Journal of Geophysical Research Earth Surface
Supporting Information for
Sediment-supply versus local-hydraulic controls on sediment transport and storage
in a river with large sediment loads
David J. Dean,1 David J. Topping,1 John C. Schmidt, 2 Ronald E. Griffiths,1 Thomas A.
Sabol,1
1
U.S. Geological Survey, Southwest Biological Science Center, Grand Canyon
Monitoring and Research Center, Flagstaff, AZ 86001, USA
2
Utah State University, Quinney College of Natural Resources, Department of Watershed
Sciences, Logan, UT 84322, USA
Contents of this file
Text S1 to S4
Figures S1 to S4
Introduction
Included in this Supporting Information file are four text entries and four figures. The
text entries provide detail concerning (1) the method of calibrating two-dimensional
hydraulic models by optimizing zo roughness values using surveyed high-water lines, (2)
the uncertainties used for sediment mass-balance computations, (3) explanation of the α
parameter, and the relative-median-grain-size parameter of bed sand β, and (4)
uncertainties regarding our channel cross-section measurements. The four figures include
an example of a calibrated acoustic dataset, maps of channel cross sections in three
geomorphic monitoring reaches, relations between discharge and suspended-sediment
concentration at Castolon and RGV, and correlations between suspended-sand
concentration, flow depth, and channel width during the Lagrangian sampling campaign.
Text S1
Calibration of the two-dimensional hydraulic modeling efforts described in
section 4.2 are as follows. Modeled high flows were calibrated using a zo roughness based
on the grain-size distribution of the channel bed, and an initial estimate of discharge for
the most well-defined surveyed high-water line. We iteratively ran the model by varying
the discharge and zo until the root-mean-square error between the modeled water-surface
1
elevation and the surveyed high-water line was minimized. We then held zo constant and
repeated the procedure of varying the discharge until we minimized the root-mean-square
error between the modeled water-surface elevations and the other surveyed high-water
marks [Griffiths et al. 2010]. A stage-discharge relation was constructed using the
calibrated model results. We then used the stage data from the pressure transducer to
calculate a 15-minute record of discharge at the site.
Text S2
Calculations of the sediment mass-balance incorporate many terms with different
levels of uncertainty. One source of uncertainty includes the persistent biases that
possibly exist in discharge or suspended-sediment measurements made at specific river
cross sections. These bias-type uncertainties result largely from instrumentation bias
whereby different values of suspended-sediment concentration and/or discharge
(generally <5%) may be measured at adjacent cross sections. This bias thus represents
how current meters, ADCPs, and suspended-sediment samplers perform in slightly
different cross sections [Topping et al., 2010]. There is no way to independently know
what the “true” value of concentration or discharge is, and thus, uncertainties that
represent the greatest likely magnitude of these persistent differences are assigned to each
load value. Because these uncertainties are biases (and not random errors), they
accumulate over time, resulting in mass-balance calculations with uncertainty that gets
larger over time. Using this logic, we assign 10% uncertainty in the calculation of
suspended-sediment loads at Castolon and RGV.
We assume bedload is equivalent to 5% of the suspended-sediment load at
Castolon and RGV. This assumption is based on findings of Rubin et al. [2001] on the
Colorado River in Grand Canyon, AZ. The bed of the Rio Grande is considerably finer
than that of the Colorado River in Grand Canyon, and is largely composed of fine and
very fine sand, and silt and clay. These grain sizes are easily entrained into suspension
and thus contribute little to bedload during moderate- and high-discharge events.
Therefore, this estimate is likely a conservative estimate for the Rio Grande, such that
bedload in the Rio Grande likely contributes less than 5% to the total load
Uncertainties regarding computed loads from Tornillo Creek may arise from two
sources: possible bias in the stage-discharge rating curve, and the assumption that
suspended-sediment data obtained from the pump samples are representative of the
suspended-sediment conditions in the entire cross section. Tornillo Creek is relatively
narrow and steep at the monitoring site. Thus, the assumption that sediment is well-mixed
across the cross section is reasonable. Uncertainties in suspended-sediment load
calculations are likely more strongly influenced by uncertainty in the stage-discharge
rating curve, which we assume to be accurate to within 20%, and is the uncertainty we
therefore apply to our Tornillo Creek suspended-sediment load calculations. We hope to
further constrain this uncertainty in the future through additional field work during
Tornillo Creek floods.
The last source of uncertainty associated with the suspended-sediment budgets is
the estimation of the sediment loads contributed by ungaged tributaries. Flash floods
from ungaged tributaries are easily identifiable in the suspended-sediment record as
outlined in the methods of Section 4.3 (that use silt and clay as a tracer). Comparisons of
deposition rates during discrete flash flood events recorded at Castolon and RGV indicate
2
that the assumed deposition rate of approximately 1/3 of the total silt and clay load is
reasonable, with some flash floods depositing slightly more, and others depositing
slightly less than 1/3 of the load. Thus, over time, deposition rates likely average out to
approximately 1/3 of the contributed load within the study area.
There is larger uncertainty associated with the estimation of the sand contributed
by ungaged tributaries, because it is assumed that the ungaged tributaries have the same
ratio of silt and clay to sand as observed in Terlingua and Tornillo Creeks (i.e., ~12.5).
Based on the Terlingua and Tornillo Creek records, this percentage varies by up to 40%
around that ratio. We thus use a conservative estimate of 50% uncertainity in the ungaged
tributary loads.
The reader is referred to
http://www.gcmrc.gov/discharge_qw_sediment/reaches/BIBE where an automated
sediment-mass-balance computation tool is provided. There are default uncertainties and
estimations of bedload loaded into this tool that are the uncertainties that we used for
calculations in the main text; these uncertainties, and estimations of bedload, can be
changed by any user, and alternative budgets with varying uncertainty can be calculated.
Lastly, during periods of rapidly changing suspended-sediment conditions, such
as during tributary-sourced flash floods, some biases in the acoustic data may exist over
short time periods during periods of extremely high silt and clay concentration. These
biases are manifested in the differences in concentrations between physical sample
measurements and acoustic measurements (see Figure 2a). Since these are short-lived
biases, and because data can be biased positively or negatively during any given event,
these biases tend to average out over time.
Text S3

