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Closing a sediment budget for a reconfigured reach of the Provo
River, Utah, United States
Susannah O. Erwin,
1
John C. Schmidt,
1,2
Joseph M. Wheaton,
1
and Peter R. Wilcock
3
Received 9 June 2011; revised 25 August 2012; accepted 27 August 2012; published 6 October 2012.
[1] We quantified all components of a fluvial sediment budget for a discrete flood on an
aggrading gravel bed river. Bed load transport rates were measured at the upstream and
downstream ends of a 4 km study area on the Provo River, Utah, during a dam-controlled
flood. We also collected high-resolution measurements of channel topography before and
after the controlled flood for the entire reach. Topographic uncertainty in the digital
elevation models (DEM) was characterized using a spatially variable approach. The net
sediment flux provided unambiguous indication of storage. Sediment input to the reach
(319 m
3
) exceeded output (32 m
3
), producing a net accumulation of approximately 290 m
3
.
The difference between the scour and fill was also positive (470 m
3
), but uncertainty in the
topographic differencing was larger than the observed net storage. Thus, the budget would
have been indeterminate if based on morphologic data alone. Although topographic
differencing was not sufficiently accurate to indicate net storage, it was able to demonstrate
that internal erosion was a larger sediment source than the net sediment flux. The magnitude
of total erosion (1454 m
3
) and deposition (1926 m
3
) was considerably larger than net
change in storage, showing that internal sources and sinks were the dominant driver of
channel change. The findings provide guidance for the development of sediment budgets in
settings in which one must choose between a morphological approach and the direct
measurement of sediment flux.
Citation: Erwin, S. O., J. C. Schmidt, J. M. Wheaton, and P. R. Wilcock (2012), Closing a sediment budget for a reconfigured reach of
the Provo River, Utah, United States, Water Resour. Res., 48, W10512, doi:10.1029/2011WR011035.
1. Introduction
[2] Sediment budgets are a fundamental tool in geomor-
phology, used across the discipline in theoretical and applied
studies [Reid and Dunne, 2003]. A fluvial sediment budget
provides the context needed to evaluate channel response to
changes in flow or sediment supply [e.g., Trimble,1983;
Wathen and Hoey,1998;Grams and Schmidt,2005].A
sediment budget balances sediment input (I) and sediment
export (E), against sediment storage (S),
I E ¼ S: (1)
Numerous studies have focused on quantifying either the
flux side [Singer and Dunne, 2004; Vericat and Batalla,
2006] or the storage side of (1) [Lane et al., 1995; Martin
and Church, 1995; Ashmore and Church,1998;Ham and
Church, 2000; Brasington et al., 2003; Surian et al., 2009].
Few studies have computed both sides of the budget. In the
absence of closing a budget, the unmeasured components of
the budget cannot be separated from the errors associated
with the measured terms in the budget [Kondolf and
Matthews, 1991]. Closure of the budget, i.e., independently
calculating the left and right sid es of (1) and determinin g if
the two quantities match, provides a rigorous means by
which the accuracy and pre cision of the budget can be eval-
uated. Spatial partitioning of the right side of (1), i.e., deter-
mining the amount of change in sedim ent st orage in different
parts of th e channel and/or floodplain, provides even mo re
insight into how channels adjust to longitudinal changes in
sediment transport.
[
3] One of the persistent problems with developing sedi-
ment budgets is that measurement error is typically large.
Both transport and storage sides of the budget often involve
the small difference between two large and uncertain num-
bers, such that even the sign of either side of (1) is uncer-
tain. Sediment transport estimated from either formulas
[Gomez and Church, 1989; Martin, 2003] or direct mea-
surement [Ham and Church, 2000; Wilcock, 2001] may not
be sufficiently accurate to determine the sign of the net flux.
Topographic monitoring may not be sufficient to determine
the sign of S, even with recent advances in techniques for
measurement and analysis [Heritage and Hetherington,
2007; Wheaton et al., 2010; Milan et al., 2011]. The result
of measurement uncertainty in either flux or topographic
change is that sediment budgets may be indeterminate, in
1
Watershed Sciences Department, Utah State University, Logan, Utah,
USA.
2
Now at Grand Canyon Monitoring and Research Center, U.S. Geologi-
cal Survey, Flagstaff, Arizona, USA.
3
Department of Geography and Environmental Engineering, Johns
Hopkins University, Baltimore, Maryland, USA.
Corresponding author: S. O. Erwin, Watershed Sciences Department,
Utah State University, 5210 Old Main Hill, Logan, UT 84322, USA.
(s.erwin@usu.edu)
©2012. American Geophysical Union. All Rights Reserved.
0043-1397/12/2011WR011035
W10512 1of13
WATER RESOURCES RESEARCH, VOL. 48, W10512, doi:10.1029/2011WR011035, 2012
the sense that one cannot explicitly demonstrate that aggra-
dation or degradation has occurred [Grams and Schmidt,
2005]. In some cases, budgets are indeterminate even where
measurement programs are extensive [Topping et al., 2000].
[
4] The ability to calculate a sediment budget with a defin-
itive balance is influenced by the spatial and temporal scale
of the analysis. For example, budgets may be developed over
sufficiently long reaches such that there is a significant differ-
ence in fluxes at the upstream and downstream boundaries or
over sufficiently sh ort temporal scales so one can accurately
relate topographic measurements to a discrete flow event.
Even under these circumstances, however, challenges
remain. Detecting the changes in storage for sho rt time spans
may be diffic ult because there may have been li ttle net topo-
graphic change during the period fo r which the budget is cal-
culated. It may be diffi cult to extrapolate the budget to longer
time scales because a longer time sp an introduces more
uncertainty about the stability of sediment transport relations.
Additionally, investigations sp anning multiple years, or deca-
des, are often limited by the lack of his toric data. Calculation
of budgets over sh ort spatial scales provides the advantage
that changes in storage can be measured with re l ative ease.
