Environmental Engineering Reference
In-Depth Information
The exponent of eqn. 2 contains a term for the
relative acoustic backscatter,
RB
, measured by an
instrument such as an ADCP as well as terms for an
intercept,
A
, and slope,
B
, determined by regression
of concurrent ABS with known mass SSC measure-
ments (SSC
measured
) on a semi-log plane in the form of
log(SSC
measured
) =
A
+ (
B*RB
). The relative backscat-
ter is the sum of the echo level measured at the
transducer plus the two-way transmission losses
(Thevenot
et al
. 1992) as defi ned below.
In its simplifi ed form, the sonar equation (Urick
1975) can be written as:
centimeters, and
λ
is acoustic wavelength. The near-
fi eld correction,
, for spreading loss can be calcu-
lated from the formula in Downing
et al.
(1995) as:
ψ
[
]
32
.
32
.
ψ =+
1 135
.
ZZ
+
( .
25
)
⎣
135
.
Z Z
+ (
25
.
)
⎦
(5)
where:
Z
is
R
/
R
critical
.
As an example,
R
critical
is 167 cm for a 1200-kHz
ADCP with a 5.1-cm diameter transducer.
For the particle-size range and acoustic frequencies
of interest here, attenuation from suspended sedi-
ment consists of a viscous loss component and a
scattering loss component (Flammer 1962; Richards
et al
. 1996). In the presence of suspended sediments
that are generally less than 100-200
RL
=−
SL
2
TL
+
TS
(3)
m, the viscous
and scattering components of attenuation change in
opposing ways to changes in size (for typical ADCP
transducer frequencies). Attenuation from viscous
losses increases inversely with sediment size.
Attenuation from scattering losses increases directly
with sediment size. Scattering characteristics are a
function of
μ
where:
RL
is the reverberation level;
SL
is the source
level, which is the intensity of emitted signal that is
known or measurable;
2TL
is the two-way transmis-
sion loss; and
TS
is the target strength, which is
dependent on the ratio of wavelength to particle
diameter.
All variables in eqn. 3 are measured in decibels. In
terms of ADCP parameters,
RL
=
K
c
(
E
λ
to particle circumference
2
π
a
p
, where
Er
), where
E
is ADCP echo intensity recorded in counts,
Er
is
ADCP received signal strength indicator (RSSI) refer-
ence level (the echo baseline when no signal is
present), in counts, and
K
c
is the RSSI scale factor
used to convert counts to decibels.
K
c
varies among
instruments and transducers and has a value of 0.35-
0.55 (Deines 1999). The two-way transmission loss
is defi ned as:
−
a
p
is particle radius. When
a
p
, most of the scat-
tering pattern propagates backward; however, as
λ
>>
2
π
λ
approaches
2
a
p
, the scattering pattern increases in
complexity, and when
π
a
p
half the scattered
pattern propagates forward and the remainder is
scattered through all directions (Flammer 1962). In
the case of 1200-kHz acoustic sources,
λ
<<
2
π
λ
=
2
π
a
p
for
m diameter particle size. Taken together, scat-
tering- and viscous-loss terms account for little atten-
uation with 1200-kHz frequency unless particle size
is very small or SSCs are very high, in which case
corrections for attenuation are needed. However, in
the case of higher frequencies, total attenuation may
need to be accounted for even at lower SSC if parti-
cles are very small (viscous losses) or larger than
about 100- to 150-
400-
μ
2
TL
=
2
(
αα
ws
+
)
R
+
20
log
R
(4)
where:
R
is the range to the ensonifi ed volume, in
meters;
s
is an attenuation coeffi cient accounting for viscous
and scattering losses due to suspended sediment (see
below), both in decibels per meter; 2(
α
w
is an absorption coeffi cient for water;
α
s
)
R
is the
combined transmission loss due to water absorption
and sediment attenuation; and 20log
R
is the loss due
to spreading.
The absorption coeffi cient for water is a function
of acoustic frequency, salinity, temperature, and
pressure (Schulkin & Marsh 1962). Because of non-
spherical spreading in the transducer near fi eld, the
spreading loss is different in near and far transducer
fi elds. The transition between near and far trans-
ducer fi elds is called the critical range,
R
critical
.
R
critical
=
α
w
+
α
m diameter (scattering losses).
The result is a nonlinear (backscatter intensity)
response at high SSC (Hamilton
et al
. 1998).
Although a function of frequency, attenuation from
sediment may need to be accounted for in the pres-
ence of as little as 0.1 g/L (Libicki
et al
. 1989; Thorne
et al
. 1991); multiple scattering produces nonlinear
response when SSC is on the order of 10 g/L (Sheng
& Hay 1988; Hay 1991). Thorne
et al
. (1991) found
that, in the case of 3.0- and 5.65-MHz acoustic fre-
quencies, attenuation from fi ne sands may become
signifi cant at ranges on the order of a meter when
μ
π
a
t
/
λ
where
a
t
is the transducer radius, in
