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108 THE ADVECTION/WAVE EQUATION


and talus slope both have height H /2. Assume Assume that the rock and talus slope have equal
that the cliff retreat can be modeled advec- densities.
tively with retreat rate c = 1 m/kyr. Model the 4.6 Repeat the above for a case in which the channel
evolution of the cliff and talus slope through crosses a major lithologic boundary (e.g. the Kaibab
time. Impose conservation of mass at the base limestone at the rim of the Grand Canyon). Choose
of the cliff (i.e. the volume of rock removed a smaller value of c to represent the more resistant
from the slope must be deposited on the slope). unit.
119° W 118° W
along-dip profile
3.5
(b) 1°
(a)
h
(km)
along-strike
2.5
profile in (b)
0 50
x (km)
San Joaquin R.
along-dip
profile in (b)
37° N



inset in (c)
Kings R.



Kaweah R.

Chagoopa
Boreal
along-strike profile
36° N
Boreal
3.0
Kern R.
h
(km)

Chagoopa
1.0
100 150
0 50
x (km)
3.0 Boreal
(e)
(d)
(c)
longitudinal
h2.5
profile in (f)
(km)
2.0 Chagoopa
Boreal
Kern R.
1.5
x (km)
15
0 30
Chagoopa
(f)
3.0 knickpoints
h
(km)
linear 2.0
Kern R.
profile in (e)
1.0
slopemap
x (km)
50
0 100
S (m/m)
h (km)
0.0 0.5 >1.0
3.0 4.0
1.0 2.0

Plate 1.8 Major geomorphic features of the southern Sierra Nevada. (a) Shaded relief map of topography indicating major rivers
and locations of transects plotted in b. (b) Maximum extents of the Chagoopa and Boreal Plateaux based on elevation ranges of
1750“2250 m and 2250“3500 m a.s.l. Also shown are along-strike and along-dip topographic transects illustrating the three levels
of the range in the along-strike pro¬le (i.e. incised gorges, Chagoopa and Boreal Plateaux) and the westward tilt of the Boreal
Plateau in the along-strike transect. (c) and (d) Grayscale map of topography (c) and slope (d) of the North Fork Kern River,
illustrating the plateau surfaces (e) and their associated river knickpoints (f). Modi¬ed from Pelletier (2007c). Reproduced with
permission of Elsevier Limited.
116° W
117° W Plate 2.18 (a) Location map and
(b)
(a)
Yucca LANDSAT image of Eagle Mountain
Mtn.
Eagle piedmont and adjacent Franklin
Mtn.
Nevada Lake Playa, southern Amargosa
Valley, California. Predominant wind
N direction is SSE, as shown by the
e Amargosa
Ca vad Valley
wind-rose diagram (adapted from
Funeral li a
36.5° N Mtns. fo
January 2003“January 2005 data
rn
ia
Eagle from Western Regional Climate
Mtn. Center, 2005). Calm winds are
Death de¬ned to be those less than 3 m/s.
Valley Qa2
(b) Soil-geomorphic map and
Qa3
oblique aerial perspective of Eagle
Qa4
Black
Mtns. Qa5“Qa7 Mountain piedmont, looking
36.0° N N 10 km Soil-geomorphic map and predominant playa
southeast. Terrace map units are
N pits
sample-pit locations wind direction
based on the regional classi¬cation
by Whitney et al. (2004).
outline of active
wind (c)
Approximate ages: Qa2 “ middle
modern playa
direction
Pleistocene, Qa3 “ middle to late
Eagle
3“6 m/s
calm
Pleistocene, Qa4 “ late Pleistocene,
Mtn.
6“9 m/s
90%

