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At least 91 records · Page 5Linked to original sources
USGS1986

Evaluation of six methods for estimating magnitude and frequency of peak discharges on urban streams in New York

Six methods of estimating peak discharges of urban streams were compared and evaluated for applicability to urban streams in New York. Discharge and frequency values developed from a series of synthesized annual flood records were compared with values obtained from the six methods. The synthesized flood records were computed from rainfall-runoff models of 11 urban basins in three counties across the State. Four of these basins had a sufficient period of record to enable rainfall-runoff modeling of two different 5-year periods so that increases in peak flow due to increased urbanization could also be used for comparison of the six methods. A graphical analysis and three types of mathematical analyses were made to evaluate the closeness of fit and bias of the methods. All methods showed a tendency to overestimate synthetic urban flood-magnitude values, but the two adjust rural flood-frequency estimates on a nationwide basis showed smallest standard errors of estimate and bias. The standard errors for these two methods ranged from 44 to 57 percent over the six recurrence intervals (2, 5, 10, 25, 50, and 100 year), and the bias ranged from +28 to +53 percent. The bias , however, is probably due to errors inherent in using synthetic records and in applying the New York rural flood-frequency equations to urban basins with small drainage areas. (USGS)

Water-Resources Investigations Report↗
USGS1981

Modeling natural gas reservoirs: A simple model

A mathematical model is developed and tested for the production of natural gas with water encroachment and gas entrapment. The model is built on the material and volumetric balance relations, the Schilthuis water drive model, and a gas entrapment mechanism which assumes that the rate of gas entrapment is proportional to the volumetric rate of water influx. This model represents an alternative to the large grid models because of its low computer, maintenance, and manpower costs.

Society of Petroleum Engineers journal↗
USGS2000

Uncertainty estimation for resource assessment-an application to coal

The U.S. Geological Survey is conducting a national assessment of coal resources. As part of that assessment, a geostatistical procedure has been developed to estimate the uncertainty of coal resources for the historical categories of geological assurance: measured, indicated, inferred, and hypothetical coal. Data consist of spatially clustered coal thickness measurements from coal beds and/or zones that cover, in some cases, several thousand square kilometers. Our procedure involved trend removal, an examination of spatial correlation, computation of a sample semivariogram, and fitting a semivariogram model. This model provided standard deviations for the uncertainty estimates. The number of sample points (drill holes) in each historical category also was estimated. Measurement error in the thickness of the coal bed/zone was obtained from the fitted model or supplied exogenously. From this information approximate estimates of uncertainty on the historical categories were computed. We illustrate the methodology using drill hole data from the Harmon coal bed located in southwestern North Dakota. The methodology will be applied to approximately 50 coal data sets.

Mathematical Geology↗
USGS1979

Mathematical model for simulating discharges on the Sabine River between Tatum and Ruliff, Texas

A mathematical model for simulating discharges on the Sabine River between Tatum and Ruliff, TX., was developed to evaluate the effects of release schedules on discharges from the Toledo Bend Reservoir compared to discharges under natural conditions. Using the discharge at Tatum, TX., the rainfall over the basin, and the discharge release schedule for the reservoir, discharge hydrographs for the natural and reservoir-controlled conditions can be computed.

Texas↗
USGS1977

Fluorite solubility equilibria in selected geothermal waters

Calculation of chemical equilibria in 351 hot springs and surface waters from selected geothermal areas in the western United States indicate that the solubility of the mineral fluorite, CaF 2 , provides an equilibrium control on dissolved fluoride activity. Waters that are undersaturated have undergone dilution by non-thermal waters as shown by decreased conductivity and temperature values, and only 2% of the samples are supersaturated by more than the expected error. Calculations also demonstrate that simultaneous chemical equilibria between the thermal waters and calcite as well as fluorite minerals exist under a variety of conditions. Testing for fluorite solubility required a critical review of the thermodynamic data for fluorite. By applying multiple regression of a mathematical model to selected published data we have obtained revised estimates of the p K (10,96), ΔG o f (−280.08 kcal/mole), ΔH o f (−292.59 kcal/mole), S° (16.39 cal/deg/mole) and C o P (16.16 cal/deg/mole) for CaF 2 at 25°C and 1 atm. Association constants and reaction enthalpies for fluoride complexes with boron, calcium and iron are included in this review. The excellent agreement between the computer-based activity products and the revised p K suggests that the chemistry of geothermal waters may also be a guide to evaluating mineral solubility data where major discrepancies are evident.

