Search USGS⌕ Search

SEARCH · Search USGS

Results for “Mathematical and Computer Modelling”

Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3Linked to original sources
USGS2002

A bibliography of terrain modeling (geomorphometry), the quantitative representation of topography: Supplement 4.0

Terrain modeling, the practice of ground-surface quantification, is an amalgam of Earth science, mathematics, engineering, and computer science. The discipline is known variously as geomorphometry (or simply morphometry), terrain analysis, and quantitative geomorphology. It continues to grow through myriad applications to hydrology, geohazards mapping, tectonics, sea-floor and planetary exploration, and other fields. Dating nominally to the co-founders of academic geography, Alexander von Humboldt (1808, 1817) and Carl Ritter (1826, 1828), the field was revolutionized late in the 20th Century by the computer manipulation of spatial arrays of terrain heights, or digital elevation models (DEMs), which can quantify and portray ground-surface form over large areas (Maune, 2001). Morphometric procedures are implemented routinely by commercial geographic information systems (GIS) as well as specialized software (Harvey and Eash, 1996; Köthe and others, 1996; ESRI, 1997; Drzewiecki et al., 1999; Dikau and Saurer, 1999; Djokic and Maidment, 2000; Wilson and Gallant, 2000; Breuer, 2001; Guth, 2001; Eastman, 2002). The new Earth Surface edition of the Journal of Geophysical Research, specializing in surficial processes, is the latest of many publication venues for terrain modeling. This is the fourth update of a bibliography and introduction to terrain modeling (Pike, 1993, 1995, 1996, 1999) designed to collect the diverse, scattered literature on surface measurement as a resource for the research community. The use of DEMs in science and technology continues to accelerate and diversify (Pike, 2000a). New work appears so frequently that a sampling must suffice to represent the vast literature. This report adds 1636 entries to the 4374 in the four earlier publications1. Forty-eight additional entries correct dead Internet links and other errors found in the prior listings. Chronicling the history of terrain modeling, many entries in this report predate the 1999 supplement. Coverage is representative from about 1800 through early–mid 2002. Papers increasingly are published exclusively or in duplicate on the Internet's World Wide Web; the dates given here for Web addresses (URLs) that lack a print publication indicate a Web site's last update or my last access of it. The bibliography is arranged alphabetically and thus is not readily summarized. This introduction cites about 500 entries, a third of them grouped under 24 morphometric topics, as a guide to the listing's contents. Continuing the practice of previous bibliographies in the series to provide more information on a few applications (see summary of past topics in Pike, 2000a), this report elaborates further on topographic data, putative new parameters, tectonic geomorphology/neo-orometry, biogeography, ice-cap morphometry, results from the Mars Global DEM, landslide-hazard mapping, terrain modeling as physics, Hack's law, and broad-scale computer visualization. The literature of some of these subjects is large, and none of the summaries is intended to more than introduce the topic and comment on some of the current contributions of terrain modeling. Closing the essay is a discussion of pre-1900 papers that trace the evolution of ridge-line and watercourse quantification by descriptive geometry, as well as comments on some new books and an on-line bulletin board.

Open-File Report↗
USGS2003

Tag loss can bias Jolly-Seber capture-recapture estimates

We identified cases where the Jolly-Seber estimator of population size is biased under tag loss and tag-induced mortality by examining the mathematical arguments and performing computer simulations. We found that, except under certain tag-loss models and high sample sizes, the population size estimators (uncorrected for tag loss) are severely biased high when tag loss or tag-induced mortality occurs. Our findings verify that this misconception about effects of tag loss and tag-induced mortality could have serious consequences for field biologists interested in population size. Reiterating common sense, we encourage those engaged in capture-recapture studies to be careful and humane when handling animals during tagging, to use tags with high retention rates, to double-tag animals when possible, and to strive for the highest capture probabilities possible.