Qa5“Qa7 “ latest Pleistocene to
Franklin Lake
active. (c) Map of eolian silt
1% Playa
thickness on Qa3 (middle to late
2%
Pleistocene) surface, showing
3% maximum thicknesses of 80 cm
close to the playa source,
Amargosa Eagle
River decreasing by approximately a
Mtn.
factor of 2 for each 1 km
secondary hotspot
downwind. Far from the playa,
background values of approximately
1 km 20 cm were observed. Modi¬ed
0 10 20 40 80 cm
Silt thickness on Qa3
from Pelletier and Cook (2005).
(a) 80 (b)
Qa2
u = 5 m/s
Qa3
K = 5 m2/s
Qa4
p = 0.05 m/s
60
z
analytic
silt
depositional
thickness
topography
(cm)
40
(x', y')
cross-wind
direction
y
20
a
u = 5 m/s
K = 10 m2/s source
p = 0.075 m/s
wind x
0
2 3 4
1
0 direction
distance downwind from playa (km)
(c)
2 km
0.1 0.2 0.4 1.0
0



wind direction




numerical model results
u = 5 m/s, K = 5 m2/s, p = 0.05 m/s
wind direction
(d) (e)
numerical model results
numerical model results
u = 5 m/s, K = 5 m2/s, p = 0.05 m/s
1 km
u = 5 m/s, K = 5 m2/s, p = 0.05 m/s




q = 10
q = ’10 q = 30
10 20 40
0 80 cm


Plate 2.19 (a) Plot of eolian silt thickness versus downwind distance, with analytic solutions for the two-dimensional model for
representative values of the model parameters. (b) Schematic diagram of model geometry. Depositional topography shown in this
example is an inclined plane located downwind of source (but model can accept any downwind topography). (c) Color maps of
three-dimensional model results, illustrating the role of variable downwind topography. In each case, model parameters are
u = 5 m/s, K = 5 m2 /s, and p = 0.05 m/s. Downwind topography is, from left to right, a ¬‚at plane, an inclined plane, and a
triangular ridge. Width and depth of model domain are both 6 km. (d) Color maps of three-dimensional model results for
deposition downwind of Franklin Lake Playa, illustrating the role of variable wind direction. From left to right, wind direction is
θ = ’10—¦ (0—¦ is due south), 10—¦ , and 30—¦ . (e) Map of three-dimensional model results obtained by integrating model results over a
range of wind conditions, weighted by the wind-rose data in Figure 2.18a. Modi¬ed from Pelletier and Cook (2005).
(a) Plate 3.1 Comparison of steepest-descent and MFD
¬‚ow-routing algorithms. (a) Steepest descent: a unit of
precipitation that falls on a grid point (shown at top) is
successively routed to the lowest of the eight nearest
neighbors (including diagonals) until the outlet is reached.
Precipitation can be dropped and routed in the landscape in
steepest descent MFD method
any order. MFD: all incoming ¬‚ow to a grid point is
117.05° W 117.00 116.95 116.90
(b) distributed between the down-slope pixels, weighted by bed
2 km slope. To implement this algorithm ef¬ciently, grid points
36.225° N
should be ranked from highest to lowest, and routing should
be done in that order to ensure that all incoming ¬‚ow from
up-slope is accumulated before downstream routing is
36.20
calculated. (b) Map of contributing area calculated with
steepest descent for Hanaupah Canyon, Death Valley,
California, using USGS 30 m DEMs. Grayscale is logarithmic
36.175
and follows the legend at ¬gure bottom. (c) Map of
steepest descent
contributing area computed with bifurcation routing, for the
(c) same area and grayscale as (b). Multiple-¬‚ow-direction
routing results in substantially different and more realistic
¬‚ow distribution, particularly for hillslopes and areas of
distributary ¬‚ow. Modi¬ed from Pelletier (2004d).




