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Load estimation and trend analysis for nitrogen, phosphorus, and suspended sediment in the Eucha-Spavinaw drainage area, northeastern Oklahoma and northwestern Arkansas, 2011–18

Lake Eucha is a source of water for public supply and recreation for the residents of Tulsa and other municipalities in northeastern Oklahoma. Beaty Creek and Spavinaw Creek flow into Lake Eucha and drain about 388 square miles of agricultural and forested land in northeastern Oklahoma and northwestern Arkansas. Beginning in the 1990s, eutrophication of Lake Eucha characterized by excessive algal blooms resulted in taste and odor problems associated with lake water when it is used for public supply. The predominant sources of phosphorus in the Eucha-Spavinaw drainage area were identified by previous investigators as runoff from fertilized agricultural areas (nonpoint sources) and treated effluent from a wastewater-treatment plant (point source). To further evaluate the transport of nitrogen, phosphorus, and suspended sediment in the Eucha-Spavinaw drainage area, the U.S. Geological Survey (USGS), in collaboration with the City of Tulsa, estimated the loads and computed temporal trends of these constituents from water-quality and streamflow data collected at five USGS streamgages in the Beaty Creek and Spavinaw Creek subbasins. Estimates and comparisons of total nitrogen, total phosphorus, and suspended-sediment loads from the Beaty Creek and Spavinaw Creek subbasins to Lake Eucha during 2011–18 were made by using different types of regression equations. The first type of regression equation is referred to as “daily mean load regression equations” and was developed from water-quality data obtained from periodic water-quality samples and daily mean streamflow data collected at five USGS streamgages. The second type of regression equation is referred to as “instantaneous continuous load regression equations.” In addition to water-quality data obtained from periodic water-quality samples, continuous real-time (every 15 minutes) measurements of physicochemical properties (specific conductance, water temperature, and turbidity), and continuous streamflow data were used to estimate instantaneous continuous loads of total nitrogen, total phosphorus, and suspended sediment at two of the same five streamgages where daily mean loads were estimated. The use of these two types of regression equations was documented by previous investigators who estimated loads of total nitrogen, total phosphorus, and suspended sediment in the study area by using data collected during 2002–10. The regression equations used to estimate constituent loads that were based on water-quality data obtained from periodic water-quality samples and continuous water-quality and streamflow data (instantaneous continuous load regression equations) better described the temporal variance in constituent loads compared to the regression equations based only on periodic water-quality data and daily mean streamflows (daily mean load regression equations). Estimates computed using instantaneous continuous load regression equations showed that mean annual loads of 1,844,000 pounds of total nitrogen, 150,300 pounds of total phosphorus, and 78,735,000 pounds of suspended sediment were transported into Lake Eucha from the Beaty Creek and Spavinaw Creek subbasins. Most of the estimated mean annual loads from the Beaty Creek and Spavinaw Creek subbasins entered Lake Eucha during runoff conditions, including about 80 percent of total nitrogen, 95 percent of total phosphorus, and 98 percent of suspended sediment. Daily, annual, and mean annual load estimates varied substantially, depending on streamflow conditions and the independent variables used to develop the regression equations. Daily and annual loads estimated from instantaneous continuous load regression equations that included specific conductance, water temperature, turbidity, and streamflow described the variability in the field data better than did loads estimated from daily mean load regression equations that included streamflow, seasonality, and time. Loads estimated from the instantaneous continuous load regression equations generally were greater than those estimated from the daily mean load regression equations. Temporal trends in total nitrogen concentrations showed statistically significant (probability value less than or equal to 0.05) downward trends during both base-flow and runoff conditions at all five USGS streamgages except for the streamgage 07191179 Spavinaw Creek near Cherokee City, Ark. Temporal trends in total phosphorus concentrations were not consistent between streamgages over the study period, showing upward and downward trends throughout the Eucha-Spavinaw drainage area. Total phosphorus concentrations during base-flow and runoff conditions showed statistically significant upward trends at USGS streamgages 07191160 Spavinaw Creek near Maysville, Ark., and 07191222 Beaty Creek near Jay, Okla. Total phosphorus concentrations showed a statistically significant downward trend during base-flow conditions at USGS streamgage 071912213 Spavinaw Creek near Colcord, Okla., and in both base-flow and runoff conditions at USGS streamgage 07191179 Spavinaw Creek near Cherokee City, Ark. Temporal trends in suspended-sediment concentrations were not consistent between streamgages over the study period and were similar to temporal trends in total phosphorus concentrations.

