Showing papers in "Water Resources Research in 1975"

A Stochastic-Conceptual Analysis of One-Dimensional Groundwater Flow in Nonuniform Homogeneous Media

Abstract: The most realistic representation of a naturally occurring porous medium is a stochastic set of macroscopic elements in which the values of the three basic hydrogeologic parameters (hydraulic conductivity K, compressibility α, and porosity n) are defined by frequency distributions. A homogeneous formation under this representation is one in which the frequency distributions do not change through space. All soils and geologic formations, even the ones that are homogeneous, show random variations in the values of the hydrogeological parameters through space; that is, they are nonuniform, and a measure of the nonuniformity is provided by the standard deviation of the frequency distributions. If K and α are log normally distributed and n is normally distributed, and if we define Y = log K and C = log α, then the parameters Y, C, and n can be generated from a multivariate normal density function with means μy, μc, and μn, standard deviations σy, σc, and σn, and correlation coefficients ρyc, ρyn, and ρcn The analysis of groundwater flow in nonuniform media requires a stochastic-conceptual approach in which the effects of stochastic parameter distributions on predicted hydraulic heads are analyzed with the aid of a set of Monte Carlo solutions to the pertinent boundary value problems. In this study, two one-dimensional saturated flow problems are analyzed: steady state flow between two specified heads and transient consolidation of a clay layer. The primary output is the statistical distribution of hydraulic head ϕ, through space and time, as indicated by the mean values and their standard deviations Sϕ¯(x, t) Results show that the standard deviations of the input hydrogeologic parameters, particularly σy and σc, are important index properties; changes in their values lead to different responses for even when the means μy, μc, and μn are fixed. The degree of uncertainty associated with hydraulic head predictions increases as the degree of nonuniformity of the porous medium increases. For large values of σy and σc it becomes virtually impossible to obtain meaningful hydraulic head predictions. For transient flow the output distribution of hydraulic head values is almost never normal; in some cases it approaches a uniform distribution. The results of this study throw into question the validity of the hidden assumption that underlies all deterministic groundwater modeling; namely, that it is possible to select a single value for each flow parameter in a homogeneous but nonuniform medium that is somehow representative and hence define an ‘equivalent’ uniform porous medium. For transient flow there may be no way to define an equivalent medium. The fact that nine index parameters rather than three are required to describe a nonuniform geologic formation, the large uncertainties in predicted hydraulic heads for relatively simple flow problems in nonuniform soils, and the contention that there may be no simple way to define an equivalent uniform porous medium all have important implications in the development of groundwater flow theory and in its most fundamental applications.

On a derivable formula for long-wave radiation from clear skies

Abstract: A derivation is presented for the effective atmospheric emissivity to predict downcoming long-wave radiation at ground level under a clear sky and for a nearly standard atmosphere. The results are in good agreement with those obtainable with empirical formulae based on water vapor pressure and temperature. However, the proposed formulation has the advantage that its simple functional form is based on physical grounds without the need for empirical parameters from radiation measurements. Also, in contrast to the empirical equations, it may be adjusted in a simple way to reflect changes in climatic and atmospheric conditions.

The Effect of Urbanization on Floods of Different Recurrence Interval

Abstract: Studies have shown that the urbanization ofa catchment can drastically change the flood characteristics of a river. Published results are synthesized to show the general relationship between the increase in flood flows following urbanization and both the percentage of the basin paved and the flood recurrence interval. In general, (1) floods with a return period of a year or longer are not affected by a 5% paving of their catchment, (2) small floods may be increased by 10 times by urbanization, (3) floods with a return period of 100 yr may be doubled in size by a 30% paving of the basin, and (4) the effect of urbanization declines, in relative terms, as flood recurrence intervals increase. The development of an urban area within a catchment is a drastic change of land use, and it has major effects on the functioning of the hydrological cycle during flood conditions. When large areas of land are rendered impervious by roads, footpaths, roofs, and parking areas, the area in which rainfall can infiltrate into the soil is reduced, depression and interception storage of precipitation may be reduced, and overland flow can take place readily on the relatively smooth impermeable surfaces. The construction of an urban storm water drainage system invariably increases the drainage density of the catchment and so reduces the time necessary for overland flow to reach a drainage line. Moreover, well-designed and well-graded sewer systems are normally efficient channels in which water velocities are usually in excess of those in natural channels; therefore the drainage from a large area can be more rapidly conducted to the main river channel. The net effects of these changes are that a higher proportion of rainfall is translated into runoff, this runoff occurs more quickly, and flood flows are therefore higher and 'flashier' than was the case in the catchment before urbanization. There have been a number of studies that have measured these changes for individual catchments or groups of catchments, and these have been reviewed by Moore and Morgan [1969], Costin and Dooge [1973], and Hollis [1974]. Reports of research at Charlotte,

