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At least 55 records · Page 3Linked to original sources
USGS2013

Watershed Regressions for Pesticides (WARP) models for predicting stream concentrations of multiple pesticides

Watershed Regressions for Pesticides for multiple pesticides (WARP-MP) are statistical models developed to predict concentration statistics for a wide range of pesticides in unmonitored streams. The WARP-MP models use the national atrazine WARP models in conjunction with an adjustment factor for each additional pesticide. The WARP-MP models perform best for pesticides with application timing and methods similar to those used with atrazine. For other pesticides, WARP-MP models tend to overpredict concentration statistics for the model development sites. For WARP and WARP-MP, the less-than-ideal sampling frequency for the model development sites leads to underestimation of the shorter-duration concentration; hence, the WARP models tend to underpredict 4- and 21-d maximum moving-average concentrations, with median errors ranging from 9 to 38% As a result of this sampling bias, pesticides that performed well with the model development sites are expected to have predictions that are biased low for these shorter-duration concentration statistics. The overprediction by WARP-MP apparent for some of the pesticides is variably offset by underestimation of the model development concentration statistics. Of the 112 pesticides used in the WARP-MP application to stream segments nationwide, 25 were predicted to have concentration statistics with a 50% or greater probability of exceeding one or more aquatic life benchmarks in one or more stream segments. Geographically, many of the modeled streams in the Corn Belt Region were predicted to have one or more pesticides that exceeded an aquatic life benchmark during 2009, indicating the potential vulnerability of streams in this region.

Journal of Environmental Quality↗
USGS2007

Statistical analysis of water-quality data containing multiple detection limits II: S-language software for nonparametric distribution modeling and hypothesis testing

Analysis of low concentrations of trace contaminants in environmental media often results in left-censored data that are below some limit of analytical precision. Interpretation of values becomes complicated when there are multiple detection limits in the data-perhaps as a result of changing analytical precision over time. Parametric and semi-parametric methods, such as maximum likelihood estimation and robust regression on order statistics, can be employed to model distributions of multiply censored data and provide estimates of summary statistics. However, these methods are based on assumptions about the underlying distribution of data. Nonparametric methods provide an alternative that does not require such assumptions. A standard nonparametric method for estimating summary statistics of multiply-censored data is the Kaplan-Meier (K-M) method. This method has seen widespread usage in the medical sciences within a general framework termed "survival analysis" where it is employed with right-censored time-to-failure data. However, K-M methods are equally valid for the left-censored data common in the geosciences. Our S-language software provides an analytical framework based on K-M methods that is tailored to the needs of the earth and environmental sciences community. This includes routines for the generation of empirical cumulative distribution functions, prediction or exceedance probabilities, and related confidence limits computation. Additionally, our software contains K-M-based routines for nonparametric hypothesis testing among an unlimited number of grouping variables. A primary characteristic of K-M methods is that they do not perform extrapolation and interpolation. Thus, these routines cannot be used to model statistics beyond the observed data range or when linear interpolation is desired. For such applications, the aforementioned parametric and semi-parametric methods must be used.

Computers & Geosciences↗
USGS2014

Methods for estimating the magnitude and frequency of floods for urban and small, rural streams in Georgia, South Carolina, and North Carolina, 2011

