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Results for “Applied Mathematical Modelling”

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At least 91 records · Page 5Linked to original sources
USGS2020

Landslide disparities, flume discoveries, and Oso despair

Landslide dynamics is the branch of science that seeks to understand the motion of landslides by applying Newton's laws. This memoir focusses on a 40‐year effort to understand motion of highly mobile—and highly lethal—landslides such as debris avalanches and debris flows. A major component of this work entailed development and operation of the U.S. Geological Survey debris flow flume, a unique, large‐scale experimental facility in Oregon. Experiments there yielded new insights that informed development of mathematical models that were aimed not only at explaining landslide dynamics but also at evaluating landslide and debris flow hazards. The most sophisticated of these models, called D‐Claw, found its first practical application during investigations of the 2014 Oso, Washington, landslide disaster. That event provided indelible lessons about the utility and sociology of science in the real world.

Washington↗
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↗
USGS2006

Performance assessments of nuclear waste repositories: A dialogue on their value and limitations

Performance Assessment (PA) is the use of mathematical models to simulate the long-term behavior of engineered and geologic barriers in a nuclear waste repository; methods of uncertainty analysis are used to assess effects of parametric and conceptual uncertainties associated with the model system upon the uncertainty in outcomes of the simulation. PA is required by the U.S. Environmental Protection Agency as part of its certification process for geologic repositories for nuclear waste. This paper is a dialogue to explore the value and limitations of PA. Two “skeptics” acknowledge the utility of PA in organizing the scientific investigations that are necessary for confident siting and licensing of a repository; however, they maintain that the PA process, at least as it is currently implemented, is an essentially unscientific process with shortcomings that may provide results of limited use in evaluating actual effects on public health and safety. Conceptual uncertainties in a PA analysis can be so great that results can be confidently applied only over short time ranges, the antithesis of the purpose behind long-term, geologic disposal. Two “proponents” of PA agree that performance assessment is unscientific, but only in the sense that PA is an engineering analysis that uses existing scientific knowledge to support public policy decisions, rather than an investigation intended to increase fundamental knowledge of nature; PA has different goals and constraints than a typical scientific study. The “proponents” describe an ideal, sixstep process for conducting generalized PA, here called probabilistic systems analysis (PSA); they note that virtually all scientific content of a PA is introduced during the model-building steps of a PSA, they contend that a PA based on simple but scientifically acceptable mathematical models can provide useful and objective input to regulatory decision makers. The value of the results of any PA must lie between these two views and will depend on the level of knowledge of the site, the degree to which models capture actual physical and chemical processes, the time over which extrapolations are made, and the proper evaluation of health risks attending implementation of the repository. The challenge is in evaluating whether the quality of the PA matches the needs of decision makers charged with protecting the health and safety of the public.

Risk Analysis↗
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↗
USGS2008

Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback

This paper studies a parsimonious model of landslide motion, which consists of the one-dimensional diffusion equation (for pore pressure) coupled through a boundary condition to a first-order ODE (Newton's second law). Velocity weakening of sliding friction gives rise to nonlinearity in the model. Analysis shows that solutions of the model equations exhibit a subcritical Hopf bifurcation in which stable, steady sliding can transition to cyclical, stick-slip motion. Numerical computations confirm the analytical predictions of the parameter values at which bifurcation occurs. The existence of stick-slip behavior in part of the parameter space is particularly noteworthy because, unlike stick-slip behavior in classical models , here it arises in the absence of a reversible (elastic) driving force. Instead, the driving force is static (gravitational), mediated by the effects of pore-pressure diffusion on frictional resistance.