Arkansas, Oklahoma

Analysis of the variability in ground-motion synthesis and inversion

In almost all past inversions of large-earthquake ground motions for rupture behavior, the goal of the inversion is to find the “best fitting” rupture model that predicts ground motions which optimize some function of the difference between predicted and observed ground motions. This type of inversion was pioneered in the linear-inverse sense by Olson and Apsel (1982), who minimized the square of the difference between observed and simulated motions (“least squares”) while simultaneously minimizing the rupture-model norm (by setting the null-space component of the rupture model to zero), and has been extended in many ways, one of which is the use of nonlinear inversion schemes such as simulated annealing algorithms that optimize some other misfit function. For example, the simulated annealing algorithm of Piatanesi and others (2007) finds the rupture model that minimizes a “cost” function which combines a least-squares and a waveform-correlation measure of misfit. All such inversions that look for a unique “best” model have at least three problems. (1) They have removed the null-space component of the rupture model—that is, an infinite family of rupture models that all fit the data equally well have been narrowed down to a single model. Some property of interest in the rupture model might have been discarded in this winnowing process. (2) Smoothing constraints are commonly used to yield a unique “best” model, in which case spatially rough rupture models will have been discarded, even if they provide a good fit to the data. (3) No estimate of confidence in the resulting rupture models can be given because the effects of unknown errors in the Green’s functions (“theory errors”) have not been assessed. In inversion for rupture behavior, these theory errors are generally larger than the data errors caused by ground noise and instrumental limitations, and so overfitting of the data is probably ubiquitous for such inversions. Recently, attention has turned to the inclusion of theory errors in the inversion process. Yagi and Fukahata (2011) made an important contribution by presenting a method to estimate the uncertainties in predicted large-earthquake ground motions due to uncertainties in the Green’s functions. Here we derive their result and compare it with the results of other recent studies that look at theory errors in a Bayesian inversion context particularly those by Bodin and others (2012), Duputel and others (2012), Dettmer and others (2014), and Minson and others (2014). Notably, in all these studies, the estimates of theory error were obtained from theoretical considerations alone; none of the investigators actually measured Green’s function errors. Large earthquakes typically have aftershocks, which, if their rupture surfaces are physically small enough, can be considered point evaluations of the real Green’s functions of the Earth. Here we simulate smallaftershock ground motions with (erroneous) theoretical Green’s functions. Taking differences between aftershock ground motions and simulated motions to be the “theory error,” we derive a statistical model of the sources of discrepancies between the theoretical and real Green’s functions. We use this model with an extended frequency-domain version of the time-domain theory of Yagi and Fukahata (2011) to determine the expected variance 2 τ caused by Green’s function error in ground motions from a larger (nonpoint) earthquake that we seek to model. We also differ from the above-mentioned Bayesian inversions in our handling of the nonuniqueness problem of seismic inversion. We follow the philosophy of Segall and Du (1993), who, instead of looking for a best-fitting model, looked for slip models that answered specific questions about the earthquakes they studied. In their Bayesian inversions, they inductively derived a posterior probability-density function (PDF) for every model parameter. We instead seek to find two extremal rupture models whose ground motions fit the data within the error bounds given by 2 τ , as quantified by using a chi-squared test described below. So, we can ask questions such as, “What are the rupture models with the highest and lowest average rupture speed consistent with the theory errors?” Having found those models, we can then say with confidence that the true rupture speed is somewhere between those values. Although the Bayesian approach gives a complete solution to the inverse problem, it is computationally demanding: Minson and others (2014) needed 1010 forward kinematic simulations to derive their posterior probability distribution. In our approach, only about107 simulations are needed. Moreover, in practical application, only a small set of rupture models may be needed to answer the relevant questions—for example, determining the maximum likelihood solution (achievable through standard inversion techniques) and the two rupture models bounding some property of interest. The specific property that we wish to investigate is the correlation between various rupturemodel parameters, such as peak slip velocity and rupture velocity, in models of real earthquakes. In some simulations of ground motions for hypothetical large earthquakes, such as those by Aagaard and others (2010) and the Southern California Earthquake Center Broadband Simulation Platform (Graves and Pitarka, 2015), rupture speed is assumed to correlate locally with peak slip, although there is evidence that rupture speed should correlate better with peak slip speed, owing to its dependence on local stress drop. We may be able to determine ways to modify Piatanesi and others’s (2007) inversion’s “cost” function to find rupture models with either high or low degrees of correlation between pairs of rupture parameters. We propose a cost function designed to find these two extremal models.

Open-File Report

Simulation of groundwater flow and brine discharge to the Dolores River in the Paradox Valley, Montrose County, Colorado

Salinity, or total dissolved solids (TDS), of the Colorado River affects agricultural, municipal, and industrial water users and is an important concern in the Western United States. In the Paradox Valley of southwestern Colorado, natural discharge of sodium-chloride brine to the Dolores River from the underlying core of a salt-valley anticline accounts for about 6 percent of the salinity load to the Colorado River. Formation of the Paradox Valley began during the Miocene, and subsequent erosion exposed the Pennsylvania Paradox Formation in the core of the anticline where a cap rock, collapse features, breccia, and sodium-chloride saturated brine developed at the top of the exposed salt diapir. The discharge of brine to the Dolores River is affected by these dissolution features, along with seasonal hydrologic conditions and density-dependent flow between older dense brine and the younger fresh groundwater in the overlying alluvial aquifer. To reduce TDS concentrations in the Dolores River through the Paradox Valley, the Bureau of Reclamation has pumped brine from a series of shallow wells adjacent to the river since July 1996. The pumped brine is collected and piped to a deep disposal well where it is injected into the Mississippian Leadville Limestone at a depth of about 4,570-meters below land surface. The pumping and injection operation is collectively known as the Paradox Valley Unit (PVU), and by 2015, the PVU had