(abstract from the Users' Manual)

The BLTM model solves the one-dimensional advective dispersion equation by using a Lagrangian reference frame in which the computational nodes move with the flow. This solution sheme minimizes numerical dispersion and allows the user to tabulate the effect of each physical process on the computed concentrations. The BLTM model can route any number of interactive constituents for which the physical and (or) chemical reaction rates are defined in a subroutine; special subroutines have been developed to route, for example, rhotone, salinity, and bass eggs.

Because the US Environmental Protection Agency's (EPA) stream-water-quality model QUAL2 (EPA-QUAL2) was in wide use at the time the BLTM was published in 1987, the BLTM model was supplied with a subroutine called QUAL2 that simulated the reaction kinetics in the EPA model. The QUAL2 subroutine linked to BLTM allowed the EPA-QUAL2 kinetics to be applied to unsteady, reversing flow such as occurs in one-dimensional estuaries. A new subroutine, called QUAL2E, simulates the reaction kinetics used in the newer version of the EPA-QUAL2E model.

(Abstract from Proceedings of the First Federal Interagency Hydrologic Modeling Conference, held in Las Vegas, NV, April 19-23, 1998, prepared by the Subcommittee on Hydrology of the Interagency Advisory Committee on Water Data)

A Branched Lagrangian Transport Model was calibrated and validated for the tidally influenced portions of the Waccamaw and Pee Dee Rivers, Bull Creek, and the Atlantic Intracoastal Waterway near Myrtle Beach, South Carolina. In determining the assimilative capacity of the Atlantic Intracoastal Waterway, 1-hour, 24-hour, 14-day, and 30-day averaging intervals were used. For each averaging interval, point-source loadings in the model were increased until the State dissolved-oxygen standard was violated. Results of the averaging intervals and point-source loadings for two locations were evaluated by comparing time series of dissolved-oxygen concentration at critical locations and longitudinal profiles of average dissolved-oxygen concentration for particular reaches of the system. The concentrations of the oxygen-consuming constituents that can be assimilated vary by 180 percent, depending upon the averaging interval used for interpreting the simulation model output.

(Abstract from U.S. Geological Survey Water-Resources Investigations Report 91-4088)

The transport of striped bass eggs in the Congaree, Wateree, and Santee Rivers was studied by using a one-dimensional unsteady-flow model and a Lagrangian-type transport model. Simulated streamflows from the flow model were used with channel geometry information as input to the transport model. The results of a dye study were used to calibrate the transport model. The dispersion coefficients determined by the calibration were used to simulate movement of striped bass eggs spawned in 1988.

Striped bass eggs were collected every 8 hours at 4 sites over a period of 6 weeks during 1988. The density and average age of the eggs at the time of sampling were then determined by South Carolina Wildlife and Marine Resources personnel. Water temperature, monitored at five locations, was used to identify critical periods for egg sampling and to predict egg development time.

Egg survival and striped-bass recruitment depend on four physical factors: spawning location, water temperature, streamflow, and flow velocity. Laboratory tests indicate that the eggs, which have a specific gravity of 1.001, will settle to the streambed if flow velocity falls below about 0.2 foot per second. The eggs that settle in the river channel or in Lake Marion might not survive because they could be covered with silt and smother. Eggs that hatch near the lake may have a greater probability of survival than eggs that hatch in the upstream riverine habitat, because the lake habitat produces greater quantities of food (zooplankton) required by striped bass larvae during feeding stages.

The tranpsort simulation results indicate that the eggs were spawned from river mile 5.8 to river mile 44.0 on the Congaree River and from River mile 14.5 to upstream of the study limit, river mile 66.3, on the Wateree River. Additionally, the eggs hatched from the upper reaches of Lake Marion to river mile 16.7 on the Congaree River and from river mile 0.0 to river mile 46.5 on the Wateree River. For the 1988 spawning period, the modeled results indicate that nearly all of the striped bass eggs hatched in the Santee River near Lake Marion.

Model results were used to develop equations to predict distance to hatching point and distance to spawning point from the sample sites. The equations are site specific but provide an easy method for estimating travel distance of the eggs.

