NAME
branch - Branch-Network Dynamic Flow Model
ABSTRACT
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.
METHOD
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.
HISTORY
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.
DATA REQUIREMENTS
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.
OUTPUT OPTIONS
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.
SYSTEM REQUIREMENTS
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.
SUPPORT SOFTWARE
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.
DOCUMENTATION
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.
RELATED DOCUMENTATION
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.
REFERENCES
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.
TRAINING
Implementation and Calibration of Unsteady Open-Channel Flow
Transport Models (SW3091TC), offered annually at the USGS National
Training Center.
CONTACTS
Operation and Distribution:
U.S. Geological Survey
Hydrologic Analysis Software Support Program
437 National Center
Reston, VA 20192
h2osoft@usgs.gov
Official versions of U.S. Geological Survey water-resources analysis
software are available for electronic retrieval via the World Wide
Web (WWW) at:
http://water.usgs.gov/software/
and via anonymous File Transfer Protocol (FTP) from:
water.usgs.gov (path: /pub/software).
The WWW page and anonymous FTP directory from which the BRANCH
software can be retrieved are, respectively:
http://water.usgs.gov/software/branch.html
--and--
/pub/software/surface_water/branch
--and--
/pub/software/general/libutl
SEE ALSO
cgap(1) - Channel Geometry Analysis Program
daflow(1) - Flow routing in channels or channel
networks
libutl(1) - Utility libraries for simulation models
tdds(1) - Time-Dependent Data System
wdm(1) - Watershed Data Management system