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USGS2023

HyWaves: Hybrid downscaling of multimodal wave spectra to nearshore areas

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

Ocean Modeling↗

USGS2010

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

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

Utah↗

USGS2018

A spatial approach to combatting wildlife crime

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

Conservation Biology↗

USGS2024

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

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

Laurentian Great Lakes↗

USGS1985

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

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

Nebraska↗

USGS2014

Hydraulic modeling development and application in water resources engineering

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

Book chapter↗

USGS2019

Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction

Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Annals of Applied Statistics↗

USGS1977

Chemical variability in the Lakeview Mountains pluton, southern California batholith: A comparison of the methods of correspondence analysis and extended Q-mode factor analysis

An extended method of Q -mode factor analysis that has been described previously offers a number of important advantages over conventional Q -mode factor analysis and correspondence analysis when applied to compositional data. Among these are the ability to compute the compositions, in the original units of the data, represented by the reference axes. The only special requirement of the data is that the values for each observation sum to a constant. Mathematically derived reference axes, such as the principal-components and varimax axes, commonly represent compositions that are partly negative. Even where no negative values are present, these compositions are comparatively difficult to interpret in petrologic terms and impossible or inappropriate to include in petrogenetic models. A model has been developed for the Lakeview Mountains pluton which employs vectors representing the compositions of melanocratic schlieren, leucocratic schlieren, and inclusions as the reference axes. When the effect of the inclusions is removed, the compositional zoning in the pluton is like that found in otherwise similar plutons in the Sierra Nevada batholith. The genetic implication of the model is that the inclusions were separated from the magma at least in its marginal parts. In the central part of the pluton, the inclusions were either separated to a lesser extent than in the marginal parts, or were reincorporated into the magma.

California↗

USGS2003

Modeling radium and radon transport through soil and vegetation

A one-dimensional flow and transport model was developed to describe the movement of two fluid phases, gas and water, within a porous medium and the transport of 226Ra and 222Rn within and between these two phases. Included in this model is the vegetative uptake of water and aqueous 226Ra and 222Rn that can be extracted from the soil via the transpiration stream. The mathematical model is formulated through a set of phase balance equations and a set of species balance equations. Mass exchange, sink terms and the dependence of physical properties upon phase composition couple the two sets of equations. Numerical solution of each set, with iteration between the sets, is carried out leading to a set-iterative compositional model. The Petrov-Galerkin finite element approach is used to allow for upstream weighting if required for a given simulation. Mass lumping improves solution convergence and stability behavior. The resulting numerical model was applied to four problems and was found to produce accurate, mass conservative solutions when compared to published experimental and numerical results and theoretical column experiments. Preliminary results suggest that the model can be used as an investigative tool to determine the feasibility of phytoremediating radium and radon-contaminated soil. ?? 2003 Elsevier Science B.V. All rights reserved.

Journal of Contaminant Hydrology↗

USGS2023

Geology and assessment of coal resources for the Cherokee coal bed in the Fort Union Formation, south-central Wyoming

