[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.