[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.]
Analysis of
UVM Rating Curves
Using a
Gaussian Loop Rating Model
(
references
|Delta Discharge
|Rating Curves
)
The rating curve shows the ADCP velocity, which is easily related to the
discharge, as a function of UVM velocity. (See tms3 calibration.) One might expect
this relation to be a simple one, perhaps a straight line. However,
accurate calibration measurements show a more complicated, double-valued
relation; the calibration as the current changes from negative to
positive ("turning in") is different from when the current changes from
positive to negative ("turning out"). To study the effects of this
phenomenon we have found a fairly simple functional form to represent
the rating curve.

**See Mathematical Form of
Gaussian-Loop Rating.**
This rating curve can be applied to time series of stage and UVM
velocity to calculate the instantaneous discharge. The effect of the
tides can be smoothed out by averaging to obtain the Delta Discharge.
the effects of different assumptions about the rating can be compared.
**See Comparisonal of
Straight-Line Rating with Simple Gaussian-Bulge Model.
**
**See Comparisonal of
Full Gaussian-Bulge Model, Including Kink and Offset, with Simple
Gaussian-Bulge Model.
**
**Summary of ****Numerical
results.**