A review and evaluation of multiobjective programing techniques

Abstract: Three criteria are established for the evaluation of the utility of multiobjective programing techniques for water resource planning. The criteria are computational efficiency, explicitness of trade offs among objectives, and the amount of information generated for decision making. The multiobjective approaches are classified into generating techniques, techniques which rely on the prior articulation of preferences, and techniques which foster iterative definition of preferences. The methods in the various classes are reviewed and evaluated in terms of the hypothesized criteria. The evaluations are then used in establishing conclusions about the applicability of the multiobjective approaches to water resource problems.

Analysis of Pumping Test Data From Anisotropic Unconfined Aquifers Considering Delayed Gravity Response

Abstract: Previously a new analytical model was proposed by the author for the delayed response process characterizing flow to a well in an unconfined aquifer. The new approach differs from that of Boulton (1954, 1963, 1970, 1973) and Boulton and Pontin (1971) in that it is based only on well-defined physical parameters of the aquifer system. As such, it can be used to develop methods for determining the hydraulic properties of anisotropic unconfined aquifers from field drawdown data. Two methods of analysis are described, one based on the matching of field data with theoretical type curves and the other based on the semilogarithmic relationship between drawdown and time. Owing to the reversible nature of the delayed response process as represented by the analytical model, data from recovery tests can be used to deterrnine aquifer transmissivity. All of these methods are illustrated by applying them to pumping test data collected by the French Bureau de Recherches Geologiques et Minieres in Gironde (Bonnet et al., 1970). Similar procedures can be used to analyze data from partially penetrating wells, but this method requires that a special set of theoretical curves be developed for each field situation. Such theoretical curves can easily be developed with the aid of a computer program available from the author. An explicit mathematical relationship is derived between Boulton's (1963) delay index, 1/α, and the physical characteristics of the aquifer. It is shown that contrary to the assumption of Boulton the parameter a is not a characteristic constant of the aquifer but decreases linearly with the logarithm of r, the radial distance from the pumping well. This discovery makes it possible to reinterpret the results of pumping tests that were previously obtained with the aid of Boulton's theory without necessarily reexamining the original drawdown data. Results from pumping tests performed by the Bureau de Recherches Geologiques et Minieres in Gironde and by Prickett (1965) in Illinois are used to illustrate this last point.

A theory for local evaporation(or heat transfer)from rough and smooth surfaces at ground level.

Abstract: A model proposed earlier (Brutsaert, 1965) for evaporation as a molecular diffusion process into a turbulent atmosphere is extended by joining it with the similarity models for turbulent transfer in the surface sublayer. The assumed mechanisms were suggested by available flow visualization studies near smooth and rough walls; the theoretical result is in good agreement with available experimental evidence. The important dimensionless parameters governing the phenomenon near the surface are the Dalton (or Stanton) number (i.e., mass transfer coefficient), the drag coefficient (u*2/U2), the roughness Reynolds number (u*z0/v) (except for smooth surfaces), and the Schmidt (or Prandtl) number (v/k). The proposed formulation allows the evaluation of the effects of some parameters, such as surface roughness or molecular diffusivity, that were hitherto not well understood. An important practical result is that in contrast to the drag coefficient, the Dalton number is relatively insensitive to changes in roughness length Z0.

A Galerkin‐finite element technique for calculating the transient position of the saltwater front

Abstract: The set of nonlinear partial differential equations that describe the movement of the saltwater front in a coastal aquifer is solved by the Galerkin-finite element method. Pressure and velocities are obtained simultaneously in order to guarantee continuity of velocities between elements. A layered aquifer is modeled either with a functional representation of permeability or by a constant value of permeability over each element.