However, when budgets are calculated for a short reach of
river, there may not be a significant difference between the
measured influx and efflux of sediment. Conversely, larger
spatial scales provide the advantage that there may be a more
substantial diffe rence between influx and efflux. Yet, changes
in storage are more difficult to comprehensively measure
over longer reaches.
[
5] Here we present a sediment budget for a reconfigured
4 km segment of the middle Provo River, near Heber City,
Utah, USA (Figure 1) for a single flood that lasted approxi-
mately 3 weeks. We highlight the challenges and uncertain-
ties associated with construction and closure of a sediment
budget in an unusually well-constrained situation—a dis-
crete flood on a relatively short segment of a gravel bed
river. The study area had been reconfigured approximately
3 years earlier, and qualitative evidence indicated that the
channel was accumulating gravel, primarily in point bars.
Preliminary measurements of transport rates at the upstream
and downstream boundaries of the study area suggested that
sediment influx exceeded efflux by an order of magnitude
[Olsen, 2006]. In constructing a sediment budget, we sought
to (1) confirm whether or not aggradation was occurring, (2)
understand the magnitude of difference between upstream
sediment delivery and downstream sediment export, and (3)
evaluate whether the observed channel changes could be
attributed to sediment accumulation in the reach. By quanti-
fying both sides of (1), this study provides guidance and
insights into the merits, and demerits, of using either meas-
urements of flux or morphologic change in understanding
geomorphic systems.
2. Study Area
2.1. History of Flow Manipulation on the Provo River
[
6] Th e Provo River flows from its headwaters in the
Uinta Mountains in northern Utah to its outlet in Uta h Lake.
The ri ver sy stem is subject to large-scale flow manipula tion
and augmentation, primarily caused by two water resource
development projects: the Provo Ri ver Project (PRP) and the
Central Utah Project (CUP). As part of the PRP, trans-basin
diversions from the Weber and Duchesne Rivers into the
Provo River were constructed in 1930 and 1952, re spec-
tively. These diversions nearly doubled the magnitude of
peak flows on the Provo River and substantially increase d
base flows. Deer Creek Dam wa s constructed at the down -
stream end of Heber Valley to provid e reservoir storage for
the augmented flow (Figure 1). Deer Creek Reservoir was
filled soon after completion of the dam in 1941. To accom-
modate the additional flow and to protect adjacent lands
from flooding, the Provo River in Heber Valley was
Figure 1. The middle Provo River, located in Heber
Valley, Utah. The river flows approximately 19 km from the
outlet of Jordanelle Dam (top right) to Deer Creek Reservoir
(bottom left). The entire channel was reconfigured as part of
the Provo River Restoration Project, with the exception of
the Never Channelized Reach (NCR). Today, the NCR pro-
vides a local source of sediment to the study area.
W10512 ERWIN ET AL.: CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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straightened, enlarg ed, and confined between dik es along the
entire length of the valley between 1960 and 1965. The only
exception wa s a 2.5 km reach, which we re fer to as th e Never
Channelized Reach (NCR; see Figure 1). During the period
between 1965 and 1994, upstream bed incision caused gravel
to accumulate in the NC R.
[
7] Jordanelle Dam, at the upstream end of the Heber
Valley, was completed in 1993 as part of the CUP. Opera-
tions of Jordanelle Dam reduced the magnitude of peak
floods by 25% from those of the postflow-augmentation pe-
riod. Additionally, trans-basin diversions maintain summer
flows that are much higher than natural base flows. Within
the study area, streamflow has been measured since 1938 at
U.S. Geological Survey gauging station 10155500 (Provo
River near Charleston). There are no significant tributaries.
2.2. Provo River Restoration Project
[
8] The Provo River Restoration Project (PRRP)
involved reconfiguration of 16 km of the middle Provo
River to restore elements of the pr echannelization ecosys-
tem that can be maintained by the regulated flow regime
provided by Jordanelle Dam. Twelve km of the PRRP are
upstream from the NCR and 4 km are downstream from the
NCR. Project construction began in 1999 and consisted of
removing dikes, creating a wandering, gravel bed channel,
reconnecting the river to existing remnants of historic second-
ary channels, and constructing small side channels to recreate
natural aquatic features and wetlands. The reconstructed
channel morphology is intended to maximize diversity of
habitat conditions and establish a complex template on which
ecosystem processes will thrive [Utah Reclamation, 1997].
[
9] Jordanelle Dam eliminated the sediment supply once
delivered to the Heber Valley; thus, the upstream 12 km of
the PRRP has no sediment input. Previous transport obser-
vations [Olsen, 2006] indicated that the NCR is now a
source of gravel for the reconfigured 4 km segment down-
stream. Air photo observations in this segment indicated that
point bars had grown since completion of channel reconfigu-
ration in 2004 (Figure 2), suggesting a trend of sediment
accumulation.
[
10] This study focuses on the 4 km segment immedi-
ately downstream from the NCR where qualitative observa-
tions suggested sediment is actively accumulating. The
substantial influx of gravel into the study area (Figure 3)
has the potential to augment channel dynamics, and per-
haps aid in achieving restoration goals, but these channel
changes also have the potential to be detrimental to the
original restoration objectives. Thus, it is useful to deter-
mine the sediment balance in order to better understand the
impact of sediment influx on channel morphology and dy-
namics. The PRRP upstream from the NCR has no sedi-
ment supply and gravel augmentation will be considered as
a tool for promoting channel dynamics. Studies of the seg-
ment downstream from the NCR will inform plans for
gravel augmentation plans upstream.
3. Methods
[11] We quantified both net flux and change in storage,
quantified their uncertainty, and evaluated the mass balance
with respect to the uncertainty in all terms. Here we divide
our discussion of methods into the quantification of bed
load flux (section 3.1) and estimation of change in storage
through measurement of topographic change (section 3.2).
