.
'
cos
)
(
b
)
(
a
)
(
K
sun
b
0
d
θ
λ
+
λ
⋅
κ
=
λ
(5)
a(Ȝ) is calculated according to eq. (3), b b (Ȝ) using eq. (4). ș’ sun is the sun zenith angle in
water. The coefficient κ 0 depends on the scattering phase function. Gordon (1989)
determined a value of κ 0 = 1.0395 from Monte Carlo simulations in Case 1 waters,
Albert and Mobley (2003) found a value of κ 0 = 1.0546 from simulations in Case 2
waters using the radiative transfer program Hydrolight (Mobley et al., 1993). Some
authors use eq. (5) with κ 0 = 1 (Sathyendranath and Platt, 1988, 1997; Gordon et al.,
1975). In WASI, κ 0 is read from the WASI.INI file; the default value is 1.0546.
2.3.2 Diffuse attenuation for upwelling irradiance
For upwelling irradiance two attenuation coefficients are used: K uW for the
radiation backscattered in the water, and K uB for the radiation reflected from the
bottom. The following parameterization is adopted from Albert and Mobley (2003):
[
] [
]
1.9991
0.2995
( )
( )
( ) 1
( )
1
.
cos '
uW
b
b
sun
K
a
b
ª
º
=
+
⋅ +
⋅ +
«
»
¬
¼
(6)
[
] [
]
1.2441
0.5182
( )
( )
( ) 1
( )
1
.
cos '
uB
b
b
sun
K
a
b
ª
º
=
+
⋅ +
⋅ +
«
»
¬
¼
(7)
The function ω b (Ȝ) depends on absorption a(Ȝ) and backscattering b b (Ȝ) of the water
body:
.
)
(
b
)
(
a
)
(
b
)
(
b
b
b
λ
+
λ
λ
=
λ
ω
(8)
Eqs. (6) and (7) are used in the model of irradiance reflectance in shallow waters.
2.3.3 Attenuation for upwelling radiance
For upwelling radiance two attenuation coefficients are used: k uW for the radiation
backscattered in the water, and k uB for the radiation reflected from the bottom. The
following parameterization is adopted from Albert and Mobley (2003):
[
]
3.5421
( )
( )
0.2786
( )
1
( )
1
,
cos '
cos '
b
uW
b
v
s u n
a
b
k
ª
º
+
=
⋅ +
⋅ −
«
»
¬
¼
(9)
[
]
2.2658
( )
( )
0.0577
( )
1
( )
1
,
cos '
cos '
b
uB
b
v
s u n
a
b
k
ª
º
+
=
⋅ +
⋅ +
«
»
¬
¼
(10)
where ș’ v is the viewing angle in water measured from the nadir direction. These
equations are used in the model of remote sensing reflectance in shallow waters.
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
ω
ω
ș
ș
λ
λ
λ
λ
λ
λ
λ
λ
ș
ș
ș
ș
ω
ω
86
Gege and Albert
'
cos
)
(
b
)
(
a
)
(
K
sun
b
0
d
θ
λ
+
λ
⋅
κ
=
λ
(5)
a(Ȝ) is calculated according to eq. (3), b b (Ȝ) using eq. (4). ș’ sun is the sun zenith angle in
water. The coefficient κ 0 depends on the scattering phase function. Gordon (1989)
determined a value of κ 0 = 1.0395 from Monte Carlo simulations in Case 1 waters,
Albert and Mobley (2003) found a value of κ 0 = 1.0546 from simulations in Case 2
waters using the radiative transfer program Hydrolight (Mobley et al., 1993). Some
authors use eq. (5) with κ 0 = 1 (Sathyendranath and Platt, 1988, 1997; Gordon et al.,
1975). In WASI, κ 0 is read from the WASI.INI file; the default value is 1.0546.
2.3.2 Diffuse attenuation for upwelling irradiance
For upwelling irradiance two attenuation coefficients are used: K uW for the
radiation backscattered in the water, and K uB for the radiation reflected from the
bottom. The following parameterization is adopted from Albert and Mobley (2003):
[
] [
]
1.9991
0.2995
( )
( )
( ) 1
( )
1
.
cos '
uW
b
b
sun
K
a
b
ª
º
=
+
⋅ +
⋅ +
«
»
¬
¼
(6)
[
] [
]
1.2441
0.5182
( )
( )
( ) 1
( )
1
.
cos '
uB
b
b
sun
K
a
b
ª
º
=
+
⋅ +
⋅ +
«
»
¬
¼
(7)
The function ω b (Ȝ) depends on absorption a(Ȝ) and backscattering b b (Ȝ) of the water
body:
.
)
(
b
)
(
a
)
(
b
)
(
b
b
b
λ
+
λ
λ
=
λ
ω
(8)
Eqs. (6) and (7) are used in the model of irradiance reflectance in shallow waters.
2.3.3 Attenuation for upwelling radiance
For upwelling radiance two attenuation coefficients are used: k uW for the radiation
backscattered in the water, and k uB for the radiation reflected from the bottom. The
following parameterization is adopted from Albert and Mobley (2003):
[
]
3.5421
( )
( )
0.2786
( )
1
( )
1
,
cos '
cos '
b
uW
b
v
s u n
a
b
k
ª
º
+
=
⋅ +
⋅ −
«
»
¬
¼
(9)
[
]
2.2658
( )
( )
0.0577
( )
1
( )
1
,
cos '
cos '
b
uB
b
v
s u n
a
b
k
ª
º
+
=
⋅ +
⋅ +
«
»
¬
¼
(10)
where ș’ v is the viewing angle in water measured from the nadir direction. These
equations are used in the model of remote sensing reflectance in shallow waters.
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
Ȝ
ω
ω
ș
ș
λ
λ
λ
λ
λ
λ
λ
λ
ș
ș
ș
ș
ω
ω
86
Gege and Albert