Factors influencing infiltration and sediment production of semiarid rangelands in Nevada

Abstract: Simulated rainfall was used to study infiltration rates and sediment production of28 plant communities and soils of five watershed areas in central and eastern Nevada. Two antecedent moisture conditions were used: soil initially air dry and initially at field capacity. InfiltratIOn rates and sediment production of the various soils are largely controlled by extent and surface morphology of dune interspace soils. Vesicular horizons are unstable in dune interspace surface soils. These horizons seldom occur in coppice dunes or in well-aggregated dune interspace soils. Infiltration rate is negatively related, and sediment production positively related to the occurrence and morphology of vesicular horizons. More sediment is produced from soils with antecedent moisture initially at field capacity than from'initially dry soil because of the instability of vesicular horizons when the soils were saturated. High-intensity summer thunderstorms in the Great Basin account for most of the runoff and sediment production from rangelands. Runoff is the major force initiating soil movement and transporting sediment. In order to manage rangeland watersheds effectively, factors influencing infiltration and sediment production need to be understood. Infiltration and erosion on rangelands have been studied for some time. Review of the literature includes Chapline [1929], Forsling [1932], U.S. Department of Agriculture [1940], Harper [1953], Gifford [1968], and Branson et al. [1972]. However, for Nevada rangeland there is practically no infor­ matIOn on infiltration and sediment production or on the in­ fluence of dune interspace areas and associated vesicular hori­ zons on infiltration and sediment production. The objective of this study was to determine which ground cover and soil pa­ rameters most influence infiltration and sediment production. METHODS

An empirical method of estimating the retention of phosphorus in lakes

Abstract: The relationship between phosphorus retention and several other lake and watershed parameters was examined for 15 lakes. A model relating the areal water load (qs) to phosphorus retention was proposed:Rp = 0.426 exp (−0.271qs) + 0.574 exp (−0.00949qs). This model was found to be theoretically sound, and the predicted and measured values were in close agreement (r = 0.94).

Changes in storm hydrographs after road building and clear‐cutting in the Oregon Coast Range

Abstract: Changes in storm hydrographs after road building, clear-cutting, and burning were determined for six small watersheds in the Oregon Coast Range. Peak flows were increased significantly after road building, but only when roads occupied at least 12% of the watershed. Roads had no detectable effect on volumes ot storm hydrographs. By reducing transpiration and interception, partial clear-cutting increased peak flow, quick flow, delayed flow, and total storm hydrograph volume of some streams. Most increases were largest in the fall when maximum differences in soil water content existed between cut and uncut watersheds. Maximum increases in storm flow occurred after a 175-acre watershed was 82% clear-cut. Here peak flow increased 16 fta/s/m?, quick flow 1.5 in., and total storm hydrograph volume 2.6 in. dur- ing the fall. The average increase in winter peak flows was smaller. The effect of roads on peak flows has significance for design of culverts and bridges in headwater areas, but probably does not influence downstream flooding. Increases in streamflow after clear-cutting should have no appreciable effect on either damage to bridges and culverts in headwater areas or downstream flooding. Caution must be used in extending results of this study to storm runoff events of low frequency and large magnitude.

One‐dimensional simulation of aquifer system compaction near Pixley, California: 1. Constant parameters

Abstract: Aggregate one-dimensional compaction (consolidation) of a series of aquitards in a compacting aquifer system has been simulated through use of a finite difference representation of the vertical stress distribution within an idealized aquitard Among the parameters affecting the simulated compaction are two storage coefficients (compressibility values), one for recoverable and the other for nonrecoverable compression These two storage coefficients introduce a transient heterogeneity within an aquitard that is generally ignored by hydrologists A computer program with two sets of constant coefficients calculates the daily deformation due to observed changes in applied stress near Pixley, California Although water levels fluctuate annually, no long-term water level decline occurred near Pixley between January 1, 1959, and February 4, 1971 During this period, 319 ft (0972 m) of compaction was observed The net difference between simulated and observed compaction on February 4, 1971, was 13% of the observed value Maximum deviation occurred in mid-1964 and equaled 7% of the observed compaction