3.1. Determining Bed Load Flux
3.1.1. Bed Load Transport Measurements
[
12] In spring 2009 we worked with the U.S. Bureau of
Reclamation (USBR) and the Central Utah Water Conserv-
ancy District (CUWCD) to design a controlled flood that
allowed for an effective bed load sampling program. On
both rising and falling limbs, discharge was changed in
intervals of approximately 5.7 m
3
s
1
each day and then
held steady for at least 8 h (Figure 4), allowing us to collect
bed load measurements at the same constant flow rate at
two sites. We collected transport samples at discharges
ranging from 22.7 to 53.5 m
3
s
1
. The peak of the 2009
flood had a recurrence interval of 4 years for the 17-year re-
cord following closure of Jordanelle Dam.
[
13] We established bed load transport measurement
sites at the upstream and downstream boundaries of our
study area, which we refer to as Midway and Charleston,
respectively. At each bed load sampling site (Figure 3), we
used a raft-based sampling platform [Graham Matthews
Figure 2. Aerial photos of reach 4 taken in (a) 2004 and
(b) 2006. The 2004 image (Figure 2a) was taken shortly
after reconfiguration of this reach. Figure 2b depicts point
bars that grew during floods in 2005 and 2006. The location
of the reach is shown in Figure 3.
W10512 ERWIN ET AL. : CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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and Associates, 2010] and a Toutle River 2 (TR-2) bed
load sampler [Childers, 1999]. The TR-2 sampler is well
suited for measurements of the large grain sizes in transport
during Provo River floods and the sampler has been used
successfully on other large rivers [Gaeuman et al., 2009;
Wallick et al., 2009; Erwin et al., 2011]. We used a modi-
fied version of the equal width interval [Edwards and
Glysson, 1988] sampling method; one sample consisted of
a single pass across the channel, during which data were
collected at 8–10 points along the cross section. The sampler
remained on the bed for 5 min at each sampling station. We
sieved and weighed all samples in 1/2- size classes.
[
14] Discharge at the time of each measurement was
taken to be that measured at the USGS gauge Provo River
near Charleston. We also installed stage plates upstream
and downstream of both bed load sampling sites. We meas-
ured the water surface slope over a distance of approxi-
mately 5 channel widths at the two sampling sites during
each measurement. When flows receded after the flood, we
conducted bed material point counts of the submerged bed
in the vicinity of each sampling site to determine the gra in
size distribution of the bed surface.
3.1.2. Computation of Sediment Flux
[
15] The bed load measurements from each site conform
closely to a power function and showed no hysteresis.
Transport rates were characterized using sediment rating
curves,
Q
s
¼ aQ
b
;
(2)
where Q
s
is sediment flux and Q is discharge. For each site
we calculated cumulative sediment transport for the 2009
flood using mean daily discharge data provided by the
USGS gauging station.
[
16] We used a bootstrap approach to calculate the uncer-
tainty associated with our estimates of the annual sediment
load. For each data set, we generated 1000 random samples
with replacement from the transport data. We fit a rating
curve to each random sample and used the function to calcu-
late total sediment load over the flood hydrograph. From the
1000 samples we generated a distribution and calculated the
median value and 95% confidence interval to estimate influx,
efflux, and net storage. We used a bulk density of 1855
kg m
3
to convert sediment mass to volume [Bunte and Abt,
2001].
3.2. Determining Change in Storage
[
17] We divided the study area into seven reaches for the
purpose of calculating change in sediment storage (Figure 3).
Reach boundaries were defined to provide consistent within-
reach properties based on channel planform and measure-
ment technique. Reaches 1 and 2 are confined by a levee
along the right bank protecting a wast ewater treatment plant
and, as a result, are relatively straight. In th ese reaches the
channel is steep and there is little space in the channel to
accommodate new deposits. In re aches 3 through 7 the river
is relativ ely unconst rained, and the channel was constructed
with a meandering planform.
[
18] Three reaches (1, 4, and 6), accounting for nearly
one-third of the study area, were surveyed before the flood
using total stations and rtkGPS systems. It was not possible
to survey channel topography in the remaining four reaches
prior to the flood. Preflood bathymetery for reaches 2, 3, 5,
and 7 was determined from a combination of aerial LiDAR
and multispectral aerial imagery. We surveyed the entire
study area after the flood using total station and rtkGPS sur-
veys. We used the topographic data to construct pre- and
postflood digital elevation models (DEMs). We computed
changes in bed material storage using geomorphic change
detection techniques [Milan et al., 2011], which we describe
below.
3.2.1. Direct Measurement of Topography via Ground
Surveys
[
19] In reaches 1, 4, and 6 we surveyed preflood topogra-
phy during low flows in September–October 2008 and
Figure 3. The study area : The lower 4 km of the Provo
River Restoration Proje ct (PRRP). A local sediment source,
provided by the Never Channelized Reach (NCR), is
located immediately upst ream of the Midway sampling site
(Figure 1). In 2009 we measured bed load transport at the
upstream (Midway) and downstream (Charleston) sampling
sites. Morphologic change associated with the 2009 flood
was measured in each of the study reaches.
W10512 ERWIN ET AL.: CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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postflood topography during October–November 2009. All
survey data were collected in WGS84, using a Topcon Hiper-
Pro rtkGPS, Leica GS15 rtkGPS, and Leica TCRA 1203 þ
total station. The total station was used in portions of the
channel that were too deep to safely survey with rtkGPS. Av-
erage point density of pre- and postflood surveys was approxi-
mately 0.32 points m
2
. Point densities were greater in areas
with steeper or more complex topography and less dense in
parts of the channel with little relief [McCullagh, 1981;
Brasington et al., 2000; Valle and Pasternack, 2006].