(Abstract from U.S. Geological Survey Water-Resources Investigations Report 93-4105)

This report presents the results of a study by the U.S. Geological Survey (USGS), in cooperation with the National Park Service, to investigate the transport and factors affecting mitigation of a hypothetical spill of a soluble contaminant into the New River in the New River Gorge National River, West Virginia. The study reach, 53 miles of the lower New River between Hinton and Fayette, is characterized as a pool-and-riffle stream that becomes narrower, steeper, and deeper in the downstream direction. A USGS unsteady-flow model, DAFLOW (Diffusion Analogy FLOW), and a USGS solute-transport model, BLTM (Branch Lagrangian Transport Model), were applied to the study reach. Increases in discharge caused decreases in peak concentration and traveltime of peak concentration. Decreases in discharge caused increases in peak concentration and traveltime of peak concentration. This study indicated that the effects of an accidental spill could be mitigated by regulating discharge from Bluestone Dam. Knowledge of the chemical characteristics of the spill, location and time of the spill, and discharge of the river can aid in determining a mitigation response.

(Abstract from U.S. Geological Survey Water-Resources Investigations Report 96-4237)

The one-dimensional, unsteady-flow model, BRANCH, and the Branched Lagrangian Transport Model (BLTM) were calibrated and validated for the Cooper and Wando Rivers near Charleston, South Carolina. Data used to calibrate the BRANCH model included water-level data at four locations on the Cooper River and two locations on the Wando River, measured tidal-cycle streamflows at five locations on the Wando River, and simulated tidal-cycle streamflows (using an existing validated BRANCH model of the Cooper River) for four locations on the Cooper River. The BRANCH model was used to generate the necessary hydraulic data used in the BLTM model. The BLTM model was calibrated and validated using time series of salinity concentrations at two locations on the Cooper River and at two locations on the Wando River. Successful calibration and validation of the BRANCH and BLTM models to water levels, stream flows, and salinity were achieved after applying a positive 0.45 foot datum correction to the downstream boundary. The sensitivity of the simulated salinity concentrations to changes in the downstream gage datum, channel geometry, and roughness coefficient in the BRANCH model, and to the dispersion factor in the BLTM model was evaluated. The simulated salinity concentrations were most sensitive to changes in the downstream gage datum. A decrease of 0.5 feet in the downstream gage datum increased the simulated 3-day mean salinity concentration by 107 percent (12.7 to 26.3 parts per thousand). The range of the salinity concentration went from a tidal oscillation with a standard deviation of 3.9 parts per thousand to a nearly constant concentration with a standard deviation of 0.0 parts per thousand. An increase in the downstream gage datum decreased the simulated 3-day mean salinity concentration by 47 percent (12.7 to 6.7 parts per thousand) and decreased the standard deviation from 3.9 to 3.4 parts per thousand.

(abstract from US Geological Survey Water-Supply Paper 2477, 1996)

A one-dimensional, unstead-flow model utilizing the Full de Saint-Venant EQations (FEQ) for one-dimensional, unsteady flow in open channels was verified for a 30.6-mile reach of the Fox River in northeastern Illinois. The model, which was calibrated prior to the verification study by the Illinois Department of Natural Resources and the Illinois State Water Survey, was used to simulate a period of unsteady, within-bank flow induced by dam operations at the upstream end of the river reach, Stratton Dam near McHenry, Illinois, During November 1990. The river reach included three low-head dams that resulted in backwater effects where the channel slope was small. The river stages and streamflows imulated by the model, together with dye-injection rate and concentration data measured at Stratton Dam, were used as input for a transport model, the Branched Lagrangian Transport Model (BLTM). The simulation results from both models were compared graphically with stage, streamflow, and (or) dye-concentration data collected during the unsteady-flow period at a total of 31 downstream sites. The celerity of the induced low-flow wave was simulated accurately, with no significant error at any location. Differences during low-flow conditions between measured and simulated stage were less than about 0.2 foot at most of the sites, although differences up to 0.8 foot resulted at four sites where depths were shallow or head losses were inadequately represented through bridges. The differences may have resulted from the increase in effective roughness in the channel at very low depths that was not effectively modeled. Furthermore, accurate and representative measurements were difficult under some conditions of very low velocities or water-head buildup on the upstream side of bridges. The traveltime and concentration attenuation of the dye cloud were accurately simulated.