Wildlife Society Bulletin↗
USGS1996

A three-dimensional method-of-characteristics solute-transport model (MOC3D)

This report presents a model, MOC3D, that simulates three-dimensional solute transport in flowing ground water. The model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport, hydrodynamic dispersion (including both mechanical dispersion and diffusion), mixing (or dilution) from fluid sources, and mathematically simple chemical reactions (including linear sorption, which is represented by a retardation factor, and decay). The transport model is integrated with MODFLOW, a three-dimensional ground-water flow model that uses implicit finite-difference methods to solve the transient flow equation. MOC3D uses the method of characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step. This implementation of the method of characteristics uses particle tracking to represent advective transport and explicit finite-difference methods to calculate the effects of other processes. However, the explicit procedure has several stability criteria that may limit the size of time increments for solving the transport equation; these are automatically determined by the program. For improved efficiency, the user can apply MOC3D to a subgrid of the primary MODFLOW grid that is used to solve the flow equation. However, the transport subgrid must have uniform grid spacing along rows and columns. The report includes a description of the theoretical basis of the model, a detailed description of input requirements and output options, and the results of model testing and evaluation. The model was evaluated for several problems for which exact analytical solutions are available and by benchmarking against other numerical codes for selected complex problems for which no exact solutions are available. These test results indicate that the model is very accurate for a wide range of conditions and yields minimal numerical dispersion for advection-dominated problems. Mass-balance errors are generally less than 10 percent, and tend to decrease and stabilize with time.

Water-Resources Investigations Report↗
USGS1970

Hydrologic effects of floodwater-retarding structures on Garza-Little Elm Reservoir, Texas

The Texas District of the Water Resources Division of the U.S. Geological Survey has collected and analyzed hydrologic data since 1953 to define the effects of systems of floodwater-retarding structures on downstream water and sediment yield. The district project includes 11 study areas ranging from 18 to 80 square miles in size and from 0 to 67 in percent of study area controlled by floodwaterretarding structures. The 11 study areas are within that part of Texas where the west-to-east average annual runoff ranges from about 2 to 7 inches. This report presents results of analyses, development of methodolgy, and results of application of methods for defining the downstream effects of systems of floodwaterretarding structures. Annual inflow to and outflow from the system of floodwater-retarding reservoirs in seven of the 11 study areas were found to be related by the equation: O=0.98/ 0.68, where O is annual outflow, in inches, and / is annual net inflow, in inches. Transmission loss of structure outflow to the downstream study-area stream-gaging station was determined and compared with the transmission loss of natural flood flow between tandem stream-gaging stations on Denton Creek, a tributary to Elm Fork Trinity River above Dallas. Trap efficiency of most floodwater-retarding structures was found by the U.S. Soil Conservation Service to be about 97 percent. Downstream increases in suspended-sediment concentration in the outflow were found to be large in a study area with mostly silt and clay sediments, but even a large increase in suspendedsediment concentration did not represent a significant quantitative pickup of sediment by the outflow water. Water consumption in floodwater-retarding reservoirs from the combined actions of evaporation, evapotranspiration, and seepage was found to be as much as twice the average annual consumption attributable to evaporation alone. Average annual consumption in reservoirs in the seven study areas analyzed ranged from 1.57 inches of equivalent runoff in the easternmost study area, where annual runoff averaged 6.96 inches, to 0.77 inch of equivalent runoff in the westernmost study area, where the average annual runoff was 2.35 inches. The effect of consumption on downstream flow is partially offset by rainfall on pool surface. Studies covering as much as 15 years of streamflow record at the stream-gaging stations that gage outflow from the Deep and Honey Creek study areas indicated no increase in base flow. Multiple-linear-regression techniques were used in developing methodology to determine reservoir consumption in seven study areas. The physical and climatic fnctors influencing consumption were grouped as variables in regard to their relative effect on the actions of evaporation, evapotranspiration, and seepage. The resulting generalized equation was then used in synthesizing the consumptive effects of a planned system of 162 floodwater-retarding reservoirs controlling 26 percent of a 1,660-square-mile drainage basin upstream from a major water-supply reservoir. The analyses were based on the assumption that all water consumed at the floodwater-retarding reservoirs would have reached the downstream watersupply reservoir. Water-sediment discharge relationships were derived for the runoff into the structures as well as for the runoff through and below the structures. A mathematical response model of the floodwater-retarding reservoir systems and the entire drainage basin was computer programed to yield monthly water and sediment inflow to the water-supply reservoir. Results of the response model showed that with full development, depletion of annual yield to the large reservoir would be as much as 10 percent in the early years; but after the permanent pools of the floodwater-retarding structures had mostly filled with sediment, depletion of annual yield would be generally less than 1 percent. The depletion of yield to Garza-Little Elm Reservoir during the 39-year synthesized period of study was estimated as 296,800 acre-feet out of 18,256,000 acre-feet total yield. During the same period, the floodwater-retarding structures were estimated to have kept 19,700 acre-feet of sediment from being deposited in the reservoir. "Firm"- or "critical"-yield studies were made of the large reservoir on the basis of two sets of conditions : with floodwater-retarding structures in the drainage basin, and without such structures. Results of the firm-yield studies indicated that with full development, annual firm yield would be initially reduced by 10 percent. After 30 or more years, when the permanent pools of the floodwaterretarding reservoirs would be mostly filled with sediment, the firm yield would be almost the same with or without the upstream development.