Reliable estimates of the magnitude and frequency of floods are essential for the design of transportation and water-conveyance structures, flood-insurance studies, and flood-plain management. Such estimates are particularly important in densely populated urban areas. In order to increase the number of streamflow-gaging stations (streamgages) available for analysis, expand the geographical coverage that would allow for application of regional regression equations across State boundaries, and build on a previous flood-frequency investigation of rural U.S Geological Survey streamgages in the Southeast United States, a multistate approach was used to update methods for determining the magnitude and frequency of floods in urban and small, rural streams that are not substantially affected by regulation or tidal fluctuations in Georgia, South Carolina, and North Carolina. The at-site flood-frequency analysis of annual peak-flow data for urban and small, rural streams (through September 30, 2011) included 116 urban streamgages and 32 small, rural streamgages, defined in this report as basins draining less than 1 square mile. The regional regression analysis included annual peak-flow data from an additional 338 rural streamgages previously included in U.S. Geological Survey flood-frequency reports and 2 additional rural streamgages in North Carolina that were not included in the previous Southeast rural flood-frequency investigation for a total of 488 streamgages included in the urban and small, rural regression analysis. The at-site flood-frequency analyses for the urban and small, rural streamgages included the expected moments algorithm, which is a modification of the Bulletin 17B log-Pearson type III method for fitting the statistical distribution to the logarithms of the annual peak flows. Where applicable, the flood-frequency analysis also included low-outlier and historic information. Additionally, the application of a generalized Grubbs-Becks test allowed for the detection of multiple potentially influential low outliers. Streamgage basin characteristics were determined using geographical information system techniques. Initial ordinary least squares regression simulations reduced the number of basin characteristics on the basis of such factors as statistical significance, coefficient of determination, Mallow’s Cp statistic, and ease of measurement of the explanatory variable. Application of generalized least squares regression techniques produced final predictive (regression) equations for estimating the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability flows for urban and small, rural ungaged basins for three hydrologic regions (HR1, Piedmont–Ridge and Valley; HR3, Sand Hills; and HR4, Coastal Plain), which previously had been defined from exploratory regression analysis in the Southeast rural flood-frequency investigation. Because of the limited availability of urban streamgages in the Coastal Plain of Georgia, South Carolina, and North Carolina, additional urban streamgages in Florida and New Jersey were used in the regression analysis for this region. Including the urban streamgages in New Jersey allowed for the expansion of the applicability of the predictive equations in the Coastal Plain from 3.5 to 53.5 square miles. Average standard error of prediction for the predictive equations, which is a measure of the average accuracy of the regression equations when predicting flood estimates for ungaged sites, range from 25.0 percent for the 10-percent annual exceedance probability regression equation for the Piedmont–Ridge and Valley region to 73.3 percent for the 0.2-percent annual exceedance probability regression equation for the Sand Hills region.

Georgia, North Carolina, South Carolina↗
USGS2013

Comparison between two statistically based methods, and two physically based models developed to compute daily mean streamflow at ungaged locations in the Cedar River Basin, Iowa

A variety of individuals from water resource managers to recreational users need streamflow information for planning and decisionmaking at locations where there are no streamgages. To address this problem, two statistically based methods, the Flow Duration Curve Transfer method and the Flow Anywhere method, were developed for statewide application and the two physically based models, the Precipitation Runoff Modeling-System and the Soil and Water Assessment Tool, were only developed for application for the Cedar River Basin. Observed and estimated streamflows for the two methods and models were compared for goodness of fit at 13 streamgages modeled in the Cedar River Basin by using the Nash-Sutcliffe and the percent-bias efficiency values. Based on median and mean Nash-Sutcliffe values for the 13 streamgages the Precipitation Runoff Modeling-System and Soil and Water Assessment Tool models appear to have performed similarly and better than Flow Duration Curve Transfer and Flow Anywhere methods. Based on median and mean percent bias values, the Soil and Water Assessment Tool model appears to have generally overestimated daily mean streamflows, whereas the Precipitation Runoff Modeling-System model and statistical methods appear to have underestimated daily mean streamflows. The Flow Duration Curve Transfer method produced the lowest median and mean percent bias values and appears to perform better than the other models.

