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At least 37 records · Page 2Linked to original sources
USGS1986

Cluster analysis of phytoplankton data collected from the National Stream Quality Accounting Network in the Tennessee River basin, 1974-81

A computer program, Numerical Taxonomy System of Multivariate Statistical Programs (NTSYS), was used with interfacing software to perform cluster analyses of phytoplankton data stored in the biological files of the U.S. Geological Survey. The NTSYS software performs various types of statistical analyses and is capable of handling a large matrix of data. Cluster analyses were done on phytoplankton data collected from 1974 to 1981 at four national Stream Quality Accounting Network stations in the Tennessee River basin. Analysis of the changes in clusters of phytoplankton genera indicated possible changes in the water quality of the French Broad River near Knoxville, Tennessee. At this station, the most common diatom groups indicated a shift in dominant forms with some of the less common diatoms being replaced by green and blue-green algae. There was a reduction in genera variability between 1974-77 and 1979-81 sampling periods. Statistical analysis of chloride and dissolved solids confirmed that concentrations of these substances were smaller in 1974-77 than in 1979-81. At Pickwick Landing Dam, the furthest downstream station used in the study, there was an increase in the number of genera of ' rare ' organisms with time. The appearance of two groups of green and blue-green algae indicated that an increase in temperature or nutrient concentrations occurred from 1974 to 1981, but this could not be confirmed using available water quality data. Associations of genera forming the phytoplankton communities at three stations on the Tennessee River were found to be seasonal. Nodal analysis of combined data from all four stations used in the study did not identify any seasonal or temporal patterns during 1974-81. Cluster analysis using the NYSYS programs was effective in reducing the large phytoplankton data set to a manageable size and provided considerable insight into the structure of phytoplankton communities in the Tennessee River basin. Problems encountered using cluster analysis were the subjectivity introduced in the definition of meaningful clusters, and the lack of taxonomic identification to the species level. (Author 's abstract)

Tennessee↗
USGS2018

Statistical approach to neural network imaging of karst systems in 3D seismic reflection data

The current lack of a robust, standardized technique for geophysical mapping of karst systems can be attributed to both the complexity of the environment and prior technological limitations. Abrupt lateral variations in physical properties that are inherent to karst systems generate significant geophysical noise, challenging conventional seismic signal processing and interpretation. Modern application of neural networks to multi-attribute seismic interpretation now provide a semiautomated method for identifying and leveraging the nonlinear relationships exhibited among seismic attributes. The ambiguity generally associated with designing neural networks for seismic object detection can be reduced via statistical analysis of the extracted attribute data. A data-driven approach to selecting the appropriate set of input seismic attributes, as well as the locations and minimum number of training examples, provides a more objective and computationally efficient method for identifying karst systems using reflection seismology. This statistically optimized neural network technique is thoroughly demonstrated using three-dimensional seismic reflection data collected from the southeastern portion of the Florida carbonate platform. Several dimensionality reduction methods are applied and the resulting karst probability models are evaluated relative to one another based on both quantitative and qualitative criteria. Comparing the preferred model, using quadratic discriminant analysis, to previously available seismic object detection workflows demonstrates the karst-specific nature of the tool. Results suggest that the karst multi-attribute workflow presented is capable of approximating the structural boundaries of karst systems with more accuracy and efficiency than a human counterpart or previously presented seismic interpretation schemes. This objective technique, using solely three-dimensional seismic reflection data, likely represents the most practical approach to mapping karst systems for subsequent hydrogeological modeling.

