BRANCH (Branch-Network Dynamic Flow Model)

The Branch-Network Dynamic Flow Model--BRANCH--is used to simulate steady or unsteady flow in a single open-channel reach (branch) or throughout a system of branches (network) connected in a dendritic or looped pattern.

steady or unsteady flowopen-channel reach



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       The Branch-Network Dynamic Flow Model--BRANCH--is used to simulate steady or unsteady flow in a single open-channel reach (branch) or throughout a system of branches (network) connected in a dendritic or looped pattern.  BRANCH is applicable to a wide range of hydrologic situations wherein flow and transport are governed by time-dependent forcing functions.  BRANCH is particularly suitable for simulation of flow in complex geometric configurations involving regular or irregular cross sections of channels having multiple interconnections, but can be easily used to simulate flow in a single, uniform open-channel reach.  Time-varying water levels, flow discharges, velocities, and volumes can be computed at any location within the open-channel network.  Streamflow routing and computation by the BRANCH model is superior to simplified-routing methods in open-channel reaches wherein severe backwater and (or) dynamic flow conditions prevail.  Typical uses of the model encompass the assessment of flow and transport in upland rivers in which flows are highly regulated or backwater effects are evident, or in coastal networks of open channels wherein flow and transport are governed by the interaction of freshwater inflows, tidal action, and meteorological conditions.  Surface- and ground-water interactions can be simulated by the coupled BRANCH and USGS modular, three-dimensional, finite-difference ground-water flow (MODFLOW) models, referred to as MODBRNCH.


       The BRANCH model uses a weighted four-point, implicit, finite-difference approximation of the unsteady-flow equations. Flow equations are formulated, using water level and discharge as dependent variables, to account for nonuniform velocity distributions through the momentum Boussinesq coefficient, to accommodate flow storage and conveyance separation, to treat pressure differentials due to density variations, and to include wind shear as a forcing function.  The extended form of the de Saint Venant equations is formulated so as to provide a high degree of flexibility for simulating diverse flow conditions produced by varied forcing functions in channels of variable cross-sectional properties.  Subdivision of branches into segments of unequal lengths is accommodated by the finite-difference technique and the implicit solution scheme permits computations at large time steps. The effects of hydraulic control structures within the model domain are treated by a multi-parameter rating method.  The model accommodates tributary inflows and diversions as well as lateral overbank flows, and includes a Lagrangian, particle-tracking scheme for conservative constituents.  Transformation equations are formulated that describe the relationship between unknowns at the ends of branches thereby reducing the order of the coefficient matrices and producing a significant saving of execution time and computer memory.  The resultant matrix of BRANCH-transformation and boundary-condition equations is solved by Gaussian elimination using maximum pivot strategy.


       Version 4.3 1997/06/05 - Corrected program to correctly handle four-byte stage data (previously, the model assumed stage data to be two-byte integer values).  Corrected problems related to interactive update of comment records, global geometry print flag, and flag specifying coupled MODFLOW/BRANCH simulation. Minor changes to appearance or printed results file related to print of input cross section information and non-convergence warnings.

       Version 4.2 1997/03/06 - Added three computation-control variables: GPRBCH (global flag to override values set for PRTBCH and PRTSUM for each branch to print results for all or none of the branches), GPLBCH (global flag to override values set for PLTBCH and PPLTBH for each branch to plot results for all or none of the branches), and GPRTXS (global flag to override values set for PRTXSG for each branch to print input geometry for all or none of the branches).  Added use of new CalComp to INTERACTER library included in LIBUTL version 6.0 so that hard-copy graphics output is available for DOS versions.  Added option (IMODFW=2) to cause BRANCH to read but ignore MODBRNCH specific input records. Improved labeling of graphics.  Changed metric minimum (2000 meters) and maximum (8000 meters) segment lengths at which a warning message is printed.  Fixed print of input boundary-value definition as equation to print without adding the stage computational datum.  Increased default number of cross section from 150 to 175.  Important code correction:  Fixed code so that the model correctly retrieves data from a data base for simulations of longer than 30 days.  This problem was introduced in version 3.11.