3.2.2. Remotely Sensed Topography
[
20] In reaches 2, 3, 5, and 7 we mapped 2008 topogra-
phy using a combination of remotely sensed data: LiDAR
and multispectral (RGB) imagery. These data were acquired
by Sanborn Mapping Inc. on 23 September 2008. We used
the data to create a composite terrain model for each reach,
using LiDAR for above-water locations and estimating sub-
merged elevations by subtracting estimated channel depth
from the water surface elevation [Legleiter, 2012]. Channel
depth was estimated using a statistical relation between
flow depth and spectral intensity of the RGB imagery [e.g.,
Winterbottom and Gilvear,1997;Marcus and Fonstad,
2008; Legleiter et al., 2009]. Although this approach is
inherently less accurate than ground-based surveys, it pro-
vides useful information in the absence of other data. The
Provo River provided ideal conditions to apply this tech-
nique; the flow is relatively shallow with very low turbidity,
aquatic vegetation is minimal, and there is little overhang-
ing riparian vegetation.
[
21] We calibrated relations between RGB intensity and
measured flow depth using the preflood survey data in reach
4. We collected these ground survey data within two weeks
of the time when the air photos were acquired, and dis-
charges during this time varied little (Table 1). We selected
reach 4 because the ground survey was conducted within
two weeks of aerial photographs and discharge and stage
were nearly identical on both dates.
Figure 4. The 2009 flood hydrograph measured at USGS gauge 10155500, Provo River near Charles-
ton. We selected the stair-step pattern to facilitate measurement of bed load transport rates. The flow was
increased or decreased by approximately 5.7 m
3
s
1
increments, and was held constant for 1–2 days at
each discharge. Arrows indicate days when we sampled bed load transport.
Table 1. Mean Daily Discharge and Stage for USGS Gauge 10155500, Provo River Near Charleston for Days With Aerial Photography
or Ground Surveys
a
Date Q (m
3
s
1
) Stage (m)
Difference in
Stage (m)
Aerial Photography Flight 9/23/2008 6.43 1.173 –
Ground Surveys
Longitudinal Profile 10/12/2008 6.60 1.181 0.008
Reach 1 9/12/2008 7.65 1.227 0.054
Reach 1 9/17/2008 6.12 1.158 0.015
Reach 4 10/6/2008 6.31 1.167 0.005
Reach 4 10/7/2008 6.23 1.163 0.009
Reach 6 9/26/2008 6.09 1.156 0.016
Reach 6 9/27/2008 6.03 1.155 0.019
Reach 6 9/28/2008 6.06 1.155 0.018
Reach 6 10/3/2008 5.58 1.131 0.042
Reach 6 10/4/2008 5.86 1.145 0.028
Reach 6 10/5/2008 6.31 1.167 0.005
a
The absolute difference in the stage on the date of the air photo flight and the date of the ground surveys ranges from 0.5 to 5.4 cm.
W10512 ERWIN ET AL. : CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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[22] For reach 4 we developed a multiple linear regres-
sion between depth and reflectance intensity of the three
bands [ Winterbottom and Gilvear, 1997] :
h ¼0:08672 – 0:000374R þ 0:000311G þ 0:0000777B; (3)
where h is depth of the water column, R is the reflectance
of the red band, G of the green band, and B of the blue
band. We evaluated a variety of relations between reflec-
tance and depth, including ratios of bands [Legleiter and
Roberts, 2005] and found equation (3) to be the best predic-
tor of depth (R
2
¼ 0.94; Figure 5). We validated the rela-
tion using survey data from reaches 1 and 6, and found that
the relations were a good predictor of depths in these
reaches as well (R
2
¼ 0.89 and 0.92, respectively).
[
23] We surveyed a longitudinal profile of water surface
elevation along the channel centerline on 12 October 2008,
and used these data to convert estimates of depth to abso-
lute elevations. Discharges recorded at gauge 10155500 for
the day of the air photo flight and the day of the water sur-
face survey were 6.43 and 6.60 m
3
s
1
, respectively. This
difference in flow corresponds to a difference in stage of
8 mm at the Charleston gauge. We neglected this stage
difference because it is small relative to the magnitude of
the uncertainty inherent in computation of depths using the
RGB imagery (on the order of 20 cm). GPS points on the
longitudinal profile were collected every 5–10 m, with an
effort to survey points at locations where there was a
change in water surface slope. We linearly interpolated the
water surface between survey points to develop a continu-
ous water surface profile. We then subtracted the estimated
depths from the interpolat ed water surface profile to com-
pute elevations. We merged the spectrally based bathyme-
try with the bare-earth topography generated from the
LiDAR to create a composi te DEM.
3.2.3. Computing Change in Storage
[
24] With the hybrid mix of topographic survey data
described above, we derived 1 m DEMs for the seven
reaches for preflood and postflood conditions based on either
ground survey or LiDAR and spectrally derived bathymetry.
We selected a 1 m resolution because it adequately repre-
sents the topography of mapped geomorphic units and was
supported by the point density availa ble. We calculate d the
difference between DEMs for the pre- and postflood periods
on a cell-by-cell basis to calculate a DEM of difference
(DoD) using the geomorphic change detection software
[Wheaton et al., 2010]. The change detection software was
used to (i) independently estimate the errors in the input
DEMs; (ii) propagate those errors into the DoD change cal-
culation; (iii) estimate the probability that calculated DoD
changes are real; and (iv) use the probability estima tes to
exclude areas of change that were not above a selected confi-
dence in terval from the volumetri c estimates of erosion and
deposition.
[
25] We used two techniques to estimate errors in the
individual DEMs. In reaches 1, 4, and 6, where ground sur-
vey data were available before and after the flood, we used
a spatially variable fuzzy inference system calibrated to
rtkGPS and total station surveys to estimate DEM errors
[Wheaton et al., 2010]. The fuzzy inference system is based
on the idea that construction of a DEM from survey data is
a tradeoff between sampling intensity and the topographic
complexity of the surface being surveyed. In reaches 2, 3,
5, and 7, where the spectral bathymetry technique was used
to generate preflood DEMs, we used a more conservative
spatially uniform estimate of DEM error. We assigned a
20 cm err or to the preflood DEMs derived from the multi-
spectral imagery (20 cm is the standard deviation of observed
minus predicted elevations for reach 4) and a 6 cm uniform
error for the post flood su rveys.
