2.2.2 Large particles
Backscattering by large particles is calculated as the product of concentration C L ,
specific backscattering coefficient b b,L *, and normalized scattering function b L (Ȝ)җ . The
user has several options for calculation:
• C L can be treated either as an independent parameter, or C L = C 0 can be
assigned, where C 0 is the concentration of phytoplankton class no. 0 (see eq.
1). The latter is useful for Case 1 water types where the concentrations of
particles and phytoplankton are highly correlated.
• b b,L * can be treated either as a constant with a default value of 0.0086 m
2 g
–1
(Heege 2000), or as b b,L * = A · C L
B
. Such a non-linear dependency of
scattering on concentration was observed for phytoplankton (Morel, 1980). It
may be used for Case 1 water types, while b b,L * = constant is appropriate for
Case 2 waters with significant sources of non-phytoplankton suspended
matter. Typical values of the empirical constants are A = 0.0006 m
2 g
–1 and B
= –0.37 (Sathyendranath et al., 1989).
• b L (Ȝ) can either be read from file, or it can be calculated as b L (Ȝ) = a 0 *(Ȝ L ) /
a 0 *(Ȝ), where a 0 *(Ȝ) is the specific absorption spectrum of phytoplankton class
no. 0 (see eq. 1), and Ȝ L denotes a reference wavelength. This method assumes
that backscattering by large particles originates mainly from phytoplankton
cells, and couples absorption and scattering according to the Case 1 waters
model of Sathyendranath et al. (1989). However, such coupling may be used
in exceptional cases only, since living algae have a negligible influence on the
backscattering process by oceanic waters (Ahn et al., 1992), and in Case 2
waters particle scattering is weakly related to phytoplankton absorption in
general. In WASI, b L (Ȝ) = 1 is set as default.
2.2.3 Small particles
Backscattering by small particles is calculated as the product of concentration C S ,
specific backscattering coefficient b b,S *, and a normalized scattering function (Ȝ/Ȝ S )
n
.
The exponent n, which determines the spectral shape, depends on particle size
distribution. The variable “n” is typically about –1 (Sathyendranath et al., 1989) and
b b,S * is about 0.005 m
2 g
–1 for Ȝ S = 500 nm.
2.3 ATTENUATION
The diffuse attenuation coefficient of irradiance E is defined as K = – (1/E) dE/dz,
where z is the depth. Similarly, the attenuation coefficient of radiance L is defined as k
= – (1/L) dL/dz. Attenuation is an apparent optical property (AOP) and depends not
only on the properties of the medium, but additionally on the geometric distribution of
the illuminating light field.
2.3.1 Diffuse attenuation for downwelling irradiance
The most important attenuation coefficient is K d , which describes the extinction of
downwelling irradiance E d
– . The following parameterization is adapted from Gordon
(1989), which largely eliminates the light field effect near the surface:
85
Inverse Modeling of Spectral Measurements
Backscattering by large particles is calculated as the product of concentration C L ,
specific backscattering coefficient b b,L *, and normalized scattering function b L (Ȝ)җ . The
user has several options for calculation:
• C L can be treated either as an independent parameter, or C L = C 0 can be
assigned, where C 0 is the concentration of phytoplankton class no. 0 (see eq.
1). The latter is useful for Case 1 water types where the concentrations of
particles and phytoplankton are highly correlated.
• b b,L * can be treated either as a constant with a default value of 0.0086 m
2 g
–1
(Heege 2000), or as b b,L * = A · C L
B
. Such a non-linear dependency of
scattering on concentration was observed for phytoplankton (Morel, 1980). It
may be used for Case 1 water types, while b b,L * = constant is appropriate for
Case 2 waters with significant sources of non-phytoplankton suspended
matter. Typical values of the empirical constants are A = 0.0006 m
2 g
–1 and B
= –0.37 (Sathyendranath et al., 1989).
• b L (Ȝ) can either be read from file, or it can be calculated as b L (Ȝ) = a 0 *(Ȝ L ) /
a 0 *(Ȝ), where a 0 *(Ȝ) is the specific absorption spectrum of phytoplankton class
no. 0 (see eq. 1), and Ȝ L denotes a reference wavelength. This method assumes
that backscattering by large particles originates mainly from phytoplankton
cells, and couples absorption and scattering according to the Case 1 waters
model of Sathyendranath et al. (1989). However, such coupling may be used
in exceptional cases only, since living algae have a negligible influence on the
backscattering process by oceanic waters (Ahn et al., 1992), and in Case 2
waters particle scattering is weakly related to phytoplankton absorption in
general. In WASI, b L (Ȝ) = 1 is set as default.
2.2.3 Small particles
Backscattering by small particles is calculated as the product of concentration C S ,
specific backscattering coefficient b b,S *, and a normalized scattering function (Ȝ/Ȝ S )
n
.
The exponent n, which determines the spectral shape, depends on particle size
distribution. The variable “n” is typically about –1 (Sathyendranath et al., 1989) and
b b,S * is about 0.005 m
2 g
–1 for Ȝ S = 500 nm.
2.3 ATTENUATION
The diffuse attenuation coefficient of irradiance E is defined as K = – (1/E) dE/dz,
where z is the depth. Similarly, the attenuation coefficient of radiance L is defined as k
= – (1/L) dL/dz. Attenuation is an apparent optical property (AOP) and depends not
only on the properties of the medium, but additionally on the geometric distribution of
the illuminating light field.
2.3.1 Diffuse attenuation for downwelling irradiance
The most important attenuation coefficient is K d , which describes the extinction of
downwelling irradiance E d
– . The following parameterization is adapted from Gordon
(1989), which largely eliminates the light field effect near the surface:
85
Inverse Modeling of Spectral Measurements