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Q = 1000 m3/s

Fig 3.7 Illustration of a successive ¬‚ow-routing algorithm inundation, and can be used on a reconnoitering
applied to Fortymile Wash alluvial fan in Amargosa Valley, basis to determine relative ¬‚ood risk. Successive
Nevada. (a) Shaded-relief image of a high resolution
¬‚ow-routing analysis can be performed for a sin-
(1 m/pixel) photogrammetric DEM of Fortymile Wash, (b)“(d)
gle master channel network by specifying ¬‚ow
¬‚ow depths predicted by the model for different values of the
at an upstream boundary, or a uniform runoff
prescribed upstream discharge: (b) 300 m3 /s, (c) 1000 m3 /s,
depth can be speci¬ed for the entire DEM in or-
and (d) 3000 m3 /s. For color version, see plate section.
der to model distributed ¬‚ow routing. Appendix
2 provides code for implementing the distributed
increments of ¬‚ow until the input ¬‚ow depth ¬‚ow routing case.
corresponding to the upstream discharge is
achieved. This algorithm is useful at identifying
distributary channels and adjacent overbank ar-
eas that are activated when certain threshold 3.5 Contaminant transport in
¬‚ow depths are exceeded. This technique makes
channel bed sediments
a number of simplifying assumptions about the
steadiness of the ¬‚ow, and hence cannot be
used for detailed ¬‚ood-hazard assessment. Nev- Predicting the transport and fate of contami-
ertheless, it is a simple, fast method for iden- nants in ¬‚uvial systems is a critical aspect of
tifying ¬‚ow pathways and their thresholds of applied geomorphology. Worldwide, many river

systems have channel-bed sediments with in order to map the fraction of contaminated
elevated heavy-metal concentrations as a result sediments in all the channels of the Fortymile
of centuries of ore-mining activity (James, 1989; Wash drainage basin. The contaminant fraction
Miller, 1997). Similarly, radionuclide contami- computed for channels in the area of the critical
nation of channel-bed sediments is a potential population provides a basis for estimating the po-
human health hazard downstream of areas tential dose rate to that population in the event
of high-level nuclear processing and testing of an eruption.
(Reneau et al., 2004). The model divides the Fortymile Wash
In this section, we explore a model for the drainage basin into two domains: (1) the tribu-
prediction of contaminant distributions in ¬‚u- tary drainage basin of Fortymile Wash and (2) its
vial channel sediments. The motivation for de- distributary alluvial fan where the nearest pop-
veloping the model was the need to quantify ulation resides (Figure 3.8). The Fortymile Wash
the dispersal of radionuclide-contaminated sed- drainage basin includes the proposed repository
iments in the event of a volcanic eruption at location and the area of most of the primary fall-
the proposed nuclear-waste repository at Yucca out in the event of a volcanic eruption through
Mountain. Underground storage of nuclear waste the repository. The drainage basin and the fan are
primarily poses a hydrologic risk associated with divided at the fan apex. The model assumes that
contaminated groundwater. However, volcanism primary fallout is mobilized and transported to-
in the Yucca Mountain region could pose a signif- ward the alluvial fan if it falls on slopes steeper
icant geomorphic hazard if an eruption were to than a threshold gradient or on channels greater
occur. Probabilistic volcanic hazard analyses con- than a threshold stream power. To do this calcu-
strain the annual risk of an eruption through the lation, the model performs a spatially distributed
proposed repository to be a very low 1.5 — 10’8 analysis of the slopes and stream powers for the
(CRWMS M&O, 1996). In the event of an erup- entire Fortymile Wash drainage basin using an
tion, individuals living on the Fortymile Wash input 30-m resolution US Geological Survey Digi-
alluvial fan 18 km south of the repository (i.e. tal Elevation Model (DEM).
the closest residents to the repository; Figure 3.8) Before the mobilized tephra and radionu-
could be affected by radionuclide-contaminated clides are deposited on the alluvial fan, they are
tephra deposited as fallout or redistributed from transported through the alluvial channel system
upstream. Under most wind direction scenarios of Fortymile Wash where mixing with uncon-
(i.e. southerly winds), primary fallout tephra is taminated channel sediments results in the di-
concentrated to the north of the proposed repos- lution of contaminated tephra. During extreme
itory location and entirely within the Nevada Test ¬‚ood events, contaminated tephra deposited in
Site (BSC, 2004a,b). In such cases, ¬‚uvial redis- channels or mobilized into channels from ad-
tribution of contaminated tephra from the pri- jacent hillslopes will be entrained and poten-
mary fallout location to the Fortymile Wash allu- tially mixed with uncontaminated channel-bed
vial fan could be signi¬cant and hence must be sediments within the scour zone. The cumu-
evaluated. lative effect of many ¬‚oods is to mix the
In collaboration with scientists at Los Alamos tephra with any uncontaminated channel-bed
National Laboratory, my graduate students sediments located beneath the tephra but within
Stephen DeLong, Mike Cline, and I developed the scour zone both locally and with dis-
a model that quanti¬es the concentration of tance downstream. Quantifying this dilution pro-
tephra and radionuclides in channels of the cess requires a spatially distributed model of
Fortymile Wash alluvial fan as a result of hill- long-term ¬‚ood scour depths throughout the
slope and ¬‚uvial redistribution processes in the drainage basin. The MFD ¬‚ow routing model,
event of a volcanic eruption through the repos- together with empirical relationships between
itory. The model uses the MFD ¬‚ow-routing al- discharge and scour depth, provide the means
gorithm to route contaminated and uncontam- for mapping the scour depths necessary for the
inated sediments through the ¬‚uvial system model.

