were subsequently present in shallow wells dug several meters from the wetted part of the channel. Sediment samples collected approximately 3 weeks after the start of the injection contained increased concentrations of the injected cations.
Stochastic Modeling of Groundwater Flow by Unconditional and Conditional Probabilities: The Inverse Problem
Authors: Dagan Gedeon
Published: February 2008

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.
Analysis of River Wave Types
Authors: Ferrick Michael G.
Published: February 2008

In this paper we consider long‐period, shallow‐water waves in rivers that are a consequence of unsteady flow. River waves result from hydroelectric power generation or flow control at a dam, the breach of a dam, the formation or release of an ice jam, and rainfall‐runoff processes. The Saint‐Venant equations are generally used to describe river waves. Dynamic, gravity, diffusion, and kinematic river waves have been defined, each corresponding to different forms of the momentum equation and each applying to some subset of the overall range of river hydraulic properties and time scales of wave motion. However, the parameter ranges corresponding to each wave description are not well defined, and the transitions between wave types have not been explored. This paper is an investigation into these areas, which are fundamental to river wave modeling. The analysis is based on the concept that river wave behavior is determined by the balance between friction and inertia. The Saint‐Venant equations are combined to form a system equation that is written in dimensionless form. The dominant terms of the system equation change with the relative magnitudes of a group of dimensionless scaling parameters that quantify the friction‐inertia balance. These scaling parameters are continuous, indicating that the various river wave types and the transitions between them form a spectrum. Additional data describing the physical variability of a river and wave are incorporated into the analysis by interpreting the scaling parameters as random variables. This probabilistic interpretation provides an improved estimate of the friction‐inertia balance, further insight into the continuous nature of wave transitions, and a measure of the reliability of wave type assessments near a transition. Case studies are used to define the scaling parameter ranges representing each wave type and transition and to provide data with which to evaluate the usefulness of the analysis for general application.
An Ice Jam Prediction Model as a Tool in Floodplain Management
Authors: Barnes‐Svarney Patricia L. , Montz Burrell E.
Published: February 2008

Currently, ice jam flooding does not enter into consideration of floodplain designation or flood hazard management in areas experiencing irregular occurrences of ice jams, except as a reaction to past events. Therefore it is important to test prediction techniques for their application to this problem. One such model is the Wiener Filtering technique which is used to correlate the occurrence of ice jams with climatological data for Conklin, New York. It is postulated that ice jam events are directly related to seasonal precipitation, snowfall, temperature, and temperature fluctuations. Monthly and 15‐day averages of these variables are correlated using the Wiener Filtering model. The results of these preliminary analyses show that in Conklin, New York, different combinations of climatological data with past ice jam occurrence appear to show promise in predicting ice jam events. Further study is needed to test the significance and reliability of this prediction model.
Estimating Nonpotential Evapotranspiration by Means of the Equilibrium Evaporation Concept
Authors: Mawdsley J. A. , Ali M. F.
Published: February 2008

Equilibrium evaporation was first described by Slatyer and McIlroy (1961). Priestley and Taylor (1972) later developed an equation which used the concept to estimate potential evapotranspiration. Subsequently, their equation has been widely tested with some success. Both Priestley and Taylor and soon after Davies and Allen (1973) extended the concept still further to estimate nonpotential evapotranspiration. We have further modified and developed these ideas so that the model can be applied using only regularly recorded data. We fitted the model and then tested it using three data sets from the United Kingdom: one planted with barley, one with turf, and one with rye grass. The results demonstrate, as one might expect, that the model does not provide a full description of nonpotential evapotranspiration, but this does not mean that the model may not be useful in applied hydrology. To assess the model's potential in this respect we compared the results with those obtained from the Penman‐Grindley model, a model widely applied in the United Kingdom at least. This comparison suggests that despite the model's deficiencies it should still prove useful in climates similar to the United Kingdom, and with further testing, in all climates.
The Collection of Fog Drip
Authors: Goodman Jindra
Published: February 2008

