Richard M. Yager

Detecting influential observations in nonlinear regression modeling of groundwater flow

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cooks D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cooks D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Simulation of the effects of seasonally varying pumping on intraborehole flow and the vulnerability of public-supply wells to contamination

Public-supply wells with long screens in alluvial aquifers can produce waters of differing quality from different depths. Seasonal changes in quality are linked to seasonal changes in pumping rates that influence the distribution of flow into the well screens under pumping conditions and the magnitude and direction of intraborehole flow within the wells under ambient conditions. Groundwater flow and transport simulations with MODFLOW and MT3DMS were developed to quantify the effects of changes in average seasonal pumping rates on intraborehole flow and water quality at two long-screened, public-supply wells, in Albuquerque, New Mexico and Modesto, California, where widespread pumping has altered groundwater flow patterns. Simulation results indicate that both wells produce water requiring additional treatment to maintain potable quality in winter when groundwater withdrawals are reduced because less water is derived from parts of the aquifer that contain water requiring less treatment. Simulation results indicate that the water quality at both wells could be improved by increasing average winter-pumping rates to induce more lateral flow from parts of the aquifer that contain better quality water. Arsenic-bearing water produced by the Albuquerque well could be reduced from 55% to 45% by doubling average winter-pumping rate, while nitrate- and uranium-bearing water produced by the Modesto well could be reduced from 95% to 65% by nearly tripling the average winter-pumping rate. Higher average winter-pumping rates would also reduce the volume of intraborehole flow within both wells and prevent the exchange of poor quality water between shallow and deep parts of both aquifers.

Infiltration and hydraulic connections from the Niagara River to a fractured-dolomite aquifer in Niagara Falls, New York

Abstract The spatial distribution of hydrogen and oxygen stable-isotope values in groundwater can be used to distinguish different sources of recharge and to trace groundwater flow directions from recharge boundaries. This method can be particularly useful in fractured-rock settings where multiple lines of evidence are required to delineate preferential flow paths that result from heterogeneity within fracture zones. Flow paths delineated with stable isotopes can be combined with hydraulic data to form a more complete picture of the groundwater flow system. In this study values of δD and δ 18 O were used to delineate paths of river-water infiltration into the Lockport Group, a fractured dolomite aquifer, and to compute the percentage of river water in groundwater samples from shallow bedrock wells. Flow paths were correlated with areas of high hydraulic diffusivity in the shallow bedrock that were delineated from water-level fluctuations induced by diurnal stage fluctuations in man-made hydraulic structures. Flow paths delineated with the stable-isotope and hydraulic data suggest that river infiltration reaches an unlined storm sewer in the bedrock through a drainage system that surrounds carrying river water to hydroelectric power plants. This findings is significant because the storm sewer is the discharge point for contaminated groundwater from several chemical waste-disposal sites and the cost of treating the storm sewers discharge could be reduced if the volume of infiltration from the river were decreased.

Hydrogeology and simulation of groundwater flow in fractured-rock aquifers of the Piedmont and Blue Ridge Physiographic Provinces, Bedford County, Virginia