Interpretation↗
USGS1999

Selected nutrients and pesticides in streams of the eastern Iowa basins, 1970-95

Water-quality data from 17 surface-water monitoring sites were compiled for 1970 through 1995 and analyzed to determine historical waterquality conditions and possible trends in the Eastern Iowa Basins study unit as part of the U.S. Geological Survey's National Water-Quality Assessment Program. The Eastern Iowa Basins encompasses the Wapsipinicon, Cedar, Iowa, and Skunk River Basins and covers about 19,500 square miles. Seven of the monitoring sites were sampled by the Iowa Department of Natural Resources, three sites by the Minnesota Pollution Control Agency, three sites by the University of Iowa Institute for Hydraulic Research, and four sites by the U.S. Geological Survey. Water-quality analyses typically consisted of nitrate, ammonia, total nitrogen, and total phosphorus, with limited analyses available for organic nitrogen, dissolved phosphorus, dissolved orthophosphate, and water-soluble pesticides. Long-term historical nutrient and pesticide data were not available for the Wapsipinicon River Basin. Median concentrations for total nitrogen ranged from 4.6 to 9.4 milligrams per liter, and maximum concentrations of total nitrogen ranged from 4.6 to 31 milligrams per liter. The majority of nitrogen transported in surface waters of the Eastern Iowa Basins study unit is in the form of nitrate (nitrogen). Median concentrations of total phosphorus ranged from less than 0.10 to 0.66 milligram per liter, and maximum concentrations of total phosphorus ranged from less than 0.10 to 5.4 milligrams per liter. Nitrate varied seasonally. Median concentrations of nitrate were largest during the spring and the winter (6.0 to 7.0 milligrams per liter) compared to the summer and fall (2.0 to 4.0 milligrams per liter). Concentrations of nitrate greater than 10 milligrams per liter typically occurred during spring runoff. Median ammonia concentrations generally were highest during the winter (approximately 0.3-0.5 milligram per liter) compared to the spring and summer when ammonia concentrations were often close to the detection limit (0.01 milligram per liter). In general, the median concentrations of total phosphorus varied less than 0.1 milligram per liter between seasons. The statistical analysis of the nutrient data typically indicated a strong positive correlation of nitrate with streamflow. Total phosphorus concentrations with streamflow showed greater variability than nitrate, perhaps reflecting the greater potential of transport of phosphorus on sediment rather than in the dissolved phase as with nitrate. Ammonia and ammonia plus organic nitrogen showed no correlation with streamflow or a weak positive correlation. Seasonal variations and the relations of nutrients and pesticides to streamflow generally corresponded with nonpoint‑source loadings, although possible point sources for nutrients were indicated by the data at selected monitoring sites. Statistical trend tests for concentrations and loads were computed for nitrate, ammonia, and total phosphorus. Trend analysis indicated decreases for ammonia and total phosphorus concentrations at several sites and increases for nitrate concentrations at other sites in the study unit.

Iowa, Minnesota↗
USGS2010

Hydraulic modeling of mussel habitat at a bridge-replacement site, Allegheny River, Pennsylvania, USA

The Allegheny River in Pennsylvania supports a large and diverse freshwater-mussel community, including two federally listed endangered species, Pleurobema clava (Clubshell) and Epioblasma torulosa rangiana (Northern Riffleshell). It is recognized that river hydraulics and morphology play important roles in mussel distribution. To assess the hydraulic influences of bridge replacement on mussel habitat, metrics such as depth, velocity, and their derivatives (shear stress, Froude number) were collected or computed. The objectives of the project were to evaluate mussel and hydraulic data at a reference site and to compare those findings to a bridge-replacement site. The findings were used to support a statistical analysis, which establishes correlations between mussel count and hydraulics, and a numerical model to forecast habitat based on the statistics. ArcGIS was selected to manage the data and generate a grid to compute area statistics for 3319, 4.9-m × 4.9-m cells (cell) for total mussel count, depth, velocity, shear stress, and Froude number. The Wilcoxon Rank Sum test indicated no statistical significance between the total mussel count and the hydraulic variables; however, trellis graphs were used to account for the spatial variability in the data set. For the flow conditions measured, the total mussel count per cell is greatest at sections where (1) velocities range from 0.061 to 0.21 m/s, (2) shear stresses range from 0.48 to 3.8 dyne/cm 2 , and (3) Froude numbers range from 0.006 to 0.04. Based on the statistical targets established, the hydraulic model results suggest that an additional 2428 m 2 or a 30-percent increase in suitable mussel habitat could be generated at the replacement-bridge site when compared to the baseline condition associated with the existing bridge at that same location. The study did not address the influences of substrate, acid mine drainage, sediment loads from tributaries, and surface-water/ground-water exchange on mussel habitat. Future studies could include methods for quantifying (1) channel–substrate composition and distribution using tools such as hydroacoustic echosounders specifically designed and calibrated to identify bed composition and mussel populations, (2) surface-water and ground-water interactions, and (3) a high-streamflow event.