substantially reduced TDS concentrations in the Dolores River by about 70 percent. Since 2019, injection-pressure limits and related seismic activity have constrained deep-well injection and thus brine pumping at the PVU. In cooperation with the Bureau of Reclamation, the U.S. Geological Survey developed a MODFLOW-6 three-dimensional, variable-density groundwater flow and TDS transport model of the Paradox Valley to evaluate the effects of PVU pumping operations on brine discharge to the Dolores River and to guide additional research. The finite-difference model grid consists of 76 rows and 48 columns oriented from northwest to southeast in alignment with valley topography and groundwater-flow directions in the near-surface freshwater alluvial aquifer. A 7-layer hydrogeologic framework was developed from existing datasets to represent the alluvial aquifer, cap rock, collapse breccia, and groundwater flow and TDS transport from the underlying Paradox Formation salt to the Dolores River. The model represents a 33-year transient calibration period from 1987 through 2020 that includes pre-PVU conditions from 1987 through June 1996 and post-PVU conditions from July 1996 through 2020. A 1,000-year simulation of groundwater flow and coupled TDS transport computed the initial conditions for the subsequent 33-year transient simulation. Observations of precipitation, streamflow, evaporation, agricultural land use, and PVU brine pumping rates were used to specify appropriate boundary conditions to the model representing time-varying recharge, tributary streamflow, groundwater underflow, evapotranspiration (ET), and PVU pumping. Values for average monthly streamflow and TDS concentration at the upstream streamgage, the Dolores River at Bedrock (USGS streamgage 09169500), were specified as model input where the Dolores River enters Paradox Valley. Observed pumping from the PVU, water levels and TDS concentrations in groundwater, and streamflow and estimated TDS concentrations at the downstream streamgage, the Dolores River near Bedrock (USGS streamgage 09171100), were calibration targets that constrained the manual calibration of model parameters representing aquifer hydraulic conductivity, storage, streambed conductance, recharge, and (ET). Two primary model-calibration targets were the match between observed and simulated TDS mass flux from PVU pumping wells and the match between estimated and simulated TDS mass flux to the Dolores River. The simulated TDS mass withdrawn by pumping wells is calculated by the model as the product of the assigned pumping rate and simulated groundwater TDS concentrations. Because actual pumping rates were assigned as simulated values, the total simulated PVU pumping for the 33-year calibration is within 0.5 percent of the observed values. However, simulated concentrations and thus mass flux of TDS withdrawn by the PVU pumping wells were consistently about 26 percent less than observed values for all the simulated time periods (33-year simulation, pre-PVU, and post-PVU). The representation of brine inflow was explored through additional modeling to evaluate the effect of the simulated brine source on groundwater TDS concentrations. Results indicated that a saturated-salt constant-flux brine source best replicated the magnitude and transient pattern observed for TDS mass flux from PVU pumping wells. The simulated TDS mass flux to the Dolores River is compared to estimates based on observed streamflow and specific conductance (SC) data for the downstream streamgage. The calibrated model provided a close fit of simulated to measured streamflow at the downstream streamgage, and the calibrated model fit to estimated TDS concentrations at the downstream streamgage was reasonable. The greatest differences between simulated and estimated values occurred during drought periods from June 2000 to March 2003, May 2012 to June 2013, and October 2013 to October 2014, when simulated TDS concentrations in the river were greater than estimated concentrations. In general, simulated TDS mass flux to the river for the pre-PVU period is in good agreement with estimated values (2-percent difference), but the model overestimated TDS mass flux to the river by about 41 percent during the post-PVU period. The model uncertainty with respect to TDS mass flux to the river indicates other processes or model parameters not well represented by the model are affecting the system, especially during drought. During model calibration, the most sensitive parameters were identified as vertical hydraulic conductivity of the alluvial aquifer, conductance of the Dolores River streambed, ET extinction depth and rate, and recharge rate. Five 5-year scenarios of conditions for 2021–25 were simulated to assist evaluation of alternative strategies to manage the discharge of brine into the Dolores River. The first scenario simulates no PVU pumping and serves as a base case for comparison to the other scenarios. Two scenarios simulate the effects of varying withdrawal timing at an annual rate about one-third less than during 2010 through 2018. During high-flow spring snowmelt runoff periods when brine discharge is naturally minimized, PVU pumping does not substantially affect salinity in the Dolores River, and comparison of these two scenarios indicates that scheduling brine withdrawals during times of low river stage is nearly as effective at reducing TDS mass flux to the river as pumping brine year-round. Cessation of pumping during periods of high river stage may be advantageous for system maintenance, brine injection, and seismic-risk reduction. The fourth scenario tested the effect of reducing irrigation-return flow on brine discharge and predicted a slight reduction of TDS mass flux to the Dolores River, but not as great a reduction as that of using the PVU to remove brine. The fifth scenario simulated 5 years of drought conditions without PVU pumping and indicates brine discharge during drought about 15 percent greater than during average hydrologic conditions. Results from scenario 5 are consistent with the calibrated model results and indicate that aquifer properties and ET processes and parameters may be affecting simulation results during drought. The Paradox Valley groundwater model provides a reasonable overall match to observed conditions in the Dolores River. The model is useful for evaluating relative differences between brine management scenarios to inform PVU operational decisions and to identify gaps in data and process understanding. Representation of the brine source, hydraulic-conductivity parameters, and recharge and ET processes were identified as potential areas for additional field and modeling research. Additional research in the Paradox Valley might include field-data collection that provides additional information on the hydrogeologic framework, groundwater levels, groundwater TDS concentrations, stream characteristics, and aquifer properties. Additional modeling efforts could benefit from applying advanced tools for model development, calibration, and visualization including parameter-estimation and sensitivity analysis. Statistical evaluation of known model uncertainties such as hydraulic conductivity, streambed conductance, representations of the brine source, recharge, and ET could improve the match between simulated and estimated TDS mass flux from PVU pumping wells and to the Dolores River further informing model predictions and system understanding for the Paradox Valley.