The effects of the physical and computational model parameters also were examined. The converged model was insensitive to distance-step and time-step size. The initial conditions were varied by 50 percent, and the simulated stage and discharge still converged to a common solution within twelve 1-hour time steps. The sensitivity of the model to geometric data was studied by replacing measured cross sections with interpolated cross sections within branches. The changes in distance-step size and geometric information had no effect on flood-wave celerity or discharge, but simulated stage was affected by how well the remaining cross sections represented local channel geometry. Deletion of bridge representations from the model caused no significant effects on the overall hydraulic routing, and only local effect on stage probably because the period simulated did not include high flow. Because of low-head controlling dams throughout the study reach, sensitivity to error in gage datum depended on the type of boundary condition used and whether the datum error was in the upstream or downstream boundary. The FEQ model was evaluated as accurate and robust for this application.

¹US Geological Survey, Urbana, IL 61801

(Abstract from U.S. Geological Survey Water-Resources Investigations Report 94-4009)

The Straight River, in north-central Minnesota, is a trout stream having cold, clear water. The 75-square-mile Straight River watershed contributes flow to the stream. The watershed is underlain by highly transmissive surficial and confined-drift aquifers. Ground-water discharge from these aquifers sustains flow in the Straight River, and the cold water supports a population of trout. Water withdrawals from these aquifers are increasing in response to changes in land use from dry-land to irrigated farming. Degradation of the stream's habitat for trout could result from the following: a decrease in ground-water discharge to the stream caused by ground-water withdrawals for irrigation, an increase in ground-water temperature resulting from percolation of irrigated water to the ground-water system, and introduction of agricultural chemicals to the stream through ground-water flow or runoff.

Physical data indicate a hydraulic connection between the stream and the surficial aquifer. Discharge of the Straight River increases from about 25 cubic feet per second at the outfall from a reservoir near the headwaters to about 51 cubic feet per second near the mouth. The rate of streamflow gain during summer decreases downstream, possibly as a result of ground-water withdrawal for irrigation. The water table and potentiometric surface of the uppermost confined-drift aquifer generally slope to the southeast and locally toward rivers and lakes; gradients decline to about 5 feet per mile from spring to summer.

Daily fluctuations of stream temperature are as great as 15 degrees Celsius during the summer, primarily in response to changes in air temperature. Ground-water discharge to the Straight River decreases stream temperature during the summer. Results of simulations from a stream-temperature model indicate that daily changes in stream temperature are strongly influenced by solar radiation, wind speed, stream depth, and ground-water inflow. Results of simulations from ground-water-flow and stream-temperature models developed for the investigation indicate a significant decrease in ground-water flow could result from ground-water withdrawal at rates similar to those measured during 1988. This reduction in discharge to the stream could result in an increase in stream temperature of 0.5 to 1.5 degrees Celsius. Nitrate concentrations in shallow wells screened at the water table, in some areas, are locally greater than the limit set by the Minnesota Pollution Control Agency. Nitrate concentrations in water from deeper wells and in the stream axe low, generally less than 1.0 milligram per liter.

(Abstract from U.S. Geological Survey Water-Resources Investigations Report 97-4071)