Pennsylvania↗
USGS2005

A regional classification scheme for estimating reference water quality in streams using land-use-adjusted spatial regression-tree analysis

Various approaches are used to subdivide large areas into regions containing streams that have similar reference or background water quality and that respond similarly to different factors. For many applications, such as establishing reference conditions, it is preferable to use physical characteristics that are not affected by human activities to delineate these regions. However, most approaches, such as ecoregion classifications, rely on land use to delineate regions or have difficulties compensating for the effects of land use. Land use not only directly affects water quality, but it is often correlated with the factors used to define the regions. In this article, we describe modifications to SPARTA (spatial regression-tree analysis), a relatively new approach applied to water-quality and environmental characteristic data to delineate zones with similar factors affecting water quality. In this modified approach, land-use-adjusted (residualized) water quality and environmental characteristics are computed for each site. Regression-tree analysis is applied to the residualized data to determine the most statistically important environmental characteristics describing the distribution of a specific water-quality constituent. Geographic information for small basins throughout the study area is then used to subdivide the area into relatively homogeneous environmental water-quality zones. For each zone, commonly used approaches are subsequently used to define its reference water quality and how its water quality responds to changes in land use. SPARTA is used to delineate zones of similar reference concentrations of total phosphorus and suspended sediment throughout the upper Midwestern part of the United States. ?? 2006 Springer Science+Business Media, Inc.

Environmental Management↗
USGS2019

Bringing Bayesian models to life

Bringing Bayesian Models to Life empowers the reader to extend, enhance, and implement statistical models for ecological and environmental data analysis. We open the black box and show the reader how to connect modern statistical models to computer algorithms. These algorithms allow the user to fit models that answer their scientific questions without needing to rely on automated Bayesian software. We show how to handcraft statistical models that are useful in ecological and environmental science including: linear and generalized linear models, spatial and time series models, occupancy and capture-recapture models, animal movement models, spatio-temporal models, and integrated population-models.

