Showing papers in "Water Resources Research in 1968"

Noah, Joseph, and Operational Hydrology

Abstract: By ‘Noah Effect’ we designate the observation that extreme precipitation can be very extreme indeed, and by ‘Joseph Effect’ the finding that a long period of unusual (high or low) precipitation can be extremely long. Current models of statistical hydrology cannot account for either effect and must be superseded. As a replacement, ‘self-similar’ models appear very promising. They account particularly well for the remarkable empirical observations of Harold Edwin Hurst. The present paper introduces and summarizes a series of investigations on self-similar operational hydrology.

Steady Infiltration from a Shallow Circular Pond

Abstract: Steady infiltration from a shallow, circular, inundated area on the horizontal surface of a semi-infinite porous medium is treated by a method of linearization proposed by J. R. Philip. Using this method, Philip retains most of the properties of the nonlinear system but reduces the differential equation to a linear type governing steady diffusion in a steady uniform flow. On the surface of the medium, the boundary conditions are of mixed type, although linear. These conditions are reduced to a system of dual integral equations solved by a modification of Tranter's method. Expressions for the distributions of vertical flux density, moisture content, and Stokes' stream function are derived, and numerical values of the last two quantities are illustrated graphically. It is found that the total flux depends almost linearly upon a parameter α, defined as the logarithmic derivative of the hydraulic conductivity with respect to capillary potential. Curves of mean flux over various radii (fractions of the total source radius) for various values of α indicate the importance of the guard ring in infiltrometer design.

Onset of Thermohaline Convection in a Porous Medium

Abstract: The problem of the onset of convection, induced by buoyancy effects resulting from vertical thermal and solute concentration gradients, in a horizontal layer of a saturated porous medium, is treated by linear perturbation analysis. It is shown that oscillatory instability may be possible when a strongly stabilizing solute gradient is opposed by a destabilizing thermal gradient, but attention is concentrated on monotonic instability. The eigenvalue equation, which involves a thermal Rayleigh number R and an analogous solute Rayleigh number S, is obtained, by a Fourier series method, for a general set of boundary conditions. Numerical solutions are found for some special limiting cases, extending existing results for the thermal problem. When the thermal and solute boundary conditions are formally identical, the net destabilizing effect is expressed by the sum of R and S.

The Sediment Yield of Major Rivers of the World

Abstract: The amount of suspended sediment transported by rivers to the seas each year is tabulated. The major rivers are ranked in order of tons of sediment transported per year and drainage area and water discharge data are included. The rivers are listed by, continents in subsequent tables with data on drainage area, annual sediment yields in tons, sediment production rates in tons per square mile per year, the years of sediment measurement, and the sources of data. This sample represents more than one-third of the land contributing water-borne sediment to the seas and, if representative, indicates an annual world sediment yield of 20 billion (20 × 109) tons. The data suggest that Africa, Europe, and Australia have very low sediment yields (<120 tons per square mile per year), South America's rate is low, North America's is moderate, and Asia's is high to the degree of yielding up to 80% of the sediment reaching the oceans annually.

Base-Flow Recessions—A Review

Abstract: Hydrologists have studied base-flow recessions for one hundred years or more. By the early nineteen hundreds much of the basic mathematical development was completed, and some methods of hydrograph analysis were known. Recent mathematical work, although repetitive to some extent of the earlier efforts, has the advantage that it assesses more closely the effects of the simplifying assumptions used to obtain solutions. Most workers have preferred to follow graphical or statistical rather than mathematical approaches. The reasons appear to lie mainly in problems caused by the assumptions and in difficulties in interpreting the real stream hydrograph. Also, base flow can come from numerous sources besides ground water. Other complications arise from the question of whether the basin response is linear or nonlinear, because the response is a function of various geologic and hydrologic factors in addition to those considered in the mathematical derivations.

