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An improved method for size distribution of stream bed gravel
Random sampling of surface rocks on a gravel bar is biased toward larger sizes which, because of their area, are more likely to be picked up. Weighting can eliminate this bias. Data on average weight of a single rock are used to change numbers of rocks to weights, thus yielding size frequency data in general agreement with a sieved and weighed sample. The question of what to sample depends on the use to which the data are to be put, and is not treated in detail in this paper.
Saline groundwater resources of the conterminous United States
Saline water is arbitrarily defined as water containing more than 1000 milligrams per liter of dissolved solids. Saline ground water is known to underlie about two‐thirds of the 48 states. Locally, aquifers yield saline ground water in profuse quantities, some of which is used by industry, particularly for cooling. Generally, however, saline water has been considered a nuisance. In this report it is dealt with as a resource, especially for the future. Forty chemical types of mineralized ground water were recognized, but sodium chloride dominates the occurrences and is almost the only type found where concentrations exceed about 20,000 mg/l. The occurrence and hydrologic properties of saline water aquifers deserve much more study than they have had. Copyright 1970 by the American Geophysical Union.
An approach to the design of statewide or regional ground water information systems
The design of water information or basic data systems must be flexible enough to provide information and data for a broad range of interests from national to local. The system must satisfy the need for information for accounting, surveillance, and areal synthesis purposes. The network is designed by identifying specific needs in terms of maps, analyses, and studies that will provide the basic knowledge for understanding each particular phase of the groundwater system. Each specific need is then analyzed with respect to whether it will provide information on accounting, surveillance, or areal synthesis. If a particular type of map, analysis, or observation can serve any of these three functions, a network of data collection or a program of studies is outlined in detail that will provide the information needed. The method of design necessitates the establishment of accuracy levels for maps, the density of data points, confidence limits, and so forth. The information system should be under the general guidance of a single agency, but much of the work and responsibility to carry out the details of the system must be shared by a number of agencies.
New tritium data on movement of groundwater in western Fresno County, California
Well waters along two traverse lines were sampled in 1963 and tested for tritium concentration. Haskell et al . [1966] estimated from the apparent thermonuclear tritium concentrations that groundwater had moved westward in the lower water‐bearing zone at a maximum velocity of 14–16.5 mi (23–27 km) in 9 yr. The maximum velocities and permeabilities estimated from the 1963 sampling were about an order of magnitude greater than the velocities and permeabilities suggested by prior hydrologic and geologic evidence. Consequently, in 1966–1970 the U.S. Geological Survey sampled and tested the tritium concentrations of well waters along the same two traverses but also extended the sampling eastward. On the basis of these analyses it is concluded that (1) thermonuclear tritium had not invaded the lower zone by 1970 within the extent of the 1963 sampling and (2) although the maximum westward movement of groundwater in the lower zone from 1955 to 1970 is indeterminate, it has been less than 4 mi (6.5 km) from the recharge area in 15 yr.
Economic basis of resource information systems: The case of streamflow network design
A general method for the economic design of natural resource information systems is presented for a certain class of natural phenomena. The system design is determined by the interaction of the technical input‐output relationship, i.e., the production function, the set of resource constraints, and an economic loss function defined in terms of parameter uncertainty. An application of the proposed method to streamflow network design is presented. Results of this analysis indicate that the method is fairly robust with respect to the assumptions. Observations are made which suggest extensions to flood measurement networks, long‐term precipitation networks, and seismic observation network design.
Classification of the hydrologic settings of lakes in the north central United States
The hydrologic settings of 150 lakes in the north central United States were investigated by principal component analysis as a first attempt to develop a general classification of the hydrologic settings of lakes. Precipitation-evaporation balance and the water quality variables have high loadings on the first principal component. Highest loadings on component 2 are for streamflow in and out of the lakes. Components 3 and 4 are characterized by geologic and groundwater flow variables. The drainage basin area/lake area ratio, the overland runoff variable, has the highest loading on component 5. The stability of the principal components was tested by randomly splitting the data and comparing a principal component analysis of each subsample. This showed the first two principal components to be the most stable. The components described by the groundwater variables are less stable, but there is justification for using them with caution. Of the variables examined in this study the distribution of dissolved solids of groundwater is most closely related to the distribution of lake types as determined by other limnological typologies in the north central United States. The study indicates that the following are the most important variables to be considered in classifying the hydrologic settings of lakes: dissolved solids concentration of groundwater, precipitation-evaporation balance, streamflow inlet and outlet, the ratio of drainage basin area to lake area, and lake depth. Of the groundwater variables, local relief and regional slope are more important than is regional position. Texture of the drift and bedrock, which is related to hydraulic conductivity of the rocks, is very important.