       Version 4.1 1996/10/15 - Corrected program error that wrote incorrect results to user-table output file. The file name of the user-table output is now retained as the last entry in the "master" file.  Fixed incorrect multiplication by 100 of computed results to be stored in a TDDB or WDM data base (error introduced in version 3.11).  Lahey F90 compiler dependencies added.  Fixed incorrect indexing of observed data in multiple- day, computed-versus-measured, line-printer plots.  Fixed labeling of metric output when data are input in English units.

       Version 4.0 1996/03/04 - DSPRSN field width increased.  Added computation of storage area for output to BLTM.FLW file.

       Version 3.11 1995/11/01 - MODFLOW/BRANCH interface fully implemented, and considerable restructuring, modularization, and cleanup of the code.  Pressure gradient term added to account for density variations.  Lateral flow implemented.  Code reordering and restructuring.  Global default values updated and expanded (air density, water temperature, longitudinal dispersion).  Allow input of time step increment in seconds.  Allow boundary condition to be input by SIN equation and flood-wave hydrograph. Time-Dependent Data Base (TDDB) input can be as real or double-precision values.  Output results as floating-point values to TDDB and Watershed Data Management (WDM).  A new variable (FVFLG) was added to the first geometry record for each cross section. This addition means that the variable GDATUM has been shifted two positions to the left (columns 64-70).  Thus, users who previously coded GDATUM in columns 66-72 will need to adjust their geometry data to be compatible with this version.  The FVFLG allows individual cross sections to be selected for flow-volume computations.  Added option to input and use wetted perimeter in computation of ETA instead of approximating the value as hydraulic radius.  Input of wetted perimeter as piece-wise linear functions of water-surface elevation is added to the Cross-Sectional Geometry Data records.  This addition has caused functional eta, QA, and TA to be moved 10-columns to the right on these records.  Output of simulation results at each time step (IPROPT=0) changed to fit on 80-column wide screen.  Old format is selected by specifying the new computational-control parameter IPRMFT as 1.  Added option to file results in a text file for postprocessing.  Added new Initial Condition record for data (row, column, and layer in MODFLOW model that coincides with the cross section and leakage coefficient and channel bottom elevation) as needed by coupled MODFLOW/BRANCH simulations. Three-parameter rating for culverts added.  Added input of hydraulic structures for MODFLOW/BRANCH simulations.  Added error message routines to make messages more consistent in appearance. Particle tracking problem when a particle was exactly at a cross- section location identified and corrected.  The simulation time step can now be input as a number of seconds by specifying IDTM < 0.  Computational-Control records modified to include new variables and remove others.  OTMAP, OTBLTM, OTNCDF, NTDIOF, and OTTDB removed and replaced by output file option OTFILE.  Added computational-control parameter IMODFW.

       Version 2.11 1994/05/03 - Cleaned up code (renumbered statement labels, set indention of IF and DO blocks to 2 spaces, converted many integer*2 variables to integer, made comments look more similar), combined subroutines into functional code groups instead of all in separate files, new option to produce snap-shot file of computational results, global defaults for initial-condition discharge and stage, input of water density (RHO), lateral flow (QLAT) and lateral velocity (ULAT) as an initial condition for each cross section.

       Version 2.8 1994/02/15 - Added setting of initial conditions using default or prorated boundary-value data, flow-resistent coefficient optimization, particle-tracking of multiple-paths, output of results in NETCDF format, automatic revision and date to executable, and made minor bug fixes and code cleanup.

       Version 92/05/07 - First UNIX release, computational efficiency increased by a factor of 10, made UNIX compatible.

       Version 90/10/29 - Station numbers now specified in 16-digit field instead of 8, graphics written using CalComp-style calls instead of DISSPLA, data base support for WDM files added.

       Version 89/02/08 - Dimensions moved to single include file, Time-Dependent Data System (TDDS) support added for PC's, digital graphics added for PC's, wind data can now be retrieved from data base, added overbank storage, rating tables for specification of boundary conditions, and time step for printed results independent of computation time step.

       Version 86/06/20 - Restructuring of code for ease of portability and dimensioning, PC compatible, added interactive file-name designation, self-setting boundary conditions, and print of model dimensions.

       Version 85/11/01 - Added flow resistance as tabular functions or quadratic function, extrapolation out of defined geometry tables, digital graphics.

       Version 83/05/12 - Added data base storage of results.