Aquatic research has long shown that the survival of cold-water fish, such as salmon and trout, decreases markedly as water temperatures increase above a critical threshold, particularly during sensitive life stages of the fish. In an effort to improve the overall health of aquatic ecosystems, the State of Oregon in 1996 adopted a maximum water-temperature standard of 17.8 degrees Celsius (68 degrees Fahrenheit), based on a 7-day moving average of daily maximum temperatures, for most water bodies in the State. Anthropogenic activities are not permitted to raise the temperature of a water body above this level. In the Tualatin River, a tributary of the Willamette River located in northwestern Oregon, water temperatures periodically surpass this threshold during the low-flow summer and fall months. An investigation by the U.S. Geological Survey quantified existing seasonal, diel, and spatial patterns of water temperatures in the main stem of the river, assessed the relation of water temperatures to natural climatic conditions and anthropogenic factors (such as wastewater-treatment-plant effluent and modification of riparian shading), and assessed the impact of various flow management practices on stream temperatures. Half-hourly temperature measurements were recorded at 13 monitoring sites from river mile (RM) 63.9 to RM 3.4 from May to November of 1994. Four synoptic water-temperature surveys also were conducted in the upstream and downstream vicinities of two wastewater-treatment-plant outfalls. Temperature and streamflow time-series data were used to calibrate two dynamic-flow heat-transfer models, DAFLOW-BLTM (RM 63.9-38.4) and CE-QUAL-W2 (RM 38.4-3.4). Simulations from the models provided a basis for approximating "natural" historical temperature patterns, performing effluent and riparian-shading sensitivity analyses, and evaluating mitigation management scenarios under 1994 climactic conditions. Findings from the investigation included (1) under "natural" conditions the temperature of the river would exceed the State standard of 17.8 degrees Celsius at many locations during the low-flow season, (2) current operation of wastewater-treatment plants increases the temperature of the river downstream of the plants under low-flow conditions, (3) river temperature is significantly affected by riparian shade variations along both the tributaries and the main stem, (4) flow releases during the low-flow season from the Henry Hagg Lake reservoir decrease the river temperature in the upper section, and (5) removal of a low diversion dam at RM 3.4 would slightly decrease temperatures below RM 10.0.

(Abstract from the Proceedings of the American Water Resources Syposium on Urban Hydrology held in Denver, Colorado, November 4-8, 1990, p. 177-181)

A rainfall-runoff model, a runoff-quality model, a one-dimensional river-flow model, and a branched Lagrangian transport model were used to simulate water quality of urban runoff into the San Joaquin River near Fresno, California. The runoff models were applied using data from the U.S. Environmental Protection Agency's Fresno National Urban Runoff Project. The river-flow model required for the transport computations used available data for channel geometry and hydraulic characteristics, and the mean daily discharge (40 cubic feet per second) that is exceeded 90 percent of the time on the first day of a storm. Water-quality data collected along the river were used in the transport model. The models simulated a critical case of urban-runoff quality and river loading in a 24-hour period for total-recoverable aluminum, arsenic, chromium, copper, lead, mercury, nickel, and zinc. A comparison of simulated 1-hour peak concentrations and the U.S. Environmental Protection Agency's 1-hour freshwater aquatic-life criteria indicates that mercury, nickel, and arsenic safely meet the Environmental Protection Agency's 1-hour criteria and would not require further analysis.

(Abstract from U.S. Geological Survey Water-Resources Investigations Report 98-4150)

Longitudinal dissolved-oxygen profiles of the Ashley River for various hydrologic and point-source loading conditions were determined using results from water-quality simulations by the Branched Lagrangian Transport Model. The study area included the Ashley River from S.C. Highway 165 at Bacon Bridge to S.C. Highway 17 near the confluence with the Charleston Harbor. Hydraulic data for the Branched Lagrangian Transport Model were simulated using the U.S. Geological Survey BRANCH one-dimensional unsteady-flow model. Data used to apply and calibrate the BRANCH model included timeseries of water-level data at three locations and measured tidal-cycle streamflows at four locations. Data used to apply and calibrate the Branched Lagrangian Transport Model included timeseries of salinity concentrations at three locations, high- and low-slack tide longitudinal salinity profiles from six sampling locations, nutrient and biochemical oxygen demand concentrations collected over a tidal cycle during two sampling surveys for six locations, nutrient and biochemical oxygen demand concentrations collected over five slack tides over two and three days during two sampling surveys for three locations, and continuous water temperature data and dissolved oxygen concentrations at three locations.

A sensitivity analysis of the simulated dissolved-oxygen concentrations to model coefficients and data inputs indicated the simulated dissolved-oxygen concentrations were most sensitive to equilibrium temperatures due to the effect of temperature on reaction rate kinetics. Of the model coefficients, the simulated dissolved-oxygen concentrations were most sensitive to sediment oxygen demand.

