DAMBRK (A Dam-Break Flood Forecasting Model)

VERSION/DATE: 6/20/88

**** Please Note: FLDWAV is the replacement for this program ****

OPERATING SYSTEM: DOS

DISTRIBUTOR: NWS (National Weather Service, NOAA)

DOCUMENTATION (559 Pages):

THE NWS DAMBRK MODEL: THEORETICAL BACKGROUND/USER DOCUMENTATION By D.L. Fread, Hydrologic Research Laboratory, Office of Hydrology, National Weather Service (NWS) June 20, 1988 (Reprinted October 1988)

ADDITIONAL PROGRAMS

In addition to DAMBRK '88, the following models are included with program installation and documentation:

SMPDBK -- Version 9/91 -- an interactive simplified dam-break model which computes the peak discharge, water surface elevation, and time of occurrence for selected cross sections downstream of a breached dam (more information below).

BREACH -- Version 7/88  -- a deterministic model of the erosionformed breach (overtopping or piping initiated) in an earthen dam (man-made or landslide-formed); it computes the outflow hydrograph and the breach parameters used in DAMBRK and SMPDBK (more information below).

DWOPER -- Enhanced Network Version 7/18/84 (latest revision 8/89) -- an unsteady flow dynamic routing model (one-dimensional Saint-Venant equations) for a single channel or network (dendritic and/or bifurcated) of channels for free surface or pressurized flow (more information below).

CROSS-SECTION -- plots topwidth-elevation from cross-section data in x-y coordinates; also computes distance weighted average cross sections; also converts HEC "GR" cards to the correct NWS Format.

DAMBRK: ABSTRACT

A dam-break flood forecasting model (DAMBRK) is described and applied to two actual dam-break flood waves. The model consists of a breach component which utilizes simple parameters to provide a temporal and geometrical description of the breach. The model computes the reservoir outflow hydrograph resulting from the breach via a broad-crested weir flow approximation, which includes effects of submergence from downstream tailwater depths and corrections for approach velocities. Also, the effects of storage depletion and upstream inflows on the computed outflow hydrograph are accounted for through storage routing within the reservoir. The basic component of the DAMBRK model is a dynamic routing technique for determining the modifications to the dambreak flood wave as it advances through the downstream valley, including its travel time and resulting water surface elevations. The dynamic routing component is based on a weighted four-point, nonlinear finite-difference solution of the one- dimensional equations of unsteady flow (Saint-Venant equations) which allows variable time and distance steps to be used in the solution procedure. Provisions are included for routing supercritical flows, subcritical flows, or a spontaneous mixture of each, and incorporating the effects of downstream obstructions such as road-bridge embankments and/or other dams, routing mud/debris flows, pressurized flow, landslide-generated reservoir waves, accounting for volume and flow losses during the routing of the dambreak wave, considering the effects of off-channel (dead storage), floodplains, and floodplain compartments. Model input/output may be in either English or metric units. Modeling difficulties and parameter uncertainties are described and methods of treating them are discussed. Model data requirements are flexible, allowing minimal data input when it is not available while permitting extensive data to be used when appropriate. The model was tested on the Teton Dam failure and the Buffalo Creek coal-waste dam collapse. Computed outflow volumes through the breaches coincided with the observed values in magnitude and timing. Observed peak discharges along the downstream valleys were satisfactorily reproduced by the model even though the flood waves were severely attenuated as they advanced downstream. The computed peak flood elevations were within an average of 1.9 ft and 2.1 ft of the observed maximum elevations for Teton and Buffalo Creek, respectively. Both the Teton and Buffalo Creek simulations indicated an important lack of sensitivity of downstream discharge to errors in the forecast of the breach size and timing. Such errors produced significant differences in the peak discharge in the vicinity of the dams; however, the differences were rapidly reduced as the waves advanced downstream. Computational requirements of the model are quite feasible for mainframe, mini- or microcomputers. Suggested ways for using the DAMBRK model in preparation of pre-computed flood information and in real-time forecasting are presented along with several examples illustrating the use of the DAMBRK model.