       Input data consist of channel geometry and initial flow conditions defined at all cross-section locations and boundary conditions defined at channel extremities.  Cross-sectional data, in the form of tables of top-width and area as functions of water level, describing the open-channel reaches can be manually prepared and formatted for input to the model or interactively entered, processed, and formatted using the Channel Geometry Analysis Program (CGAP).  Initial flow conditions can be measured, assumed, or interpolated values.  Boundary conditions can be specified by equation, functional relations, or time-series values.  Time series of boundary conditions, i.e., water levels or discharges, can be input directly via formatted sequential files or automatically retrieved from the data base of either the TDDS or the WDM system. Input values can be either in metric or inch-pound units.


       Time series of computed flow results can be directly output in tabular or graphical form at all, or selected, cross-section locations.  Tabular output options include discrete flow results at every time step or iteration; daily summaries of minimum, maximum, and average flow conditions; monthly flow-volume summaries; or river-mile locations of injected particles.  Digital or line-printer graphical options include hydrograph plots of computed water levels or discharges or comparative plots of computed results versus measured data.  Graphical plots can be produced on CRT devices, directly, and (or) in CGM, PostScript, or HPGL formatted files for postprocessing.  Computed results can be stored directly in text files or in the data base of either the TDDS or WDM.  Interfaces are available for the USGS/WRD National Water Information System (NWIS) and the Branched Lagrangian Transport Model (BLTM).  Output results can be either in metric or inch-pound units.


       BRANCH is written in Fortran 77 with the following extensions:  use of integer*2 declarations, use of include files, variable names longer than 6 characters, use of underscores in variable names, use of mixed case, and reference to compiler-dependent system date and time routines.  To compile BRANCH the LIBUTL utility library is required.  LIBUTL includes software/user, software/computer, software/data base, and software/graphics interaction routines. BRANCH graphics are coded using CalComp graphics calls.  The LIBUTL software provides graphics libraries to convert CalComp graphic references to Graphical Kernel System (GKS) library references and Interactive Software Services's INTERACTER library references. BRANCH memory requirements depend on array dimensioning parameters found in the dimens.cmn include file.  The memory requirements can be tailored to suit application needs and computer system memory constraints by modifying the parameters in the dimens.cmn file and then recompiling the code.  Generally, the program is easily adapted to most computer systems that have access to the LIBUTL software and one of the mentioned graphics libraries.  The code has been used on UNIX-based computers and DOS-based 386 or greater computers having a math coprocessor and 4 mb of memory.


       BRANCH is optionally supported by CGAP for preparation of channel cross-sectional data and TDDS for preprocessing of boundary-value data and postprocessing of simulation results.  Graphical plots of particle-tracking results are produced by the TRKPLOT support program included with the BRANCH model distribution software.


       Latest version enhancements and additions to the BRANCH model are documented and maintained in a file included in the software distribution.  

   The latest model version is downward compatible with the original documentation: Schaffranek, R.W., Baltzer, R.A., and Goldberg, D.E., 1981, A model for simulation of flow in singular and interconnected channels: U.S. Geological Survey Techniques of Water-Resources Investigations, book 7, chap. C3, 110 p.

       Schaffranek, R.W., 1987, Flow model for open-channel reach or network:  U.S.  Geological Survey Professional Paper 1384, 12 p.


       Fulford, J.M., 1995, User's guide to the Culvert Analysis Program: U.S.  Geological Survey Open-File Report 95-137, 69 p.

       Jobson, H.E., and Schoellhamer, D.H., 1987, Users manual for a branched Lagrangian transport model: U.S. Geological Survey Water-Resources Investigations Report 87-4163, 73 p.

       Regan, R.S., and Schaffranek, R.W., 1985, A computer program for analyzing channel geometry: U.S. Geological Survey Water-Resources Investigations Report 85-4335, 49 p.

       Regan, R.S., Schaffranek, R.W., and Baltzer, R.A., 1996, Time-Dependent Data System (TDDS)--An interactive program to assemble, manage, and appraise input data and numerical output of flow/transport simulation models: U.S. Geological Survey Water-Resources Investigations Report 96-4143, 104 p.

       Sanders, C.L., 1995, The use of three-parameter rating table lookup programs, RDRAT and PARM3, in hydraulic flow models: U.S. Geological Survey Water-Resources Investigations Report 95-4090, 18 p.

       Swain, E.D., 1992, Incorporating hydraulic structures in an open-channel model: Proc. 1992 National Hydraulic Engineering Conf., American Society of Civil Engineers, New York, N.Y., p. 1118-1123.