Colorado

The use of process models to inform and improve statistical models of nitrate occurrence, Great Miami River Basin, southwestern Ohio

Statistical models of nitrate occurrence in the glacial aquifer system of the northern United States, developed by the U.S. Geological Survey, use observed relations between nitrate concentrations and sets of explanatory variables—representing well-construction, environmental, and source characteristics— to predict the probability that nitrate, as nitrogen, will exceed a threshold concentration. However, the models do not explicitly account for the processes that control the transport of nitrogen from surface sources to a pumped well and use area-weighted mean spatial variables computed from within a circular buffer around the well as a simplified source-area conceptualization. The use of models that explicitly represent physical-transport processes can inform and, potentially, improve these statistical models. Specifically, groundwater-flow models simulate advective transport—predominant in many surficial aquifers— and can contribute to the refinement of the statistical models by (1) providing for improved, physically based representations of a source area to a well, and (2) allowing for more detailed estimates of environmental variables. A source area to a well, known as a contributing recharge area, represents the area at the water table that contributes recharge to a pumped well; a well pumped at a volumetric rate equal to the amount of recharge through a circular buffer will result in a contributing recharge area that is the same size as the buffer but has a shape that is a function of the hydrologic setting. These volume-equivalent contributing recharge areas will approximate circular buffers in areas of relatively flat hydraulic gradients, such as near groundwater divides, but in areas with steep hydraulic gradients will be elongated in the upgradient direction and agree less with the corresponding circular buffers. The degree to which process-model-estimated contributing recharge areas, which simulate advective transport and therefore account for local hydrologic settings, would inform and improve the development of statistical models can be implicitly estimated by evaluating the differences between explanatory variables estimated from the contributing recharge areas and the circular buffers used to develop existing statistical models. The larger the difference in estimated variables, the more likely that statistical models would be changed, and presumably improved, if explanatory variables estimated from contributing recharge areas were used in model development. Comparing model predictions from the two sets of estimated variables would further quantify—albeit implicitly—how an improved, physically based estimate of explanatory variables would be reflected in model predictions. Differences between the two sets of estimated explanatory variables and resultant model predictions vary spatially; greater differences are associated with areas of steep hydraulic gradients. A direct comparison, however, would require the development of a separate set of statistical models using explanatory variables from contributing recharge areas. Area-weighted means of three environmental variables—silt content, alfisol content, and depth to water from the U.S. Department of Agriculture State Soil Geographic (STATSGO) data—and one nitrogen-source variable (fertilizer-application rate from county data mapped to Enhanced National Land Cover Data 1992 (NLCDe 92) agricultural land use) can vary substantially between circular buffers and volume-equivalent contributing recharge areas and among contributing recharge areas for different sets of well variables. The differences in estimated explanatory variables are a function of the same factors affecting the contributing recharge areas as well as the spatial resolution and local distribution of the underlying spatial data. As a result, differences in estimated variables between circular buffers and contributing recharge areas are complex and site specific as evidenced by differences in estimated variables for circular buffers and contributing recharge areas of existing public-supply and network wells in the Great Miami River Basin. Large differences in areaweighted mean environmental variables are observed at the basin scale, determined by using the network of uniformly spaced hypothetical wells; the differences have a spatial pattern that generally is similar to spatial patterns in the underlying STATSGO data. Generally, the largest differences were observed for area-weighted nitrogen-application rate from county and national land-use data; the basin-scale differences ranged from -1,600 (indicating a larger value from within the volume-equivalent contributing recharge area) to 1,900 kilograms per year (kg/yr); the range in the underlying spatial data was from 0 to 2,200 kg/yr. Silt content, alfisol content, and nitrogen-application rate are defined by the underlying spatial data and are external to the groundwater system; however, depth to water is an environmental variable that can be estimated in more detail and, presumably, in a more physically based manner using a groundwater-flow model than using the spatial data. Model-calculated depths to water within circular buffers in the Great Miami River Basin differed substantially from values derived from the spatial data and had a much larger range. Differences in estimates of area-weighted spatial variables result in corresponding differences in predictions of nitrate occurrence in the aquifer. In addition to the factors affecting contributing recharge areas and estimated explanatory variables, differences in predictions also are a function of the specific set of explanatory variables used and the fitted slope coefficients in a given model. For models that predicted the probability of exceeding 1 and 4 milligrams per liter as nitrogen (mg/L as N), predicted probabilities using variables estimated from circular buffers and contributing recharge areas generally were correlated but differed significantly at the local and basin scale. The scale and distribution of prediction differences can be explained by the underlying differences in the estimated variables and the relative weight of the variables in the statistical models. Differences in predictions of exceeding 1 mg/L as N, which only includes environmental variables, generally correlated with the underlying differences in STATSGO data, whereas differences in exceeding 4 mg/L as N were more spatially extensive because that model included environmental and nitrogen-source variables. Using depths to water from within circular buffers derived from the spatial data and depths to water within the circular buffers calculated from the groundwater-flow model, restricted to the same range, resulted in large differences in predicted probabilities. The differences in estimated explanatory variables between contributing recharge areas and circular buffers indicate incorporation of physically based contributing recharge area likely would result in a different set of explanatory variables and an improved set of statistical models. The use of a groundwater-flow model to improve representations of source areas or to provide more-detailed estimates of specific explanatory variables includes a number of limitations and technical considerations. An assumption in these analyses is that (1) there is a state of mass balance between recharge and pumping, and (2) transport to a pumped well is under a steady state flow field. Comparison of volumeequivalent contributing recharge areas under steady-state and transient transport conditions at a location in the southeastern part of the basin shows the steady-state contributing recharge area is a reasonable approximation of the transient contributing recharge area after between 10 and 20 years of pumping. The first assumption is a more important consideration for this analysis. A gradient effect refers to a condition where simulated pumping from a well is less than recharge through the corresponding contributing recharge area. This generally takes place in areas with steep hydraulic gradients, such as near discharge locations, and can be mitigated using a finer model discretization. A boundary effect refers to a condition where recharge through the contributing recharge area is less than pumping. This indicates other sources of water to the simulated well and could reflect a real hydrologic process. In the Great Miami River Basin, large gradient and boundary effects—defined as the balance between pumping and recharge being less than half—occurred in 5 and 14 percent of the basin, respectively. The agreement between circular buffers and volume-equivalent contributing recharge areas, differences in estimated variables, and the effect on statisticalmodel predictions between the population of wells with a balance between pumping and recharge within 10 percent and the population of all wells were similar. This indicated process-model limitations did not affect the overall findings in the Great Miami River Basin; however, this would be model specific, and prudent use of a process model needs to entail a limitations analysis and, if necessary, alterations to the model.

