bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite element analysis of solute transport under hysteretic unsaturated flow conditions
Authors: Pickens John F. , Gillham Robert W.
Published: February 2008

The finite element method based on a Galerkin technique was used to formulate a model for the two‐dimensional simulation of the transient movement of water and solutes in saturated‐unsaturated soils. The model allows either nonhysteretic or hysteretic water content‐pressure head relationships in the unsaturated zone. The finite element model results, including the effect of hysteresis, compared well with experimental and finite difference results for transient flow in an unsaturated sand column and provided confidence in the method of incorporation of the hysteretic relationships. The finite element model was applied to a hypothetical one‐dimensional case involving vertical infiltration and redistribution of a slug of water containing a nonreactive tracer in a column of sand. Simulations were conducted using hysteretic properties and also nonhysteretic properties given by either the main drying or the main wetting curve. For the given hydraulic properties and boundary conditions, the simulations indicated that the effect of including or neglecting hysteresis was greatest in the pressure head and water content profiles and was of minor importance in the concentration profiles. Since the measurement of the hysteretic hydraulic properties of a soil material is both costly and time consuming, the illustration of the minor effect of hysteresis is of considerable practical importance in the evaluation of solute transport in unsaturated soils.
Hydrologic regression with weighted least squares
Authors: Tasker Gary D.
Published: February 2008

Ordinary least squares (OLS) regression and weighted least squares (WLS) regression are compared by simulating a model of the form Q50 =αAβ1, where Q50 is the 50‐year peak discharge, A is drainage area, and α and β1 are regional parameters estimated from a regression of observed 50‐year peaks at gaging stations. Results indicate that OLS has a larger expected standard error of prediction than WLS when the following weighting function is used:
for i = 1, 2,…, N, where ĉ0 and ĉ1 are constants estimated from sample data, ni, is the record length of station i, N is the number of stations, and ŵi, is the weight given to data for station i.
Measurement and computation of bed‐material discharge in a shallow sand‐bed stream, Muddy Creek, Wyoming
Authors: Andrews E. D.
Published: February 2008

Both the measurement and computation of the bed‐material discharge of a stream involve large uncertainties because of the difficulties in determining bedload discharge. Measurements of bedload discharge are rare and frequently of unknown accuracy because no bedload sampler has been extensively tested and calibrated over a wide range of hydraulic conditions. Bed‐material discharge equations have been derived primarily from laboratory flume data where the effects of channel pattern, alluvial banks, sediment availability, sediment sorting, and unsteady flow upon the sediment discharge of a natural stream have not been simulated. Bed‐material discharge equations generally are applicable only within the range of flow conditions and sediment sizes for which the equations were derived. To compare the relative value of measuring versus computing bed‐material discharges, the bed‐material discharge of Muddy Creek, a shallow sand‐bed stream in southwestern Wyoming, was determined on 35 occasions for water discharges ranging from 0.15 to 1.57 m3/s by separately sampling the suspended‐ and bedload‐sediment discharges. Measured bed‐material discharges were statistically indistinguishable, at an 0.02 level of significance, from flume data collected under the same flow conditions. This agreement indicates that the measured bed‐material discharges are reasonable estimates of the true values. Bed‐material discharges computed by Engelund‐Hansen, Yang, Shen‐Hung, and Ackers‐White equations were compared with the measured values and found to be in good agreement. These equations predicted bed‐material discharges of between 0.5 to 2 times the observed rates 60% to 79% of the time.
First order analysis of uncertainty in numerical models of groundwater flow part: 1. Mathematical development
Authors: Dettinger Michael D. , Wilson John L.
Published: February 2008

In part 1 of this paper, first and second order analysis of uncertainty is applied to numerical models of groundwater flow. The models are cast in state‐space form, with boundary conditions and inputs that are functionally dependent, but statistically independent, of time. Using a compact matrix calculus notation, first and second order Taylor series expansions of the model equations are derived and used to estimate the mean and variance‐covariance properties of piezometric head predictions, given corresponding statistics for aquifer parameters: material properties, initial conditions, boundary conditions, and inputs. The mathematical results demonstrate that the prediction uncertainty is a function of the magnitude of the parameter uncertainty, and sensitivity of the predictions to the parameters. Furthermore, the first order estimate of the piezometric head is identical to the deterministic result. Part 2 of this paper, to be presented later, will illustrate these and other results through numerous applications of the methodology.
Flow through fractures
Authors: Neuzil C. E. , Tracy James V.
Published: February 2008