[
26] We calculated the combined error for the individual
DEMs on a cell-by-cell basis using
E ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
e
2
DEM1
þ e
2
DEM2
q
;
(4)
where E is the combined, or propagated error, and e
DEM1
and e
DEM2
are the errors associated with the 2008 and 2009
DEMs [Brasington et al., 2003]. We compared the propa-
gated errors to the DoD to calculate a T-Score and estimate a
probability that the calculated change was real, as desc ribed
by Lane et al. [2003]. We used a mo re conserv ative 95%
confidence interv al in reaches 2, 3, 5, and 7, where we were
less confident in th e topographic surfaces generated from the
multispectral imagery. In reaches where topography was
directly measured with rtkGPS both pre- and postflood, we
used a less conservative 80% confidence interval.
[
27] We calculated change in storage by comparing net
volume differences between erosion and deposition (i.e.,
deposition minus erosion). We calculated volumetric errors
(6volume) for the estimates of scour and fill volumes by
multiplying the estimated propagated DEM error on a cell-
by-cell basis by the area of the cell. Those individual volu-
metric errors were used to estimate the total uncertainty in
the net volumetric change in storage calculated for each
reach. Additionally, to facilitate compariso n of the magni-
tudes of change in each reach, we calculated the relative
change in storage (a volume to surface area ratio) by
dividing the net volumetric change by the total area of the
reach.
Figure 5. Relation between measured bed elevations and
elevations derived from spectrally based bathymetry. Data
is from reach 4, the reach used to develop the multivariate
regression (equation (3)). The multivariate regression was
used to model flow depths. Bed elevations were obtained
by subtracting the spectrally derived depths from the water
surface profile.
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4. Results
4.1. Bed Load Flux
[
28] Bed load measurements were made on the rising
and receding limbs of the flood at both sites. Sampling
began at the onset of detectable gravel transport. We col-
lected 32 samples at Midway and 31 samples at Charleston.
Measured transport rates ranged from 0.01 to 57 g m
1
s
1
at Midway and 0.2 to 27 g m
1
s
1
at Charleston (Figure 6).
At both sampling sites, measured bed load transport rates
showed a strongly nonlinear relation with discharge and did
not display any hysteresis. Table 2 reports the values of
parameters a and b from equation (2) that were determined
for at each measurement station.
[
29] Total sediment loads computed from the sediment
rating curves demonstrate that there was net accumulation
during 2009. Approximately 5.84 10
5
kg (95% CI is
3.93 10
5
and 9.64 10
5
kg) entered at Midway and
5.96 10
4
kg (5.18 10
4
and 6.79 10
4
kg) exited at
Charleston. These estimates correspond to sediment vol-
umes of 319 m
3
(212–519 m
3
) and 32 m
3
(28–37 m
3
)at
Midway and Charleston, respectively. Thus, despite the
uncertainty associated with these estimates, these calcula-
tions demonstrate that bed load influx exceeded bed load
efflux by an order of magnitude. The estimated net sedi-
ment accumulation based on these transport measurements
is 287 m
3
(180–489 m
3
).
4.2. Change in Storage
[
30] Both scour and fill were small in reaches 1 and 2,
where the channel is confined along the right bank by a
levee (Table 3 ; Figures 7 and 8). Both scour and fill
increased in reaches 3 and 4, where the channel is more able
to adjust. Scour and fill were both larger in reach 4 than in
any other reach. Deposition remained large in reaches 5, 6,
and 7 and deposition exceeded erosion in all reaches except
1 and 3. The only reaches in which the net storage exceeded
the uncertainty in erosion and deposition estimates were
reaches 1 and 5 (Table 3). If minimum and maximum error
values are propagated in the along stream accumulation of
scour, fill, and storage, the net reach storage of 472 m
3
is
dwarfed by the accumula ted error of 61344 m
3
(Figure 8).
This error estimate is likely too large, however, because it
assumes that the minimum and maximum errors consistently
propagate from one reach to the next. In contrast to the net
storage, both scour and fill estimates exceed the error bounds
in all reaches except for erosion in reach 6. The cumulative
scour and fill for the entire study reach is roughly twice that
of the cumulative error in each term (Table 3), even using
the simple and conservative accumulation of minimum and
maximum errors. Both cumulative scour (1454 m
3
) and fill
(1926 m
3
) are significantly larger than the measured sedi-
ment flux at the upstream (319 m
3
) and downstream (32 m
3
)
ends of the study reach.
[
31] The calculated change in storage computed from the
analysis of pre- and postflood topography is consistent with
the imbalance in bed load transport described above. Based
on the volumes of sediment scour and fill calculated from
DoDs developed for each reach (Figure 7), we computed
approximately 472 m
3
(61344 m
3
) of net sediment deposi-
tion, resulting from approximately 1454 m
3
(6796 m
3
)of
scour and 1926 m
3
(61043 m
3
) of fill (Table 3).
Figure 6. Bed load rates at (a) Midway and (b) Charles-
ton. Diamonds indicate fiel d measurements of bed load
transport collected during the flood in 2009. The lines rep-
resent the sediment rating curves.
Table 2. Values of Coefficient a and Exponent b From Equation
(2) That Were Determined for the Two Bed Load Measurement
Sites, Midway and Charleston
a
Sampling Site ab
Midway 1.863E-06 4.642
Charleston 2.865E-09 7.000
a
In equation (2), Q is in units of m
3
s
1
and Qs is expressed in g s
1
.
