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Lathrop Wells
x (km)
36.69 1405.10 lava flows
Volcanic Cone
west channel
measured data

1505.09 3D model

1505.12 0.3
N west channel
x (km)
0.5 km
(a) (b)
are relatively high to the north of the cone where
Fig 3.10 (a) Sample location map for tephra concentration
most of the tephra was deposited (11.1% and 6.8%
in the east and west channels draining the Lathrop Wells
in samples SD091405.06 and SD091505.05, respec-
tephra sheet. (b) Comparison plots of measured and modeled
predictions for tephra concentration as a function of distance tively) and lower to the south (3.0% in sample
along-channel (note logarithmic scale on vertical axis, needed SD091505.08). These background samples were
to visualize data over 1“2 orders of magnitude). Also graphed collected in large drainages that provide repre-
are best-¬t exponential curves. Modi¬ed from Pelletier et al.
sentative average values over large areas. In or-
der to resolve the two background values in the
model, a ternary mask (Figure 3.12a) was used
with a source concentration of 73%, a distal
concentration of basaltic tephra is reduced by source value of 9% (north of the primary tephra
more than 50. sheet) and background value of 3% (everywhere
The Lathrop Wells tephra sheet was mapped else).
by Valentine et al. (2005), providing a prelimi- Additional inputs to the model are the thresh-
nary source map for input to the scour-dilution- old stream power and a 10-m resolution US Geo-
mixing model for this application. The source logical Survey DEM (Figure 3.12a). The value for
map is complicated in this case by the fact that the stream-power threshold was chosen to be
tephra from the 77 ka eruption dispersed tephra 0.015 km by forward modeling. In this forward-
in all directions. Samples collected in the study modeling procedure, a map of incised channels
reveal three separate groups of values. On the was made by comparing the stream power at
tephra sheet itself, contaminant concentrations each point in the grid to a threshold value. This
vary between 61% and 83%, with an average value threshold was varied in value to produce differ-
of 73%. Therefore, 73% was used as the value ent incised-channel maps. Maps were then over-
for the source concentration in the model. Off lain and visually compared with US Geological
of the tephra sheet, background concentrations Survey orthophotographs to identify which value

Fig 3.11 Field photos illustrating
(a) (b)
the three-dimensional pattern of
contaminant dilution near Lathrop
Wells tephra sheet. (a) and (b)
Channel pits on the tephra sheets
scour zone
expose a ¬‚uvially mixed scour zone
76% tephra
15 cm scour zone ranging from 12 to 29 cm in
29 cm SD091405.08
70% tephra
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
debris flow
tephra predominantly by Miocene volcanic
sheet tuff and eolian silt and sand
transported from the upper tephra
sheet. (c) The effects of dilution
middle sheet lower sheet visible as high-concentration
channels draining the tephra sheet
(c) (channel at right, 76% tephra) join
with low-concentration channels (at
“low”-concentration “high”-concentration
left, 26% tephra). Tephra
tephra sheet
channel channel
concentration in these channels
26% tephra (SD091405.07) 76% tephra (SD091405.08)
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. For color version, see
plate section. From Pelletier et al.
(2008). Reproduced with permission
of Elsevier Limited.

“mixed” channel
tributary junction
41% tephra (SD091405.09)

of the critical stream power produced the most of drainage basins in the Yucca Mountain region.
accurate map. Maximum discharge is used because the largest
In the ¬rst step of the model run, all pix- ¬‚oods control the long-term scour/mixing depth.
els of the contributing area grid were initial- The unit-discharge map was then used to create
ized to 10’4 km2 (i.e. the pixel area for a 10-m- a relative map of scour/mixing depth in channels
resolution DEM). The MFD algorithm was then (Figure 3.12c) using the square-root dependence
used to calculate the contributing-area grid. In of Leopold et al. (1966) and a stream-power
the second step, the contributing-area grid was threshold of 0.015 km. Only a relative grid of
converted to a unit discharge map using the re- scour/mixing depth was needed in this case be-
gional ¬‚ood-envelope curve of Squires and Young cause the scour depths in the source area were
(1984). These authors found the maximum dis- used to calculate the effective volume of contam-
charge to be proportional to the contributing inant routed downstream, and the scour depths
area to the 0.57 power using available stream downstream of the source region were used to
gage data and paleo¬‚ood estimates from a range dilute that contaminant. Since the contaminant