SIAM Journal on Applied Mathematics↗
USGS2007

Bayesian multimodel inference for dose-response studies

Statistical inference in dose-response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose-response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Environmental Toxicology and Chemistry↗
USGS2009

Multi-state succession in wetlands: a novel use of state and transition models

The complexity of ecosystems and mechanisms of succession are often simplified by linear and mathematical models used to understand and predict system behavior. Such models often do not incorporate multivariate, nonlinear feedbacks in pattern and process that include multiple scales of organization inherent within real-world systems. Wetlands are ecosystems with unique, nonlinear patterns of succession due to the regular, but often inconstant, presence of water on the landscape. We develop a general, nonspatial state and transition (S and T) succession conceptual model for wetlands and apply the general framework by creating annotated succession/management models and hypotheses for use in impact analysis on a portion of an imperiled wetland. The S and T models for our study area, Water Conservation Area 3A South (WCA3), Florida, USA, included hydrologic and peat depth values from multivariate analyses and classification and regression trees. We used the freeware Vegetation Dynamics Development Tool as an exploratory application to evaluate our S and T models with different management actions (equal chance [a control condition], deeper conditions, dry conditions, and increased hydrologic range) for three communities: slough, sawgrass ( Cladium jamaicense ), and wet prairie. Deeper conditions and increased hydrologic range behaved similarly, with the transition of community states to deeper states, particularly for sawgrass and slough. Hydrology is the primary mechanism for multi-state transitions within our study period, and we show both an immediate and lagged effect on vegetation, depending on community state. We consider these S and T succession models as a fraction of the framework for the Everglades. They are hypotheses for use in adaptive management, represent the community response to hydrology, and illustrate which aspects of hydrologic variability are important to community structure. We intend for these models to act as a foundation for further restoration management and experimentation which will refine transition and threshold concepts.

Florida↗
USGS2015

Effects of dispersal on total biomass in a patchy, heterogeneous system: Analysis and experiment

An intriguing recent result from mathematics is that a population diffusing at an intermediate rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. We extended the current mathematical theory to apply to logistic growth and also showed that the result applies to patchy systems with dispersal among patches, both for continuous and discrete time. This allowed us to make specific predictions, through simulations, concerning the biomass dynamics, which were verified by a laboratory experiment. The experiment was a study of biomass growth of duckweed ( Lemna minor Linn.), where the resources (nutrients added to water) were distributed homogeneously among a discrete series of water-filled containers in one treatment, and distributed heterogeneously in another treatment. The experimental results showed that total biomass peaked at an intermediate, relatively low, diffusion rate, higher than the total carrying capacity of the system and agreeing with the simulation model. The implications of the experiment to dynamics of source, sink, and pseudo-sink dynamics are discussed.

Mathematical Biosciences↗
USGS2010

Approaches to highly parameterized inversion: A guide to using PEST for model-parameter and predictive-uncertainty analysis

Analysis of the uncertainty associated with parameters used by a numerical model, and with predictions that depend on those parameters, is fundamental to the use of modeling in support of decisionmaking. Unfortunately, predictive uncertainty analysis with regard to models can be very computationally demanding, due in part to complex constraints on parameters that arise from expert knowledge of system properties on the one hand (knowledge constraints) and from the necessity for the model parameters to assume values that allow the model to reproduce historical system behavior on the other hand (calibration constraints). Enforcement of knowledge and calibration constraints on parameters used by a model does not eliminate the uncertainty in those parameters. In fact, in many cases, enforcement of calibration constraints simply reduces the uncertainties associated with a number of broad-scale combinations of model parameters that collectively describe spatially averaged system properties. The uncertainties associated with other combinations of parameters, especially those that pertain to small-scale parameter heterogeneity, may not be reduced through the calibration process. To the extent that a prediction depends on system-property detail, its postcalibration variability may be reduced very little, if at all, by applying calibration constraints; knowledge constraints remain the only limits on the variability of predictions that depend on such detail. Regrettably, in many common modeling applications, these constraints are weak. Though the PEST software suite was initially developed as a tool for model calibration, recent developments have focused on the evaluation of model-parameter and predictive uncertainty. As a complement to functionality that it provides for highly parameterized inversion (calibration) by means of formal mathematical regularization techniques, the PEST suite provides utilities for linear and nonlinear error-variance and uncertainty analysis in these highly parameterized modeling contexts. Availability of these utilities is particularly important because, in many cases, a significant proportion of the uncertainty associated with model parameters-and the predictions that depend on them-arises from differences between the complex properties of the real world and the simplified representation of those properties that is expressed by the calibrated model. This report is intended to guide intermediate to advanced modelers in the use of capabilities available with the PEST suite of programs for evaluating model predictive error and uncertainty. A brief theoretical background is presented on sources of parameter and predictive uncertainty and on the means for evaluating this uncertainty. Applications of PEST tools are then discussed for overdetermined and underdetermined problems, both linear and nonlinear. PEST tools for calculating contributions to model predictive uncertainty, as well as optimization of data acquisition for reducing parameter and predictive uncertainty, are presented. The appendixes list the relevant PEST variables, files, and utilities required for the analyses described in the document.

