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Statistical methods in water resources

This text began as a collection of class notes for a course on applied statistical methods for hydrologists taught at the U.S. Geological Survey (USGS) National Training Center. Course material was formalized and organized into a textbook, first published in 1992 by Elsevier as part of their Studies in Environmental Science series. In 2002, the work was made available online as a USGS report. The text has now been updated as a USGS Techniques and Methods Report. It is intended to be a text in applied statistics for hydrology, environmental science, environmental engineering, geology, or biology that addresses distinctive features of environmental data. For example, water resources data tend to have many variables with a lower bound of zero, tend to be more skewed than data from many other disciplines, commonly contain censored data (less than values), and assumptions that the data are normally distributed are not appropriate. Computer-intensive methods (bootstrapping and permutation tests) now improve upon and replace the dependence on t-intervals, t-tests, and analysis of variance. A new chapter on sampling design addresses questions such as “How many observations do I need?” The chapter also presents distribution-free methods to help plan sampling efforts. The trends chapter has been updated to include the WRTDS (Weighted Regressions on Time, Discharge, and Season) method for analysis of water-quality data. This new version contains updated graphics and updated guidance on the use of statistical techniques. The text utilizes R, a programming language and open-source software environment, for all exercises and most graphics, and the R code used to generate figures and examples is provided for download.

Techniques and Methods↗

Advanced instrumentation for the collection, retrieval, and processing of urban stormwater data

The U.S. Geological Survey, in cooperation with the City of Charlotte and Mecklenburg County, North Carolina, has developed a data-collection network that uses advanced instrumentation to automatically collect, retrieve, and process urban stormwater data. Precipitation measurement and water-quality networks provide data for (1) planned watershed simulation models, (2) early warning of possible flooding, (3) computation of material export, and (4) characterization of water quality in relation to basin conditions. Advantages of advanced instrumentation include remote access to real-time data, reduced demands on and more efficient use of limited human resources, and direct importation of data into a geographical information system for display and graphic analysis.

Conference Paper↗

Hanson Russian River Ponds floodplain restoration: Feasibility study and conceptual design; Appendix G: Physical evaluation of the restoration alternatives

Appendix G: Hanson Russian River Ponds Floodplain Restoration: Feasibility Study and Conceptual Design |G-1Appendix GPhysical Evaluation of the Restoration AlternativesRichard McDonald and Jonathan Nelson, PhDU.S. Geological Survey Geomorphology and Sediment Transport Laboratory, Golden, ColoradoIntroductionTo assess the relative and overall impacts of the scenarios proposed in Chapters 7 and 9,(Stage I-A–I-D and Stage II-A –II-E), each of the topographic configurations were evaluated over a range of flows. Thisevaluation was carried out using computational flow modeling tools available in the iRIC public-domain river modeling interface (www.i-ric.org, Nelsonet al.in press). Using the iRIC modeling tools described in more detail below, basic hydraulic computations of water-surface elevation, velocity, shear stress, and other hydraulic variables were carried out for the alternatives in the reach surrounding the project area, from the confluence of Dry Creek upstream to the Wohler road bridge downstream, for the full range of observed flows. This methodology allows comparison of the current channel configuration with the proposed alternatives in terms of inundation period and frequency, depth, water velocity, and other hydraulic information. By integrating this kind of information over the reach of interest and the flow record, critical metrics assessing the impacts of various topographic modifications can be compared to those same metrics for the existing condition or other modification scenarios. In addition, because the iRIC tools include predictions of sediment mobility, suspension of fines, and the potential evolution of the land surface in response to flow, these methods provide evaluation of sediment transport, stability of current and proposed surfaces, and evaluation of how these surfaces might evolve into the future. This hydraulic and sediment transport information is critically important for understanding theimpacts of various proposed alternatives on the physical system; perhaps even more importantly given the objectives of the proposed restoration, this information can be related to biological impacts, as is discussed in subsequent chapters of this document.

