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David J. Holtschlag

Publications and source records attributed to David J. Holtschlag.

At least 19 recordsLinked to original sources
USGS2022

A computer-aided approach for adapting stage-discharge ratings and characterizing uncertainties of streamflow data with discrete measurements

Relations between stage (water level) and discharge of streamflow through a natural channel are the result of time-varying processes, which are commonly described by time-varying stage-discharge ratings. Hydrographers with the U.S. Geological Survey successfully maintain the accuracy of streamflow data by manually applying time-tested approaches to adapt ratings to temporal changes in hydraulic conditions. The difficulty with the manual approach is that it is a subjective, time-consuming process that requires considerable skill and experience to implement. In addition, manual adjustments of ratings make quantification of resulting streamflow data uncertainties problematic. A computer-aided adaptive stage-discharge estimation approach is proposed to track sequential changes in the relation between stage and discharge at continuous-record streamgages. In this report, adaptations are based strictly on discrete measurement data that are then used to compute the magnitudes and uncertainties of streamflow. The approach entails the parameterization of a cubic regression spline (CRS) for the stage-discharge relation based on an existing rating or on a set of discrete measurements. A state-space model is then parameterized to track temporal changes in stage-discharge relations beginning with the initial CRS parameterization using discrete measurements. Finally, Kalman estimation is used with the state-space model to estimate the magnitude and uncertainty of flows. In a case study using data from streamgage U.S. Geological Survey 04122500 Marquette River at Scottville, Michigan, a five-parameter CRS model was estimated from data in an existing stage-discharge rating to provide an initial CRS parameter set for a state-space model. The initial CRS parameters were updated sequentially in a state-space model based on periodic discrete measurements of stage and discharge that spanned a 30-year period for this analysis. Additional analysis is needed to determine the timing of rapidly varying shifts more precisely in stage-discharge relations than the relatively infrequent discrete measurements currently enabled. Unit streamflow estimates based on flow in a local streamgaging network may provide a basis for adapting a stage-discharge rating at unit time intervals by augmenting discrete measurement data within the state-space model.

Michigan↗
USGS2019

Basin, climatic, and irrigation factors associated with median summer water yields for streams in Southwestern Michigan, 1945-2015

Median summer water yields and resultant flows for streams are used in Michigan to regulate large water withdrawals to help prevent negative effects on characteristic fish populations. Large water withdrawals commonly are associated with irrigation in rural areas. In an earlier statewide report, an index-flow statistic for the period of record, defined as the median flow during the summer month of lowest flow, was used to characterize median summer flows and associated water yields. In this report, the annual series of median summer water yields for the period July 1 through September 30 within the period of record is used to characterize median summer water yields. For 27 streamgages included in both reports, the average index water yield was at the 37th percentile of the distribution of median summer water yields. In contrast to an index statistic, an annual time series provides a basis for detecting trends in median summer water yields and for determining basin, climatic, and irrigation factors affecting spatial and temporal variations in summer water yields. Daily flow data from 40 selected U.S. Geological Survey streamgages in southwestern Michigan were used in this analysis. Two mixed models were identified to estimate median summer water yields based on fixed basin characteristics and temporally varying climatic factors for 1945–2015. No irrigation data were available prior to 1970, so no irrigation variables were included in the mixed models for 1945–2015. Then, two mixed models were developed for 1970–2015, a period in which a partial annual series of county-level irrigation data also were available. One of the 1970–2015 mixed models provides a basis for estimating median summer water yields at sites in southwestern Michigan using an estimated trend component, and selected basin, climatic, and irrigation factors. Re-estimation of model parameters in this mixed model with more spatially precise information on irrigation withdrawals may improve model accuracy.