Flow through fractures is often idealized as flow between two parallel plates (plane Poiseuille flow). The opening or aperture between parallel plates is unambiguous and its relation to flowrate is well known. However, fractures in rock have uneven walls and a variable aperture. A model for flow in a fracture is proposed wherein the fracture is represented by a set of parallel plate openings with different apertures. The model leads to a modified Poiseuille equation for flow which includes an aperture frequency distribution for the fracture. Any arbitrary aperture distribution can be used; in order to simplify computation and demonstrate the properties of the model a log normal form of distribution is assumed. Even when an analytical form of the distribution is assumed, two parameters, rather than a single value representing ‘aperture size’ are required to determine flowrate. Models of aperture change for a fracture undergoing compression (fracture walls deforming) and extension (fracture walls separating) are developed which constrain the additional parameter and allow calculation of flowrate as a function of mean aperture. The theoretical relationships developed between mean aperture and flowrate can be used to interpret published laboratory data for single fractures.
A geomorphologic synthesis of nonlinearity in surface runoff
Authors: Wang C. T. , Gupta Vijay K. , Waymire Ed
Published: February 2008

The geomorphic approach leading to a representation of an instantaneous unit hydrograph (iuh) which we developed earlier is generalized to incorporate nonlinear effects in the rainfall‐runoff transformation. It is demonstrated that the nonlinearity in the transformation enters in part through the dependence of the mean holding time on the rainfall intensity. Under an assumed first approximation that this dependence is the sole source of nonlinearity an explicit quasi‐linear representation results for the rainfall‐ runoff transformation. The kernel function of this transformation can be termed as the instantaneous response function (irf) in contradistinction to the notion of an iuh for the case of a linear rainfall‐runoff transformation. The predictions from the quasi‐linear theory agree very well with predictions from the kinematic wave approach for the one small basin that is analyzed. Also, for two large basins in Illinois having areas of about 1100 mi2 the predictions from the quasi‐linear approach compare very well with the observed flows. A measure of nonlinearity, α naturally arises through the dependence of the mean holding time KB(i0) on the rainfall intensity i0via KB (i0) ∼ i0 −α. Computations of α for four basins show that α approaches ⅔ as basin size decreases and approaches zero as the basin size increases. A semilog plot of α versus the square root of the basin area gives a straight line. Confirmation of this relationship for other basins would be of basic importance in predicting flows from ungaged basins.
A survey of mathematical optimization models and algorithms for designing and extending irrigation and wastewater networks
Authors: Mandl Christoph E.
Published: February 2008

This paper presents a state of the art survey of network models and algorithms that can be used as planning tools in irrigation and wastewater systems. It is shown that the problem of designing or extending such systems basically leads to the same type of mathematical optimization model. The difficulty in solving this model lies mainly in the properties of the objective function. Trying to minimize construction and/or operating costs of a system typically results in a concave cost (objective) function due to economies of scale. A number of ways to attack such models are discussed and compared, including linear programing, integer programing, and specially designed exact and heuristic algorithms. The usefulness of each approach is evaluated in terms of the validity of the model, the computational complexity of the algorithm, the properties of the solution, the availability of software, and the capability for sensitivity analysis.
Mathematical model for regional land subsidence due to pumping: 1. Integrated aquifer subsidence equations based on vertical displacement only
Authors: Bear Jacob , Corapcioglu M. Yavuz
Published: February 2008

A mathematical model for regional land subsidence has been developed by employing Terzaghi's concept of effective stress and assuming vertical solid compressibility only. First the groundwater mass conservation equation in a compressible aquifer is developed for a three‐dimensional space. Assuming that the problem justifies an assumption of a thin aquifer, relative to horizontal lengths of interest, this equation is then integrated over the aquifer's thickness, taking into account the conditions on top and bottom surfaces bounding the aquifer. The result is the commonly used aquifer flow equation in terms of averaged piezometric head. By introducing a relationship between changes in averaged piezometric head and corresponding changes in aquifer thickness, a single equation is obtained in terms of land subsidence. The development is carried out for a single and a multi‐layered confined aquifer and for a phreatic one. An example is given of the application of the equation in radial coordinates describing land subsidence in a hypothetical six‐layered aquifer.
A parametric crop water use model
Authors: Burt J. E. , Hayes J. T. , O'Rourke P. A. , Terjung W. H. , Todhunter P. E.
Published: February 2008

The model WATER provides feasible computational methods for the determination of temporal and spatial agricultural water consumption. A solution was sought through the creation of a crop‐specific, growth‐stage‐specific soil moisture model. This model, which has been programmed for digital simulation, is a compromise between area‐specific, data‐based regression models and expensive, complex energy‐mass exchange models. It is suitable for evaluating the impact of droughts and other climatic vagaries on crop water requirements. Input scenarios make possible the application of the model to regions where precise data are not available.
A stochastic cluster model of daily rainfall sequences
Authors: Kavvas M. L. , Delleur J. W.
Published: February 2008