Texas↗
USGS1980

Channel and dynamic flow characteristics of the Chattahoochee River, Buford Dam to Georgia Highway 141

Detailed flow and cross-section data for a 17-mile reach of the Chattahoochee River in northeast Georgia are described and summarized. Flow data include measurements of highly dynamic stage and discharge at five stations during the period March 21-23, 1976. Flow data were collected at 5-minute intervals and are listed accordingly. Coordinate data for 39 cross sections in the study reach are also listed. A mathematical model is developed and applied whereby stage data collected at a single station can be used to compute highly dynamic discharge at the station. The model is based on the continuity and momentum equations that describe unsteady, one-dimensional flow in open channels. Both equations are transformed to a single quadratic equation which describes mean flow velocity at a single station. Flow-geometry parameters used by the model are computed using cross-section coordinates and the equation which describes the area of an irregular polygon. Use of the model in conjunction with highly dynamic stage data collected on March 23, 1976, provided close agreement between measured and computed discharges. The model was also used to investigate the sensitivity of highly dynamic discharge to channel and flow parameters. Computed discharge was most sensitive to changes in channel roughness and slope.

Georgia↗
USGS2024

Bayesian approaches to proxy uncertainty quantification in paleoecology: A mathematical justification and practical integration

Paleoenvironmental data are essential for reconstructing environmental conditions in the distant past, and these reconstructions strongly depend on proxies and age–depth models. Proxies are indirect measurements that substitute for variables that cannot be directly measured, such as past precipitation. Conversely, an age–depth model is a tool that correlates the observed proxy with a specific moment in time. Bayesian age–depth modelling has proved to be a powerful method for estimating sediment ages and their associated uncertainties. However, there remains considerable potential for further integration into proxy analysis. In this paper, we explore a mathematical justification and a computational approach that integrates uncertainty at the age–depth level and propagates it to the proxy scale in the form of a posterior predictive distribution. This method mitigates potential biases and errors by removing the need to assign a single age to a given proxy measurement. It allows for quantifying the likelihood that proxy data values correspond to modelled ages, thus enabling the quantification of uncertainty in both the temporal and proxy value domains. The use of Bayesian statistics in proxy analysis represents a relatively recent advancement. We aim to mathematically justify incorporating the Markov chain Monte Carlo output from age–depth models into proxy analysis and to present a novel methodology for constructing environmental reconstructions using this approach.

Journal of Agricultural, Biological and Environmen↗
USGS2004

Granular avalanches across irregular three-dimensional terrain: 2. Experimental tests

Scaling considerations indicate that miniature experiments can be used to test models of granular avalanches in which the effects of intergranular fluid and cohesion are negligible. To test predictions of a granular avalanche model described in a companion paper, we performed bench top experiments involving avalanches of dry sand across irregular basal topography that mimicked the complexity of natural terrain. The experiments employed a novel method of laser-assisted cartography to map the three-dimensional morphology of rapidly moving avalanches, thereby providing high-resolution data for comparison with model output. Model input consisted of two material properties (angles of internal and basal Coulomb friction of the sand), which were measured in independent tests, and of initial and boundary conditions that characterized the geometry of the experimental apparatus. Experimental results demonstrate that the model accurately predicts not only the gross behavior but also many details of avalanche motion, from initiation to deposition. We attribute this accuracy to a mathematical and computational formulation that conserves mass and momentum in three-dimensional physical space and satisfies the Coulomb equation in three-dimensional stress space. Our results support the hypothesis that a Coulomb proportionality between shear and normal stresses applies in moderately rapid granular flows and that complicated constitutive postulates are unnecessary if momentum conservation is strictly enforced in continuum avalanche models. Furthermore, predictions of our Coulomb continuum model contrast with those of a Coulomb point mass model, illustrating the importance of multidimensional modeling and model testing.