The Cherokee coal bed is a locally thick and laterally continuous coal bed in the Overland Member of the Paleocene Fort Union Formation in south-central Wyoming. It represents a significant resource that is easily accessible and may be extractable through both surface and underground mining methods. A database of more than 600 data points, comprising coalbed methane wells, coal exploration drill holes, and measured sections, was compiled from a previously released geologic database and reinterpreted to provide a more detailed geologic model for the Cherokee coal bed. The thickest part of the Cherokee coal bed lies along the crest of the Wamsutter arch, an east-west trending anticlinal feature that separates the Great Divide subbasin to north from the Washakie subbasin to the south. The Cherokee coal bed consists of several laterally persistent benches separated by partings that range in thickness from one inch to greater than 100 feet. A series of detailed geologic cross sections through the study area show both the structural geology and the distribution and areal extent of the individual coal benches of the Cherokee coal bed. Data generated from the geologic model were used in stochastic geostatistical analyses to estimate the remaining or in-place coal resources. Certain parameters, as described later in the text, were applied to calculate available coal resources for surface and underground mining. This study is part of an ongoing process by the U.S. Geological Survey (USGS) to transition from a distance-based approach to a probabilistic approach for determining uncertainty in coal resource assessment. This probabilistic approach uses quantitative statistical methods to determine the potential range of uncertainty in coal resource estimates, whereas the distance-based approach does not provide any mathematical method to determine the range of uncertainty. Using stochastic geostatistical methods, utilizing 100 realizations or gridding iterations of the data, in-place resources were calculated, with a 90 percent probability, to be 15.261 ± 0.464 billion short tons (bst). Available coal resources tonnages were calculated using separate sets of criteria for surface and underground mining methods, based on probable mining parameters. Tonnage values were calculated based on estimated coal densities determined from available coal quality data. Available coal resources that meet the parameters for surface mining methods were calculated, with a 90 percent probability, to be 0.813 ± 0.038 bst. Available coal resources that meet the parameters for underground mining methods were calculated, with a 90 percent probability, to be 2.393 ± 0.055 bst. The calculations were based on estimates of the resources that meet the parameters for the optimum mining of the thickest coal benches of the Cherokee coal bed. This is depicted in a series of cross sections through the study area that show projected underground mining horizons in the Cherokee coal bed, based on the thickest combinations of individual coal benches.

Wyoming↗

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↗

USGS1988

Linear solvation energy relationships for toxicity of selected organic chemicals to Daphnia pulex and Daphnia magna

In the Laurentian Great Lakes, more than 300 contaminants have been identified in fish, other biota, water, and sediment. Current hazard assessment of these chemicals by the National Fisheries Research Center-Great Lakes is based on their toxicity, occurrence in the environment, and source. Although scientists at the Center have tested over 70 chemicals with the crustacean Daphnia pulex , the number of experimental data needed to screen the huge array of chemicals in the Great Lakes exceeds the practical capabilities of conducting bioassays. This limitation can be partly circumvented, however, by using mathematical models based on quantitative structure-activity relationships (QSAR) to provide rapid, inexpensive estimates of toxicity. Many properties of chemicals, including toxicity, bioaccumulation and water solubility are well correlated and can be predicted by equations of the generalized linear solvation energy relationships (LSER). The equation we used to model solute toxicity is Toxicity = constant + m VI/100 + s (π* + dδ) + b βm + a αm where VI = intrinsic (Van der Waals) molar volume; π* = molecular dipolarity/polarizability; δ = polarizability 'correction term'; βm = solute hydrogen bond acceptor basicity; and αm = solute hydrogen bond donor acidity. The subscript m designates solute monomer values for α and β. We applied the LSER model to 48-h acute toxicity data (measured as immobilization) for six classes of chemicals detected in Great Lakes fish. The following regression was obtained for Daphnia pulex (concentration = μM): log EC50 = 4.86 - 4.35 VI/100; N = 38, r2 = 0.867, sd = 0.403 We also used the LSER modeling approach to analyze to a large published data set of 24-h acute toxicity for Daphnia magna ; the following regression resulted, for eight classes of compounds (concentration = mM): log EC50 = 3.88 - 4.52 VI/100 - 1.62 π* + 1.66 βm - 0.916 αm; N = 62, r2 = 0.859, sd = 0.375 In addition we developed computer software that identifies chemical structures, estimates the LSER parameters, and predicts toxicity. The LSER models promise to be effective in differentiating between reactive and nonreactive toxicity behavior where other models have failed. Contaminants with reactive behavior are generally the most toxic and rank highest in hazard assessment of environmental chemicals.