Michigan↗
USGS2018

An exploratory Bayesian network for estimating the magnitudes and uncertainties of selected water-quality parameters at streamgage 03374100 White River at Hazleton, Indiana, from partially observed data

An exploratory discrete Bayesian network (BN) was developed to assess the potential of this type of model for estimating the magnitudes and uncertainties of an arbitrary subset of unmeasured water-quality parameters given the measured complement of parameters historically measured at a U.S. Geological Survey streamgage. Water-quality data for 27 water-quality parameters from 596 discrete measurements at U.S. Geological Survey streamgage 03374100 White River at Hazleton, Indiana, were used to develop this BN. Data for each of the water-quality parameters were discretized into five intervals based on the quintiles of the measured values. The 596 discrete measurements were randomly partitioned into a training set with 80 percent of the data and a testing set with 20 percent of the data to identify, estimate, and assess the training and testing accuracy of the Bayesian network. A BN with 28 nodes was formed from the 27 water-quality parameters and the month of sample collection. Based on data in the training set, a network with 53 directed edges and month as the target node was identified by minimizing the negative log-likelihood function for all nodes treated, in turn, as the target variable. The edge structure determines the number and magnitude of elements in conditional probability tables associated with all nodes. The effectiveness of the BN was assessed on the basis of correct classification rates to one of the five discrete intervals, which were computed separately for the training and testing datasets and for two conditioning variable sets. The selected sets of conditioning variables represent two of many possible sets of measured parameters on which to base estimates of unmeasured parameters. The first set includes only the month of sample collection ( month ), and an expanded set includes month and six other continuously measurable parameters, referred to as the ContMeasSet , all of which were obtained from the discrete data. Results indicated that the training dataset had average correct classification rates of 41.7- and 61.2-percent rates conditioned on the month and ContMeasSet sets, respectively. The testing dataset had somewhat lower average correct classification rates of 40.8 and 56.5 percent for the two conditioning variable sets. When conditioned on month only, the average correct classification rate for the testing dataset was only slightly lower than the average correct classification rate in the training dataset, indicating little model overfitting. When using the ContMeasSet , however, the average decrease in accuracy between training and testing sets was 4.9 percent. The training and testing datasets and both sets of conditioning variables, however, indicate that the BN would substantially outperform a random assignment model, which would be expected to have a 20-percent correct classification rate. In addition, the edge structure of the BN depicts how information can flow through the network, which may help prioritize parameters for measurement to facilitate estimation of unmeasured parameters. Finally, extension of a static BN, like the one developed in this report, to a dynamic BN may provide a basis for using high-frequency or continuous water-quality data to extend information in time between discrete water-quality samples, and this integration could mitigate some of the limitations of high-frequency and discrete water-quality sampling methods.

Indiana↗
USGS2018

UFINCH: A method for simulating unit and daily flows in networks of channels described by NHDPlus using continuous flow data at U.S. Geological Survey streamgages

The UFINCH (Unit Flows In Networks of Channels) computer application can be used to simulate daily and unit flows in networks of streams based on geospatial data in the National Hydrography Dataset NHDPlus (with value added attributes), and U.S. Geoogical Survey daily streamflow data from a downstream (or base) streamgage. Among streamflow augmentation methods, UFINCH has the unique capability to estimate time series of flows from a single base (downstream) streamgage to many upstream reaches, while conserving flows within the basin. UFINCH also provides a simple statistical model to adjust simulated flows to better match continuous flows from data at an upstream streamgage. Parameters of the statistical model are estimated using overlapping periods of record at the two streamgages, but the adjustment can be applied to all years of record available at the base streamgage. This report describes the main features of UFINCH and presents results from a sample application. Interactive graphical user interfaces and automated geographical information processing facilitate flow-data retrievals provide an intuitive environment for efficient and effective generation of flow information in a network. UFINCH is coded in the Matlab programming language and can be run in the Matlab programming environment, with supporting statistical, optimization, and mapping toolboxes, or from compiled code on a Microsoft Windows computer.

