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Results for “Applied Mathematical Modelling”

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At least 109 records · Page 6Linked to original sources
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↗
USGS2003

Modeling radium and radon transport through soil and vegetation

A one-dimensional flow and transport model was developed to describe the movement of two fluid phases, gas and water, within a porous medium and the transport of 226Ra and 222Rn within and between these two phases. Included in this model is the vegetative uptake of water and aqueous 226Ra and 222Rn that can be extracted from the soil via the transpiration stream. The mathematical model is formulated through a set of phase balance equations and a set of species balance equations. Mass exchange, sink terms and the dependence of physical properties upon phase composition couple the two sets of equations. Numerical solution of each set, with iteration between the sets, is carried out leading to a set-iterative compositional model. The Petrov-Galerkin finite element approach is used to allow for upstream weighting if required for a given simulation. Mass lumping improves solution convergence and stability behavior. The resulting numerical model was applied to four problems and was found to produce accurate, mass conservative solutions when compared to published experimental and numerical results and theoretical column experiments. Preliminary results suggest that the model can be used as an investigative tool to determine the feasibility of phytoremediating radium and radon-contaminated soil. ?? 2003 Elsevier Science B.V. All rights reserved.

Journal of Contaminant Hydrology↗
USGS2005

Virus fate and transport during artificial recharge with recycled water

A field‐scale experiment was conducted at a research site using bacterial viruses (bacteriophage) MS2 and PRD1 as surrogates for human viruses, bromide as a conservative tracer, and tertiary‐treated municipal wastewater (recycled water) to investigate the fate and transport of viruses during artificial recharge. Observed virus concentrations were fitted using a mathematical model that simulates virus transport in one‐dimensional, homogeneous, water‐saturated porous media accounting for virus sorption (or filtration), virus inactivation, and time‐dependent source concentration. The fitted time‐dependent clogging rate constants were used to estimate the collision efficiencies for bacteriophage MS2 and PRD1 during vertical fully saturated flow. Furthermore, the corresponding time‐dependent collision efficiencies for both bacteriophage asymptotically reached similar values at the various sampling locations. These results can be used to develop an optimal management scenario to maximize the amount of recycled water that can be applied to the spreading grounds while still maintaining favorable attachment conditions for virus removal.

Water Resources Research↗
USGS2001

User's Guide for Mixed-Size Sediment Transport Model for Networks of One-Dimensional Open Channels

This user's guide describes a mathematical model for predicting the transport of mixed sizes of sediment by flow in networks of one-dimensional open channels. The simulation package is useful for general sediment routing problems, prediction of erosion and deposition following dam removal, and scour in channels at road embankment crossings or other artificial structures. The model treats input hydrographs as stepwise steady-state, and the flow computation algorithm automatically switches between sub- and supercritical flow as dictated by channel geometry and discharge. A variety of boundary conditions including weirs and rating curves may be applied both external and internal to the flow network. The model may be used to compute flow around islands and through multiple openings in embankments, but the network must be 'simple' in the sense that the flow directions in all channels can be specified before simulation commences. The location and shape of channel banks are user specified, and all bedelevation changes take place between these banks and above a user-specified bedrock elevation. Computation of sediment-transport emphasizes the sand-size range (0.0625-2.0 millimeter) but the user may select any desired range of particle diameters including silt and finer (<0.0625 millimeter). As part of data input, the user may set the original bed-sediment composition of any number of layers of known thickness. The model computes the time evolution of total transport and the size composition of bed- and suspended-load sand through any cross section of interest. It also tracks bed -surface elevation and size composition. The model is written in the FORTRAN programming language for implementation on personal computers using the WINDOWS operating system and, along with certain graphical output display capability, is accessed from a graphical user interface (GUI). The GUI provides a framework for selecting input files and parameters of a number of components of the sediment-transport process. There are no restrictions in the use of the model as to numbers of channels, channel junctions, cross sections per channel, or points defining the cross sections. Following completion of the simulation computations, the GUI accommodates display of longitudinal plots of either bed elevation and size composition, or of transport rate and size composition of the various components, for individual channels and selected times during the simulation period. For individual cross sections, the GUI also allows display of time series of transport rate and size composition of the various components and of bed elevation and size composition.

