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Results for “Applied Mathematical Modelling”

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118 records · Page 7Linked to original sources
USGS2022

Connecting regional-scale tree distribution models with seed dispersal kernels

Regional scale forest distribution models are important tools for biogeography and understanding the structure of forest communities in space. These models take climate and geographic variables as input and are therefore helpful for long-term decision support and climate adaptation planning. Generally, local processes of tree germination and seedling survival are resolved probabilistically with explanatory variables such as elevation, latitude, exposure, soil type, moisture availability, climate and weather inputs and `trained’ using landscape and regional presence-absence data and machine learning techniques. How seeds are distributed in these models, that is, determining the dispersal kernel, is far more problematic. The challenge is that variables conditioning vertebrate seed dispersal (motility and probability of utilization or caching in response to cover type) are not represented in large scale distribution models, and in fact vary on scales (10-100 meters) that are much smaller than the smallest pixel size for the distribution model (1-10 kilometers). We present a homogenized seed digestion kernel (HSDK) which incorporates this scale separation. Homogenization naturally links highly variable small-scale processes (like seed foraging and caching by birds and rodents) with large scale effects (like dispersal of seeds over tens of kilometers). We develop a homogenization strategy to predict seed dispersal on landscape scales, analytically linking small-scale variables (landscape fraction cover by tree type, gut residence times and cover type utilization by frugivorous birds) with large scale behaviors. Closed form approximations are developed in two dimensions for two limiting cases of seed handling behavior, and the approach is illustrated using landscape data and piñon-pine dispersal in a 630,000 square kilometer region in the southwestern US.

Applied Mathematics and Computation↗
USGS2002

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

Water-Resources Investigations Report↗
USGS2020

Probabilistic application of an integrated catchment-estuary-coastal system model to assess the evolution of inlet-interrupted coasts over the 21st century

Inlet-interrupted sandy coasts are dynamic and complex coastal systems with continuously evolving geomorphological behaviors under the influences of both climate change and human activities. These coastal systems are of great importance to society (e.g., providing habitats, navigation, and recreational activities) and are affected by both oceanic and terrestrial processes. Therefore, the evolution of these inlet-interrupted coasts is better assessed by considering the entirety of the Catchment-Estuary-Coastal (CEC) systems, under plausible future scenarios for climate change and increasing pressures due to population growth and human activities. Such a holistic assessment of the long-term evolution of CEC systems can be achieved via reduced-complexity modeling techniques, which are also ably quantifying the uncertainties associated with the projections due to their lower simulation times. Here, we develop a novel probabilistic modeling framework to quantify the input-driven uncertainties associated with the evolution of CEC systems over the 21 st century. In this new approach, probabilistic assessment of the evolution of inlet-interrupted coasts is achieved by (1) probabilistically computing the exchange sediment volume between the inlet-estuary system and its adjacent coast, and (2) distributing the computed sediment volumes along the inlet-interrupted coast. The model is applied at three case study sites: Alsea estuary (United States), Dyfi estuary (United Kingdom), and Kalutara inlet (Sri Lanka). Model results indicate that there are significant uncertainties in projected volume exchange at all the CEC systems (min-max range of 2.0 million cubic meters in 2100 for RCP 8.5), and the uncertainties in these projected volumes illustrate the need for probabilistic modeling approaches to evaluate the long-term evolution of CEC systems. A comparison of 50 th percentile probabilistic projections with deterministic estimates shows that the deterministic approach overestimates the sediment volume exchange in 2100 by 15–30% at Alsea and Kalutara estuary systems. Projections of coastline change obtained for the case study sites show that accounting for all key processes governing coastline change along inlet-interrupted coasts in computing coastline change results in projections that are between 20 and 134% greater than the projections that would be obtained if only the Bruun effect were taken into account, underlining the inaccuracies associated with using the Bruun rule at inlet-interrupted coasts.

Frontiers in Applied Mathematics and Statistics↗
USGS2009

Estimation of Unsaturated Zone Traveltimes for Rainier Mesa and Shoshone Mountain, Nevada Test Site, Nevada, Using a Source-Responsive Preferential-Flow Model

