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At least 1,423 records · Page 79Linked to original sources
USGS2008

Errors and parameter estimation in precipitation-runoff modeling: 1. Theory

Errors in complex conceptual precipitation-runoff models may be analyzed by placing them into a statistical framework. This amounts to treating the errors as random variables and defining the probabilistic structure of the errors. By using such a framework, a large array of techniques, many of which have been presented in the statistical literature, becomes available to the modeler for quantifying and analyzing the various sources of error. A number of these techniques are reviewed in this paper, with special attention to the peculiarities of hydrologic models. Known methodologies for parameter estimation (calibration) are particularly applicable for obtaining physically meaningful estimates and for explaining how bias in runoff prediction caused by model error and input error may contribute to bias in parameter estimation.

Water Resources Research↗
USGS2008

Errors and parameter estimation in precipitation-runoff modeling: 2. Case study

A case study is presented which illustrates some of the error analysis, sensitivity analysis, and parameter estimation procedures reviewed in the first part of this paper. It is shown that those procedures, most of which come from statistical nonlinear regression theory, are invaluable in interpreting errors in precipitation-runoff modeling and in identifying appropriate calibration strategies.

Water Resources Research↗
USGS2008

Sorting of bed load sediment by flow in meander bends

Equilibrium sorting of coarse mobile bed load sediment in meander bends is considered. A theory of two-dimensional bed load transport of graded material, including the effects of gravity on lateral slopes and secondary currents, is developed. This theory is coupled with a simple treatment of flow in bends, an analytically determined bend shape, and the condition of continuity of each grain size range in transport to describe sorting. The theory indicates that the locus of coarse sediment shifts from the inside bank to the outside bank near the bend apex, as is observed.

Water Resources Research↗
USGS2008

Type curve analysis of inertial effects in the response of a well to a slug test.

The water level response to a slug or bailer test in a well completed in a confined aquifer has been evaluated taking into account well-bore storage and inertial effects of the water column in the well. The response range, from overdamped with negligible inertial effects to damped oscillation, was covered employing numerical inversions of the Laplace-transform solution. By scaling the time with respect to the undamped natural period of the well-aquifer system and by using the damping parameter for a second-order damped, inertial-elastic system, a set of type curves was constructed that enables water level response data from a slug or bailer test to be analyzed under conditions where the inertial parameter is large. Values of transmissivity and effective static water column length can be determined when an estimate of storage coefficient is available. The numerical solution and resulting type curves cover the transition range between the limiting cases of negligible inertial effects and of damped oscillation that have been treated by others. Two examples of slug test analysis show that precise results depend on accurate measurements of water level displacement (±1% of initial value).

Water Resources Research↗
USGS2008

Downstream dilution of a lahar: Transition from debris flow to hyperconcentrated streamflow

Nearly instantaneous melting of snow and ice by the March 19, 1982, eruption of Mount St. Helens released a 4 × 10 6 m 3 flood of water from the crater that was converted to a lahar (volcanic debris flow) through erosion and incorporation of sediment by the time it reached the base of the volcano. Over the next 81 km that it traveled down the Toutle River, the flood wave was progressively diluted through several mechanisms. A transformation from debris flow to hyperconcentrated streamflow began to occur about 27 km downstream from the crater, when the total sediment concentration had decreased to about 78% by weight (57% by volume). The hyperconcentrated lahar-runout flood wave, transporting immense quantities of sand in suspension, continued to experience progressive downstream dilution. Although turbulence was significantly dampened by the extremely high suspended load, very large standing waves and antidune waves were observed. The hyperconcentrated lahar-runout flow deposited an unusual, faintly stratified, coarse sand which locally contained small, isolated gravel lenses. Very similar deposits in the Quaternary stratigraphy of Mount St. Helens and other Cascades volcanoes suggest that lahars may be more frequent than previously recognized.