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[32] The morphologic changes documented during the
flood were subtle relative to the uncertainty associated with
the topographic measurements. Figure 9 depicts two differ-
ent DoDs for reach 4 that were calculated using the same
topographic inputs. One DoD—the gross DoD—does not
consider uncertainty (Figure 9a). The other DoD incorpo-
rates the spatially variable uncertainty threshold (Figure 9b)
that was used to calculate changes in storage in this study.
The computed volumes of scour, fill, and net channel
change differ substantially between the two DoDs, high-
lighting the significant effect of uncertainty on the budget
calculations. The DoDs shown in Figures 9a and 9b corre-
spond to histograms (Figures 9c and 9d, respectively), illus-
trating the large proportion of the channel where the
magnitude of the topographic change did not exceed the
defined uncertainty threshold. Areas not included in the budget
Table 3. Calculated Change in Storage for All Seven Reaches
a
Reach Scour (m
3
) Fill (m
3
) Net Storage (m
3
)
Cumulative
Storage (m
3
)
Reach
Area (m
2
)
Relative Change in
Storage (m
3
m
2
)
1 122 (622) 51 (643) 71 (649) 71 (649) 4376 0.016
2
b
172 (651) 208 (687) 36 (6100) 35 (6149) 10,170 0.004
3
303 (6200) 283 (6126) 20 (6237) 55 (6386) 19,573 0.001
4 311 (6190) 440 (6293) 129 (6349) 74 (6735) 10,972 0.012
5
106 (630) 306 (6135) 200 (6139) 274 (6874) 16,752 0.012
6 183 (6223) 348 (6255) 165 (6339) 439 (61213) 10,692 0.015
7
257 (680) 290 (6104) 33 (6131) 472 (61344) 13,514 0.002
1 þ 4 þ 6 616 (6435) 839 (6591) 223 (6737) NA 26,040 0.009
1–7 1454 (6796) 1926 (61043) 472 (61344) NA 86,059 0.005
a
Scour, fill, net change in storage, and cumulative downstream change in storage were determined from the DEMs of difference (DoDs). Relative
change in storage is net volumetric change divided by reach area.
b
Asterisks denote preflood topography determined using surveyed water surface elevation and water depth estimated from aerial photography.
Figure 7. Volumetric change in storage for each reach calculated from the DEMs of difference
(DoDs).
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calculations are primarily those with small elevation change.
The impact of the uncertainty analysis on our estimates of
change in storage is apparent in the histograms of channel
change derived for the DoDs from all seven reaches (Figure 7).
Distributions from reaches 2, 3, 5, and 7 are truncated because
small changes were excluded from the analysis due to the
more conservative uncertainty threshold applied to the DEMs
derived from LiDAR and multis pectral imagery.
[
33] The error bars bracketing our estimated net change
in storage are relatively large (61344 m
3
; Figures 8 and
10) because the propagated error estimates are large rela-
tive to the modest magnitudes of net change that actually
occurred (Table 3). It should be noted that even though the
estimated DEM errors are much larger in the reaches where
preflood topography was derived from multispectral im-
agery (reaches 2, 3, 5, and 7), these errors do not necessarily
result in larger estimates of volumetric uncertainty (Table 3,
column 4). This is because the volumetric error is based
only on the areas in the DoDs where the magnitude of chan-
nel change exceeded the calculated uncertainty threshold.
4.3. Closure of the Sediment Budget
[
34] With a flux estimate of approximately 290 m
3
of net
aggradation and an estimate of change in storage of approx-
imately 470 m
3
of net aggradation, both the change in stor-
age as determined from bed load transport and from
topographic data demonstrate that sediment accumulation
occurred during the 2009 flood (Figure 10). Had the analy-
sis relied solely on morphologic data, however, the budget
would have been indeterminate. The magnitude of the
uncertainty for reaches in which pre- and postflood topog-
raphy were measured via rtkGPS (reaches 1, 4, and 6;
Table 3, column 4) suggests that this would have been the
case even if we were to have surveyed the entire study area
prior to the flood using traditional ground survey techniques.
5. Discussion
5.1. Provo River Sediment Budget
[
35] There are inevitable uncertainties asso ciated with cal-
culation of each term of a sediment budget. Had we so lely
based the budget on topographic measurements, we wo uld
not have reached a conclusion consi stent with earlier obser-
vations of aggradation. However, estimates of change in stor-
age calcula ted from flux me asurements of input minus export
unambiguously demonstra te that aggra dation occurred during
the 2009 flood, because the volume of accumulation greatly
exceeded the uncertainty in the transport measurements. Had
we only est imated change in storage fr om topographic meas-
urements, we would not have reached this conclusion
because th e topographic changes that occurred were small in
relation to the uncertainty in those measurements.
[
36] Grams and Schmidt [2005] emphasized that without
faithful accounting of uncertainty a budget may be consid-
ered closed, when in fact, it is indeterminate. Our findings
provide a reminder that wherever the uncertainty exceeds
the absolute value of the net change in sediment storage, a
budget is unavoidably indeterminate. Thus, it is critical to
use the appropriate technique at the appropriate temporal
and spatial scale to have the best chance of avoiding inde-
terminacy in sediment budgets.
[
37] In the case of the 2009 flood season budget for the
Provo River, the topographic changes were subtle and the
uncertainty was large. The theoretical basis for and applica-
tion of multispectral and hyperspectral imagery to quantify
channel depths is well documented using both empirical
and theoretical approaches [Winterbottom and Gilvear,
1997; Wright et al., 2000; Whited et al., 2002; Legleiter
et al., 2009], and the technique performs well in systems
where the water is relativ ely clear, shallow, and free of
aquatic vegetation, such as in our study area. Despite hav-
ing near ideal conditions for application of this technique,
the DEMs derived from spectral bathymetry provided less
accurate representations of channel topography than the
Figure 8. Cumulative (a) erosion, (b) deposition, and (c)
net sediment storage in the study area, based on the analy-
sis of the topographic data. The dashed lines represent the
cumulative uncertainty.
