Water Resources Surface Water Software: Full Equations (FEQ) Model Web Resources

Water Resources Applications Software

## Summary of FEQ

```NAME

feq - Full EQuations Model
fequtl - Full EQuations UTiLity

ABSTRACT
FEQ simulates flow in a stream system by solving the full, dynamic
equations of motion for one-dimensional unsteady flow in open
channels and through control structures.  The structure of the
program is designed to follow the structure of a stream system while
providing maximum generality and flexibility of description.  A
stream system that is simulated with FEQ is subdivided into three
broad classes of flow paths: (1) stream reaches (branches), (2)
parts of the stream system for which complete information on flow
and depth are not required (dummy branches), and (3) level-pool
reservoirs.  These components are connected by special features or
hydraulic control structures, such as junctions, bridges, culverts,
dams, waterfalls, spillways, weirs, side weirs, pumps, and others.
The hydraulic characteristics of channel cross sections and special
features are stored in function tables calculated by the companion
program FEQUTL.  FEQ can interpolate hydraulic properties of cross
sections between measured sections.  FEQ can be applied in the
simulation of a wide range of stream configurations (including
loops), lateral-inflow conditions, and special features.  Boundary
conditions can be water-surface stage, discharge, or the stage-
discharge relationship at a node.  Wind stress terms are supported.
The effects of lateral inflows can also be simulated in FEQ when
given local runoff intensity data.

METHOD
In FEQ, the principles of conservation of mass and conservation of
momentum are used to calculate the flow and depth throughout the
stream system resulting from known initial and boundary conditions
with an implicit finite-difference approximation.  FEQUTL is used to
compute the hydraulic properties of various structures, each with
its own computational theory.  Thorough discussion of computational
theory is given in the sources listed under DOCUMENTATION.

HISTORY
The Full Equations (FEQ) model for the simulation of one-dimensional
unsteady flow in open channels and through control structures was
first developed in 1976 to model the Sanitary and Ship Canal,
Chicago, Ill., as part of the 208 Water Quality Management Studies
conducted by the Northeastern Illinois Planning Commission with
principal support from the U.S. Environmental Protection Agency.
This original version was then expanded over the next several years.
The first numbered version, 2.0, appeared in March 1986 when a
version for personal computers was prepared.  In subsequent years,
the capabilities of the software were expanded at frequent intervals
to meet the needs of the expanding user base.  The USGS published
documentation for version 8.10 in 1997.  The later features of FEQ
are documented below.  Refer to the file RELEASE.TXT distributed
with the software for additional information on these enhancements
and code corrections.

Version 10.61, posted 2009/03/31 - (A) Options for user control of
the Newton correction factors are available.  The Newton
solution scheme continues to be used, but additional diagnostic
information is provided in the iteration logs and outputs for
nodes that failed to converge. (B) The ability to vary the
maximum timestep as a function of time has been added. (C) Small
errors in eddy losses that could occur in reverse flow under the
condition of single time-step convergence (essentially constant
flow), and in timestep synchronization have been corrected. (D)
Additional checks and reports have been added for various table
types. (E) The binary point time series files and diffuse time
series files are now read as direct-access unformatted files.
A utlity is available to convert the previous compiler-dependent
versions of the files. Similarly, the initial condition files
are now read with direct access statements. (F) The DTSF can
now start at any initial time in addition to 0.0. (G) The forced
boundary condition can be switched mid-run to read in either
tabular or binary file input. (H) The tributary delay option
relative balance has been improved from the order of 0.001 to
0.000001 by upgrading from linear correction to the Newton
solution scheme.  (I) Smoothing routines for table types 20-25
are available.

Version 9.98, posted 2005/05/31 - (A) Generalized effect of detention
of flow within reservoirs and delay of flow from tributary areas
enabled.  (B) Control of gate operations as a function of 3
exterior nodes.  (C) Irrigation runoff and withdrawal effects
from near-surface and imported water.  (D) Table numbers changed
to labels resulting in heading-dependent formats for many blocks.
Convertfeq utility available for conversion.  (E)Rainfall and
evaporation from open surfaces.  (F) Adjustment factor for
conveyance in a branch.  (G) Crest and flow adjustment for side
weirs.  (H) Master files and scenario-selector variable option for
complex project management.  (I) Automatic counting of nodes and
branches, disabling of weirs with datum errors.  (J) Formats to
facilitate conversion between linux and dos operating systems
incorporated.

Version 8.92, posted 1999/04/07 - (A) The negative constant-flow boundary
was corrected from an applied constant value of 0.  Positive
constant flow boundaries into and out of the system were
unaffected.  (B) An undefined variable was defined to end
potential error in the interpolation between weir and orifice
flow for underflow gates.  (C) An undefined variable that caused
potential error in checking for overflow in side-weir 2-D tables
was defined.