Scientific Investigations Report↗
USGS2016

An evaluation of methods for estimating decadal stream loads

Effective management of water resources requires accurate information on the mass, or load of water-quality constituents transported from upstream watersheds to downstream receiving waters. Despite this need, no single method has been shown to consistently provide accurate load estimates among different water-quality constituents, sampling sites, and sampling regimes. We evaluate the accuracy of several load estimation methods across a broad range of sampling and environmental conditions. This analysis uses random sub-samples drawn from temporally-dense data sets of total nitrogen, total phosphorus, nitrate, and suspended-sediment concentration, and includes measurements of specific conductance which was used as a surrogate for dissolved solids concentration. Methods considered include linear interpolation and ratio estimators, regression-based methods historically employed by the U.S. Geological Survey, and newer flexible techniques including Weighted Regressions on Time, Season, and Discharge (WRTDS) and a generalized non-linear additive model. No single method is identified to have the greatest accuracy across all constituents, sites, and sampling scenarios. Most methods provide accurate estimates of specific conductance (used as a surrogate for total dissolved solids or specific major ions) and total nitrogen – lower accuracy is observed for the estimation of nitrate, total phosphorus and suspended sediment loads. Methods that allow for flexibility in the relation between concentration and flow conditions, specifically Beale’s ratio estimator and WRTDS, exhibit greater estimation accuracy and lower bias. Evaluation of methods across simulated sampling scenarios indicate that (1) high-flow sampling is necessary to produce accurate load estimates, (2) extrapolation of sample data through time or across more extreme flow conditions reduces load estimate accuracy, and (3) WRTDS and methods that use a Kalman filter or smoothing to correct for departures between individual modeled and observed values benefit most from more frequent water-quality sampling.

Journal of Hydrology↗
USGS2015

Estimation of monthly water yields and flows for 1951-2012 for the United States portion of the Great Lakes Basin with AFINCH

Monthly water yields from 105,829 catchments and corresponding flows in 107,691 stream segments were estimated for water years 1951–2012 in the Great Lakes Basin in the United States. Both sets of estimates were computed by using the Analysis of Flows In Networks of CHannels (AFINCH) application within the NHDPlus geospatial data framework. AFINCH provides an environment to develop constrained regression models to integrate monthly streamflow and water-use data with monthly climatic data and fixed basin characteristics data available within NHDPlus or supplied by the user. For this study, the U.S. Great Lakes Basin was partitioned into seven study areas by grouping selected hydrologic subregions and adjoining cataloguing units. This report documents the regression models and data used to estimate monthly water yields and flows in each study area. Estimates of monthly water yields and flows are presented in a Web-based mapper application. Monthly flow time series for individual stream segments can be retrieved from the Web application and used to approximate monthly flow-duration characteristics and to identify possible trends.

Great Lakes Basin↗
USGS2011

Use of instantaneous streamflow measurements to improve regression estimates of index flow for the summer month of lowest streamflow in Michigan

In Michigan, index flow Q50 is a streamflow characteristic defined as the minimum of median flows for July, August, and September. The state of Michigan uses index flow estimates to help regulate large (greater than 100,000 gallons per day) water withdrawals to prevent adverse effects on characteristic fish populations. At sites where long-term streamgages are located, index flows are computed directly from continuous streamflow records as GageQ50. In an earlier study, a multiple-regression equation was developed to estimate index flows IndxQ50 at ungaged sites. The index equation explains about 94 percent of the variability of index flows at 147 (index) streamgages by use of six explanatory variables describing soil type, aquifer transmissivity, land cover, and precipitation characteristics. This report extends the results of the previous study, by use of Monte Carlo simulations, to evaluate alternative flow estimators, DiscQ50, IntgQ50, SiteQ50, and AugmQ50. The Monte Carlo simulations treated each of the available index streamgages, in turn, as a miscellaneous site where streamflow conditions are described by one or more instantaneous measurements of flow. In the simulations, instantaneous flows were approximated by daily mean flows at the corresponding site. All estimators use information that can be obtained from instantaneous flow measurements and contemporaneous daily mean flow data from nearby long-term streamgages. The efficacy of these estimators was evaluated over a set of measurement intensities in which the number of simulated instantaneous flow measurements ranged from 1 to 100 at a site. The discrete measurement estimator DiscQ50 is based on a simple linear regression developed between information on daily mean flows at five or more streamgages near the miscellaneous site and their corresponding GageQ50 index flows. The regression relation then was used to compute a DiscQ50 estimate at the miscellaneous site by use of the simulated instantaneous flow measurement. This process was repeated to develop a set of DiscQ50 estimates for all simulated instantaneous measurements, a weighted DiscQ50 estimate was formed from this set. Results indicated that the expected value of this weighted estimate was more precise than the IndxQ50 estimate for all measurement intensities evaluated. The integrated index-flow estimator, IntgQ50, was formed by computing a weighted average of the index estimate IndxQ50 and the DiscQ50 estimate. Results indicated that the IntgQ50 estimator was more precise than the DiscQ50 estimator at low measurement intensities of one to two measurements. At greater measurement intensities, the precision of the IntgQ50 estimator converges to the DiscQ50 estimator. Neither the DiscQ50 nor the IntgQ50 estimators provided site-specific estimates. In particular, although expected values of DiscQ50 and IntgQ50 estimates converge with increasing measurement intensity, they do not necessarily converge to the site-specific value of Q50. The site estimator of flow, SiteQ50, was developed to facilitate this convergence at higher measurement intensities. This is accomplished by use of the median of simulated instantaneous flow values for each measurement intensity level. A weighted estimate of the median and information associated with the IntgQ50 estimate was used to form the SiteQ50 estimate. Initial simulations indicate that the SiteQ50 estimator generally has greater precision than the IntgQ50 estimator at measurement intensities greater than 3, however, additional analysis is needed to identify streamflow conditions under which instantaneous measurements will produce estimates that generally converge to the index flows. A preliminary augmented index regression equation was developed, which contains the index regression estimate and two additional variables associated with base-flow recession characteristics. When these recession variables were estimated as the medians of recession parameters compute