Scenario simulations were used to evaluate four point-source loading conditions to the system by comparing simulated dissolved-oxygen concentrations with a condition where there is no point-source discharge into the system (no-load condition). The September 1992 loading condition decreased the one-day dissolved-oxygen concentration of September 25, 1992, by 29.0 percent or less as compared to a no-load condition. Setting all the point-source loadings to advanced secondary treatment (10 milligrams per liter of ammonia-nitrogen (mg/L) and 20 mg/L of 5-day biochemical oxygen demand) decreased the total ultimate oxygen demand loading to the system by 28 percent and decreased the one-day mean dissolved-oxygen concentrations from the no-load condition by 29.9 percent or less.

Setting all the point-source loadings to advanced treatment (2 mg/L of ammonia-nitrogen and 10 mg/L of 5-day biochemical oxygen demand) decreased the total ultimate oxygen demand loading to the system by 78 percent and decreased the one-day mean dissolved-oxygen concentrations from the no-load condition by 8.1 percent or less. Setting all the point-source loadings to reclaimed-use treatment (0.5 mg/L of ammonia-nitrogen and 5 mg/L of 5-day biochemical oxygen demand) decreased the total ultimate oxygen demand loading to the system by 91 percent and decreased the one-day mean dissolved-oxygen concentrations from the no-load condition by 5.2 percent or less.

Bulak, James S., Hurley, Noel M. Jr., and Crane, John S., 1993: Production, Mortality, and Transport of Striped Bass Eggs in Congaree and Wateree Rivers, South Carolina, American Fisheries Society Symposium 14, p. 29-37.

California Water Resources Control Board, 1994, Methodology for flow and salinity estimates in the Sacramento-San Joaquin Delta and Suisun Marsh: Fifteenth annual progress report to the State Water Resources Control Board inaccordance with Water Right Decision 1485, Order 9, June 1994, 91 p.

California Water Resources Control Board, 1995, Methodology for flow and salinity estimates in the Sacramento-San Joaquin Delta and Suisun Marsh: Sixteenth annual progress report to the State Water Resources Control Board in accordance with Water Right Decision 1485, Order 9, June 1995.

Conrads, P.A., 1998, Simulation of temperature, nutrients, biochemical oxygen deman, and dissolved oxygen in the Ashley River near Charleston, South Carolina: U.S. Geological Survey Water-Resources Investigations Report 98-4150, 56 p.

Conrads, P.A. and Smith, P.A., 1996: Simulation of water level, streamflow, and mass transport for the Cooper and Wando Rivers near Charleston, South Carolina, 1992-95, USGS Water-Resources Investigations Report 96-4237, 51 p.

Conrads, P.A. and P.A. Smith, 1997, Simulation of temperature, Nutrients, Biochemical Oxygen Demand, and Dissolved Oxygen in the Cooper and Wando Rivers near Charleston, South Carolina, 1992-95: U.S. Geological Survey Water Resources Investigations Report 97-5151, Columbia, South Carolina, 58 p.

Drewes, P.A., and Conrads, P.A., 1995: Assimilative capacity of the Waccamaw River and the Atlantic Intracoastal Waterway near Myrtle Beach, South Carolina, 1989-92. U.S. Geological Survey Water-Resources Investigations Report 95-4111, 58 p.

Goodwin, C.R., 1991: Simulation of the effects of proposed tide gates on circulation, flushing, and water quality in residential canals, Cape Coral, Florida: U.S. Geological Survey Open-File Report 91-237, 43 p.

Graf, J. B., 1995: Measured and predicted velocity and longitudinal dispersion at steady and unsteady flow, Colorado River, Glen Canyon Dam to Lake Mead: Water Resources Bulletin, American Water Resources Association, vol. 31, no. 2, p. 265-281.

Guay, J.R., 1991. Simulation of urban runoff and river water quality in the San Joaquin River near Fresno, California: American Water Resources Association symposium on urban hydrology, Denver, Colorado,November 4-8, 1990, Proceedings, p. 177-181.

Hurley, N.M., Jr., 1991: Transport simulation of Striped Bass Eggs in the Congaree, Wateree, and Santee Rivers, South Carolina: U.S. Geological Survey Water-Resources Investigations Report 91-4088, 57 p.