Version 8.92, posted 1997/06/18 - (A) Blank lines are now allowed
anywhere in the input except in the Branch Description Block where
they indicate repeated cross sections.  The blank lines are echoed to
the output.  (B) FORTRAN I/O numbers are no longer needed.  They
can be left in old inputs however.  (C) Space-delimited format is
allowed for the Network Matrix Control Input Block, when the
block is specified as NEW Network Matrix Control Input Block.  A
asterisk is used as a place holder for optional items.  (D) The
Special Output Block has been modified to allow user-customized
specification of output variables or single-line output.  The new
values are given in an OPTIONS line following the UNIT line.  The
variables that may be output include mean velocity (V), cross-
sectional area (A), main channel area (MCA), flow (MCQ), and
velocity (MCV), flood plain flow area (FPA), flow (FPQ), and
velocity (FPV).  In order to have single-line special output, the
Special Output Block is specified as "Special" rather than
"SPECIAL."  Only flow and velocity will be output.  (E) Access to
HECDSS time series is supported for the input of flow or
elevation at a boundary node, for output of flow or elevation
from any node, and for the unit-area runoff intensity used to
compute lateral inflow from a tributary area.  (F) Explicit
specification of side nodes (Code 13) is allowed to provide for
conservation of momentum for inflows.  The angle of entry is also
specified.  (G) The difference in elevation between two exterior
nodes can be used as the argument for control structures in the
Operations Control Block.  The difference from the NODE elevation
is specified by identifying the second node in the KEY variable
field.  (H) An optional Define Macros and Instructions Block has
been added to streamline the definition of the Network Control
Matrix.  (I) Two-way pumps have been added.  (J) An argument
scale factor has been added for function tables type 2,3, and 4
to allow for variable unit systems.  (K) A linear reservoir delay
factor for tributary runoff areas can be specified by the
variable KLR added at the end of the branch specification line.
KLR has the units of minutes delay time for a linear reservoir
interposed between the branch and the tributary area.

The Full Equations Utilities (FEQUTL) model for the approximation of
hydraulic characteristics of open channels and control structures
during unsteady flow was first developed in early 1984-85 using some
ideas from earlier piecemeal utility programs.  The first numbered
versions appeared in early 1988 as the user base expanded.  The
software has been expanded at frequent intervals to meet the needs
of the user base.  The U.S. Geological Survey published the
documentation for FEQUTL Version 4.15 in 1997.  Many additional
capabilities have been added to FEQ and FEQUTL during the time the
documentation was prepared.  The capabilities added to FEQUTL are
described below.  Refer to the file RELEASE.TXT distributed with the
software for additional information on these enhancements and code
corrections.

Version 5.80, posted 2009/03/31 - (A) Location descriptions for
specifying horizontal and vertical datums and units are supported.
(B) Table ID initializations were fixed. Some uninitialized
variables were found to have the potential to create minor bugs.
See http://il.water.usgs.gov/proj/feq/bug_notice2.html for more
details. (C) An area increment error caused by single-precision
in the routine that checks for duplicate and near-duplicate
elevations for elevations exceeding 700.0 is corrected. See
http://il.water.usgs.gov/proj/feq/bug_notice2.html for more
detail. (D) Smoothed outputs for table types 20-25 are available.

Version 5.46, posted 2005/05/31 - (A) Gate control table development
from underflow-gate rating partly supported in routine--INV_GATE.
(B) Sluice gate on upstream face of box culvert routine--UFGCULV.
(C) Support for function-table labels rather than function-table
numbers, requires conversion to heading-dependent formats in many
routines, see release.txt for details.  Conversion program,
convertutl, available.  (D) Exact specification of conversion
factors for Manning's n and the acceleration due to gravity
available.  (E) Cross-section conversion from FEQUTL to WSPRO
format.  (F) Estimate of surface area for level-pool reservoirs
where only elevation-storage capacity relation is know.  (G)
Formats to facilitate conversion between linux and Dos operating
systems incorporated.

Version 4.68, posted 1997/05/29 - (A) SI units are now supported. The
subdirectory METRIC under the test directory in FEQUTL contains
the SI version of the standard example file and the SI version of
the weir coefficients for embankment-shaped weirs.  (B) Added
another global convergence tolerance to the header block for
FEQUTL. The new convergence tolerance, EPSABS, is to be used in
those cases in which the residual function returns a length
value.  Thus when switching to using meters for the length unit,
EPSF will remain unchanged but EPSABS must be changed to reflect
the larger length unit.  In the US standard unit system, EPSABS
has the same numeric value as EPSF but has a different meaning.