Scientific Investigations Report↗
USGS2010

Application of AFINCH as a tool for evaluating the effects of streamflow-gaging-network size and composition on the accuracy and precision of streamflow estimates at ungaged locations in the southeast Lake Michigan hydrologic subregion

Bootstrapping techniques employing random subsampling were used with the AFINCH (Analysis of Flows In Networks of CHannels) model to gain insights into the effects of variation in streamflow-gaging-network size and composition on the accuracy and precision of streamflow estimates at ungaged locations in the 0405 (Southeast Lake Michigan) hydrologic subregion. AFINCH uses stepwise-regression techniques to estimate monthly water yields from catchments based on geospatial-climate and land-cover data in combination with available streamflow and water-use data. Calculations are performed on a hydrologic-subregion scale for each catchment and stream reach contained in a National Hydrography Dataset Plus (NHDPlus) subregion. Water yields from contributing catchments are multiplied by catchment areas and resulting flow values are accumulated to compute streamflows in stream reaches which are referred to as flow lines. AFINCH imposes constraints on water yields to ensure that observed streamflows are conserved at gaged locations. Data from the 0405 hydrologic subregion (referred to as Southeast Lake Michigan) were used for the analyses. Daily streamflow data were measured in the subregion for 1 or more years at a total of 75 streamflow-gaging stations during the analysis period which spanned water years 1971–2003. The number of streamflow gages in operation each year during the analysis period ranged from 42 to 56 and averaged 47. Six sets (one set for each censoring level), each composed of 30 random subsets of the 75 streamflow gages, were created by censoring (removing) approximately 10, 20, 30, 40, 50, and 75 percent of the streamflow gages (the actual percentage of operating streamflow gages censored for each set varied from year to year, and within the year from subset to subset, but averaged approximately the indicated percentages). Streamflow estimates for six flow lines each were aggregated by censoring level, and results were analyzed to assess (a) how the size and composition of the streamflow-gaging network affected the average apparent errors and variability of the estimated flows and (b) whether results for certain months were more variable than for others. The six flow lines were categorized into one of three types depending upon their network topology and position relative to operating streamflow-gaging stations. Statistical analysis of the model results indicates that (1) less precise (that is, more variable) estimates resulted from smaller streamflow-gaging networks as compared to larger streamflow-gaging networks, (2) precision of AFINCH flow estimates at an ungaged flow line is improved by operation of one or more streamflow gages upstream and (or) downstream in the enclosing basin, (3) no consistent seasonal trend in estimate variability was evident, and (4) flow lines from ungaged basins appeared to exhibit the smallest absolute apparent percent errors (APEs) and smallest changes in average APE as a function of increasing censoring level. The counterintuitive results described in item (4) above likely reflect both the nature of the base-streamflow estimate from which the errors were computed and insensitivity in the average model-derived estimates to changes in the streamflow-gaging-network size and composition. Another analysis demonstrated that errors for flow lines in ungaged basins have the potential to be much larger than indicated by their APEs if measured relative to their true (but unknown) flows. “Missing gage” analyses, based on examination of censoring subset results where the streamflow gage of interest was omitted from the calibration data set, were done to better understand the true error characteristics for ungaged flow lines as a function of network size. Results examined for 2 water years indicated that the probability of computing a monthly streamflow estimate within 10 percent of the true value with AFINCH decreased from greater than 0.9 at about a 10-percent network-censoring level to less than 0.6 as the censoring level approached 75 percent. In addition, estimates for typically dry months tended to be characterized by larger percent errors than typically wetter months.