A two‐level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension. The model is a cluster process of the Neyman‐Scott type. The model has the rainfall‐generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level. It uses infinite superposition of rainfalls and has a very flexible dependence structure. The model is fitted to daily rainfall sequences in Indiana after these are stationarized by a transformation. The fit of the model is then tested in terms of its correlation and marginal probability characteristics. The present form of the Neyman‐Scott cluster model is time homogeneous. Therefore the Neyman‐Scott process, as presented in this paper, may be of practical use only for modeling the stationary rainfall occurrences.
Two‐phase flow simulation of air storage in an aquifer
Authors: Meiri David
Published: February 2008

A two‐phase flow model is presented for simulating air storage in an aquifer used for a compressed air storage system. The governing equations describing the flow of air and water are coupled nonlinear partial differential equations and are solved by a Galerkin finite element method. The resulting computer model is used to simulate the air‐water displacement in a one‐dimensional storage reservoir during daily air cycling. The corresponding saturation and pressure variations and the effects of reservoir permeability on the system are presented. The results obtained realistically describe a variable volume storage system with only a small change in pressure.
Boundary integral equation solutions to moving interface between two fluids in porous media
Authors: Liu Philip L‐F. , Cheng Alexander H‐D. , Liggett James A. , Lee Joseph H.
Published: February 2008

The boundary integral equation method is formulated for and applied to problems concerning a moving interface between two fluids in porous media. The mixing between two fluids is assumed to be insignificant; a sharp interface exists between them. Numerical and experimental results are presented for the tilting of a vertical interface in a Hele‐Shaw cell. During the initial stage of the interfacial movement, nonlinear effects are clearly demonstrated. The BIEM results are also compared to experimental results for a transient salt water intrusion problem.
Worth of short‐term rainfall forecasting for combined sewer overflow control
Authors: Labadie John W. , Lazaro Rogelio C. , Morrow Dennis M.
Published: February 2008

Real‐time, short‐term rainfall forecasting is gaining recognition as a valuable input to more effective performance of a variety of urban water management activities, including controlling the incidence of untreated combined sewer overflows. An important question is, What levels of forecast error can be tolerated before it is better to abandon adaptive control policies utilizing forecast information in favor of simple reactive control methods? Experiments with an autoregressive‐transfer function model for shortterm forecasting are presented, utilizing the San Francisco North Shore Outfalls Consolidation Project as a case study. A split data technique is used to gain insight into expected forecast errors for selected overflow‐producing storms varying from high intensity‐low duration to low intensity‐high duration. These results are then compared with the performance of the planned system, utilizing automatically controlled gates in a large shoreline tunnel, for various levels of forecast error. The results of a limited number of simulation runs indicate that expected forecast model errors are generally lower than the error threshold above which reactive policies become more attractive.
Transport of ion‐exchanging solutes in groundwater: Chromatographic theory and field simulation
Authors: Valocchi Albert J. , Street Robert L. , Roberts Paul V.
Published: February 2008

Equations describing the transport of ion‐exchanging solutes governed by local chemical equilibrium through a saturated porous medium are well established in the literature. Concentration profiles resulting from the numerical solution of the general multispecies equations typically exhibit unusual and complicated features such as multiple fronts and plateau zones. This paper presents an analytical framework, based upon the theory of chromatography, which permits a priori characterization of certain key concentration profile features. The cases studied include both homovalent and heterovalent exchange in binary and ternary systems. In order to test its validity, the chromatographic analysis is applied to a field project involving direct injection of advanced treated municipal effluent into an aquifer. All of the major features observed in the available field data are accurately predicted by the chromatographic theory.
Data requirements for kriging: Estimation and network design
Authors: Hughes James P. , Lettenmaier Dennis P.
Published: February 2008

Kriging, a technique for interpolating nonstationary spatial phenomena, has recently been applied to such diverse hydrologic problems as interpolation of piezometric heads and transmissivities estimated from hydrogeologic surveys and estimation of mean areal precipitation accumulations. An important concern for users of this technique is the effect of sample size on the precision of estimates obtained. Comparisons made between conventional least squares and kriging estimators indicate that for samples of size less than approximately 50, kriging offered no clear advantage over least squares in a Bayesean sense, although kriging may be preferable from the minimax viewpoint. A network design algorithm was also developed; tests performed using the algorithm indicated that the information content of identified networks was relatively insensitive to the size of the pilot network. These results suggest that within the range of sample sizes typically of hydrologic interest, kriging may hold more potential for network design than for data analysis.
A simple method for estimating convective rain volume over an area
Authors: Doneaud André A. , Smith Paul L. , Dennis Arnett S. , Sengupta Sumedha
Published: February 2008