The Response of Water Temperatures to Meteorological Conditions

Abstract: The exchange of heat across the air-water interface is one of the more important factors that govern the temperature of a water body. The net rate of heat exchange at the water surface is the sum of the rates at which heat is transferred by radiative processes, by evaporation, and by conduction between water and overlying air. The net rate can be evaluated in terms of a thermal exchange coefficient and an equilibrium temperature, both of which depend on observable meteorological variables. Any one of the many evaporation formulas and mathematical descriptions of the other heat exchange processes may be used to develop equations involving the thermal exchange coefficient and equilibrium temperature. Such equations are useful in developing relations that describe the temporal and spatial temperature distributions within a water body. They provide additional insight into the effects of meteorological conditions on water temperatures, and they facilitate estimates of various terms of the heat budget.

Application of the Digital Computer for Aquifer Evaluation

Abstract: The unsteady-state flow of a fluid in a confined aquifer can be approximated by linear, parabolic, partial-differential equations. A digital-computer program was written to solve these equations based upon an implicit finite-difference technique. Calculated values compared favorably with analytical solutions for homogeneous, isotropic aquifers of simple geometry. An analysis of an aquifer at Musquodoboit Harbour, Nova Scotia, was made using this technique. Aquifer parameters in the digital model were modified until the results computed fitted the pump-test data. The results indicate that this aquifer would come to equilibrium in about 100 days and would easily provide an adequate supply of water for the village of Musquodoboit Harbour. As a check of the digital model for this problem an electric analog of this aquifer was also constructed; the two solutions obtained compared favorably.

Uniform Flood-Frequency Estimating Methods for Federal Agencies

Abstract: Large-scale planning for improved flood-plain management and expanding water-resources development has made it increasingly important that a consistent approach be adopted for estimating flood frequencies, a major analytical component in studies required in flood-plain management and, in a larger sense, in river-basin management. A Federal interagency group has studied the most commonly used methods of flood-frequency analysis and has compared the results of applying these methods to a selected group of long-record representative sites in different parts of the country. Based on these comparisons and on other considerations, it is recommended that all government agencies adopt a uniform procedure for flood-frequency analysis at sites where records are available. The log-Pearson Type III distribution has been selected as the base method, with provisions for departures from the base method where justified. Continuing study leading toward improvement or revision of methods is recommended.

Point dilution methods of investigating ground water flow by means of radioisotopes

Abstract: To apply the point-dilution method of measuring the rate of ground water flow by tracers, the distortion of the flow field by the well must be known. The distortion can be calculated with sufficient accuracy if the permeabilities of the aquifer, k3, of the gravel pack, k2, and of the well screen, k1, fulfill the condition k3 ≤ k2 ≤ k1. The tracer must be adequately mixed during the dilution procedure. Experiences obtained from model tests are applied in investigations in the field. By using peak-to-peak and total count methods in wells where vertical flow occurred, we could determine the depths and the rates of inflow and outflow, which relate to seepage under dams and water exploration. To determine the direction of ground water flow, a radio tracer was injected into a well-screen section and, after having left the well-screen, was detected by a collimated detector. The use of tracers that are fixed on the soil is advisable; 198Au, having been homogeneously distributed within the dilution volume initially, has proved most suitable. Strong vertical currents in the well represent a serious obstacle in field measurements of the rate and of the direction of ground water flow.

The Use of Oxygen 18 and Deuterium Concentrations in the Water Balance of Lakes

Abstract: Natural concentrations of stable isotopes of hydrogen and oxygen are used to determine the water balance of lakes situated in a subhumid climate in southwestern Turkey. A salt lake in that region is used as an index to the molecular exchange process between the lake and the atmospheric moisture. Such use of stable isotopes of oxygen and hydrogen in water balance studies appears to yield promising results and indicates that environmental isotopic studies might be a useful tool in limnological studies. (Key words: Environmental isotopes; molecular exchange; lake water balance)