Ohio

Evaluation of some software measuring displacements using GPS in real-time

For the past decade, the USGS has been monitoring deformation at various locations in the western United States using continuous GPS. The main focus of these measurements are estimates of displacement averaged over one day. Essentially, these consist of recording at 30 seconds intervals the carrier-frequency phase-data (equivalent to travel-time) between a GPS receiver and the GPS satellite network. In turn, these observations, which are converted to pseudo—ranges, are processed using one of the “research grade” programs (GIPSY, Zumberge et al., or GAMIT, wwwgpsg.mit.edu/~simon/gtgk) to estimate the position of the GPS receiver averaged over 24 hours. However, it is possible and desirable to estimate the position of the receiver (actually the antenna) more frequently and to do this within a few seconds of the time actual measurement (known as real-time). A recent example, the 2004 Magnitude 6, Parkfield, California earthquake, demonstrated that having GPS estimates of position more frequently than simply a daily average is required if one requires discrimination between co-seismic and post-seismic deformation (Langbein et al., 2006). The high-rate estimates of position obtained at Parkfield show that post-seismic deformation started less than one-hour after the mainshock and that this deformation was roughly the same magnitude as the co-seismic deformation. The high-rate solutions for Parkfield were done by others including Yehuda Bock at UCSD and Kristine Larson at U. of Colorado, but not the USGS. The Parkfield experience points out the need for an in-house capability by the USGS to be able to accurately measure co-seismic displacements and other rapid, deformation signals using GPS. This applies to both the Earthquake and Volcano Hazard programs. Although at many locations where we monitor deformation, we have strainmeters and tiltmeters in addition to GPS which, in principle, are far more sensitive to rapid deformation over periods of less than a day (Langbein and Bock, 2004). But, not all locales include strain and tiltmeters. Thus, having the capability to extract signals with periods of less than a day is desirable since the distribution of GPS is more extensive than strain and tilt. At both Parkfield and Long Valley, the USGS has been using other software packages to process the GPS data at sub-daily intervals and in real-time. The underlying goal of these types of measurements is to detect any deformation event as it evolves; the 24 hour processing might not provide timely results if such a deformation event is precursory to a geologic hazard (an earthquake for Parkfield and either a volcanic event or an earthquake for Long Valley). In Long Valley, We use the software package called 3DTracker (http://www.3dtracker.com, http://www.condorearth.com) to estimate the changes of in position of a remote site relative to a “fixed” site. The 3DTracker software uses double difference GPS code measurements and receiversatellite-time triple differences from one epoch to the next of the GPS phase data (a proxy for travel-time measurements) and employs a Kalman filter to obtain stability in the estimate of position. That is, the estimate of the current position depends upon the estimate of the prior position. Hence, a time series of position looks fairly smooth depending upon the coefficient selected for the Kalman filter. With triple differences, the sometimes troublesome initial integer cycle ambiguity terms cancel (number of wavelengths between the receiver and each satellite), but only the incremental change in position is calculated. This triple difference Kalman filter solution is slow to converge and less accurate than a double difference (e.g., RTD, Track) solution, but it is robust and computationally efficient (Remondi and Brown, 2000). 3D-Tracker allows use of various single-frequency and dual-frequency GPS phase and code observables including the ionospheric-free combinations (known as LC or L3 and P(L3)) formed from an linear combination of the L1 and L2 carrier phase and code data. The lowest noise observable is the L1 carrier, but it is biased by ionospheric refraction that has amplitudes of about 1 to 10 ppm. This results in a systematic scale error in the relative positions. The L3 phase noise is about 3 times greater than the L1 phase noise, but it is generally used to solve for all but the shortest baselines (< 5 km). In addition, the software does output the position changes is a standard format that can be used for other analysis. At Parkfield, we use the software package called RTD (http://www.geodetics.com). The RTD software has been described in the literature (Bock et al., 2000) but basically, it estimates the position without the constraint of a Kalman filter. It uses double differences (in our studies the LC or ionospheric free observable is used) and the integer ambiguities are resolved independently for each 1-second measurement; Most GPS software that use double-differences require several epochs of measurements to resolve the integer ambiguities. The data files use a proprietary format and can not be read by me or others; rather, Yehuda Bock at UCSD (and author of RTD) translates these files into a standard format that can be read by me. Recently, Tom Herring of MIT has modified the GAMIT software to process kinematically GPS data (www-gpsg.mit.edu/~simon/gtgk/tutorial/Lecture_13.pdf). At this time, the software, known as TRACK, does not process the observations in real-time. Consequently, the latency between the time of the observation and the time when a position estimate is available depends upon the frequency that the data are downloaded and the speed of actually processing the observations; there could be a delay of an hour or two before the a position estimates are available. Unlike RTD and 3DTracker, TRACK comes with GAMIT (which is distributed freely) and is currently operating in a test mode at the USGS office in Pasadena. The LC or ionosphere free observable is used in our TRACK solutions. JPL has a version of their GIPSY software called “Real-time GIPSY (RTG)” (gipsy.jpl.nasa.gov/orms/rtg), which, like TRACK, can process the pseudo-range data “off—line”. However, this software is not freely distributed. Instead, at least one company, NAVCOM, has teamed with JPL to integrate RTG with GPS receivers and telemetry that yields positions in realtime. Kristine Larson of University of Colorado has modified the original GIPSY to estimate positions kinematically. Again, like TRACK, the positions are estimated off—line. Much of her research is described in Larson et al. (2003), and Choi et al. (2004). For Long Valley, out of the 17 GPS sites, we monitor 5 baselines within the caldera at 5 second intervals relative to the Bald Mountain site at the edge of the caldera using 3DTracker. The baseline measurement using 3DTracker consists of determination of the 3 dimensional positions of the 5 remote points (GPS receivers) relative to a GPS site at Bald. A second, independent system collects and downloads once a day the 30-second data used for the 24-hour solutions for the 12 sites not monitored with 3DTracker. For the sites monitored with 3DTracker, the pseudo—range data are decimated to 30 seconds and converted to a form used for the 24-hour solutions. Both sets of telemetry employ 900 MHz spread spectrum radios which require line of site between all of the links. The telemetry for the 3DTracker sites require a dedicated radios at each end and intermediate repeaters as needed, while the telemetry required for the other sites use a single master radio, repeaters as needed, and a radio at each remote site. (The 5 sites being monitored with 3DTracker require 13 radios.) At Parkfield, RTD is used to measure the position changes all 12 baselines at 1 second intervals relative to a site, Pomm, adjacent to the San Andreas Fault. The complete RTD package (hardware and software) collects all of the data and determines the position of each site relative to Pomm. In addition, the system stores both the 1-second and 30-second pseudo-range data for later downloading which are ultimately used in the 24-hour solutions. To do this, each site has a 2.4 GHz radio and a telemetry buffer. The telemetry buffer holds 24-hours of data (in the event that the telemetry link is broken) and converts the RS232 data stream from the GPS receiver into a form compatible with an IP (Internet protocol) network connection. In contrast with the Long Valley system, the telemetry link for GPS at Parkfield consists of a single radio at each remote sites and a single radio at the central site. Although position estimates are produced within 1-second of the observations, these results are not immediately available because there is no high speed Internet connection to Parkfield. Instead, the data are stored on a removable disk and sent to UCSD once per month. Below, I describe the results of a simple experiment to examine the response of some of these systems to simulated deformation that could be an analogue of a tectonic or volcanic event. In many engineering applications, the system response is tested by inputting a step to the system and measuring the output of the system. Essentially, this is what I've done. The experiment described below moves the GPS antenna from its original position to a new position within 1 second; the software tracks the translation. These measurements were conducted in August 2004 with the RTD software at Parkfield, and twice in Long Valley. The first Long Valley test was conducted in September 2004 using 3DTracker on a single baseline. The test was repeated in September 2005 using 3DTracker on two baselines and, importantly, saving the RINEX files of the data so that the data could be replayed through 3DTracker using other options in the program and, using other software packages including TRACK. In addition, we observed a short-term event at the Three Sisters volcano in Oregon. This event was snow melt at a remote GPS site which gave an apparent 15 cm displacement in vertical in less than one-day. 3DTracker is used to monitor this site, and the event was captured with this software. In addition, with the assistance of others, I got additional estimates of position using other software packages; those results are presented. Finally, the precision of both 3DTracker and RTD are compared using a power spectrum. Those results would suggest that 3DTracker using appropriate Kalman filter coefficients would have better precision than RTD; instead, the lower noise level from 3DTracker is a result of smoothing from the Kalman filter. Given the results described in this report, high-rate GPS is certainly capable of accurately measuring displacements of 1 centimeter with a high degree of statistical confidence. Plotting these results show that the time of the displacement can be visually determined to that of the sampling interval of the data. However, especially with small amplitude signals, any of the software packages can yield erroneous deformation “signals” that are either due excess travel-time of the GPS carrier frequency from multipath or a limitation in the software. Thus, the time series of displacements must be viewed with caution and knowledge of external circumstances that might cause a change in position. The casual reader should continue with the next section describing the methods then jump to the last two sections for the discussion and conclusions. I have made some recommendations there.

