WSP03492

• File Number: 8220.101.10.A
• Description: Colorado River-Water Projects-Glen Canyon Dam/Lake Powell-Glen Canyon Adaptive Management-AMWG
• State: AZ
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 3/3/2004
• Author: USGS
• Title: AMWG Meeting Attachments-March 3-4 2004-Variations in Sand Storage Measured at Monumented Cross Sections in the Colorado River Between Canyon Dam and Lava Falls Rapid-Northern Arizona 1992-99
• Water Supply Pro - Doc Type: Report/Study

used in the chanoe-in-area calculation. The Wilcoxon
rank-sum test (Devore, 1991; Helsel and Hirsch, 2000)
was used to detect statistically significant differences in
mean bed elevations. This test was used because it does
not require knowledge of the underlying statistical
distribution of the bed-elevation recordings. [n this
application the test has the null hypothesis that, at each
increment, the mean bed elevation in one measurement
is equal to the mean bed elevation in the next
measurement. To evaluate the hypothesis, the test
statistic W is computed on the basis of bed-elevation
data for the two measurements, and then a two-sided
p-value associated with rejecting the null hypothesis is
determined on the basis of the value of Wand the
number of depth recordings for each measurement.
For this investigation the null hypothesis was rejected
for p-values less than or equal to 0.05, which means
that the null hypothesis is rejected with a 5-percent
chance of it being true.
Because of differences in water level or in cross-
section geometry. or because of missing records as a
result of interference of the depth-sounder signal, the
depth at some parts of a cross-sectional transect may
not have been recorded; therefore, fewer than 10 depth
recordings exist for some 0.25-111 increments in some
cross-section measurements. For increments at which
the number of depth recordings equaled or exceeded
eight for both measurements, the p-value was
computed from the normal approximation for the
distribution of W For increments at which the number
of depth recordings for either or both measurements
was less than eight but greater than two, the p-value
was detennined from the exact distribution of W
The test was not applied for increments at which the
number of depth recordings for either or both
measurements was equal to or less than two.
The fraction of the cross section to which the rank-sum
test was applied and the fraction of the total cross
section for which bed-elevation differences between
measurements were signiticant were also calculated.
Changes in cross-sectional area between
measurements were calculated for each incremental
distance (0.25 m), using the selected or interpolated
point as the center of the increment, by first computing
the incremental area as the difference in mean bed
elevations multiplied by 0.25 m. The change in area for
the entire crnss section then was computed by summing
those incremental areas for which the p-value was less
than or equal tu 0.05. Although the original data from
the 10 transects recorded for cross section p06 on

August 24, 1992, were unrecoverable from the
database, the processed mean bed elevations at the
0.25-m increments had been calculated from the
original data and stored in the database. Calculations of
change in area using these data from this date.
therefore, did not consider the p-values. The change in
area of the bed elevation represents the change in
sediment storage in the cross section. As a consequence
of detennining changes in cross-sectional area using
this method, increases in area indicate sediment
deposition and decreases indicate sediment removal.
A standard error that can be applied to the
computed cross-sectional change in area was calculated
for an averaged cross section. The standard error is a
measure of the accuracy with which the computed
(mean) change in area estimates the true mean change
in area. A range, in which there is a
68.3-percent level of confidence that the true mean
change in area lies within this range, can be calculated
by subtracting the standard error from the computed
mean change in area for the lower end of the range and
by adding the standard error to the computed mean
change in area for the upper end of the range. For a
95-percent level of confidence, the range is calculated
as previously described, but the standard error is first
multiplied by 2 (Harford, 1985).
The standard error uses the standard deviation
calculated when computing mean bed elevations from
the 10 transects collected during a measurement
(fig. 9A, step 5), and the number of 0.25-m increments
for each transect, which is a function of stream width.
The standard error must be propagated through the
change-in-area calculations (fig. 98) and accumulated
change-in-area calculations (summing changes in area
for a cross section across many measurements).
A representative standard error was estimated and
propagated through the calculations. This representa-
tive standard error was calculated using a standard
deviation of 0.15 m for the elevations and a stream
width of 131 m. These values were calculated from the
transect data from all cross sections in the primary data
set (table 4) and represent an average standard
deviation and stream width. Table 5 shows the
estimated standard error that can be applied to changes
in area documented in this report. The table shows the
standard error for a single change in area calculated
between two measurements (I period) and accumu-
lated changes in area over several measurements
(periods), for 68.3-percent and 95-percent levels of
confidence. For example, if the change in area between

20 Variations in Sand Storage Measured io the Cot~r,;doRive; Between Gten~n~iri..) Leve Fells Rapid. Northern Arizo.e, l!1!12-gg