Iowa↗
USGS2005

Estimating the number of animals in wildlife populations

INTRODUCTION In 1938, Howard M. Wight devoted 9 pages, which was an entire chapter in the first wildlife management techniques manual, to what he termed 'census' methods. As books and chapters such as this attest, the volume of literature on this subject has grown tremendously. Abundance estimation remains an active area of biometrical research, as reflected in the many differences between this chapter and the similar contribution in the previous manual. Our intent in this chapter is to present an overview of the basic and most widely used population estimation techniques and to provide an entree to the relevant literature. Several possible approaches could be taken in writing a chapter dealing with population estimation. For example, we could provide a detailed treatment focusing on statistical models and on derivation of estimators based on these models. Although a chapter using this approach might provide a valuable reference for quantitative biologists and biometricians, it would be of limited use to many field biologists and wildlife managers. Another approach would be to focus on details of actually applying different population estimation techniques. This approach would include both field application (e.g., how to set out a trapping grid or conduct an aerial survey) and detailed instructions on how to use the resulting data with appropriate estimation equations. We are reluctant to attempt such an approach, however, because of the tremendous diversity of real-world field situations defined by factors such as the animal being studied, habitat, available resources, and because of our resultant inability to provide detailed instructions for all possible cases. We believe it is more useful to provide the reader with the conceptual basis underlying estimation methods. Thus, we have tried to provide intuitive explanations for how basic methods work. In doing so, we present relevant estimation equations for many methods and provide citations of more detailed treatments covering both statistical considerations and field applications. We have chosen to present methods that are representative of classes of estimators, rather than address every available method. Our hope is that this chapter will provide the reader with enough background to make an informed decision about what general method(s) will likely perform well in any particular field situation. Readers with a more quantitative background may then be able to consult detailed references and tailor the selected method to suit their particular needs. Less quantitative readers should consult a biometrician, preferably one with experience in wildlife studies, for this 'tailoring,' with the hope they will be able to do so with a basic understanding of the general method, thereby permitting useful interaction and discussion with the biometrician. SUMMARY Estimating the abundance or density of animals in wild populations is not a trivial matter. Virtually all techniques involve the basic problem of estimating the probability of seeing, capturing, or otherwise detecting animals during some type of survey and, in many cases, sampling concerns as well. In the case of indices, the detection probability is assumed to be constant (but unknown). We caution against use of indices unless this assumption can be verified for the comparison(s) of interest. In the case of population estimation, many methods have been developed over the years to estimate the probability of detection associated with various kinds of count statistics. Techniques range from complete counts, where sampling concerns often dominate, to incomplete counts where detection probabilities are also important. Some examples of the latter are multiple observers, removal methods, and capture-recapture. Before embarking on a survey to estimate the size of a population, one must understand clearly what information is needed and for what purpose the information will be used. The key to derivin

Book chapter↗
USGS2023

Seismic hazard assessment for areas of volcanic activity in western Kingdom of Saudi Arabia

Earthquake swarms caused by volcanic activity, tectonic stresses, or industrial operations (oil and gas production) can pose considerable risk for nearby settlements. As a rule, a probabilistic seismic hazard assessment (PSHA) that is based on time-independent earthquakes does not take into account earthquake swarms because of their statistically time-dependent nature. We describe the technique and application of a scenario-based method for the estimation of seismic hazard from earthquake swarms that may occur in areas of volcanic activity in western Saudi Arabia. The method consists of the generation of a large number of scenario seismic swarms followed by the calculation of ground motion in a site of interest for all earthquakes in all of the swarms. The set of calculated ground-motion values permits the construction and analysis of probability distribution functions for possible ground-motion levels during the hypothetical earthquake swarms. The level of ground motion representing the hazard is selected considering an appropriate value of the probability of exceedance or non-exceedance, depending on the goal of the study. This swarm-scenario-based seismic hazard assessment may provide a valuable supplement to an ordinary PSHA and (or) deterministic seismic hazard assessment that are commonly used for emergency response and post-earthquake recovery management.

Professional Paper↗
USGS2009

Incorporating uncertainty into the ranking of SPARROW model nutrient yields from Mississippi/Atchafalaya River basin watersheds