Indiana, Michigan↗
USGS2009

Detection of conveyance changes in St. Clair River using historical water-level and flow data with inverse one-dimensional hydrodynamic modeling

St. Clair River is a connecting channel that transports water from Lake Huron to the St. Clair River Delta and Lake St. Clair. A negative trend has been detected in differences between water levels on Lake Huron and Lake St. Clair. This trend may indicate a combination of flow and conveyance changes within St. Clair River. To identify where conveyance change may be taking place, eight water-level gaging stations along St. Clair River were selected to delimit seven reaches. Positive trends in water-level fall were detected in two reaches, and negative trends were detected in two other reaches. The presence of both positive and negative trends in water-level fall indicates that changes in conveyance are likely occurring among some reaches because all reaches transmit essentially the same flow. Annual water-level fall in reaches and reach lengths was used to compute conveyance ratios for all pairs of reaches by use of water-level data from 1962 to 2007. Positive and negative trends in conveyance ratios indicate that relative conveyance is changing among some reaches. Inverse one-dimensional (1-D) hydrodynamic modeling was used to estimate a partial annual series of effective channel-roughness parameters in reaches forming the St. Clair River for 21 years when flow measurements were sufficient to support parameter estimation. Monotonic, persistent but non-monotonic, and irregular changes in estimated effective channel roughness with time were interpreted as systematic changes in conveyances in five reaches. Time-varying parameter estimates were used to simulate flow throughout the St. Clair River and compute changes in conveyance with time. Based on the partial annual series of parameters, conveyance in the St. Clair River increased about 10 percent from 1962 to 2002. Conveyance decreased, however, about 4.1 percent from 2003 to 2007, so that conveyance was about 5.9 percent higher in 2007 than in 1962.

St. Clair River↗
USGS2009

An initial investigation of multidimensional flow and transverse mixing characteristics of the Ohio River near Cincinnati, Ohio