Open-File Report

Flood-frequency analyses from paleoflood investigations for Spring, Rapid, Boxelder, and Elk Creeks, Black Hills, western South Dakota

Flood-frequency analyses for the Black Hills area are important because of severe flooding of June 9-10, 1972, that was caused by a large mesoscale convective system and caused at least 238 deaths. Many 1972 peak flows are high outliers (by factors of 10 or more) in observed records that date to the early 1900s. An efficient means of reducing uncertainties for flood recurrence is to augment gaged records by using paleohydrologic techniques to determine ages and magnitudes of prior large floods (paleofloods). This report summarizes results of paleoflood investigations for Spring Creek, Rapid Creek (two reaches), Boxelder Creek (two subreaches), and Elk Creek. Stratigraphic records and resulting long-term flood chronologies, locally extending more than 2,000 years, were combined with observed and adjusted peak-flow values (gaged records) and historical flood information to derive flood-frequency estimates for the six study reaches. Results indicate that (1) floods as large as and even substantially larger than 1972 have affected most of the study reaches, and (2) incorporation of the paleohydrologic information substantially reduced uncertainties in estimating flood recurrence. Canyons within outcrops of Paleozoic rocks along the eastern flanks of the Black Hills provided excellent environments for (1) deposition and preservation of stratigraphic sequences of late-Holocene flood deposits, primarily in protected slack-water settings flanking the streams; and (2) hydraulic analyses for determination of associated flow magnitudes. The bedrock canyons ensure long-term stability of channel and valley geometry, thereby increasing confidence in hydraulic computations of ancient floods from modern channel geometry. Stratigraphic records of flood sequences, in combination with deposit dating by radiocarbon, optically stimulated luminescence, and cesium-137, provided paleoflood chronologies for 29 individual study sites. Flow magnitudes were estimated from elevations of flood deposits in conjunction with hydraulic calculations based on modern channel and valley geometry. Reach-scale paleoflood chronologies were interpreted for each study reach, which generally entailed correlation of flood evidence among multiple sites, chiefly based on relative position within stratigraphic sequences, unique textural characteristics, or results of age dating and flow estimation. The FLDFRQ3 and PeakfqSA analytical models (assuming log-Pearson Type III frequency distributions) were used for flood-frequency analyses for as many as four scenarios: (1) analysis of gaged records only; (2) gaged records with historical information; (3) all available data including gaged records, historical flows, paleofloods, and perception thresholds; and (4) the same as the third scenario, but ?top fitting? the distribution using only the largest 50 percent of gaged peak flows. The PeakfqSA model is most consistent with procedures adopted by most Federal agencies for flood-frequency analysis and thus was (1) used for comparisons among results for study reaches, and (2) considered by the authors as most appropriate for general applications of estimating low-probability flood recurrence. The detailed paleoflood investigations indicated that in the last 2,000 years all study reaches have had multiple large floods substantially larger than in gaged records. For Spring Creek, stratigraphic records preserved a chronology of at least five paleofloods in approximately (~) 1,000 years approaching or exceeding the 1972 flow of 21,800 cubic feet per second (ft 3 /s). The largest was ~700 years ago with a flow range of 29,300-58,600 ft 3 /s, which reflects the uncertainty regarding flood-magnitude estimates that was incorporated in the flood-frequency analyses. In the lower reach of Rapid Creek (downstream from Pactola Dam), two paleofloods in ~1,000 years exceeded the 1972 flow of 31,200 ft 3 /s. Those occurred ~440 and 1,000 years ago, with flows of 128,000-256,000 and 64,000-128,000 ft 3 /s, respectively. Five smaller paleofloods of 9,500-19,000 ft 3 /s occurred between ~200 and 400 years ago. In the upper reach of Rapid Creek (above Pactola Reservoir), the largest recorded floods are substantially smaller than for lower Rapid Creek and all other study reaches. Paleofloods of ~12,900 and 12,000 ft 3 /s occurred ~1,000 and 1,500 years ago. One additional paleoflood (~800 years ago) was similar in magnitude to the largest gaged flow of 2,460 ft 3 /s Boxelder Creek was treated as having two subreaches because of two tributaries that affect peak flows. During the last ~1,000 years, paleofloods of ~39,000-78,000 ft 3 /s and 40,000-80,000 ft 3 /s in the upstream subreach have exceeded the 1972 peak flow of 30,800 ft 3 /s. One other paleoflood was similar to the second largest gaged flow (16,400 ft 3 /s in 1907). For the downstream subreach, paleofloods of 61,300-123,000 ft 3 /s and 52,500-105,000 ft 3 /s in the last ~1,000 years have substantially exceeded the 1972 flood (50,500 ft 3 /s). Four additional paleofloods had flows between 14,200 and 33,800 ft 3 /s. The 1972 flow on Elk Creek (10,400 ft 3 /s) has been substantially exceeded at least five times in the last 1,900 years. The largest paleoflood (41,500-124,000 ft 3 /s) was ~900 years ago. Three other paleofloods between 37,500 and 120,000 ft 3 /s occurred between 1,100 and 1,800 years ago. A fifth paleoflood of 25,500-76,500 ft 3 /s was ~750 years ago. Considering analyses for all available data (PeakfqSA model) for all six study reaches, the 95-percent confidence intervals about the low-probability quantile estimates (100-, 200-, and 500-year recurrence intervals) were reduced by at least 78 percent relative to those for the gaged records only. In some cases, 95-percent uncertainty intervals were reduced by 99 percent or more. For all study reaches except the two Boxelder Creek subreaches, quantile estimates for these long-term analyses were larger than for the short-term analyses. The 1972 flow for the Spring Creek study reach (21,800 ft 3 /s) corresponds with a recurrence interval of ~400 years. Recurrence intervals are ~500 years for the 1972 flood magnitudes along the lower Rapid Creek reach and the upstream subreach of Boxelder Creek. For the downstream subreach of Boxelder Creek, the large 1972 flood magnitude (50,500 ft 3 /s) exceeds the 500-year quantile estimate by about 35 percent. The recurrence interval of ~100 years for 1972 flooding along the Elk Creek study reach is small relative to other study reaches along the eastern margin of the Black Hills. All of the paleofloods plot within the bounds of a national envelope curve, indicating that the national curve represents exceedingly rare floods for the Black Hills area. Elk Creek, lower Rapid Creek, and the downstream subreach of Boxelder Creek all have paleofloods that plot above a regional envelope curve; in the case of Elk Creek, by a factor of nearly two. The Black Hills paleofloods represent some of the largest known floods, relative to drainage area, for the United States. Many of the other largest known United States floods are in areas with physiographic and climatologic conditions broadly similar to the Black Hills-semiarid and rugged landscapes that intercept and focus heavy precipitation from convective storm systems. The 1972 precipitation and runoff patterns, previous analyses of peak-flow records, and the paleoflood investigations of this study support a hypothesis of distinct differences in flood generation within the central Black Hills study area. The eastern Black Hills are susceptible to intense orographic lifting associated with convective storm systems and also have high relief, thin soils, and narrow and steep canyons-factors favoring generation of exceptionally heavy rain-producing thunderstorms and promoting runoff and rapid concentration of flow into stream channels. In contrast, storm potential is smaller in and near the Limestone Plateau area, and storm runoff is further reduced by substantial infiltration into the limestone, gentle topography, and extensive floodplain storage. Results of the paleoflood investigations are directly applicable only to the specific study reaches and in the case of Rapid Creek, only to pre-regulation conditions. Thus, approaches for broader applications were developed from inferences of overall flood-generation processes, and appropriate domains for application of results were described. Example applications were provided by estimating flood quantiles for selected streamgages, which also allowed direct comparison with results of at-site flood-frequency analyses from a previous study. Several broad issues and uncertainties were examined, including potential biases associated with stratigraphic records that inherently are not always complete, uncertainties regarding statistical approaches, and the unknown applicability of paleoflood records to future watershed conditions. The results of the paleoflood investigations, however, provide much better physically based information on low-probability floods than has been available previously, substantially improving estimates of the magnitude and frequency of large floods in these basins and reducing associated uncertainty.

