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Results for “Journal of Applied Probability”

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

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At least 109 records · Page 6Linked to original sources
USGS1983

A reconnaissance geochemical study of La Primavera geothermal area, Jalisco, Mexico

The Sierra La Primavera, a late Pleistocene rhyolitic caldera complex in Jalisco, Me??xico, contains fumaroles and large-discharge 65??C hot springs that are associated with faults related to caldera collapse and to later magma insurgence. The nearly-neutral, sodium bicarbonate, hot springs occur at low elevations at the margins of the complex, whereas the water-rich fumaroles are high and central. The Comisio??n Federal de Electricidad de Me??xico (CFE) has recently drilled two deep holes at the center of the Sierra (PR-1 and Pr-2) and one deep hole at the western margin. Temperatures as high as 285??C were encountered at 1160 m in PR-1, which produced fluids with 820 to 865 mg/kg chloride after flashing to one atmosphere. Nearby, PR-2 encountered temperatures to 307??C at 2000 m and yielded fluids with chloride contents fluctuating between 1100 and 1560 mg/kg after flashing. Neither of the high-temperature wells produced steam in commercial quantities. The well at the western margin of the Sierra produced fluids similar to those from the hot springs. The temperature reached a maximum of 100??C near the surface and decreased to 80??C at 2000 m. Various geothermometers (quartz conductive, Na/K, Na-K-Ca, ??18O(SO4-H2O) and D/H (steam-water) all yield temperatures of 170 ?? 20??C when applied to the hot spring waters, suggesting that these spring waters flow from a large shallow reservoir at this temperature. Because the hot springs are much less saline than the fluids recovered in PR-1 and PR-2, the mixed fluid in the shallow reservoir can contain no more than 10-20% deep fluid. This requires that most of the heat is transferred by steam. There is probably a thin vapor-dominated zone in the central part of the Sierra, through which steam and gases are transferred to the overlying shallow reservoir. Fluids from this reservoir cool from ???170??C to 65??C by conduction during the 5-7 km of lateral flow to the hot springs. ?? 1983.

Journal of Volcanology and Geothermal Research↗
USGS2015

Mapping of coal quality using stochastic simulation and isometric logratio transformation with an application to a Texas lignite

Coal is a chemically complex commodity that often contains most of the natural elements in the periodic table. Coal constituents are conventionally grouped into four components (proximate analysis): fixed carbon, ash, inherent moisture, and volatile matter. These four parts, customarily measured as weight losses and expressed as percentages, share all properties and statistical challenges of compositional data. Consequently, adequate modeling should be done in terms of a logratio transformation, a requirement that is commonly overlooked by modelers. The transformation of choice is the isometric logratio transformation because of its geometrical and statistical advantages. The modeling is done through a series of realizations prepared by applying sequential simulation for the purpose of displaying the parts in maps incorporating uncertainty. The approach makes realistic assumptions and the results honor the data and basic considerations, such as percentages between 0 and 100, all four parts adding to 100% at any location in the study area, and a style of spatial fluctuation in the realizations equal to that of the data. The realizations are used to prepare different results, including probability distributions across a deposit, E-type maps displaying average properties, and probability maps summarizing joint fluctuations of several parts. Application of these maps to a lignite bed clearly delineates the deposit boundary, reveals a channel cutting across, and shows that the most favorable coal quality is to the north and deteriorates toward the southeast.