Geochimica et Cosmochimica Acta↗
USGS2011

Computational considerations for collecting and using data in the equidistant cylindrical map projection and the bounds of sampling geographic data at progressively higher resolution

The Equidistant Cylindrical Map projection is popular with digital modelers and others for storing and processing worldwide data sets because of the simple association of latitude and longitude to cell values or pixels in the resulting grid. This projection does not accurately display area, and the diminished geographic area represented by cells at high latitudes is not often carefully considered. A simple mathematical analysis quantifies the discrepancy in area sampled by cells at different latitudes. The presence of this discrepancy indicates that the use of this projection can induce bias in data sets when both sampling and reporting data. It is demonstrated that as the resolution requirements of input data for models increase, the necessity of providing data to accurately describe smaller cells, particularly at high latitude, will be a challenge.

Techniques and Methods↗
USGS1973

Mathematical simulation of temperatures in deep impoundments: verification tests of the Water Resources Engineers, Inc. model - Horsetooth and Flaming Gorge Reservoirs

Successful use of predictive mathematical models requires verification of the accuracy of the models by applying them to existing situations where the prediction can be compared with reality. A Corps of Engineers' modification of a deep reservoir thermal stratification model developed by Water Resources Engineers, Inc., was applied to two existing Bureau of Reclamation reservoirs for verification. Diffusion coefficients used for the Corps' Detroit Reservoir were found to apply to Horsetooth Reservoir in Colorado, for which very food computer input data were available. The Detroit diffusion coefficients gave a reasonable simulation of Flaming Gorge Reservoir in Wyoming and Utah, which has very complex and variable physical characteristics and for which only average-quality computer input data were available.

Colorado↗
USGS1994

Data requirements for simulation of hydrogeologic effects of liquid waste injection, Harrison and Jackson Counties, Mississippi

Available literature and data were reviewed to quantify data requirements for computer simulation of hydrogeologic effects of liquid waste injection in southeastern Mississippi. Emphasis of each review was placed on quantifying physical properties of current Class I injection zones in Harrison and Jackson Counties. Class I injection zones are zones that are used for injection of hazardous or non-hazardous liquid waste below a formation containing the lowermost underground source of drinking water located within one-quarter of a mile of the injection well. Several mathematical models have been developed to simulate injection effects. The Basic Plume Method was selected because it is commonly used in permit applications, and the Intercomp model was selected because it is generally accepted and used in injection-related research. The input data requirements of the two models were combined into a single data requirement list inclusive of physical properties of injection zones only; injected waste and well properties are not included because such information is site-specific by industry, which is beyond the scope of this report. Results of the reviews of available literature and data indicated that Class I permit applications and standard-reference chemistry and physics texts were the primary sources of information to quantify physical properties of injection zones in Harrison and Jackson Counties. With the exception of a few reports and supplementary data for one injection zone in Jackson County, very little additional information pertaining to physical properties of the injection zones was available in sources other than permit applications and standard-reference texts.

Mississippi↗
USGS1994

Development and application of generalized-least-squares regression models to estimate low-flow duration discharges in Massachusetts

Physically based mathematical models were developed by use of generalized-least-squares regression analyses to estimate long-term 95-, 98-, and 99-percent duration discharges for ungaged streams in Massachusetts. Duration discharges for 61 sites were used in the recession analyses; 37 sites were streamflow-gaging stations and 24 sites were low-flow partial-record stations. The duration discharges were related to basin chacteristics measured from digital data bases, by use of geographic information systems computer software. Significant chacterisfics used in the models were drainage area, area underlain by stratified-drift deposits per unit of stream length in the basin, and a surrogate for the effective head on the aquifer in the stratified-drift deposits, computed by subtracting the minimum basin elevation from the mean basin elevation. Standard errors of prediction were 57.5, 85.6, and 98.5 percent for models for the 95-, 98-, and 99-percent duration discharges, respectively. Model error variances were about 10 times the sampling error variances, indicating that the precision of future models are likely to be improved more by obtaining better measurements of basin characteristics or by adding new sites to the analyses than by collecting more streamflow data at the sites presently used in the analyses. The models were used to predict duration discharges for 35 selected sites in the Concord River, Noah Coastal, South Coastal, Narragansett and Tenmile River Basins. Ninety-perrcent prediction intervals were computed for the estimates at each of the sites, except at sites where values of the independent variables were outside the ranges of those for the sites used in the regression analyses.

