Estimate the flood flow at DCEW Lower Gauge using Manning’s equation for a storm that occurred in Jan 2011.
Manning’s equation calculates the average velocity, U, of uniform flow in an open channel based on channel properties:
where R is the hydraulic radius (L), S is the channel slope (L/L), n is Manning’s roughness coefficient, and k is a unit conversion factor (k = 1 if R is in meters and U is m/s; k = 1.49 if R is in feet and U in ft/s).
The channel discharge can be computing by multiplying U by the channel cross section area (A),
The hydraulic radius is computed as the cross-section area, divided by the wetted perimeter, P as indicated in equation 3:
The wetter perimeter is the distance along the channel bottom between water levels at each bank. Manning’s roughness, n, is a factor that characterizes the channel resistance. An internet search will reveal many different ways to estimate n. Ultimately, n is a site-specific factor that is determined by the scientist/engineer.
On January 15, 2011 approximately 2 inches of rain fell on the Dry Creek Experimental Watershed, much of which was covered by snow. The combined rain and snowmelt produced a depth of streamflow approximately 2 ft higher than the highest stage for which we had a discharge measurement, rendering the stage-discharge relationship for the Lower Gauge unreliable (see Streamflow Measurement Exercise for an explanation of stage-discharge relationships). This flood presented an opportunity to add a very high water point to the rating curve. We know the stage from our instream datalogger, but nobody was in the stream making measurements during the flood. Instead of using the velocity-area gauging method, we used Manning’s equation in a forensic sense to estimate discharge. To do so, field crews walked a section of the stream near the Lower Gauge and identified high water marks. Indicators of high water included debris clinging to brush, erosion scours, and anything else that gave clues to the highest height that water reached. The field crews then selected two locations along the channel reach and measured the shape of the flooded cross-sections. Each cross-section survey was completed by setting a survey instrument in line with the cross-section, and then measuring the elevation of the ground surface or stream bed at increasing distances away from the station, perpendicular to the channel. The distance and elevation drop between cross-sections along the stream were also surveyed to calculate channel slope.
Estimate the peak flood flow at DCEW Lower Gauge from the January 15, 2011 storm event.
The instructions below outline specific steps to complete the exercise based on the fieldwork which was conducted near Lower Gauge. The field crew identified the flood water marks on each bank and then, two locations were used to survey the shape of the flooded channel resulting in an UPstream cross-section and DOWNstream cross-section. In the workbook provided, these cross-sections are automatically plotted in the “FloodFlow Calculation” tab.
In the orange table, calculate
For each of the cross-sections in its corresponding red table, complete the following
At a permanent gauging station, a stage-discharge relationship (also called a Rating Curve) is used to convert continuous records of stage into continuous records of Q (See Streamflow Measurement exercise for background). To construct a rating curve, instantaneous streamflow measurements are made at various stages. A power function is then fit to the range of stage-discharge pairs. The power function is then used to predict Q for all stages. However, the equation should not be used to calculate Q for stages higher than the highest stage for which there is a measured Q.
The “Rating Curve” workbook tab contains several measured stage-discharge pairs. Note that the highest stage for which we have a corresponding measured discharge was 2.12 ft (which equates to 37.6 cfs). Peak stage for this exercise’s flood at the LG station was 4.18 ft. To illustrate the problem, you will use the rating curve to compute Q for the high stage.
Compare your discharge estimate derived from Manning’s equation to that derived from the rating curve. Discuss reasons for differences.