Development and testing of snow pack energy balance equations

Abstract: By making several minor assumptions and using an empirical technique in one situation, the energy balance of a snow pack can be computed on a continuous basis. Net radiation or its components, air temperature, dew-point temperature, atmospheric pressure, amount of precipitation and its temperature, surface snow density, and a wind function that relates vapor pressure gradient to moisture transfer as a function of wind speed, must be either measured or estimated. Comparison of computed versus observed snow pack runoff and snow surface temperature for the Lower Meadow lysimeter studies of 1954 at the Central Sierra Snow Laboratory reveals good agreement. A model was constructed by combining the energy balance equations with relationships describing the other components of the snow accumulation and ablation processes. The Stanford Watershed Model is used to determine the time delay from when water leaves the snow pack to the streamflow gaging station. Tests of the model on 5 years of data from the Central Sierra Snow Laboratory resulted in a reasonable simulation of the observed mean daily flow hydrograph and seasonal areal snow cover plot. It is concluded that the model is at least a good approximation to the actual physical processes and should be a valuable tool in further snow hydrology investigations.

Steady Infiltration From Buried Point Sources and Spherical Cavities

Abstract: Steady infiltration in two- and three-dimensional systems has been treated classically as a process of saturated flow with a free surface. The series this paper initiates deals with the generally unsaturated flow regimes set up by prolonged infiltration into regions with no shallow ambient water table. The analysis is simpler than the classical one in the sense that it does not involve a free surface. With hydraulic conductivity represented by an exponential function of moisture potential, the nonlinear equation for steady flow is transformed into a linear equation which is formally equivalent to that for diffusion in a moving medium. The fundamental point source solution is explored and is used as the basis of an analysis of steady infiltration from spherical cavities. For cavities of small (dimensionless) radius, the infiltration rate is determined almost wholly by capillarity; on the other hand, gravity distorts the pattern of moisture distribution strongly, even when the cavity radius is small.

Linear programming applied to water quality management

Abstract: Linear programming is applied to the management of water quality in a river basin. The charge is to select the efficiencies of the treatment plants on the river that will achieve the dissolved oxygen standards at a minimum cost. The objective function is structured in terms of the costs of the treatment plants. The principal constraints prevent violation of the dissolved oxygen standards. A simplified version of the Willamette River in Oregon is studied, using the linear programming formulation, and the results are compared with those obtained by dynamic programming. The effects of changes in the dissolved oxygen standards are explored by use of the dual variables.

Optimization of the Operation of a Multiple-Purpose Reservoir by Dynamic Programming

Abstract: A technique of analysis is presented by which the dynamic operation policies for planning complex reservoir systems producing hydroelectric power and providing water can be optimized for the maximum return from firm water, firm power, dump water, and dump power. The technique provides for complex constraints, such as mandatory flood control reservations variable in time, fish, wildlife, and recreational releases, navigation minimum flows, etc., as well as evaporation losses and inter-basin diversions. The paper presents in detail the operational analysis of a component reservoir-river system and the procedure to be used to combine optimally a number of such subsytems into a coordinated, mutually reinforcing, multiple-river system.

Statistical Properties of Stream Lengths

Abstract: Two basic assumptions are employed in this treatment of the statistics of stream lengths: (1) All topologically distinct networks with a given number of sources are equally likely (after Shreve). (2) Lengths of interior links in a given network are independent random variables drawn from the same population. The mathematical development leads to an approximate expression for L¯ω that contains no adjustable parameters and that depends only on the stream numbers and the mean link length. This expression gives somewhat better agreement with data on actual stream systems than does Horton's law of stream lengths; other advantages over Horton's law are cited. Quantitatively, our procedure appears to account for about 65% of the variance in mean stream length data for third- and fourth-order basins. If exact values of the link numbers are introduced into the calculation, the unexplained variance is reduced to about 15%. For a complete statistical description of stream lengths, it is necessary to know the distribution of interior link lengths. Results of computer simulation studies suggest that this distribution is negative exponential. Data taken on two small watersheds (140 links) show reasonable agreement with this hypothesis.