Water Resources Research↗
USGS2008

A comparison of several methods of solving nonlinear regression groundwater flow problems

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher-Reeves method, and this was followed closely by the quasi-Newton method. The Marquardt and quasi-linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi-linearization methods than for the other two. Hence the quasi-Newton (and perhaps Fletcher-Reeves) method might be more efficient than either the Marquardt or quasi-linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi-linearization metilod for three of the four problems. For all four problems the quasi-Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher-Reeves method required slightly less memory than the quasi-Newton method. Memory requirements were not excessive for any of the four methods.

Water Resources Research↗
USGS2008

Geochemistry of groundwater in Cretaceous sediments of the southeastern coastal plain of eastern Mississippi and western Alabama

Geochemical samples of waters along two hydrologic flow paths in four Upper Cretaceous aquifers of northeastern Mississippi and western Alabama indicate similar geochemical evolution of their respective waters. The waters of the Coker, Gordo, and Eutaw-McShan aquifers, noncalcareous sands, increase downgradient in dissolved solids and p H, and are dominated by sodium and bicarbonate ions, which generally result from a calcite dissolution-cation exchange process. Increases in dissolved iron from oxidation reduction reactions followed by decreases in total inorganic carbon from siderite precipitation occur along the flow paths. As the total inorganic carbon increases, carbon 13 (δ 13 C) generally is enriched in the moving waters, indicating the addition of a predominantly heavy source of carbon, most likely dissolving calcite. In the Coker aquifer δ 13 C values in the waters become more negative downgradient, resulting from lignite oxidation, followed by δ 13 C values becoming more positive, resulting from dissolving calcite and perhaps some mixing with brines. In northeastern Mississippi the Ripley aquifer, a calcareous sand, initially contains calcium-bicarbonate dominated water that evolves to a sodium- bicarbonate dominated water downgradient, primarily from the calcite dissolution-cation exchange process. Feldspar hydrolysis to kaolinite dominates aluminosilicate reactions in the upgradient parts of the aquifers. Authigenesis of smectite clay may be occurring in the deeper, downgradient parts of the aquifers.

Alabama, Mississippi↗
USGS2008

Assessment of long-term salinity changes in an irrigated stream-aquifer system

Changes in salinity in groundwater and surface water in the Arkansas River valley of southeastern Colorado are primarily related to irrigation practices. A solute transport model was applied to an 11-mile reach of the valley to compute salinity changes in response to spatially and temporally varying stresses. The model was calibrated in 1973 using detailed field measurements made during 1971 and 1972. In 1973 the calibrated model was used to predict that a gradual long-term increase in groundwater salinity of about 2–3% per year would occur if the observed irrigation practices continued. The study area was resampled during the winter of 1982 to help evaluate if any long-term changes in salinity are actually occurring. Nonparametric and parametric statistical tests were used to help assess the significance of observed changes in groundwater salinity. These tests indicate that a statistically significant increase in salinity occurred between the winters of 1971 and 1972 (the model calibration period). However, a comparison of the winter 1972 and winter 1982 data indicates that no significant net change in salinity has occurred during this 10-year period. An analysis of the few available historical data (1895, 1923, 1959–1961, and 1964) supports the hypothesis that groundwater salinity in this irrigated area has reached a long-term dynamic equilibrium in response to irrigation practices. The model predictions of long-term salinity increases were invalid probably because the calibration period occurred during a short-term annual trend of increasing salinity in the river (and hence in leaky irrigation canals and in applied irrigation water), which was not representative of the long-term trend.

Colorado↗
USGS2008

Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media: 1. Theory

A field method is proposed for determining the three-dimensional hydraulic conductivity tensor and specific storage of an anisotropic porous or fractured medium. The method, known as cross-hole testing (to distinguish it from conventional single-hole packer tests), consists of injecting fluid into (or withdrawing fluid from) packed-off intervals in a number of boreholes and monitoring the transient head response in similar intervals in neighboring boreholes. The directions of the principal hydraulic conductivities need not be known prior to the test, and the boreholes may have arbitrary orientations (e.g., they can all be vertical). An important aspect of the proposed method is that it provides direct field information on whether it is proper to regard the medium as being uniform and anisotropic on the scale of the test. The first paper presents theoretical expressions describing transient and steady state head response in monitoring intervals of arbitrary lengths and orientations, to constant-rate injection into (or withdrawal from) intervals having similar or different lengths and orientations. The conditions under which these intervals can be treated mathematically as points are investigated by an asymptotic analysis. The effect of planar no-flow and constant-head boundaries on the response is analyzed by the theory of images. The second paper describes the field methodology and shows how the proposed approach works in the case of fractured granitic rocks.