Water-Resources Investigations Report↗
USGS2023

Geology and assessment of coal resources for the Cherokee coal bed in the Fort Union Formation, south-central Wyoming

The Cherokee coal bed is a locally thick and laterally continuous coal bed in the Overland Member of the Paleocene Fort Union Formation in south-central Wyoming. It represents a significant resource that is easily accessible and may be extractable through both surface and underground mining methods. A database of more than 600 data points, comprising coalbed methane wells, coal exploration drill holes, and measured sections, was compiled from a previously released geologic database and reinterpreted to provide a more detailed geologic model for the Cherokee coal bed. The thickest part of the Cherokee coal bed lies along the crest of the Wamsutter arch, an east-west trending anticlinal feature that separates the Great Divide subbasin to north from the Washakie subbasin to the south. The Cherokee coal bed consists of several laterally persistent benches separated by partings that range in thickness from one inch to greater than 100 feet. A series of detailed geologic cross sections through the study area show both the structural geology and the distribution and areal extent of the individual coal benches of the Cherokee coal bed. Data generated from the geologic model were used in stochastic geostatistical analyses to estimate the remaining or in-place coal resources. Certain parameters, as described later in the text, were applied to calculate available coal resources for surface and underground mining. This study is part of an ongoing process by the U.S. Geological Survey (USGS) to transition from a distance-based approach to a probabilistic approach for determining uncertainty in coal resource assessment. This probabilistic approach uses quantitative statistical methods to determine the potential range of uncertainty in coal resource estimates, whereas the distance-based approach does not provide any mathematical method to determine the range of uncertainty. Using stochastic geostatistical methods, utilizing 100 realizations or gridding iterations of the data, in-place resources were calculated, with a 90 percent probability, to be 15.261 ± 0.464 billion short tons (bst). Available coal resources tonnages were calculated using separate sets of criteria for surface and underground mining methods, based on probable mining parameters. Tonnage values were calculated based on estimated coal densities determined from available coal quality data. Available coal resources that meet the parameters for surface mining methods were calculated, with a 90 percent probability, to be 0.813 ± 0.038 bst. Available coal resources that meet the parameters for underground mining methods were calculated, with a 90 percent probability, to be 2.393 ± 0.055 bst. The calculations were based on estimates of the resources that meet the parameters for the optimum mining of the thickest coal benches of the Cherokee coal bed. This is depicted in a series of cross sections through the study area that show projected underground mining horizons in the Cherokee coal bed, based on the thickest combinations of individual coal benches.

Wyoming↗
USGS1983

Characteristic analysis-1981: Final program and a possible discovery

The latest ornewest version of thecharacteristicanalysis (NCHARAN)computer program offers the exploration geologist a wide variety of options for integrating regionalized multivariate data. The options include the selection of regional cells for characterizing deposit models, the selection of variables that constitute the models, and the choice of logical combinations of variables that best represent these models. Moreover, the program provides for the display of results which, in turn, makes possible review, reselection, and refinement of a model. Most important, the performance of the above-mentioned steps in an interactive computing mode can result in a timely and meaningful interpretation of the data available to the exploration geologist. The most recent application of characteristic analysis has resulted in the possible discovery of economic sulfide mineralization in the Grong area in central Norway. Exploration data for 27 geophysical, geological, and geochemical variables were used to construct a mineralized and a lithogeochemical model for an area that contained a known massive sulfide deposit. The models were applied to exploration data collected from the Gjersvik area in the Grong mining district and resulted in the identification of two localities of possible mineralization. Detailed field examination revealed the presence of a sulfide vein system and a partially inverted stratigraphic sequence indicating the possible presence of a massive sulfide deposit at depth. ?? 1983 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS2007

Probabilistic prediction models for aggregate quarry siting

Weights-of-evidence (WofE) and logistic regression techniques were used in a GIS framework to predict the spatial likelihood (prospectivity) of crushed-stone aggregate quarry development. The joint conditional probability models, based on geology, transportation network, and population density variables, were defined using quarry location and time of development data for the New England States, North Carolina, and South Carolina, USA. The Quarry Operation models describe the distribution of active aggregate quarries, independent of the date of opening. The New Quarry models describe the distribution of aggregate quarries when they open. Because of the small number of new quarries developed in the study areas during the last decade, independent New Quarry models have low parameter estimate reliability. The performance of parameter estimates derived for Quarry Operation models, defined by a larger number of active quarries in the study areas, were tested and evaluated to predict the spatial likelihood of new quarry development. Population density conditions at the time of new quarry development were used to modify the population density variable in the Quarry Operation models to apply to new quarry development sites. The Quarry Operation parameters derived for the New England study area, Carolina study area, and the combined New England and Carolina study areas were all similar in magnitude and relative strength. The Quarry Operation model parameters, using the modified population density variables, were found to be a good predictor of new quarry locations. Both the aggregate industry and the land management community can use the model approach to target areas for more detailed site evaluation for quarry location. The models can be revised easily to reflect actual or anticipated changes in transportation and population features. ?? International Association for Mathematical Geology 2007.