DAMBRK: INTRODUCTION

Dams provide society with essential benefits such as water supply, flood control, recreation, hydropower, and irrigation. However, catastrophic flooding occurs when a dam fails and the impounded water escapes through the breach into the downstream valley. Usually, the magnitude of the flow greatly exceeds all previous floods and the response time available for warning is much shorter than for precipitation-runoff floods. According to reports by the international Commission on Large Dams (ICOLD, 1973) and the United States Committee on Large Dams in cooperation with the American Society of Civil Engineers (ASCE/USCOLD, 1975), about 38% of all dam failures are caused by overtopping of the dam due to inadequate spillway capacity and by spillways being washed out during large inflows to the reservoir from heavy precipitation runoff. About 33% of dam failures are caused by seepage or piping through the dam or along internal conduits, while about 23% of the failures are associated with foundation problems, and the remaining failures are due to slope embankment slides, damage or liquefaction of earthen dams from earthquakes, and landslide-generated waves within the reservoir. Middlebrooks (1952) describes earthen dam failures that occurred with the U.S. prior to 1951. Johnson and Illes (1976) summarize 300 dam failures throughout the world.

The potential for catastrophic flooding due to a dam failure was brought to the Nation's attention during the 1970's by several floods due to dam failures such as the Buffalo Creek coal-waste dam, the Teton Dam, the Toccoa Dam, and the Laurel Run Dam. Also, there are many dams that are 30 or more years old, and many of the older dams are a matter of serious concern because of increased hazard potential due to downstream development and increased risk of failure due to structural. deterioration or inadequate spillway capacity. A report by the U.S. Army (1981) gives an inventory of the Nation's approximately 70,000 dams with heights greater than 25 ft or storage volumes in excess of 50 acre-ft. The report also classifies some 20,000 of these as being "so located that failure of the dam could result in loss of human life and appreciable property damage ..."

The National Weather Service (NWS) has the responsibility to advise the public of downstream flooding when there is a failure of a dam. Although this type of food has many similarities to floods produced by precipitation runoff, the dam-break flood has some very important differences which make it difficult to analyze with the common techniques which have worked so well for the precipitation-runoff floods. To aid NWS flash flood hydrologists who are called upon to forecast the downstream flooding (flood inundation information and warning times) resulting from dam-failures, a numerical model (DAMBRK) has been developed. The DAMBRK model may also be used for a multitude of purposes by engineering planners, designers, and analysts who are concerned with possible future flood inundation mapping due to dam-break floods and/or reservoir spillway floods. The DAMBRK model can also be used for routing any specified flood hydrograph through reservoirs, rivers, canals, or estuaries as part of general engineering studies of waterways. Its principal limitation is its confinement to analyzing flow through a single waterway rather than a network of mutually interactive channels, e.g., dendritic (tree-type network of rivers, distributary network of irrigation canals, and estuarial network of waterways. Two other NWS models may be used for channel networks, DWOPER (Fread, 1978, 1983), and FLDWAV (Fread, 1985b; Fread and Lewis, 1988). The models are available for mainframe, mini- or microcomputers. The FLDWAV model is scheduled for release sometime during the latter part of 1988.

Model Development

The DAMBRK model represents the current state-of-the-art in understanding of dam failures and the utilization of hydrodynamic theory to predict the dam-break wave formation and downstream progression. The model has wide applicability; it can function with various levels of input data ranging from rough estimates to complete data specification; the required data is readily accessible; and it is economically feasible to use, i.e., it requires minimal computational effort on mainframe computing facilities and is feasible for use on microcomputers (IBM PC compatibles). DAMBRK is used by most fedral/state agencies in the U.S. and in over forty nations around the world. It is also extensively used by private consultants, hydropower and mining companies, and is utilized in more than 40 universities for teaching and research purposes.