Book chapter↗

Chemical character of ground water in the shallow water-table aquifer at selected localities in the Memphis area, Tennessee

The City of Memphis depends solely on ground water for its water supply. About 97 percent of inventoried pumpage in the Memphis area, which totaled about 194 Mgal/d in 1979, is from the Memphis Sand. This aquifer generally has been believed to be separated from the shallow water-table aquifer (alluvium and fluvial deposits) by a relatively thick and wide-spread confining bed consisting chiefly of clay. Studies by the Geological Survey in recent decades, however, have indicated that part of the recharge to the Memphis Sand probably is derived by vertical leakage from the shallow water-table aquifer through the confining bed and that locally "windows" of sand exist in the confining bed through which any contaminants in the shallow water-table aquifer could enter the Memphis Sand (See Criner and others, 1964, p. 30; Bell and Nyman, 1968, p. 7-8; Parks and Lounsbury, 1976, p. 26-27). More recently, additional evidence of vertical leakage being a component of recharge to the Memphis Sand was provided during the calibration of a digital computer model of the aquifers in the Memphis area. For this calibration a leakage factor, averaging about 20 percent over the Memphis area, had to be applied to the model in order to simulate known historic water levels in the Memphis Sand (J. V. Brahana, 1980, oral commun. ). This discovery has heightened concern about the possibility of contaminants being in the shallow water table aquifer, and thus, the potentiality for any contaminants to enter the Memphis Sand. Areas where the shallow water-table aquifer is most susceptible to contamination are those that have been or are being used for waste disposal. Historically, Memphis and Shelby County along with private concerns and industries have used dumps and landfills in two geologically and topographically different areas -- the flood plains of nearby streams and abandoned gravel pits in upland areas. These dumps and landfills have received a large variety of wastes including ashes, construction and demolition materials, garbage, rubbish, street refuse, and chemical and industrial wastes. Most of these dumps and landfills were closed in the early 1970's at the beginning of state regulation of waste disposal practices. Nevertheless, leachates from these waste disposal facilities presumably have been and are entering the shallow water-table aquifer.

Tennessee↗

Nonlinear inversion of borehole-radar tomography data to reconstruct velocity and attenuation distribution in earth materials

A nonlinear tomographic inversion method that uses first-arrival travel-time and amplitude-spectra information from cross-hole radar measurements was developed to simultaneously reconstruct electromagnetic velocity and attenuation distribution in earth materials. Inversion methods were developed to analyze single cross-hole tomography surveys and differential tomography surveys. Assuming the earth behaves as a linear system, the inversion methods do not require estimation of source radiation pattern, receiver coupling, or geometrical spreading. The data analysis and tomographic inversion algorithm were applied to synthetic test data and to cross-hole radar field data provided by the US Geological Survey (USGS). The cross-hole radar field data were acquired at the USGS fractured-rock field research site at Mirror Lake near Thornton, New Hampshire, before and after injection of a saline tracer, to monitor the transport of electrically conductive fluids in the image plane. Results from the synthetic data test demonstrate the algorithm computational efficiency and indicate that the method robustly can reconstruct electromagnetic (EM) wave velocity and attenuation distribution in earth materials. The field test results outline zones of velocity and attenuation anomalies consistent with the finding of previous investigators; however, the tomograms appear to be quite smooth. Further work is needed to effectively find the optimal smoothness criterion in applying the Tikhonov regularization in the nonlinear inversion algorithms for cross-hole radar tomography.

New Hampshire↗

The stream-gaging program of the U.S. Geological Survey

The U.S. Geological Survey stream-gaging program provides streamflow data for a variety of purposes. The uses of streamflow data are described, and the growth of the stream-gaging program is related to legislation and the need to manage the Nation's water resources more effectively. A brief description is provided of the data-collection processes, computation of streamflow records, dissemination of data, and the nationwide evaluations of the stream-gaging program. Finally, the challenges for maintaining a viable stream-gaging program are described.

Circular↗

Earth science photographs from the U.S. Geological Survey Library

This CD-ROM set contains 1,500 scanned photographs from the U.S. Geological Survey Library for use as a photographic glossary of elementary geologic terms. Scholars are encouraged to copy these public domain images into their reports or databases to enhance their presentations. High-quality prints and (or) slides are available upon request from the library. This CD-ROM was produced in accordance with the ISO 9660 standard; however, it is intended for use on DOS-based computer systems only.

