WATER SCIENCE AND APPLICATION, VOL. 5, PP. 127-146, 2002
Robust determination of stage and discharge: An example from an extreme flood on the Verde River, Arizona
Depth-averaged models can simulate nearly all aspects of three-dimensional flow in rivers, yet are more efficiently applied
to large areas. The assumption that fluid pressure is hydrostatic is found to provide a good approximation for shallow water
flow over complex three-dimensional terrain. Here we compare depth-averaged flow simulations with data from two large floods
that occurred on the Verde River, Arizona, in January and February, 1993. Using a combination of photogrammetric and geodetic
data, we construct a 6 km by 3 km grid of a reach of the river that contains a USGS stream gage and a narrow bedrock constriction.
Elevation accuracy is 0.05 m and grid accuracy is 0.2 m. In the study area the channel is bedrock-controlled and forms a right-angle
bend followed by a constriction at Sheep Bridge. Water dammed by this constriction during the 1993 floods created a 3 m drop
in water-surface elevation over a distance of 50 m. High velocities generated by this drop scoured the channel and built a
large bar of boulders and cobbles that stretched across the channel 150 m downstream. Indicators of minimum water surface
elevation, including mudlines, debris stranded on hillsides, and grass wrapped around trees were mapped at 45 sites along
the channel. Discharge was monitored through a spillway at Horseshoe Dam, 15 km down-stream of the bridge, during the larger
January flood, and stage and velocity were measured at the USGS Tangle Creek gage during the smaller February flood. High-water
indicators near the gage are 0.07 m lower than the peak stage measured at the gage in January 1993. Peak stage and peak velocities
exceeding 6 m/s lasted 4 hours during the January flood, justifying the use of a steady-flow model for the 6 km long reach.
The flow simulations for a discharge of 3398 m3/s (120,000 ft3/s) and a Manning's n value of 0.038 agree closely with direct velocity and stage measurements at the gage, a direct measurement
of discharge through the spillway, and with the distribution of high-water marks along the channel. Other combinations of
discharge and Manning's n result in larger residual errors in model fits to high-water indicators, and cannot fit both the
high water marks and the observed combination of stage and peak velocity at the Tangle Creek gage for the 1993 floods. Thus
discharge and bed roughness are uniquely constrained using profiles of maximum inundation along the channel margins extending
upstream and downstream from the constriction. The inclusion of surface velocity measurements is not required, but improves
resolution and statistical confidence in peak discharge estimates.
Citation: Denlinger, R. P.,