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At least 37 records · Page 2Linked to original sources
USGS2023

BatTool: Projecting bat populations facing multiple stressors using a demographic model

Bats provide ecologically and agriculturally important ecosystem services but are currently experiencing population declines caused by multiple environmental stressors, including mortality from white-nose syndrome and wind energy development. Analyses of the current and future health and viability of these species may support conservation management decision making. Demographic modeling provides a quantitative tool for decision makers and conservation managers to make more informed decisions, but widespread adoption of these tools can be limited because of the complexity of the mathematical, statistical, and computational components involved in implementing these models. In this work, we provide an exposition of the BatTool R package, detailing the primary components of the matrix projection model, a publicly accessible graphical user interface ( https://rconnect.usgs.gov/battool ) facilitating user-defined scenario analyses, and its intended uses and limitations (Wiens et al., US Geol Surv Data Release 2022; Wiens et al., US Geol Surv Softw Release 2022). We present a case study involving wind energy permitting, weighing the effects of potential mortality caused by a hypothetical wind energy facility on the projected abundance of four imperiled bat species in the Midwestern United States.

Methods in Ecology and Evolution↗
USGS2002

A bibliography of terrain modeling (geomorphometry), the quantitative representation of topography: Supplement 4.0

Terrain modeling, the practice of ground-surface quantification, is an amalgam of Earth science, mathematics, engineering, and computer science. The discipline is known variously as geomorphometry (or simply morphometry), terrain analysis, and quantitative geomorphology. It continues to grow through myriad applications to hydrology, geohazards mapping, tectonics, sea-floor and planetary exploration, and other fields. Dating nominally to the co-founders of academic geography, Alexander von Humboldt (1808, 1817) and Carl Ritter (1826, 1828), the field was revolutionized late in the 20th Century by the computer manipulation of spatial arrays of terrain heights, or digital elevation models (DEMs), which can quantify and portray ground-surface form over large areas (Maune, 2001). Morphometric procedures are implemented routinely by commercial geographic information systems (GIS) as well as specialized software (Harvey and Eash, 1996; Köthe and others, 1996; ESRI, 1997; Drzewiecki et al., 1999; Dikau and Saurer, 1999; Djokic and Maidment, 2000; Wilson and Gallant, 2000; Breuer, 2001; Guth, 2001; Eastman, 2002). The new Earth Surface edition of the Journal of Geophysical Research, specializing in surficial processes, is the latest of many publication venues for terrain modeling. This is the fourth update of a bibliography and introduction to terrain modeling (Pike, 1993, 1995, 1996, 1999) designed to collect the diverse, scattered literature on surface measurement as a resource for the research community. The use of DEMs in science and technology continues to accelerate and diversify (Pike, 2000a). New work appears so frequently that a sampling must suffice to represent the vast literature. This report adds 1636 entries to the 4374 in the four earlier publications1. Forty-eight additional entries correct dead Internet links and other errors found in the prior listings. Chronicling the history of terrain modeling, many entries in this report predate the 1999 supplement. Coverage is representative from about 1800 through early–mid 2002. Papers increasingly are published exclusively or in duplicate on the Internet's World Wide Web; the dates given here for Web addresses (URLs) that lack a print publication indicate a Web site's last update or my last access of it. The bibliography is arranged alphabetically and thus is not readily summarized. This introduction cites about 500 entries, a third of them grouped under 24 morphometric topics, as a guide to the listing's contents. Continuing the practice of previous bibliographies in the series to provide more information on a few applications (see summary of past topics in Pike, 2000a), this report elaborates further on topographic data, putative new parameters, tectonic geomorphology/neo-orometry, biogeography, ice-cap morphometry, results from the Mars Global DEM, landslide-hazard mapping, terrain modeling as physics, Hack's law, and broad-scale computer visualization. The literature of some of these subjects is large, and none of the summaries is intended to more than introduce the topic and comment on some of the current contributions of terrain modeling. Closing the essay is a discussion of pre-1900 papers that trace the evolution of ridge-line and watercourse quantification by descriptive geometry, as well as comments on some new books and an on-line bulletin board.