Natural Resources Research↗
USGS1988

Linear solvation energy relationships for toxicity of selected organic chemicals to Daphnia pulex and Daphnia magna

In the Laurentian Great Lakes, more than 300 contaminants have been identified in fish, other biota, water, and sediment. Current hazard assessment of these chemicals by the National Fisheries Research Center-Great Lakes is based on their toxicity, occurrence in the environment, and source. Although scientists at the Center have tested over 70 chemicals with the crustacean Daphnia pulex , the number of experimental data needed to screen the huge array of chemicals in the Great Lakes exceeds the practical capabilities of conducting bioassays. This limitation can be partly circumvented, however, by using mathematical models based on quantitative structure-activity relationships (QSAR) to provide rapid, inexpensive estimates of toxicity. Many properties of chemicals, including toxicity, bioaccumulation and water solubility are well correlated and can be predicted by equations of the generalized linear solvation energy relationships (LSER). The equation we used to model solute toxicity is Toxicity = constant + m VI/100 + s (π* + dδ) + b βm + a αm where VI = intrinsic (Van der Waals) molar volume; π* = molecular dipolarity/polarizability; δ = polarizability 'correction term'; βm = solute hydrogen bond acceptor basicity; and αm = solute hydrogen bond donor acidity. The subscript m designates solute monomer values for α and β. We applied the LSER model to 48-h acute toxicity data (measured as immobilization) for six classes of chemicals detected in Great Lakes fish. The following regression was obtained for Daphnia pulex (concentration = μM): log EC50 = 4.86 - 4.35 VI/100; N = 38, r2 = 0.867, sd = 0.403 We also used the LSER modeling approach to analyze to a large published data set of 24-h acute toxicity for Daphnia magna ; the following regression resulted, for eight classes of compounds (concentration = mM): log EC50 = 3.88 - 4.52 VI/100 - 1.62 π* + 1.66 βm - 0.916 αm; N = 62, r2 = 0.859, sd = 0.375 In addition we developed computer software that identifies chemical structures, estimates the LSER parameters, and predicts toxicity. The LSER models promise to be effective in differentiating between reactive and nonreactive toxicity behavior where other models have failed. Contaminants with reactive behavior are generally the most toxic and rank highest in hazard assessment of environmental chemicals.

Proceedings of the QSAR↗
USGS2004

Linear model describing three components of flow in karst aquifers using 18O data

The stable isotope of oxygen, 18O, is used as a naturally occurring ground-water tracer. Time-series data for ??18O are analyzed to model the distinct responses and relative proportions of the conduit, intermediate, and diffuse flow components in karst aquifers. This analysis also describes mathematically the dynamics of the transient fluid interchange between conduits and diffusive networks. Conduit and intermediate flow are described by linear-systems methods, whereas diffuse flow is described by mass-balance methods. An automated optimization process estimates parameters of lognormal, Pearson type III, and gamma distributions, which are used as transfer functions in linear-systems analysis. Diffuse flow and mixing parameters also are estimated by these optimization methods. Results indicate the relative proximity of a well to a main conduit flowpath and can help to predict the movement and residence times of potential contaminants. The three-component linear model is applied to five wells, which respond to changes in the isotopic composition of point recharge water from a sinking stream in the Madison aquifer in the Black Hills of South Dakota. Flow velocities as much as 540 m/d and system memories of as much as 71 years are estimated by this method. Also, the mean, median, and standard deviation of traveltimes; time to peak response; and the relative fraction of flow for each of the three components are determined for these wells. This analysis infers that flow may branch apart and rejoin as a result of an anastomotic (or channeled) karst network.

