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78th Annual AMS Meeting
Phoenix, Arizona
January 1998


Enhancements of River Forecasts Using Dynamic Hydraulic Flow Routing


Janice Lewis
Office of Hydrology
NOAA/National Weather Service
1325 East-West Highway
Silver Spring, Maryland 20910

1.   INTRODUCTION

  There are many phenomena in river systems that complicate the National Weather Service's  river forecasts of our
Nation's streams including man-made structures (bridges, levees, etc.).  Almost all rivers are forecast using simple
hydrologic (storage) routing techniques to convey the water downstream, and empirical rating curves to convert the
discharges to stages.  It was quite evident in the 1993 flood on the Mississippi-Illinois-Missouri river system and the
1997 flood on the Red River of the North that this process is severely limited on river systems with levee
overtopping/failures which cause the flood waters to leave the channel, go into storage, and in some instances re-enter
farther downstream; and on backwater effects due to bridges and natural channel constrictions.

  In situations where the flood elevations go beyond the flood of record, existing rating curve extension techniques
may not be adequate to forecast peak stages. To improve river forecasts in these situations, a dynamic hydraulic
routing technique can be used to properly extend the rating curve so as to account for bridge backwater, levee effects,
and the actual river overbank flow area.  This paper describes the effects of bridges, floodplains, and levees on river
flooding and shows how river forecasts may be improved by accounting for hydraulic effects.

2.   RATING CURVES

  One of the critical tools used in river forecasting is the rating curve which describes the relationship between
discharges (Q) and the water-surface elevations (h).  Although quite adequate for most rivers, this empirical rating curve
is single-valued (i.e., one-to-one relationship between h and Q) and may not reflect the hydraulic conditions in the river
system (e.g., backwater due to very mild river bottom slopes (<0.005%)).  In such rivers, the water-surface elevation
tends to be higher on the falling limb of the hydrograph than on the rising limb at the same discharge producing a
"looped" rating curve.  The band-width of the loop can range from a few centimeters to several meters depending on
the hydraulic conditions (i.e., primarily, the slope of the river profile and the rate of rise of the hydrograph).  The
magnitude of the loop increases as the slope decreases and as the rate of rise increases.  Usually a single-valued rating
curve is drawn through the loop producing an average error of half the band-width of the loop.

  Other rating changes (shifts) or erratic loops are caused by tributary inflow, natural channel constrictions, or man-
made constrictions (e.g., dams, bridges), and by sand/gravel river bed changes due to sediment transport effects.

2.1  Rating Curve Shifts

  In the National Weather Service River Forecast System (NWSRFS), single-valued rating curves are specified at
gage locations.  Techniques exist to allow the forecaster to shift the rating curve to accommodate existing conditions
(e.g., a rating curve on the Missouri River may be shifted by a constant amount due to the amount of sediment in the
river).
  
  An entire rating curve may be shifted by increasing/ decreasing the flow by a constant amount or by a percentage
amount.  Also, a portion of the rating curve may be shifted by specifying the endpoints of the shift as well as a point
within that range that will be modified.  Shifting the rating curve is an attempt to account for the hydraulic conditions
observed at the time of the forecast.

2.2  Rating Curve Extensions

  When forecasting peak stages that go beyond the flood of record, the rating curve must be extended.  In NWSRFS, 
rating curve extension techniques include a linear/logarithmic extrapolation technique which extends the rating curve
at the same rate as the known curve; and an hydraulic extension technique based on Manning's equation.   Although
the linear/logarithmic extrapolation technique may account for some of the hydraulic effects which are included in the
empirical rating curve, hydraulic conditions may change as the flow increases and cause the rating curve to change
in a nonlinear manner.  

  In the hydraulic extension technique, the following are used to compute the water-surface elevation using the
Manning equation: 1) a cross section at the gage, 2) the hydraulic roughness coefficient, and 3) the slope representing
the downstream reach.  This technique may represent the reach effects due to topography (e.g., channel constrictions);
however, it cannot account for the effects of a variable energy slope caused by flow accelerations of unsteady,
nonuniform flow (Fread, 1973).  It also cannot account for head losses due to bridge effects.