Open-File Report↗
USGS1968

Water-discharge determinations for the tidal reach of the Willamette River from Ross Island Bridge to Mile 10.3, Portland, Oregon

Water-discharge, velocity, and slope variations for a 3.7-mile-Iong tidal reach of the Willamette River at Portland, Oreg., were defined from discharge measurements and river stage data collected between July 1962 and January 1965. Observed water discharge during tide-affected flows, during floods, and during backwater from the Columbia River and recorded stages at each end of the river reach were used to determine water discharge from two mathematical models. These models use a finite-difference method to solve the equations of moderately unsteady open-channel streamflow, and discharges are computed by an electronic digital computer. Discharges computed by using the mathematical models compare satisfactorily with observed discharges, except during the period of backwater from the annual flood of the Columbia River. The flow resistance coefficients used in the models vary with discharge; for one model, the coefficients for discharges above 30,000 cfs (cubic feet per second) are 12 and 24 percent less than the coefficient used for discharges below 30,000 cfs. Daily mean discharges were determined by use of one mathematical model for approximately two-thirds of the water year, October 1963 through September 1964. Agreement of computed with routed daily mean discharges is fair; above 30,000 cfs, average differences between the two discharges are about 10 percent, and below 30,000 cfs, computed daily discharges are consistently greater (by as much as 25 percent) than routed discharges. The other model was used to compute discharges for the unusually high flood flows of December 1964.

Water Supply Paper↗
USGS2013

Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models

The conditional spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground-motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground-motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions, as well as the epistemic uncertainties in ground-motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western United States. The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the United States using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

Bulletin of the Seismological Society of America↗
USGS1988

A simple approach to nonlinear estimation of physical systems

Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared.

Mathematical and Computer Modelling↗
USGS2020

Carrying capacity of a population diffusing in a heterogeneous environment

The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction-diffusion equations describing populations in space. Analysis of reaction-diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space, conditions exist for which the total population size at equilibrium (i) exceeds the total population that which would occur in the absence of diffusion and (ii) exceeds that which would occur if the system were homogeneous and the total carrying capacity, computed as the integral over the local carrying capacities, was the same in the heterogeneous and homogeneous cases. We review here work over the past few years that has explained these apparently counter-intuitive results in terms of the way input of energy or another limiting resource (e.g., a nutrient) varies across the system. We report on both mathematical analysis and laboratory experiments confirming that total population size in a heterogeneous system with diffusion can exceed that in the system without diffusion. We further report, however, that when the resource of the population in question is explicitly modeled as a coupled variable, as in a reaction-diffusion chemostat model rather than a model with logistic growth, the total population in the heterogeneous system with diffusion cannot exceed the total population size in the corresponding homogeneous system in which the total carrying capacities are the same.

Mathematics and Computers in Modern Science - Acou↗
USGS2024

Bayesian approaches to proxy uncertainty quantification in paleoecology: A mathematical justification and practical integration

Paleoenvironmental data are essential for reconstructing environmental conditions in the distant past, and these reconstructions strongly depend on proxies and age–depth models. Proxies are indirect measurements that substitute for variables that cannot be directly measured, such as past precipitation. Conversely, an age–depth model is a tool that correlates the observed proxy with a specific moment in time. Bayesian age–depth modelling has proved to be a powerful method for estimating sediment ages and their associated uncertainties. However, there remains considerable potential for further integration into proxy analysis. In this paper, we explore a mathematical justification and a computational approach that integrates uncertainty at the age–depth level and propagates it to the proxy scale in the form of a posterior predictive distribution. This method mitigates potential biases and errors by removing the need to assign a single age to a given proxy measurement. It allows for quantifying the likelihood that proxy data values correspond to modelled ages, thus enabling the quantification of uncertainty in both the temporal and proxy value domains. The use of Bayesian statistics in proxy analysis represents a relatively recent advancement. We aim to mathematically justify incorporating the Markov chain Monte Carlo output from age–depth models into proxy analysis and to present a novel methodology for constructing environmental reconstructions using this approach.

Journal of Agricultural, Biological and Environmen↗
USGS2005

Parallel Fortran-MPI software for numerical inversion of the Laplace transform and its application to oscillatory water levels in groundwater environments

A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwater environment. The software is a parallel version of ACM (The Association for Computing Machinery) Transactions on Mathematical Software (TOMS) Algorithm 796. Running 38 test examples indicated that implementation of MPI techniques with distributed memory architecture speedups the processing and improves the efficiency. Applications to oscillatory water levels in a well during aquifer tests are presented to illustrate how this package can be applied to solve complicated environmental problems involved in differential and integral equations. The package is free and is easy to use for people with little or no previous experience in using MPI but who wish to get off to a quick start in parallel computing. ?? 2004 Elsevier Ltd. All rights reserved.

Environmental Modelling and Software↗
USGS1982

An electric-analog simulation of elliptic partial differential equations using finite element theory

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct.

Mathematics and Computers in Simulation↗
USGS1987

The space transformation in the simulation of multidimensional random fields

Space transformations are proposed as a mathematically meaningful and practically comprehensive approach to simulate multidimensional random fields. Within this context the turning bands method of simulation is reconsidered and improved in both the space and frequency domains.