Numerical simulation of steady state three-dimensional groundwater flow near lakes
Numerical simulation of three-dimensional groundwater flow near lakes shows that the continuity of the boundary encompassing the local groundwater flow system associated with a lake is the key to understanding the interaction of a lake with the groundwater system. The continuity of the boundary can be determined by the presence of a stagnation zone coinciding with the side of the lake nearest the downgradient side of the groundwater system. For most settings modeled in this study the stagnation zone underlies the lakeshore, and it generally follows its curvature. The length of the stagnation zone is controlled by the geometry of the lake's drainage basin divide on the side of the lake nearest the downgradient side of the groundwater system. In the case of lakes that lose water to the groundwater system, three-dimensional modeling also allows for estimating the area of lake bed through which outseepage takes place. Analysis of the effects of size and lateral and vertical distribution of aquifers within the groundwater system on the outseepage from lakes shows that the position of the center point of the aquifer relative to the littoral zone on the side of the lake nearest the downgradient side of the groundwater system is a critical factor. If the center point is downslope from this part of the littoral zone, the local flow system boundary tends to be weak or outseepage occurs. If the center point is upslope from this littoral zone, the stagnation zone tends to be stronger (to have a higher head in relation to lake level), and outseepage is unlikely to occur.
Variation of rain chemistry during storms at two sites in northern California
The chemical composition of rainfall at Menlo Park, on San Francisco Bay, is compared with rainfall at Petrolia, which is near the coast about 500 km north of San Francisco. Sequential samples representing 1.35 to 5.4 mm of rain were collected from November 1971 to January 1972. At rural Petrolia the Cl:Na ratio was that of seawater for Cl concentrations ranging from 0.02 to 38 mg/l. In metropolitan Menlo Park the Cl:Na ratio in rain closely approximated that in seawater above about 0.5 mg/l Cl, but at lower Cl concentrations the ratio exceeded that in seawater, a fact attributed to the presence of anthropogenic Cl. Other constituents dissolved in Menlo Park rain (along with their concentration ranges in milligrams per liter), and believed to be derived in part from anthropogenic sources, were Ca (0.01–1.07), Mg (<0.01–1.08), Pb (0.003–0.035), Zn (0.002–0.013), Mn (0.0001–0.0057), Cu (0.0008–0.0024), NO 3 ‐N (0.02–0.54), and Br (<0.01–0.12). The range of p H values was smaller in the rural than in the metropolitan areas; average H + activity corresponded to a p H of 5.1 to 5.2 in both areas. At Petrolia, p H decreased with increased dissolved salts in rainfall, but no relation between p H and dissolved salts was evident at Menlo Park.
Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form
Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.
Probability weighted moments compared with some traditional techniques in estimating Gumbel Parameters and quantiles
Estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared. Results were derived from Monte Carlo experiments by using both independent and serially correlated Gumbel numbers. The method of probability weighted moments was seen to compare favorably with the other two techniques.
Some basic considerations in the design of hydrologic data networks
Two preeminent considerations of data network design are the random nature of the hydrologic phenomena and the uses that will be made of the data. Information distilled from the data is usually measured in a parametric statistical sense, although the data user is more concerned with the integrated measure of information - what impact does the lack of perfect hydrologic information have on the ensuing decisions? Two facets of the network, the efficiency of the data collection and the effectiveness of the resulting information, must be integrated to achieve a complete network design.
Worth of data and natural disaster insurance
The Federal Government in the past has provided medical and economic aid to victims of earthquakes and floods. However, regulating the use of hazard-prone areas would probably be more efficient. One way to implement such land use regulation is through the national flood and earthquake insurance program. Because insurance firms base their premium rates on available information, the benefits from additional data used to improve parameter estimates of the probability distribution (governing actual disaster events) can be computed by computing changes in the premiums as a function of additional data. An insurance firm is assumed to set rates so as to trade off penalties of overestimation and underestimation of expected damages. A Bayesian preposterior analysis is applied to determine the worth of additional data, as measured by changes in consumers’ surplus, by examining the effects of changes in premiums as a function of a longer hydrologic record.