South Dakota

Groundwater quality and geochemistry of West Virginia’s southern coal fields

Coal mining has been the dominant industry and land use in West Virginia’s southern coal fields since the mid-1800s. Mortality rates for a variety of serious chronic conditions, such as diabetes, heart disease, and some forms of cancer in Appalachian coal mining regions, are higher than in areas lacking substantial coal mining activity within the Appalachian Region or elsewhere in the United States. Causes of the increased mortality and morbidity are not clear, but poor diet, high rates of smoking, socioeconomic factors, and the quality of groundwater used by area residents are all possible contributing factors. This study was conducted by the U.S. Geological Survey in cooperation with the West Virginia Department of Health and Human Resources and the West Virginia Department of Environmental Protection, with grant support from the Centers for Disease Control and Prevention (CDC) to assess the quality of groundwater in southern West Virginia. The data from this assessment of groundwater quality may be used by the CDC and other agencies to potentially investigate the role or lack thereof of groundwater quality with respect to mortality and morbidity rates in the region. The study was conducted in a region where a high density of current or past coal mining combined with a lack of advanced sewage treatment could affect concentrations of commonly occurring constituents plus contaminants, including nitrate, trace metals, major ions, indicator bacteria, radon, hydrogen sulfide, and dissolved hydrocarbons. Because rural residential wells and mine outfalls are considered private sources of water in the region, and are therefore unregulated and unmonitored, water-quality data are sparse. To fill the data gap and assess the groundwater quality in the region, water-quality samples were collected from 60 sites in a 10-county area. The 60 sites sampled included 46 rural residential homeowner wells and 14 mine outfall discharges used for residential supply. For this study, all samples were collected prior to any filtration or other treatments, typically at the pressure tank, and are indicative of total and dissolved constituents in the untreated water. Generally, data for the 60 sites indicate that most waters sampled do not exceed thresholds for most U.S. Environmental Protection Agency (EPA) drinking-water standards and U.S. Geological Survey (USGS) drinking-water screening criteria. However, there were several notable exceptions. Turbidity exceeded the 5-Nephelometric Turbidity Unit (NTU) EPA treatment technique (TT) drinking-water standard in 14 of 60 (23 percent) sites sampled and exceeded the 1-NTU TT standard in 51 of 60 (85 percent) sites sampled. Turbidity is common in many wells in southern West Virginia and may be attributed to iron oxyhydroxide precipitates, sediment carried into the aquifers from the shallow soil zone due to improperly constructed or cased wells or transported to the aquifer in shallow stress-relief fracture zones or through permeable bedding-plane partings. For the sites sampled, 31 of 60 (52 percent) had pH values at, above, or below the upper and lower range of the EPA Secondary Maximum Contaminant Level (SMCL, 6.5–8.5 standard units). Of those 31 sites, 28 (90 percent) were indicative of acidic corrosive water and 3 (10 percent) were indicative of alkaline water. The Langelier Saturation Index (LSI), which is a measure of the corrosivity of the water, was computed for all sites sampled for the study. Eighty-two percent of the sites sampled had waters that were classified as corrosive, based on a LSI less than −0.5. Corrosive water has the potential to leach lead, copper, and other metals from lead, copper, galvanized, or lead-tin soldered connections in water lines. The chloride to sulfate mass ratio also was assessed with the alkalinity to indicate the potential to promote galvanic corrosion (PPGC) of water lines and plumbing fixtures. Only one of the sites (1.7 percent) classified as a corrosive water site, had a PPGC considered high; the remaining sites were classified as having either a moderate (53.3 percent) or low (45 percent) PPGC. Therefore, the type of plumbing systems sampled for this study may be affected by corrosive water, but the potential for leaching trace metals and other constituents from residential plumbing systems containing older galvanized pipes or lead-tin soldered copper pipes is moderate to low. The indicator bacteria total coliform and Escherichia coli ( E. coli ) also were detected in groundwater samples to varying degrees. Total coliforms, which are a broad class of indicator bacteria, are common in groundwater in southern West Virginia and were detected in 39 of the 60 sites (65 percent) sampled. The presence of total coliform bacteria is a potential indicator of surface contamination, due to improperly constructed or cased wells, or infiltration of soil or other surface contaminants into the aquifer or well bore. E. coli bacteria, however, are much more indicative of fecal contamination of groundwater from either human or animal sources, and 14 of the 60 (23 percent) sites sampled had detections of E. coli . Although only a few strains of E. coli are known pathogens, their presence in groundwater may be an indicator of other related pathogens such as viruses and should be regarded as a serious potential issue. Water treatment such as chlorination, ozonation, or ultraviolet light may be appropriate to kill potential pathogenic bacteria or viruses in the source water. Manganese and iron were prevalent contaminants in the groundwater samples collected for this study, with 30 of 60 (50 percent) sites analyzed for manganese and 25 of 60 (42 percent) sites analyzed for iron exceeding the proposed 50- and 300-micrograms per liter (µg/L) SMCL drinking-water standards, respectively, for aesthetic criteria such as taste, odor, or staining of plumbing fixtures. Fourteen of the 60 sites sampled (23 percent) had concentrations of manganese that exceeded the 300-µg/L USGS health-based screening level, and 1 site exceeded the 1,600-µg/L EPA drinking-water equivalent level, which is based on a lifetime exposure