Theoretical Analysis of Regional Ground Water Flow: 3. Quantitative Interpretations

Abstract: The natural basin yield of a ground water basin can be calculated from a quantitative analysis of the flow net obtained from a digital computer solution to a numerical mathematical model of the basin. The natural basin yield is an unique property of the basin and can be considered as a measure of the ground water recharge to the basin and a conservative estimate of the safe yield. Rates of ground water recharge and discharge vary from place to place throughout the areal extent of a basin; a quantitative analysis can be used to determine the positions of concentration. Quantitative interpretation of ground water flow nets can play an important role in the calculation of basin-wide water balances due to the inter- relationships between ground water recharge and infiltration at one end of the flow system and ground water discharge, evapotranspiration, and stream baseflow at the other.

Conversion of Hardwood-Covered Watersheds to White Pine Reduces Water Yield

Abstract: Mixed mature hardwoods were cleared from two Southern Appalachian experi- mental watersheds, and the areas were planted with eastern white pine in 1956-1957. Once the pine crowns began to close, streamflow steadily declined at a rate of 1 to 2 inches per year. By 1967, water yield was 3.7 inches less from a 10-year-old pine stand on a south- facing watershed than expected water yield from the original hardwood forest. Most of the water yield reduction occurred during the dormant season and was attributed mainly to greater interception loss from white pine than from hardwoods. Because interception differ- ences increase as white pine matures, an even greater reduction in streamflow is expected. (Key words: Water yield; watershed management; interception; basins; white pine)

Atmospheric Contributions to Water Quality of Streams in the Hubbard Brook Experimental Forest, New Hampshire

Abstract: The balances of input in atmospheric precipitation and discharge in streams have been determined for selected mineral constituents in three small tributaries to Hubbard Brook in the White Mountains of New Hampshire. Inputs and discharge of sulfate, ammonium, and nitrate were calculated from hydrologic data, together with chemical analyses of weekly samples of precipitation and streamwater taken over a 2-year period. The calculations show that precipitation provides most of the 30–50 kilograms of sulfate per hectare carried annually by the streams and that inputs exceed outflows of ammonium and of nitrate. Maximum effluent nitrate concentrations of 2 mg/l (milligrams per liter) are observed in early spring. Measurements of pH indicate that the hydrogen ion is one of the major cations in precipitation over the area. Determinations were made of the discharge of bicarbonate, silica, and aluminum in the streams. Annual stream loads of silica ranged from 20 to 40 kilograms per hectare. Effluent bicarbonate and silica concentrations vary directly with each other and inversely with aluminum.

Some Factors Affecting Baseflow

Abstract: For a shallow aquifer and a fully penetrating stream, the ideal baseflow curve does not plot as a straight line on semilog paper, and its recession rate continuously decreases with time. For a deep aquifer and a shallow-entrenched stream, the ideal baseflow generally decays exponentially, and its recession rate decreases with increasing stream entrenchment. In the case of loss from evapotranspiration, the baseflow curves steepen progressively with time, and the stream may become influent. In the case of gain from confined aquifers, the baseflow curves become flatter. The recharge results in shifting of the baseflow curves upward in magnitude or laterally in time. The baseflow peak occurs at about 0.75T from the beginning of recharge to the aquifer, where T denotes the effective duration of recharge. The lag between the total flow peak and the baseflow peak depends on rainfall, soil, and basin factors. The variability of these factors precludes the notion of a constant lag.