Ishii, A.L., and Turner, M.J., 1997, Verification of a one-dimensional, unsteady flow model for the Fox River in Illinois: U.S. Geological Survey Water-Supply Paper 2477, 65 p.

Jobson, Harvey E., 1985 Simulating Unsteady Transport of Nitrogen, Biochemical Oxygen Demand, and Dissolved Oxygen in the Chattahoochee River Downstream from Atlanta, Georgia: US Geological Survey Water Supply Paper No-2264, 36 pages.

Jobson, 1987, Estimation of Dispersion and First-Order Rate Coefficients by Numerical Routing: Water Resources Research, January, Vol. 23, No.1, P 169-180.

Paybins, Katherine Schipke, Tracy Nishikawa, John A. Izbicki, and Eric G. Reichard, 1997 "Statistical analysis and mathematical modeling of a tracer test on the Santa Clara River, Ventura County, California, US Geological Survey Water-Resources Investigations Report 97-4275, 19 p.

Rajbhandari, Haridarshan Lal, 1995, Dynamic simulation of Water Quality in Surface Water Systems Utilizing a Lagrangian Reference Frame: Dissertation presented to the University of California Davis in partial satisfaction of the requirements for the degree of Doctor of Philosophy, 264 p.

Risley, John C., 1997: Relations of Tualatin River Water Temperatures to Natural and Human-Caused Factors: U.S. Geological Survey Water-Resources Investigations, Report 97-4071, 143 p.

Schoellhamer, D.H., and Curwick, P.B., 1986, Selected functions for sediment transport models: Fourth Federal Interagency Sedimentation Conference, LasVegas, Nevada, March 24-27, 1986, v. 2, pp. 6-157 - 6-166. (routed fine sediment through the lower reaches of the Mississippi River using the LTM transport model. The LTM model is a predecessor of the BLTM.)

Schoellhamer, D.H., 1987, Lagrangian modeling of a suspended-sediment pulse: ASCE National Conference on Hydraulic Engineering, Williamsburg, Virginia, August 3-7, 1987, pp. 1040-1045.

Schoellhamer, D.H., 1988, Simulation and video animation of canal flushing created by a tide gate: National Conference on Hydraulic Engineering, ColoradoSprings, Colorado, August 8-12, 1988, pp. 788-793.

Schoellhamer, D.H., 1989, Implementation of the Lagrangian Transport Model, in Schaffranek, R.W., ed., Proceedings of the Advanced Seminar on One-Dimensional Open-Channel Flow and Transport Modeling: U.S. Geological Survey Water-Resources Investigations Report 89-4061, Reston, Virginia, pp. 20-21.

Schoellhamer, D.H., and Goodwin, C.R., 1989, Tide-induced circulation and flushing using tide gates in residential canals of Cape Coral, Florida, in Schaffranek, R.W., ed., Proceedings of the Advanced Seminar on One-Dimensional Open-Channel flow and Transport Modeling: U.S. Geological Survey Water-Resources Investigations Report 89-4061, Reston, Virginia, pp. 45-52.

Schoellhamer, D.H., 1988: Lagrangian Transport Modeling with QUAL II Kinetics, Journal of Environmental Engineering, vol. 14, No. 2, p 368-381.

Stark, J.R., D.S. Armstrong, and D.R. Zwilling, 1994, Stream-Aquifer Interactions in the Straight River Area, Becker and Hubbaard Counties, Minnesota: U.S. Geological Survey Water-Resources Investigations, Report 94-4009, Mounds View, Minnesota, 83 pages.

Weiss, L.A., Schaffranek, R.W., and deVries, M.P., 1994: Flow and chloride transport in the tidal Hudson River, New York, in Hydraulic Engineering '94:Proceedings of the American Society of Civil Engineers, v. 2, p. 1300-1305.

Wiley, J.B., 1993: Simulated flow and solute transport, and mitigation of a hypothetical soluble-contaminant spill for the New River in the New River Gorge National River, West Virginia, USGS Water-Resources Investigations Report 93-4105, 39 p.

Wiley, J.B., 1992, Flow and solute-transport models for the New River in the New River Gorge National River, West Virginia, U.S. Geological Survey Open-File Report 92-65.

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