3.   DYNAMIC ROUTING

  The NWS FLDWAV model (Fread and Lewis, 1988) is an unsteady flow, dynamic, hydraulic routing model which
determines the water-surface elevation (h) and discharge (Q) at specified locations along the length (x) of the waterway
(river, reservoir, etc) when subjected to an unsteady flow event such as a flood wave or dam-break wave. The model
is based on an implicit finite-difference solution of the complete one dimensional Saint-Venant unsteady flow equations
coupled with an assortment of internal boundary conditions representing unsteady flows controlled by a wide spectrum
of hydraulic structures.  The flow may occur in a single waterway or a system of inter-connected waterways, including
those having dendritic structures (nth-order tributaries) in which sinuosity effects are considered.  Additional 
capabilities of FLDWAV include: 1) the capability to dynamically model dam failures as well as flows which are
affected by bridge constrictions; 2) the ability to simulate flows which overtop and crevasse levees located along either 
or both sides of a main stem and/or its principal tributaries; and 3) the provisions to handle flows in the subcritical 
and/or supercritical flow regime.

The expanded Saint-Venant equations of conservation of mass and momentum consist of the following (Fread, 1993):



                                                              
in which Q is discharge (flow), A is wetted active cross-sectional area, Ao is wetted inactive off-channel (dead) storage
area associated with topographical embayments or tributaries, B is the channel flow width, sc and sm are depth-
dependent sinuosity coefficients for mass and momentum, respectively, that account for meander, ß is the momentum
coefficient for nonuniform velocity, q is lateral flow (inflow is positive, outflow is negative), t is time, x is distance
measured along the mean flow-path of the floodplain, g is the gravitational acceleration constant, h is the water-surface
elevation, L is the momentum effect of lateral flows (L=-qvx for lateral inflow where vx is the lateral inflow 
velocity in the x-direction, L=-qQ/(2A) for seepage lateral outflows, L= -qQ/A for bulk lateral outflows such as flows 
over levees), Sf is the boundary friction slope, Se is the slope due to local expansion-contraction 
(large eddy loss), and Wf is the wind term.

The information necessary to execute FLDWAV includes: 1) an upstream time series of h or Q; 2) a downstream
boundary condition (time series of h or a rating curve); 3) cross section geometry (top width vs. elevation table); 4)
information about hydraulic structures (dams, bridges, levees); 5) hydraulic roughness coefficients which may vary with
h or Q and with location along the waterway (these values have been calibrated using data from prior floods); and 6)
the initial h and Q at each cross section location.  Given this information, FLDWAV will simultaneously solve for the
h and Q at each cross section location along the routing reach for each time interval during the specified simulation time
period.  

  The results from FLDWAV may be used to extend rating curves.  In situations where the dynamic unsteady flow
effects are negligible, FLDWAV may be run a priori to determine the rating curve for beyond the flood-of-record flow. 
The extended rating curve points (h,Q) may then be added to the current rating curve.  When the dynamic effects are
significant (e.g., backwater due to tributary inflow, channel constrictions, dams, or bridges), a single valued 
rating curve cannot adequately represent the Q(h) relationship, and the simple hydrologic (storage) routing technique 
should be replaced by the unsteady, dynamic FLDWAV model.

4.   HYDRAULIC EFFECTS

  During the 1997 flood, the peak stage at Grand Forks, ND on the Red River of the North was influenced by several
hydraulic conditions including: three bridges located within 3 km (1.8 mi) downstream of the gage; a flat sloping
(0.0095%) constricted channel 183 m (600 ft) wide with levees on both sides transitioning to a downstream reach having 
an even flatter sloping (0.0038%) floodplain, over 8 km (5 mi) wide.  

  Figure 1 compares the rating curves from the various techniques with the observed rating curve at Grand Forks. 
The rating curve generated by FLDWAV, which  models  the hydraulic effects, behaves most like the observed 
rating curve. These effects are analyzed below.