Water-Resources Investigations Report↗
USGS1977

Chemical variability in the Lakeview Mountains pluton, southern California batholith: A comparison of the methods of correspondence analysis and extended Q-mode factor analysis

An extended method of Q -mode factor analysis that has been described previously offers a number of important advantages over conventional Q -mode factor analysis and correspondence analysis when applied to compositional data. Among these are the ability to compute the compositions, in the original units of the data, represented by the reference axes. The only special requirement of the data is that the values for each observation sum to a constant. Mathematically derived reference axes, such as the principal-components and varimax axes, commonly represent compositions that are partly negative. Even where no negative values are present, these compositions are comparatively difficult to interpret in petrologic terms and impossible or inappropriate to include in petrogenetic models. A model has been developed for the Lakeview Mountains pluton which employs vectors representing the compositions of melanocratic schlieren, leucocratic schlieren, and inclusions as the reference axes. When the effect of the inclusions is removed, the compositional zoning in the pluton is like that found in otherwise similar plutons in the Sierra Nevada batholith. The genetic implication of the model is that the inclusions were separated from the magma at least in its marginal parts. In the central part of the pluton, the inclusions were either separated to a lesser extent than in the marginal parts, or were reincorporated into the magma.

California↗
USGS2017

Documentation for the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6

This report describes the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6. The XT3D option extends the capabilities of MODFLOW by enabling simulation of fully three-dimensional anisotropy on regular or irregular grids in a way that properly takes into account the full, three-dimensional conductivity tensor. It can also improve the accuracy of groundwater-flow simulations in cases in which the model grid violates certain geometric requirements. Three example problems demonstrate the use of the XT3D option to simulate groundwater flow on irregular grids and through three-dimensional porous media with anisotropic hydraulic conductivity. Conceptually, the XT3D method of estimating flow between two MODFLOW 6 model cells can be viewed in terms of three main mathematical steps: construction of head-gradient estimates by interpolation; construction of fluid-flux estimates by application of the full, three-dimensional form of Darcy’s Law, in which the conductivity tensor can be heterogeneous and anisotropic; and construction of the flow expression by enforcement of continuity of flow across the cell interface. The resulting XT3D flow expression, which relates the flow across the cell interface to the values of heads computed at neighboring nodes, is the sum of terms in which conductance-like coefficients multiply head differences, as in the conductance-based flow expression the NPF Package uses by default. However, the XT3D flow expression contains terms that involve “neighbors of neighbors” of the two cells for which the flow is being calculated. These additional terms have no analog in the conductance-based formulation. When assembled into matrix form, the XT3D formulation results in a larger stencil than the conductance-based formulation; that is, each row of the coefficient matrix generally contains more nonzero elements. The “RHS” suboption can be used to avoid expanding the stencil by placing the additional terms on the right-hand side of the matrix equation and evaluating them at the previous iteration or time step. The XT3D option can be an alternative to the Ghost-Node Correction (GNC) Package. However, the XT3D formulation is typically more computationally intensive than the conductance-based formulation the NPF Package uses by default, either with or without ghost nodes. Before deciding whether to use the GNC Package or XT3D option for production runs, the user should consider whether the conductance-based formulation alone can provide acceptable accuracy for the particular problem being solved.

Techniques and Methods↗
USGS2011

A distribution-based parameterization for improved tomographic imaging of solute plumes

Difference geophysical tomography (e.g. radar, resistivity and seismic) is used increasingly for imaging fluid flow and mass transport associated with natural and engineered hydrologic phenomena, including tracer experiments, in situ remediation and aquifer storage and recovery. Tomographic data are collected over time, inverted and differenced against a background image to produce ‘snapshots’ revealing changes to the system; these snapshots readily provide qualitative information on the location and morphology of plumes of injected tracer, remedial amendment or stored water. In principle, geometric moments (i.e. total mass, centres of mass, spread, etc.) calculated from difference tomograms can provide further quantitative insight into the rates of advection, dispersion and mass transfer; however, recent work has shown that moments calculated from tomograms are commonly biased, as they are strongly affected by the subjective choice of regularization criteria. Conventional approaches to regularization (Tikhonov) and parametrization (image pixels) result in tomograms which are subject to artefacts such as smearing or pixel estimates taking on the sign opposite to that expected for the plume under study. Here, we demonstrate a novel parametrization for imaging plumes associated with hydrologic phenomena. Capitalizing on the mathematical analogy between moment-based descriptors of plumes and the moment-based parameters of probability distributions, we design an inverse problem that (1) is overdetermined and computationally efficient because the image is described by only a few parameters, (2) produces tomograms consistent with expected plume behaviour (e.g. changes of one sign relative to the background image), (3) yields parameter estimates that are readily interpreted for plume morphology and offer direct insight into hydrologic processes and (4) requires comparatively few data to achieve reasonable model estimates. We demonstrate the approach in a series of numerical examples based on straight-ray difference-attenuation radar monitoring of the transport of an ionic tracer, and show that the methodology outlined here is particularly effective when limited data are available.