International Journal of Coal Geology↗
USGS2011

A Bayesian network to predict coastal vulnerability to sea level rise

Sea level rise during the 21st century will have a wide range of effects on coastal environments, human development, and infrastructure in coastal areas. The broad range of complex factors influencing coastal systems contributes to large uncertainties in predicting long-term sea level rise impacts. Here we explore and demonstrate the capabilities of a Bayesian network (BN) to predict long-term shoreline change associated with sea level rise and make quantitative assessments of prediction uncertainty. A BN is used to define relationships between driving forces, geologic constraints, and coastal response for the U.S. Atlantic coast that include observations of local rates of relative sea level rise, wave height, tide range, geomorphic classification, coastal slope, and shoreline change rate. The BN is used to make probabilistic predictions of shoreline retreat in response to different future sea level rise rates. Results demonstrate that the probability of shoreline retreat increases with higher rates of sea level rise. Where more specific information is included, the probability of shoreline change increases in a number of cases, indicating more confident predictions. A hindcast evaluation of the BN indicates that the network correctly predicts 71% of the cases. Evaluation of the results using Brier skill and log likelihood ratio scores indicates that the network provides shoreline change predictions that are better than the prior probability. Shoreline change outcomes indicating stability (-1 < rate < 1 m/yr) or erosion (rate < -1 m/yr) tend to occur for two sets of input scenarios. Stable shoreline change rates occur mainly for low rates of relative sea level rise and occur in low-vulnerability geomorphic settings. Rates indicating erosion result for cases where the rate of relative sea level rise is high and moderate-to-high vulnerability geomorphic settings occur. In contrast, accretion (rate > 1 m/yr) was not well predicted. We find that BNs can assimilate important factors contributing to coastal change in response to sea level rise and can make quantitative, probabilistic predictions that can be applied to coastal management decisions. Copyright ?? 2011 by the American Geophysical Union.

Journal of Geophysical Research F: Earth Surface↗
USGS2010

Predicting species distributions from checklist data using site-occupancy models

Aim: (1) To increase awareness of the challenges induced by imperfect detection, which is a fundamental issue in species distribution modelling; (2) to emphasize the value of replicate observations for species distribution modelling; and (3) to show how 'cheap' checklist data in faunal/floral databases may be used for the rigorous modelling of distributions by site-occupancy models. Location: Switzerland. Methods: We used checklist data collected by volunteers during 1999 and 2000 to analyse the distribution of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly in Switzerland. We used data from repeated visits to 1-ha pixels to derive 'detection histories' and apply site-occupancy models to estimate the 'true' species distribution, i.e. corrected for imperfect detection. We modelled blue hawker distribution as a function of elevation and year and its detection probability of elevation, year and season. Results: The best model contained cubic polynomial elevation effects for distribution and quadratic effects of elevation and season for detectability. We compared the site-occupancy model with a conventional distribution model based on a generalized linear model, which assumes perfect detectability (p = 1). The conventional distribution map looked very different from the distribution map obtained using site-occupancy models that accounted for the imperfect detection. The conventional model underestimated the species distribution by 60%, and the slope parameters of the occurrence-elevation relationship were also underestimated when assuming p = 1. Elevation was not only an important predictor of blue hawker occurrence, but also of the detection probability, with a bell-shaped relationship. Furthermore, detectability increased over the season. The average detection probability was estimated at only 0.19 per survey. Main conclusions: Conventional species distribution models do not model species distributions per se but rather the apparent distribution, i.e. an unknown proportion of species distributions. That unknown proportion is equivalent to detectability. Imperfect detection in conventional species distribution models yields underestimates of the extent of distributions and covariate effects that are biased towards zero. In addition, patterns in detectability will erroneously be ascribed to species distributions. In contrast, site-occupancy models applied to replicated detection/non-detection data offer a powerful framework for making inferences about species distributions corrected for imperfect detection. The use of 'cheap' checklist data greatly enhances the scope of applications of this useful class of models. ?? 2010 Blackwell Publishing Ltd.

Journal of Biogeography↗
USGS2007

Effect of compost age and composition on the atrazine removal from solution

Compost samples from two composting facilities, the Urbana (Illinois) Landscape Recycling Center (ULRC) and Illinois State University (ISU), were selected to examine the effect of compost age on atrazine removal from solution. The ULRC samples were made from yard waste without an additional nitrogen source. The ISU samples were made from yard waste or sawdust with the addition of manure. The 6-month-old ULRC compost had the greater capacity to remove atrazine from solution, which we attributed to its greater organic carbon content. The addition of nitrate into ULRC compost could influence the extent of atrazine removal, but did not have a significant impact on atrazine removal when applied to ISU compost, probably because manure was added to the yard waste to produce the compost. For both ULRC and ISU samples, the presence of sodium azide inhibited atrazine removal, suggesting that microbial activity contributed to the atrazine removal. Metabolic analysis demonstrated that hydroxyatrazine was the major identified metabolite that accumulated in solution before significant ring mineralization could occur. When compared with the ISU compost, the ULRC compost sample had a greater capacity to remove atrazine from solution during the 120 days of study because of the larger humic acid content. The experimental results suggested that less-mature compost may be better suited for environmental applications such as removing atrazine from tile-drainage waters. ?? 2006 Elsevier B.V. All rights reserved.