MFD


106 107 m2
100 104
102

scour/mixing depth tephra concentration

10%
1% 100%
1.0 m
0.5
0.1 0.2
(a) (b)




vent
location




Plate 3.14 Digital grids output by the modeling of tephra outlet
redistribution following a potential volcanic eruption at Yucca concentration
southwesterly = 1.97%
Mountain. (a) Map of scour-depth grid, calculated from
winds
contributing area grid. (b) Grayscale map of tephra
concentration in channels, calculated using the
scour-dilution-mixing model. Modi¬ed from Pelletier et al.
N 3 km
(2008). Reproduced with permission of Elsevier Limited.
(a) (b)




(c) (d)




Plate 3.7 Illustration of a successive ¬‚ow-routing algorithm applied to Fortymile Wash alluvial fan in Amargosa Valley,
Nevada. (a) Shaded-relief image of a high resolution (1 m/pixel) photogrammetric DEM of Fortymile Wash, (b)“(d) ¬‚ow depths
predicted by the model for different values of the prescribed upstream discharge: (b) 300 m3 /s, (c) 1000 m3 /s, and (d) 3000 m3 /s.
(a) (b)




(c)




Plate 3.11 Field photos illustrating the three-dimensional pattern of contaminant dilution near Lathrop Wells tephra sheet.
(a) and (b) Channel pits on the tephra sheets expose a ¬‚uvially mixed scour zone ranging from 12 to 29 cm in thickness. Two types
of deposits occur beneath the scour zone: the tephra sheet itself (exposed on the upper and lower sheet) and debris-¬‚ow
deposits comprised predominantly by Miocene volcanic tuff and eolian silt and sand transported from the upper tephra sheet.
(c) The effects of dilution visible as high-concentration channels draining the tephra sheet (channel at right, 76% tephra) join with
low-concentration channels (at left, 26% tephra). Tephra concentration in these channels correlates with the darkness of the
sediments, with the dark-colored channel at right joining with the (larger) light-colored channel at left to form a light-colored
channel downstream. From Pelletier et al. (2008). Reproduced with permission of Elsevier Limited.
(b)
116.52° W 116.50° 10 ’2 10’1
116.48° 101 km
100
(a)
N1 km
36.74°N
3%


9%
(d)
36.72°



tephra sheet
36.70° slope*area1/2

(c)


36.68°
73%
Lathrop Wells cone
relative tephra
concentration
36.66°
0.01 0.1 1.0
0.001



topography and source mask
relative
scour/mixing depth 0.1 0.3 1.0
900 1000 m
800

Plate 3.12 Model prediction for tephra concentration and scour/mixing depth downstream from the tephra sheet of the
Lathrop Wells volcanic center. (a) Model inputs include a 10-m resolution US Geological Survey Digital Elevation Model (DEM) of
the region and a grid of source and background concentrations. Input concentration values are: 73% (Lathrop Wells tephra sheet),
9% (distal source region), and 3% (background). (b) Map of stream power in the vicinity of the source region. Scale is logarithmic,
ranging from 10’2 to 101 km. (c) Map of scour/mixing depth (scale is quadratic, ranging from 10 cm to 1 m). (d) Map of tephra
concentration (scale is quadratic, ranging from 0.001 to 1). From Pelletier et al. (2008). Reproduced with permission of Elsevier
Limited.
slope*area1/2
tephra thickness slope

10 ’3 10 ’2 10 ’1 100 km
0.01 0.1 1m 0.01 0.03 0.1 0.3 1.0

(b)
(a) (c)




vent
location




southwesterly
winds


N 3 km
slope*area1/2
slope > 0.3 (17°) > 0.05 km
Plate 3.13 Digital grids used in the modeling of tephra redistribution following a volcanic eruption at Yucca Mountain.
(a) Shaded relief image of DEM and Fortymile Wash drainage basin (darker area). Tephra from only this drainage basin is
redistributed to the RMEI location. (b) Grayscale image of DEM slopes within the Fortymile Wash drainage basin.
(c) Black-and-white grid of areas in the drainage basin with slopes greater than 17—¦ . (d) Black-and-white grid of active channels in
the drainage basin (de¬ned as pixels with contributing areas greater than 0.05 km2 ). All tephra deposited within the black areas of
(c) and (d) are assumed to be mobilized by mass movement, intense rilling, or channel ¬‚ow. Modi¬ed from Pelletier et al. (2008).
Reproduced with permission of Elsevier Limited.
(b) (c)
(a)

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