Environmental Engineering Reference
In-Depth Information
where:
v
p
is the particle velocity calculated from van
Rijn (1984);
w
b
is the weighting factor for percentage
of bed mobile;
w
f
= weighting factor for position over
bedform.
The weighting function,
w
b
, evaluates the propor-
tion of the bed particles that are moving and accounts
for the relative strength of the backscatter from the
immobile bed particles versus mobile particles.
Gaeuman & Jacobson (2006) considered particles
moving in different layers of the active bed, with the
immobile bed consisting of those bed particles that
are not acoustically blocked by moving particles in
any layer above them.
the sand-bed runs, and was least sensitive to positive
bias at low transport rates in the gravel-bed runs.
The results confi rmed that longer pulse lengths are
more subject to water bias.
Instrument error constitutes most of the measure-
ment error for apparent bed velocity (Rennie
et al.
2002). The probability density function (PDF) of
particle velocities measured in the ensonifi ed beam
areas of gravel beds at Agassiz and Norrish Creek
was modeled by deconvolving the PDF of the instru-
ment error from that of the measured data (Rennie &
Millar 2007). In gravel-bed reaches, bed-load trans-
port occurs as discrete events. A large percentage of
the bed is immobile at any given time, with the bed
velocity assumed to be an average of moving and
stationary particles. Two velocity distributions were
used to model the actual bed velocities, a compound
Poisson-gamma distribution and an empirically fi t
gamma distribution. There was good fi t between the
modeled and measured distributions. However, each
of many possible particle velocity distributions
yielded a reasonable fi t, owing to the strong infl uence
of instrument noise on the measured signal. The com-
pound Poisson-gamma distribution was found to fi t
better with optimized parameters. The particle- and
bed-velocity distributions were positively skewed,
which would result from a few high values among
mostly low values, as expected for partial transport
of gravel. The instrument noise was found to be
0.21 m/s for the Agassiz (adjusted to single ping) and
0.31 m/s for the single ping Norrish Creek data.
This error was similar to that for water velocity
measurement, estimated to be 0.23 m/s for a 1-second
average (nine pings) with 0.20 m pulse length (bin
size) for the narrowband ADCP utilized.
b
bbF
⎛
⎜
⎞
⎟
p
w
=
(6)
b
+
p
b
where:
b
p
is the fraction of bed area with moving bed
particles;
b
b
is the fraction of immobile bed “visible”
to transducer beam;
F
is the relative strength of
echoes refl ected from immobile bed.
The bed fractions depend on the particle concen-
tration in the bed-load layer and the height of the
top of the bed load layer, both calculated according
to van Rijn (1984). The value of
F
was assumed to
be roughly 10. An additional scaling factor,
w
f
, was
proposed, but not defi ned, to account for spatial
differences due to the infl uence of bedform morphol-
ogy. As expected, the ratio of
v
b
/
v
p
increased
with the transport stage,
T
*, (the ratio of non-
dimensional shear stress to critical non-dimensional
shear stress) and the modeled
v
b
was found to be
close to the measured
v
b
.
Ramooz & Rennie (in press) performed calibra-
tion tests on bed velocity versus bed-load transport
rates at St. Anthony's Falls Laboratory at the
University of Minnesota, USA, in 2006. Apparent
bed velocity was reasonably correlated with bed-load
transport rate from physical sampling using a con-
tinuous-weighing slot sampler and from dune track-
ing for the sand bed runs. This was the only study
to evaluate the sensitivity of
v
b
correlation with
g
b
to
the ADCP transmit frequency (600 kHz versus
1200 kHz) and bottom track pulse length. Of the
operating parameters tested, the most reliable results
were obtained with the 1200 kHz ADCP with bottom
track pulse length set to the default value of 20% of
range to the bottom. This confi guration yielded the
highest correlation with measured transport rates in
2.2.1.2.2 Studies from moving boats.
Three studies
of the spatial distribution of apparent bed velocity in
a reach have been conducted: Rennie & Millar
(2004), Gaeuman and Jacobson (2006), and Rennie
& Church (2007). In the studies led by Rennie,
kriging was used to smooth the raw data to produce
coherent distributions from moving-boat apparent
bed-velocity measurements. Assessment of these dis-
tributions was achieved by comparison to those of
shear velocity, depth, near-bed water velocity, and
depth-averaged water velocity.
The near-bed velocity was measured in the bin
located between 25-50 cm above the bed. The bed
