Availability of an Alternative One-Dimensional, Unsteady Flow Model; the Full Equations Model (FEQ) 

To: "A  - Division Chief and Staff",
        "B  - Branch Chiefs and Offices",
        "FO - State, District, Subdistrict and other Field Offices",
        "PO - Project Offices"
cc: " , WRD Archive File, Reston, VA ",
        "L. Jane Rose, Secretary, Reston, VA "
Subject: OSW Technical Memorandum No. 98.03
Date: Wed, 18 Feb 1998 17:10:01 -0500
From: "L. Jane Rose, Secretary, Reston, VA "

In Reply Refer To:                                          February 10, 1998
Mail Stop 415


Subject:  Availability of an Alternative One-Dimensional, Unsteady Flow
          Model; the Full Equations Model (FEQ) 

The Illinois District recently distributed copies of WRIR 96-4240, entitled 
"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" by Delbert D. Franz and Charles S. Melching. The purpose 
of this memo is to confirm that the model has received sufficient testing to 
be considered as an operational tool for use in WRD. The FEQ model and its 
companion utility program, Full Equations UTiLities (FEQUTL) (Franz and 
Melching, in press) are distributed by the Hydrologic Analysis and Support 
Software (HASS) group and is included on the last WRDAPP tape release, as well 
as the HASS software-distribution tape and internet site. Support for the 
model is provided by the Illinois District (contact Steve Melching or
Audrey Ishii).

FEQ and FEQUTL are non-proprietary programs developed by Dr. Delbert Franz of 
Linsley, Kraeger Associates in Mountain View, California. The
U.S. Geological Survey (USGS) involvement with FEQ began in the late 1980's at 
the Illinois District when two major cooperators became interested in applying 
FEQ for flood-plain delineation utilizing runoff input from the watershed 
model, Hydrologic Simulation Program Fortran (HSPF), and operational 
management of low-head dams. FEQ also has been applied in the State of 
Washington, by the South Florida Water Management District, and by numerous 
consulting firms. The FEQ output has been linked to the USGS GENerate 
SCeNarios (GENSCN) software for post-processing analytical and graphical 
tools. FEQ is capable of modeling a system constrained by a wide variety of 
fixed and variable-geometry hydraulic controls such as bridges, culverts, 
weirs, side weirs, and pumps. Specifying these controls is simplified in FEQ 
by use of its companion program, FEQUTL, which is used to supply function 
tables for cross-sections and hydraulic controls. FEQ is capable of modeling 
dendritic flow networks that contain loops. It accounts for lateral-inflow and 
wind and has a zero-inertia option for use on steeper streams. The accuracy of 
FEQ in simulating field conditions has been documented in Turner and others 
(1996) and Ishii and Turner (1997).

FEQ is a computer program that solves the one dimensional, unsteady flow 
equations (St. Venant equations) for water-surface elevation and mean water 
velocity. It uses the four point implicit finite difference numerical scheme 
and solves the equations with an iterative method that uses interpolation 
for functional values at computational nodes.

Other 1-D unsteady flow models available from the USGS are DAFLOW, BRANCH, and 

    DAFLOW is well suited to applications simulating steeper upland 
    channel networks in support of transport models, where limited 
    geometric data are available. DAFLOW does not support backwater 
    conditions or looped networks. 

    BRANCH has a long-proven history of successful application in WRD 
    projects and for computing discharge from slope measurement sites. 
    BRANCH is recommended for slope station applications. A solution of 
    the advection-dispersion transport equation has been incorporated in 
    the BRANCH model to facilitate simulations where density gradients 
    are important. BRANCH has also been coupled to the groundwater flow 
    model, MODFLOW, for simulating groundwater/surface water 
    interactions. The stream/aquifer linked version is referred to as 
    MODBRANCH. A window-based graphical user interface (GUI) for creation 
    and modification of model-input files, compatible with MicroSoft 
    Windows environment, has been developed for BRANCH and is available 
    via the WWW at the Internet site http://stress.er.usgs.gov.

    The FOURPT has an excellent range of options for model start up in 
    either upland or tidally affected reaches. FOURPT or FEQ should be 
    considered for networks where subsectioning of cross-sections is 
    needed to improve behavior of the depth-conveyance relationship or 
    the behavior of hydraulic controls is important.

Any of the models can be used in conjunction with the BLTM transport model. 
Users should consider the weaknesses and strengths of each of the available 
models when selecting a model for a particular application. The Office of 
Surface Water, either Janice Fulford or Harvey Jobson, will be happy to 
discuss the strengths and weaknesses of each model and provide help in 
selecting the model that is best suited for a particular application.

Training on the application of FEQ may be offered in FY98 at the National 
Training Center or in the Northeastern Region (sponsored by Northeastern 
Region) depending on interest within the USGS. For more information on FEQ 
or to express interest in the training course, contact Steve Melching at 
(217)344-0037, ext. 3031 (email: csmelchi) or Audrey Ishii at (217)344-0037, 
ext 3026 (email: alishii). The training course, (ID2020TC) Modeling Flow and 
Transport in a Riverine Environment, emphasizes the DAFLOW model; the 
course, (G0913) Implementation and Calibration of Unsteady Open-Channel Flow 
and Transport Models, emphasizes the BRANCH model; and the course, (G0403 
One-Dimensional Streamflow Modeling Concepts, emphasizes the FourPt model.

References cited 

Franz, D.D. and Melching. C.S., in press, 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.

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, 66p.

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 

                                Thomas H. Yorke
                                Chief, Office of Surface Water

WRD Distribution:  A, B, FO, PO