Previous authors have reported significant correlations between the horizontal extent of convective showers or storms and the volume of rain they produce. This paper employs that idea to develop a simplified method for estimating convective rainfall by considering only the horizontal extent and duration of the precipitation. The present analysis is based on rain gage and radar data from an area in western North Dakota. A synoptic adjustment is applied to the radar rain volume estimates. A quantity called the integrated rainfall coverage can be calculated from either gage or radar data and is found to be well correlated with the rain volumes. The maximum echo area during any one scan in one hour seems to be the hourly radar measurement best correlated with the rain volumes. This limited study suggests that the accuracy of the simplified method approaches that of methods using radar reflectivity data and may have operational value in some special situations.
Modeling of scale‐dependent dispersion in hydrogeologic systems
Authors: Pickens John F. , Grisak Gerald E.
Published: February 2008

An approach for handling scale‐dependent dispersion using a finite element (linear triangular) solute transport model was developed. Dispersivity is allowed to vary temporally as a function of the mean travel distance of the solute from an input source. Various scale‐dependent dispersivity relationships were presented including types which approach continuously to a maximum or asymptotic value. The finite element model results were verified for a one‐dimensional case by comparison of the theoretical variances of the solute distribution for a given dispersivity‐travel distance function with the variances calculated from the finite element model concentration distributions. The model was applied successfully to the results of several tracer tests reported in the literature that have exhibited a scale effect. For systems that exhibit a constant (asymptotic) dispersivity at large times or mean travel distances, the importance of scale‐dependent dispersion at early times or short travel distances was shown to be minimal in long‐term predictions of solute transport.
Linear crop response functions to soil salinity with a threshold salinity level
Authors: Feinerman E. , Yaron D. , Bielorai H.
Published: February 2008

The response function of a crop yield to soil salinity level is essential in decision‐making in regard to irrigation with saline water. A switching regression approach to estimate the piecewise linear response function with critical threshold level is presented, and the asymptotical stochastic properties of the estimates are described. The empirical estimates, based on grapefruit yield data, are compared with those of a recent published study by Maas and Hoffman (1977) and the statistical significance of the differences is discussed. Finally, the threshold hypothesis is tested empirically against some alternative formulations. It turns out that the ‘threshold hypothesis’ is confirmed.
Robust flood frequency models
Authors: Kuczera George
Published: February 2008

The concept of a robust model is briefly explored. In the context of flood frequency analysis, two necessary properties of a robust model are advanced, namely, resistance and efficiency. Strategies for seeking more robust models are discussed. Because of its versatility, the five‐parameter Wakeby distribution can credibly be considered a parent flood distribution. Four regionalized Wakeby parents are employed in simulation studies to search for robust models. These parents were shown by Houghton to be representative of U.S. flood experience in the sense that certain raw flood data characteristics could be reproduced. A limited range of sampling experiments were undertaken. The results suggest that of the site‐specific estimators considered, the two‐parameter log normal maximum likelihood estimator is most resistant, with Gumbel estimators employing either maximum likelihood or probability‐weighted moments displaying comparable resistance. Several estimators which utilize regional flood information were compared. Included were empirical Bayes estimators which are structurally similar to James‐Stein rules and regionalized estimators based on the flood index method. These estimators exhibited substantial improvements in aggregate risk performance over their site‐specific counterparts, particularly for short record lengths. Regionalized estimators appear to be preferable for short record lengths, while estimators which combine both site and regional flood information are preferable for longer record lengths. When such estimation procedures are considered, other distributional models such as log Pearson type III and Wakeby become practical alternatives to the two‐parameter log normal model.
The effects of acid rain on forest nutrient status
Authors: Johnson Dale W. , Turner John , Kelly J. M.
Published: February 2008

The effects of acidic atmospheric inputs on forest nutrient status must be assessed within the context of natural, internal acid production by carbonic and organic acids as well as the nutrient inputs and drains by management practices such as harvesting, fire, and fertilization. In all cases the anion associated with acid inputs must be mobile in the soil if leaching is to occur; immobilization of anions can effectively prevent cation leaching. Soil acidification will occur only if the often substantial buffering capacity of the soil in question is exceeded by acid inputs and if cation weathering from primary minerals is insufficient to offset cation losses by leaching. Such circumstances are rare but certainly could occur in theory, at least, given sufficiently large acid inputs on poorly buffered soils. Soils most sensitive to change are thought to be those of moderately acid pH and low cation exchange capacity. Neither very acid soils nor neutral, highly buffered soils are sensitive to acidification by acid rain. Given extremely high acid inputs, acid rain can cause temporary increases in nitrogen mineralization and nitritication as well as Al mobilization in soils. While temporary increases in N availability can cause increased forest growth in N‐deficient forests, increased Al availability can cause toxic reactions in tree roots. Little is known about tree Al toxicity levels as yet, however. It must be emphasized that assessment of acid rain effects is a problem of quantification. Given sufficiently high inputs on sensitive sites, negative effects of acid rain must occur, as is true of inputs of any substance, including H2O. Acid rain inputs of sufficient magnitude to cause acute effects, such as growth increase due to N mobilization or growth decrease due to Al mobilization, are apparently very rare under ambient field conditions. Long‐term effects on forest nutrient status can be either beneficial or adverse, depending on site nutrient status, silvicultural practices, and amount of atmospheric inputs.
A dimensionless parameter approach to the thermal behavior of an aquifer thermal energy storage system
Authors: Doughty Christine , Hellström Göran , Tsang Chin Fu , Claesson Johan
Published: February 2008