The model consists of two conceptual parts, namely: (1 ) description of the dam failure mode, i.e., the temporal and geometrical description of the breach; and (2) a hydraulic computational algorithm for determining the time history (hydrograph) of the outflow through the breach as affected by the breach description, reservoir inflow, reservoir storage characteristics, spillway outflows, and downstream tailwater elevations; and for routing of the outflow hydrograph through the downstream valley in order to account for the changes in the hydrograph due to valley storage, frictional resistance, downstream bridges or dams. The model also determines the resulting water surface elevations (stages) and flood-wave travel times.

The latest version of DAMBRK is an expanded version of a practical operational model first presented in 1977 by the author (Fread, 1977). Other versions were previously released in 1979, 1980, 1981, 1982, and 1,384 as reported by the author in a paper titled "The NWS Dam-Break Flood Forecasting Model" (Fread, 1984b). The first model was based on previous work by the author on modeling breached dams (Fread and Harbaugh, 1973) and routing of flood waves (Fread, 1974a, 1976). There have been a number of other operational dam-break models that have appeared in the literature, e.g., Price, et al. (1977), Gundlach and Thomas (1 977), Thomas (1 977), Keefer and Simons (1 977), Chen and Druffel (1977), Balloffet, et al. (1974), Balloffet (1977), Brown and Rogers (1977), Rajar (1978), Brevard and Theurer (1979), Bodine, and HEC (1981). DAMBRK differs from each of these models in either or all of the following essential functions: the treatment of the breach formation, the outflow hydrograph generation, and the downstream flood routing.

During the last 6-7 years, there have been a number of studies in which various models suitable for dam-break analysis were compared, e.g., Land (1980) with the U.S. Geological Survey; McMahon (1981) with the U.S. Corps of Engineers; Tschantz and Mojib (1981) with the University of Tennessee; Singh and Snorrason (1982) with the Illinois State Water Survey; Keefer and Peck (1982), and Binnie & Partners (1986) from the private consulting sphere; and Wurbs (1985, 1986) with Texas A & M University. The general conclusion of these studies was that DAMBRK is preferred over, the other models on the basis accuracy, theoretical foundation, range of applicability, and relative ease of application. However,, the DAMBRK model's limitations and difficulties in application were pointed out in these studies. Research has been on-going in developing improvements in the DAMBRK model allowing it to have fewer limitations, and an increasing range of applicability and numerical robustness for more convenient usage.

Scope

Herein, the 1988 version of DAMBRK is described. New developments are delineated, information on model application difficulties along with suggested means of overcoming the difficulties are provided, some example applications are given, a data input description along with some examples are provided, and model output is described.

Summary Preview of DAMBRK

DAMBRK is used to develop the outflow hydrograph from a dam and hydraulically route the flood through the downstream valley. The governing equations of the model are the complete one-dimensional Saint-Venant equations of unsteady flow which are coupled with internal boundary equations representing the rapidly varied (broad-crested weir) flow through structures such as dams and bridge/embankments which nay develop a time- dependent breach. Also, appropriate external boundary equations at the upstream and downstream ends of the routing reach are utilized. The system of equations is solved by a nonlinear weighted 4-point implicit finite- difference method. The flow may be either subcritical or supercritical or a combination of each varying in space and time from one to the other; fluid properties may obey either the principles of Newtonian (water) flow or non-Newtonian (mud/debris flows or the contents of a mine-tailings dam) flow. The hydrograph to be routed may be specified as an input time series or it can be developed by the model using specified breach parameters (size, shape, time of development). The possible presence of downstream dams which may be breached by the flood, bridge/ embankment flow constrictions, tributary inflows, river sinuosity, levees located along the downstream river, and tidal effects are each properly considered during the downstream propagation of the flood. DAMBRK also may be used to route mud and debris flows or rainfall/snowmelt floods using specified upstream hydrographs. High water profiles along the valley, flood arrival times, and hydrographs at user selected locations are standard model output. Model input/output may be in either English or metric units.