116.40 116.30
116.50° W

N 2 km
36.90 N
116° W
117° W
contours for
1 cm
southwesterly wind
1 mm
Nevada Fortymile
N Ca

ev lif
ad or

a ni

36.5 N Mtns.
Fortymile Wash

drainage boundary


N 10 km
36.0 N


Fig 3.8 Location map of the study areas in Amargosa Valley, non-source areas weighted by their relative up-
Nevada. Shaded relief image includes Lathrop Wells volcanic
stream areas:
center, the footprint of the proposed nuclear-waste
As A ns
C= Cs +
repository at Yucca Mountain, and the southern portion of C ns (3.2)
A s + A ns A s + A ns
the Fortymile Wash drainage basin (i.e. the site of primary
fallout for tephra with potential for redistribution to the where C is the contaminant concentration at a
Fortymile Wash fan where the nearest population resides. point downstream, A s and A ns are the source and
From Pelletier et al. (2008). Reproduced with permission of
non-source areas upstream from the point, and
Elsevier Limited.
C s and C ns are the source and non-source concen-
trations. The value of C ns is usually zero, but in
cases where contaminants have a ¬nite natural
Previous work on the dilution and mix- background level, or in cases where non-¬‚uvial
ing of ¬‚uvial-system contaminants predict one- (e.g. eolian) processes have transported contam-
dimensional (1D) concentration of contaminants inants from source to non-source areas in the
in channel systems. These models are 1D in basin, C ns may be greater than zero. Equation
the sense that vertical and cross-channel concen- (3.2) reduces to an exponential form if the source
tration variations are not considered. The clas- area is located in the basin headwaters and the
sic dilution-mixing model of Hawkes (1976) and upstream area is written as a function of x, the
Marcus (1987) assumes that the primary process along-channel distance:
of downstream dilution is the mixing of con-
C = C ns + C s exp(’x/xs ) (3.3)
taminants with uncontaminated sediments deliv-
ered from upstream. Mathematically, the model where xs is a length scale controlled by the
states that the concentration at a point down- relative areas of source and non-source regions
stream from a contaminant source is an average and the along-channel distance through the
of the contaminant concentration at source and source area. Equation (3.3) is an approximation

