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At least 37 records · Page 2Linked to original sources
USGS2007

Calculation of nonlinear confidence and prediction intervals for ground-water flow models

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

Journal of the American Water Resources Associatio↗
USGS2000

Geomorphometry-Diversity in quantitative surface analysis

A widening variety of applications is diversifying geomorphometry ( digital terrain modelling ), the quantitative study of topography. An amalgam of earth science, mathematics, engineering and computer science, the discipline has been revolutionized by the computer manipulation of gridded terrain heights, or digital elevation models (DEMs). Its rapid expansion continues. This article reviews the remarkable diversity of recent morphometric work in 15 selected topics and discusses their significance and prospects. The quantitative analysis of industrial microsurface topography is introduced to the earth science community. The 14 other topics are Internet access to geomorphometry; global DEMs; DEM modelling of channel networks; self-organized criticality; fractal and wavelet analysis; soil resources; landslide hazards; barchan dunes; harvesting wind energy; sea-ice surfaces; sea-floor abyssal hills; Japanese work in morphometry; and the emerging fields of landscape ecology and image understanding. Closing remarks note reasons for the diversity within geomorphometry, speculate on future trends and recommend creating a unified field of surface representation.

Progress in Physical Geography: Earth and Environm↗
USGS2019

Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction

Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Annals of Applied Statistics↗
USGS1981

Mathematical model of gamma-ray spectrometry borehole logging for quantitative analysis

A technique for analyzing gamma-ray spectral-logging data has been developed, in which a digital computer is used to calculate the effects of gamma-ray attentuation in a borehole environment. The computer model allows for the calculation of the effects of lithology, porosity, density, and the thickness of a horizontal layer of uniformly distributed radioactive material surrounding a centralized probe in a cylindrical borehole. The computer program also contains parameters for the calculation of the effects of well casing, drilling fluid, probe housing, and losses through the sodium-iodide crystal. Errors associated with the commonly used mathematical assumption of a point detector are eliminated in this model. (USGS)

Open-File Report↗
USGS1992

Mass-conserving method of characteristics for streamflow modeling

A robust numerical model is presented for the computation of unsteady streamflow on steep river slopes. The one-dimensional model uses the method of characteristics on a specified space-time grid to solve the Saint-Venant equations. An additional continuity equation requirement on each space-time element provides greatly improved conservation of mass over traditional implementations of the method of characteristics on a fixed grid. The space-time geometry of the problem is described in a finite element setting. Hermite interpolation of channel parameters is used to avoid numerical difficulties that may occur with steep slopes due to discontinuities in the derivatives of data such as channel top width. Manning's equation for friction slope can be modified by a factor to make the slope more appropriate for steep rivers. The standard Manning's friction slope can also be used, if preferred. The computer model is not restricted to steep slopes, and applies as well to gently sloping streams. Two numerical examples support the mathematical approach and computational algorithm.

Water Supply Paper↗
USGS1989

Thermal maturity of the Anadarko Basin

Levels of thermal maturity are estimated for Paleozoic strata in five areas of the central Anadarko basin for times between the Paleozoic and the present, and depths of the oil window are plotted as a function of geologic time. Mean surface temperature assumed here for calculating Lopatin's time-temperature index of thermal maturity (TTl) in the central Anadarko basin declines from 80°F (27°C) to 60°F (16°C) from early Paleozoic time to the present. Shallow-water carbonates and lower paleolatitudes suggest warmer climates in the Paleozoic for this area. The geothermal gradient is assumed to equal 4.0°F/100 ft (7.3°C/100 m) in the Late Cambrian and to decay over a 100-m.y. period to the present regional gradient of 1.3°F/100 ft (2.4°C/100 m). Initial basin formation was caused by crustal thinning. Accumulation of thick Pennsylvanian sediments in a foreland-style basin dominated by vertical lithospheric flexure represents a second major period of subsidence. An elevated geothermal gradient during this time is not assumed for TTl calculations, because mathematical models suggest time-invariant heat flows in such basins. TTl computations based on these assumptions indicate that oil could have been generated in the ancestral Anadarko basin >350 m.y. ago. By the end of the Pennsylvanian, significant volumes of kerogen were in the oil window (and perhaps beyond), and significant volumes have remained in the oil window up to the present day. These circumstances may partially explain the unusual richness of the Anadarko basin as a Paleozoic hydrocarbon province.

Oklahoma↗
USGS2004

The value of long-term monitoring in the development of ground-water-flow models

As environmental issues have come to the forefront of public concern, so has the awareness of the importance of ground water in the overall water cycle and as a source of the Nation’s drinking water. Heightened interest has spawned a host of scientific enterprises (Taylor and Alley, 2001). Some activities are directed toward collection of water-level data and related information to monitor the physical and chemical state of the resource. Other activities are directed at interpretive studies undertaken, for example, to optimize the location of new water-supply wells or to protect rivers and lakes fed by ground water. An important type of interpretive study is the computer ground-water-flow model that inte- grates field data in a mathematical framework. Long-term, systematic collection of hydro- logic data is crucial to the construction and testing of ground-water models so that they can reproduce the evolution of flow systems and forecast future conditions.

Wisconsin↗
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↗
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↗
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

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↗