α is a parameter that scales the effect that changes in bed-sediment grain size and
flow exert on suspended-sediment transport. α is defined as
  (log Cs ) 
L 
 J
 K    (log Ds ) 
 

 J  1    (log Cs ) 
M
K
  (log Ds ) 
(1)
where σ(logCs) and σ(logDs) are the standard deviations of the logs of the suspendedsediment concentrations (Cs) and median grain sizes of suspended sediment (Ds),
respectively, measured over a flow event of interest. K, J, L, and M are exponents of
equations (2) – (8) Rubin and Topping [2001], the values of which are listed Table 1
[Rubin and Topping, 2001]. These values were derived from numerical modeling of more
than 1000 combinations of flow and sediment variables using theory based on McLean
[1992].

Rubin and Topping [2001] developed a dimensionless measure of bed-sediment
grain size, defined as
3
 Db 

 Dbm 
 
(2)
such that Db is the median grain-size diameter of bed sediment at a specific time and Dbm
is the average of a sequence of median diameters at the same location.  = 1 is
equivalent to the average value of Db over some period in time or space (for the assumed
condition of As = 1). Using relations developed between ratios of Db, Cs, and Ds at
different times [equation 6 in Rubin and Topping, 2001; 2008], was recast in terms of
those variables, and defined as
C 
  s 
 Cm 
0.1
 Ds 


