[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.]
Indexing: Overview
( references |indexing )

In many monitoring applications it is inconvenient or difficult to measure the property of interest directly, but it is much easier to measure some other, strongly correlated physical property. As an example, the salinity of ocean water is usually determined by measuring the electrical conductivity of the water, rather than directly detecting the presence of salt.

There are a few conditions which a good index should satisfy:

  1. The index property should be easy to measure accurately. In the example above, the electrical conductivity of a liquid is a fairly easy property to measure.
  2. A calibration procedure of sufficient accuracy must be available.
  3. The quantity of interest should depend only on the index property; or, if other parameters are involved, their effect should be well understood and they should be easy to measure. In the example above, the salinity depends not only on the conductivity, but also on the temperature. However, temperature can easily be measured along with salinity, and the role of temperature in ionic conductivity is well understood.
The property of interest in our case is the instantaneous rate of flow of water through a surface crossing the river channel (the discharge). This discharge can be written as the product of the channel cross-sectional area (easy to determine) and an average perpendicular velocity. A tempting indexing procedure is to measure the current velocity at some "typical" point, and to look for a simple relation between this point velocity and the average perpendicular velocity. However, it is clear that a velocity averaged over as much of the channel as possible would be a better index. The UVM velocity is an average of the velocity parallel to the UVM baseline, along that baseline. With a baseline covering the full width of the channel, this is a very promising index property.

In this report we discuss how well the UVM index velocity satisfies the three conditions given above. The accuracy of this measurement, condition (1) above, and the accuracy of the calibration measurement (by ADCP), condition (2) above, are discussed in other sections of this report. In the present section we discuss condition (3), the heart of the indexing process. We attempt to identify other parameters in the indexing procedure and to determine their effect.

We find that there are several additional parameters required to determine the discharge from the UVM velocity. One is the branch of the rating curve; we find that for a given value of the index velocity, the calibration is different for a waxing or waning flow. It also seems likely that the stage height is a parameter which enters into the calibration. Wind shear at the water's surface may also affect the discharge.

The final outcome of this section is a tabulation of errors expected in discharge measurements, due to uncertainties in measurements and due to our limited understanding of the indexing procedure.