Traveltimes for contaminant transport by water from a point in the unsaturated zone to the saturated zone are a concern at Rainier Mesa and Shoshone Mountain in the Nevada Test Site, Nevada. Where nuclear tests were conducted in the unsaturated zone, contaminants must traverse hundreds of meters of variably saturated rock before they enter the saturated zone in the carbonate rock, where the regional groundwater system has the potential to carry them substantial distances to a location of concern. The unsaturated-zone portion of the contaminant transport path may cause a significant delay, in addition to the time required to travel within the saturated zone, and thus may be important in the overall evaluation of the potential hazard from contamination. Downward contaminant transport through the unsaturated zone occurs through various processes and pathways; this can lead to a broad distribution of contaminant traveltimes, including exceedingly slow and unexpectedly fast extremes. Though the bulk of mobile contaminant arrives between the time-scale end members, the fastest contaminant transport speed, in other words the speed determined by the combination of possible processes and pathways that would bring a measureable quantity of contaminant to the aquifer in the shortest time, carries particular regulatory significance because of its relevance in formulating the most conservative hazard-prevention scenarios. Unsaturated-zone flow is usually modeled as a diffusive process responding to gravity and pressure gradients as mediated by the unsaturated hydraulic properties of the materials traversed. The mathematical formulation of the diffuse-flow concept is known as Richards' equation, which when coupled to a solute transport equation, such as the advection-dispersion equation, provides a framework to simulate contaminant migration in the unsaturated zone. In recent decades awareness has increased that much fluid flow and contaminant transport within the unsaturated zone takes place as preferential flow, faster than would be predicted by the coupled Richards' and advection-dispersion equations with hydraulic properties estimated by traditional means. At present the hydrologic community has not achieved consensus as to whether a modification of Richards' equation, or a fundamentally different formulation, would best quantify preferential flow. Where the fastest contaminant transport speed is what needs to be estimated, there is the possibility of simplification of the evaluation process. One way of doing so is by a two-step process in which the first step is to evaluate whether significant preferential flow and solute transport is possible for the media and conditions of concern. The second step is to carry out (a) a basic Richards' and advection-dispersion equation analysis if it is concluded that preferential flow is not possible or (b) an analysis that considers only the fastest possible preferential-flow processes, if preferential flow is possible. For the preferential-flow situation, a recently published model describable as a Source-Responsive Preferential-Flow (SRPF) model is an easily applied option. This report documents the application of this two-step process to flow through the thick unsaturated zones of Rainier Mesa and Shoshone Mountain in the Nevada Test Site. Application of the SRPF model involves distinguishing between continuous and intermittent water supply to preferential flow paths. At Rainier Mesa and Shoshone Mountain this issue is complicated by the fact that contaminant travel begins at a location deep in the subsurface, where there may be perched water that may or may not act like a continuous supply, depending on such features as the connectedness of fractures and the nature of impeding layers. We have treated this situation by hypothesizing both continuous and intermittent scenarios for contaminant transport to the carbonate aquifer and reporting estimation of the fastest speed for both of th

Open-File Report↗
USGS2025

A partnership between the USGS and the Klamath Tribes to apply structured decision making for chronic wasting disease management

Project Overview: The Klamath Tribes (TKT) are the Klamath, Modoc, and Yahooskin Paiute peoples, and are the first peoples of the land, having lived in ancestral lands of Oregon and California since time immemorial. Members of TKT have rights to hunt, fish, trap, and gather, including the harvest of mule deer ( Odocoileus hemionus ) and elk ( Cervus canadensis nelsoni ) within the 1.19 million acres of their Reserved Treaty Rights Area. Anthropogenic changes threaten the well-being of mule deer and elk and of the Tribes that rely on them. Today, these species are a primary protein source for TKT. They are traded within TKT and among other Tribes and provide materials for cultural and sacred items such as regalia. However, mule deer numbers have been declining across the western states for the past several decades because of multiple stressors, including persistent and frequent drought and wildfires, habitat loss and degradation, vehicle mortality, and increasing barriers to migratory movements between summer and winter ranges. The migratory movements of mule deer, which allow deer to access the best available seasonal habitats, put them at risk of another potential stressor—infection with chronic wasting disease (CWD). Chronic wasting disease is a fatal prion disease of deer that has been detected in 36 U.S. states. It was detected in free-ranging mule deer in northern Idaho in 2021, prompting the Tribes to initiate a planning process for CWD surveillance, prevention, and response measures to preserve and protect the deer and elk within the Reserved Treaty Rights Area. In 2023, the Klamath Tribes Natural Resources Department began to develop their CWD plan by incorporating preliminary input provided by the Klamath Indian Game Commission (KIGC) and working with scientists from the U.S. Geological Survey (USGS). This collaborative effort includes the application of structured decision making and the development of mathematical models to analyze potential CWD management strategies. The result will be a transparent assessment that incorporates TKT values throughout the process and can inform place-based management of the cultural, natural, and physical resources upon which the Tribes depend. In addition, this process may provide opportunities for broader coordination by natural resource management agencies to work together to ensure the long-term health and sustainability of deer and elk populations within the Reserved Treaty Rights Area and throughout the state of Oregon.

