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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↗

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↗

USGS1989

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Open-File Report↗

USGS2007

Hydrologic response of the Crow Wing Watershed, Minnesota, to mid-Holocene climate change

In this study, we have integrated a suite of Holocene paleoclimatic proxies with mathematical modeling in an attempt to obtain a comprehensive picture of how watersheds respond to past climate change. A three-dimensional surface-water-groundwater model was developed to assess the effects of mid-Holocene climate change on water resources within the Crow Wing Watershed, Upper Mississippi Basin in north central Minnesota. The model was first calibrated to a 50 yr historical record of average annual surface-water discharge, monthly groundwater levels, and lake-level fluctuations. The model was able to reproduce reasonably well long-term historical records (1949-1999) of water-table and lake-level fluctuations across the watershed as well as stream discharge near the watershed outlet. The calibrated model was then used to reproduce paleogroundwater and lake levels using climate reconstructions based on pollen-transfer functions from Williams Lake just outside the watershed. Computed declines in mid-Holocene lake levels for two lakes at opposite ends of the watershed were between 6 and 18 m. Simulated streamflow near the outlet of the watershed decreased to 70% of modern average annual discharge after ???200 yr. The area covered by wetlands for the entire watershed was reduced by ???16%. The mid-Holocene hydrologic changes indicated by these model results and corroborated by several lake-core records across the Crow Wing Watershed may serve as a useful proxy of the hydrologic response to future warm, dry climatic forecasts (ca. 2050) made by some atmospheric general-circulation models for the glaciated Midwestern United States. ?? 2007 Geological Society of America.

Geological Society of America Bulletin↗

USGS2004

Ground-water and surface-water flow and estimated water budget for Lake Seminole, southwestern Georgia and northwestern Florida

Lake Seminole is a 37,600-acre impoundment formed at the confluence of the Flint and Chattahoochee Rivers along the Georgia?Florida State line. Outflow from Lake Seminole through Jim Woodruff Lock and Dam provides headwater to the Apalachicola River, which is a major supply of freshwater, nutrients, and detritus to ecosystems downstream. These rivers,together with their tributaries, are hydraulically connected to karst limestone units that constitute most of the Upper Floridan aquifer and to a chemically weathered residuum of undifferentiated overburden. The ground-water flow system near Lake Seminole consists of the Upper Floridan aquifer and undifferentiated overburden. The aquifer is confined below by low-permeability sediments of the Lisbon Formation and, generally, is semiconfined above by undifferentiated overburden. Ground-water flow within the Upper Floridan aquifer is unconfined or semiconfined and discharges at discrete points by springflow or diffuse leakage into streams and other surface-water bodies. The high degree of connectivity between the Upper Floridan aquifer and surface-water bodies is limited to the upper Eocene Ocala Limestone and younger units that are in contact with streams in the Lake Seminole area. The impoundment of Lake Seminole inundated natural stream channels and other low-lying areas near streams and raised the water-level altitude of the Upper Floridan aquifer near the lake to nearly that of the lake, about 77 feet. Surface-water inflow from the Chattahoochee and Flint Rivers and Spring Creek and outflow to the Apalachicola River through Jim Woodruff Lock and Dam dominate the water budget for Lake Seminole. About 81 percent of the total water-budget inflow consists of surface water; about 18 percent is ground water, and the remaining 1 percent is lake precipitation. Similarly, lake outflow consists of about 89 percent surface water, as flow to the Apalachicola River through Jim Woodruff Lock and Dam, about 4 percent ground water, and about 2 percent lake evaporation. Measurement error and uncertainty in flux calculations cause a flow imbalance of about 4 percent between inflow and outflow water-budget components. Most of this error can be attributed to errors in estimating ground-water discharge from the lake, which was calculated using a ground-water model calibrated to October 1986 conditions for the entire Apalachicola?Chattahoochee?Flint River Basin and not just the area around Lake Seminole. Evaporation rates were determined using the preferred, but mathematically complex, energy budget and five empirical equations: Priestley-Taylor, Penman, DeBruin-Keijman, Papadakis, and the Priestley-Taylor used by the Georgia Automated Environmental Monitoring Network. Empirical equations require a significant amount of data but are relatively easy to calculate and compare well to long-term average annual (April 2000?March 2001) pan evaporation, which is 65 inches. Calculated annual lake evaporation, for the study period, using the energy-budget method was 67.2 inches, which overestimated long-term average annual pan evaporation by 2.2 inches. The empirical equations did not compare well with the energy-budget method during the 18-month study period, with average differences in computed evaporation using each equation ranging from 8 to 26 percent. The empirical equations also compared poorly with long-term average annual pan evaporation, with average differences in evaporation ranging from 3 to 23 percent. Energy budget and long-term average annual pan evaporation estimates did compare well, with only a 3-percent difference between estimates. Monthly evaporation estimates using all methods ranged from 0.7 to 9.5 inches and were lowest during December 2000 and highest during May 2000. Although the energy budget is generally the preferred method, the dominance of surface water in the Lake Seminole water budget makes the method inaccurate and difficult to use, because surface water makes up m