Excessive loads of nutrients transported by tributary rivers have been linked to hypoxia in the Gulf of Mexico. Management efforts to reduce the hypoxic zone in the Gulf of Mexico and improve the water quality of rivers and streams could benefit from targeting nutrient reductions toward watersheds with the highest nutrient yields delivered to sensitive downstream waters. One challenge is that most conventional watershed modeling approaches (e.g., mechanistic models) used in these management decisions do not consider uncertainties in the predictions of nutrient yields and their downstream delivery. The increasing use of parameter estimation procedures to statistically estimate model coefficients, however, allows uncertainties in these predictions to be reliably estimated. Here, we use a robust bootstrapping procedure applied to the results of a previous application of the hybrid statistical/mechanistic watershed model SPARROW (Spatially Referenced Regression On Watershed attributes) to develop a statistically reliable method for identifying “high priority” areas for management, based on a probabilistic ranking of delivered nutrient yields from watersheds throughout a basin. The method is designed to be used by managers to prioritize watersheds where additional stream monitoring and evaluations of nutrient-reduction strategies could be undertaken. Our ranking procedure incorporates information on the confidence intervals of model predictions and the corresponding watershed rankings of the delivered nutrient yields. From this quantified uncertainty, we estimate the probability that individual watersheds are among a collection of watersheds that have the highest delivered nutrient yields. We illustrate the application of the procedure to 818 eight-digit Hydrologic Unit Code watersheds in the Mississippi/Atchafalaya River basin by identifying 150 watersheds having the highest delivered nutrient yields to the Gulf of Mexico. Highest delivered yields were from watersheds in the Central Mississippi, Ohio, and Lower Mississippi River basins. With 90% confidence, only a few watersheds can be reliably placed into the highest 150 category; however, many more watersheds can be removed from consideration as not belonging to the highest 150 category. Results from this ranking procedure provide robust information on watershed nutrient yields that can benefit management efforts to reduce nutrient loadings to downstream coastal waters, such as the Gulf of Mexico, or to local receiving streams and reservoirs.

Atchafalaya River;Gulf Of Mexico;Mississippi River↗
USGS2013

Computed statistics at streamgages, and methods for estimating low-flow frequency statistics and development of regional regression equations for estimating low-flow frequency statistics at ungaged locations in Missouri

The weather and precipitation patterns in Missouri vary considerably from year to year. In 2008, the statewide average rainfall was 57.34 inches and in 2012, the statewide average rainfall was 30.64 inches. This variability in precipitation and resulting streamflow in Missouri underlies the necessity for water managers and users to have reliable streamflow statistics and a means to compute select statistics at ungaged locations for a better understanding of water availability. Knowledge of surface-water availability is dependent on the streamflow data that have been collected and analyzed by the U.S. Geological Survey for more than 100 years at approximately 350 streamgages throughout Missouri. The U.S. Geological Survey, in cooperation with the Missouri Department of Natural Resources, computed streamflow statistics at streamgages through the 2010 water year, defined periods of drought and defined methods to estimate streamflow statistics at ungaged locations, and developed regional regression equations to compute selected streamflow statistics at ungaged locations. Streamflow statistics and flow durations were computed for 532 streamgages in Missouri and in neighboring States of Missouri. For streamgages with more than 10 years of record, Kendall’s tau was computed to evaluate for trends in streamflow data. If trends were detected, the variable length method was used to define the period of no trend. Water years were removed from the dataset from the beginning of the record for a streamgage until no trend was detected. Low-flow frequency statistics were then computed for the entire period of record and for the period of no trend if 10 or more years of record were available for each analysis. Three methods are presented for computing selected streamflow statistics at ungaged locations. The first method uses power curve equations developed for 28 selected streams in Missouri and neighboring States that have multiple streamgages on the same streams. Statistical estimates on one of these streams can be calculated at an ungaged location that has a drainage area that is between 40 percent of the drainage area of the farthest upstream streamgage and within 150 percent of the drainage area of the farthest downstream streamgage along the stream of interest. The second method may be used on any stream with a streamgage that has operated for 10 years or longer and for which anthropogenic effects have not changed the low-flow characteristics at the ungaged location since collection of the streamflow data. A ratio of drainage area of the stream at the ungaged location to the drainage area of the stream at the streamgage was computed to estimate the statistic at the ungaged location. The range of applicability is between 40- and 150-percent of the drainage area of the streamgage, and the ungaged location must be located on the same stream as the streamgage. The third method uses regional regression equations to estimate selected low-flow frequency statistics for unregulated streams in Missouri. This report presents regression equations to estimate frequency statistics for the 10-year recurrence interval and for the N-day durations of 1, 2, 3, 7, 10, 30, and 60 days. Basin and climatic characteristics were computed using geographic information system software and digital geospatial data. A total of 35 characteristics were computed for use in preliminary statewide and regional regression analyses based on existing digital geospatial data and previous studies. Spatial analyses for geographical bias in the predictive accuracy of the regional regression equations defined three low-flow regions with the State representing the three major physiographic provinces in Missouri. Region 1 includes the Central Lowlands, Region 2 includes the Ozark Plateaus, and Region 3 includes the Mississippi Alluvial Plain. A total of 207 streamgages were used in the regression analyses for the regional equations. Of the 207 U.S. Geological Survey streamgages, 77 were located in Region 1, 120 were located in Region 2, and 10 were located in Region 3. Streamgages located outside of Missouri were selected to extend the range of data used for the independent variables in the regression analyses. Streamgages included in the regression analyses had 10 or more years of record and were considered to be affected minimally by anthropogenic activities or trends. Regional regression analyses identified three characteristics as statistically significant for the development of regional equations. For Region 1, drainage area, longest flow path, and streamflow-variability index were statistically significant. The range in the standard error of estimate for Region 1 is 79.6 to 94.2 percent. For Region 2, drainage area and streamflow variability index were statistically significant, and the range in the standard error of estimate is 48.2 to 72.1 percent. For Region 3, drainage area and streamflow-variability index also were statistically significant with a range in the standard error of estimate of 48.1 to 96.2 percent. Limitations on the use of estimating low-flow frequency statistics at ungaged locations are dependent on the method used. The first method outlined for use in Missouri, power curve equations, were developed to estimate the selected statistics for ungaged locations on 28 selected streams with multiple streamgages located on the same stream. A second method uses a drainage-area ratio to compute statistics at an ungaged location using data from a single streamgage on the same stream with 10 or more years of record. Ungaged locations on these streams may use the ratio of the drainage area at an ungaged location to the drainage area at a streamgage location to scale the selected statistic value from the streamgage location to the ungaged location. This method can be used if the drainage area of the ungaged location is within 40 to 150 percent of the streamgage drainage area. The third method is the use of the regional regression equations. The limits for the use of these equations are based on the ranges of the characteristics used as independent variables and that streams must be affected minimally by anthropogenic activities.