Two-dimensional hydrodynamic and transport models were applied to a 34-mile reach of the Ohio River from Cincinnati, Ohio, upstream to Meldahl Dam near Neville, Ohio. The hydrodynamic model was based on the generalized finite-element hydrodynamic code RMA2 to simulate depth-averaged velocities and flow depths. The generalized water-quality transport code RMA4 was applied to simulate the transport of vertically mixed, water-soluble constituents that have a density similar to that of water. Boundary conditions for hydrodynamic simulations included water levels at the U.S. Geological Survey water-level gaging station near Cincinnati, Ohio, and flow estimates based on a gate rating at Meldahl Dam. Flows estimated on the basis of the gate rating were adjusted with limited flow-measurement data to more nearly reflect current conditions. An initial calibration of the hydrodynamic model was based on data from acoustic Doppler current profiler surveys and water-level information. These data provided flows, horizontal water velocities, water levels, and flow depths needed to estimate hydrodynamic parameters related to channel resistance to flow and eddy viscosity. Similarly, dye concentration measurements from two dye-injection sites on each side of the river were used to develop initial estimates of transport parameters describing mixing and dye-decay characteristics needed for the transport model. A nonlinear regression-based approach was used to estimate parameters in the hydrodynamic and transport models. Parameters describing channel resistance to flow (Manning’s “n”) were estimated in areas of deep and shallow flows as 0.0234, and 0.0275, respectively. The estimated RMA2 Peclet number, which is used to dynamically compute eddy-viscosity coefficients, was 38.3, which is in the range of 15 to 40 that is typically considered appropriate. Resulting hydrodynamic simulations explained 98.8 percent of the variability in depth-averaged flows, 90.0 percent of the variability in water levels, 93.5 percent of the variability in flow depths, and 92.5 percent of the variability in velocities. Estimates of the water-quality-transport-model parameters describing turbulent mixing characteristics converged to different values for the two dye-injection reaches. For the Big Indian Creek dye-injection study, an RMA4 Peclet number of 37.2 was estimated, which was within the recommended range of 15 to 40, and similar to the RMA2 Peclet number. The estimated dye-decay coefficient was 0.323. Simulated dye concentrations explained 90.2 percent of the variations in measured dye concentrations for the Big Indian Creek injection study. For the dye-injection reach starting downstream from Twelvemile Creek, however, an RMA4 Peclet number of 173 was estimated, which is far outside the recommended range. Simulated dye concentrations were similar to measured concentration distributions at the first four transects downstream from the dye-injection site that were considered vertically mixed. Farther downstream, however, simulated concentrations did not match the attenuation of maximum concentrations or cross-channel transport of dye that were measured. The difficulty of determining a consistent RMA4 Peclet was related to the two-dimension model assumption that velocity distributions are closely approximated by their depth-averaged values. Analysis of velocity data showed significant variations in velocity direction with depth in channel reaches with curvature. Channel irregularities (including curvatures, depth irregularities, and shoreline variations) apparently produce transverse currents that affect the distribution of constituents, but are not fully accounted for in a two-dimensional model. The two-dimensional flow model, using channel resistance to flow parameters of 0.0234 and 0.0275 for deep and shallow areas, respectively, and an RMA2 Peclet number of 38.3, and the RMA4 transport model with a Peclet number of 37.2, may have utility for emergency-planning purposes. Emergency-response efforts would be enhanced by continuous streamgaging records downstream from Meldahl Dam, real-time water-quality monitoring, and three-dimensional modeling. Decay coefficients are constituent specific.

Kentucky, Ohio↗
USGS2009

Application guide for AFINCH (Analysis of Flows in Networks of Channels) described by NHDPlus

AFINCH (Analysis of Flows in Networks of CHannels) is a computer application that can be used to generate a time series of monthly flows at stream segments (flowlines) and water yields for catchments defined in the National Hydrography Dataset Plus (NHDPlus) value-added attribute system. AFINCH provides a basis for integrating monthly flow data from streamgages, water-use data, monthly climatic data, and land-cover characteristics to estimate natural monthly water yields from catchments by user-defined regression equations. Images of monthly water yields for active streamgages are generated in AFINCH and provide a basis for detecting anomalies in water yields, which may be associated with undocumented flow diversions or augmentations. Water yields are multiplied by the drainage areas of the corresponding catchments to estimate monthly flows. Flows from catchments are accumulated downstream through the streamflow network described by the stream segments. For stream segments where streamgages are active, ratios of measured to accumulated flows are computed. These ratios are applied to upstream water yields to proportionally adjust estimated flows to match measured flows. Flow is conserved through the NHDPlus network. A time series of monthly flows can be generated for stream segments that average about 1-mile long, or monthly water yields from catchments that average about 1 square mile. Estimated monthly flows can be displayed within AFINCH, examined for nonstationarity, and tested for monotonic trends. Monthly flows also can be used to estimate flow-duration characteristics at stream segments. AFINCH generates output files of monthly flows and water yields that are compatible with ArcMap, a geographical information system analysis and display environment. Chloropleth maps of monthly water yield and flow can be generated and analyzed within ArcMap by joining NHDPlus data structures with AFINCH output. Matlab code for the AFINCH application is presented.

Scientific Investigations Report↗
USGS2008

Environmental factors and flow paths related to Escherichia coli concentrations at two beaches on Lake St. Clair, Michigan, 2002–2005