Journal of Geophysical Research Earth Surface↗
USGS2004

Extracting transient Rayleigh wave and its application in detecting quality of highway roadbed

This paper first explains the tau-p mapping method of extracting Rayleigh waves (LR waves) from field shot gathers. It also explains a mathematical model of physical character parameters of quality of high-grade roads. This paper then discusses an algorithm of computing dispersion curves using adjacent channels. Shear velocity and physical character parameters are obtained by inversion of dispersion curves. The algorithm using adjacent channels to calculating dispersion curves eliminates average effects that exist by using multi-channels to obtain dispersion curves so that it improves longitudinal and transverse resolution of LR waves and precision of non-invasive detection, and also broadens its application fields. By analysis of modeling results of detached computation of the ground roll and real examples of detecting density and pressure strength of a high-grade roadbed, and by comparison of shallow seismic image method with borehole cores, we concluded that: 1 the abnormal scale and configuration obtained by LR waves are mostly the same as the result of shallow seismic image method; 2 an average relative error of density obtained from LR waves inversion is 1.6% comparing with borehole coring; 3 transient LR waves in detecting density and pressure strength of a high-grade roadbed is feasible and effective.

Conference Paper↗
USGS1987

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Water-Resources Investigations Report↗
USGS1987

On the functional optimization of a certain class of nonstationary spatial functions

Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail. ?? 1987 Plenum Publishing Corporation.

Journal of Optimization Theory and Applications↗
USGS2005

MODFLOW-2005 : the U.S. Geological Survey modular ground-water model--the ground-water flow process

This report presents MODFLOW-2005, which is a new version of the finite-difference ground-water model commonly called MODFLOW. Ground-water flow is simulated using a block-centered finite-difference approach. Layers can be simulated as confined or unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and rivers, also can be simulated. The report includes detailed explanations of physical and mathematical concepts on which the model is based, an explanation of how those concepts are incorporated in the modular structure of the computer program, instructions for using the model, and details of the computer code. The modular structure consists of a MAIN Program and a series of highly independent subroutines. The subroutines are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system that is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving the set of simultaneous equations resulting from the finite-difference method. Several solution methods are incorporated, including the Preconditioned Conjugate-Gradient method. The division of the program into packages permits the user to examine specific hydrologic features of the model independently. This also facilitates development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program also are designed to permit maximum flexibility. The program is designed to allow other capabilities, such as transport and optimization, to be incorporated, but this report is limited to describing the ground-water flow capability. The program is written in Fortran 90 and will run without modification on most computers that have a Fortran 90 compiler.

Techniques and Methods↗
USGS1989

A general method for generating bathymetric data for hydrodynamic computer models

To generate water depth data from randomly distributed bathymetric data for numerical hydrodymamic models, raw input data from field surveys, water depth data digitized from nautical charts, or a combination of the two are sorted to given an ordered data set on which a search algorithm is used to isolate data for interpolation. Water depths at locations required by hydrodynamic models are interpolated from the bathymetric data base using linear or cubic shape functions used in the finite-element method. The bathymetric database organization and preprocessing, the search algorithm used in finding the bounding points for interpolation, the mathematics of the interpolation formulae, and the features of the automatic generation of water depths at hydrodynamic model grid points are included in the analysis. This report includes documentation of two computer programs which are used to: (1) organize the input bathymetric data; and (2) to interpolate depths for hydrodynamic models. An example of computer program operation is drawn from a realistic application to the San Francisco Bay estuarine system. (Author 's abstract)

Open-File Report↗
USGS2014

A computer program for uncertainty analysis integrating regression and Bayesian methods

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s–100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s–1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s–100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.

Environmental Modelling and Software↗
USGS2003

Probabilistic assessment methodology for continuous-type petroleum accumulations

The analytic resource assessment method, called ACCESS (Analytic Cell-based Continuous Energy Spreadsheet System), was developed to calculate estimates of petroleum resources for the geologic assessment model, called FORSPAN, in continuous-type petroleum accumulations. The ACCESS method is based upon mathematical equations derived from probability theory in the form of a computer spreadsheet system. ?? 2003 Elsevier B.V. All rights reserved.