Data Series↗

Estimating Monthly Water Withdrawals, Return Flow, and Consumptive Use in the Great Lakes Basin

Water-resource managers and planners require water-withdrawal, return-flow, and consumptive-use data to understand how anthropogenic (human) water use affects the hydrologic system. Water models like MODFLOW and GSFLOW use calculations and input values (including water-withdrawal and return flow data) to simulate and predict the effects of water use on aquifer and stream conditions. Accurate assessments of consumptive use, interbasin transfer, and areas that are on public supply or sewer are essential in estimating the withdrawal and return-flow data needed for the models. As the applicability of a model to real situations depends on accurate input data, limited or poor water-use data hampers the ability of modelers to simulate and predict hydrologic conditions. Substantial differences exist among the many agencies nationwide that are responsible for compiling water-use data including what data are collected, how the data are organized, how often the data are collected, quality assurance, required level of accuracy, and when data are released to the public. This poster presents water-use information and estimation methods summarized from recent U.S. Geological Survey (USGS) reports with the intent to assist water-resource managers and planners who need estimates of monthly water withdrawals, return flows, and consumptive use. This poster lists references used in Shaffer (2009) for water withdrawals, consumptive use, and return flows. Monthly percent of annual withdrawals and monthly consumptive-use coefficients are used to compute monthly water withdrawals, consumptive use, and return flow for the Great Lakes Basin.

Open-File Report↗

Low-flow characteristics of streams in South Carolina

An ongoing understanding of streamflow characteristics of the rivers and streams in South Carolina is important for the protection and preservation of the State’s water resources. Information concerning the low-flow characteristics of streams is especially important during critical flow periods, such as during the historic droughts that South Carolina has experienced in the past few decades. Between 2008 and 2016, the U.S. Geological Survey, in cooperation with the South Carolina Department of Health and Environmental Control, updated low-flow statistics at 106 continuous-record streamgages operated by the U.S. Geological Survey for the eight major river basins in South Carolina. The low-flow frequency statistics included the annual minimum 1-, 3-, 7-, 14-, 30-, 60-, and 90-day mean flows with recurrence intervals of 2, 5, 10, 20, 30, and 50 years, depending on the length of record available at the streamflow-gaging station. Computations of daily mean flow durations for the 5-, 10-, 25-, 50-, 75-, 90-, and 95-percent probability of exceedance also were included. This report summarizes the findings from publications generated during the 2008 to 2016 investigations. Trend analyses for the annual minimum 7-day average flows are provided as well as trend assessments of long-term annual precipitation data. Statewide variability in the annual minimum 7-day average flow is assessed at eight long-term (record lengths from 55 to 78 years) streamgages. If previous low-flow statistics were available, comparisons with the updated annual minimum 7-day average flow, having a 10-year recurrence interval, were made. In addition, methods for estimating low-flow statistics at ungaged locations near a gaged location are described.

South Carolina↗

Hydrologic data collection activities in the Solomon Gulch basin near Valdez, Alaska

In 1981, the Alaska Power Authority completed construction of a dam spillway at the north end of Solomon Lake near Valdez. Regulation and diversion from the dam since 1982 have significantly altered the natural flow characteristics of Solomon Gulch. In September 1986, the Geological Survey began data collection to determine mean daily discharge at four sites below Solomon Lake and thus document the effects of regulation and diversion of water on the flow at various points in the system. Periodic discharge measurements and continuous records of water stage were obtained at two of the sites, and daily discharge values were computed for all four sites. The report contains descriptions of the data collection sites and the discharge records for each site for September 1986 and water year 1987. (USGS)

Open-File Report↗

Geographic Information Systems Methods for Determining Drainage-Basin Areas, Stream-Buffered Areas, Stream Length, and Land Uses for the Neosho and Spring Rivers in Northeastern Oklahoma