NOTICE TO DAMBRK USERS

The existing DAMRK Model (version 07/18/84) has been substantially improved in that its capabilities have been increased as well as its numerical robustness. The new model is referred to as DAMBRK '88 with a release version date of 06/20/88. The model's documentation has been expanded from sixty pages to approximately three hundred pages. DAMRK '88 (Fortran source) is available on magnetic tape (9-track, EBCDIC, nonlabeled, 1600 BPI, LRECL = 80, BLOCKSIDE = 800) for main-frame or minicomputers, or it is available on 5 1/4 inch (DS-DD) floppy diskettes (both Fortran source and executable load) for IBM PC compatible microcomputers having 640K and a 8087 math coprocessor.

The new capabilities of DAMBRK '88 are:

1 . An option which allows all input/output to be expressed in either English or metric units.

2. Saint-Venant implicit solution algorithm has been expanded so as to be able to simulate mixed (subcritical/supercritical) flows which occur and may change from one regime to the other and vice versa in both space (along the river) and time; the algorithm requires approximately 20 percent more CPU than the '84 algorithm which blows-up when the flow passes through critical depth as it changes from subcritical to supercritical or vice versa. Also, the algorithm in DAMBRK '88 for supercritical flows has been improved concerning its numerical stability.

3. Saint-Venant implicit equations have been expanded to include the effects of channel sinuosity, momentum coefficient, a viscous internal dissipation term for non-Newtonian fluids such as mud/debris or mine-tailings flows, and the option to use channel conveyance to compute the friction slope term (Sf) which increases numerical stability when cross sections with a top width vs. elevation relation has an abrupt change at the elevation where a flat overbank floodplain joins the main channel.

4. The ability to automatically create cross sections for the Saint- Venant solution algorithm for reservoirs where only a surface area - elevation relation is known.

5. An option to use either the computed wetted perimeter or the topwidth for the computed hydraulic radius which is used to compute the friction slope (Sf).

6. An option to route the dam-break wave in a dry channel by expanding the computational net along the channel at the same velocity as the approximated wave-front velocity.

7. Automatic determination of the computational distance step (Ax) to account for: (1) limitations imposed by expanding/contracting sections, (2) the condition: Dx where c is the wave speed which is computed within DAMBRK by the technique used in the NWS simplified dam-break model (SMPDBK), and (3) sudden changed in bottom slope.

8. Saint-Venant algorithm is applicable to unsteady flows which change with space or time from free surface gravity flow to pressurized flow and vice versa for any shape of channel or closed conduit.

9. Breach development may be linear or nonlinear as specified by the user.

10. Dam crest length may be a function of elevation for dams that are not level.

11. Breach may encompass only the spillway section of the dam.

12. Breach may commence when either a specified elevation is reached by the reservoir waters or when a specified time after beginning of simulation has been attained.

13. Piping failure may occur after beginning of simulation according to criteria described previously in item (12).

14. Bridge flow areas are specified as a separate top width Bbr- elevation table which enable cross sections, used by the Saint- Venant algorithm, to be located somewhat upstream or downstream of the bridge opening to avoid critical flow at the contracted bridge opening.

15. The time-dependent gate option was modified to use gate width and gate opening as user specified time series.

16. The turbine flow (QT) may be constant or time-dependent (time series).

17. Automatic interpolation of cross sections for computational convenience also now includes interpolation of landslide properties, and levee overflow sections along the channel.

18. The type of model output has been increased by adding more output options.

19. A decrease in execution time of about 50 percent due to a new compiler which is used to obtain the "load" diskette (PC-version).

The first update, which included revision 1 through revision 3, was released in August 1989 and included the following:

1. Allowed for the spillway crest length to vary with elevation in the dam discharge computation; the computation uses flow area instead of top width.