Michigan↗
USGS2023

HyWaves: Hybrid downscaling of multimodal wave spectra to nearshore areas

Long-term and accurate wave hindcast databases are often required in different coastal engineering projects. The assessment of the nearshore wave climate is often accomplished by using downscaling techniques to translate offshore waves to coastal areas. However, dynamical downscaling approaches may incur huge computational cost. Additionally, the common use of bulk parameterizations are often not accurate for multidimensional waves. To overcome these limitations, we present a hybrid downscaling approach that combines mathematical algorithms (statistical downscaling) and numerical modeling (dynamical downscaling) over the individual spectral partitions. Every wave partition is downscaled and aggregated afterward by using principles of wave linear theory. By assuming linearity in the propagation of the wave celerity, the application of the method is limited from offshore to intermediate water depths. In addition, the method proposed uses a technique to simplify the spectral boundary conditions in complex domains. The methodology has been applied and validated in the island states of Samoa, American Samoa, Majuro, and Kwajalein, showing good skill at reproducing the spectral hourly time series of significant wave height, peak period, and peak direction. Moreover, an accurate representation of the observed energy spectrum was achieved. This study provides insight into the numerical approximation of the combined sea-swell states while improving the quality of fast spectral forecasting and early warning systems.

Ocean Modeling↗
USGS2010

A methodology for the assessment of unconventional (continuous) resources with an application to the Greater Natural Buttes gas field, Utah

The Greater Natural Buttes tight natural gas field is an unconventional (continuous) accumulation in the Uinta Basin, Utah, that began production in the early 1950s from the Upper Cretaceous Mesaverde Group. Three years later, production was extended to the Eocene Wasatch Formation. With the exclusion of 1100 non-productive (“dry”) wells, we estimate that the final recovery from the 2500 producing wells existing in 2007 will be about 1.7 trillion standard cubic feet (TSCF) (48.2 billion cubic meters (BCM)). The use of estimated ultimate recovery (EUR) per well is common in assessments of unconventional resources, and it is one of the main sources of information to forecast undiscovered resources. Each calculated recovery value has an associated drainage area that generally varies from well to well and that can be mathematically subdivided into elemental subareas of constant size and shape called cells. Recovery per 5-acre cells at Greater Natural Buttes shows spatial correlation; hence, statistical approaches that ignore this correlation when inferring EUR values for untested cells do not take full advantage of all the information contained in the data. More critically, resulting models do not match the style of spatial EUR fluctuations observed in nature. This study takes a new approach by applying spatial statistics to model geographical variation of cell EUR taking into account spatial correlation and the influence of fractures. We applied sequential indicator simulation to model non-productive cells, while spatial mapping of cell EUR was obtained by applying sequential Gaussian simulation to provide multiple versions of reality (realizations) having equal chances of being the correct model. For each realization, summation of EUR in cells not drained by the existing wells allowed preparation of a stochastic prediction of undiscovered resources, which range between 2.6 and 3.4 TSCF (73.6 and 96.3 BCM) with a mean of 2.9 TSCF (82.1 BCM) for Greater Natural Buttes. A second approach illustrates the application of multiple-point simulation to assess a hypothetical frontier area for which there is no production information but which is regarded as being similar to Greater Natural Buttes.