Journal of Hazardous Materials↗
USGS2016

Calorific value and compositional ultimate analysis with a case study of a Texas lignite

Measurements to determine coal quality as fuel include proximate analysis, ultimate analysis and calorific value. The latter is an attribute taking non-negative real values, so a simple transformation is sufficient for its spatial modeling applying geostatistics. The analyses, however, involve proportions that follow the properties of compositional data, thus requiring special preprocessing for an adequate modeling already described in a previous publication for the case of proximate analysis data. 1 Here we model the results of calorific value and ultimate analysis. We propose to use two different binary partitions, one per analysis, map the corresponding isometric logratio transformations, and backtransform the results. The methodology is illustrated using the same coal bed in the previous paper modeling proximate analysis data. Results are summarized using probability maps that, in the case of this deposit, show a prominent channel crossing the deposit and separating the best quality coal from that of lower quality.

International Journal of Coal Geology↗
USGS2022

Quantifying the relationship between prey density, livestock and illegal killing of leopards

Many large mammalian carnivores are facing population declines due to illegal killing (e.g., shooting) and habitat modification (e.g., livestock farming). Illegal killing occurs cryptically and hence is difficult to detect. However, reducing illegal killing requires a solid understanding of its magnitude and underlying drivers, while accounting for the imperfect detection of illegal killing events. Despite the importance of illegal killing of large carnivores in comparison with other causes of mortality, its relationship with potential drivers such as livestock density and wild prey abundance is rarely described. Using ranger-collected data (2007-2019) of leopard killing events and data on covariates (livestock density, wild prey abundance, road length, protected area size, elevation) across Iran, we applied a single-visit N-mixture model to jointly model variation in detection probability and expected annualized number of leopard killing events. Over the study period, we estimated 428 leopard mortalities (95% CI 184–1014), which was 45% larger than the observed number. Expected intensity of leopard killing was positively related to protected area size, livestock density and wild prey abundance. Detection of leopard killing was higher in areas with more developed road networks. Synthesis and applications: Ranger based monitoring data on poaching of carnivores are cost effective, but traditional analysis does not take into account imperfect detection. We show that innovative statistics (single-visit N-mixture modeling) can reliably quantify poaching events and address their drivers, at large geographical scales. We used the example of the Persian leopard across Iran, but our approach is also applicable to understand killing dynamics of other species. Results suggest that a high frequency of leopard killing is likely to occur in areas with > 100 livestock per km 2 and > 450 individuals of wild prey per km 2 . This highlights the need for improved management of livestock grazing and effective measures around high-risk protected areas to mitigate human-leopard conflict and reduce killing of leopards.

Journal of Applied Ecology↗
USGS2015

Toward a mechanistic understanding of human-induced rapid environmental change: A case study linking energy development, avian nest predation, and predators

Demographic consequences of human-induced rapid environmental change (HIREC) have been widely documented for many populations. The mechanisms underlying such patterns, however, are rarely investigated and yet are critical to understand for effective conservation and management. We investigated the mechanisms underlying reduced avian nest survival with intensification of natural gas development, an increasing source of human-induced rapid environmental change globally. We tested the hypothesis that energy development increased the local activity of important nest predator species, thereby elevating nest predation rates. During 2011&ndash;2012, we surveyed predators and monitored 668 nests of Brewer's sparrows Spizella breweri (BRSP), sagebrush sparrows Artemisiospiza nevadensis (SASPs) and sage thrashers Oreoscoptes montanus (SATHs) breeding at twelve sites spanning a gradient of habitat loss from energy development in western Wyoming, USA. Nine species, representing four mammalian and three avian families, were video-recorded depredating eggs and nestlings. Important nest predator species differed across songbird species, despite similar nesting habitats. Approximately 75% of depredation events were by rodents. Consistent with our predictions, detections of most rodent nest predators increased with surrounding habitat loss due to natural gas development, which was associated with increased probability of nest predation for our three focal bird species. An altered nest predator assemblage was therefore at least partly responsible for elevated avian nest predation risk in areas with more surrounding energy development. Synthesis and applications . We demonstrate one mechanism, that is the local augmentation of predators, by which human-induced rapid environmental change can influence the demography of local populations. Given the accelerating trajectory of global energy demands, an important next step will be to understand why the activity and/or abundance of rodent predators increased with surrounding habitat loss from energy development activities.

