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Results for “Applied Mathematics and Computation”

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

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At least 37 records · Page 2Linked to original sources
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↗
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↗
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↗
USGS2004

Use of RORA for Complex Ground-Water Flow Conditions

The RORA computer program for estimating recharge is based on a condition in which ground water flows perpendicular to the nearest stream that receives ground-water discharge. The method, therefore, does not explicitly account for the ground-water-flow component that is parallel to the stream. Hypothetical finite-difference simulations are used to demonstrate effects of complex flow conditions that consist of two components: one that is perpendicular to the stream and one that is parallel to the stream. Results of the simulations indicate that the RORA program can be used if certain constraints are applied in the estimation of the recession index, an input variable to the program. These constraints apply to a mathematical formulation based on aquifer properties, recession of ground-water levels, and recession of streamflow.

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↗
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↗
USGS1996

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

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

Water-Resources Investigations Report↗
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↗
USGS2004

Section 1. Simulation of surface-water integrated flow and transport in two-dimensions: SWIFT2D user's manual

A numerical model for simulation of surface-water integrated flow and transport in two (horizontal-space) dimensions is documented. The model solves vertically integrated forms of the equations of mass and momentum conservation and solute transport equations for heat, salt, and constituent fluxes. An equation of state for salt balance directly couples solution of the hydrodynamic and transport equations to account for the horizontal density gradient effects of salt concentrations on flow. The model can be used to simulate the hydrodynamics, transport, and water quality of well-mixed bodies of water, such as estuaries, coastal seas, harbors, lakes, rivers, and inland waterways. The finite-difference model can be applied to geographical areas bounded by any combination of closed land or open water boundaries. The simulation program accounts for sources of internal discharges (such as tributary rivers or hydraulic outfalls), tidal flats, islands, dams, and movable flow barriers or sluices. Water-quality computations can treat reactive and (or) conservative constituents simultaneously. Input requirements include bathymetric and topographic data defining land-surface elevations, time-varying water level or flow conditions at open boundaries, and hydraulic coefficients. Optional input includes the geometry of hydraulic barriers and constituent concentrations at open boundaries. Time-dependent water level, flow, and constituent-concentration data are required for model calibration and verification. Model output consists of printed reports and digital files of numerical results in forms suitable for postprocessing by graphical software programs and (or) scientific visualization packages. The model is compatible with most mainframe, workstation, mini- and micro-computer operating systems and FORTRAN compilers. This report defines the mathematical formulation and computational features of the model, explains the solution technique and related model constraints, describes the model framework, documents the type and format of inputs required, and identifies the type and format of output available.

Techniques and Methods↗
USGS1990

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses.

Applied Mathematical Modelling↗
USGS1986

Evaluation of six methods for estimating magnitude and frequency of peak discharges on urban streams in New York

Six methods of estimating peak discharges of urban streams were compared and evaluated for applicability to urban streams in New York. Discharge and frequency values developed from a series of synthesized annual flood records were compared with values obtained from the six methods. The synthesized flood records were computed from rainfall-runoff models of 11 urban basins in three counties across the State. Four of these basins had a sufficient period of record to enable rainfall-runoff modeling of two different 5-year periods so that increases in peak flow due to increased urbanization could also be used for comparison of the six methods. A graphical analysis and three types of mathematical analyses were made to evaluate the closeness of fit and bias of the methods. All methods showed a tendency to overestimate synthetic urban flood-magnitude values, but the two adjust rural flood-frequency estimates on a nationwide basis showed smallest standard errors of estimate and bias. The standard errors for these two methods ranged from 44 to 57 percent over the six recurrence intervals (2, 5, 10, 25, 50, and 100 year), and the bias ranged from +28 to +53 percent. The bias , however, is probably due to errors inherent in using synthetic records and in applying the New York rural flood-frequency equations to urban basins with small drainage areas. (USGS)

Water-Resources Investigations Report↗
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↗
USGS2025

lasertram: A Python library for time resolved analysis of laser ablation inductively coupled plasma mass spectrometry data

Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) data has a wide variety of uses in the geosciences for in-situ chemical analysis of complex natural materials. Improvements to instrument capabilities and operating software have drastically reduced the time required to generate large volumes of data relative to previous methodologies. Raw data from LA-ICP-MS, however, is in counts per unit time (typically counts per second), not elemental concentrations and converting these count ratesto concentrations requires additional processing. For complex materials where the ablated volume may contain a range of material compositions, a moderate amount of user input is also required if appropriate concentrations are to be accurately calculated. In geologic materials such as glasses and minerals that potentially have numerous heterogeneities (e.g., microlites or other inclusions) within them, this is typically determiningwhether the total ablation signal should be filtered to remove these heterogeneities. This necessitates that the LA-ICP-MS data processing pipeline is one that is not automated, but is also designed to enable rapid and efficient processing of large volumes of data. Here we introduce , a Python library for the time resolved analysis of LA-ICP-MS data. We outline its mathematical theory, code structure, and provide an example of how it can be used to provide the time resolved analysis necessitated by LA-ICP-MS data of complex geologic materials. Throughout the pipeline we show how metadata and data are incrementally added to the objects created such that virtually any aspect of an experiment may be interrogated and its quality assessed. We also show, that when combined with other Python libraries for building graphical user interfaces, it can be utilized outside of a pure scripting environment. can be found at https://doi.org/10.5066/P1DZUR3Z