Water Resources Research↗
USGS2008

Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media: 2. Methodology and application to fractured rocks

The analytical solutions developed in the first paper can be used to interpret the results of cross-hole tests conducted in anisotropic porous or fractured media. In the particular case where the injection and monitoring intervals are short relative to the distance between them, the test results can be analyzed graphically. From the transient variation of hydraulic head in a given monitoring interval, one can determine the directional hydraulic diffusivity, K d ( e )/ S s , and the quantity D / S s , by curve matching. (Here K d ( e ) is directional hydraulic conductivity parallel to the unit vector, e , pointing from the injection to the monitoring interval, S s is specific storage, and D is the determinant of the hydraulic conductivity tensor, K .) The principal values and directions of K , together with S s , can then be evaluated by fitting an ellipsoid to the square roots of the directional diffusivities. Ideally, six directional measurements are required. In practice, a larger number of measurements is often necessary to enable fitting an ellipsoid to the data by least squares. If the computed [ K d ( e )/ s s ] ½ values fluctuate so severely that a meaningful least squares fit is not possible, one has a direct indication that the subsurface does not behave as a uniform anisotropic medium on the scale of the test. Test results from a granitic rock near Oracle in southern Arizona are presented to illustrate how the method works for fractured rocks. At the site, the Oracle granite is shown to respond as a near-uniform, anisotropic medium, the hydraulic conductivity of which is strongly controlled by the orientations of major fracture sets. The cross-hole test results are shown to be consistent with the results of more than 100 single-hole packer tests conducted at the site.

Water Resources Research↗
USGS2008

Assessment of the instantaneous unit hydrograph derived from the theory of topologically random networks

An instantaneous unit hydrograph (iuh) based on the theory of topologically random networks (topological iuh) is evaluated in terms of sets of basin characteristics and hydraulic parameters. Hydrographs were computed using two linear routing methods for each of two drainage basins in the southeastern United States and are the basis of comparison for the topological iuh's. Elements in the sets of basin characteristics for the topological iuh's are the number of first-order streams only, ( N ), or the nuber of sources together with the number of channel links in the topological diameter ( N, D ); the hydraulic parameters are values of the celerity and diffusivity constant. Sensitivity analyses indicate that the mean celerity of the internal links in the network is the critical hydraulic parameter for determining the shape of the topological iuh, while the diffusivity constant has minimal effect on the topological iuh. Asymptotic results (source-only) indicate the number of sources need not be large to approximate the topological iuh with the Weibull probability density function.

Water Resources Research↗
USGS2008

Modeling the rate-controlled sorption of hexavalent chromium

Sorption of chromium VI on the iron-oxide- and hydroxide-coated surface of alluvial material was numerically simulated with rate-controlled reactions. Reaction kinetics and diffusional processes, in the form of film, pore, and particle diffusion, were simulated and compared with experimental results. The use of empirically calculated rate coefficients for diffusion through the reacting surface was found to simulate experimental data; pore or particle diffusion is believed to be a possible rate-controlling mechanism. The use of rate equations to predict conservative transport and rate- and local-equilibrium-controlled reactions was shown to be feasible.

Water Resources Research↗
USGS1985

A policy evaluation tool: Management of a multiaquifer system using controlled stream recharge

A model for the optimal allocation of water resources was developed for a multiaquifer groundwater and surface water system near Livermore, California. The complex groundwater system was analyzed using a transient, quasi-three-dimensional model that considers the nonlinear behavior of the unconfined aquifer. The surface water system consists of a reservoir that discharges water to three streams which in turn recharge the upper aquifer. Nonlinear streamflow-recharge relationships were developed based upon synoptic field measurements of streamflow. The management model uses constrained optimization to minimize the cost of allocating surface water subject to physical and economic restrictions. Results indicate that a combined hydrologic and economic management model can be used to evaluate management practices of a complex hydrogeologic system. Questions can be posed which either would be impossible or extremely difficult to solve without the management model. We demonstrate the utility of such a model in three areas. First, the efficiency of intra-basin water allocations is evaluated. Second, critical factors that control management decisions of the basin are identified. Third, the influence of economic incentives that can best satisfy the conflicting objectives of various water users is explored.