An annual groundwater budget was computed as part of a hydrogeologic characterization and monitoring effort of fractured-rock aquifers in Bedford County, Virginia, a growing 764-square-mile (mi2) rural area between the cities of Roanoke and Lynchburg, Virginia. Data collection in Bedford County began in the 1930s when continuous stream gages were installed on Goose Creek and Big Otter River, the two major tributaries of the Roanoke River within the county. Between 2006 and 2014, an additional 2 stream gages, 3 groundwater monitoring wells, and 12 partial-record stream gages were operated. Hydrograph separation methods were used to compute base-flow recharge rates from the continuous data collected from the continuous stream gages. Mean annual base-flow recharge ranged from 8.3 inches per year (in/yr) for the period 1931–2012 at Goose Creek near Huddleston (drainage area 188 mi2) to 9.3 in/yr for the period 1938–2012 at Big Otter River near Evington (drainage area 315 mi2). Mean annual base-flow recharge was estimated to be 6.5 in/yr for the period 2007–2012 at Goose Creek at Route 747 near Bunker Hill (drainage area 125 mi2) and 8.9 in/yr for the period 2007–2012 at Big Otter River at Route 221 near Bedford (drainage area 114 mi2). Base-flow recharge computed from the partial-record data ranged from 5.0 in/yr in the headwaters of Goose Creek to 10.5 in/yr in the headwaters of Big Otter River. A steady-state groundwater-flow simulation for Bedford County was developed to test the conceptual understanding of flow in the fractured-rock aquifers and to compute a groundwater budget for the four major drainages: James River, Smith Mountain and Leesville Lakes, Goose Creek, and Big Otter River. Model results indicate that groundwater levels mimic topography and that minimal differences in aquifer properties exist between the Proterozoic basement crystalline rocks and Late Proterozoic-Cambrian cover crystalline rocks. The Big Otter River receives 40.8 percent of the total daily groundwater outflow from fractured-rock aquifers in Hydrogeology and Simulation of Groundwater Flow in Fractured-Rock Aquifers of the Piedmont and Blue Ridge Physiographic Provinces, Bedford County, Virginia By Kurt J. McCoy,1 Bradley A. White,2 Richard M. Yager,1 and George E. Harlow, Jr.1 Bedford County; Goose Creek receives 25.8 percent, the James River receives 18.2 percent, and Smith Mountain and Leesville Lakes receive 15.2 percent. The remaining percentage of outflow is attributed to pumping from the aquifer (consumptive use). Introduction Groundwater resources in Bedford County, Virginia (Va.), are increasingly relied upon to supply water to local communities, industry, and individual residences. Groundwater withdrawals from fractured-rock aquifers are the primary source of water for most rural households and the majority of the county’s residents. Since 2003, more than 2,000 new wells have been permitted and drilled in Bedford County to meet the needs of individual residences (T.R. Fowler, Bedford County Health Department, oral commun., 2012). The area has a growing rural population which has expanded from approximately 38,300 residents in 1985 to 68,700 residents in 2010 (Maupin and others, 2014). To meet future water needs of individual residences, additional domestic development of these bedrock aquifers is likely. Previous hydrologic work in rural areas of the central Piedmont and Blue Ridge Physiographic Provinces of Virginia is limited, and basic knowledge of aquifer systems in this area is needed to support the expanding economy and growing population of Bedford County. From 2006 to 2014, the U.S. Geological Survey (USGS), in cooperation with the Bedford County Board of Supervisors and the Virginia Department of Environmental Quality (DEQ), collected hydrologic data in Bedford County to assess county-wide groundwater conditions and provide technical data and a scientific foundation that could be used as a basis for management and future planning of Bedford County water resources. A conceptual model of groundwater flow in Bedford County was developed based on (1) previous studies in the Piedmont and Blue Ridge fractured-rock aquifers, (2) compilation of existing data, and (3) results of new hydrologic data collected from wells and streams. Base-flow yields, general well construction information, and borehole 1U.S. Geological Survey. 2Virginia Department of Environmental Quality. 