Fog and low stratus clouds are the dominant climatic feature along the central California coastline during the summer months. This moisture source is not only a critical feature in the local hydrologic cycle, but may prove to be a valuable source for augmenting the water supplies. During the summer of 1982 an experiment was conducted to examine the relative efficiency of two man‐made fog collection systems, the harp and cylinder. The systems were designed to maximize the collection of water droplets on vertically strung wires. The systems collected a rain gauge equivalent of between 25.2 and 80.4 cm/unit vertical area as compared to the mean annual rainfall of 60 cm.
A Stochastic Model of Dimensionless Thunderstorm Rainfall
Authors: Woolhiser D. A. , Osborn H. B.
Published: February 2008

A concise stochastic model for the nondimensional thunderstorm rainfall process at a point is proposed. The accumulated precipitation process for individual thunderstorms is nondimensionalized by dividing the precipitation at any time by the total precipitation and the elapsed time by the total duration. The dimensionless process is divided into 100 equal time increments, and the depth increments are rescaled to range between 0 and 1. The sequence of rescaled increments Z1, Z2,…, Z9 are assumed to represent a nonhomogeneous Markov process in discrete time with continuous state space. The expected value of the kth rescaled increment, given the k‐1st increment, is assumed to be a linear function of that increment, and the marginal distribution of the first increment and the conditional distributions are assumed to be described by the beta distribution. An analyses of data for 275 thunderstorms observed at the Walnut Gulch Experimental Watershed in southeastern Arizona showed that the proposed model structure is a good approximation for this region. The number of model parameters can be reduced from 26 to a minimum of 10 by approximating the 2 parameters in the conditional expectation function and the conditional beta parameter as polynomial functions of the dimensionless time. Likelihood ratio tests and the Akaike information criterion suggest that the dependence parameters are independent of storm amount and duration, but the conditional beta parameter αk is larger for short‐duration storms than for long‐duration storms. A 13‐parameter model is recommended for disaggregating thunderstorm rainfall in southeastern Arizona.
Transport of Immiscible Fluids Within and Below the Unsaturated Zone: A Numerical Model
Authors: Faust Charles R.
Published: February 2008

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 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 the potential application of the model and the sensitivity of results to fluid properties.
Runoff from glacierized mountains: A model for annual variation and its forecasting
Authors: Ferguson R. I.
Published: February 2008

The only practical means of forecasting spring and summer runoff in remote high mountain basins such as the upper Indus in Pakistan is from preseason snow cover on satellite images. Previous studies have shown that regression coefficients of runoff on snow cover differ between basins in magnitude and sign. A conceptual analysis explains this, identifies the glaciological and snowpack variables that control annual variation in meltwater runoff, and forms the basis of a parametric forecasting model that is successfully applied to contrasting tributaries of the upper Indus, despite very crude parameter values. It incorporates the uncertainty due to possible nonaverage summer weather. Suggestions are made about additional remote sensing and ground reconnaissance investigations that could improve forecasting capability in this and similar regions.
Numerical calculation of saturated‐unsaturated infiltration in a cracked soil
Authors: Davidson Malcolm R.
Published: February 2008

Two‐dimensional infiltration in a soil containing regularly spaced, water‐filled, vertical cracks is determined by a finite difference numerical solution of the saturated‐unsaturated flow equations for selected soil hydraulic characteristics. The equivalent Green‐Ampt model gives results which correspond well with finite difference solutions. Differences in cumulative infiltration and infiltration rates, expressed as percentages of the corresponding finite difference results, typically vary up to about 4%. When the crack spacing‐depth ratio and the magnitude of the moisture potential at the wetting front are both small, calculations predict that wetted tongues moving away from adjacent cracks interact to temporarily enclose an unwetted pocket, an event coinciding with a sudden drop in the infiltration rate and the breakdown of the corresponding Green‐Ampt calculation.
Unit hydrograph approximations assuming linear flow through topologically random channel networks
Authors: Troutman Brent M. , Karlinger Michael R.
Published: February 2008