Utah↗
USGS1989

A direct method for calculating instrument noise levels in side-by-side seismometer evaluations

The subject of determining the inherent system noise levels present in modem broadband closed loop seismic sensors has been an evolving topic ever since closed loop systems became available. Closed loop systems are unique in that the system noise can not be determined via a blocked mass test as in older conventional open loop seismic sensors. Instead, most investigators have resorted to performing measurements on two or more systems operating in close proximity to one another and to analyzing the outputs of these systems with respect to one another to ascertain their relative noise levels. The analysis of side-by-side relative performance is inherently dependent on the accuracy of the mathematical modeling of the test configuration. This report presents a direct approach to extracting the system noise levels of two linear systems with a common coherent input signal. The mathematical solution to the problem is incredibly simple; however the practical application of the method encounters some difficulties. Examples of expected accuracies are presented as derived by simulating real systems performance using computer generated random noise. In addition, examples of the performance of the method when applied to real experimental test data are shown.

Open-File Report↗
USGS2018

A spatial approach to combatting wildlife crime

Poaching can have devastating impacts on animal and plant numbers, and in many countries has reached crisis levels, with illegal hunters employing increasingly sophisticated techniques. Here, we show how geographic profiling – a mathematical technique originally developed in criminology and recently applied to animal foraging and epidemiology – can be adapted for use in investigations of wildlife crime, using data from an eight-year study in Savé Valley Conservancy, Zimbabwe that in total includes more than 10,000 incidents of illegal hunting and the deaths of 6,454 wild animals. Using a subset of these data for which the illegal hunters’ identities are known, we show that the model can successfully identify the illegal hunters’ home villages using the spatial locations of hunting incidences (for example, snares) as input, and show how this can be improved by manipulating the probability surface inside the Conservancy to reflect the fact that – although the illegal hunters mostly live outside the Conservancy, the majority of hunting occurs inside (in criminology, ‘commuter crime’). The results of this analysis – combined with rigorous simulations – show for the first time how geographic profiling can be combined with GIS data and applied to situations with more complex spatial patterns – for example, where landscape heterogeneity means that some parts of the study area are unsuitable (e.g. aquatic areas for terrestrial animals, or vice versa), or where landscape permeability differs (for example, forest bats tending not to fly over open areas). More broadly, these results show how geographic profiling can be used to target anti-poaching interventions more effectively and more efficiently, with important implications for the development of management strategies and conservation plans in a range of conservation scenarios.

Conservation Biology↗
USGS1986

Estimating monthly streamflow values by cokriging

Cokriging is applied to estimation of missing monthly streamflow values in three records from gaging stations in west central Virginia. Missing values are estimated from optimal consideration of the pattern of auto- and cross-correlation among standardized residual log-flow records. Investigation of the sensitivity of estimation to data configuration showed that when observations are available within two months of a missing value, estimation is improved by accounting for correlation. Concurrent and lag-one observations tend to screen the influence of other available observations. Three models of covariance structure in residual log-flow records are compared using cross-validation. Models differ in how much monthly variation they allow in covariance. Precision of estimation, reflected in mean squared error (MSE), proved to be insensitive to this choice. Cross-validation is suggested as a tool for choosing an inverse transformation when an initial nonlinear transformation is applied to flow values. ?? 1986 Plenum Publishing Corporation.