Missouri↗
USGS2008

Hierarchical modeling and inference in ecology: The analysis of data from populations, metapopulations and communities

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.

Book↗
USGS1966

Preliminary flood-frequency relations for small streams in Kansas

Preliminary flood-frequency relations have been defined for small streams in Kansas for floods having recurrence intervals not greater than 10 years. The defined relations will be useful for the design of culverts and other hydraulic structures. The relations are expressed in terms of basin characteristics. Peakflow records at 95 sites in Kansas for an 8-year period provided the basic data. The records were analyzed with respect to 20 basin characteristics by multiple-regression techniques. The resulting formulas relate flood magnitude and frequency to size of contributing drainage area, an index of stream-bed slope, and the average number of days per year when rainfall exceeded 1.0 inch. The other 17 factors had no statistical significance. To illustrate a typical application of the flood-frequency relation, a step-bystep method is presented for computing a frequency curve for Rock Creek near Meriden, Kans. The frequency curve shows that a peak discharge of 3,620 cfs (cubic feet per second) can be expected once every 10 years on the average, and that the 67 percent confidence interval ranges from 1,820 cfs to 7,230 cfs. The large range results from the fact that only 8 years of record have been collected and emphasizes the need for collecting records for a longer period.

Kansas↗
USGS1999

An evaluation of alternative chemical classifications of sandstones

Chemical classification of sandstone is worth attempting because modern analytical methods are producing extensive data sets on rock composition. Previous compilations and statistical studies have demonstrated the application of chemical data to problems in sandstone petrology, but classification has been largely ignored. Chemical data has value for classification, but the limitations of using chemical data for classification must be identified. Consideration of the processes of sandstone formation permits formulation of classification guidelines and systems for classification. Alternative systems for chemical classification can be then evaluated for their power to identify major types of sandstones and to facilitate genetic interpretation.

