WSP00684

• File Number: 8220.101.16
• Description: Glen Canyon Dam/Lake Powell
• State: AZ
• Basin: Colorado Mainstem
• Date: 1/1/2000
• Author: Webb et al.
• Title: Sediment Delivery by Ungaged Tributaries of the Colorado River in Grand Canyon Arizona
• Water Supply Pro - Doc Type: Report/Study

Table 15. Model for frequency of debris-flow occurrence In tributaries ofthe Colorado River In
Grand Canyon, Arizona (from Griffiths and others, 1996).

Variable
Eastern Grand Canyon
River aspect
Log of drainage-basin area
Log of channel gradient to Hermit Shale
Log of main channel gradient
Elevation of Hermit Shale
Western Grand Canyon
Log of drainage-basin area
Log of channel gradient to Hermit Shale
Log of main channel gradient
Elevation of Muav Limestone
Log of channel gradient to Muav Limestone

Units

Interoept Verlable CoeHlolents
Bo B,

km2

2.981 3.246
2.192
0.955
3.558
-0.002

m

km2

3.367 -2.226
0.715
-5.221
-0.003
0.768

n, variable has no units

m

distributed variables are always greater than 0, we
transformed the logistic-regression probabilities
into a lognormal space to reflects true debris-flow
frequency.
We adopted a frequency-factor approach
similar to that used in traditional flood-frequency
analysis (Kite, 1988). The frequency factor, F, is:

F= e (~+ Kln(x)]. crl,

where F = expected number of debris flows per
century, K [71(x)]= standard normal deviate, and J.l
and cr are the mean and standard deviation of a
lognormal distribution describing all debris-flow
frequencies in Grand Canyon tributaries.
The values of J.l and cr can not be known
directly. Instead, values were chosen for J.l and cr so
as to constrain the distribution of F to the known
characteristics ofdebris flows in Grand Canyon: (I)
all 736 Grand Canyon tributaries produce debris
flows, albeit some at a low frequency (F> 0 for all
tributaries); (2) about 60 percent of tributaries
produce one or more debris flows per century (F ~
I for 60 percent of tributaries); (3) about 5 percent
of tributaries produce 2 or more debris flows per
century (F ~ 2 for 5 percent of tributaries); and (4)
no tributary has produced more than 6 debris flows
in the last century (F is never greater than 6). Using
these constraints, and J.l = 0.95 and cr = 1.75, we
calculated a histogram of F for all Grand Canyon
tributaries (fig. 12).

Debris-Flow Volumes

Esfimation techniques

(9)

Debris-flow volumes were estimated by the
product of fan area and an average thickness. We
determined area of debris fans using several
techniques. Some fans were surveyed directly. In
most cases, we measured fan areas on rectified
vertical and oblique aerial photographs. The most
numerous oblique aerial photographs were taken
from low altitudes by P.T. Reilly between 1950 and
1965. Other photographs were taken by the Bureau
of Reclamation and are stored in its offices in Salt
Lake City, Utah. Photographs were rectified using
surveyed control points on the debris fans and
image-processing software (Webb and others,
1999b). Control points were established at the
corners of easily identified boulders or other sharp
points that were clearly visible in the photographs.
These points were surveyed using an arbitrary
coordinate system or were tied into the Universal
Transverse Mercator System using geographical
positioning system (GPS) technology or established
benchmarks. The resulting areas compared
favorably with areas estimated directly from
surveying data. All debris-fan areas are rounded to
the nearest 100 m2 (Webb and others, 1999b).
Thicknesses of debris fans were estimated
using several techniques. The thickness of some

28 Sediment Delivery by Ungeged Trlbuterles of the Colorado River In Grand Canyon