       Swain, E.D., and Wexler, E.J., 1993, A coupled surface-water and ground-water model for simulation of stream-aquifer interaction: U.S. Geological Survey Open-File Report 92-138, 162 p.


       Bergquist, R.J., and Ligteringen, H., 1988, The BRANCH model and the Segara Anakan study: Proc. 1988 National Hydraulic Engineering Conf., American Society of Civil Engineers, New York, N.Y., p. 794-799.

       Bower, D.E., Sanders, C.L., and Conrads, P.A., 1993, Retention time simulation for Bushy Park Reservoir near Charleston, S.C.: U.S. Geological Survey Water-Resources Investigations Report 93-4079, 47 p.

       Bulak, J.S., Hurley, N.M., and Crane, J.S., 1993, Production, mortality, and transport of striped bass eggs in Congaree and Wateree Rivers, S.C.: Proc. American Fisheries Society Symposium, p. 29-37.

       Cameron McNamara Consultants, 1987, Sungai Sarawak flood plain model study: Report No. 86-1702 to Drainage and Irrigation Dept., Govt. of Sarawak.

       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.

       Holtschlag, D.J., 1981, Flow model of Saginaw River near Saginaw, Michigan: U.S. Geological Survey Open-File Report 81-1061, 20 p.

       Hurley, N.M., Jr., 1991, Transport simulation of striped bass eggs in the Congaree, Wateree, and Santee Rivers, S.C.: U.S. Geological Survey Water-Resources Investigations Report 91-4088.

       Jennings, M.E., and Jeffcoat, H.H., 1987, Computation of unsteady flows in the Alabama River: Water Resources Bulletin, v. 23, no. 2, p. 313-315.

       Lipscomb, S.W., 1989, Flow and hydraulic characteristics of the Knik-Matanuska River estuary, Cook Inlet, southcentral Alaska: U.S. Geological Survey Water-Resources Investigations Report 89-4064, 52 p.

       MacBroom, J.G., and Hart, E., 1992, Pine Creek tidal hydraulic study: Proc. 1992 National Hydraulic Engineering Conf., American Society of Civil Engineers, New York, N.Y., p. 1154-1158.

       Mantz, P.A., and Manopinives, S., 1987, Computer aided hydraulic studies of the Lower Neches Valley Authority canal system, Lamar University report to LNVA Canal Authority.

       Schaffranek, R.W., 1982, A flow model for assessing the tidal Potomac River: Proc. Hydraulics Div. Specialty Conf., Applying Research to Hydraulic Practice Symp., American Society of Civil Engineers, New York, N.Y., p 531-545.

       Schaffranek, R.W., 1985, Model for simulating floods in rivers: Society for Computer Simulation, Simulation Series, v. 15, no. 1, p. 132-139.

       Schaffranek, R.W., 1987, A flow simulation model of the tidal Potomac River: U.S. Geological Survey Water-Supply Paper 2234-D, 41 p.

       Schaffranek, R.W., 1989, Proc. Advanced seminar on one-dimensional, open-channel flow and transport modeling: U.S. Geological Survey Water-Resources Investigations Report 89-4061, 99 p.

       Schoellhamer, D.H., 1988, Simulation and video animation of canal flushing created by a tide gate: Proc. 1988 National Hydraulic Engineering Conf., American Society of Civil Engineers, New York, N.Y., p. 788-793.

       Stedfast, D.A., 1982, Flow model of the Hudson River estuary from Albany to New Hamburg, New York: U.S. Geological Survey Water-Resources Investigations Report 81-55, 69 p.

       Strickland, A.G., and Bales, J.D., 1992, Modeling flow and flood-plain storage in a tidally affected river: Proc. 1992 National Hydraulic Engineering Conf., American Society of Civil Engineers, New York, N.Y., p. 1130-1135.

       Weiss, L.A., Schaffranek, R.W., and deVries, M.P., 1994, Flow and chloride transport in the tidal Hudson River, N.Y.: Proc. 1994 National Hydraulic Engineering Conf., American Society of Civil Engineers, New York, N.Y., p. 1300-1305.

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U.S. Geological Survey (2020). BRANCH (Branch-Network Dynamic Flow Model), Model Item, OpenGMS,


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