Open-File Report↗
USGS2020

Keeping up with the times: Mapping range-wide habitat suitability for endangered species in a changing environment

Biologists and policy-makers have the difficult task of allocating limited resources to habitat conservation and management for endangered species in the face of changing environmental conditions. Satellite remote sensing can inform conservation because it is an efficient means to obtain environmental data over broad spatial and temporal extents. Yet, the challenges of accessing, processing, and analyzing remote sensing data hinder wider application of these techniques in conservation planning. We used Landsat data and hierarchical statistical models to link satellite-derived habitat measurements with abundance of endangered Yuma Ridgway's rails ( Rallus obsoletus yumanensis ) within the Lower Colorado River Basin and Salton Sink, USA. We addressed many of the challenges facing the application of remote sensing techniques by using the web-based, freely-available Google Earth Engine to process Landsat datasets, apply habitat models, and generate maps to predict habitat suitability at a fine spatial grain (30 m) across the range of the species. These maps are shareable, interactive, and easy to update annually as habitat conditions change using a Google Earth Engine App we developed. Thus, we provide a framework for building habitat suitability models and maps to help target adaptive habitat management over broad extents for sensitive species, enabling biologists to improve conservation and restoration efforts regularly as conditions change in highly variable ecosystems. We demonstrate this approach for Yuma Ridgway's rails, but our methods for merging hierarchical statistical models with open-source mapping software to describe spatial-temporal heterogeneity in habitat quality are applicable to any species, and are especially helpful to species inhabiting highly variable ecosystems.

Arizona, California, Nevada↗
USGS2019

Advances in quantifying streamflow variability across continental scales: 2. Improved model regionalization and prediction uncertainties using hierarchical Bayesian methods

The precise estimation of process effects in hydrological models requires applying models to large scales with extensive spatial variability in controlling factors. Despite progress in large‐scale applications of hydrological models in conterminous United States (CONUS) river basins, spatial constraints in model parameters have prevented the interbasin sharing of data, complicating quantification of process effects and limiting the accuracy of model predictions and uncertainties. Hierarchical Bayesian methods enable data sharing between basins and the identification of the causes of model uncertainties, which can improve model accuracy and interpretability; however, computational inefficiencies have been an obstacle to their large‐scale application. We used a new generation of Bayesian methods to develop a hierarchical version of a previous hybrid (statistical‐mechanistic) SPAtially Referenced Regression On Watershed attributes model of long‐term mean annual streamflow in the CONUS. We identified hierarchical (regional) variations in model coefficients and uncertainties and evaluated their effects on model accuracy and interpretability across diverse environments in 16 major CONUS regions. Hierarchical coefficients significantly improved spatial accuracy of model predictions, with the largest improvements in humid eastern regions, where uncertainties were approximately one third of those in arid western regions. Half of the coefficients varied regionally, with the largest variations in coefficients associated with water losses in streams and reservoirs. Our unraveling of the causes of model uncertainties identified a small latent process component of runoff that varies inversely with river size in most CONUS regions. Our study advances the use of hierarchical Bayesian methods to improve the predictive capabilities of hydrological models.