2. Allowed for the length of road embankment of the bridge to vary with elevation in computing the bridge flow over the embankment; the computational use flow area instead of top width.

3. Replaced the old GATE subroutine with a new GATE subroutine to comply with the technique developed by Randy Wortman of the Army Corps of Engineers (Portland Division).

4. Included sinuosity effect of meandering channel following the work of DeLong (Journal of Hydraulics, February, 1989).

5. Corrected metric conversion errors in options 7 and 11, and metric conversion errors in the lateral weir flow and subroutines (OUTPUT and PLOT).

The latest update (revision 4) was released in August 1991; it included the following updated enhancements/corrections.

1. Increased the model's numerical robustness as follows:

a. Implemented improvements in the mixed-flow algorithm to take advantage of flow characteristics from a previous time step. The model is better able to handle problems with reaches near critical flow and problems with gradual slope changes in which the flow changes gradually from supercritical flow to subcritical flow.

b. Included the loop rating boundary in initial flow computation to smooth out the numerical shock encountered at the start of Saint-Venant solution. Previously, if channel control existed at the downstream end, a single-valued rating boundary was assumed to establish the initial conditions. For a nonuniform, nonprismatic downstream reach, the shock due to switching from a single-valued rating boundary to a loop-rating boundary sometimes caused the model to blow-up.

c. Provided a temporary fix for a divergent solution of the Saint- Venant equations from going below channel bed and producing a negative area or from going above channel's highest topwidth; and sometimes, for very flat overbanks, producing computational overflow; this prevents model blow-up and allows the automatic time step reduction to occur which often allows a convergent solution to be achieved.

d. Corrected the internal boundary algorithm in options 11 and 12 so that the model does not blow-up during supercritical flow. Supercritical flow may develop due to a dam/bridge being located on a supercritical slope. For a dam, the flow upstream of the dam can change from subcritical to supercritical as the reservoir storage is depleted due to a dam breach.

2. Included a more efficient 2-stage solution scheme for solving the normal water depth equation, critical depth equation, and backwater/downwater equation. The efficient Newton-Raphson method is used first; if it does not converge, the less efficient bisection method is used to assure a solution.

3. Improved the numerical computational method for estimating how well the model conserves mass.

4. Allowed for initial flow to occur in the floodplain rather than only within the channel bank when using the floodplain (conveyance) option.

5. Eliminated possibility of premature initiation of dam failure due to very high water-surface elevation obtained during the iterative solution of the Saint-Venant equations, especially when the solution is diverging.

6. Corrected errors in the metric version for the bridge option and the timedependent gate and turbine flow options for dams.

THE NWS SIMPLIFIED DAM-BREAK (SMPDBK) FLOOD FORECASTING MODEL By Jonathan N. Wetmore and Danny L. Fread Revised 12/18/91 by Danny L. Fread, Janice M. Lewis, and Stephen M. Wiele

SMPDBK: SYNOPSIS

The National Weather Service (NWS) developed a simplified procedure in 1983 for predicting downstream flooding produced by a dam failure. This procedure, known as the Simplified Dam Break (SMPDBK) Flood Forecasting Model, produces information needed for delineating areas endangered by dam- break floodwaters while substantially reducing the amount of time, data, computer facilities, and technical expertise required in employing more highly sophisticated unsteady flow routing models such as the NWS DAMBRK model. The SMPDBK model can easily be processed on an inexpensive microcomputer; and with a minimal amount of data, the user may within minutes predict the dam-break floodwave peak flows, peak flood elevations, and peak travel times at selected downstream points. This capacity for providing results quickly and efficiently makes the SMPDBK model a useful forecasting tool in a dam failure emergency when warning response time is short, data are sparse, or large computer facilities are inaccessible. The SMPDBK model is also useful for pre-event dam failure analysis by emergency management personnel engaged in preparing disaster contingency plans when the use of other flood routing models is precluded by limited resources.