Florida, Georgia↗

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↗

USGS1988

Multi-model approach to petroleum resource appraisal using analytic methodologies for probabilistic systems

The geologic appraisal model that is selected for a petroleum resource assessment depends upon purpose of the assessment, basic geologic assumptions of the area, type of available data, time available before deadlines, available human and financial resources, available computer facilities, and, most importantly, the available quantitative methodology with corresponding computer software and any new quantitative methodology that would have to be developed. Therefore, different resource assessment projects usually require different geologic models. Also, more than one geologic model might be needed in a single project for assessing different regions of the study or for cross-checking resource estimates of the area. Some geologic analyses used in the past for petroleum resource appraisal involved play analysis. The corresponding quantitative methodologies of these analyses usually consisted of Monte Carlo simulation techniques. A probabilistic system of petroleum resource appraisal for play analysis has been designed to meet the following requirements: (1) includes a variety of geologic models, (2) uses an analytic methodology instead of Monte Carlo simulation, (3) possesses the capacity to aggregate estimates from many areas that have been assessed by different geologic models, and (4) runs quickly on a microcomputer. Geologic models consist of four basic types: reservoir engineering, volumetric yield, field size, and direct assessment. Several case histories and present studies by the U.S. Geological Survey are discussed. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗

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↗

USGS2008

Dynamics of seismogenic volcanic extrusion resisted by a solid surface plug, Mount St. Helens, 2004-2005

The 2004-5 eruption of Mount St. Helens exhibited sustained, near-equilibrium behavior characterized by nearly steady extrusion of a solid dacite plug and nearly periodic occurrence of shallow earthquakes. Diverse data support the hypothesis that these earthquakes resulted from stick-slip motion along the margins of the plug as it was forced incrementally upward by ascending, solidifying, gas-poor magma. I formalize this hypothesis with a mathematical model derived by assuming that magma enters the base of the eruption conduit at a steady rate, invoking conservation of mass and momentum of the magma and plug, and postulating simple constitutive equations that describe magma and conduit compressibilities and friction along the plug margins. Reduction of the model equations reveals a strong mathematical analogy between the dynamics of the magma-plug system and those of a variably damped oscillator. Oscillations in extrusion velocity result from the interaction of plug inertia, a variable upward force due to magma pressure, and a downward force due to the plug weight. Damping of oscillations depends mostly on plug-boundary friction, and oscillations grow unstably if friction exhibits rate weakening similar to that observed in experiments. When growth of oscillations causes the extrusion rate to reach zero, however, gravity causes friction to reverse direction, and this reversal instigates a transition from unstable oscillations to self-regulating stick-slip cycles. The transition occurs irrespective of the details of rate-weakening behavior, and repetitive stick-slip cycles are, therefore, robust features of the system’s dynamics. The presence of a highly compressible elastic driving element (that is, magma containing bubbles) appears crucial for enabling seismogenic slip events to occur repeatedly at the shallow earthquake focal depths (<1 km) observed during the 2004-5 eruption. Computations show that fluctuations in magma pressure accompanying such slip events are <3 kPa, indicating that deviations from mechanical equilibrium are slight and that coseismic force drops are <10 8 N. These results imply that the system’s self-regulating behavior is not susceptible to dramatic change--provided that the rate of magma ascent remains similar to the rate of magma accretion at the base of the plug, that plug surface erosion more or less compensates for mass gain due to basal accretion, and that magma and rock properties do not change significantly. Even if disequilibrium initial conditions are imposed, the dynamics of the magma-plug system are strongly attracted to self-regulating stick-slip cycles, although this self-regulating behavior can be bypassed on the way to runaway behavior if the initial state is too far from equilibrium.