Water Resources Research↗
USGS2017

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

The U.S. Geological Survey (USGS), in cooperation with the U.S. Nuclear Regulatory Commission, has investigated statistical methods for probabilistic flood hazard assessment to provide guidance on very low annual exceedance probability (AEP) estimation of peak-streamflow frequency and the quantification of corresponding uncertainties using streamgage-specific data. The term “very low AEP” implies exceptionally rare events defined as those having AEPs less than about 0.001 (or 1 × 10 –3 in scientific notation or for brevity 10 –3 ). Such low AEPs are of great interest to those involved with peak-streamflow frequency analyses for critical infrastructure, such as nuclear power plants. Flood frequency analyses at streamgages are most commonly based on annual instantaneous peak streamflow data and a probability distribution fit to these data. The fitted distribution provides a means to extrapolate to very low AEPs. Within the United States, the Pearson type III probability distribution, when fit to the base-10 logarithms of streamflow, is widely used, but other distribution choices exist. The USGS-PeakFQ software, implementing the Pearson type III within the Federal agency guidelines of Bulletin 17B (method of moments) and updates to the expected moments algorithm (EMA), was specially adapted for an “Extended Output” user option to provide estimates at selected AEPs from 10 –3 to 10 –6 . Parameter estimation methods, in addition to product moments and EMA, include L-moments, maximum likelihood, and maximum product of spacings (maximum spacing estimation). This study comprehensively investigates multiple distributions and parameter estimation methods for two USGS streamgages (01400500 Raritan River at Manville, New Jersey, and 01638500 Potomac River at Point of Rocks, Maryland). The results of this study specifically involve the four methods for parameter estimation and up to nine probability distributions, including the generalized extreme value, generalized log-normal, generalized Pareto, and Weibull. Uncertainties in streamflow estimates for corresponding AEP are depicted and quantified as two primary forms: quantile (aleatoric [random sampling] uncertainty) and distribution-choice (epistemic [model] uncertainty). Sampling uncertainties of a given distribution are relatively straightforward to compute from analytical or Monte Carlo-based approaches. Distribution-choice uncertainty stems from choices of potentially applicable probability distributions for which divergence among the choices increases as AEP decreases. Conventional goodness-of-fit statistics, such as Cramér-von Mises, and L-moment ratio diagrams are demonstrated in order to hone distribution choice. The results generally show that distribution choice uncertainty is larger than sampling uncertainty for very low AEP values.

Scientific Investigations Report↗
USGS2022

Bayesian applications in environmental and ecological studies with R and Stan

Modern ecological and environmental sciences are dominated by observational data. As a result, traditional statistical training often leaves scientists ill-prepared for the data analysis tasks they encounter in their work. Bayesian methods provide a more robust and flexible tool for data analysis, as they enable information from different sources to be brought into the modelling process. Bayesian Applications in Evnironmental and Ecological Studies with R and Stan provides a Bayesian framework for model formulation, parameter estimation, and model evaluation in the context of analyzing environmental and ecological data. Features: An accessible overview of Bayesian methods in environmental and ecological studies Emphasizes the hypothetical deductive process, particularly model formulation Necessary background material on Bayesian inference and Monte Carlo simulation Detailed case studies, covering water quality monitoring and assessment, ecosystem response to urbanization, fisheries ecology, and more Advanced chapter on Bayesian applications, including Bayesian networks and a change point model Complete code for all examples, along with the data used in the book, are available via GitHub The book is primarily aimed at graduate students and researchers in the environmental and ecological sciences, as well as environmental management professionals. This is a group of people representing diverse subject matter fields, who could benefit from the potential power and flexibility of Bayesian methods.

Book↗
USGS2010

Nonparametric statistical methods for comparing two sites based on data with multiple nondetect limits

As concern over the effects of trace amounts of pollutants has increased, so has the need for statistical methods that deal appropriately with data that include values reported as “less than” the detection limit. It has become increasingly common for water quality data to include censored values that reflect more than one detection limit for a single analyte. For such multiply censored data sets, standard statistical methods (for example, to compare analyte concentration in two areas) are not valid. In such cases, methods from the biostatistical field of survival analysis are applicable. Several common two‐sample censored data rank tests are explained, and their behaviors are studied via a Monte Carlo simulation in which sample sizes and censoring mechanisms are varied under an assumed lognormal distribution. These tests are applied to shallow groundwater chemistry data from two sites in the San Joaquin Valley, California. The best overall test, in terms of maintained α level, is the normal scores test based on a permutation variance. In cases where the α level is maintained, however, the Peto‐Prentice statistic based on an asymptotic variance performs as well or better.

California↗
USGS2026

Fifteen years of WRTDS for advancing water-quality science: A critical review of methodological developments and global applications

Contamination by nutrients, major ions, and metals poses a major threat to global water sustainability. Understanding how these pollutants vary across time and space requires long-term monitoring and robust statistical approaches. Traditional methods, however, often struggle to account for streamflow variability, seasonality, and nonlinear responses. Introduced in 2010, the Weighted Regressions on Time, Discharge, and Season (WRTDS) method offers a flexible, data-driven framework that generates both observed and flow-normalized estimates of concentration and load. Over the past 15 years, WRTDS has become a state-of-the-art tool for water-quality science and management, with applications spanning a wide range of hydrologic, climatic, and policy contexts─including major watersheds across North America, Europe, Asia, Australia, and the Arctic. In this review of WRTDS, we document the method’s major advancements, examine its expanding geographic and thematic applications, and summarize its relevance to water-quality management programs and policies worldwide. We also discuss its performance relative to other regression and machine-learning approaches. Finally, we identify key priorities for future development to support the continued evolution of WRTDS as a trusted and practical tool for scientists and managers working to protect and sustain water resources.