Geophysical Journal International↗
USGS1980

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The solution procedure has the further advantages, relative to conventional Eulerian solution schemes, of being easy to understand in the physical sense, of being extremely stable numerically, and of providing an accounting system which is very useful for model calibration. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance, such as dye, through a reach of a river. The simplified temperature model is used to predict water temperature in rivers, either with or without thermal loading, when few meteorological data are available. Only equilibrium temperature and windspeed are required. It is suggested that air temperature can be used to approximate equilibrium temperature. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. The mathematical description of the interaction between the constituents, which does not need to be linear, is generally up to the user to supply. An example problem is solved for a three-parameter system involving temperature, dissolved oxygen, and biochemical oxygen demand. For simplicity, all models are developed and presented assuming steady non-uniform flow. Generalization of the models to allow unsteady flow is extremely simple, involving the addition of no more than 18 cards to the program deck. The report is concluded by describing this generalization for any of the models. Before using the models with unsteady flow, a flow model must be used to calculate and store the necessary flow data at each cross section and time step. Such a flow model is available and documented.

Water-Resources Investigations Report↗
USGS1977

State of stress in the lithosphere: Inferences from the flow laws of olivine

The experimental flow data for rocks and minerals are reviewed and found to fit a law of the form {Mathematical expression} where {Mathematical expression} This law reduces to the familiar power-law stress dependency at low stress and to an exponential stress dependency at high stress. Using the material flow law parameters for olivine, stress profiles with depth and strain rate are computed for a representative range of temperature distributions in the lithosphere. The results show that the upper 15 to 25 km of the oceanic lithosphere must behave elastically or fail by fracture and that the remainder deforms by exponential law flow at intermediate depths and by power-law flow in the rest. A model computation of the gravitational sliding of a lithospheric plate using olivine rheology exhibits a very sharp decoupling zone which is a consequence of the combined effects of increasing stress and temperature on the flow law, which is a very sensitive function of both. ?? 1977 Birkha??user Verlag.

Pure and Applied Geophysics PAGEOPH↗
USGS2023

Source contributions to suspended sediment and particulate selenium export from the Loutsenhizer Arroyo and Sunflower Drain watersheds in Colorado

Selenium in aquatic ecosystems of the lower Gunnison River Basin in Colorado is affecting the recovery of populations of endangered, native fish species. Dietary exposure is the primary pathway for bioaccumulation of selenium in fish, and particulate selenium can be consumed directly by fish or by the invertebrates on which fish feed. Although selenium can be incorporated into particulate matter via biogeochemical processes, particulate selenium can also enter aquatic ecosystems of the lower Gunnison River Basin from sediments derived from the selenium-rich Mancos Shale. The U.S. Geological Survey, in cooperation with the Colorado Water Conservation Board, conducted this study during 2018–19 to identify sources of selenium-rich suspended sediments from two watersheds underlain by Mancos Shale: Loutsenhizer Arroyo and Sunflower Drain, which is a locally known agricultural drainage near the municipality of Delta, Colorado. A multipronged approach (fieldwork, laboratory work, and computer modeling) referred to as “sediment fingerprinting” was used to evaluate sources of suspended sediments in the streams flowing out of the two studied watersheds. Four potential source types for suspended sediments were identified and sampled (using soil plugs) within the watersheds: rangelands, agricultural fields, arroyo walls, and streambanks. The sediment fingerprinting approach used elemental concentrations and naturally occurring fallout radionuclides as tracers to apportion percent contributions from the four source types of suspended sediments found in streamflow from both watersheds. To determine the dominant sources of suspended sediment in streamflow from both watersheds, a mathematical “unmixing” model was used. Unmixing models apportion source percentages to samples of material in which those sources are mixed. These models used elemental and isotopic data in the suspended sediments to unmix them into proportional contributions from source types. The results indicated that arroyo walls and streambanks generally dominated as sources of the suspended sediment. Arroyo walls and streambanks were channel-adjacent sources, with sediments mobilized by water flowing within the stream channel. These sources accounted for greater than 50 percent of suspended sediment in all but one sample and accounted for 100 percent of suspended sediment in 5 of the 11 samples collected. Rangeland and agricultural field sources were located in uplands outside of stream channels and were detected more often during the non-irrigation season. Rangeland and agricultural field sources each were found in 5 of the 11 samples collected. Concentrations of selenium in sediment-source samples were comparatively greater in streambanks and lower in rangelands, with agricultural fields and arroyo walls being intermediate. As a result, source apportionments for particulate selenium skewed towards sources adjacent to stream channels more than for suspended sediments. Water imports for irrigation have changed the hydrology of the watersheds, and a notable fraction of imported water passes through the watersheds rapidly. The rapid flowthrough water during the irrigation season likely contributes heavily to sediment erosion and transport in Loutsenhizer Arroyo and Sunflower Drain, particularly from channel-adjacent sources of sediment. Decreases in irrigation season streamflow, at least in Loutsenhizer Arroyo, may have decreased sediment erosion and transport during the 2018–20 irrigation seasons compared to the 2015–17 seasons.