level. Sodium is another common constituent in groundwater within the study area. Sodium has an EPA health-based value (HBV) of 20 milligrams per liter (mg/L) for individuals who are on a sodium-restricted diet for blood pressure or other health reasons. Sodium concentrations exceeded the 20-mg/L EPA HBV in 27 of 60 (45 percent) samples. Radon, a naturally occurring carcinogenic radioactive gas known to cause lung cancer, was detected at concentrations at or exceeding the proposed 300-picocuries per liter (pCi/L) EPA Maximum Contaminant Level (MCL) in 12 of the 60 (20 percent) sites sampled. Sites with radon gas concentrations exceeding the 300-pCi/L proposed MCL have the potential for airborne concentrations of radon to exceed the 4-pCi/L indoor air standard. Inhalation of radon can cause lung cancer, and the 4-pCi/L indoor air standard is based on an inhalation standard. Therefore, homeowners whose wells have radon gas concentrations exceeding 300 pCi/L may be advised to have their indoor air tested to determine if indoor air concentrations exceed the 4-pCi/L indoor air standard established by the EPA. Various factors were analyzed statistically and graphically to determine whether they have an influence on groundwater quality within the study area, including topographic setting, well depth, type of mining (surface or underground), type of site (well or mine outfall), and geologic formation. Only geologic formation and the type of site sampled had strong statistical correlations with one or more of the constituents of concern for this study. The overall chemistry of outfalls (mine outfalls) and wells was significantly different, with a much higher dissolved oxygen content in outfalls than in wells. The dissolved oxygen content is the primary component driving the oxidation and reduction of minerals, and the precipitation of minerals that are saturated or super saturated with respect to various cations and anions. Median dissolved oxygen concentrations for the outfalls sampled was 8.75 mg/L, and only 0.4 mg/L for the wells sampled. Median concentrations of sulfate and selenium were much higher in waters from the outfalls sampled, with median concentrations of 73.75 mg/L and 2.35 µg/L, respectively, compared to the wells sampled, which had median concentrations of 18.3 mg/L and less than (<) the 0.05-µg/L method detection limit, respectively. The maximum selenium concentration was for a well, with a concentration of 16.6 µg/L. The geochemical processes that control sulfate and selenium concentrations in groundwater are similar and are the result of the oxidation of sulfide minerals such as pyrite and ferroselite. Iron and manganese concentrations were elevated in most of the wells sampled, with median concentrations of 269.5 and 124.5 µg/L, respectively, but were rarely detected in the outfalls sampled, with median concentrations of < 4.0 and < 0.4 µg/L, respectively. The difference in iron and manganese between wells and outfalls is indicative of the role of dissolved oxygen on processes controlling groundwater chemistry in the region. Three principal geologic formations were assessed for the study, and the overall chemistry for the Pocahontas, New River, and Kanawha Formations varied substantially with respect to several constituents. Concentrations of calcium, magnesium, and total dissolved solids were highest for sites sampled in the Pocahontas Formation, with median concentrations of 41.9, 18.6, and 312 mg/L, respectively. For constituents that are commonly associated with mining activity, the highest concentrations were for sites sampled in the New River Formation, with median concentrations of iron and manganese of 2,450 µg/L and 482 µg/L, respectively, and a median pH of 6.35 standard units. Concentrations of barium also were elevated in samples collected from sites in the New River Formation, with a median barium concentration of 184 µg/L. The source of the barium is not fully known but may be associated with commingling of shallow groundwater with deeper brines or dissolution of the mineral barite. The highest median sulfate concentrations were from sites sampled in the Pocahontas Formation, with a median concentration of 64.0 mg/L. Of the 12 sites at or exceeding the 300-pCi/L proposed drinking-water standard for radon, 8 (67 percent of MCL exceedances) were for sites deriving water from the Kanawha Formation, 3 (25 percent of MCL exceedances) were for sites deriving water from the New River Formation, and only 1 site was for water from the Pocahontas Formation (8 percent of proposed MCL exceedances). Dissolved hydrocarbons, including methane, ethane, propane, propene, n - and i -butane, 1-butene, n - and i -pentane, pentane, 2- and 3-ethyl pentane, hexane, and benzene were analyzed in samples collected from 59 of the 60 sites to assess the potential occurrence and sources of these trace gases in groundwater within the study area. Results of the analysis indicate that most of the gas is of shallow biogenic origin, possibly associated with coal-bed methane, but a subset of samples has a gas signature and a chloride to bromide ratio indicative of potential mixing with deeper thermogenic gases. Only 2 of the 59 (3.3 percent) sites sampled had concentrations of methane gas, which is a highly combustible and explosive gas, exceeding the 10 milligrams per kilogram level of concern established by the U.S. Office of Surface Mining Reclamation and Enforcement. Principal components analysis was used to assess the primary geochemical processes occurring in the aquifers sampled. The first principal component had significant positive loadings for bromide, chloride, silica, ammonia, barium, iron, manganese, and arsenic, and significant negative loadings for dissolved oxygen, potassium, nitrate, and uranium, and reflects reduction and oxidation (redox) processes occurring in deeper anoxic groundwater or shallow oxic groundwater. The strong positive loadings for iron, manganese, barium, and arsenic are correlated with reducing conditions often found deeper in the aquifer. More oxic water is correlated with oxidation of nitrogen species to nitrate and environmental mobilization of uranium and sulfate in shallow wells and mine outfalls.

West Virginia