Geographic Information Systems have many uses, one of which includes the reproducible computation of environmental characteristics that can be used to categorize hydrologic features. The Oklahoma Department of Wildlife Conservation and the Oklahoma Department of Environmental Quality are investigating Geographic Information Systems techniques to determine partial drainage-basin areas, stream-buffer areas, stream length, and land uses (drainage basin and stream characteristics) in northeastern Oklahoma. The U.S Geological Survey, in cooperation with Oklahoma Department of Wildlife Conservation and the Oklahoma Department of Environmental Quality, documented the methods used to determine drainage-basin and stream characteristics for the Neosho and Spring Rivers above Grand Lake Of the Cherokees in northeastern Oklahoma and calculated the characteristics. The drainage basin and stream characteristics can be used by the Oklahoma Department of Wildlife Conservation and the Oklahoma Department of Environmental Quality to aid in natural-resource assessments.

Scientific Investigations Report↗

Source contributions to suspended sediment and particulate selenium export from the Loutsenhizer Arroyo and Sunflower Drain watersheds in Colorado

Selenium in aquatic ecosystems of the lower Gunnison River Basin in Colorado is affecting the recovery of populations of endangered, native fish species. Dietary exposure is the primary pathway for bioaccumulation of selenium in fish, and particulate selenium can be consumed directly by fish or by the invertebrates on which fish feed. Although selenium can be incorporated into particulate matter via biogeochemical processes, particulate selenium can also enter aquatic ecosystems of the lower Gunnison River Basin from sediments derived from the selenium-rich Mancos Shale. The U.S. Geological Survey, in cooperation with the Colorado Water Conservation Board, conducted this study during 2018–19 to identify sources of selenium-rich suspended sediments from two watersheds underlain by Mancos Shale: Loutsenhizer Arroyo and Sunflower Drain, which is a locally known agricultural drainage near the municipality of Delta, Colorado. A multipronged approach (fieldwork, laboratory work, and computer modeling) referred to as “sediment fingerprinting” was used to evaluate sources of suspended sediments in the streams flowing out of the two studied watersheds. Four potential source types for suspended sediments were identified and sampled (using soil plugs) within the watersheds: rangelands, agricultural fields, arroyo walls, and streambanks. The sediment fingerprinting approach used elemental concentrations and naturally occurring fallout radionuclides as tracers to apportion percent contributions from the four source types of suspended sediments found in streamflow from both watersheds. To determine the dominant sources of suspended sediment in streamflow from both watersheds, a mathematical “unmixing” model was used. Unmixing models apportion source percentages to samples of material in which those sources are mixed. These models used elemental and isotopic data in the suspended sediments to unmix them into proportional contributions from source types. The results indicated that arroyo walls and streambanks generally dominated as sources of the suspended sediment. Arroyo walls and streambanks were channel-adjacent sources, with sediments mobilized by water flowing within the stream channel. These sources accounted for greater than 50 percent of suspended sediment in all but one sample and accounted for 100 percent of suspended sediment in 5 of the 11 samples collected. Rangeland and agricultural field sources were located in uplands outside of stream channels and were detected more often during the non-irrigation season. Rangeland and agricultural field sources each were found in 5 of the 11 samples collected. Concentrations of selenium in sediment-source samples were comparatively greater in streambanks and lower in rangelands, with agricultural fields and arroyo walls being intermediate. As a result, source apportionments for particulate selenium skewed towards sources adjacent to stream channels more than for suspended sediments. Water imports for irrigation have changed the hydrology of the watersheds, and a notable fraction of imported water passes through the watersheds rapidly. The rapid flowthrough water during the irrigation season likely contributes heavily to sediment erosion and transport in Loutsenhizer Arroyo and Sunflower Drain, particularly from channel-adjacent sources of sediment. Decreases in irrigation season streamflow, at least in Loutsenhizer Arroyo, may have decreased sediment erosion and transport during the 2018–20 irrigation seasons compared to the 2015–17 seasons.