of Eq. (3.2); it describes the general downstream- con¬‚uence to be an average of the upstream
dilution trend but does not capture the abrupt concentrations, weighted by the upstream sedi-
concentration decrease that occurs as large trib- ment yields or basin areas. The model makes no
utaries enter the main channel. Equation (3.2) prediction regarding the vertical distribution of
has been tested in many contaminated rivers (e.g. contaminants.
Hawkes, 1976; Marcus, 1986) and its accuracy is The basic operation of the scour-dilution-
often remarkable considering the simplicity of mixing model is illustrated by the diagram in
the model relative to the complexity of the pro- the lower left corner of Figure 3.9b. The scour-
cesses involved. dilution-mixing model is conceptually similar to
In addition to mixing of the contaminant the classic model because the contaminant con-
with uncontaminated sediments from upstream, centration downstream is an average of upstream
dilution can also occur by mixing of contami- concentrations. However, the vertical component
nants with local channel-bed sediments down- of mixing is explicitly included, and the local
stream. In this process, a ¬‚ood wave moves contributions of contaminant and uncontami-
though the channel causing net erosion dur- nated channel-bed sediments are incorporated
ing the growing phase of the ¬‚ood, turbulent into the mixture. The basic assumption of the
mixing of the contaminant with uncontami- model is that the concentration at each point is
nated channel-bed sediments during the ¬‚ood, a mixture of contaminant and channel-bed sed-
and redeposition of the sediment--contaminant iments upstream from the point. As such, the
mixture as the ¬‚ood wave passes. The depth contaminant concentration at a channel point
of contaminant mixing by this process is the is a ratio of the total contaminant volume de-
scour depth, i.e. the thickness of sediments that livered from upstream to the total mobile-bed
undergo active transport during extreme ¬‚ood volume. One signi¬cant advantage of the scour-
events. The scour depth, in turn, is proportional dilution-mixing model is that it predicts the
to the square root of the unit discharge (dis- vertical distribution of contaminants as well as
charge per unit channel width) (Leopold et al., the surface concentration. In addition, by using
1966). A numerical model that maps unit dis- spatially distributed routing of runoff and con-
charge and uses Leopold et al.™s empirical rela- taminants, the model can predict cross-channel
tionship to predict scour depth, therefore, pro- distributions and can be applied to distributary
vides a basis for estimating the dilution effect environments. In this sense, the model predicts
caused by contaminant mixing with channel-bed a 3D distribution rather than the 1D distribution
sediments downstream. In our model, the mobile of the classic model.
portion of the bed (including both contaminants The scour-dilution-mixing model can be read-
and uncontaminated channel-bed sediments) is ily implemented using a raster-based framework.
assumed to be lifted from the bed, mixed by tur- In this framework, the contributing-area grid is
bulence, and deposited back onto the bed down- ¬rst initialized with the value of the pixel area,
( x)2 . Second, the MFD ¬‚ow-routing algorithm
stream. The dilution effect caused by this process
of Freeman (1991) is used to calculate the con-
can be quanti¬ed as a function of source and non-
tributing area routed through each pixel in the
source upstream areas as in the classic model.
DEM. Third, a critical stream-power threshold is
The classic dilution-mixing and scour-
used to distinguish between hillslopes and chan-
dilution-mixing models are compared schemat-
nels in the DEM, where the stream power is de-
ically in Figure 3.9. The basic operation of the
¬ned as the product of the local slope S and the
classic model is illustrated by the diagram
square root of the drainage area A (Montgomery
in the lower left corner of Figure 3.9a. The
and Dietrich, 1988). The critical stream power is
lengths of arrows coming into the central point
related to the drainage density X through the re-
represent the sediment yield from the two
lationship 1/ X . The value of the drainage density
upstream tributaries (one contaminated and
can be directly measured in the ¬eld or by using
one uncontaminated). The model predicts the
digital map products. Pixels with stream-power
contaminant concentration downstream of the

contaminant concentration



classic dilution-mixing model scour-dilution-mixing model
0 100
contaminant concentration
estimated scour depth in each channel pixel. As
Fig 3.9 Schematic diagram of (a) classic dilution-mixing
model, and (b) scour-dilution-mixing model. (a) The basic a simple example, assume that the ¬‚ood-envelope
operation of the classic model is illustrated in the lower left. curve shows the peak unit discharge for extreme
Here, lines with arrows represent upstream contributing
¬‚oods to be linearly proportional to contributing
area, a proxy for sediment yield. Concentrations downstream
area. Then, if the scour depth is observed to be
of a con¬‚uence are equal to the average of the upstream
1 m (e.g. using a scour chain emplaced prior to
concentrations weighted by contributing area. In a drainage
a recent extreme ¬‚ood) at a channel pixel with
basin, concentrations decrease rapidly with distance
a contributing area of 100 km2 , then the scour
downstream from a localized contaminant source, with
depth at any channel pixel in the basin will be
abrupt decreases at major con¬‚uences (illustrated by
equal to the square root of the normalized con-
grayscale pattern). (b) In the scour-dilution-mixing model, the
vertical and cross-channel distributions of contaminant are tributing area at that pixel (i.e. the contributing
also considered. At each pixel (i , j ), the total volumes of area divided by 100 km2 ) multiplied by 1 m.
upstream contaminant and uncontaminated channel-bed
The model routes the contaminant (expressed
sediments are mixed with the local volumes of contaminant
as an equivalent thickness for each pixel) down-
and uncontaminated sediments. The contaminant distribution
stream using the same ¬‚ow-routing algorithm
at that pixel is de¬ned by that concentration value and the
used for routing contributing area. Finally, as the
local scour depth. The resulting mixture is transported
contaminant is routed downstream, the model
downstream where the same operation is repeated.
calculates the concentration at each pixel as the
ratio of total contaminant volume upstream di-
vided by the total volume of scour depth for all
values less than 1/ X are made zero in the grid,
active channels upstream. Mathematically, the
leaving ¬nite values in the remaining pixels.
model states that the concentration at a pixel (i,j)
Fourth, the contributing-area grid is converted
is given by
to a unit-discharge grid using empirical data (i.e.
a ¬‚ood-envelope curve), which, in turn, is con-
h l,m + h i, j · Hl,m + Hi, j
verted to a scour/mixing-depth grid using the min up up
C i, j =
empirical square-root relationship documented
Hl,m + Hi, j
by Leopold et al. (1966). Following this series up

