[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.]
The Calculation of the
Rating Curve for VADCP vs V UVM
( references indexing )

It is clear that the discharge depends both on the stage height (controlling the cross-sectional area) and the average fluid velocity. One might hope that the discharge could be accurately represented as a function of stage height times a function of the UVM velocity. The first function can be determined by channel soundings, and can be safely taken to depend only on the stage. The second function gives vADCP as a function of vUVM. So, the calibration process starts with taking a set of simultaneous measurements of discharge, stage height and index velocity. Then the discharge is divided by the cross-sectional area to give vACDP. This set of data defines the rating curve.
Examples from TMS3 calibration
(Click on graph for blow-up.)
Measured discharge, stage height, and index velocity. (p80730a.m) Channel cross section, and measured velocity and index velocity compared. (p80730.m) Average velocity as a function of index velocity (a rating curve). (p80729b.m)

DISCUSSION

The rating curve for ADCP velocity as a function of UVM velocity is approximately a straight line of slope 1, encouraging us to think that these two measurements are equivalent. This would be the ideal case for an indexing scheme. However, the following deviations from perfect equality are noted:

1. The slope of the line is not equal to 1. There are several possible causes which come to mind. The UVM baseline samples preferentially in the center of the channel, where the velocity is greater. In addition, the UVM samples fairly near the surface, missing the slower-moving water near the bottom. Both of these effects would make the UVM speed systematically greater than the ADCP speed, as observed.
2. The curve has two branches, one corresponding to the current turning in (going from negative to positive) and the other to the current turning out (the opposite). When turning in, the ADCP current is higher than the UVM current. This seems to correspond to the know tendency for the current at the edges of a tidally dominated channel to turn before the center.
3. The points seem to follow a line which is bent in the middle, kinking down. This is not a big effect, but is important in calculating the daily discharge, since it affects the incoming and outgoing tides differently.

The three effects above, whatever they are due to, do not introduce errors in the calculated discharge, as long as all conditions are identical to those on the day of the calibration. However: will the slope of the line be the same on another day, when tides are lower or higher, or when the outflow is less or more? What is the kink due to? Will it be the same under other conditions? What are the conditions that matter?