W10512 ERWIN ET AL. : CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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DEMs derived from high-density ground surveys and
necessitated a large threshold of detection in reaches 2, 3,
5, and 7. Yet even in reaches where both the pre- and post-
flood DEMs were derived from ground survey data, the
thickness of deposition and erosion in large areas was
less than the inherent uncertainty of those measurements
(Figure 9).
5.2. Net Change, Total Change, and Channel Activity
[
38] Despite the large uncertainty associated with topo-
graphic differencing, these measurements provided unique
insights into system behavior. Although the flux measure-
ments provided a better-constrained estimate of large-scale
change in storage, direct measurements of topographic
Figure 9. Volumetric change in storage for reach 4 computed from (a) the gross DoD and (b) the DoD
calculated using the spatially variable approach for quantifying uncertainty, as described in the methods.
(c) A histogram computed from the gross DoD, corresponding to Figure 9a; (d) a histogram computed
from the DoD calculated using the spatially variable uncertainty threshold (Figure 9b).
Figure 10. The sediment budget for the 2009 flood. (a) The four measured components of the budget:
estimated influx and efflux (calculated from the sediment rating curves), and deposition and erosion
(determined from topographic measurements). (b) The change in storage computed from each of these
components of the budget.
W10512 ERWIN ET AL.: CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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change provide documentation of spatial patterns of mor-
phologic adjustment. Additionally, the topographic data pro-
vided an estimate of the relation between net channel change
and total channel change (or channel activity). For this partic-
ular scale of study area and study period, the magnitude of
total scour and fill was signifi cantly larger than the magnitude
of the net difference betw een influx and efflux (Figure 10).
Total channel change—calculated as the sum of the total
volume of scour and of fill—greatly exceeded the magnitude
of the net change, indicating that there was significant local
reorganization of sediment within the study area.
[
39] Even in this ‘‘event- based’’ study there were in consis-
tencies between the time domain of the flux measu rements
and the time when change in storage was measured. Most
budgets are calculated over larger areas and over longer time
periods. Morphological sediment budgets, for example, are
often integrated over many bed-m obilizing floods. We sought
to minimize these inconsistencies by calculating a sediment
mass balance for a dis crete flood event. Topographic data
were collected during the course of a year and sediment flux
data were collected during a 3 we ek period, but the dam-
controlled hydrology limited bed-mobilizing flows to a single
period between the topogra phic measurements. The con-
trolled dam release presented a relatively unique field oppor-
tunity to isolate the erosion and deposition associated with a
discrete flood; when integrating over multiple bed-mobilizing
flows, the occurrence of compensating scour and fill make it
probable that measurements of channel change are underesti-
mates of total channel activity [Lindsay and Ashmore, 2002].
[
40] For the Provo River sediment budget, we su spect that
more accurate measurements would likely amplify the differ-
ence between the total volumetric change in storage and the
total volume of sediment flux. With higher resolution topo-
graphic measurements, smaller topographic changes would
have been detectable. This wo uld have improved our ability
to document both total and net channel change. Because
compensating scour and fill cannot be me asured from before
and after topography, measured volumetric change will inevi-
tably be an underestimate of total volumetric change. These
factors su ggest that the magnitude of the erosion and deposi-
tion terms may be even larger relative to the net change in
storage in the Provo River sediment budget. Although the
reachstudiedherehadbeenrebuilt 5 years before the dam
release, su ch that extensive reworking is not surpri sing, our
work nonetheless is a reminder that an inference of total
channel activity from net sediment flux should be verified by
observations of channel change wi thin the reach.
5.3. Uncertainties and Implications for Fluvial
Sediment Budgeting
[
41] Develo pment of sediment budgets is an essential
exercise in geomo rphology, used across the disc ipline in the-
oretical and applied studies. This study provides some gen-
eral insi ghts into the challenges and uncertainties associated
with developing a reach -scale budget in a fluvial se tting.
Closing a sediment budget— matching measu red changes in
storage with calculated diff erences between inputs and out-
puts—is a difficult task even in well-c onstrained settings.
Although we attempted to quantify all components of the
sediment budget for the Provo River, in so me cases the
uncertainties assoc iated with different budget terms exceeded
the measured value.
[
42] Quantification of inputs and outputs is inevitably
subject to the uncertainty associated with estimating trans-
port rates. The magnitude of uncertainty that is associated
with our estimates of sediment flux is a reflection of the
fact that bed load transport rates exhibit great spatial and
temporal variability [Ashmore and Church, 1998; Hicks
and Gomez, 2003]. Even under steady flow conditions, bed
load transport rates are highly variable [Davies, 1987 ;
Gomez, 1991]. Bed load transport is also difficult to mea-
sure. The bed load transport predictions we developed for
the Provo River represented a significant effort to constrain
the estimates of influx and efflux by directly measuring
transport rates during a controlled flood, in a system without
any supply limitation or hysteresis. Despite these efforts and
despite the unique sampling opportunity, there is still
unavoidable imprecision in our estimates of sediment flux.
However, for the temporal and spatial scale of the budget
developed here, the uncertainty associated with our esti-
mates of change in storage based on flux measurement was
much less than the uncertainty based on measurements of
topographic change (Figure 10). Thus, for a relatively sim-
ple system such as the Provo River, direct measurements of
flux may provide a better estimate of net change in storage.
[
43] The two computational approaches to calculating a
sediment budget—the difference in flux measurements and
the difference between topographic surfaces—have differ-
ent merits and different limitation s that depend on the tem-
poral and spatial scales of analysis and depend on the way
that uncertainty propagates through time and space. For
example, over shorter time steps, morphologic adjustment
may be widely distributed and small relative to grain size
of the bed material. Thus, the magnitude of erosion and
deposition may be measureable but the difference between
the two, the net storage, may not be detectable. A standard
approach to dealing with uncertainty when determining dif-
ferences between two DEMs is to establish a minimum
level of dete ction threshold, below which change in eleva-
tion is neglected [Brasington et al., 2000]. The approach
used here Wheaton et al. [2010] is an attempt to improve
upon this standard approach by incorporating knowledge of
data quality, density, and topographic complexity to refine
estimates of uncertainty. Nevertheless, this approach does
nothing to constrain or limit uncertainties, but is simply
one approach for determining whether the ‘‘signal’’ of
topographic change exceeds the associated ‘‘noise’’ [Milan
et al., 2011]. In systems where change is subtle and there is
substantial uncertainty associated with the strategy used to
measure topography, it may not be possible to accurately
identify real morphologic adjustments.