Regression analyses and hydrodynamic modeling were used to identify environmental factors and flow paths associated with Escherichia coli ( E. coli ) concentrations at Memorial and Metropolitan Beaches on Lake St. Clair in Macomb County, Mich. Lake St. Clair is part of the binational waterway between the United States and Canada that connects Lake Huron with Lake Erie in the Great Lakes Basin. Linear regression, regression-tree, and logistic regression models were developed from E. coli concentration and ancillary environmental data. Linear regression models on log 10 E. coli concentrations indicated that rainfall prior to sampling, water temperature, and turbidity were positively associated with bacteria concentrations at both beaches. Flow from Clinton River, changes in water levels, wind conditions, and log 10 E. coli concentrations 2 days before or after the target bacteria concentrations were statistically significant at one or both beaches. In addition, various interaction terms were significant at Memorial Beach. Linear regression models for both beaches explained only about 30 percent of the variability in log 10 E. coli concentrations. Regression-tree models were developed from data from both Memorial and Metropolitan Beaches but were found to have limited predictive capability in this study. The results indicate that too few observations were available to develop reliable regression-tree models. Linear logistic models were developed to estimate the probability of E. coli concentrations exceeding 300 most probable number (MPN) per 100 milliliters (mL). Rainfall amounts before bacteria sampling were positively associated with exceedance probabilities at both beaches. Flow of Clinton River, turbidity, and log 10 E. coli concentrations measured before or after the target E. coli measurements were related to exceedances at one or both beaches. The linear logistic models were effective in estimating bacteria exceedances at both beaches. A receiver operating characteristic (ROC) analysis was used to determine cut points for maximizing the true positive rate prediction while minimizing the false positive rate. A two-dimensional hydrodynamic model was developed to simulate horizontal current patterns on Lake St. Clair in response to wind, flow, and water-level conditions at model boundaries. Simulated velocity fields were used to track hypothetical massless particles backward in time from the beaches along flow paths toward source areas. Reverse particle tracking for idealized steady-state conditions shows changes in expected flow paths and traveltimes with wind speeds and directions from 24 sectors. The results indicate that three to four sets of contiguous wind sectors have similar effects on flow paths in the vicinity of the beaches. In addition, reverse particle tracking was used for transient conditions to identify expected flow paths for 10 E. coli sampling events in 2004. These results demonstrate the ability to track hypothetical particles from the beaches, backward in time, to likely source areas. This ability, coupled with a greater frequency of bacteria sampling, may provide insight into changes in bacteria concentrations between source and sink areas.

Lake St. Clair↗
USGS2008

A regression model for computing index flows describing the median flow for the summer month of lowest flow in Michigan

In 2006, Michigan enacted laws to prevent new large capacity withdrawals from decreasing flows to the extent that they would functionally impair a stream's ability to support characteristic fish populations. The median streamflow for the summer month of lowest flow was specified by state decision makers as the index flow on which likely impacts of withdrawals would be assessed. At sites near long-term streamflow-gaging stations, analysis of streamflow records during July, August, and September was used to determine the index flow. At ungaged sites, an alternate method for computing the index flow was needed. This report documents the development of a method for computing index flows at ungaged stream sites in Michigan. The method is based on a regression model that computes the index water yield, which is the index flow divided by the drainage area. To develop the regression model, index flows were determined on the basis of daily flows measured during July, August, and September at 147 streamflow-gaging stations having 10 or more years of record (considered long-term stations) in Michigan. The corresponding index water yields were statistically related to climatic and basin characteristics upstream from the stations in the regression model. Climatic and basin characteristics selected as explanatory variables in the regression model include two aquifer-transmissivity and hydrologic-soil groups, forest land cover, and normal annual precipitation. Regression model estimates of water yield explain about 70.8 percent of the variability in index water yields indicated by streamflow-gaging station records. Index flows computed on the basis of regression-model estimates of water yield and corresponding drainage areas explain about 94.0 percent of the variability in index flows indicated by streamflow-gaging station records. No regional bias was detected in the regression-based estimates of water yield within seven hydrologic subregions spanning Michigan. Thus, the single regression model developed in this report can be used to produce unbiased estimates of index water yield and flow statewide. In addition, a technique is presented for computing prediction intervals about the index flow estimates.