Book↗
USGS1998

Summary of ground-water quality in West Virginia

Water-quality data for the 28 sites in the West Virginia ambient ground-water-quality network and for wells in the U.S. Geological Survey National Water Information System (NWIS) data base for West Virginia were analyzed statistically to identify any water-quality trends and relations and to compare data from the two data sets. Data for 10 selected properties and constituents (pH, fecal coliform, iron, manganese, sulfate, hardness, nitrate plus nitrite, chloride, fluoride, and dissolved solids) were grouped by geologic unit, topographic setting, well depth, and season; simple statistical descriptors such as mean, median, maximum, minimum, standard deviation, and 10th and 90th percentiles were computed for each property and constituent and are summarized in tables. Analysis of the data for wells from the NWIS data base showed that highest median concentrations of dissolved iron and dissolved manganese are in samples from the Lower Pennsylvanian units, which are found mainly in the low-sulfur coal fields of southern West Virginia; the highest median concentration of dissolved sulfate is in samples from the Quaternary alluvium along the Ohio and Kanawha Rivers; and the highest median hardness and concentrations of dissolved nitrate plus nitrite are in samples from the Cambrian and Ordovician karst limestone units found mainly in the Eastern Panhandle. The highest median concentrations of dissolved iron and dissolved manganese are in samples from valley wells and wells of shallow depth, and hardness is greatest in samples from hilltop wells. Analysis of data for all wells and springs in the ambient network corroborated statistics for the NWIS data set in that median concentration of total iron is highest in samples from the Lower Pennsylvanian units, median concentration of dissolved sulfate is highest in samples from the Quaternary alluvium, and hardness and median concentrations of total nitrate plus nitrite are highest in samples from the Cambrian and Ordovician units. Data from the ambient network did not show any significant seasonal variations in groundwater quality. Of the additional constituents sampled for in the ambient network, median concentrations of metals were less than U.S. Environmental Protection Agency drinking-water standards, and organic chemical constituents were rarely detected. Statistical comparisons of data from the NWIS data base and the ambient network data set showed no significant differences except for fecal coliform, iron, and manganese. Median concentrations of these three constituents were several times greater for samples from wells and springs in the ambient network. Statistical differences in values for these constituents could be attributed to differences in the state of constituents sampled (dissolved concentrations of iron and manganese for the NWIS data set as opposed to total concentrations for the ambient network data set) and the smaller number of sites in the ambient network. Statistical resolution could be improved by sampling a greater number of wells and springs that have a greater diversity of geologic and topographic conditions for the ambient network. The present ambient network does not include sites in Silurian or Middle Pennsylvanian geologic units nor sites in hilltop settings. The statistical validity of the ambient network could be improved by sampling additional sites, especially those for aquifers underrepresented in the data set.

West Virginia↗
USGS2018

SWToolbox: A surface-water tool-box for statistical analysis of streamflow time series

This report is a user guide for the low-flow analysis methods provided with version 1.0 of the Surface Water Toolbox (SWToolbox) computer program. The software combines functionality from two software programs—U.S. Geological Survey (USGS) SWSTAT and U.S. Environmental Protection Agency (EPA) DFLOW. Both of these programs have been used primarily for computation of critical low-flow statistics. The main analysis methods are the computation of hydrologic frequency statistics such as the 7-day minimum flow that occurs on average only once every 10 years (7Q10), computation of design flows including biologically based flows, and computation of flow-duration curves and duration hydrographs. Other annual, monthly, and seasonal statistics can also be computed. The interface facilitates retrieval of streamflow discharge data from the USGS National Water Information System and outputs text reports for a record of the analysis. Tools for graphing data and screening tests are available to assist the analyst in conducting the analysis.

Techniques and Methods↗
USGS1984

Compilation of ground water quality data in Pennsylvania

The U.S. Geological Survey's water quality file of 4,671 wells and springs in Pennsylvania provided ground-water-quality data for Pennsylvania. The data were assembled into computer-readable format and sorted into 15 major aquifer groups based on principal lithology, physiographic province, and age. Nineteen variables in each group were summarized by the Statistical Analysis Systems UNIVARIATE procedures to produce descriptive statistics including extreme values and quartiles. The bulk of the water-quality data are in the important aquifers in the unconsolidated Coastal Plain sediments, the Triassic sedimentary rocks, the igneous and metamorphic rocks, and the carbonate rocks. On the other hand, water-quality data for aquifer groups in the Appalachian Plateau and Valley and Ridge Province are sparse. Statewide, only six wells provide sufficient long-term data for trend analyses. Ground-water quality in Pennsylvania is highly diverse. High concentrations of dissolved solids, iron, manganese, sulfate, and nitrate are prevalent forms of natural and manmade contamination. The unconsolidated Coastal Plain aquifers have been most severely degraded. On the other hand, some of the best quality water is found in the quartzite, sandstone, and conglomerate rock units in the Cambrian and Precambrian rocks.