Applied Computing and Geosciences↗
USGS2007

Effective groundwater model calibration: With analysis of data, sensitivities, predictions, and uncertainty

Methods and guidelines for developing and using mathematical models Turn to Effective Groundwater Model Calibration for a set of methods and guidelines that can help produce more accurate and transparent mathematical models. The models can represent groundwater flow and transport and other natural and engineered systems. Use this book and its extensive exercises to learn methods to fully exploit the data on hand, maximize the model's potential, and troubleshoot any problems that arise. Use the methods to perform: Sensitivity analysis to evaluate the information content of data Data assessment to identify (a) existing measurements that dominate model development and predictions and (b) potential measurements likely to improve the reliability of predictions Calibration to develop models that are consistent with the data in an optimal manner Uncertainty evaluation to quantify and communicate errors in simulated results that are often used to make important societal decisions Most of the methods are based on linear and nonlinear regression theory. Fourteen guidelines show the reader how to use the methods advantageously in practical situations. Exercises focus on a groundwater flow system and management problem, enabling readers to apply all the methods presented in the text. The exercises can be completed using the material provided in the book, or as hands-on computer exercises using instructions and files available on the text's accompanying Web site. Throughout the book, the authors stress the need for valid statistical concepts and easily understood presentation methods required to achieve well-tested, transparent models. Most of the examples and all of the exercises focus on simulating groundwater systems; other examples come from surface-water hydrology and geophysics. The methods and guidelines in the text are broadly applicable and can be used by students, researchers, and engineers to simulate many kinds systems.

Book↗
USGS1977

State of stress in the lithosphere: Inferences from the flow laws of olivine

The experimental flow data for rocks and minerals are reviewed and found to fit a law of the form {Mathematical expression} where {Mathematical expression} This law reduces to the familiar power-law stress dependency at low stress and to an exponential stress dependency at high stress. Using the material flow law parameters for olivine, stress profiles with depth and strain rate are computed for a representative range of temperature distributions in the lithosphere. The results show that the upper 15 to 25 km of the oceanic lithosphere must behave elastically or fail by fracture and that the remainder deforms by exponential law flow at intermediate depths and by power-law flow in the rest. A model computation of the gravitational sliding of a lithospheric plate using olivine rheology exhibits a very sharp decoupling zone which is a consequence of the combined effects of increasing stress and temperature on the flow law, which is a very sensitive function of both. ?? 1977 Birkha??user Verlag.

Pure and Applied Geophysics PAGEOPH↗
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↗
USGS1998

Computer programs for describing the recession of ground-water discharge and for estimating mean ground-water recharge and discharge from streamflow records-update

The computer programs included in this report can be used to develop a mathematical expression for recession of ground-water discharge and estimate mean ground-water recharge and discharge. The programs are intended for analysis of the daily streamflow record of a basin where one can reasonably assume that all, or nearly all, ground water discharges to the stream except for that which is lost to riparian evapotranspiration, and where regulation and diversion of flow can be considered to be negligible. The program RECESS determines the master reces-sion curve of streamflow recession during times when all flow can be considered to be ground-water discharge and when the profile of the ground-water-head distribution is nearly stable. The method uses a repetitive interactive procedure for selecting several periods of continuous recession, and it allows for nonlinearity in the relation between time and the logarithm of flow. The program RORA uses the recession-curve displacement method to estimate the recharge for each peak in the streamflow record. The method is based on the change in the total potential ground-water discharge that is caused by an event. Program RORA is applied to a long period of record to obtain an estimate of the mean rate of ground-water recharge. The program PART uses streamflow partitioning to estimate a daily record of base flow under the streamflow record. The method designates base flow to be equal to streamflow on days that fit a requirement of antecedent recession, linearly interpolates base flow for other days, and is applied to a long period of record to obtain an estimate of the mean rate of ground-water discharge. The results of programs RORA and PART correlate well with each other and compare reasonably with results of the corresponding manual method.

Water-Resources Investigations Report↗
USGS1985

Comparative study of aggregations under different dependency assumptions for assessment of undiscovered recoverable oil resources in the world

The U.S. Geological Survey assessed all significant sedimentary basins in the world for undiscovered conventionally recoverable crude-oil resources. Probabilistic methodology was applied to each basin assessment to produce estimates in the form of probability distributions. Basin probability distributions were computer aggregated to produce resource estimates for the entire world. Aggregation was approximated by a three-parameter lognormal distribution by combining the first three central moments of basin distributions. For purposes of experiment and study, world aggregation was conducted under four different sets of assumptions. The four cases are (1) dependent assessments of all basins, (2) dependent assessments within continental areas, but independent assessments among continental areas, (3) dependent assessments within countries, but independent assessments among countries, and (4) independent assessments of all basins. Mean estimate remained the same in all four cases, but the width of interval estimate formed using the 95th and 5th fractiles decreased with reduced dependency in going from first to fourth case. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