Colorado↗

An "optimal" filter for maps showing nominal data

An "optimal" filtering technique for use with nominal data, such as land use and land cover categories, has been developed. This method is based on the conditional probability joins of neighboring data elements. In addition to its use in performing filtering, the method can be used to calculate the likelihood of each data element being properly classified. The technique was tested on a land use data set for an area in Walnut Valley, Calif. The computer program performing the filtering process proved to be computationally efficient and produced satisfactory results. Useful statistics of the error estimation process were also generated. Future applications of the method to spectrally classified Landsat data are being explored.

Journal of Research of the U.S. Geological Survey↗

Measurements of erosion potential using Gust chamber in Yolo Bypass near Sacramento, California

This report describes work performed to quantify the erodibility of surface soils in the Yolo Bypass (Bypass) near Sacramento, California, for use in the California Department of Water Resources (DWR) Yolo Bypass D-MCM mercury model. The Bypass, when not serving as a floodway, is heavily utilized for agriculture. During flood events, surface water flows over the soil, resulting in the application of a shear stress to the soil. The shear stress is a function of flow speed and is often assumed to vary as the square of flow speed. Once the shear stress reaches a critical value, erosion commences, and the erosion rate typically increases with applied shear stress. The goal of the work described here was to quantify this process and how it varies throughout the major land uses found in the Yolo Bypass. Each of the major land uses found in the Bypass was targeted for sediment coring and two side-by-side cores, 10 centimeters in diameter, were extracted at each site for testing in a Gust erosion chamber. This device consists of a cylinder with a piston and cap installed to contain a sediment sample and overlying water. In most instances, coring was done with the cylinder, the piston and cap were installed, and testing commenced immediately. The cap at the top of the cylinder contains vanes to induce rotation of the flow and is driven by an electric motor, simulating the bed shear stress experienced by the soil in a flood event. Ambient water is introduced to the cylinder, passes through the device, and carries eroded sediment out of the chamber. The exiting water is tested for turbidity, and water samples obtained to relate turbidity to suspended sediment concentration are used to compute erosion rates for each of the applied shear stresses. The result for each sediment core is (1) definition of the critical shear stress required to initiate sediment erosion and (2) estimation of coefficients required to relate erosion rate to applied shear stress once this critical shear-stress threshold has been exceeded. These quantities were computed for each of the sites sampled. In total, 10 locations were sampled, representing 10 land uses ranging from wild and white rice fields to the flooded Liberty Island and the Toe Drain that receives runoff from much of the cultivated land (table 1). The Gust chamber test causes the erosion of a very small layer of sediment, typically less than a millimeter thick. The strength of the soil within this layer increases with depth, typically, and this soil strength versus depth is measured in the testing process. Results for each land use type tested are presented as the initial critical shear stress at which erosion began and the rate at which erosion increases as shear stress increases (table 2). Of the land use types sampled, irrigated pasture displayed the lowest critical shear stress, meaning that it required the smallest flow speed to initiate erosion. But in this case, the rate of increase of the subsequent erosion, given higher flow speeds, was small. The wild rice field samples exhibited a higher critical shear stress but also exhibited a much higher erosion rate once the critical shear stress was exceeded. The erosion rate for wild rice was about three times greater than that for white rice. Bear in mind that these results are based on only two cores tested per site, and variability between fields with the same crop could be significant. Approved digital data can be viewed and downloaded from ScienceBase, at https://doi.org/10.5066/F7BV7DQC . These results are being used to calculate erosion rates in the DWR Yolo Bypass D-MCM mercury model. The Toe Drain was very difficult to sample, owing to hard, consolidated sediments on the channel bed. On the first visit, two cores were obtained successfully, and testing revealed very different results. A second visit was made, but it was not possible to obtain cores suitable for testing with the coring equipment used. The available results suggest that Toe Drain soil is highly erodible (low critical shear stress and high erosion rate once initiated) despite being difficult to sample. As a collector of runoff, it also has the potential to accumulate soils eroded from adjacent areas, subsequent to storm events, as flows subside. This deposited material will typically be more erodible than the material that it lands on. The deposition and resuspension of material was not simulated in the testing described here because the applied shear stress increases monotonically during testing. The spatial distribution of mean grain size, loss on ignition, and percent fines of Yolo Bypass soils are also presented. Sediment sampling for this effort was performed by DWR; the U.S. Geological Survey (USGS) performed the sample analysis. These data should thus be considered provisional, but the remainder of the data presented here, and this report, have been through the formal U.S. Geological Survey review process. A separate effort has been made by others to develop numerical model results defining the spatially varying, time-dependent hydrodynamics in the Yolo Bypass. These model results are being used to quantify shear stress on the soil surface, which together with the Gust chamber results shown here, are used for the DWR Yolo Bypass D-MCM mercury transport model to compute erosion rates for each time step.

