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<br />FINAL REPORT, November 2003 <br />High-jlow Requirements for the Duchesne River <br /> <br />associated with a positional error described quantified by the RMS error reported by the <br />digitizing software. Actual errors at specific points on each coverage are vectors whose <br />magnitudes and directions are spatially variable. The RMS error for each of the two coverages <br />therefore represent a large number of individual error vectors that are independent of the error <br />vectors on the other coverage, such that the errors for the two coverages can be combined as the <br />squ~e root ofthe sum oftheir squares (Benjamin and Cornell 1970) to give the average total <br />displacement error for the overlay coverage (Dr). Average total displacement errors for <br />successive pairs of coverages range from 9.4 to 19.2 meters (Table 5). <br />For their morphology-based analysis of gravel transport on the Chilliwack River, Ham <br />and Church (2000) assumed that planimetric errors produced by spatial overlay are self- <br />compensating, and ignored them. While positional errors produce false areas of erosion and <br />deposition on the overlay coverage, they also conceal similar areas of real erosion and <br />deposition. This type of error compensation requires that actual channel movement producing <br />real areas of erosion and deposition occurred during the time period being analyzed. For periods <br />when the areas of real erosion and deposition are less than the potential errors, only a portion of <br />the potential error can be compensated. For periods when no real channel change occurred, all <br />apparent change is due to positional error. It is therefore necessary to evaluate the magnitude of <br />the potential area of false erosion and deposition relative to the measured areas of erosion and <br />deposition to determine what portion of the planimetric error is likely to be compensated. <br />We evaluated the average effect of independent positional shifts by determining the net <br />relative displacement of polygons from successive coverages and using a sine wave to model the <br />sliver area generated by error displacement of a meandering channel. The channel bank is <br />represented by a sine function multiplied by an amplitude coefficient that produces a sinusoidal <br />curve with a sinuosity value equal to the sinuosity of the river channel (Figure 7). This <br />sinusoidal curve is then translated a distance equal to the total displacement error between the <br />two successive photo pairs being evaluated. The error generated by the curve translation is equal <br />to the area between the two curves, and is computed according to: <br />3:Vz <br />h= JISin(x-Sin(r))Drm-Sin(x)mldx (3) <br />-:Vz <br /> <br />19 <br />