9493

• UCREFRP Catalog Number: 9493
• Author: Gaeuman, D., P. R. Wilcock and J. C. Schmidt.
• Title: High Flow Requirements for Channel and Habitat Maintenance of the Lower Duchesne River between Randlett and Ouray, Utah.
• USFW Year: 2003.
• USFW - Doc Type: \
• Copyright Material: NO

FINAL REPORT, November 2003
High-jlow Requirements for the Duchesne River

where h is the sum of all area between the two curves, DT is the magnitude of the displacement
vector, r is the spatially-variable azimuth ofthe displacement vector, and m is the amplitude of
the sinusoidal curves. The magnitude of DT is equal to the root mean square ofthe positional
errors associated with each ofthe two coverages. The azimuth (r) is unknown, but is equally
likely to take any value between 0 degrees and 359 degrees. Because of the symmetry of the
curve, only values between 0 degrees and 90 degrees need be considered. The mean value of h
for all possible azimuths is determined as:
1 ~
h = 1[/ f h dr
/2 0
Another pair of sinusoidal curves is needed to represent the opposite river bank, so that the
expected total planimetric error (Ga) is equal to 2h. The average displacement error calculated
in this manner represents the area of false polygons expected to result from the spatial overlay of
two independent coverages (Table 5).
We experimentally evaluated the proportion of Ga that would remain uncompensated by
real change with computer simulations in which two sinusoidal curves, one representing error
displacements and one representing real changes in channel position, were independently
displaced. The mean and standard deviation of the uncompensated area between the two
displaced curves was numerically determined for all possible combinations of displacement
azimuths. Simulation results showed that the expected uncompensated planimetric errors (Gae)
for the six overlays range between I percent and 10 percent of the measured areas of erosion and
deposition (Table 5). Subtracting Gae from the measured areas of change gives an improved
estimate for the actual area of change. The standard deviations of the simulated uncompensated
planimetric errors were used to calculate uncertainty margins about the corrected estimates of
erosion and deposition areas. These margins of error are denoted by Gau, and range between
about 8 percent and 20 percent for the six overlays (Table 5). A more detailed description of the
methods used for calculating Gau is given in Gaeuman et al. (submitted).
The areas of displacement errors calculated from the original RMS errors associated with
the digitized coverages overestimate the actual probable displacement errors by an unknown
amount. Actual errors are reduced in this study by manual corrections applied t9 the coverages
before overlay. Some false polygons generated by displacement errors are obvious, and help to

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