The instantaneous unit Hydrograph (IUH) of a drainage basin is derived in terms of fundamental basin characteristics (Z, α, β), where α parameterizes the link (channel segment) length distribution, and β is a vector of hydraulic parameters, Z is one of three basin topological properties, N, (N, D), or (N, M), where N is magnitude (number of first‐order streams), D is diameter (mainstream length), and M is order. The IUH is derived based on assumptions that the links are independent and identically distributed random variables and that the network is a member of a topologically random population. Linear routing schemes, including translation, diffusion, and general linear routing are used, and constant drainage density is assumed. By using (N, α, β) as the fundamental basin characteristics, asymptotic (for large N) considerations lead to a Weibull probability density function for the IUH, with time to peak given by tp = (2N)½ α*/β* where α* is mean link length, and β* is a scalar hydraulic parameter (usually average celerity). This asymptotic IUH is identical for all linear routing schemes.
Analysis of Some Laboratory Tracer Runs in Natural Fissures
Authors: Moreno Luis , Neretnieks Ivars , Eriksen Tryggve
Published: February 2008

Tracer tests in natural fissures performed in the laboratory are analyzed by means of fitting two different models. In the experiments, sorbing and nonsorbing tracers were injected into a natural fissure running parallel to the axis of a drill core. The models take into account advection, dispersion, diffusion into the rock matrix, and sorption onto the surface of the fissure and on the microfissures inside the matrix. For the second mechanism, one of the models considers hydrodynamic dispersion, while the other model assumes channeling dispersion. The models take into account time delays in the inlet and outlet channels. The dispersion characteristics and water residence time were determined from the experiments with nonsorbing tracers. Surface and volume sorption coefficients and data on diffusion into the rock matrix were determined for the sorbing tracers. The results are compared with values independently determined in the laboratory. Good agreement was obtained using either model. When these models are used for prediction of tracer transport over larger distances, the results will depend on the model. The model with channeling dispersion will show a greater dispersion than the model with hydrodynamic dispersion, assuming constant dispersivity.
Transient Movement and Transformation of Carbon Species in Soil During Wastewater Application
Authors: Angelakis A. N. , Rolston D. E.
Published: February 2008

The transport and transformation of three C species (insoluble, soluble, and gaseous) in soil were mathematically described as functions of depth and time, subject to intervals of 0 <t≤t1 andt1<t≤tmax, where t1 refers to time of application of insoluble and/or soluble C. Convective and convective‐dispersive transport for the first and second C species, respectively, gas diffusion for the third species, and first‐order kinetics as a tranformational mechanism were assumed. Linear adsorption isotherms for the first two species and a constant gas solubility were also assumed. Combined analytical and numerical solutions of three coupled partial differential equations were developed. The numerical model was used to study the microbial mineralization of organic C transformed under a biophasic scheme by applying a primary wastewater effluent to topsoil columns. Distribution of insoluble C concentrations were accurately predicted, particularly at large times. On the other hand, soluble C profiles were more accurately predicted at early times and shallow depths than for t>t1 and large depths. Fitted gaseous diffusion coefficients were required to describe the measured CO2 profiles instead of those measured in the top of the soil columns. Gaseous C profiles were accurately predicted, especially at early times and shallow depths.
Scaling Limits and Self‐Similarity in Precipitation Fields
Authors: Waymire Ed
Published: February 2008

It has been recognized in the literature on rainfall models in hydrology that the exact calculations of probabilities for models which incorporate cluster structure is typically not possible. Consequently, one is led to considerations of limiting approximations. However, because of the presence of dependencies and/or fat tails in several of the current models, the nature of the approximations involves some important issues for both theoretical as well as experimental consideration in precipitation research. The objective of the present paper is to systematically describe these issues as they pertain to rainfall models. Some specific large‐scale approximations are given for models of the type currently in the literature.
Effect of Salinity and Ionic Composition on Evaporation: Analysis of Dead Sea Evaporation Pans
Authors: Salhotra Atul M. , Adams E. Eric , Harleman Donald R. F.
Published: February 2008