To predict the performance of an aquifer thermal energy storage system, an understanding of the system's hydrothermal behavior is needed. One possibility is to run a detailed numerical simulation of the system. However, for a single‐well system in which fluid flow is limited to steady radial flow, a characterization scheme based on a set of four dimensionless parameter groups allows production temperatures and energy recovery factors to be read from graphs. The assumption of radial fluid flow is valid when buoyancy flow can be neglected and a well is fully screened in a horizontal aquifer which is confined above and below by impermeable layers. Criteria for little buoyancy flow include a low permeability or vertically stratified aquifer, a small temperature difference between injected and ambient water, and short cycle length. The basic energy transport equations for the aquifer‐confining layer system with steady radial fluid flow in the aquifer are nondimensionalized to derive the key parameter groups. Next a numerical model which calculates the heat transfer in the aquifer and confining layers for an injection‐storage‐production cycle is run for a range of values of these groups. The calculated production temperatures and energy recovery factors are then presented graphically as a function of the parameter groups. Comparisons between results of field experiments and recovery factors read from the graphs show good agreement.
Reliability programing in reservoir management: 3. System of multipurpose reservoirs
Authors: Simonović Slobodan P. , Marino Miguel A.
Published: February 2008

A reliability programing technique, which includes the concept of ‘reliability or risk’ in an optimization, is applied to multiple multipurpose reservoir systems. The procedure can be applied to any multipurpose multiunit reservoir system with two general types of linkage: normal channel flow for reservoir releases and pipelines or pumping canals. Thus each reservoir could be connected to every other reservoir, and each could receive releases from any or all other reservoirs as dictated by a particular system configuration. A two‐level solution algorithm is proposed. A solution can be obtained for a reservoir system with few purposes (flood control, power production, irrigation, water supply, and water quality enhancement) and random inflows and demands. The random inflows and demands are represented by conditional distribution functions. The objective function of economic efficiency, representing the tradeoff between benefits and risks embodied by a risk‐loss function, is included in the present approach. The reliability programing model is nonlinear and can be split into two models: search model and special linear programing model. The procedure is illustrated using a portion of the Red River system in Oklahoma and Texas, a system of three multipurpose reservoirs. The three reservoirs individually satisfy purposes (flood protection, hydroelectric power generation, water supply, and water quality enhancement), and two of the reservoirs work together to satisfy additional water requirements (flood control and water quality enhancement downstream). Input data necessary for solving the optimization model are presented. Results of the operation of the system, including optimal operating policies for the reservoirs and reliabilities of the operation, illustrate the major advantages of the reliability programing approach compared with other stochastic optimization techniques.
A model of thermal radiation from partly cloudy and overcast skies
Authors: Kimball B. A. , Idso S. B. , Aase J. K.
Published: February 2008

A mathematical model for predicting thermal radiation from partly cloudy and overcast skies was developed. The model uses previous clear sky equations for predicting full‐spectrum sky emittance and 8–14 μm atmospheric window transmittance and then assumes that the cloud contribution to sky thermal radiation must be transmitted to the earth's surface through the atmospheric window. Unlike previous ‘cloud corrections,’ the cloud contribution is computed from surface vapor pressure and temperature, cloud amount, and elevation data, as recorded by National Weather Service observers. The average predicted increase due to 100% cloud cover was 18% for Phoenix in 1978 with a theoretical upper limit of about 40%. Comparisons were made between model predictions and measured values of sky radiation for a wide range of weather conditions. The agreement was excellent with an overall coefficient of determination for fit to a 1:1 line of 0.941 on an hourly basis and of 0.960 on a daily total basis.
ARMA Model identification of hydrologic time series
Authors: Salas J. D. , Obeysekera J. T. B.
Published: February 2008