of operations, the resulting grid represents the (3.4)

where h l,m is the effective contaminant thickness Zone (CFVZ) (Crowe and Perry, 1990). Its relative
at pixel (l,m), Hl,m is the scour depth, and the youth and location with respect to Yucca Moun-
sums are computed over all pixels (l,m) upstream tain has made it a focus of intense study as a
from pixel (i, j). possible analog for an eruption through the pro-
The fundamental tool for the scour-dilution- posed nuclear waste repository.
mixing model is the MFD algorithm. In this al- There are two principal drainages that trans-
gorithm, contributing area, contaminants, and port tephra from Lathrop Wells (Figure 3.10).
scour depths are routed from each pixel to all The western drainage system transports material
of its neighboring pixels weighted by topographic from the exposed tephra sheet on the northwest
slope. This algorithm is implemented by initializ- side of Lathrop Wells cone west and south into
ing the grid with the quantity to be routed. In the Amargosa Valley. The eastern drainage system
case of contributing area, the grid is initialized heads near the northern margin of the tephra
with the area of that pixel, x 2 (e.g. 900 m2 for a sheet and transports material around the east-
30-m resolution DEM). In the case of contaminant ern side of the Lathrop Wells cone and adja-
routing, each pixel is equal to the effective thick- cent lava ¬‚ows. Twenty ¬ve samples of channel-
ness of contaminant in channels of the source re- bed sediments were collected along these two
gion. The MFD or bifurcation-routing algorithm channel systems in order to evaluate the signif-
then ranks all grid points in the basin from high- icance of the dilution process and validate the
est to lowest in elevation. Routing is then calcu- scour-dilution-mixing model. In small channels
lated successively at grid points in rank order on the tephra sheet, the bottom of the scour
from highest to lowest, thereby ensuring that zone was clearly visible and ranged from 12 to
all incoming areas of contaminant have been 29 cm in depth in channel-bed-sediment sam-
accounted for before downstream routing is ple pits (Figure 3.11). In larger channels down-
performed. stream from the tephra sheet, the bottom of the
To test the model, we consider the concen- scour zone was not visible within our sample pits
tration of basaltic sediment in channels drain- (which were limited to 30--40 cm in depth). Sam-
ing the Lathrop Wells tephra sheet. This tephra ples were taken by uniformly sampling pit-wall
sheet provides a concentrated source of ash and material to a depth of 30 cm, or to visible scour
lapilli that acts as a contaminant source for depth if less than 30 cm. Samples were sieved
downstream channels. The tephra found in chan- and material larger than silt size was separated
nels downstream from the tephra sheet is com- into basaltic and non-basaltic fractions with a
parable in texture to the non-basaltic sand of magnet and visually checked for complete sep-
downstream channel beds. As such, the model as- aration using a stereomicroscope. The basaltic
sumption that contaminant material and uncon- material was strongly magnetic and total sepa-
taminated channel sediments are transported at ration error was estimated to be less than 5%
similar rates is likely to be a good approximation by mass. Non-basaltic material was composed of
in this case. In addition, the proximity of this Miocene welded tuff and eolian sand. The frac-
area to Yucca Mountain (i.e. 18 km south of the tion of basaltic sediment by mass was calculated
proposed repository location) makes it an ideal for each sample. This value was converted to a
analog (e.g. similar climate, hydrology, and geo- fraction by volume (for comparison to the volu-
morphology) for tephra redistribution following metric dilution-mixing model) using an average
measured basalt density of 1.5 g/cm3 (a relatively
a hypothetical volcanic eruption at Yucca Moun-
tain. The physical volcanology of the Lathrop low value for rock because of its high vesicular-
ity) and a tuff density of 2.7 g/cm3 .
Wells volcanic center was described in detail by
Mixing occurs along both the eastern and
Valentine et al. (2005). At 77 000-years old (Hei-
western drainages according to the trend ev-
zler et al., 1999), the Lathrop Wells cone is the
ident in the plots of basalt concentration as
youngest basaltic volcano in the Yucca Mountain
a function of distance from the channel head
region. It is the southern-most surface expression
in Figure 3.10b. These data indicate that the
of the Plio--Pleistocene-age Crater Flat Volcanic

116.51° W

measured data
36.70 N
1505.02 3D model
1505.01 1505.04 1505.05 1505.06
1405.04 1405.01
1405.02 tephra sheet
east channel 0.1
1405.06 1405.03
BG BG 1505.08
major tributary
1505.07 junctions
east channel
3 5

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