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At least 55 records · Page 3Linked to original sources
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↗
USGS1997

The role of mesocosm studies in ecological risk analysis

Mesocosms have been primarily used as research tools for the evaluation of the fate and effects of xenobiotic chemicals at the population, community, and ecosystem levels of biological organization. This paper provides suggestions for future applications of mesocosm research. Attention should be given to the configuration of mesocosm parameters to explicitly study regional questions of ecological interest. The initial physical, chemical, and biological conditions within mesocosms should be considered as factors shaping the final results of experiments. Certain fundamental questions such as the ecological inertia and resilience of systems with different initial ecological properties should be addressed. Researchers should develop closer working relationships with mathematical modelers in linking computer models to the outcomes of mesocosm studies. Mesocosm tests, linked with models, could enable managers and regulators to forecast the regional consequences of chemicals released into the environment.

Ecological Applications↗
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↗
USGS2003

Tag loss can bias Jolly-Seber capture-recapture estimates

We identified cases where the Jolly-Seber estimator of population size is biased under tag loss and tag-induced mortality by examining the mathematical arguments and performing computer simulations. We found that, except under certain tag-loss models and high sample sizes, the population size estimators (uncorrected for tag loss) are severely biased high when tag loss or tag-induced mortality occurs. Our findings verify that this misconception about effects of tag loss and tag-induced mortality could have serious consequences for field biologists interested in population size. Reiterating common sense, we encourage those engaged in capture-recapture studies to be careful and humane when handling animals during tagging, to use tags with high retention rates, to double-tag animals when possible, and to strive for the highest capture probabilities possible.

Wildlife Society Bulletin↗
USGS1977

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : Basic theory and the formulation of the numerical method

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Water-Resources Investigations Report↗
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↗
USGS2019

Analog experiments of lava flow emplacement

Laboratory experiments that simulate lava flows have been in use by volcanologists for many years. The behavior of flows in the lab, where “eruption” parameters, material properties, and environmental settings are tightly controlled, provides insight into the influence of various factors on flow evolution. A second benefit of laboratory lava flows is to provide a set of observations with which numerical models of flow emplacement can be tested. Models of lava flow emplacement vary in mathematical approach, physical assumptions, and computational cost. Nonetheless, all models require thorough testing and evaluation, and laboratory experiments produce an excellent test for models. This paper provides a primer on modern analog laboratory lava flow experiments. It reviews scaling con- siderations and provides quantitative information meant to guide future experimentalists in designing their experiments to be relevant to natural processes. Traditional and novel laboratory techniques are described, including a discussion of current limitations. New insights from recent experiments highlight the impact of topographic conditions and highlight the importance of considering bed roughness, major obstacles, and slope breaks. The influence of episodic or non-uniform effusion rate is demonstrated through recent experi- mental works. Lastly, the paper discusses several open questions about lava flow emplacement and the ways in which future improvements in experimental methods, such as the ability to utilize three-phase suspensions and materials with complex rheologies and to image the interior of flows could help answer these.

Annals of Geophysics↗
USGS2016

Simulating groundwater flow in karst aquifers with distributed parameter models—Comparison of porous-equivalent media and hybrid flow approaches

Understanding karst aquifers, for purposes of their management and protection, poses unique challenges. Karst aquifers are characterized by groundwater flow through conduits (tertiary porosity), and (or) layers with interconnected pores (secondary porosity) and through intergranular porosity (primary or matrix porosity). Since the late 1960s, advances have been made in the development of numerical computer codes and the use of mathematical model applications towards the understanding of dual (primary [matrix] and secondary [fractures and conduits]) porosity groundwater flow processes, as well as characterization and management of karst aquifers. The Floridan aquifer system (FAS) in Florida and parts of Alabama, Georgia, and South Carolina is composed of a thick sequence of predominantly carbonate rocks. Karst features are present over much of its area, especially in Florida where more than 30 first-magnitude springs occur, numerous sinkholes and submerged conduits have been mapped, and numerous circular lakes within sinkhole depressions are present. Different types of mathematical models have been applied for simulation of the FAS. Most of these models are distributed parameter models based on the assumption that, like a sponge, water flows through connected pores within the aquifer system and can be simulated with the same mathematical methods applied to flow through sand and gravel aquifers; these models are usually referred to as porous-equivalent media models. The partial differential equation solved for groundwater flow is the potential flow equation of fluid mechanics, which is used when flow is dominated by potential energy and has been applied for many fluid problems in which kinetic energy terms are dropped from the differential equation solved. In many groundwater model codes (basic MODFLOW), it is assumed that the water has a constant temperature and density and that flow is laminar, such that kinetic energy has minimal impact on flow. Some models have been developed that incorporate the submerged conduits as a one-dimensional pipe network within the aquifer rather than as discrete, extremely transmissive features in a porous-equivalent medium; these submerged conduit models are usually referred to as hybrid models and may include the capability to simulate both laminar and turbulent flow in the one-dimensional pipe network. Comparisons of the application of a porous-equivalent media model with and without turbulence (MODFLOW-Conduit Flow Process mode 2 and basic MODFLOW, respectively) and a hybrid (MODFLOW-Conduit Flow Process mode 1) model to the Woodville Karst Plain near Tallahassee, Florida, indicated that for annual, monthly, or seasonal average hydrologic conditions, all methods met calibration criteria (matched observed groundwater levels and average flows). Thus, the increased effort required, such as the collection of data on conduit location, to develop a hybrid model and its increased computational burden, is not necessary for simulation of average hydrologic conditions (non-laminar flow effects on simulated head and spring discharge were minimal). However, simulation of a large storm event in the Woodville Karst Plain with daily stress periods indicated that turbulence is important for matching daily springflow hydrographs. Thus, if matching streamflow hydrographs over a storm event is required, the simulation of non-laminar flow and the location of conduits are required. The main challenge in application of the methods and approaches for developing hybrid models relates to the difficulty of mapping conduit networks or having high-quality datasets to calibrate these models. Additionally, hybrid models have long simulation times, which can preclude the use of parameter estimation for calibration. Simulation of contaminant transport that does not account for preferential flow through conduits or extremely permeable zones in any approach is ill-advised. Simulation results in other karst aquifers or other parts of the FAS may differ from the comparison demonstrated herein.