Oregon↗
USGS2001

Flow of variably fluidized granular masses across three-dimensional terrain I. Coulomb mixture theory

Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces, govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, threedimensional mathematical model that accounts explicitly for solid- and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales.

Journal of Geophysical Research B: Solid Earth↗
USGS2017

Defining and classifying migratory habitats as sources and sinks: The migratory pathway approach

Understanding and conserving migratory species requires a method for characterizing the seasonal flow of animals among habitats. Source-sink theory describes the metapopulation dynamics of species by classifying habitats as population sources (i.e. net contributors) or sinks (i.e. net substractors). Migratory species may have non-breeding habitats important to the species (e.g. overwintering or stopover habitats) that traditional source-sink theory would classify as sinks because these habitats produce no individuals. Conversely, existing migratory network models can evaluate the relative contribution of non-breeding nodes, but these models make an equilibrium assumption that is difficult to meet when examining real migratory populations. We extend a pathway-based metric allowing breeding habitats, non-breeding habitats and migratory pathways connecting these habitats to be classified as sources or sinks. Rather than being based on whether place- or season-specific births exceed deaths, our approach quantifies the total demographic contribution from a node or migratory pathway over a flexibly defined yet limited time period across an organism's life cycle. As such, it provides a snapshot of a migratory system and therefore does not require assumptions associated with equilibrium dynamics. We first develop a generalizable mathematical notation and then demonstrate how the metric may be used with two case studies: the common loon ( Gavia immer ) and Yellowstone cutthroat trout ( Oncorhynchus clarkii bouvieri ). These examples highlight how stressors can impact stopover and wintering habitats (loons) and habitat management targeting migratory pathways can improve population status (trout). Synthesis and applications . Each of the two case studies presented describes how effects at one location are felt by populations in another through the seasonal flow of individuals. The contribution metric we present should be helpful in allocating regulatory and management attention to times and locations most critical to migratory species persistence.

Journal of Applied Ecology↗
USGS1971

Techniques for assessing water resource potentials in the developing countries: with emphasis on streamflow, erosion and sediment transport, water movement in unsaturated soils, ground water, and remote sensing in hydrologic applications

Hydrologic instrumentation and methodology for assessing water-resource potentials have originated largely in the developed countries of the temperature zone. The developing countries lie largely in the tropic zone, which contains the full gamut of the earth's climatic environments, including most of those of the temperate zone. For this reason, most hydrologic techniques have world-wide applicability. Techniques for assessing water-resource potentials for the high priority goals of economic growth are well established in the developing countries--but much more are well established in the developing countries--but much more so in some than in other. Conventional techniques for measurement and evaluation of basic hydrologic parameters are now well-understood in the developing countries and are generally adequate for their current needs and those of the immediate future. Institutional and economic constraints, however, inhibit growth of sustained programs of hydrologic data collection and application of the data to problems in engineering technology. Computer-based technology, including processing of hydrologic data and mathematical modelling of hydrologic parameters i also well-begun in many developing countries and has much wider potential application. In some developing counties, however, there is a tendency to look on the computer as a panacea for deficiencies in basic hydrologic data collection programs. This fallacy must be discouraged, as the computer is a tool and not a "magic box." There is no real substitute for sound programs of basic data collection. Nuclear and isotopic techniques are being used increasingly in the developed countries in the measurement and evaluation of virtually all hydrologic parameter in which conventional techniques have been used traditionally. Even in the developed countries, however, many hydrologists are not using nuclear techniques, simply because they lack knowledge of the principles involved and of the potential benefits. Nuclear methodology in hydrologic applications is generally more complex than the conventional and hence requires a high level of technical expertise for effective use. Application of nuclear techniques to hydrologic problems in the developing countries is likely to be marginal for some years to come, owing to the higher costs involved and expertise required. Nuclear techniques, however, would seem to have particular promise in studies of water movement in unsaturated soils and of erosion and sedimentation where conventional techniques are inadequate, inefficient and in some cases costly. Remote sensing offers great promise for synoptic evaluations of water resources and hydrologic processes, including the transient phenomena of the hydrologic cycle. Remote sensing is not, however, a panacea for deficiencies in hydrologic data programs in the developing countries. Rather it is a means for extending and augmenting on-the-ground observations ans surveys (ground truth) to evaluated water resources and hydrologic processes on a regionall or even continental scale. With respect to economic growth goals in developing countries, there are few identifiable gaps in existing hydrologic instrumentation and methodology insofar as appraisal, development and management of available water resources are concerned. What is needed is acceleration of institutional development and professional motivation toward more effective use of existing and proven methodology. Moreover, much sophisticated methodology can be applied effectively in the developing countries only when adequate levels of indigenous scientific skills have been reached and supportive institutional frameworks are evolved to viability.