Journal of Applied Ecology↗
USGS2011

Discrete choice modeling of shovelnose sturgeon habitat selection in the Lower Missouri River

Substantive changes to physical habitat in the Lower Missouri River, resulting from intensive management, have been implicated in the decline of pallid ( Scaphirhynchus albus ) and shovelnose ( S. platorynchus ) sturgeon. To aid in habitat rehabilitation efforts, we evaluated habitat selection of gravid, female shovelnose sturgeon during the spawning season in two sections (lower and upper) of the Lower Missouri River in 2005 and in the upper section in 2007. We fit discrete choice models within an information theoretic framework to identify selection of means and variability in three components of physical habitat. Characterizing habitat within divisions around fish better explained selection than habitat values at the fish locations. In general, female shovelnose sturgeon were negatively associated with mean velocity between them and the bank and positively associated with variability in surrounding depths. For example, in the upper section in 2005, a 0.5 m s −1 decrease in velocity within 10 m in the bank direction increased the relative probability of selection 70%. In the upper section fish also selected sites with surrounding structure in depth (e.g., change in relief). Differences in models between sections and years, which are reinforced by validation rates, suggest that changes in habitat due to geomorphology, hydrology, and their interactions over time need to be addressed when evaluating habitat selection. Because of the importance of variability in surrounding depths, these results support an emphasis on restoring channel complexity as an objective of habitat restoration for shovelnose sturgeon in the Lower Missouri River.

Kansas, Missouri, Nebraska, South Dakota↗
USGS2023

Territories within groups: The dynamic competition of drift-feeding juvenile Chinook salmon in 3-dimensional space

Salmonid populations are often regulated by territorial competition among juveniles for food and space. In the canonical view, salmonid territories are spaced horizontally across the river bottom in a 2-D mosaic. However, some juveniles instead feed in tight, three-dimensional (3-D) social groups. To investigate whether territoriality is possible within such groups, we applied a new concept—the momentary home range—to quantify the size, exclusivity, and temporal dynamics of 3-D space use by juvenile Chinook Salmon ( Oncorhynchus tshawytscha ) in the Chena River, Alaska. Individual strategies spanned a broad continuum of exclusivity and stationarity. However, some of the largest, most dominant fish in each group aggressively defended stationary, exclusive feeding spaces and thus were unambiguously territorial. Transient floaters entered and left the group quickly. A majority of fish were not aggressive but nevertheless occupied exclusive, stationary spaces that probably function as territories with regard to resource distribution and population regulation. The presence of territoriality within social groups, in a 3-D configuration, expands the known domain of this important behavior.

Alaska↗
USGS2002

Comparison of mitochondrial DNA control region sequence and microsatellite DNA analyses in estimating population structure and gene flow rates in Atlantic sturgeon Acipenser oxyrinchus

