Chapter 7: APPLICATIONS
The bulk scattering coefficient and backscattering coefficient respectively
for a given bubble size distribution are calculated in the following way
(Terrill et al., 2001):
2
(
)
b
b bubbles
Q r N r dr
S
³
,
(7.3)
2
b
b b
b bubbles
Q r N r dr
S
³
,
(7.4)
where N(r) is the bubble size distribution function (see Section 6.1.3).
Equations (7.3) and (7.4) treat the bubbly water as a mixture of random,
single-scattering particles. The inherent bulk properties are the sum of the
contributions by the individual bubbles (Mobley, 1994).
The range of bubble radii present in the near-surface layer of the ocean
defines the limits of the integrals. Small bubbles with radii less than r = 4
Pm, however, have practically no contribution to the integrals and thereby to
light scattering. Larger bubbles, which do contribute to the light scattering,
practically do not depend on the wavelength of photons. Hence, bubble
mediated effects on the scattering and backscattering coefficients are
expected to have little spectral dependence.
Figure 7-7 showing scatter-plots of b and b b versus the void fraction
indicates the correspondence between the bubble densities and the bubble
contribution to the bulk light scattering properties. The void fraction of
entrained air is defined as
3
4 3 r N r dr
E
S ³
.
According to Figure 7-7, scattering levels span a range of 4-5 decades.
Backscatter coefficients b and b b vary from 10
-5 m
-1 to over 1 m
-1 and 10
-6 m
-
1 to over 10
-2 m
-1 , respectively. (Note that this is for only 20 min of
observations.) The level of bubble contribution to the total backscatter
becomes significant compared to the pure seawater scattering at bubble
densities with void fractions above 10
-6 .
Terrill et al. (2001) evaluated the contribution of entrained bubbles to
optical scattering in the open ocean by comparison with commonly accepted
relationships between the light scattering coefficient b and chlorophyll D
concentration [Chl] (Figure 7-7a). For oligotrophic (Case 1) waters the
bubble contribution to total scatter may be a significant fraction of the
contribution by chlorophyll. At low chlorophyll concentrations, the errors in
the bio-optical interpretation of measured optical properties may be very
large due to surface waves breaking. For example, at a void fraction of 10
-6 ,
scatter from bubbles can be almost as large as the scatter by particles at a
low chlorophyll [Chl] of 0.02 mg m
-3 , while in more productive waters with
[Chl] levels at 0.5 mg m
-3 , scatter from the same bubble density is only 10%
455
The bulk scattering coefficient and backscattering coefficient respectively
for a given bubble size distribution are calculated in the following way
(Terrill et al., 2001):
2
(
)
b
b bubbles
Q r N r dr
S
³
,
(7.3)
2
b
b b
b bubbles
Q r N r dr
S
³
,
(7.4)
where N(r) is the bubble size distribution function (see Section 6.1.3).
Equations (7.3) and (7.4) treat the bubbly water as a mixture of random,
single-scattering particles. The inherent bulk properties are the sum of the
contributions by the individual bubbles (Mobley, 1994).
The range of bubble radii present in the near-surface layer of the ocean
defines the limits of the integrals. Small bubbles with radii less than r = 4
Pm, however, have practically no contribution to the integrals and thereby to
light scattering. Larger bubbles, which do contribute to the light scattering,
practically do not depend on the wavelength of photons. Hence, bubble
mediated effects on the scattering and backscattering coefficients are
expected to have little spectral dependence.
Figure 7-7 showing scatter-plots of b and b b versus the void fraction
indicates the correspondence between the bubble densities and the bubble
contribution to the bulk light scattering properties. The void fraction of
entrained air is defined as
3
4 3 r N r dr
E
S ³
.
According to Figure 7-7, scattering levels span a range of 4-5 decades.
Backscatter coefficients b and b b vary from 10
-5 m
-1 to over 1 m
-1 and 10
-6 m
-
1 to over 10
-2 m
-1 , respectively. (Note that this is for only 20 min of
observations.) The level of bubble contribution to the total backscatter
becomes significant compared to the pure seawater scattering at bubble
densities with void fractions above 10
-6 .
Terrill et al. (2001) evaluated the contribution of entrained bubbles to
optical scattering in the open ocean by comparison with commonly accepted
relationships between the light scattering coefficient b and chlorophyll D
concentration [Chl] (Figure 7-7a). For oligotrophic (Case 1) waters the
bubble contribution to total scatter may be a significant fraction of the
contribution by chlorophyll. At low chlorophyll concentrations, the errors in
the bio-optical interpretation of measured optical properties may be very
large due to surface waves breaking. For example, at a void fraction of 10
-6 ,
scatter from bubbles can be almost as large as the scatter by particles at a
low chlorophyll [Chl] of 0.02 mg m
-3 , while in more productive waters with
[Chl] levels at 0.5 mg m
-3 , scatter from the same bubble density is only 10%
455