Data from eight evaporation pans containing brines of different salinity and ionic composition were analyzed to quantify the effect of salinity on evaporation. The common procedure of correcting fresh water evaporation by an empirical ratio (α) of salt water to fresh water evaporation rates is shown to be only approximate. A more accurate approach based on the effect of salinity on saturation vapor pressure is described. The activity coefficient of water (β) was computed based on the pan evaporation data. Various analytical methods to compute the effect of salinity on saturation vapor pressure based on ionic composition of the solution are described and applied with Dead Sea data. These approaches can be applied in many engineering applications including water balance calculations for saline lakes, salt production ponds, and evaporation ponds used for disposal of saline effluents.
Asymptotic Behavior of Infiltration in Soils Containing Cracks or Holes
Authors: Davidson Malcolm R.
Published: February 2008

An asymptotic, one‐dimensional Green‐Ampt model of infiltration into a soil containing regularly spaced vertical cracks, or a cylindrical soil column containing a central hole, is derived from a complete two‐dimensional or axisymmetric Green‐Ampt analysis by summing an asymptotic expansion for the infiltration rate valid at large times when the wetting front has become horizontal. The model is shown to be accurate at intermediate times when the front is not necessarily horizontal and corresponds to one‐dimensional infiltration initiated from a plane lying below the soil surface at a depth which depends only on the geometry and which lies between zero and the crack (hole) depth. When applicable, model predictions of infiltration rate and cumulative infiltration obtained for cylindrical holes, like those previously obtained for cracks, agreed well with corresponding results based on finite difference solutions of the saturated‐unsaturated flow equations, differences being in the range of 2–9%.
Finite Analytic Numerical Solution for Two‐Dimensional Groundwater Solute Transport
Authors: Hwang Jack C. , Chen Ching‐Jen , Sheikhoslami M. , Panigarahi Bijay K.
Published: February 2008

A new numerical method called the finite analytic (FA) method is used to solve a groundwater solute transport problem. The basic idea of the finite analytic method is the incorporation of local analytic solution in the numerical solution of the partial differential equation. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in an element and its neighboring nodal points. The assemble of the linear system equations results in a tridiagonal matrix. Like most finite difference method, the advantages of using efficient iterative techniques for solving tridiagonal matrices are equally applicable to FA method. The automatic localized upstream shift and the analytic property of the FA method eliminates the difficulty of numerical dispersion locally and suppresses the overall numerical dispersion for large Peclet number. For small Peclet number FA method yields excellent results in comparison with the analytic solution. For large Peclet number FA solutions are oscillation free with some degree of numerical dispersion. The results are comparable with those obtained using upstream weighted finite element method.
Improved Formulas for a Dam Phreatic Surface With Accretion
Authors: Hornung Ulrich , Krüger Thomas
Published: February 2008

The free boundary value problem of steady groundwater flow in an unconfined aquifer with accretion is solved by numerical methods in an exemplary situation. New formulas, which improve the results of the commonly used Dupuit‐Forchheimer theory, are given for the dependence of the height of the phreatic surface on the accretion rate. In this way it is shown that simple formulas, which describe the flow of groundwater in a more accurate way than the classical ones, can be derived with the help of modern mathematical techniques.
Uncertainty in Phosphorus Retention, Williams Fork Reservoir, Colorado
Authors: LaBaugh James W.
Published: February 2008

Uncertainties in the calculation of water and phosphorus budgets for a bottom‐withdrawal reservoir were determined for 1979–1982. Ungaged components of the water budget were estimated from the residual of measured terms. This residual accounted for less than 30% of total water input and for more than 45% of total phosphorus input in each year of the study. Uncertainty in phosphorus retention data was large because of uncertainty in the total phosphorus input, due to use of a residual term.