EPSABS is located in the next field from EPSF.  If omitted, the
value of EPSF is used.  (C) Modified the Preissman slot for
closed conduits to reflect the unit system. The maximum slot
level is 150 meters, which is not exactly equal to 500 feet used
in the US unit system.  However, the round number is indicative
of an arbitrary selected value. The slot detection code was
modified also to find the vertical diameter of closed conduits.
The slot width used for detection of closed conduits remains at
0.07 feet or 0.021336 meters.  A slot width larger than this will
not be detected and FEQUTL will treat the cross-section function
table as being a normal open channel and not a closed conduit in
any context in which a closed conduit must be detected.  (D)
Changed the means for eliminating close values of depth in
computing cross section tables.  Previous versions had used an
absolute tolerance for the minimum difference between adjacent
depths.  This has been changed to a relative tolerance to be
scale independent.  (E) HEC2X command has been modified to
convert units from SI to English or from English to SI under user
control.  The default action is no conversion of the elevations
and offsets on the cross section.  Adding the word CONVERT after
the MODE response will cause conversion of units.  The conversion
of station values is governed by SFAC only and is set by the
user.  (F) Provided additional options following the unit system
selection in the standard header to force FEQUTL to use the more
exact value for the factor in Manning's equation.  The factor is
technically the cubic root of the number of feet in a meter,
which to single precision in a 32-bit IEEE floating point
representation is about 1.485919. For nearly all practical
purposes this can be taken as 1.49.  (G) Provided the option to
use an equation to compute the value of g given a latitude and an
elevation.  This happens whenever the exact value for the factor
in Manning's equation is requested.  The usual value of g is 32.2
f/s^2 or  9.815 m/s^2 with an error less than 0.2 percent across
the United States.  Using more than one value of GRAV may result
in slight differences between SI and US standard units.  (H)
Added vertical scale factor (VSCALE), and horizontal shift amount
(HSHIFT), to FEQX cross sections.  (I) Added vertical scale
factor (VSCALE), vertical shift (CSHIFT), horizontal scale factor
(HSCALE) to EMBANKQ.  (J) Added an argument scale factor to the
input of function tables of type 2, 3,and 4.  The argument scale
factor is placed after the function scale factor.  This moves the
SHIFT input item to the right.  The SHIFT item is little used and
may be discontinued.  In any case if you are using it you will
have to move the SHIFT item to the right by 16 columns to leave
space for the reading of the argument scale factor.  (K) Added
two new commands to create a bottom slot in a cross section.  The
commands are SETSLOT and CLRSLOT.   The first command defines a
bottom slot and this slot is add to all cross sections that
FEQUTL encounters until the command CLRSLOT is found.  Thus the
addition of a bottom slot to a cross section is like a switch:
either on or off.  When it is on it will appear in all cross
sections processed.  (L) Flapgate losses from submerged culvert
flow are supported.  Culverts with risers and flow through
orifices are also supported.  (M) CHANRAT and EMBANKQ have
optional variables LIPREC and MINPFD to request optimization of
interpolation of two-dimensional tables of type 6 or 13.  LIPREC
is the Linear Interpolation Precision specification in terms of
relative error.  MIPFD is the minimum partial free drop to be
computed.  (N) Computation of pump rating curves and pump loss
tables supported.

DATA REQUIREMENTS
FEQ reads an input file that contains specifications of run control
parameters, an encoding of the stream schematic, and initial
conditions.  This file can contain boundary-condition tables and
function tables for special features, or it can identify additional
files that contain the information.

FEQUTL computes function tables from specifications and data
provided in input files.  FEQUTL can read HEC-2 and WSPRO cross-
section input data and calculate cross-section function tables for
use in FEQ simulation.  Function tables for bridges are computed
using the program WSPRO to compute a suite of upstream and
downstream water-surface elevations.  FEQUTL can create input files
for WSPRO and convert tables output by WSPRO into a format suitable
for FEQ.

OUTPUT OPTIONS
The FEQ simulation process is documented in an output file.  In
addition, the results of simulation at nodes selected by the modeler
can be sent to data output files, special output files, or files
readable by the USGS program GenScn.

FEQUTL creates two output files, one which documents the computation
processes in detail, and the other which contains only function
tables.  The latter file can be identified in an FEQ input file to
be read directly by FEQ.

SYSTEM REQUIREMENTS
The program was written in Fortran 77 for PC.  The code is easily
ported to Unix and linux systems.  Both PC and UNIX versions are
available.