[
44] When channel change is progressiv e toward sedi-
ment accumulation or evacuation, such as on the Provo
River, a morphological budget may be better equipped to
detect changes in storage when the budget is computed
over a longer time domain. The effects of time and error
propagation on budget calculations are conceptually repre-
sented in Figure 11. In Figures 11a and 11b, t
1
represents
the budget calculated for the 2009 flood. T
2
and t
3
represent
two hypothetical floods of longer duration that were gener-
ated using hydrologic data for previous flood releases from
Jordanelle Dam. When there is small topographic change,
as in 2009, the uncertainty associated with estimates of
topographic change is proportionally a large part of the net
W10512 ERWIN ET AL. : CLOSING A SEDIMENT BUDGET FOR THE PROVO RIVER, UTAH W10512
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change in storage. For the budget presented here, the uncer-
tainty bars bracket zero change in sediment storage, dem-
onstrating that the budget would be indeterminate if based
on changes in topography alone. In 2009 (t
1
) the uncer-
tainty associated with our estimates of sediment flux were
proportionally very small as compared to the net change in
storage. Thus, only the sediment flux measurements dem-
onstrated that the system accumulated sediment during the
2009 flood.
[
45] Assuming the sediment rating curves remain stable
through time, the relations can be used to calculate net flux
for t
2
and t
3
(Figure 11a). Although the uncertainty associ-
ated with our flux-based estimate of net storage was pro-
portionally very small for the 2009 budget, the uncertainty
associated with change in storage derived from measure-
ments of sediment flux is additive and propagates through
time. Therefore, at t
2
and t
3
the uncertainty represents a
larger proportion of the net change in storage. In contrast,
the uncertainty does not propagate through time when S is
determined from topographic measurements. In Figure 11b
the point estimates of change in storage for t
2
and t
3
are
assumed to be equal to those derived from the calculated
fluxes. The uncertainty remains constant through time because
calculation of uncertainty for the two topographic surfaces is
independent of the time when the surface was measured.
Thus, in a system that is progressively accumulating or evacu-
ating sediment, as time progresses it becomes possible to de-
velop a determinate budget based on morphologic data,
whereas flux-based estimates will become less informative as
the time domain of the budget increases. For example, if the
net change in storage remain ed small at t
3
(e.g., 2000 m
3
), the
budget would only be determinate if informed by topographic
data, and would be indeterminate if S were calculated as the
difference between sediment input and export.
6. Conclusions
[46] We measured all components of a sediment mass
balance for a single, dam-controlled flood on a reconfigured
gravel bed river. Flow was released from Jordanelle Dam
on the Provo River in a fashion that allowed measurements
of bed load transport during steady flow at sections above
and below the study reach. Detailed topographic data were
collected before and after the dam release. Based on trans-
port rate measurements, sediment input to the reach exceeded
outputs, producing a net sediment accumulation of approxi-
mately 290 m
3
(95% CI is 180–489). The difference between
the erosion and deposition was also positive (472 m
3
), but
uncertainty in th e topographic differencing (61344 m
3
)was
larger than the observed net change in storage. Both the
change in storage calculated fr om flux measurements and via
topographic changes suggest that the system accumulate d
sediment during the 2009 flood. Ho wever, had the analysi s
relied solely on morphologic data the budget would have
been indeterminate. Because the morphologic adjustments
that occurred during the 2009 flood were relatively subtle, a
morphologic sediment budget would have been indetermi-
nate even if we had measu red pre- and postflood topography
for the entire study area using ground survey techniques.
[
47] When developing sediment budgets for which the
primary interest is to quantify net accumulation or evacua-
tion of sediment, measuring sediment flux may be a better
strategy if (1) appropriate sampling locations can be found,
(2) the system is not subject to supply limitation or patterns
of hysteresis, and (3) the time domain of the analysis is rel-
atively short. However, because uncertainty associated with
estimates of sediment flux propagate through time, over lon-
ger time frames, or in systems where topographic adjustments
are pronounced, a morphological sediment budget may pro-
vide superior results. Direct measurements of topographic
change is also necessary in order to accurately determine the
total channel change, or channel activity, and to describe spa-
tial patterns of morphologic adjustment within a reach.
[48] Acknowledgments. This project was funded by the Intermoun-
tain Center for River Rehabilitation and Restoration at UT State University
and by the S. J. and Jessie E. Quinney Foundation. This work was made
possible by collaborations with the UT Reclamation Mitigation and Con-
servation Commission, the Central UT Water Conservancy District, and
the U.S. Army Corp of Engineers. We would like to extend special thanks
to Mark Holden and Tyler Allred for facilitating our field work on the
Provo River, and to Daryl Devy for modifying the flood release schedule
for Jordanelle Dam. The manuscript was greatly improved by thoughtful
reviews provided by Tom Dunne, Matt Kondolf, Andy Large, and two
anonymous reviewers.
Figure 11. A conceptual plot depicting the effects of time
and error propagation on sediment budgeting. T
1
shows the
estimated change in storage for the 2009 flood as calculated
from (a) the difference between sediment inputs and outputs
and (b) the difference between topographic surfaces. The
uncertainty associated with measurements of flux is additive
and propagates through time, whereas the uncertainty asso-
ciated with calculation of S based on topographic data
remains relatively constant as the time step increases.
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