International Journal of Coal Geology↗
USGS1994

Estimating the magnitude and frequency of low flows of streams in Massachusetts

The report presents techniques used for estimating 7-day 2-year (7Q2) and 7-day 10-year (7Q10) flows at continuous-record streamflow-gaging stations, partial-record stations, and ungaged sites on streams in Massachusetts. A two-parameter log-normal probability distribution was used to compute low flows at 31 continuous-record stream-flow-gaging stations. Graphical and mathematical techniques were used to estimate low flows at partial-record stations. Regional regression techniques commonly are used to estimate 7Q2 and 7Q10 flows at ungaged stream sites. The development and application of a low-flow regression model is described. The model contains two parameters, mean and standard deviation, computed from separate regression equations that use total drainage area and basin relief as independent variables. The coefficients of determination of the mean and standard deviation regression equations are 0.964 and 0.960, respec- tively; the percentage of standard error of the regression of each equation are 35 and 34, respec- tively. The model is applicable for basins in Massachusetts having a drainage area of 5 to 150 square miles, a slope of less than 4 percent, and an area of stratified drift greater than 4 percent of the total drainage area. A computer program is presented that can be used to compute 7Q2 and 7Q10 flows and the 95-percent intervals of confidence and prediction for a given basin.

Water-Resources Investigations Report↗
USGS1976

Flood-frequency analysis for small natural streams in Georgia

Flood information from 104 project basins (0.1 to 20 square miles) and data available from 170 larger basins (20 to 1,500 square miles) are analyzed to provide planners and designers with relations for estimating the magnitude and frequency of flood-peak discharges on small natural streams in Georgia. In 1963 the U.S. Geological Survey, in cooperation with the Georgia Department of Transportation and the Federal Highway Administration,U.S. Department of Transportation, began this program to collect and analyze flood-peak data from small drainage basins. More than 90 percent of the project activity was directed toward the acquisition and processing of data for more than two thousand rainfall-runoff periods occurring during 1964-74 at the 104 project stations. Storm rainfall data were computed at 5-minute intervals from records of six long-term (about 75 years) National Weather Service stations. The U.S. Geological Survey mathematical rainfall-runoff model is used to synthesize long-term flood records for about 80 percent of the project stations. Station flood-frequency data are developed, using the log-Pearson Type III distribution with regionalized skew coefficients. Multiple regression analysis is used to define relations between flood-frequency station data for small and large streams and 10 physical and climatological basin characteristics. The analysis indicates the drainage-basin size is the most significant variable. Five regions having distinct flood-peak characteristics are delineated. One of these regions, known as the Sand Hills, has not been delineated previously as an area of "low" flood runoff. The developed relations, expressed as equations and nomographs, are considered usable for virtually any site in Georgia where ne drainage area is between 0.1 and 20 square miles, and the flow is natural.

Georgia↗
USGS2024

Preliminary implications of viscoelastic ray theory for anelastic seismic tomography models

The recent developments in general viscoelastic ray theory provide a rigorous mathematical framework for anelastic seismic tomography. They provide closed‐form solutions of forward ray‐tracing and simple inverse problems for anelastic horizontal and spherical layered media with material gradients. They provide ray‐tracing computation algorithms valid for all angles of incidence that account for changes in wave speed, attenuation, and trajectory of anelastic P and S body waves induced by anelastic boundaries. They account for theoretical predictions that seismic waves refract as inhomogeneous waves across anelastic boundaries for all angles of incidence, which in turn accounts for energy carried by plane waves along seismic boundaries at head wave critical angles and wide‐angle refracted (WAR) ray paths that are not predicted by elastic models. Exact viscoelastic ray‐tracing numerical results for various models provide examples that illustrate the effects of anelastic boundaries on the travel times and amplitudes of seismic waves. They show the effects are strongly dependent on angle of incidence. For near‐critical and wide angles of incidence the anelastic effects on travel times and amplitudes can be large and are not explained by elastic ray theory, but the effects on travel times can be relatively small and difficult to distinguish from those for elastic media for pre‐near‐critical angles of incidence. The results for some models indicate that reflected anelastic WAR waves may be observable at the surface and possibly account for some prominent seismic arrivals not explained by elasticity. These preliminary results suggest that the application of exact viscoelastic ray‐tracing computation algorithms to exploration and teleseismic data sets can reveal new insights regarding the properties and distribution of anelastic materials in the Earth.

Bulletin of the Seismological Society of America↗