The SMPDBK model is designed for interactive use (i.e., the computer prompts the user for information on the dam, reservoir, and downstream channel and the user responds by entering the appropriate data values), and it allows the user to enter as much or as little data as are available; preprogrammed defaults can be substituted for some of the input parameters. Using the internally set default values, SMPDBK is capable of producing approximate flood forecasts after inputting only the reservoir water surface elevation when the dam starts to breach, reservoir surface area or storage volume associated with that water elevation, and elevation vs. width data for two cross sections of the downstream river valley (determined from on-site inspection or from topographic maps). If, however, the user has access to additional information (i.e., both the reservoir surface area and reservoir storage volume; estimates of the final width and depth of the breach; the time required for breach formation; the turbine, spillway, and/or overtopping flow; the Manning roughness coefficient; the flood elevation associated with a particular channel cross section where flooding becomes a problem; and/or elevation vs. width data for up to 50 downstream channel cross sections), the model will utilize this information to enhance the accuracy of the forecast.

In producing the dam-break flood forecast, the SMPDBK model first computes the peak outflow at the dam; this computation is based on the reservoir size, the size of the breach, and the length of time it takes the breach to form. The computed floodwave and channel properties are used in conjunction with peak-flow routing curves to determine how the peak flow will be attenuated as it moves downstream. Based on this predicted floodwave reduction, the model computes the peak flows at specified cross sections along the downstream valley. The average difference between the peak flow calculated with the more complete DAMBRK model and that calculated with SMPDBK is in many cases 10 percent or less. The SMPDBK model then computes the depth reached by the peak flow based on the channel geometry, slope, and roughness at the downstream cross sections. The SMPDBK model also computes the time required for the peak to reach each forecast point (cross section) and, if the user entered a flood elevation for the point, the time at which the flood elevation is reached as well as when the floodwave recedes below that elevation, thus providing the user with a time frame for evacuation and fortification upon which a preparedness plan may be based.

The SMPDBK model compares well with the DAMBRK model in test simulations of the flooding produced by the failure of Teton Dam, the Buffalo Creek coal waste dam, and in numerous theoretical dam failure simulations. Unlike DAMBRK, however, SMPDBK does not account for backwater effects created by natural channel constrictions or those due to such obstacles as downstream dams or bridge embankments, the presence of which can substantially reduce SMPDBK's accuracy.

Its speed and ease of use make it especially appropriate for use in emergencies. In addition, planners, designers, emergency managers, and consulting engineers responsible for predicting the potential effects of a dam failure may employ the model in situations where backwater effects are not significant for prevent delineation of areas facing danger should a particular dam fail.

BREACH: AN EROSION MODEL FOR EARTHEN DAM FAILURES By D. L. Fread, Senior Research Hydrologist with the Hydrologic Research Laboratory, National Weather Service, NOAA July 1988 (Revision 1, August 1991)