Space, time, and the third dimension (model error)
The space-time tradeoff of hydrologic data collection (the ability to substitute spatial coverage for temporal extension of records or vice versa) is controlled jointly by the statistical properties of the phenomena that are being measured and by the model that is used to meld the information sources. The control exerted on the space-time tradeoff by the model and its accompanying errors has seldom been studied explicitly. The technique, known as Network Analyses for Regional Information (NARI), permits such a study of the regional regression model that is used to relate streamflow parameters to the physical and climatic characteristics of the drainage basin. The NARI technique shows that model improvement is a viable and sometimes necessary means of improving regional data collection systems. Model improvement provides an immediate increase in the accuracy of regional parameter estimation and also increases the information potential of future data collection. Model improvement, which can only be measured in a statistical sense, cannot be quantitatively estimated prior to its achievement; thus an attempt to upgrade a particular model entails a certain degree of risk on the part of the hydrologist.
Accuracy of an estuarine hydrodynamic model using smooth elements
A finite element model which uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and linear basis functions for water surface elevation is used in the computation of shallow water wave motions. Specifically addressed are two common uncertainties in this class of two-dimensional hydrodynamic models: the treatment of the boundary conditions at open boundaries and the treatment of lateral boundary conditions. The accuracy of the models is tested with a set of numerical experiments in rectangular and curvilinear channels with constant and variable depth. The results indicate that errors in velocity at the open boundary can be significant when boundary conditions for water surface elevation are specified. Methods are suggested for minimizing these errors. The results also show that continuity is better maintained within the spatial domain of interest when ‘smooth’ curve-sided elements are used at shoreline boundaries than when piecewise linear boundaries are used. Finally, a method for network development is described which is based upon a continuity criterion to gauge accuracy. A finite element network for San Francisco Bay, California, is used as an example.
Flood risks and the willingness to purchase flood insurance
Computer simulation experiments were conducted to determine the effects of alternative sources of uncertainty on the willingness to pay for flood insurance. Two alternative insurance protection schemes were investigated: coinsurance and fixed coverage. The question investigated here is to what extent does the insurance scheme influence how purchasers respond to flood risks? Floods were assumed to be log normally distributed and the effects on the purchase of insurance of uncertainties in the parameters of the distribution were explored using response surface analysis. Results indicate that fixed coverage insurance provisions shift most of the uncertainty in the physical parameters governing natural disaster occurrences away from the insuree and onto the insurer. The results also show that the form of the damage function has little effect on the demand for flood insurance.
A model to forecast short-term snowmelt runoff using synoptic observations of streamflow, temperature, and precipitation
Snowmelt runoff is forecast with a statistical model that utilizes daily values of stream discharge, gaged precipitation, and maximum and minimum observations of air temperature. Synoptic observations of these variables are made at existing low- and medium-altitude weather stations, thus eliminating the difficulties and expense of new, high-altitude installations. Four model development steps are used to demonstrate the influence on prediction accuracy of basin storage, a preforecast test season, air temperature (to estimate ablation), and a prediction based on storage. Daily ablation is determined by a technique that employs both mean temperature and a radiative index. Radiation (both long- and short-wave components) is approximated by using the range in daily temperature, which is shown to be closely related to mean cloud cover. A technique based on the relationship between prediction error and prediction season weather utilizes short-term forecasts of precipitation and temperature to improve the final prediction. Verification of the model is accomplished by a split sampling technique for the 1960–1977 period. Short- term (5–15 days) predictions of runoff throughout the main snowmelt season are demonstrated for mountain drainages in western Washington, south-central Arizona, western Montana, and central California. The coefficient of prediction ( C p ) based on actual, short-term predictions for 18 years is for Thunder Creek (Washington), 0.69; for South Fork Flathead River (Montana), 0.45; for the Black River (Arizona), 0.80; and for the Kings River (California), 0.80.
Measurement and computation of bed-material discharge in a shallow sand-bed stream, Muddy Creek, Wyoming
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 m 3 /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.