In recent years, ARMA models have become popular for modeling geophysical time series in general and hydrologic time series in particular. The identification of the appropriate order of the model is an important stage in ARMA modeling. Such model identification is generally based on the autocorrelation and partial autocorrelation functions, although recently improvements have been obtained using the inverse autocorrelation and the inverse partial autocorrelation functions. This paper demonstrates the use of the generalized partial autocorrelation function (GPAF) and the R and S functions of Gray et al. (1978) for ARMA model identification of hydrologic time series. These functions are defined, and some recursive relations are given for ease of computation. All three functions, when presented in tabular form, have certain characteristic patterns that are useful in ARMA model identification. Several examples are included to demonstrate the usefulness of the proposed identification technique. Actual applications are made using the Saint Lawrence River and Nile River annual streamflow series.
Nonlinear equation governing flow in a saturated porous medium
Authors: Joseph D. D. , Nield D. A. , Papanicolaou G.
Published: February 2008

It is argued that the appropriate generalization of Darcy's law when inertia effects are included takes the form ∇p = −(μ/k) V − (ρc/k½)|V|V, div V = 0, where k is the permeability of the medium and the ‘form drag constant’ c is a coefficient which is independent of the pressure p, the seepage velocity V, and the density ρ and viscosity μ of the fluid but which is dependent on the geometry of the medium. We formulate a nonlinear extension of Brinkman's self‐consistent theory for the flow of a viscous fluid through a swarm of spherical particles. We equate the drag per unit volume given by the right hand side of the first of the above equations to the total drag ND on the N particles contained within that unit volume, in an infinite region Ω, where D is the drag on a single particle placed in a velocity field v subject to ρ(v · ∇)v + grad p = μ∇2v−μ/k v − (cρ/k½)|v|v, div v = 0, v|∂Ω is a prescribed constant, where μ is the viscosity. Without solving these equations, we obtain an estimate for c from the known experimental drag law for a solid sphere placed in a uniform stream.
Effects of kriging and inverse modeling on conditional simulation of the Avra Valley Aquifer in southern Arizona
Authors: Clifton Peter M. , Neuman Shlomo P.
Published: February 2008

The Avra Valley aquifer in southern Arizona is modeled stochastically at three levels of uncertainty. The highest level of uncertainty occurs when log transmissivity estimates are based on measured values of this parameter but without regard to the geographic location of each measurement point. The resulting steady state hydraulic heads in the aquifer, computed by unconditional simulation with the aid of a multivariate normal random number generator coupled with a finite element model, have a relatively large variance. This variance can be reduced by conditioning the log transmissivity estimates on the spatial arrangement of the data by means of kriging. When conditional simulation of the aquifer is performed at this intermediate level of uncertainty with the aid of the same technique as in the unconditional case, the variance of the predicted head values is reduced by a factor of 3.2. The lowest level of uncertainty is achieved when the log transmissivity estimates are further conditioned on data relating to the flow regime, such as flow rates and water levels in observation wells, by means of a statistical inverse procedure. Conditional simulation at this level of uncertainty is a novel concept. It results in a hydraulic head prediction variance that is 14.3 times lower than the corresponding variance based on kriged log transmissivities. The net effect of conditioning by means of kriging and inverse modeling is to reduce the prediction variance by a factor of 46.0. A similar study performed by Binsarti (1980) on the Cortaro aquifer in southern Arizona showed insignificant variance reduction due to kriging, but a factor of four reduction after inverse modeling. These results indicate that the conditioning effect of the inverse method may be much greater than that of kriging. The fact that conditioning can reduce the hydraulic head prediction variance by as much as a factor of 46 implies that one should be cautious when dealing with the results of stochastic aquifer models in which conditioning effects are disregarded.
Lake bottom dynamics and morphometry: The dynamic ratio
Authors: Håkanson Lars
Published: February 2008

This paper is a second report on the linkage between lake bottom dynamics and lake morphometry. The areal distribution of erosion and transportation (aE+T) or accumulation (aA = 100 − aE+T) processes at lake bottoms is suggested to be governed by (1) an energy factor E = ( √a/Dmax), where a is the lake area in square kilometers and Dmax is the maximum depth in meters, (2) a slope factor S = 41 exp(0.061 D¯/√a), where D¯ is the mean depth in meters, and (3) a form factor, Vd−l = Dmax/3D¯. This relationship may be given as aE+T = 100 − aA = 25 (√a/D¯) 41 exp 0.061 D¯/√/a) where aE+T is the percentage area of lake bed subject to processes of erosion and transportation. The ratio √a/D¯ is called the dynamic ratio (DR). This formula is physically more sound than an earlier model and more accurate when applied on the available empirical data from nine Swedish lakes. It also reveals new aspects of the relationship between bottom dynamics and lake morphometry. The formula may be useful since it provides a means by which to estimate the percentage of a given lake area that is dominated by erosion and transportation processes (aE+T) or accumulation processes (aA) from only two morphometric standard parameters: lake area a and mean depth D¯.
The transient response of cooling ponds
Authors: Adams E. Eric
Published: February 2008