 Dsm 
(3)
Where Cs and Ds are the concentration and median grain size of suspended sand
measured at a single time or location and Cm and Dsm are the mean of those values at all
times or locations [Rubin and Topping, 2008]. Rubin and Topping [2008] and Topping et
al. [2010] found that, in cases of relatively constant As, changes in  are directly related
to changes in Db. For cases of varying As,  includes the influence of both Db and As,
however, the behavior of is dominated by Db. Changes in As have a much weaker
influence on  than do changes in Db, e.g., a factor of 2 decrease in As causes only a 7%
increase in  [see figure 10 in Topping et al., 2010].
Values of β were calculated using equation (3) above [Rubin and Topping, 2008]
for Castolon and RGV, where the average values of suspended-sand concentration and
median grain size were first calculated for each gage individually and then averaged
together. This approach applied the same weighting to the average suspended-sand
concentrations and median grain sizes at each gage, thus ensuring that the calculated β
values would be comparable between the two gages.
Text S4
Locations of the Castolon and RGV geomorphic monitoring reaches were
collocated with the Castolon and RGV stream gages, as requested by Big Bend National
Park scientists. Location of the Solis monitoring reach was chosen because it resides
within a different geologic, geomorphic, and riparian setting than either the Castolon or
RGV reaches, such that a wider range of environments are included within the
monitoring framework. Locations of individual cross sections were chosen such that all
types of aquatic habitats and geomorphic environments were measured. Cross section
locations were established across pools, upstream, within, and downstream from riffles,
and across straight sections of river with little complexity.
There are many possible uncertainties associated with channel cross-section
measurements including the GPS uncertainty for each measured topographic point, and
uncertainties associated with each individual surveyor. During the surveys, the
uncertainty associated with the real-time kinematic solution within the GPS operating
system was specified to not exceed 3 cm; the uncertainty of the solution was often less
than 1.5 cm. GPS uncertainty for each surveyed point is likely random and thus will not
be a persistent bias over the length of the cross section. If these uncertainties are
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manifested as biases, maximum potential negative and positive biases (total of 6 cm
about the recorded value) at an individual cross section for two successive years result in
uncertainties between approximately 1.5 and 2.5% in calculations in area for wide and
narrow cross sections, respectively. Since this magnitude of a bias would be highly
unlikely, potential GPS biases are likely on the order of 1% of the total cross-section area
of a single cross section.
Uncertainties associated with surveying errors include an unplumb survey rod,
and the sinking of the survey rod into soft sediment. An unplumb survey rod results in
very minor negative biases in the vertical dimension. For example, if a 2-m rod is five
degrees off of vertical, the vertical error in the measurement is less than 1 cm. Persistent
biases of that degree are unlikely, and would have a small effect on the uncertainty of the
total cross-section topography.
A surveyor may repeatedly sink the rod into soft sediment resulting in negative
biases regarding these topographic measurements. Areas within the channel (where
sediment will likely be soft) will be more biased than measurements collected elsewhere.
These potential persistent biases will be negative, and are likely to be on the order of 1 or
2 cm. Since this is not likely to occur throughout the entire river channel, these negative
biases will result in slight over predictions in cross-section area, and will likely be
systematic for all cross sections. Thus, comparisons between cross-section areas over
time will not be greatly affected because they will be biased in the same direction.
Additionally, none of the above biases or uncertainties compound over time.
Our measurements of cross-section change show that there were highly variable
changes in cross-section area within each reach (Figure 9). For example, in each year,
there were cross sections that had negative changes and positive changes in cross-section
area, with negative changes being dominant. These results are partly controlled by the
length of the cross section that was measured. In most cases, the length of the cross
sections greatly exceeded the width of the channel, and typically exceeded the wetted
extent of the floodplain in all years. Therefore, calculations of cross-section area may be
dampened because they include large portions of the floodplain that did not change. The
extent of the wetted width of each cross section is unknown, and therefore, we are unable
to calculate changes in cross-section area that are explicitly limited to hydraulically
driven changes in geomorphology. If we were able to limit our analyses to those extents,
then measured changes (both negative and positive) will likely be greater than reported
because changes would be normalized by a smaller overall cross-section area. This
source of uncertainty likely plays a larger role in our calculations than the uncertainties or
biases mentioned above. Thus, for the purposes of our analyses, we show the minimum
and maximum measured changes in cross-section area for each reach, the bounds of
which are generally greater than any potential persistent biases or uncertainties included
in the average changes in cross-section area for any given year.
5
Figure S1. Comparison of calibrated acoustic data and physical samples at the Castolon
sediment gage between 7/20/2013 and 8/16/2013. Velocity-weighted silt and clay
concentrations (a), sand concentrations (b), and median grain size of sand (c) in the river
cross section. Note that (c) depicts data only between 7/20/2013 and 8/1/2013 because the
mount for 1-MHz instrument broke on 8/4/2013, preventing acoustic measurements of
median grain size from being made after this date (because these measurements require 2
frequencies). Error bars on the pump and EWI measurements represent the 95%
confidence interval based on both field errors [Topping et al., 2011] and lab errors [after
Topping et al., 2010].
6
Figure S2. Castolon (a), RGV (b), and Solis (c) study reaches and monitoring cross
sections. For locations of these reaches, see Figure 1b. Natural color background images
taken in 2010.
7
Figure S3. Suspended-silt-and-clay concentration plotted as a function of discharge for
Castolon (a) and RGV (b). Suspended-sand concentration plotted as a function of
discharge at Castolon (c) and RGV (d). Black circles are acoustic data, and red squares
are physical samples. Note that the physical-sample data do not cover the entire domain
of the acoustic data, because physical samples were not typically collected at low
discharges. Note that for any given discharge, silt-and-clay and sand concentrations vary
by up to ~3 orders of magnitude.
8
Figure S4. Longitudinal trends in suspended-sand concentration measured during the
Lagrangian sampling campaign, and channel width at those locations (a). Correlation
between sand concentration and channel width (b). Longitudinal trends in suspended sand
concentration during the Lagrangian sampling campaign, and mid-channel depth at those
locations (c). Correlation between sand concentration and mid-channel depth (d). The
relations of the data presented in (b) and (d) are not significant.
9
References
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Interagency Conference, Las Vegas, NV, June 27-July 1, 2010.
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to measure bedload: Proceedings of the 7th Inter-Agency Sedimentation Conference, v. 1, p.
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