[Note: this is an internal working document of a USGS-SFSU collaboration. Data, analysis and results herin should not be considered as final or accurate. Final results will be presented in print.]
Effect of the Velocity Profile
on the
Rating Curve
( references indexing )

It is clear that both velocity and stage height are necessary to determihe the discharge:

Q = Area(h)*VAVER(VUVM,branch,h?,?,?)

Factoring out the area isolates the main dependence on h. However, there is another clear dependence to be expected. As the stage changes, the UVM path effectively moves up and down the vertical velocity profile. This changes its relation to the average velocity. This effect clearly depends on the exact shape of the vertical velocity profile.

The spatial distribution of the current velocity is complicated, and changes with time. Turbulence contributes large random changes, and there are probably systematically changing flow patterns associated with the shape of the channel and the tides (spring, neap, etc.) One approach is to use the ADCP data to determine an average velocity profile.

Using this profile (we assume the standard y1/6 law below) a stage-corected index velocity can be calculated.
Effect of Velocity Profile on the TMS3 Calibration
(Click on graph for blow-up.)
Normalized velocity distributions for the first ten transects of the TMS3 calibration. (p80730c.m) Index velocity, stage, and correction factor to obtain vertically averaged velocity from index velocity (p80730d.m) TMS3 rating curve, before and after converting the index velocity to a vertically averaged value. (p80730e.m)

CONCLUSIONS
  1. The slope of the rating curve is closer to 45 degrees using the centered index velocity. The slope is still not 45 degrees, presumably because the UVM does not see the slower water near the shore.
  2. The loop character of the rating curve is unaffected, as expected.
  3. The downward curvature of the curve remains. I expected this effect to decrease or go away, but it didn't.