Mathematics and Computers in Simulation↗
USGS1988

A multiple-objective optimal exploration strategy

Exploration for natural resources is accomplished through partial sampling of extensive domains. Such imperfect knowledge is subject to sampling error. Complex systems of equations resulting from modelling based on the theory of correlated random fields are reduced to simple analytical expressions providing global indices of estimation variance. The indices are utilized by multiple objective decision criteria to find the best sampling strategies. The approach is not limited by geometric nature of the sampling, covers a wide range in spatial continuity and leads to a step-by-step procedure.

Mathematical and Computer Modelling↗
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↗
USGS1997

Identification of internal flow dynamics in two experimental catchments

Identification of the internal flow dynamics in catchments is difficult because of the lack of information in precipitation -stream discharge time series alone. Two experimental catchments, Hydrohill and Nandadish, near Nanjing in China, have been set up to monitor internal flows reaching the catchment stream at various depths, from the surface runoff to the bedrock. With analysis of the precipitation against these internal discharges, it is possible to quantify the time constants and volumes associated with various flowpaths in both catchments.

Nanjing↗
USGS2005

A frictional population model of seismicity rate change

We study models of seismicity rate changes caused by the application of a static stress perturbation to a population of faults and discuss our results with respect to the model proposed by Dieterich (1994). These models assume distribution of nucleation sites (e.g., faults) obeying rate-state frictional relations that fail at constant rate under tectonic loading alone, and predicts a positive static stress step at time to will cause an immediate increased seismicity rate that decays according to Omori's law. We show one way in which the Dieterich model may be constructed from simple general idead, illustratted using numerically computed synthetic seismicity and mathematical formulation. We show that seismicity rate change predicted by these models (1) depend on the particular relationship between the clock-advanced failure and fault maturity, (2) are largest for the faults closest to failure at to, (3) depend strongly on which state evolution law faults obey, and (4) are insensitive to some types of population hetrogeneity. We also find that if individual faults fail repeatedly and populations are finite, at timescales much longer than typical aftershock durations, quiescence follows at seismicity rate increase regardless of the specific frictional relations. For the examined models the quiescence duration is comparable to the ratio of stress change to stressing rate ????/??,which occurs after a time comparable to the average recurrence interval of the individual faults in the population and repeats in the absence of any new load may pertubations; this simple model may partly explain observations of repeated clustering of earthquakes. Copyright 2005 by the American Geophysical Union.

Journal of Geophysical Research B: Solid Earth↗
USGS1998

Lake bed classification using acoustic data

As part of our effort to identify the lake bed surficial substrates using remote sensing data, this work designs pattern classifiers by multivariate statistical methods. Probability distribution of the preprocessed acoustic signal is analyzed first. A confidence region approach is then adopted to improve the design of the existing classifier. A technique for further isolation is proposed which minimizes the expected loss from misclassification. The devices constructed are applicable for real-time lake bed categorization. A mimimax approach is suggested to treat more general cases where the a priori probability distribution of the substrate types is unknown. Comparison of the suggested methods with the traditional likelihood ratio tests is discussed.

Applied Mathematics and Computer Science↗
USGS2020

The community code verification exercise for simulating sequences of earthquakes and aseismic slip (SEAS)

Numerical simulations of sequences of earthquakes and aseismic slip (SEAS) have made great progress over past decades to address important questions in earthquake physics. However, significant challenges in SEAS modeling remain in resolving multiscale interactions between earthquake nucleation, dynamic rupture, and aseismic slip, and understanding physical factors controlling observables such as seismicity and ground deformation. The increasing complexity of SEAS modeling calls for extensive efforts to verify codes and advance these simulations with rigor, reproducibility, and broadened impact. In 2018, we initiated a community code-verification exercise for SEAS simulations, supported by the Southern California Earthquake Center. Here, we report the findings from our first two benchmark problems (BP1 and BP2), designed to verify different computational methods in solving a mathematically well-defined, basic faulting problem. We consider a 2D antiplane problem, with a 1D planar vertical strike-slip fault obeying rate-and-state friction, embedded in a 2D homogeneous, linear elastic halfspace. Sequences of quasi-dynamic earthquakes with periodic occurrences (BP1) or bimodal sizes (BP2) and their interactions with aseismic slip are simulated. The comparison of results from 11 groups using different numerical methods show excellent agreements in long-term and coseismic fault behavior. In BP1, we found that truncated domain boundaries influence interseismic stressing, earthquake recurrence, and coseismic rupture, and that model agreement is only achieved with sufficiently large domain sizes. In BP2, we found that complexity of fault behavior depends on how well physical length scales related to spontaneous nucleation and rupture propagation are resolved. Poor numerical resolution can result in artificial complexity, impacting simulation results that are of potential interest for characterizing seismic hazard such as earthquake size distributions, moment release, and recurrence times. These results inform the development of more advanced SEAS models, contributing to our further understanding of earthquake system dynamics.

Seismological Research Letters↗