Figure 1. Rating Curve at Grand Forks, ND
4.1 Bridge Effects Bridges normally cause the flow in the river to be constricted since the cross section at the bridge is usually narrower than the cross sections in the natural channel, bridge piers also constrict the section further. Channel constrictions may cause a backwater effect. Bridge decks may also affect the channel flow. As long as the water flows beneath the bottom of the bridge deck, the flow is unrestricted (normal); however, once the water impinges on the bridge deck, the flow becomes orifice (pressurized) flow resulting in a greater head loss and higher water-surface elevation upstream of the bridge. Water can also flow over the road embankment (weir). To determine the effects of the bridge components, the FLDWAV model was run with the following scenarios: 1) all three bridges were removed from the system (no bridges); 2) the bridges were added without the bridge decks to determine the effect of the bridge constrictions (constrictions); 3) the bridge decks were added to allow orifice flow through the bridge opening (decks); and 4) the bridge embankments were added to allow weir flow over the road embankments (embankments). Figure 2 shows the rating curve at the Grand Forks gage for the four scenarios along with the logarithmic and hydraulic extensions. The dominant component is the bridge constriction which resulted in 0.20 m (0.67 ft) increase at the peak elevation. The bridge decks further increase the peak elevation 0.15 m (0.49 ft); however allowing flow over the embankments causes the peak elevation to be reduced by 0.11 m (0.37 ft). It was found that the overall effect of the three bridges resulted in an increase in the water-surface elevation of 0.24 m (0.79 ft).
Figure 2. Bridge Effects: Rating Curve at Grand Forks, ND
When the single-valued rating curve with logarithmic extension is compared with the loop ratings curves generated by FLDWAV, it can be seen that it tends to behaves like the "no bridges" scenario. The hydraulic extension technique is also unsuccessful in capturing the bridge effects. One of the limitations of the hydraulic extension technique is that a constant roughness coefficient is used to compute the water-surface elevation for all flows in the extended rating curve. By allowing the roughness coefficient to vary with flow, more of the bridge effects may be able to be captured and therefore, produce a more accurate forecast. 4.2 Floodplain Effects Unsteady flow in rivers which meander through very wide floodplains is complicated by large differences in geometric and hydraulic characteristics between the river channel and the floodplain, as well as extreme differences in the hydraulic roughness coefficient (Fread, 1976). The flow is further complicated by the meandering channel which causes a longer flow path than that for the floodplain and by portions of the floodplain which act as inactive storage areas wherein the flow velocity is negligible. The floodplain on the Red River of the North was modeled in FLDWAV by treating portions of the floodplain flow area as inactive storage. As water initially flows out of the main channel into the floodplain, the water is being stored and does not contribute to the active flow area; however as the water level becomes higher and the flow in the floodplain becomes more significant, the active area includes more of the floodplain storage. The overall effect of the inactive storage is that the floodwave is attenuated as it moves downstream through the floodplain. Figure 3 shows instantaneous discharge profiles along the routing reach as the floodwave nears the peak. Near the peak flow, the river widens from about 900 m (~3,000 ft) upstream to 5,500 m (~18,000 ft) at a distance approximately 19 km from the downstream boundary (Oslo). This attenuation along with backwater effects due to the flat slope contributed to the looping effect of the rating curve shown in Figure 1.
Figure 3. Instantaneous Discharge Profiles
4.3 Levee Effects The purpose of a levee is to prevent flow from going into the natural floodplains. It therefore, constricts the flow and produces higher water-surface elevations as well as peak discharges. The attenuation of flow within the levee reach is significantly less than it would be in the natural floodplain because the water cannot spread across the floodplain as it moves downstream. However, if the water-surface exceeds the top of the levee and overtopping occurs, the peak flow may be drastically reduced due to weir flow over the levee. In the event of a levee failure due to overtopping or seepage, additional water is removed from the main channel. Water that leaves the main channel by overtopping or failure may either be stored in the floodplain independent of the main channel, or it may find another flow path wherein it may reenter the channel farther downstream at a later time. Because of the importance of the dynamic terms in the Saint-Venant equations, FLDWAV is much more capable of modeling these complex levee effects than a simple rating curve. 5. CONCLUSION Many hydraulic conditions exist that may not be represented by simple hydrologic techniques or by single-valued rating curves. Hydraulic models may be used to account for these hydraulic effects and therefore improve river forecasts. 6. REFERENCES Fread, D.L., 1993: "NWS FLDWAV Model: The Replacement of DAMBRK for Dam-Break Flood Prediction", Proceedings: 10th Annual Conference of the Association of State Dam Safety Officials, Inc., Kansas City, Missouri, September 26-29, 1993, pp. 177-184. Fread, D.L. and Lewis, J.M. 1988: "FLDWAV: A Generalized Flood Routing Model", Hydraulic Engineering, Proceedings of 1988 Conference, HY Div, ASCE, Colorado Springs, CO, pp. 668-673. Fread, D.L. 1976: "Flood Routing in Meandering Rivers with Floodplain", Rivers '76 Symposium on Inland Waterways for Navigation, Flood Control and Water Diversion, Vol. I, ASCE, Fort Collins, C, pp. 164-197. Fread, D.L. 1973, "A Dynamic Model of Stage-Discharge Relations Affected by Changing Discharge", NOAA Technical Memorandum NWS HYDRO-16, NOAA/NWS, Silver Spring, MD.

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