Washington↗

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↗

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↗

USGS2003

Simulation of unsteady flow and solute transport in a tidal river network

A mathematical model and numerical method for water flow and solute transport in a tidal river network is presented. The tidal river network is defined as a system of open channels of rivers with junctions and cross sections. As an example, the Pearl River in China is represented by a network of 104 channels, 62 nodes, and a total of 330 cross sections with 11 boundary section for one of the applications. The simulations are performed with a supercomputer for seven scenarios of water flow and/or solute transport in the Pearl River, China, with different hydrological and weather conditions. Comparisons with available data are shown. The intention of this study is to summarize previous works and to provide a useful tool for water environmental management in a tidal river network, particularly for the Pearl River, China.

Engineering Computations (Swansea, Wales)↗

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↗

USGS2014

A depth-averaged debris-flow model that includes the effects of evolving dilatancy: II. Numerical predictions and experimental tests.

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model’s five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure, and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here we recapitulate the equations and analyze their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout, and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses, and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

Proceedings of the Royal Society A↗

USGS1998

FEMFLOW3D; a finite-element program for the simulation of three-dimensional aquifers; version 1.0

This document describes a computer program that simulates three-dimensional ground- water systems using the finite-element method. The program was developed to simulate regional ground-water systems, but it can be applied to small-scale problems as well. This program can be used to simulate both confined and water-table aquifers. The program simulates a linearized three-dimensional free-surface ground-water system with a fixed grid. FEMFLOW3D is applicable to the simulation of various free-surface ground-water systems for which the change in aquifer thickness is small relative to the overall aquifer thickness. The finite-element method provides flexibility in the design of a geometric grid that represents the physical dimensions of an aquifer system. For example, features that can be well represented with a finite-element grid include irregular, random geographic and geologic features; irregular boundaries; and increased detail within localized areas of particular interest within the study area. The structure of the computer program consists of a main program, which serves as a simple driver, and a set of subroutines in which the calculations are performed. The background, mathematical basis, structure, and inputs for each of the subroutines are described in the document where applicable. Each subroutine generally handles (1) a part of the mathematical calculations related to the finite-element method, (2) a specific feature of the hydrologic system, or (3) special features related to the management input or output data. Hydrologic features that can be represented with the program include stream-aquifer interactions, phreatophytic evapotranspiration, highly permeable fault zones, land subsidence, and land-aquifer interactions associated with land-use activities. The program can also represent the primary features associated with complex irrigation systems, such as irrigated agriculture, and can calculate the ground-water recharge that results from these activities. Three boundary conditions, including specified-head boundaries, specified-flux boundaries, and variable-flux boundaries, can be represented with the program. The program also provides a method for identifying aquifer and river-bed parameters that can be used in the calibration of models. This document also includes model validation, source code, and example input and output files. Model validation was performed using four test problems. For each test problem, the results of a model simulation with FEMFLOW3D were compared with either an analytic solution or the results of an independent numerical approach. The source code, written in the ANSI x3.9-1978 FORTRAN standard, and the complete input and output of an example problem are listed in the appendixes.