Journal of Hydrology↗
USGS2023

Operationalizing crop model data assimilation for improved on-farm situational awareness

The ability of ‘digital agriculture’ to support on-farm decision making is predicated on the real-time combination of observations and prior knowledge into an integrated digital environment. The mathematical discipline that seeks to provide this integration is known as model data assimilation (DA), with demonstrated benefits including improved predictive reliability, and the capacity to identify unexpected changes in field conditions and potential measurement errors. Despite routine adoption in other fields, the delayed adoption of DA in agriculture is due to the need to express end-of-season outcomes such as yield, update forecasts of these outcomes throughout the growing season as data become available, and enhance forecast reliability. To overcome these challenges, three guiding principles are introduced, providing a means to operationalize crop model DA for robust on-farm decision support. We apply the guiding principles using a South Australian viticulture case study. Our case study involves application of an iterative form of a widely used DA algorithm (ensemble Kalman filter) to dynamically update both static parameters and states associated with a grapevine simulation model. Daily weather data as well as fortnightly ground-based leaf area index (LAI) data are used for assimilation. It is shown how crop model DA can lead to not only significant improvements in forecasts of LAI but also to forecasts of end-of-season yield. The guiding principles also enable observations of greatest value to be identified throughout the season. This study highlights the role that formal crop model DA can play in agricultural decision support through enhancing situational awareness in real time.

Agricultural and Forest Meteorology↗
USGS1980

Study plan for the regional aquifer-system analysis of alluvial basins in south-central Arizona and adjacent states

The alluvial basins in the Southwestern United States constitute a major source of ground water and are relied upon extensively for agricultural, industrial, and public water supplies. Large-scale depletion of ground water is directly related to pumping that has occurred in the past few decades and is continuing today. The U.S. Geological Survey has started a 4-year study of the alluvial basins in south-central Arizona and parts of California, Nevada, and New Mexico. The study is designed to document and describe the hydrologic setting in the basins, the ground-water resources available, and the effects of historical development on the ground-water system. To aid in the study, mathematical models of selected basins will be developed for appraising the local and regional flow systems. Major tasks necessary to accomplish the study objectives include accumulating existing data on ground-water quantity and quality, entering the data into a computer file, identifying data deficiencies, and developing a program to remedy the deficiencies by collection of additional data. The approach to the study will be to develop and calibrate models of selected basins for which sufficient data exist and then to develop interpretation-transfer techniques whereby general predevelopment and postdevelopment conceptual models of the hydrologic system in other basins may be synthesized. The results will be applied to selected basins for testing, calibration, and modification. The end result of the project will be a better definition of the hydrologic parameters and a better understanding of the workings of the hydrologic system in the alluvial basins. The results will include models that can be used to study the effects of management alternatives and water-resources development on the hydrologic system.

Arizona↗
USGS2023

Bridging the gap between mathematical biology and undergraduate education using applicable natural resource modeling

Mathematical biology is a wide field of study with many venues that undergraduate students can access through research. However, the topics of study for these students can be overwhelming, and many topics of study yield either only trivial results or abstract outcomes that are nonintuitive and diffcult to understand. We have used natural resource modeling, and more specifically, a partnership between academic researchers and federal scientists, as a bridge between undergraduate research and mathematical biology. Our collaboration is an interdisciplinary team that combines biology, mathematics, and statistics professors with government research scientists. As a team, we have mentored students through opportunities such as a Research Experiences for Undergraduates and other projects. In this article, we provide an overview of how we develop questions for undergraduates and outline two case studies, both of which resulted in peer reviewed journal articles. Last, we describe how we also transfer the results from these undergraduate projects to resource managers so the results may be applied to real world problems.

Letters in Biomathematics↗
USGS2021

Multilayer perceptrons (MLPs)

Artificial neural networks (ANNs) are adaptable systems that can solve problems that are difficult to describe with a mathematical relationship. They seek relationships between different types of datasets with their abilities to learn either with supervision or without. ANNs recognize patterns between input and output space and generalize solutions, in a way simulating the human brain’s learning experience with many relatively simple individual processing elements, called neurons. Neurons are networked (network topology) in a number of ways depending on the problem type and complexity. One of the most widely used ANN learning techniques is supervised learning coupled with a multilayer perceptron (MLP) topology due to its flexible applicability to a wide range of modeling problems involving both general classification and regression. ANNs, due to this flexibility, have been applied to many fields since the 1990s and their theory, types (such as radial basis functions, random...

Book chapter↗
USGS2025

Are equilibrium shoreline models just convolutions?

Yes. Equilibrium shoreline models, which simulate wave-driven cross-shore erosion and accretion, are mathematically equivalent to a discrete convolution (i.e., a weighted, moving average) of a time series of wave-forcing conditions with a parameterized memory-decay kernel function. The direct equivalence between equilibrium shoreline models and convolutions reveals key theoretical aspects of equilibrium behavior. Convolutions (representing quasi-low-pass filter operations) provide an intuitive theoretical description of shoreline erosion and accretion behavior in response to waves: that is, shoreline position often mirrors the weighted moving average of wave time series. Model-convolution equivalence also provides a conceptual basis to interpret, evaluate, and construct data-driven Machine-Learning/Deep-Learning (ML/DL) models that use convolutions to extract features from data and then apply them for prediction (e.g., Convolutional Neural Networks (CNNs)). Finally, our findings provide a methodological pathway (based on Fourier transforms) for future understanding of wave-driven shoreline change, which can be used to interpret the coherence between the frequency spectrum of the processes of waves and shoreline change and construct more computationally efficient and effective shoreline-modeling approaches.