Some thermodynamic relationships for soils at or below the freezing point: 1. Freezing point depression and heat capacity

Abstract: : An extended equation was derived relating the relative partial molar free energy of water in a soil to its freezing point depression and relative partial molar heat content. The equation was used to prepare a table from which each of these 3 quantities can be ascertained if the other 2 are known. The table was used with experimental data to obtain a curve of freezing point depression vs. water content for Na-Wyoming bentonite. Provided the activity of the liquid water in the clay is a single-valued function of the liquid water content and that the ice has the properties of pure bulk ice, this curve also represents the relationship between freezing point depression and unfrozen water in the partially frozen clay. An equation for the heat capacity of a partially frozen soil was also derived. This equation was employed to calculate the heat capacities of the clay at different water contents and sub-zero temperatures. A comparison of the calculated unfrozen water contents and heat capacities of the partially frozen Na-Wyoming bentonite with the available experimental data indicated satisfactory agreement, especially as regards the unfrozen water contents.

Lakeshore Property Values: A Guide to Public Investment in Recreation

Abstract: A study of lakeshore property values in which land and improvement values were regressed against attributes of the site and lake to determine the importance of the various characteristics in predicting property values indicates that swampy or steeply sloped banks are negatively correlated with value, whereas water quality, proximity to population centers, and the presence of many other lakes in the area are positively related to value. No significant relationships were discovered between land values and the amount of public land in the vicinity or the degree of fluctuation in the lake level. Property values approximately doubled in the ten-year period of the study. By suggesting characteristics that seem to be in greater demand, the study provides information to guide some of the decisions about where to spend the limited public budget for waterfront recreational facilities.

The Use of a Square Grid System for Computer Estimation of Precipitation, Temperature, and Runoff

Abstract: Studies on water resources in the last few years have had the tendency to encompass larger and larger areas The increase in size and sophistication of these studies makes the use of computers almost mandatory To adapt computers to this type of study, the study area must be converted to a schematic representation which is easily manageable by computers A simple and reasonable way of doing this is to cover the study area with a square grid, which may then be considered as consisting of a matrix of squares This system can be used to store, process, and retrieve information and may have numerous applications in the fields of hydrology, hydraulic power, economics, etc The paper presents the application of the square grid system to the estimation of the precipitation, temperature, and runoff distribution in a large area and shows how the use of the system enables efficient combination of the meteorologic and hydrologic information available in assessing the precipitation, temperature, and runoff distribution An example of such a computation for a 43,000-square-mile area is shown and the advantages of the method over the usual techniques emphasized

Miscible Displacement in an Unsaturated Glass Bead Medium

Abstract: A series of miscible displacement experiments was conducted in an unsaturated glass bead medium maintained at a constant average water content during each displacement. The variation in the form of the breakthrough curve with decreasing water content was not large and was not related in a simple way to the water content; however, there was consistent shift of the breakthrough curve to the left of the relative concentration value of 0.5 and 1 pore volume and a lone tail or slow approach to the final relative concentration of 1.0. Some of these effects may be attributed to the presence of stagnant liquid in the pores. (11 refs.)

The permeability of a porous medium determined from certain probability laws for pore size distribution

Abstract: An equation derived for the permeability of a porous medium based on the general principles of the series-parallel model contains a double integral which is solved for several continuous probability laws describing the distribution of the sizes of the interstices of the porous medium. The agreement between calculated results and available experimental data is satisfactory.

On the Quantitative Inventory of the Riverscape

Abstract: In the vicinity of Berkeley, California, 24 minor valleys were described in terms of factors chosen to represent aspects of the river landscape. A total of 28 factors were evaluated at each site. Some were directly measurable, others were estimated, but each observation was assigned to one of five categories for that factor. Each factor for each site was then expressed as a uniqueness ratio, which depended on the number of sites being in the same category. The uniqueness ratio is believed to represent one way the scarcity of a given riverscape can be ranked quantitatively without bias based on notions of good or bad, and without assigning monetary value.