Atlantic sturgeon Acipenser oxyrinchus is large, long-lived, and anadromous with subspecies distributed along the Atlantic (A. oxyrinchus oxyrinchus) and Gulf of Mexico (A. o. desotoi) coasts of North America. Although it is not certain if extirpation of some population units has occurred, because of anthropogenic influences abundances of all populations are low compared with historical levels. Informed management of A. oxyrinchus demands a detailed knowledge of its population structure, levels of genetic diversity, and likelihood to home to natal rivers. We compared the use of mitochondrial DNA (mtDNA) control region sequence and microsatellite nuclear DNA (nDNA) analyses in identifying the stock structure and homing fidelity of Atlantic and Gulf coast populations of A. oxyrinchus. The approaches were concordant in that they revealed moderate to high levels of genetic diversity and suggested that populations of Atlantic sturgeon are highly structured. At least six genetically distinct management units were detected using the two approaches among the rivers surveyed. Mitochondrial DNA sequences revealed a significant cline in haplotype diversity along the Atlantic coast with monomorphism observed in Canadian populations. High levels of nDNA diversity were also observed among populations along the Atlantic coast, including the two Canadian populations, probably resulting from the more rapid rate of mutational and evolutionary change at microsatellite loci. Estimates of gene flow among populations were similar between both approaches with the exception that because of mtDNA monomorphism in Canadian populations, gene flow estimates between them were unobtainable. Analyses of both genomes provided high resolution and confidence in characterizing the population structure of Atlantic sturgeon. Microsatellite analysis was particularly informative in delineating population structure in rivers that were recently glaciated and may prove diagnostic in rivers that are geographically proximal along the south Atlantic coast of the US.

Journal of Applied Ichthyology↗
USGS1985

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

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

Journal of the International Association for Mathe↗
USGS2025

An approach to modeling abundance of marine wildlife over space and time using unstructured aerial surveys

Estimating spatial and temporal patterns in abundance is often a goal of ecological studies and can be useful for informing management decisions, such as determining the optimal placement of wildlife protection zones. However, estimating abundance can be difficult in practice, especially over large areas, because of imperfect detection, where individuals are present but not detected because of either availability or observer error. Several methods for estimating abundance that account for imperfect detection exist but can be logistically challenging to implement. We present a simpler approach to some of the more commonly used techniques for estimating the abundance of marine wildlife over space and time from unstructured aerial surveys. This approach combines a spatial model for count data with auxiliary information on detection probability obtained from small-scale or previous studies. We employ generalized linear models and generalized additive models with spatial habitat covariates to illustrate this approach using maximum-likelihood with free, open-source statistical software. This framework is intended to be accessible and flexible, requiring lower survey costs and less computation time than other alternatives for estimating abundance. Indeed, our simulation results show that this approach can reduce computation times, while appropriately characterizing uncertainty, compared to a Bayesian approach. We also present R code for our approach using an example of estimating Florida manatee ( Trichechus manatus latirostris ) abundance in Indian River County in Florida, USA. This approach could be applied to other study systems and marine wildlife species using unstructured aerial surveys.

Florida↗
USGS2021

Behavioral responses of sea lamprey (Petromyzon marinus) and white sucker (Catostomus commersonii) to turbulent flow during fishway passage attempts

An understanding of how undesirable and desirable fish species respond behaviorally to turbulent flow in fishways would guide development of selective fish passage techniques. We applied high-resolution computational fluid dynamics modeling and competing risks analysis towards the development of predictive selective passage models. Sea lamprey ( Petromyzon marinus ; an invasive fish in the Great Lakes Basin, North America) upstream passage probability declined from 0.73 to 0.03 as flow conditions became increasingly turbulent, while declines in white sucker ( Catostomus commersonii , a native fish in the region) upstream passage probability were less substantial (0.53 to 0.44). Deploying a sea lamprey trap in the fishway did not effectively reduce sea lamprey upstream passage probability, though capture rate increased during trials with cooler water temperature and low total kinetic energy. Bifurcated fishways that maintain low turbulent flow in the entrapment route and high turbulent flow in the upstream passage route could increase the effectiveness of trapping sea lamprey in fishways as a means to advance selective passage goals.