Open-File Report↗
USGS2018

Digital Shoreline Analysis System (DSAS) version 5.0 user guide

Overview The Digital Shoreline Analysis System (DSAS) is a freely available software application that works within the Esri Geographic Information System (ArcGIS) software. DSAS computes rate-of-change statistics for a time series of shoreline vector data. DSAS version 5.0 (v5.0) was released in December 2018 and has been tested for compatibility with ArcGIS versions 10.4 and 10.5. It is supported on Windows 7 and Windows 10 operating systems. If you use it, please cite it as follows and make note of the current version: Himmelstoss, E.A., Farris, A.S., Henderson, R.E., Kratzmann, M.G., Ergul, Ayhan, Zhang, Ouya, Zichichi, J.L., Thieler, E. R., 2018, Digital Shoreline Analysis System (version 5.0): U.S. Geological Survey software release, https://code.usgs.gov/cch/dsas . This user guide describes the system requirements, installation procedures, and necessary inputs to establish measurement locations with DSAS-generated transects and compute rate-of-change calculations. Although the nomenclature for this software utility is based on use in a coastal environment, the DSAS application could be used to compute rates of change for any boundary-change problem that incorporates a clearly identified feature position at discrete times, such as glacier limits, river banks, or land use/cover boundaries.

Open-File Report↗
USGS1982

Design of surface-water data networks for regional information

This report describes a technique, Network Analysis of Regional Information (NARI), and the existing computer procedures that have been developed for the specification of the regional information-cost relation for several statistical parameters of streamflow. The measure of information used is the true standard error of estimate of a regional logarithmic regression. The cost is a function of the number of stations at which hydrologic data are collected and the number of years for which the data are collected. The technique can be used to obtain either (1) a minimum cost network that will attain a prespecified accuracy and reliability or (2) a network that maximizes information given a set of budgetary and time constraints.

Water Supply Paper↗
USGS2022

U.S. Geological Survey Hydrologic Toolbox — A graphical and mapping interface for analysis of hydrologic data

The Hydrologic Toolbox is a Windows-based desktop software program that provides a graphical and mapping interface for analysis of hydrologic time-series data with a set of widely used and standardized computational methods. The software combines the analytical and statistical functionality provided in the U.S. Geological Survey Groundwater and Surface-Water Toolboxes and provides several enhancements to these programs. The main analytical methods are the computation of hydrologic-frequency statistics such as the 7-day minimum flow that occurs on average only once every 10 years (7Q10); the computation of design flows, including biologically based flows; the computation of flow-duration curves and duration hydrographs; eight computer-programming methods for hydrograph separation of a streamflow time series, including the Base-Flow Index (BFI), HYSEP, PART, and SWAT Bflow methods and Eckhardt’s two-parameter digital-filtering method; and the RORA recession-curve displacement method and associated RECESS program to estimate groundwater-recharge values from streamflow data. Several of the statistical methods provided in the Hydrologic Toolbox are used primarily for computation of critical low-flow statistics. The Hydrologic Toolbox also facilitates retrieval of streamflow and groundwater-level time-series data from the U.S. Geological Survey National Water Information System and outputs text reports that describe their analyses. The Hydrologic Toolbox was developed by use of the DotSpatial geographic information system (GIS) programming library, which is part of the MapWindow project. DotSpatial is a nonproprietary, open-source program written for the .NET framework that includes a spatial data viewer and GIS capabilities. Advantages of the DotSpatial system include its pure .NET implementation for both the user interface and the GIS mapping engine, and thus the DotSpatial system simplifies software deployment and installation. In addition to combining the functionality of the separate Groundwater and Surface-Water Toolboxes, the Hydrologic Toolbox also organizes the functionality by theme (Groundwater Tools, Surface-Water Tools, and general Time-Series Tools). This report provides a description of how to build a Hydrologic Toolbox project and to download and manage hydrologic time-series data. It includes an overview of the analytical and statistical capabilities of the Hydrologic Toolbox and highlights the primary differences between the Hydrologic Toolbox and the Groundwater and Surface-Water Toolboxes. The report supplements information available in an extensive online Help manual and is intended to provide a set of instructions that will allow users to quickly develop skills to use the mapping, data-retrieval, and computational tools of the program.