Colorado↗
USGS1975

Optimal exploitation strategies for an animal population in a Markovian environment: A theory and an example

Optimal exploitation strategies were studied for an animal population in a Markovian (stochastic, serially correlated) environment. This is a general case and encompasses a number of important special cases as simplifications. Extensive empirical data on the Mallard (Anas platyrhynchos) were used as an example of general theory. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. A general mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. The literature and analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, two hypotheses were explored: (1) exploitation mortality represents a largely additive form of mortality, and (2) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under the rather general conditions. Direct feedback control was an integral component in the optimal decision—making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. If we assume that exploitation is largely an additive force of mortality in Mallards, then optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slight concave function of the environmental conditions. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the Mallard breeding population. Dynamic programming is suggested as a very general formulation for realistic solutions to the general optimal exploitation problem. The concepts of state vectors and stage transformations are completely general. Populations can be modeled stochastically and the objective function can include extra—biological factors. The optimal level of exploitation in year t must be based on the observed size of the population and the state of the environment in year t unless the dynamics of the population, the state of the environment, and the result of the exploitation decisions are completely deterministic. Exploitation based on an average harvest, or harvest rate, or designed to maintain a constant breeding population size is inefficient.

Ecology↗
USGS2015

PRMS-IV, the precipitation-runoff modeling system, version 4

Computer models that simulate the hydrologic cycle at a watershed scale facilitate assessment of variability in climate, biota, geology, and human activities on water availability and flow. This report describes an updated version of the Precipitation-Runoff Modeling System. The Precipitation-Runoff Modeling System is a deterministic, distributed-parameter, physical-process-based modeling system developed to evaluate the response of various combinations of climate and land use on streamflow and general watershed hydrology. Several new model components were developed, and all existing components were updated, to enhance performance and supportability. This report describes the history, application, concepts, organization, and mathematical formulation of the Precipitation-Runoff Modeling System and its model components. This updated version provides improvements in (1) system flexibility for integrated science, (2) verification of conservation of water during simulation, (3) methods for spatial distribution of climate boundary conditions, and (4) methods for simulation of soil-water flow and storage.

Techniques and Methods↗
USGS1974

Optimal exploitation strategies for an animal population in a stochastic serially correlated environment

Optimal exploitation strategies were studied for an animal population in a stochastic, serially correlated environment. This is a general case and encompasses a number of important cases as simplifications. Data on the mallard (Anas platyrhynchos) were used to explore the exploitation strategies and test several hypotheses because relatively much is known concerning the life history and general ecology of this species and extensive empirical data are available for analysis. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. Desirable properties of an optimal exploitation strategy were defined. A mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. Both the literature and the analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, alternative hypotheses were formulated: (1) exploitation mortality represents a largely additive form of mortality, or (2 ) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under rather general conditions. Direct feedback control was an integral component in the optimal decision-making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. Assuming that exploitation is largely an additive force of mortality, optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slightly concave function of the environmental conditions. Optimal exploitation under this hypothesis tends to reduce the variance of the size of the population. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the breeding population. Environmental variables may be somewhat more important than the size of the breeding population to the production of young mallards. In contrast, the size of the breeding population appears to be more important in the exploitation process than is the state of the environment. The form of the exploitation strategy appears to be relatively insensitive to small changes in the production rate. In general, the relative importance of the size of the breeding population may decrease as fecundity increases. The optimal level of exploitation in year t must be based on the observed size of the population and the state of the environment in year t unless the dynamics of the population, the state of the environment, and the result of the exploitation decisions are completely deterministic. Exploitation based on an average harvest, harvest rate, or designed to maintain a constant breeding population size is inefficient.

Book↗