Michigan↗
USGS2004

Hydrodynamic simulation and particle-tracking techniques for identification of source areas to public-water intakes on the St. Clair-Detroit River waterway in the Great Lakes Basin

Source areas to public water intakes on the St. Clair-Detroit River Waterway were identified by use of hydrodynamic simulation and particle-tracking analyses to help protect public supplies from contaminant spills and discharges. This report describes techniques used to identify these areas and illustrates typical results using selected points on St. Clair River and Lake St. Clair. Parameterization of an existing two-dimensional hydrodynamic model (RMA2) of the St. Clair-Detroit River Waterway was enhanced to improve estimation of local flow velocities. Improvements in simulation accuracy were achieved by computing channel roughness coefficients as a function of flow depth, and determining eddy viscosity coefficients on the basis of velocity data. The enhanced parameterization was combined with refinements in the model mesh near 13 public water intakes on the St. Clair-Detroit River Waterway to improve the resolution of flow velocities while maintaining consistency with flow and water-level data. Scenarios representing a range of likely flow and wind conditions were developed for hydrodynamic simulation. Particle-tracking analyses combined advective movements described by hydrodynamic scenarios with random components associated with sub-grid-scale movement and turbulent mixing to identify source areas to public water intakes.

Michigan, Ontario↗
USGS2003

An acoustic doppler current profiler survey of flow velocities in St. Clair River, a connecting channel of the Great Lakes

Acoustic Doppler current profilers (ADCP) were used to measure flow velocities in St. Clair River during a survey in May and June of 2002, as part of a study to assess the susceptibility of public water intakes to contaminants on the St. Clair-Detroit River Waterway. The survey provides 2.7 million point velocity measurements at 104 cross sections. Sections are spaced about 1,630 ft apart along the river from Port Huron to Algonac, Michigan, a distance of 28.6 miles. Two transects were obtained at each cross section, one in each direction across the river. Along each transect, velocity profiles were obtained 2-4 ft apart. At each velocity profile, average water velocity data were obtained at 1.64 ft intervals of depth. The raw position and velocity data from the ADCP field survey were adjusted for local magnetic anomalies using global positioning system (GPS) measurements at the end points of the transects. The adjusted velocity and ancillary data can be retrieved through the internet and extracted to column-oriented data files.

St. Clair River↗
USGS2002

Flow distribution in selected branches of St. Clair and Detroit rivers

St. Clair and Detroit rivers, which are connecting channels between Lake Huron and Lake Erie in the Great Lakes basin, form part of the boundary between the state of Michigan and the province of Ontario. In 13 reaches, this flow divides locally around islands and dikes to form 31 branches. This study develops a set of simple linear regression equations for computing expected flow proportions in branches, generally as a function of the total flow within the reach. The equations are based on 533 acoustic Doppler current profiler measurements of flow obtained between 1996 and 2000. Root-mean-square errors of these regressions range from 0.00323 to 0.0895. In seven upstream reaches where flow is known because of flow specifications at the boundaries of the waterway and continuity constraints, the uncertainties of the flow proportions can be used to directly infer the uncertainties of the corresponding flows. In six downstream reaches, the uncertainties of flows are determined by both the uncertainties of the flow proportions and the uncertainties of the total flow in the reach. For these reaches, Monte Carlo simulations quantify the ratios of total uncertainty to flow proportion uncertainty, which range from 1.0026 to 13.984. To facilitate routine calculation, polynomial regression equations are developed to approximate these ratios as a function of flow. Results provide a mechanism for computing the magnitudes and uncertainties of steady-state flows within selected branches of the connecting channels by specifying inflows at the headwaters of St. Clair River, seven intervening tributaries, and Lake St. Clair.

Michigan, Ontario↗
USGS2002

Visualization of drifting buoy deployments on upper Detroit River within the Great Lakes Waterway from August 28-30, 2001

Detroit River is a connecting channel on the Great Lakes waterway that joins Lake St. Clair with Lake Erie. The river forms part of the international boundary between the United States and Canada in southeastern Michigan and southern Ontario. Drifting buoys were deployed on Detroit River to help investigate flow characteristics of four selected reaches as part of a source water assessment study of public water intakes. The drifting buoys contained global positioning system (GPS) receivers to help track their movements following their deployment. In some deployments, buoys were released across a transect at approximately uniform intervals to better understand flow patterns. In other deployments, buoys were released in clusters to investigate turbulent dispersion characteristics. Computer animations of buoy movements, which can be viewed through the Internet, are developed to help visualize the results of the buoy deployments.

Detroit River↗