The Log Pearson type 3 distribution and its application in hydrology

Abstract: A mathematical and statistical study which shows the flexibility and limitations of the log Pearson type 3 distribution is carried out. The results obtained indicate the various forms of density function and relationships that exist between distribution parameters and moments, coefficient of variation, and coefficient of skewness. The method of fitting proposed by the Hydrology Committee of the Water Resources Council is compared with a new method which instead of using moments of the logarithmic values retains the moments of the original data. In the case of events with a large return period the results obtained by the two methods may deviate appreciably, and because in the proposed method the same weight is given to each of the observed values, it will result in a better fit of the data.

A discrete kernel generator for stream-aquifer studies

Abstract: A finite difference model of the behavior of an aquifer without stream interaction was developed as a first-stage component of a management model of a stream-aquifer system. The model is not built as a usual simulator but as a discrete impulse response generator. Once the basic response coefficients have been generated, the finite difference model is no longer necessary to simulate the behavior of the aquifer. Any aquifer response (e.g., return flow to a given reach for a given week) is expressed as an explicit function of the pumping rates. A complete description of the ‘discrete kernel generator’ is provided including the basic equations, truncation error propagation, accuracy, and run costs.

Longitudinal dispersion in natural channels

Abstract: The longitudinal dispersion of fluid particles in natural channels is investigated in an extensive series of experiments in small mountain streams (New Zealand). These experiments extend over a maximum distance of 2250 m, a mean velocity range of 0.32–1.57 m/s, and a mean flow width range of 2.7–21.8 m. It is conclusively shown for these channels and others as well that the spread or standard deviation of an initially concentrated mass increases linearly with distance and not as its square root, as is necessary for the application of Taylor's mixing model. One consequence of the linearity is an ever-increasing dispersion coefficient along the channel. It is also shown that the time-concentration curve of a dispersing tracer mass maintains a persistent asymmetry. This persistent asymmetry and the continued linear spreading appear to be characteristic of dispersion in natural channels and as such show the inadequacies of applying Taylor's analysis.

The Impact of Suburbanization on Fluvial Geomorphology

Abstract: Analysis of aerial photography for the period 1950-1971 and field data collected from 1970 to 1974 indicate that in the Denver area suburban development has caused significant changes in fluvial systems. By first introducing large quantities of sediment and later by increasing surface runoff, suburban development leads to an expansion of floodplains followed by downcutting of streams. As areas of suburban development increase, greater percentages of stream lengths are dominated by transportation, and lesser percentages are dominated by erosion and deposition. Rapid expansion of the suburban area of southeast Denver, Colorado, has pushed housing development into two small drainage basins in the Meadow Hills area, causing significant changes in the fluvial systems of the basins. Previous studies of the impact of suburban development on streams in other areas have emphasized increased discharges associated with increased amounts of impervious surface and large sediment yields that result from surficial disruption [Leopold, 1968]. Recent research has revealed that as suburbanization progresses, the stream channels become larger to handle larger, more frequent flood peaks [Hammer, 1972]. Analysis of aerial photographs taken several times from 1950 to 1971 and field measurements made in the period 1970-1974 indicate that the fluvial geomorphic systems in the two basins have responded to the process of suburban development by changes

Regional Skew in Search of a Parent

Abstract: The relationship between the mean and the standard deviation of regional estimates of skewness for historical flood sequences is not compatible with the relations derived from several well-known distribution functions.

A Bayesian framework for the use of regional information in hydrology

Abstract: Water resource designs are perfect examples of decision making under uncertainty. In fact, three types of uncertainties may exist in any design problem: natural, parameter, and model uncertainties. The last two may be considered as informational uncertainties that are due to the lack of perfect information about the streamflow processes. The use of regional information has been suggested as a technique for reducing parameter uncertainties. The use of Bayesian methodology provides a framework for combining regional information with at-site historical records. Moreover, Bayesian methods allow the hydrologist to consider the parameter uncertainties as well as the natural uncertainties within the decision-making process. Because of these two advantages the Bayesian approach is a more complete and realistic approach to problems of uncertainty in hydrology and water resource planning than presently used methodologies.