Water Resources Research↗
USGS2010

Estimation of distributional parameters for censored trace level water quality data: 1. Estimation techniques

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations, for determining the best performing parameter estimation method for any particular data set. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.

Water Resources Research↗
USGS2010

Estimation of distributional parameters for censored trace level water quality data: 2. Verification and applications

Estimates of distributional parameters (mean, standard deviation, median, interquartile range) are often desired for data sets containing censored observations. Eight methods for estimating these parameters have been evaluated by R. J. Gilliom and D. R. Helsel (this issue) using Monte Carlo simulations. To verify those findings, the same methods are now applied to actual water quality data. The best method (lowest root-mean-squared error (rmse)) over all parameters, sample sizes, and censoring levels is log probability regression (LR), the method found best in the Monte Carlo simulations. Best methods for estimating moment or percentile parameters separately are also identical to the simulations. Reliability of these estimates can be expressed as confidence intervals using rmse and bias values taken from the simulation results. Finally, a new simulation study shows that best methods for estimating uncensored sample statistics from censored data sets are identical to those for estimating population parameters. Thus this study and the companion study by Gilliom and Helsel form the basis for making the best possible estimates of either population parameters or sample statistics from censored water quality data, and for assessments of their reliability.

Water Resources Research↗
USGS2010

Modeling contamination of shallow unconfined aquifers through infiltration beds

We model the transport of a simply reactive contaminant through an infiltration bed and underlying shallow, one-dimensional, unconfined aquifer with a plane, steeply sloping bottom in the assumed absence of dispersion and downgradient dilution. The effluent discharge and ambient groundwater flow under the infiltration beds are presumed to form a vertically mixed plume marked by an appreciable radial velocity component in the near field flow region. The near field analysis routes effluent contamination as a single linear reservoir whose output forms a source plane for the one-dimensional, far field flow region downgradient of the facility; the location and width of the source plane reflect the relative strengths of ambient flow and effluent discharge. We model far field contaminant transport, using an existing method of characteristics solution with frame speeds modified by recharge, bottom slope, and linear adsorption, and concentrations reflecting first-order reaction kinetics. The near and far field models simulate transport of synthetic detergents, chloride, total nitrogen, and boron in a contaminant plume at the Otis Air Force Base sewage treatment plant in Barnstable County, Massachusetts, with reasonable accuracy.

Massachusetts↗
USGS2010

Adaptation of the Carter-Tracy water influx calculation to groundwater flow simulation

The Carter-Tracy calculation for water influx is adapted to groundwater flow simulation with additional clarifying explanation not present in the original papers. The Van Everdingen and Hurst aquifer-influence functions for radial flow from an outer aquifer region are employed. This technique, based on convolution of unit-step response functions, offers a simple but approximate method for embedding an inner region of groundwater flow simulation within a much larger aquifer region where flow can be treated in an approximate fashion. The use of aquifer-influence functions in groundwater flow modeling reduces the size of the computational grid with a corresponding reduction in computer storage and execution time. The Carter-Tracy approximation to the convolution integral enables the aquifer influence function calculation to be made with an additional storage requirement of only two times the number of boundary nodes more than that required for the inner region simulation. It is a good approximation for constant flow rates but is poor for time-varying flow rates where the variation is large relative to the mean. A variety of outer aquifer region geometries, exterior boundary conditions, and flow rate versus potentiometric head relations can be used. The radial, transient-flow case presented is representative. An analytical approximation to the functions of Van Everdingen and Hurst for the dimensionless potentiometric head versus dimensionless time is given.

Water Resources Research↗