Open-File Report↗
USGS2000

Volcano geodesy: Challenges and opportunities for the 21st century

Intrusions of magma beneath volcanoes deform the surrounding rock and, if the intrusion is large enough, the overlying ground surface. Numerical models generally agree that, for most eruptions, subsurface volume changes are sufficient to produce measurable deformation at the surface. Studying this deformation can help to determine the location, volume, and shape of a subsurface magma body and thus to anticipate the onset and course of an eruption. This approach has been successfully applied at many restless volcanoes, especially basaltic shields and silicic calderas, using various geodetic techniques and sensors. However, its success at many intermediate-composition strato-volcanoes has been limited by generally long repose intervals, steep terrain, and structural influences that complicate the history and shape of surface deformation. These factors have made it difficult to adequately characterize deformation in space and time at many of the world's dangerous volcanoes. Recent technological advances promise to make this task easier by enabling the acquisition of geodetic data of high spatial and temporal resolution from Earth-orbiting satellites. Synthetic aperture radar interferometry (InSAR) can image ground deformation over large areas at metre-scale resolution over time-scales of a month to a few years. Global Positioning System (GPS) stations can provide continuous information on three-dimensional ground displacements at a network of key sites -information that is especially important during volcanic crises. By using InSAR to determine the shape of the displacement field and GPS to monitor temporal changes at key sites, scientists have a much better chance to capture geodetic signals that have so far been elusive at many volcanoes. This approach has the potential to provide longer-term warnings of impending volcanic activity than is possible with other monitoring techniques.

Philosophical Transactions of the Royal Society A:↗
USGS2009

Mathematical modelling of anisotropy of illite-rich shale

The estimation of illite-rich shale anisotropy to account for the alignment of clays and gas- or brine-filled cracks is presented via mathematical modelling. Such estimation requires analysis to interpret the dominance of one effect over another. This knowledge can help to evaluate the permeability in the unconventional reservoir, stress orientation, and the seal capacity for the conventional reservoir. Effective media modelling is used to predict the elastic properties of the illite-rich shale and to identify the dominant contributions to the shale anisotropy. We consider two principal reasons of the shale anisotropy: orientation of clay platelets and orientation of fluid-filled cracks. In reality, both of these two factors affect the shale anisotropy. The goal of this study is, first, to separately analyse the effect of these two factors to reveal the specific features in P- and S-wave velocity behaviour typical of each of the factors, and, then, consider a combined effect of the factors when the cracks are horizontally or vertically aligned. To do this, we construct four models of shale. The behaviour of P- and S-wave velocities is analysed when gas- and water-filled cracks embedded in a host matrix are randomly oriented, or horizontally or vertically aligned. The host matrix can be either isotropic or anisotropic (of VTI symmetry). In such a modelling, we use published data on mineralogy and clay platelet alignment along with other micromechanical measurements. In the model, where the host matrix is isotropic, the presence of a singularity point (when the difference V S1 - V S2 changes its sign) in shear wave velocities is an indicator of brine-filled aligned cracks. In the model with the VTI host matrix and horizontally aligned cracks filled with gas, an increase in their volume concentration leads to that the azimuth at which the singularity is observed moves toward the symmetry axis. In this case, if the clay content is small (around 20 per cent), the singularity point may even vanish. The Thomsen parameters are helpful in fluid type indication in shale. An indicator of gas-filled aligned cracks is ?? > ??. If aligned cracks in illite-rich shale are brine-filled, ?? < ??. Negative value of ?? indicates brine-filled cracks in illite-rich shale. A shale with brine-filled cracks exhibits higher V p /V s ratio in the vertical direction as compared to the gas-filled shale. A disorientation of clay platelets and brine-filled cracks may lead to that the singularity point is absent for brine-saturated shale as well. In this case one can also observe ?? > ?? and decreased values of V p /V s in the vertical direction as in the case of gas-filled cracks. In the presence of vertically aligned cracks, shales exhibit distinctly revealed features of orthorhombic symmetry. The results have important applications where seismic measurements are applied to predict the maturity state of the shale. ?? 2009 The Authors Journal compilation ?? 2009 RAS.

Conference Paper↗