Subsurface flow from snowmelt traced by tritium

Abstract: An explanation is offered of the apparent discrepancy between the small velocities of subsurface flow and the watershed response. Environmental tritium in the hydrological cycle provided evidence for a new insight into the runoff mechanism. By this concept the quick reaction of outflow to a massive groundwater recharge is brought to agreement with the long residence time of the infiltrated water.

Carbon-14 dating of groundwater from closed and open systems

Abstract: Groundwaters may be dated by using carbon 14, provided that the raw data are properly adjusted. However, adjustment factors determined from geochemical or isotopic measurements and based on simple models of carbonate dissolution do not always agree with adjustment factors obtained by independent means. In this paper, established adjustment methods are reinterpreted in terms of closed and open system models of carbonate dissolution, and it is suggested that these models provide a sounder framework for determining adjustment factors. Hypothetical and real examples are considered, and it is shown that some otherwise anomalous results may be explained in terms of the closed and open system models.

An evaluation of some linear decision rules in chance-Constrained models for reservoir planning and operation

Abstract: Several linear decision rules used in chance-constrained models for estimating efficient reservoir capacities and operating policies are compared and evaluated. A chance-constrained model that includes known or unknown reservoir release targets, or storage volume targets, permits this comparison, since regardless of the linear decision rule chosen, release or storage volume commitments can be made, and their maximum probabilities of failure estimated, well in advance of any period in which they apply. Optimization and simulation techniques are used to evaluate the performance of each decision rule.

Simulation of evapotranspiration and drainage from mature and clear‐cut deciduous forests and young pine plantation

Abstract: Prosper, a phenomenological model of water exchange between soil, plant, and atmosphere, was used to simulate evapotranspiration and annual drainage for 2 years from a mature oak-hickory forest in the southern Appalachians. The simulation was tested by comparing drainage to measured streamflow. In a year of unusually high precipitation the simulated annual drainage was within 1.5% of measured streamflow. Simulations were also performed by using the same 2 years of meteorologic data, but vegetation parameters were changed to represent a young white pine plantation and a regrowing hardwood forest 1 year after clear-cutting. The model estimated that drainage for an average rainfall year was reduced 20 cm by a 16-year-old white pine plantation and increased 36 cm by clear-cutting. These results were comparable to changes of −20 and +38 cm observed in watershed experiments at Coweeta Hydrologic Laboratory. Simulated evapotranspiration during the summer was nearly identical for hardwood and pine forests, while winter and early spring water loss was greater for pine. Simulation suggests that the greater evapotranspiration by pine was due to increased interception in all seasons and increased transpiration in the dormant season. For the clear-cut area, simulated evapotranspiration was considerably less than it was for the pine or hardwood forest and thus caused simulated soil moisture contents to be greater during the summer season.

Bayesian inference and decision making for extreme hydrologic events

Abstract: Hydrologic decision making usually occurs in an uncertain world and should combine inferences about uncertain outcomes with the decision makers’ preferences toward these outcomes. The decisions associated with flood protection are considered in detail where there exists uncertainty in the frequency of future flood discharges. Procedures are developed for analyzing and accounting for both statistical uncertainty of competing flood frequency models and statistical parameter uncertainty for the individual models. Inferences about flood frequency are combined with a decision model for which the decision rule is the maximization of expected monetary benefits. A case study to determine the optimal size of local flood protection by using prior information from a regional regression model, historical data, and realistic flood cost and damage functions is presented.

A theory for water flow through a layered snowpack

Abstract: A natural snowpack with ice layers is described in terms of an equivalent anisotropic porous medium. The anisotropic permeability is represented as a diagonalized matrix whose principal values can be calculated from a small amount of information about the prototype snowpack. Ice layers increase the transit time for water movement by a factor equal to the ratio of the principal values of permeability. The flow path, volume flux, and wave speed are determined by the slope of the snowpack and principal values of permeability. When a snowpack is assumed to be isotropic, the error in calculating transit time increases with the difference between the principal values of permeability. Usual variations in slope introduce a small change in the transit time.

