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Summary of BRANCH

       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.  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

       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

       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.

       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.

       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.

       Implementation and Calibration of Unsteady Open-Channel Flow
       Transport Models (SW3091TC), offered annually at the USGS National
       Training Center.

       Operation and Distribution:
          U.S. Geological Survey
          Hydrologic Analysis Software Support Program
          437 National Center
          Reston, VA 20192

       Official versions of U.S. Geological Survey water-resources analysis
       software are available for electronic retrieval via the World Wide
       Web (WWW) at:


       and via anonymous File Transfer Protocol (FTP) from:

         (path: /pub/software).

       The WWW page and anonymous FTP directory from which the BRANCH
       software can be retrieved are, respectively:


       cgap(1) - Channel Geometry Analysis Program
       daflow(1) - Flow routing in channels or channel
       libutl(1) - Utility libraries for simulation models
       tdds(1) - Time-Dependent Data System
       wdm(1) - Watershed Data Management system

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