101 km
116.52 W 116.50 10
116.48 10
N1 km
36.74° N


tephra sheet
36.70 slope*area1/2


LathropWells cone
relativete phra
0.01 0.1 1.0

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

Fig 3.12 Model prediction for tephra concentration and
tration (as opposed to an effective thickness), the
scour/mixing depth downstream from the tephra sheet of the
absolute value of the scour depth is not needed to
Lathrop Wells volcanic center. (a) Model inputs include a
predict concentration values downstream; only
10-m resolution US Geological Survey Digital Elevation Model
relative values are needed. The model predicted
(DEM) of the region and a grid of source and background
tephra concentrations (expressed as a fraction) in
concentrations. Input concentration values are: 73% (Lathrop
Wells tephra sheet), 9% (distal source region), and 3% all channels draining the Lathrop Wells tephra
(background). (b) Map of stream power in the vicinity of the sheet. This map has a quadratic gray scale vary-
source region. Scale is logarithmic, ranging from 10’2 to ing from < 0.01 (black) to 1.0 (white).
101 km. (c) Map of scour/mixing depth (scale is quadratic,
The numerical model prediction was com-
ranging from 10 cm to 1 m). (d) Map of tephra concentration
pared to the measured tephra concentrations by
(scale is quadratic, ranging from 0.001 to 1). For color
extracting tephra concentrations along channel
version, see plate section. From Pelletier et al. (2008).
pro¬les of the western and eastern channels in
Reproduced with permission of Elsevier Limited.
Figure 3.10b. Along both channels, concentra-
tions are near their maximum values for ap-
proximately the ¬rst 1.0 km downstream from
concentration is a ratio of these quantities,
the channel head. Along the eastern channel
the concentration was unaffected by scaling the
(Figure 3.10b, top graph), abrupt concentration
scour depth up or down by a constant factor. In
declines are associated with major tributary
all cases where the source is speci¬ed as a concen-

junctions at 1.6 and 2.7 km from the channel servations at the San Francisco volcanic ¬eld sug-
head. The ¬rst major step down is associated gest that hillslopes above a threshold gradient
of approximately 0.3 m/m (17—¦ ) are susceptible to
with an increase in discharge and scour depth
associated with a relatively uncontaminated dis- mass movements and/or rilling within 1 kyr af-
tributary channel entering the channel from the ter an eruption. The threshold stream power for
northeast just upstream of the U-shaped chan- the Fortymile Wash drainage basin was estimated
nel bend. Another abrupt drop in concentration to be 0.05 km (corresponding to a drainage den-
sity of X = 20 km’1 ), based on forward modeling
occurs approximately 2.7 km from the channel
head (just downstream of sample SD091515.07) and comparison with USGS orthophotographs.
where another large tributary enters. As the For simplicity, contaminated tephra mobilized
channel curves around the southeast corner of from steep slopes and channels was assumed to
the Lathrop Wells lava ¬eld, it bifurcates into two be transported into the channel system instantly
distributary channels. Each pair of samples lo- following the eruption, although in nature this
cated at similar distances from the channel head process will take place over decades to centuries.
were averaged to comprise the ¬nal two points As an example, input to the tephra redistribu-
on the curve. The overall downstream-dilution tion model was constructed based on the fallout
pattern can be roughly approximated by an ex- from a hypothetical eruption with a northeast-
ponential function with a characteristic length directed plume computed using the ASHPLUME
of 0.9 km. For every 0.9 km downstream, there- numerical model (Figure 3.13a) (Jarzemba, 1997;
fore, the tephra concentration decreases by ap- Jarzemba et al., 1997; BSC 2004a,b). The hypothet-
proximately a factor of 1/e. Along the western ical fallout distribution used in Figure 3.13a cor-
responds to an eruption power of 9.55 — 109 W
channel, concentrations follow a similar pattern
in the bottom graph of Figure 3.10b. Note that (a moderate-to-large magnitude eruption for the
this pro¬le extends only about half as far from Crater Flat volcanic ¬eld), a duration of approx-
the channel head as the eastern channel, due to imately 3 days, a wind speed of approximately
the presence of the mine road which disturbs the 5 m/s, and an eruption velocity of 2 m/s. The
western channel about 2.5 km from the channel contributing-area grid is used to calculate the
head. scour-depth grid in several steps for this appli-
The ability of the model to represent ob- cation. First, contributing area is related to peak
served trends of downstream dilution at Lathrop discharge on a pixel-by-pixel basis using the re-
Wells provides a basis for using the model to gional ¬‚ood envelope curve of Squires and Young
predict dilution patterns following a hypothet- (1984), as in the Lathrop Wells example. Sec-
ical eruption at Yucca Mountain. To do this, a ond, discharge is related to scour depth on a
spatially distributed model was used to calcu- pixel-by-pixel basis using unit discharge with the
late the volume of tephra fallout mobilized from square-root dependence of Leopold et al. (1966).
steep slopes and active channels (Figure 3.13). Together, these relationships imply that scour
The model accepts input from the ASHPLUME depth is proportional to contributing area to the
numerical model (e.g. Figure 3.13a, assuming a 0.29 power. To determine the proportionality con-
southwesterly wind). The ASHPLUME model is stant needed to relate contributing area to a spe-
a numerical advection-dispersion-settling model ci¬c value of scour depth, the model uses mea-
that considers variable grain sizes and wind- surements of the US Geological Survey during the
speed pro¬les from the ground to 10 km altitude. 1995 ¬‚ood at the Narrows section of Fortymile
The model then calculates the DEM slopes and Wash (Beck and Hess, 1996) located close to the
contributing areas (Figures 3.13b and 3.13c). Fall- fan apex. The contributing area at this location is
the ratio of the basin area, 670 km2 , to the width,
out tephra is assumed to be mobilized if it lands
44 m. The maximum scour depth at this location
on pixels with hillslope gradients greater than
was measured to be at least 1.14 m, and had an
a threshold value equal to S or with a stream
average value of 0.72 m. The model runs of this
power greater than a threshold value equal to
paper used 1 m as a representative average scour
1/ X , where X is the drainage density. Field ob-