Wisconsin↗
USGS2007

Transport of diazinon in the San Joaquin River Basin, California

ABSTRACT: Most of the application of the organophosphate insecticide diazinon in the San Joaquin River Basin occurs in winter to control wood-boring insects in dormant almond orchards. A federalstate collaborative study found that diazinon accounted for most of the observed toxicity of San Joaquin River water in February 1993. Previous studies focused mainly on west-side inputs to the San Joaquin River. In this 1994 study, the three major east-side tributaries to the San Joaquin River - the Merced, Tuolumne, and Stanislaus rivers - and a downstream site on the San Joaquin River were sampled throughout the hydrographs of a late January and an early February storm. In both storms, the Tuolumne River had the highest concentrations of diazinon and transported the largest load of the three tributaries. The Stanislaus River was a small source in both storms. On the basis of previous storm sampling and estimated travel times, ephemeral west-side creeks probably were the main diazinon source early in the storms, whereas the Tuolumne and Merced rivers and east-side drainages directly to the San Joaquin River were the main sources later. Although 74 percent of diazinon transport in the San Joaquin River during 1991–1993 occurred in January and February, transport during each of the two 1994 storms was only 0.05 percent of the amount applied during preceding dry periods. Nevertheless, some of the diazinon concentrations in the San Joaquin River during the January storm exceeded 0.35 μ/L, a concentration shown to be acutely toxic to water fleas. On the basis of this study and previous studies, diazinon concentrations and streamflow are highly variable during January and February storms, and frequent sampling is required to evaluate transport in the San Joaquin River Basin.

Journal of the American Water Resources Associatio↗
USGS1992

Pesticides in Iowa precipitation

Rainfall was sampled for pesticides to assess their occurrence in precipitation and potential impacts on water resources. Three areas in Iowa were sampled; two localities were in rural settings, and a third in an urban area. Fourteen pesticides, including ten herbicides and four insecticides, were detected from October 1987 through September 1990. Atrazine, alachlor, cyanazine, and metolachlor were the most commonly detected, with one or more of these four herbicides found in almost every rainfall sample during the growing season. Concentrations of individual pesticides ranged from 0.1 µg L −1 to 40.0 µg L −1 , with most detections under 1.0 µg L −1 . Pesticide detections in rainfall began in April and ended in July or August, probably related to the timing of chemical application and greater volatilization rates during warmer weather. Samples from the urban site had detections of the same agricultural chemicals found at the rural sites, but in lesser quantities. In addition to the commonly detected herbicides, three of the four insecticides detected in rainfall were only found in urban samples. Two of these have urban as well as agricultural uses. Some variation of pesticide detections were seen at the three sampling localities, related to regional and local use patterns. Concentrations were greater at sampling sites near fields where pesticides are applied, suggesting that local volatilization and distance of transport affect the concentrations in rainfall. Pesticide concentrations were highest at the beginning of a rainfall event with concentrations becoming lower in samples taken later in the event.

Journal of Environmental Quality↗
USGS2009

Patterns and determinants of mammal species occurrence in India

Many Indian mammals face range contraction and extinction, but assessments of their population status are hindered by the lack of reliable distribution data and range maps. 2. We estimated the current geographical ranges of 20 species of large mammals by applying occupancy models to data from country-wide expert. We modelled species in relation to ecological and social covariates (protected areas, landscape characteristics and human influences) based on a priori hypotheses about plausible determinants of mammalian distribution patterns. 3. We demonstrated that failure to incorporate detection probability in distribution survey methods underestimated habitat occupancy for all species. 4. Protected areas were important for the distribution of 16 species. However, for many species much of their current range remains unprotected. The availability of evergreen forests was important for the occurrence of 14 species, temperate forests for six species, deciduous forests for 15 species and higher altitude habitats for two species. Low human population density was critical for the occurrence of five species, while culturally based tolerance was important for the occurrence of nine other species. 5. Rhino Rhinoceros unicornis, gaur Bos gaurus and elephant Elephas maximus showed the most restricted ranges among herbivores, and sun bear Helarctos malayanus, brown bear Ursus arctos and tiger Panthera tigris were most restricted among carnivores. While cultural tolerance has helped the survival of some mammals, legal protection has been critically associated with occurrence of most species. 6. Synthesis and applications. Extent of range is an important determinant of species conservation status. Understanding the relationship of species occurrence with ecological and socio-cultural covariates is important for identification and management of key conservation areas. The combination of occupancy models with field data from country-wide experts enables reliable estimation of species range and habitat associations for conservation at regional scales. ?? 2009 British Ecological Society.

Journal of Applied Ecology↗
USGS2007

Calculation of nonlinear confidence and prediction intervals for ground-water flow models

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

Journal of the American Water Resources Associatio↗