California↗

Real-time control of the robotic lunar observatory telescope

The US Geological Survey operates an automated observatory dedicated to the radiometry of the Moon with the objective of developing a multispectral, spatially resolved photometric model of the Moon to be used in the calibration of Earth-orbiting spacecraft. Interference filters are used with two imaging instruments to observe the Moon in 32 passbands from 350-2500 nm. Three computers control the telescope mount and instruments with a fourth computer acting as a master system to control all observation activities. Real-time control software has been written to operate the instrumentation and to automate the observing process. The observing software algorithms use information including the positions of objects in the sky, the phase of the Moon, and the times of evening and morning twilight to decide how to observe program objects. The observatory has been operating in a routine mode since late 1995 and is expected to continue through at least 2002 without significant modifications.

Publications of the Astronomical Society of the Pa↗

Massachusetts shoreline change project: a GIS compilation of vector shorelines and associated shoreline change data for the 2013 update

Identifying the rates and trends associated with the position of the shoreline through time presents vital information on potential impacts these changes may have on coastal populations and infrastructure, and supports informed coastal management decisions. This report publishes the historical shoreline data used to assess the scale and timing of erosion and accretion along the Massachusetts coast from New Hampshire to Rhode Island including all of Cape Cod, Martha’s Vineyard, Nantucket and the Elizabeth Islands. This data is an update to the Massachusetts Office of Coastal Zone Management Shoreline Change Project. Shoreline positions from the past 164 years (1845 to 2009) were used to compute the shoreline change rates. These data include a combined length of 1,804 kilometers of new shoreline data derived from color orthophoto imagery collected in 2008 and 2009, and topographic lidar collected in 2007. These new shorelines have been added to previously published historic shoreline data from the Massachusetts Office of Coastal Zone Management and the U.S. Geological Survey. A detailed report containing a discussion of the shoreline change data presented here and a summary of the resulting rates is available and cited at the end of the Introduction section of this report.

Massachusetts↗

Estimating aftershock risk for entry into earthquake-damaged buildings

We present a simple method to estimate the risk of experiencing strong shaking from aftershocks during entry into earthquake-damaged buildings. We compute wait times until the probability of strong ground shaking from aftershocks reaches a predefined risk threshold; for example, a 0.4 percent probability of experiencing Modified Mercalli Intensity 7 or greater shaking during the planned building entry. We also develop a relation between aftershock probability and the probability of strong shaking, so that users can reference the U.S. Geological Survey aftershock forecast during an ongoing aftershock sequence to determine if the risk threshold has been met. We apply our method to active continental regions (for example, the Western United States), stable continental regions (for example, the Central and Eastern United States), and subduction zones (for example, Cascadia or Alaska).

Open-File Report↗

A computer program for simulating salinity loads in streams

A FORTRAN IV program that simulates salinity loads in streams is described. Daily values of stream-discharge in cubic feet per second, or stream-discharge and specific conductance in micromhos, are used to estimate daily loads in tons by one of five available methods. The loads are then summarized by computing either total and mean monthly loads or various statistics for each calendar day. Results are output in tabular and, if requested, punch card format. Under selection of appropriate methods for estimating and summarizing daily loads is provided through the coding of program control cards. The program is designed to interface directly with data retrieved from the U.S. Geological Survey WATSTORE Daily Values File. (Woodard-USGS)

Open-File Report↗