Environmental Engineering Reference
In-Depth Information
where:
F
d
is the Doppler shift frequency;
F
s
is the
frequency of the ADCP;
c
is the speed of sound
(
of bed-load particles. Apparent bed velocity (
v
b
)
should be representative of the average surface veloc-
ity within the ensonifi ed volume, except that
v
b
is
weighted by the relative backscatter strength of all
individual mobile and immobile particles in the
sample volume. The relative backscatter strength of
mobile particles depends in part on the frequency of
the instrument and the characteristic size of the par-
ticles. Acoustic backscatter strength, relative to par-
ticle size, is greater for particles with a diameter
equal to or greater than 2/
1500 m/s); and
V
is the relative velocity of the
scatterers.
Velocities measured along each slanted beam
are coordinate-transformed to estimate a three-
dimensional velocity for separate segments of the
water column, namely bins in the vertical profi le.
The algorithm used to determine the velocity com-
ponents assumes homogeneous conditions over the
area encircling those ensonifi ed by the transducer
beams. This assumption becomes more tenuous as
the distance from the ADCP increases.
Bottom track is a Doppler sonar measurement
designed to measure the relative velocity between
the instrument, or the boat to which it is attached,
and an immobile bed. In the case of a mobile bed,
the bottom-track velocity is biased by the movement
of the sediment along the bed; a differential global
positioning system (DGPS) system is required to
measure the velocity of the boat relative to the Earth.
The difference between the biased bottom track
velocity and the DGPS velocity is known as the
apparent bed velocity. The apparent bed velocity is
considered a measure of the bed-load transport rate.
∼
times the wavelength of
the instrument's sound wave (Thorne
et al
. 1995).
Thus, for a 1200-kHz ADCP, backscatter from par-
ticles with diameters equal to or greater than 0.8 mm
is emphasized, and the weighting of these particles
in the apparent bed velocity should be greater. The
relative contribution of mobile particles versus the
stationary bed is discussed further below.
For a sand bed where the depth and porosity of
the active layer can be assumed constant, the bed-
load transport rate can be calculated as (Rennie
et al
. 2002):
gvd
π
λρ
(3)
where:
g
b
is the bed-load transport rate;
v
p
is the
average particle velocity;
d
a
is the depth of active bed
layer;
=
(
1
−
)
b
p
a
a
s
vv
=
−
v
(2)
λ
a
is the porosity of active bed layer; and
ρ
s
is
b
DGPS
bt
the density of sediment.
where:
v
b
is the apparent bed velocity;
v
DGPS
is the
velocity of the ADCP relative to the Earth; and
v
bt
is
the bottom track velocity of the ADCP relative to
the bed.
It is essential that the ADCP internal compass is
properly calibrated, such that both
v
DGPS
and
v
bt
are
measured in the same coordinate system. The beam
homogeneity assumption is especially signifi cant for
the apparent bed velocity because fl ow depths can be
large, bed topography can be irregular, and bed-load
particle transport can be locally variable.
The bottom-track pulse measures the echoes from
a volume, not an area. The echoes from the bed
consist of echoes from particles moving in the bed
layer as well as echoes from immobile sections of the
bed. Backscatter, from particles moving just above the
bed, contributes positively to the signal and is known
as water bias. The distance above the bed to which
particle movement infl uences the signal depends on
the pulse length selected (Rennie & Millar 2004).
The average surface velocity (
v
pa
) of the bed-load
layer depends on the various sizes and velocities (
v
p
)
2.2.1.2 Example fi eld applications
The active-hydroacoustic technology has been
applied to both stationary and moving-boat studies.
Stationary measurement of apparent bed velocity has
been conducted in sand- and gravel-bed reaches
of Canada's Fraser River, and in a sand-bed reach
in the lower Missouri River, USA. Apparent bed
velocity was correlated to bed-load transport meas-
ured by physical bed-load samplers in the Fraser
River. A kinematically calculated bed-load transport
rate has also been correlated to that measured with
physical samplers. Apparent bed velocity was also
correlated to bed-load transport measured by dune
tracking in the lower Missouri River, USA. Coherent
patterns existed between spatial distributions of
apparent bed velocity and the fl ow's near-bed veloc-
ity, depth-averaged velocity, and shear velocity in
two reaches of the Fraser River, Canada. Use of a
statistical deconvolution technique has allowed suc-
cessful modeling of the distribution of actual bed