Florida↗
USGS2015

Bayesian models: A statistical primer for ecologists

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management. Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more Deemphasizes computer coding in favor of basic principles Explains how to write out properly factored statistical expressions representing Bayesian models

Book↗
USGS2001

A simple calculator of ballistic trajectories for blocks ejected during volcanic eruptions

During the past century, numerous observers have described the violent ejection of large blocks and bombs from volcanoes during volcanic explosions. Minakami (1942) mapped the locations of blocks ejected from Asama Volcano during explosions in 1937. He developed a mathematical expression relating initial velocity and trajectory angle of ejected blocks to the ejection distance, taking into account air drag and assuming a constant drag coefficient. In the late 1950’s, Gorshkov (1959) estimated ejection velocities at Bezymianny volcano during its sector-collapse eruption. Wilson (1972) developed the first mathematical algorithm for ballistic trajectories in the volcanological literature (earlier ones had been available for military applications) that considered variations in drag coefficient with Reynolds number. Fagents and Wilson (1993) advanced the method of Wilson (1972) by considering the effect of reduced drag near the vent. From the 1970’s through the 1990’s other papers, too numerous to mention, have estimated volcanic ejection velocities from ballistic blocks. Since the early 1990’s there has been a decrease in the number of published papers that quantify ejection velocities from ballistic trajectories. This decrease has resulted in part from the appreciation that ejection velocities cannot be uniquely determined by ejection distance due to uncertainties in initial trajectory angle and drag force. On the other hand, the decrease in usage has coincided with an increase in the ease with which ballistic calculations can be made, due to the vast improvement in computer power and in the user-friendliness of computers. During the 1970’s, only volcanologists with mathematical acumen or those who could collaborate with applied mathematicians were able to make such estimates. With 21st century computer power, ballistic computation should be available to anyone as a back-of-the-envelope indicator of explosive power; the only factor preventing such usage is the lack of a user-friendly computer program. In this paper, I describe a program that can be used for quick ballistics calculations. The program, Eject!, was written in Microsoft Visual Basic® and operates on any personal computer running Microsoft® Windows 95 or later. Instructions on installing Eject! version 1.4 1. Copy the file "eject_1-4.zip" to the hard drive of your Windows-based computer 2. Unzip the files in "eject_1-4.zip" 3. Double-click on the file "setup.exe". This will install the software on your computer. 4. Once it is installed, go to the "start" button, the to "programs." You will see the program in your program list.

Open-File Report↗
USGS1987

Stochastic simulation of spatially correlated geo-processes

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.

Mathematical Geology↗
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↗
USGS1961

Simplified methods for computing total sediment discharge with the modified Einstein procedure

A procedure was presented in 1950 by H. A. Einstein for computing the total discharge of sediment particles of sizes that are in appreciable quantities in the stream bed. This procedure was modified by the U.S. Geological Survey and adapted to computing the total sediment discharge of a stream on the basis of samples of bed sediment, depth-integrated samples of suspended sediment, streamflow measurements, and water temperature. This paper gives simplified methods for computing total sediment discharge by the modified Einstein procedure. Each of four homographs appreciably simplifies a major step in the computations. Within the stated limitations, use of the homographs introduces much less error than is present in either the basic data or the theories on which the computations of total sediment discharge are based. The results are nearly as accurate mathematically as those that could be obtained from the longer and more complex arithmetic and algebraic computations of the Einstein procedure.

Water Supply Paper↗
USGS1987

Linear error analysis of slope-area discharge determinations

The slope-area method can be used to calculate peak flood discharges when current-meter measurements are not possible. This calculation depends on several quantities, such as water-surface fall, that are subject to large measurement errors. Other critical quantities, such as Manning's n , are not even amenable to direct measurement but can only be estimated. Finally, scour and fill may cause gross discrepancies between the observed condition of the channel and the hydraulic conditions during the flood peak. The effects of these potential errors on the accuracy of the computed discharge have been estimated by statistical error analysis using a Taylor-series approximation of the discharge formula and the well-known formula for the variance of a sum of correlated random variates. The resultant error variance of the computed discharge is a weighted sum of covariances of the various observational errors. The weights depend on the hydraulic and geometric configuration of the channel. The mathematical analysis confirms the rule of thumb that relative errors in computed discharge increase rapidly when velocity heads exceed the water-surface fall, when the flow field is expanding and when lateral velocity variation (alpha) is large. It also confirms the extreme importance of accurately assessing the presence of scour or fill.

Journal of Hydrology↗