2 Hydrogeology and Simulation of Groundwater Flow in Fractured-Rock Aquifers, Bedford County, Virginia logs were summarized to support conceptualization of geologic features controlling the occurrence of groundwater in the Piedmont and Blue Ridge fractured-rock aquifers of Bedford County. A numerical model simulating groundwater flow in the aquifers was constructed as a component of this investigation to evaluate the conceptual model and estimate steady-state groundwater budgets for areas within Bedford County that drain to the Big Otter River, Goose Creek, the James River, and Smith Mountain and Leesville Lakes. Purpose and Scope This report provides a description of the hydrogeology and groundwater availability of the fractured-rock aquifer systems in Bedford County, Va. The primary purpose of the data collection and groundwater-flow simulation conducted as part of this study in Bedford County is to provide hydrogeologic information that can be used to guide the development and management of these important water resources in context of long-term aquifer inflows and outflows. The scope of this study included (1) the drilling of three new bedrock monitoring wells; (2) establishment of a continuous and biannual groundwater-level network; (3) continuous and partial-record measurement of stream discharge in the Big Otter River and Goose Creek Basins; and (4) borehole geophysical logging of five wells in Bedford County. Well completion reports from local and State health departments and archival State and Federal records were synthesized to document the variability in well construction and yields among hydrogeologic units. This report also documents the development of a numerical model to synthesize all currently available data and evaluate the conceptualization of groundwater flow in the fractured-rock aquifers of Bedford County at a scale of hundreds of square miles. Extrapolation of model results to smaller-scale domains would require more hydrogeologic detail than is currently (2015) available. Description of Study Area Bedford County encompasses 764 square miles (mi2) in Virginia’s Piedmont and Blue Ridge Physiographic Provinces (fig. 1), two physiographic regions that extend over much of the central portion of Virginia. The two physiographic regions are defined by large topographic differences. The Piedmont is characterized by rolling and hilly terrain while the Blue Ridge has much steeper slopes. The Piedmont in Bedford County ranges in elevation from 800 feet (ft) to 2,100 ft above sea level, while elevations in the Blue Ridge are as much as 4,000 ft. The county is bounded by the Blue Ridge Mountains on the west, the James River on the northeast, Smith Mountain and Leesville Lakes on the south, and Campbell County on the east. The county contains the headwaters of Goose Creek and Big Otter River, which are major tributaries to the Roanoke River. Bedford County has a mild climate with an average annual precipitation of 45.6 inches per year (in/yr) and a mean maximum daily temperature of 67.4 degrees Fahrenheit (PRISM Climate Group, Oregon State University, 2014). Climate station data for Bedford County were obtained from the National Oceanic and Atmospheric Administration (NOAA) National Climate Data Center (National Oceanic and Atmospheric Administration, 2014). Available precipitation data within or near Bedford County for which periods of data were available for the current normal climatological period 1981–2010 included five sites (table 1; fig. 1). Two of the sites (Holcomb Rock and Lynchburg #2) are within the James River Basin, two of the sites (Bedford 4 NW and Bedford) are within the Big Otter River Basin, and the remaining site (Huddleston 4 SW) is within the Goose Creek Basin. Mean annual precipitation for the climatological period 1981–2010 decreases in an easterly direction, ranging from 46.5 in/yr (Holcomb Rock) to 41.5 in/yr (Lynchburg #2) (fig. 1; table 1). Mean monthly precipitation amounts among Table 1. NOAA climate stations in Bedford County, Virginia. [Site locations shown in figure 1. Abbreviations: ft, feet above National Geodetic Vertical Datum of 1929; NOAA, National Oceanic and Atmospheric Administration; in/yr, inches per year; NAD 83, North American Datum of 1983] Station identification number Station name Latitude (decimal degrees) Longitude (decimal degrees) Datum Elevation (ft) Operating agency Period of record (calendar years)1 NOAA climatological period 1981–2010 mean annual precipitation (in/yr) 440561 Bedford 4 NW 37.380 –79.561 NAD 83 1,220 NOAA 1973–2014 44.2 440551 Bedford 37.348 –79.523 NAD 83 975 NOAA 1948–2006 45.1 444039 Holcomb Rock 37.544 –79.403 NAD 83 620 NOAA 1960–2014 46.5 444148 Huddleston 4 SW 37.126 –79.526 NAD 83 1,045 NOAA 1950–2014 42.5 445117 Lynchburg #2 37.385 –79.229 NAD 83 740 NOAA 1997–2014 41.5 1Discontinuous record and data gaps may exist within ranges of years.

Assessing potential effects of changes in water use with a numerical groundwater-flow model of Carson Valley, Douglas County, Nevada, and Alpine County, California

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