U slope*area1/2
tephra thickness slope

100 km
0.01 0.1 1m 0.01 0.03 0.1 0.3 1.0

(a) (c)



N 3 km
slope > 0.3 (17o) > 0.05 km
0.05 km
Fig 3.13 Digital grids used in the modeling of tephra depth for this reach. Combining these measure-
redistribution following a volcanic eruption at Yucca ments yields
Mountain. (a) Shaded relief image of DEM and Fortymile
Wash drainage basin (darker area). Tephra from only this A i, j 44
Hi, j = Hapex (3.5)
drainage basin is redistributed to the RMEI location.
670 x
(b) Grayscale image of DEM slopes within the Fortymile
Wash drainage basin. (c) Black-and-white grid of areas in the where Hi, j is the scour depth at any point in the
drainage basin with slopes greater than 17—¦ .
basin upstream from the apex, Hapex = 1 m is the
(d) Black-and-white grid of active channels in the drainage
representative scour depth at the fan apex based
basin (de¬ned as pixels with contributing areas greater than
on measurements by the US Geological Survey,
0.05 km2 ). All tephra deposited within the black areas of
and A i, j is the contributing area at point (i, j).
(c) and (d) are assumed to be mobilized by mass movement,
The scour-dilution-mixing model predicts rel-
intense rilling, or channel ¬‚ow. For color version, see plate
atively high tephra concentrations along the
section. Modi¬ed from Pelletier et al. (2008). Reproduced
northeast-directed plume track (Figure 3.14b). As
with permission of Elsevier Limited.
tephra from these channels moves downstream,
tephra in channels that are integrated into the

mately nearly 2% for the southwesterly wind case
scour/mixing depth tephra concentration
illustrated in Figure 3.14. The primary control on
1.0 m 10%
1% 100%
0.1 0.2
tephra concentration at the outlet is the topog-
(a) raphy in the primary fallout region (which con-
trols the volume of tephra mobilized on steep
slopes and in active channels). The highest out-
let tephra concentrations occur for southerly and
westerly winds (Figure 3.15), because these wind
conditions transport tephra north and east from

the repository location to areas with a relatively
high density of tephra-transporting steep slopes
and active channels within the Fortymile Wash
drainage basin.

3.1 Download a DEM of any area dominated by ¬‚uvial
processes. Implement the fillinpitsandflats
concentration routine (Appendix 2) to ¬lter out pits and ¬‚ats
southwesterly = 1.97% in the DEM. Implement the MFD ¬‚ow-routing
method to calculate the contributing area A for
each pixel and plot the results as a grayscale or
N 3 km color map.
3.2 After completing the above exercise, develop a
program module that distinguishes hillslope and
Fig 3.14 Digital grids output by the modeling of tephra
channel pixels in the DEM based on a threshold
redistribution following a potential volcanic eruption at Yucca
value of contributing area (i.e. assume channel
Mountain. (a) Map of scour-depth grid, calculated from
pixels are those with A > A c ). Create maps of the
contributing area grid. (b) Grayscale map of tephra
channel network corresponding to several differ-
concentration in channels, calculated using the
ent values of A c and compare the map to observed
scour-dilution-mixing model. For color version, see plate
channel-head positions in the DEM.
section. Modi¬ed from Pelletier et al. (2008). Reproduced
3.3 After completing the above exercise, use the FTCS
with permission of Elsevier Limited.
or ADI technique to solve the 2D diffusion equa-
tion for the evolution of the hillslope pixels in
the DEM. Assume that the channel network has
main Fortymile Wash becomes progressively di- a ¬xed elevation through time. This exercise will
luted with each successive in¬‚ow of relatively require using a mask grid to identify the channel
uncontaminated tributary sediments. Note that pixels and to ensure that only hillslope pixels are
some of the tephras draining from channels in varied through time.
the vicinity of Yucca Mountain are locally de- 3.4 Modify the fillinpitsandflats routine to map
posited in alluvial ¬‚ats and do not reach the the area of all closed depressions in a DEM by
including a counter that is incremented during
main Fortymile Wash. At the basin outlet the ef-
each loop through the routine. Download a USGS
fects of dilution mixing and localized deposition
DEM of an area that includes depressions (e.g.
of tephra limit the tephra concentration to 1.97%
karst, glacial lakes, etc.) and use the modi¬ed rou-
in this example. The effects of variable wind di-
tine to map the depressions.
rection on contaminant concentrations can be
3.5 Download a USGS Seamless DEM of an alluvial
determined (Figure 3.15) by running the scour-
channel or alluvial fan. Use the successive ¬‚ood-
dilution-mixing model on a sequence of rotated ing algorithm with MFD routing to model the in-
plumes of the same size and shape as the ex- undated area associated with some hypothetical

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