Cooling ponds are a form of closed cycle cooling used for steam‐electric power plants. Because of their thermal inertia they provide an advantage over cooling towers in filtering fluctuations in intake temperature, which results in improved plant efficiency. By using linear systems theory, the transient behavior of various types of ponds is analyzed in response to periodic meteorological conditions (characterized by equilibrium temperature) and plant operational conditions (characterized by condenser temperature rise). Frequency response is expressed in terms of dimensionless ratios involving frequency of input forcing, characteristic hydraulic residence and surface response times, and appropriate mixing parameters. Results are also interpreted with respect to physical design variables, such as pond area, depth, degree of stratification, intake submergence, discharge entrance mixing, condenser flow rate, and temperature rise.
Numerical simulation of flow and contaminant migration at an extensively monitored landfill
Authors: Sykes J. F. , Pahwa S. B. , Lantz R. B. , Ward D. S.
Published: February 2008

A multidimensional finite‐difference model for groundwater flow and contaminant transport is used to analyze the leachate migration from the Canadian Forces Base Borden landfill. Through the synthesis and interpretation of this contaminant system, the application of the model demonstrates the validation evidence that the model adequately simulates the leachate migration. The validation requires deriving parameters from independent measurements (laboratory and field) for use in the model. Review of previous hydrogeological studies leads to the use of three‐dimensional steady state flow regime of the saturated zone extending some 700 m downgradient of the landfill. Small differences between the measured and predicted piezometric surfaces are attributed to variations in potentiometric measurements, seasonal variations, and extrapolation of laboratory measurements of permeability to the field site. The contaminant migration from the landfill has been extensively monitored. Variation in observed chloride‐ion isopleths interpolated from three sampling periods over a 1‐year period are typical and indicative of significant temporal plume behavior. Three‐dimensional streamlines are used to develop a variable‐width two‐dimensional grid that allows sufficient discretization of the domain to permit the accurate simulation with small values of dispersivities. Sensitivity simulations are performed on the longitudinal and transverse dispersivity, imposed boundary condition potentials, hydraulic conductivity, landfill staging scheme, and sorption (potassium plume). Appropriate values for longitudinal and transverse dispersivities of the order of 5. m and 0.1 m, respectively, were found to be appropriate.
Linear theory of subsurface storm flow
Authors: Koussis Antonis D. , Lien Li‐Ta
Published: February 2008

A solution to the subsurface storm flow problem is developed through linearization of the complete one‐dimensional governing equation. Water surface profiles and outflow hydrographs obtained from this approximate theory are compared with the exact solution and with the kinematic approximation to this problem for a number of cases, characterized by the parameter λ = 4 i cos θ/K sin2θ. The accuracy and range of applicability of the proposed theory are greater than that of the kinematic theory. Its results may be considered satisfactory for the cases with λ ≤ 1; however, the kinematic theory is a preferable substitute for λ ≤ 0.25.
Three‐dimensional stochastic analysis of macrodispersion in aquifers
Authors: Gelhar Lynn W. , Axness Carl L.
Published: February 2008

The dispersive mixing resulting from complex flow in three‐dimensionally heterogeneous porous media is analyzed using stochastic continuum theory. Stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three‐dimensional, statistically anisotropic input covariance describing the hydraulic conductivity. With a statistically isotropic input covariance, the longitudinal macrodispersivity is convectively controlled, but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term. With an arbitrarily oriented anisotropic conductivity covariance, all components of the macrodispersivity tensor are convectively controlled, and the ratio of transverse to longitudinal dispersivity is of the order of 10−1. In this case the off‐diagonal components of the dispersivity tensor are significant, being numerically larger than the diagonal transverse terms, and the transverse dispersion process can be highly anisotropic. Dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and Monte Carlo simulations. The theory, which treats the asymptotic condition of large displacement, indicates that a classical gradient transport (Fickian) relationship is valid for large‐scale displacements.
Evaluation of Maximum Likelihood Parameter estimation techniques for conceptual rainfall‐runoff models: Influence of calibration data variability and length on model credibility
Authors: Sorooshian Soroosh , Gupta Vijai Kumar , Fulton James Lloyd
Published: February 2008