Proceedings of the QSAR↗

USGS2023

Operationalizing crop model data assimilation for improved on-farm situational awareness

The ability of ‘digital agriculture’ to support on-farm decision making is predicated on the real-time combination of observations and prior knowledge into an integrated digital environment. The mathematical discipline that seeks to provide this integration is known as model data assimilation (DA), with demonstrated benefits including improved predictive reliability, and the capacity to identify unexpected changes in field conditions and potential measurement errors. Despite routine adoption in other fields, the delayed adoption of DA in agriculture is due to the need to express end-of-season outcomes such as yield, update forecasts of these outcomes throughout the growing season as data become available, and enhance forecast reliability. To overcome these challenges, three guiding principles are introduced, providing a means to operationalize crop model DA for robust on-farm decision support. We apply the guiding principles using a South Australian viticulture case study. Our case study involves application of an iterative form of a widely used DA algorithm (ensemble Kalman filter) to dynamically update both static parameters and states associated with a grapevine simulation model. Daily weather data as well as fortnightly ground-based leaf area index (LAI) data are used for assimilation. It is shown how crop model DA can lead to not only significant improvements in forecasts of LAI but also to forecasts of end-of-season yield. The guiding principles also enable observations of greatest value to be identified throughout the season. This study highlights the role that formal crop model DA can play in agricultural decision support through enhancing situational awareness in real time.

Agricultural and Forest Meteorology↗

USGS2023

Bridging the gap between mathematical biology and undergraduate education using applicable natural resource modeling

Mathematical biology is a wide field of study with many venues that undergraduate students can access through research. However, the topics of study for these students can be overwhelming, and many topics of study yield either only trivial results or abstract outcomes that are nonintuitive and diffcult to understand. We have used natural resource modeling, and more specifically, a partnership between academic researchers and federal scientists, as a bridge between undergraduate research and mathematical biology. Our collaboration is an interdisciplinary team that combines biology, mathematics, and statistics professors with government research scientists. As a team, we have mentored students through opportunities such as a Research Experiences for Undergraduates and other projects. In this article, we provide an overview of how we develop questions for undergraduates and outline two case studies, both of which resulted in peer reviewed journal articles. Last, we describe how we also transfer the results from these undergraduate projects to resource managers so the results may be applied to real world problems.

Letters in Biomathematics↗

USGS2021

Multilayer perceptrons (MLPs)

Artificial neural networks (ANNs) are adaptable systems that can solve problems that are difficult to describe with a mathematical relationship. They seek relationships between different types of datasets with their abilities to learn either with supervision or without. ANNs recognize patterns between input and output space and generalize solutions, in a way simulating the human brain’s learning experience with many relatively simple individual processing elements, called neurons. Neurons are networked (network topology) in a number of ways depending on the problem type and complexity. One of the most widely used ANN learning techniques is supervised learning coupled with a multilayer perceptron (MLP) topology due to its flexible applicability to a wide range of modeling problems involving both general classification and regression. ANNs, due to this flexibility, have been applied to many fields since the 1990s and their theory, types (such as radial basis functions, random...

Book chapter↗

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↗

USGS2011

Homogenization of large-scale movement models in ecology

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10–100 m) habitat variability on large scale (10–100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models.

Bulletin of Mathematical Biology↗

USGS1995

Adjusting stream-sediment geochemical maps in the Austrian Bohemian Massif by analysis of variance

The Austrian portion of the Bohemian Massif is a Precambrian terrane composed mostly of highly metamorphosed rocks intruded by a series of granitoids that are petrographically similar. Rocks are exposed poorly and the subtle variations in rock type are difficult to map in the field. A detailed geochemical survey of stream sediments in this region has been conducted and included as part of the Geochemischer Atlas der Republik O??sterreich, and the variations in stream sediment composition may help refine the geological interpretation. In an earlier study, multivariate analysis of variance (MANOVA) was applied to the stream-sediment data in order to minimize unwanted sampling variation and emphasize relationships between stream sediments and rock types in sample catchment areas. The estimated coefficients were used successfully to correct for the sampling effects throughout most of the region, but also introduced an overcorrection in some areas that seems to result from consistent but subtle differences in composition of specific rock types. By expanding the model to include an additional factor reflecting the presence of a major tectonic unit, the Rohrbach block, the overcorrection is removed. This iterative process simultaneously refines both the geochemical map by removing extraneous variation and the geological map by suggesting a more detailed classification of rock types. ?? 1995 International Association for Mathematical Geology.

Mathematical Geology↗