Open-File Report↗

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↗

USGS2013

The age of scarplike landforms from diffusion-equation analysis

The purpose of this paper is to review developments in the quantitative modeling of fault-scarp geomorphology, principally those since 1980. These developments utilize diffusionequation mathematics, in several different forms, as the basic model of fault-scarp evolution. Because solutions to the general diffusion equation evolve with time, as we expect faultscarp morphology to evolve with time, the model solutions carry information about the age of the structure and thus its time of formation; hence the inclusion of this paper in this volume. The evolution of fault-scarp morphology holds a small but special place in the much larger class of problems in landform evolution. In general, landform evolution means the evolution of topography as a function of both space and time. It is the outcome of the competition among those tectonic processes that make topography, erosive processes that destroy topography, and depositional processes that redistribute topography. Deposition and erosion can always be coupled through conservation-of-mass relations, but in general deposition occurs at great distance from the source region of detritus. Moreover, erosion is an inherently rough process whereas deposition is inherently smooth, as is evident from even casual inspection of shaded-relief, digital-elevation maps (e.g., Thelin and Pike, 1990; Simpson and Anders, 1992) and the current fascination with fractal representations oferoding terrains (e.g., Huang and Turcotte, 1989; Newman and Turcotte, 1990). Nevertheless, large-scale landform-evolution modeling, now a computationally intensive, advanced numerical exercise, is generating ever more realistic landforms (e.g., Willgoose and others, 1991a,b; Kooi and Beaumont, 1994; Tucker and Slingerland, 1994), although many of the rate coefficients remain poorly prescribed

Book chapter↗

USGS2010

Approaches to highly parameterized inversion: A guide to using PEST for model-parameter and predictive-uncertainty analysis

Analysis of the uncertainty associated with parameters used by a numerical model, and with predictions that depend on those parameters, is fundamental to the use of modeling in support of decisionmaking. Unfortunately, predictive uncertainty analysis with regard to models can be very computationally demanding, due in part to complex constraints on parameters that arise from expert knowledge of system properties on the one hand (knowledge constraints) and from the necessity for the model parameters to assume values that allow the model to reproduce historical system behavior on the other hand (calibration constraints). Enforcement of knowledge and calibration constraints on parameters used by a model does not eliminate the uncertainty in those parameters. In fact, in many cases, enforcement of calibration constraints simply reduces the uncertainties associated with a number of broad-scale combinations of model parameters that collectively describe spatially averaged system properties. The uncertainties associated with other combinations of parameters, especially those that pertain to small-scale parameter heterogeneity, may not be reduced through the calibration process. To the extent that a prediction depends on system-property detail, its postcalibration variability may be reduced very little, if at all, by applying calibration constraints; knowledge constraints remain the only limits on the variability of predictions that depend on such detail. Regrettably, in many common modeling applications, these constraints are weak. Though the PEST software suite was initially developed as a tool for model calibration, recent developments have focused on the evaluation of model-parameter and predictive uncertainty. As a complement to functionality that it provides for highly parameterized inversion (calibration) by means of formal mathematical regularization techniques, the PEST suite provides utilities for linear and nonlinear error-variance and uncertainty analysis in these highly parameterized modeling contexts. Availability of these utilities is particularly important because, in many cases, a significant proportion of the uncertainty associated with model parameters-and the predictions that depend on them-arises from differences between the complex properties of the real world and the simplified representation of those properties that is expressed by the calibrated model. This report is intended to guide intermediate to advanced modelers in the use of capabilities available with the PEST suite of programs for evaluating model predictive error and uncertainty. A brief theoretical background is presented on sources of parameter and predictive uncertainty and on the means for evaluating this uncertainty. Applications of PEST tools are then discussed for overdetermined and underdetermined problems, both linear and nonlinear. PEST tools for calculating contributions to model predictive uncertainty, as well as optimization of data acquisition for reducing parameter and predictive uncertainty, are presented. The appendixes list the relevant PEST variables, files, and utilities required for the analyses described in the document.

Michigan↗