Techniques and Methods↗
USGS1995

Summary statistics and trend analysis of water-quality data at sites in the Gila River basin, New Mexico and Arizona

Summary statistics and temporal trends for 19 water-chemistry constituents and for turbidity were computed for 13 study sites in the Gila River basin, Arizona and New Mexico. A nonparametric technique, the seasonal Kendall tau test for flow-adjusted data, was used to analyze temporal changes in water-chemistry data. For the 19 selected constituents and turbidity, decreasing trends in concentrations outnumbered increasing trends by more than two to one. Decreasing trends in concentrations of constituents were found for 49 data sets at the 13 study sites. Gila River at Calva and Gila River above diversions, at Gillespie Dam (eight each) had the most decreasing trends for individual sites. The largest number of decreasing trends measured for a constituent was six for dissolved lead. The next largest number of decreasing trends for a constituent was for dissolved solids and total manganese (five each). Hardness, dissolved sodium, and dissolved chloride had decreasing trends at four of the study sites. Increasing trends in concen- trations of constituents were found for 24 data sets at the 13 study sites. The largest number of increasing trends measured for a single constituent was for pH (four), dissolved sulfate (three), dissolved chromium (three) and total manganese (three). Increased concentrations of constituents generally were found in three areas in the basin-at Pinal Creek above Inspiration Dam, at sites above reservoirs, and at sites on the main stem of the Gila River from Gillespie Dam to the mouth.

Water-Resources Investigations Report↗
USGS1977

Computer program for the calculation of grain size statistics by the method of moments

A computer program is presented for a Hewlett-Packard Model 9830A desk-top calculator (1) which calculates statistics using weight or point count data from a grain-size analysis. The program uses the method of moments in contrast to the more commonly used but less inclusive graphic method of Folk and Ward (1957). The merits of the program are: (1) it is rapid; (2) it can accept data in either grouped or ungrouped format; (3) it allows direct comparison with grain-size data in the literature that have been calculated by the method of moments; (4) it utilizes all of the original data rather than percentiles from the cumulative curve as in the approximation technique used by the graphic method; (5) it is written in the computer language BASIC, which is easily modified and adapted to a wide variety of computers; and (6) when used in the HP-9830A, it does not require punching of data cards. The method of moments should be used only if the entire sample has been measured and the worker defines the measured grain-size range. (1) Use of brand names in this paper does not imply endorsement of these products by the U.S. Geological Survey.

Open-File Report↗
USGS2026

Flood-frequency estimates for Kentucky streamgages based on data through water year 2021 and results of updating the fundamental layers in Kentucky StreamStats

The U.S. Geological Survey, in cooperation with the Kentucky Transportation Cabinet, analyzed flood-frequency statistics for streamgages in Kentucky. Using annual peak-flow data through water year 2021, flood-frequency estimates were computed for 261 streamgages, including unregulated and regulated sites as well as sites with mixed regulation records. Methods followed those outlined in “Guidelines for Determining Flood Flow Frequency—Bulletin 17C” (U.S. Geological Survey Techniques and Methods 4–B5). These estimates included flows corresponding to annual exceedance probabilities of 50, 20, 10, 4, 2, 1, and 0.2 percent. Temporal trend analyses using the Mann-Kendall test indicated that 18 percent of unregulated streamgages with (1) at least 30 years of peak-flow record and (2) peak-flow record at least as recent as water year 2000 showed statistically significant trends, most of which were weak to moderate increases in peak flows. Concurrently, the fundamental geospatial datasets that support the Kentucky StreamStats application were updated by using high-resolution digital elevation models and hydrography datasets to derive flow direction, flow accumulation, and stream definition rasters. Comparisons of regression-based flood-frequency models using the old and new layers demonstrated consistent results, with a statewide root-mean-square error of 0.019, in the base-10 logarithm of cubic feet per second. Furthermore, to assess model performance, flood-frequency estimates made by using the updated layers and previously published regression-based models were compared to flood-frequency estimates newly computed by following Bulletin 17C. This analysis showed the models performed adequately for most Kentucky stream locations. The updated statistics and geospatial layers provide stakeholders with more accurate, current data for flood-risk assessment, infrastructure design, and water-resource management.