Mathematical Geology↗
USGS2024

Assessing and implementing the concept of Blue Economy in Laurentian Great Lakes fisheries: Lessons from coupled human and natural systems

Inland fisheries often receive little to no attention in global discussions about sustainable development. The consequences of overlooking inland fisheries in sustainability dialogues are increasingly problematic as fisheries stressors (e.g., overharvest, species invasion, climate change, habitat modification) intensify. Elevating the global profile of inland fisheries requires an approach for quantifying and clearly conveying the ecological, economic, and societal values of these systems. One such approach involves the Blue Economy, a multifaceted concept initially used to describe the intersection of marine conservation and sustainable use of marine resources for economic growth. Although conceptually powerful, the Blue Economy has rarely been applied to inland waters and fisheries. To address this knowledge gap, we conceptualized Laurentian Great Lakes fisheries from a Blue Economy perspective. In particular, we evaluated the utility of the coupled human and natural systems (CHANS) framework for characterizing the ecological, economic, and societal values of Laurentian Great Lakes fisheries and associated contributions to the Blue Economy (e.g., human livelihoods, food security, recreation, conservation, economic prosperity). There are numerous opportunities to leverage CHANS methods (e.g., metacoupling, telecoupling) and associated mathematical models to advance fisheries science, inform fisheries management, and ultimately move toward a Blue Economy in the Laurentian Great Lakes. To that end, we demonstrated applications of CHANS methods, discussed strategies for communicating with stakeholders, and provided insights for navigating challenges to developing a Blue Economy in the Laurentian Great Lakes—a model that could be used in the African Great Lakes and other large ecosystems in the world.

Laurentian Great Lakes↗
USGS1985

Documentation of a Regional Aquifer Simulation Model, RAQSIM, and a description of support programs applied in the Twin Platte-Middle Republican Study Area, Nebraska

RAQSIM, a generalized flow model of a groundwater system using finite-element methods, is documented to explain how it works and to demonstrate that it gives valid results. Three support programs that are used to compute recharge and discharge data required as input to RAQSIM are described. RAQSIM was developed to solve transient, two-dimensional, regional groundwater flow problems with isotropic or anisotropic conductance. The model can also simulate radially-symmetric flow to a well and steady-state flow. The mathematical basis, program structure, data input and output procedures, organization of data sets, and program features and options of RAQSIM are discussed. An example , containing listings of data and results and illustrating RAQSIM 's capabilities, is discussed in detail. Two test problems also are discussed comparing RAQSIM 's results with analytical procedures. The first support program described, the PET Program, uses solar radiation and other climatic data in the Jensen-Haise method to compute potential evapotranspiration. The second support program, the Soil-Water Program, uses output from the PET Program, soil characteristics, and the ratio of potential to actual evapotranspiration for each crop to compute infiltration, storage, and removal of water from the soil zone. The third program, the Recharge-Discharge Program, uses output from the Soil-Water Program together with other data to compute recharge and discharge from the groundwater flow system. For each support program, a program listing and examples of the data and results for the Twin Platte-Middle Republican study are provided. In addition, a brief discussion on how each program operates and on procedures for running and modifying these programs are presented. (Author 's abstract)

Nebraska↗
USGS2014

Hydraulic modeling development and application in water resources engineering

The use of modeling has become widespread in water resources engineering and science to study rivers, lakes, estuaries, and coastal regions. For example, computer models are commonly used to forecast anthropogenic effects on the environment, and to help provide advanced mitigation measures against catastrophic events such as natural and dam-break floods. Linking hydraulic models to vegetation and habitat models has expanded their use in multidisciplinary applications to the riparian corridor. Implementation of these models in software packages on personal desktop computers has made them accessible to the general engineering community, and their use has been popularized by the need of minimal training due to intuitive graphical user interface front ends. Models are, however, complex and nontrivial, to the extent that even common terminology is sometimes ambiguous and often applied incorrectly. In fact, many efforts are currently under way in order to standardize terminology and offer guidelines for good practice, but none has yet reached unanimous acceptance. This chapter provides a view of the elements involved in modeling surface flows for the application in environmental water resources engineering. It presents the concepts and steps necessary for rational model development and use by starting with the exploration of the ideas involved in defining a model. Tangible form of those ideas is provided by the development of a mathematical and corresponding numerical hydraulic model, which is given with a substantial amount of detail. The issues of model deployment in a practical and productive work environment are also addressed. The chapter ends by presenting a few model applications highlighting the need for good quality control in model validation.

Book chapter↗
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↗