The success of an automatic calibration procedure is highly dependent on the choice of the objective function and the nature (quantity and quality) of the data used. The objective function should be selected on the basis of the stochastic properties of the errors present in the data and in the model. Also, the data should be chosen so as to contain as much valuable information about the process as possible. In this paper we compare the performance of two maximum likelihood estimators, the AMLE, which assumes the presence of first lag autocorrelated homogeneous variance errors, and the HMLE, which assumes the presence of uncorrelated inhomogeneous variance errors, to the commonly used simple least squares criterion, SLS. The model calibrated was the soil moisture accounting model of the U.S. National Weather Service's river forecast system (SMA‐NWSRFS). The results indicate that a properly chosen objective function can enhance the possibility of obtaining unique and conceptually realistic parameter estimates. Furthermore, the sensitivity of the estimation results to various characteristics of the calibration data, such as hydrologic variability and length, are substantially reduced.
Confluence scour in coarse braided streams
Authors: Ashmore Peter , Parker Gary
Published: February 2008

Laboratory models of a braided valley flat in coarse material were used in conjunction with field data to study confluence scour at braid anabranches. Correct prediction of the depth of scour is required for the design of buried pipeline crossings. Braid pattern and anabranches constantly shift and avulse so that scour holes have definable lifetimes. Although the scatter is large, the depth of water in the scour hole depends on confluence and relative anabranch discharge; this depth can be as high as six times the ambient depths in the anabranches.
Design events with specified flood risk
Authors: Stedinger Jery R.
Published: February 2008

A maximum likelihood or method of moments estimate of the 99 percentile of a flood flow distribution is the traditional choice for the 100‐year design flood event in flood plain planning. Because such estimates ignore the small‐sample properties of quantile estimators, the resulting design event values will be exceeded with a probability in excess of that intended. For a sample size of 16 the estimated 100‐year flood is, in expectation, the 50‐year flood. Bayesian and classical statistical approaches can be used to develop design flood values which, given available hydrologic information, will (on average) be exceeded with the specified 1% design probability. Bias in estimates of expected flood damages and procedures for using regional information at gauged and ungauged sites are discussed.
A Bayesian surrogate for regional skew in flood frequency analysis
Authors: Kuczera George
Published: February 2008

The problem of how to best utilize site and regional flood data to infer the shape parameter of a flood distribution is considered. One approach to this problem is given in Bulletin 17B of the U.S. Water Resources Council (1981) for the log‐Pearson distribution. Here a lesser known distribution is considered, namely, the power normal which fits flood data as well as the log‐Pearson and has a shape parameter denoted by λ derived from a Box‐Cox power transformation. The problem of regionalizing λ is considered from an empirical Bayes perspective where site and regional flood data are used to infer λ. The distortive effects of spatial correlation and heterogeneity of site sampling variance of λ are explicitly studied with spatial correlation being found to be of secondary importance. The end product of this analysis is the posterior distribution of the power normal parameters expressing, in probabilistic terms, what is known about the parameters given site flood data and regional information on λ. This distribution can be used to provide the designer with several types of information. The posterior distribution of theT‐year flood is derived. The effect of nonlinearity in λ on inference is illustrated. Because uncertainty in λ is explicitly allowed for, the understatement in confidence limits due to fixing λ (analogous to fixing log skew) is avoided. Finally, it is shown how to obtain the marginal flood distribution which can be used to select a design flood with specified exceedance probability.
Multicriteria analysis of water allocation in a river basin: The Tchebycheff Approach
Authors: Greis Noel P. , Wood Eric F. , Steuer Ralph E.
Published: February 2008

A new interactive multiple objective methodology is applied to the seasonal water allocation problem. Linear optimization and filtering procedures are combined within a multiobjective frame‐work in order to identify nondominated solutions associated with randomly sampled criteria vectors. The procedure samples from the entire nondominated set, not just the set of nondominated extreme points, by computing the nondominated criteria vector that is closest to an ideal criteria vector according to a weighted Tchebycheff metric. Unlike many other multicriteria methods, the Tchebycheff procedure is capable of finding solutions of highest utility which may not correspond to extreme point solutions. The procedure is applied to the problem of water allocation in a river basin where a large number of conflicting objectives, including environmental objectives, compete for the available supply.
Alternative structures for water rights markets
Authors: Eheart J. Wayland , Lyon Randolph M.
Published: February 2008

This paper examines the design of systems of marketable permits for water consumption from natural watercourses. The most important considerations for the work reported upon here are those associated with (1) uncertainty of future streamflows and economic conditions, (2) locational issues, and (3) efficient and effective functioning of the markets. Particular attention is given to the problem of implementing marketable rights systems in regions presently following the riparian doctorine. In these regions the most important design decisions include the basis of definition of permits, the means for initially distributing them, the type of market mechanism used for their transfer after they are issued, and the restrictions placed on their use and transfer. These design decisions are examined here with respect to program objectives, including economic efficiency, equity, ease of administration and implementation, and maintenance of instream flows. Alternative approaches to the design problems are discussed, and trade‐offs implied by the decisions are identified.