BREACH: ABSTRACT

A physically based mathematical model (BREACH) to predict the breach characteristics (size, time of formation) and the discharge hydrograph emanating from a breached earthen dam is presented. The earthen dam may be man-made or naturally formed by a landslide. The model is developed by coupling the conservation of mass of the reservoir inflow, spillway outflow, and breach outflow with the sediment transport capacity of the unsteady uniform flow along an erosion-formed breach channel. The bottom slope of the breach channel is assumed to be essentially that of the downstream face of the dam. The growth of the breach channel is dependent on the dam's material properties (D50 size, unit weight, friction angle, cohesive strength). The model considers the possible existence of the following complexities: 1) core material having properties which differ from those of the outer portions of the dam; 2) the necessity of forming an eroded ditch along the downstream face of the dam prior to the actual breach formation by the overtopping water; 3) the downstream face of the dam can have a grass cover or be composed of a meterial of larger grain size than the outer portion of the dam; 4) enlargement of the breach through the mechanism of one or more sudden structural collapses due to the hydrostatic pressure force exceeding the resisting shear and cohesive forces; 5) enlargement of the breach width by slope stability theory; 6) initiation of the breach via piping with subsequent progression to a free surface breach flow; and 7) erosion transport can be for either noncohesive (granular) materials or cohesive (clay) materials. The outflow hydrograph is obtained through a time-stepping iterative solution that requires only a few seconds for computation on a mainframe computer. The model is not subject to numerical stability or convergence difficulties. The model's predictions are compared with observations of a piping failure of the man- made Teton Dam in Idaho, the piping failure of the man-made Lawn Lake Dam in Colorado, and a breached landslide-formed dam in Peru. Also, the model has been used to predict possible downstream flooding from a potential breach of the landslide blockage of Spirit Lake in the aftermath of the eruption of Mount St. Helens in Washington. Model sensitivity to numerical parameters is minimal; however, it is sensitive to the internal friction angle of the dam's material and the extent of grass cover when simulating man-made dams and to the cohesive strength of the material composing landslide-formed dams.

THE NWS OPERATIONAL DYNAMIC WAVE MODEL (DWOPER)

by D. L. Fread, Research Hydrologist, Hydrologic Research Laboratory, W/OH3, National Weather Service, NOAA

April 1978 (Reprinted April 1987)


DWOPER: INTRODUCTION

The National Weather Service (NWS) hydrology program is to provide accurate and timely hydrologic information to the general public. This includes flood forecasts, as well as day-to-day river forecasts which are used for water supply, navigation, irrigation, power, reservoir operation, recreation, and water quality interests. Twelve River Forecast Centers prepare the forecasts which are disseminated to the public throughout the United States via local Weather Service Forecast Offices.

In the late 1960's, NWS began moving from an index type catchment runoff model to a continuous conceptual hydrologic model. with a strong physical basis (Monro and Anderson, 1974). The new conceptual model is now being implemented throughout the United States.

Where runoff generated from precipitation input to the conceptual model aggregates in fairly large, well-defined channels (rivers), it is transmitted downstream by routing techniques of the hydrologic or storage routing variety, e.g., the lag and K technique (Linsley, et al., 1958). Although the hydrologic routing techniques function adequately in many situations, they have serious shortcomings when the unsteady flows are subjected to backwater effects due to reservoirs, tides, or inflows from large tributaries. When channel bottom slopes are quite mild, the flow inertial effects ignored in the hydrologic technique also become important.

In the early 1970's, the NWS Hydrologic Research Laboratory began developing a dynamic wave routing model based on an implicit finite difference solution of the complete one-dimensional St. Venant equations of unsteady flow. This hydrodynamic model, known as DWOPER (Dynamic Wave Operational Model), has recently begun to be implemented where backwater effects and mild bottom slopes are most troublesome for hydrologic routing methods. It is either in operational service or in the process of being implemented on the Mississippi, Ohio, Columbia, Missouri, Arkansas, Red, Atchafalaya, Cumberland, Tennessee, Willamette, Platte, Kansas, Verdigris, Ouachita, and Yazoo Rivers.

DWOPER features the ability to use large time steps for slowly varying floods and to use cross-sections spaced at irregular intervals along the river system. The model is generalized for wide applicability to rivers of varying physical features, such as irregular geometry, variable roughness parameters, lateral inflows, flow diversions, off-channel storage, local head losses such as bridge contraction-expansions, lock and dam operations, and wind effects. It is suited for efficient application to dendritic river systems or to channel networks consisting of bifurcations with weir- type flow into the bifurcated channel. DWOPER has a highly efficient automatic calibration feature for determining the optimum roughness coefficients for either a single channel or system of interacting channels. Extensive data management programming features allow the model to be used in a day-to-day operational forecasting environment with minimal card coding required. It is also equally applicable for simulating unsteady flows for purposes of engineering planning, design, or analysis.
 
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