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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.
Hydrology of the North Cascades region, Washington: 1. Runoff, precipitation, and storage characteristics
The time and space distributions of measured precipitation and measured runoff and of spring storage, which is approximately equal to the subsequent summer runoff of snowmelt and stored groundwater, have been analyzed for the North Cascades region of Washington. Neither precipitation nor runoff shows a consistent relationship with altitude, chiefly because of precipitation-shadowing effects in this region of high relief. The relationship between mean annual precipitation and altitude is improved considerably when a topographic mean altitude is used instead of the actual altitude of the weather station. However, the improvement is not sufficient to explain a number of discrepancies that still occur. Some of the scatter in a precipitation-altitude plot appears to be due to a deficient precipitation catch by high-altitude gages. When the dependence of runoff on precipitation was examined on an annual, seasonal, and monthly basis, it was found that only a few low-altitude gages correlated well with basin runoff. In several instances, annual (water year) runoff could be better predicted from winter precipitation than from annual precipitation. Precipitation and runoff were tested for changes with time and both appeared to have been increasing slightly but not at a statistically significant level. When the summer (May–September) fraction of the total annual runoff is plotted against mean basin altitude, a consistent, physically reasonable, mildly curvilinear relationship is revealed. On the basis of this relationship, by using several drainages with diverse area-altitude profiles the spring storage versus altitude distribution can be estimated for each basin. The area-altitude distribution is used instead of the mean altitude in this calculation because of the apparent nonlinear relationship between runoff and altitude.
Hydrology of the North Cascades region, Washington: 2. A proposed hydrometeorological streamflow prediction method
On the basis of a linear relationship between winter (October-April) precipitation and annual runoff from a drainage basin (Rasmussen and Tangborn, 1976) a physically reasonable model for predicting summer (May-September) streamflow from drainages in the North Cascades region was developed. This hydrometeorological prediction method relates streamflow for a season beginning on the day of prediction to the storage (including snow, ice, soil moisture, and groundwater) on that day. The spring storage is inferred from an input-output relationship based on the principle of conservation of mass: spring storage equals winter precipitation on the basin less winter runoff from the basin and less winter evapotranspiration, which is presumed to be small. The method of prediction is based on data only from the years previous to the one for which the prediction is made, and the system is revised each year as data for the previous year become available. To improve the basin storage estimate made in late winter or early spring, a short-season runoff prediction is made. The errors resulting from this short-term prediction are used to revise the storage estimate and improve the later prediction. This considerably improves the accuracy of the later prediction, especially for periods early in the summer runoff season. The optimum length for the test period appears to be generally less than a month for east side basins and between 1 and 2 months for those on the west side of the Cascade Range. The time distribution of the total summer runoff can be predicted when this test season is used so that on May 1 monthly streamflow for the May-September season can be predicted. It was found that summer precipitation and the time of minimum storage are two error sources that were amenable to analysis. For streamflow predictions in seasons beginning in early spring the deviation of the subsequent summer precipitation from a long-period average will contribute up to 53% of the prediction error. This contribution decreases to nearly zero during the summer and then rises slightly for late summer predictions. The reason for the smaller than expected effect of summer precipitation is thought to be due to the compensating effect of increased evaporative losses and increased infiltration when precipitation is greater than normal during the summer months. The error caused by the beginning winter month (assumed to be October in this study) not coinciding with the time of minimum storage was examined; it appears that October may be the best average beginning winter month for most drainages but that a more detailed study is needed. The optimum beginning of the winter season appears to vary from August to October when individual years are examined. These results demonstrate that standard precipitation and runoff measurements in the North Cascades region are adequate for constructing a predictive hydrologic model. This model can be used to make streamflow predictions that compare favorably with current multiple regression methods based on mountain snow surveys. This method has the added advantages of predicting the space and time distributions of storage and summer runoff.
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.
Barometric fluctuations in wells tapping deep unconfined aquifers
Water levels in wells screened only below the water table in unconfined aquifers fluctuate in response to atmospheric pressure changes. These fluctuations occur because the materials composing the unsaturated zone resist air movement and have capacity to store air with a change in pressure. Consequently, the translation of any pressure change at land surface is slowed as it moves through the unsaturated zone to the water table, but it reaches the water surface in the well instantaneously. Thus a pressure imbalance is created that results in a water level fluctuation. Barometric effects on water levels in unconfined aquifers can be computed by solution of the differential equation governing the flow of gas in the unsaturated zone subject to the appropriate boundary conditions. Solutions to this equation for two sets of boundary conditions were applied to compute water level response in a well tapping the Ogallala Formation near Lubbock, Texas from simultaneous microbarograph records. One set of computations, based on the step function unit response solution and convolution, resulted in a very good match between computed and measured water levels. A second set of computations, based on analysis of the amplitude ratios of simultaneous cyclic microbarograph and water level fluctuations, gave inconsistent results in terms of the unsaturated zone pneumatic properties but provided useful insights on the nature of unconfined-aquifer water level fluctuations.
The geochemistry of the Fox Hills-Basal Hell Creek Aquifer in southwestern North Dakota and northwestern South Dakota
The Late Cretaceous Fox Hills Formation and the basal portion of the overlying Hell Creek Formation constitute an important aquifer in the Fort Union coal region. Throughout most of southwestern North Dakota and northwestern South Dakota the aquifer is at depths ranging from 1000 to 2000 ft, except for exposures along the Cedar Creek anticline. Water flows in the aquifer from southwest to northeast, with flow rates of a few feet per year. The recharge and discharge areas of the aquifer are separated by a north-south trending transition zone in which significant changes in water chemistry occur. Dissolved constituents in the recharge area (the western part of the study area) are Na + = 18 mmol/l, Cl − = 0.7 mmol/1, SO 4 2− = 2.7 mmol/1, and HCO 3 − = 13 mmol/l (δ 13 C = −12‰) with p H = 8.5. Ca 2+ , Mg 2+ , and K + are each less than 0.1 mmol/l, dissolved O 2 = 0, and traces of H 2 S and CH 4 are present. Computer modeling and carbon isotope data suggest the following reactions in the recharge area. CO 2 derived from lignitic carbon reacts to dissolve carbonate minerals, with cations then being exchanged for Na + on clay minerals. The high p H in the aquifer is the result of buffering by carbonate-ion exchange equilibria. In the discharge area, p H values have declined to 8.3, Cl − has increased from 0.7 to 5.5 mmol/l, with a parallel increase in Na + SO 4 2− has essentially disappeared, HCO 3 − has increased from 13 to 21 mmol/l (δ 13 C = −9‰), CH 4 has attained concentrations greater than 0.5 mmol/l, and small amounts of He are present. Traces of H 2 S are present, and Ca 2+ , Mg 2+ , and K + concentrations remain low throughout the aquifer: These changes can be accounted for by reactions in the aquifer: (1) sulfate reduction to pyrite with lignitic material as the carbon source and (2) continuous buffering of p H by the carbonate-ion exchange equilibria. Chemical and hydrologic data suggest that the increase in NaCl results from upward movement of small volumes of water into the Fox Hills aquifer from the transition zone eastward. Redox reactions in the aquifer are closely analogous to those observed in pore waters of reducing marine sediments. Reactions approach but do not achieve true thermodynamic equilibrium. Measurements of redox potential suggest a downgradient decrease in redox potential. The measurements are not amenable to quantitative interpretation.
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.