Kentucky↗
USGS2014

HydroClimATe: hydrologic and climatic analysis toolkit

The potential consequences of climate variability and climate change have been identified as major issues for the sustainability and availability of the worldwide water resources. Unlike global climate change, climate variability represents deviations from the long-term state of the climate over periods of a few years to several decades. Currently, rich hydrologic time-series data are available, but the combination of data preparation and statistical methods developed by the U.S. Geological Survey as part of the Groundwater Resources Program is relatively unavailable to hydrologists and engineers who could benefit from estimates of climate variability and its effects on periodic recharge and water-resource availability. This report documents HydroClimATe, a computer program for assessing the relations between variable climatic and hydrologic time-series data. HydroClimATe was developed for a Windows operating system. The software includes statistical tools for (1) time-series preprocessing, (2) spectral analysis, (3) spatial and temporal analysis, (4) correlation analysis, and (5) projections. The time-series preprocessing tools include spline fitting, standardization using a normal or gamma distribution, and transformation by a cumulative departure. The spectral analysis tools include discrete Fourier transform, maximum entropy method, and singular spectrum analysis. The spatial and temporal analysis tool is empirical orthogonal function analysis. The correlation analysis tools are linear regression and lag correlation. The projection tools include autoregressive time-series modeling and generation of many realizations. These tools are demonstrated in four examples that use stream-flow discharge data, groundwater-level records, gridded time series of precipitation data, and the Multivariate ENSO Index.

Techniques and Methods↗
USGS2006

The use of analysis of variance procedures in biological studies

The analysis of variance (ANOVA) is widely used in biological studies, yet there remains considerable confusion among researchers about the interpretation of hypotheses being tested. Ambiguities arise when statistical designs are unbalanced, and in particular when not all combinations of design factors are represented in the data. This paper clarifies the relationship among hypothesis testing, statistical modelling and computing procedures in ANOVA for unbalanced data. A simple two-factor fixed effects design is used to illustrate three common parametrizations for ANOVA models, and some associations among these parametrizations are developed. Biologically meaningful hypotheses for main effects and interactions are given in terms of each parametrization, and procedures for testing the hypotheses are described. The standard statistical computing procedures in ANOVA are given along with their corresponding hypotheses. Throughout the development unbalanced designs are assumed and attention is given to problems that arise with missing cells.

Applied Stochastic Models and Data Analysis↗
USGS2018

Revised recommended methods for analyzing crater size-frequency distributions

Impact crater populations crucially help us to understand solar system dynamics, planetary surface histories, and surface modification processes. A single previous effort to standardize how crater data are displayed in graphs, tables, and archives, was in a 1978 NASA report by the Crater Analysis Techniques Working Group, published in 1979 in Icarus . The report had a significant lasting effect, but later decades brought major advances in statistical and computer sciences while the crater field has remained fairly stagnant. In this new work, we revisit the fundamental techniques for displaying and analyzing crater population data and demonstrate better statistical methods that can be used. Specifically, we address (1) how crater size-frequency distributions (SFDs) are constructed, (2) how error bars are assigned to SFDs, and (3) how SFDs are fit to power laws and other models. We show how the new methods yield results similar to those of previous techniques in that the SFDs have familiar shapes but better account for multiple sources of uncertainty. We also recommend graphic, display, and archiving methods that reflect computers' capabilities and fulfill NASA's current requirements for Data Management Plans.

Meteoritics and Planetary Science↗