Relative importance of meteorological variables in snowmelt

Abstract: To improve predictive equations of the snowmelt process, we need to better understand the relative importance of various meteorological parameters. Factor analysis and regression analysis were used to determine the effectiveness of wind, air temperature, vapor pressure, and net radiation in predicting snowmelt. Analyses of meteorological and snowmelt data collected at a site near Boise, Idaho, in May 1973 showed that the standard error of daily snowmelt prediction could be decreased 13% by using vapor pressure, net radiation, and wind in predictive equations rather than just air temperature.

Intervention Analysis in Water Resources

Abstract: Intervention analysis is the stochastic transfer function modeling of natural or man-induced interventions on the mean level of a time series. The mathematics of intervention analysis is presented followed by a systematic method of analysis that is used to analyze the effect of the Aswan dam on the average annual flows of the Nile River. The analysis shows that a significant drop in the flow occurred in 1903 when the dam was brought into operation. Transfer function parameter estimates statistically describe the intervention effect while the stochastic intervention model developed can be used for forecasting and simulation. The authors maintain that the potential of intervention analysis in water resources is extensive.

A dependent domain model of capillary hysteresis

Abstract: A model of capillary hysteresis which takes into account the phenomenon of blockage against air (and water) entry is presented. The model is based on our previous (1974) model II, which predicts any hysteretic path with the aid of two functions, L(ψ) and H(ψ). This model is generalized by adding a new function,рd(θ)(and ), as has been suggested by D. H. Everett (1967) and G. C. Topp (1971). It is found that is of a lesser significance and can be neglected in most cases. A technique of deriving L(ψ),H(ψ), and from the measured boundary loop and one primary drying scanning curve is presented. A simple method of predicting any hysteretic path is suggested. It is found that the generalized model leads to better results than the models based on independent domain theories for soils having a major portion of their hysteretic loop in the range of air entry value.

Optimal cost design of branched sewer systems

Abstract: Techniques using dynamic programing (DP) and discrete differential dynamic programing (DDDP) to achieve optimal cost design of pipe sizes and elevations of branched sewer systems have been developed and demonstrated by an example. The branched system is decomposed into equivalent serial subsystems, which are then solved in sequence. DDDP requires less computer time than DP, although it cannot guarantee global optimization. Major factors affecting the efficiency in using DDDP are the location and width of the initial trial trajectory corridor, the number of states (lattice points) used, and the reduction rate of the state increment during iterations.

Nonlinear kinematic wave approximation for water routing

Abstract: Herein a simple numerical model for both overland and channel water routing is presented A second-order nonlinear scheme is developed to solve the kinematic wave equation with the boundary condition of time variant inflows The numerical solutions agree very well with analytical solutions which are available for some particular cases This model includes the effects of rainfall on flow resistance and simulates hydrographs which agree very well with experimental results for both constant rainfall and variable rainfall cases The interesting phenomena of ‘pip’ and ‘dip’ in overland flow hydrographs are successfully simulated These phenomena are found to be the results of sudden changes of flow resistance due to ceasing or starting of rainfall The same routing procedure for overland flow is employed to route flow in natural channels

Water quality changes related to the development of anaerobic conditions during artificial recharge

Abstract: Artificial recharge basins or spreading sites commonly exhibit reductions in infiltration rates after prolonged periods of submergence. This loss in infiltration rate has often been shown to be associated with a large population of anaerobic or facultative anaerobic bacteria in the material underlying the basin floor. An artificial recharge experiment in a spreading basin at Lubbock, Texas, showed a significant change in the chemical quality of recharged water that was associated with the growth of anaerobic bacteria. Sulfate-reducing bacteria reduced the sulfate concentration of the recharge water at this location by 80 mg/l. The bicarbonate concentration was increased by more than 150 mg/l, and the pH decreased 1 unit during the same time period. The change in chemical quality occurred suddenly and corresponded to a dramatic decrease in the infiltration rate in the basin. These observations on the chemical changes in recharged water make it possible to differentiate between anaerobic bacteria and other causes of reduced hydraulic conductivity in this recharge basin. The anaerobic conditions appear to start at depth and work toward the surface, thereby suggesting a process that involves adsorption of organic material and consumption of dissolved oxygen with depth.