APPLICATIONS
Snohomish County Department of Public Works, Surface Water
Management Division, 1989, Snohomish River Unsteady Flow Model
(FEQ):  Report submitted to the U.S. Army Corps of Engineers,
Seattle District.  The model developed for the Snohomish River has
been extended to include the lower portions of the Skykomish and
Snoqualmie Rivers.  This model will eventually become part of a
flood-forecasting system.

Northwest Hydraulic Consultants Inc., 1993, Mill Creek (Auburn)
Hydraulic Modeling, Report to King County, Division of Surface
Water Management, Seattle, Washington.

Model of Mississippi River from Keokuk, Iowa, to Thebes, Illinois,
including its major tributaries as well as most of its minor
tributaries.  About 600 miles of stream are represented.  Seven
dams and six sets of operable gates, under automatic program
control, are included.  A report is in progress.

Johnstown Flood of 1977.  FEQ was applied to this flood as part of a
legal action stemming from this flood.  The lower reaches of the
Little Conemaugh and Stony Brook as well as the upper reaches of
the Conemaugh River are simulated.

DuPage County, Illinois Stormwater Management Plan.  As part of
their overall planning and regulation effort, DuPage County has
applied FEQ/FEQUTL to a wide variety of streams in DuPage County.
These streams include Winfield Creek, Waubaunsee Creek, Salt
Creek, East Branch DuPage River, Klein Creek, Black Partridge
Creek, Willoway Brook, and numerous other streams.

Illinois Department of Transportation, Division of Water Resources.
The Bureau of Planning has developed models used for planning and
regulation for the Fox River, Farmer-Prairie Creek, Midlothian
Creek, and the Skokie Lagoons.  The Fox River model includes
dynamic modeling of alternative dam-gate control operations.

DOCUMENTATION
Franz, D.D., and Melching, C.S., 1997, Full Equations (FEQ) model
for the solution of the full, dynamic equations of motion for
one-dimensional unsteady flow in open channels and through
control structures: U.S. Geological Survey Water-Resources
Investigations Report 96-4240, 258 p.

Franz, D.D., and Melching, C.S., 1997,  Full Equations Utilities
(FEQUTL) model for the approximation of hydraulic characteristics
of open channels and control structures during unsteady flow:
U.S. Geological Survey Water-Resources Investigations Report
97-4037, 205 p.

REFERENCES
Franz, D.D., 1982, Tabular representation of cross-sectional
elements: Journal of the Hydraulics Division, American Society of
Civil Engineers, v. 108, no. 10, p. 1070-1081.

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.

Ishii, A.L., and Wilder, J.E., 1993, Effect of boundary condition
selection on unsteady-flow model calibration, in Proceedings of
the XXV Congress of International Association for Hydraulic
Research, Tokyo, p. 193-200.

Knapp, H.V., and Ortel, T.W., 1992, Effect of Stratton Dam operation
on flood control along the Fox River and Fox Chain of Lakes:
Illinois State Water Survey Contract Report 533, 79 p.

Turner, M.J., 1994, Data-collection methods and data summary for
verification of a one-dimensional, unsteady-flow model of the Fox
River in Illinois: U.S. Geological Survey Open-File Report
93-483, 40 p.

Turner, M.J., Pulokas, A.P., and Ishii, A.L., 1996, Implementation
and verification of a one-dimensional, unsteady-flow model for
Spring Brook near Warrenville, Illinois:  U.S. Geological Survey
Water-Supply Paper 2455, 35 p.

TRAINING
One-week courses in FEQ modeling are offered about once a year in
DuPage County as demand dictates.  Contact the local American
Society of Civil Engineers section or:
Department of Environmental Concerns
DuPage County Center
421 N. County Farm Road
Wheaton, IL 60187

Additional courses at other locations are offered but only as demand
dictates.

CONTACTS
Operation:
U.S. Geological Survey
Illinois Water Science Center
Watershed and River Modeling Support
1201 W. University Avenue
Urbana, IL  61801

feq@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://il.water.usgs.gov/proj/feq/

and via anonymous File Transfer Protocol (FTP) from:

ftpdilurb.eru.usgs.gov (path: /pub/feq).

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

http://il.water.usgs.gov/proj/feq/software/feq
--and--
/pub/feq

bltm(1) - Branched Lagrangian Transport Model
branch(1) - One-dimensional Branch-network flow model
daflow(1) - Streamflow routine in upland channels of
channel networks
wspro88(1) - A computer model for Water-Surface PROfile
computations
GenScn(1) - GENeration and analysis of model simulation SCeNarios

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U.S. Department of the Interior | U.S. Geological Survey | Illinois Water Science Center
URL: http://il.water.usgs.gov/proj/feq/software/history2.shtml
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Page Last Modified: Tuesday, December 18, 2012