Environmental Science and Technology↗
USGS2014

Statistics for stochastic modeling of volume reduction, hydrograph extension, and water-quality treatment by structural stormwater runoff best management practices (BMPs)

The U.S. Geological Survey (USGS) developed the Stochastic Empirical Loading and Dilution Model (SELDM) in cooperation with the Federal Highway Administration (FHWA) to indicate the risk for stormwater concentrations, flows, and loads to be above user-selected water-quality goals and the potential effectiveness of mitigation measures to reduce such risks. SELDM models the potential effect of mitigation measures by using Monte Carlo methods with statistics that approximate the net effects of structural and nonstructural best management practices (BMPs). In this report, structural BMPs are defined as the components of the drainage pathway between the source of runoff and a stormwater discharge location that affect the volume, timing, or quality of runoff. SELDM uses a simple stochastic statistical model of BMP performance to develop planning-level estimates of runoff-event characteristics. This statistical approach can be used to represent a single BMP or an assemblage of BMPs. The SELDM BMP-treatment module has provisions for stochastic modeling of three stormwater treatments: volume reduction, hydrograph extension, and water-quality treatment. In SELDM, these three treatment variables are modeled by using the trapezoidal distribution and the rank correlation with the associated highway-runoff variables. This report describes methods for calculating the trapezoidal-distribution statistics and rank correlation coefficients for stochastic modeling of volume reduction, hydrograph extension, and water-quality treatment by structural stormwater BMPs and provides the calculated values for these variables. This report also provides robust methods for estimating the minimum irreducible concentration (MIC), which is the lowest expected effluent concentration from a particular BMP site or a class of BMPs. These statistics are different from the statistics commonly used to characterize or compare BMPs. They are designed to provide a stochastic transfer function to approximate the quantity, duration, and quality of BMP effluent given the associated inflow values for a population of storm events. A database application and several spreadsheet tools are included in the digital media accompanying this report for further documentation of methods and for future use. In this study, analyses were done with data extracted from a modified copy of the January 2012 version of International Stormwater Best Management Practices Database, designated herein as the January 2012a version. Statistics for volume reduction, hydrograph extension, and water-quality treatment were developed with selected data. Sufficient data were available to estimate statistics for 5 to 10 BMP categories by using data from 40 to more than 165 monitoring sites. Water-quality treatment statistics were developed for 13 runoff-quality constituents commonly measured in highway and urban runoff studies including turbidity, sediment and solids; nutrients; total metals; organic carbon; and fecal coliforms. The medians of the best-fit statistics for each category were selected to construct generalized cumulative distribution functions for the three treatment variables. For volume reduction and hydrograph extension, interpretation of available data indicates that selection of a Spearman’s rho value that is the average of the median and maximum values for the BMP category may help generate realistic simulation results in SELDM. The median rho value may be selected to help generate realistic simulation results for water-quality treatment variables. MIC statistics were developed for 12 runoff-quality constituents commonly measured in highway and urban runoff studies by using data from 11 BMP categories and more than 167 monitoring sites. Four statistical techniques were applied for estimating MIC values with monitoring data from each site. These techniques produce a range of lower-bound estimates for each site. Four MIC estimators are proposed as alternatives for selecting a value from among the estimates from multiple sites. Correlation analysis indicates that the MIC estimates from multiple sites were weakly correlated with the geometric mean of inflow values, which indicates that there may be a qualitative or semiquantitative link between the inflow quality and the MIC. Correlations probably are weak because the MIC is influenced by the inflow water quality and the capability of each individual BMP site to reduce inflow concentrations.

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