JGR Earth Surface↗
USGS2011

Homogenization of large-scale movement models in ecology

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10–100 m) habitat variability on large scale (10–100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models.

Bulletin of Mathematical Biology↗
USGS1995

Adjusting stream-sediment geochemical maps in the Austrian Bohemian Massif by analysis of variance

The Austrian portion of the Bohemian Massif is a Precambrian terrane composed mostly of highly metamorphosed rocks intruded by a series of granitoids that are petrographically similar. Rocks are exposed poorly and the subtle variations in rock type are difficult to map in the field. A detailed geochemical survey of stream sediments in this region has been conducted and included as part of the Geochemischer Atlas der Republik O??sterreich, and the variations in stream sediment composition may help refine the geological interpretation. In an earlier study, multivariate analysis of variance (MANOVA) was applied to the stream-sediment data in order to minimize unwanted sampling variation and emphasize relationships between stream sediments and rock types in sample catchment areas. The estimated coefficients were used successfully to correct for the sampling effects throughout most of the region, but also introduced an overcorrection in some areas that seems to result from consistent but subtle differences in composition of specific rock types. By expanding the model to include an additional factor reflecting the presence of a major tectonic unit, the Rohrbach block, the overcorrection is removed. This iterative process simultaneously refines both the geochemical map by removing extraneous variation and the geological map by suggesting a more detailed classification of rock types. ?? 1995 International Association for Mathematical Geology.

Mathematical Geology↗
USGS2002

Comparison of two probability distributions used to model sizes of undiscovered oil and gas accumulations: Does the tail wag the assessment?

Undiscovered oil and gas assessments are commonly reported as aggregate estimates of hydrocarbon volumes. Potential commercial value and discovery costs are, however, determined by accumulation size, so engineers, economists, decision makers, and sometimes policy analysts are most interested in projected discovery sizes. The lognormal and Pareto distributions have been used to model exploration target sizes. This note contrasts the outcomes of applying these alternative distributions to the play level assessments of the U.S. Geological Survey's 1995 National Oil and Gas Assessment. Using the same numbers of undiscovered accumulations and the same minimum, medium, and maximum size estimates, substitution of the shifted truncated lognormal distribution for the shifted truncated Pareto distribution reduced assessed undiscovered oil by 16% and gas by 15%. Nearly all of the volume differences resulted because the lognormal had fewer larger fields relative to the Pareto. The lognormal also resulted in a smaller number of small fields relative to the Pareto. For the Permian Basin case study presented here, reserve addition costs were 20% higher with the lognormal size assumption. ?? 2002 International Association for Mathematical Geology.

Mathematical Geology↗
USGS2010

A compositional multiphase model for groundwater contamination by petroleum products: 1. Theoretical considerations

A mathematical model is developed to describe the fate of hydrocarbon constituents of petroleum products introduced to soils as an immiscible liquid from sources such as leaking underground storage tanks and ruptured pipelines. The problem is one of multiphase transport (oil (immiscible), air, and water phases) of a reactive contaminant with constituents such as benzene, toluene, and xylene found in refined petroleum products like gasoline. In the unsaturated zone, transport of each constituent can occur as a solute in the water phase, vapor in the air phase, and as an unaltered constituent in the oil phase. Additionally, the model allows for adsorption. Molecular transformations, microbially mediated or abiotic, are incorporated as sink terms in the conservation of mass equations. An equilibrium approximation, applicable to any immiscible organic contaminant is applied to partition constituent mass between the air, oil, water, and adsorbed phases for points in the region where the oil phase exists. Outside the oil plume the equilibrium approximation takes on a simpler form to partition constituent mass between the air, water, and adsorbed phases only. Microbial degradation of petroleum products is first discussed in a general model, then the conservation of mass equation for oxygen is incorporated into the analysis which takes advantage of the key role played by oxygen in the metabolism of hydrocarbon utilizing microbes in soil environments. Approximations to two subproblems, oil plume establishment in the unsaturated zone, and solute and vapor transport subsequent to immiscible plume establishment are then developed from the general model.

Water Resources Research↗