Annual hydrologic response to watershed conversion from oak woodland to annual grassland

Abstract: A 12-acre experimental watershed in the Sierra Nevada foothills of central California has been subjected to intensive range management practices after a six-year calibration The treatment consisted of chemically killing a dense stand of oak trees and brush to improve forage production An adjacent untreated watershed, which is geologically and hydrologically similar, provides a means of evaluating the annual hydrologie response Streamflow comparison shows an average annual increase of 45 inches in water yield Inflow-outflow analysis shows a corresponding decrease in consumptive use from an average of 20 inches per year to 15 inches per year The change in consumptive use is demonstrated in an annual water yield prediction model and in the relationship of consumptive use to precipitation Estimates of annual potential evapotranspiration from climatological data are higher than measured consumptive use Two methods for predicting annual consumptive use show close agreement with measured values for both the oak woodland and the annual grassland

Misconceptions in hydrology and their consequences

Abstract: Several misconceptions have been introduced into hydrology that have had adverse consequences on the science and on water-resources development. Persistent use of the concept of maximum precipitation and maximum probable precipitation, for which there is no physical proof, has discouraged research into the structure and probability of extreme events, and may have led to an unwarranted sense of security concerning flood-control works. Attempts at long range forecasts of water supply based entirely on meteorological processes have misdirected research and raised false expectations. A misconception that hydrologic processes are composed of a limited number of hidden periodicities has retarded the use of modern stochastic analyses of time series. Cloud-seeding to increase numbers of raindrops rather than their coalescence may have had a negative effect on precipitation in arid regions. Considering ground water, instead of the aquifer, as a resource has stressed the technology of withdrawal at the expense of study of methods of recharge and has led to much unplanned overdraft of ground water. Use of descriptive instead of numerical variables has delayed the application of modern statistical methods to planning the exploration of the ground-water environment. As a result of the neglect of the stochastic properties of porous mediums, fluid mechanics theory has not departed far from the original works of Darcy. Hydrology has developed slowly because it has been considered an appendage of hydraulic engineering rather than a natural science.

A Mathematical Model for Simulating the Hydrologic Response of a Watershed

Abstract: A general mathematical model was developed to simulate the surface runoff from watersheds. Based upon the integration of the concepts of physical hydrology into quantitative relationships, the model avoids the use of lumped parameters by delineating the watershed as a grid of small, independent elements. Because of the resultant freedom from fundamental assumptions regarding the form of the system equations and from the permissible small areal resolution of the model, very complex combinations of watershed and storm conditions may be studied. Application of the model to two very small watersheds indicated a need for additional research to define better the relationships for surface runoff and infiltration to improve the reliability of the simulated runoff hydrographs.

Some Comments on Regionalization in Hydrologic Studies

Abstract: At the jth site, a choice must be made between yi, a statistical characteristic of the observed flows, and ŷi, a regionalized estimate of the characteristic, for use in the model for generating synthetic flows at the jth site. The regional estimate is obtained from a regression of y on a set of basin characteristics. If Vˆii/Vii < 2− ρ′, then ŷi instead of yi, is used in the generating model, where Vˆii and Vii are the variances of ŷi and yi, respectively, and ρ′ is a measure of the interstation correlations. This criterion is shown to be independent of the jth basin characteristics. The criterion is a function of the jth basin characteristics if the data at the jth site are not used in developing the regression relation. For an ungaged site, ŷi may be obtained with variance that depends upon the basin characteristics at the jth ungaged site. (Key words: Statistics; regionalization; synthesis)

An Implicit Method for Numerical Flood Routing

Abstract: There is great need for fast and accurate methods for the numerical solution of the equations of unsteady flow, which play an important role in the field of water resources. An implicit method which is both fast and accurate can be established based on (1) a centered difference scheme for representing the primary differential equations in finite difference form, and (2) simultaneous solutions of the finite difference equations for each time step. The difference equations constitute a system of nonlinear algebraic equations that can be solved on a digital computer by rapidly convergent procedures based on the generalized Newton iteration method. Application of the implicit method to the movement of floods in long channels confirms the efficiency and accuracy of the method.