2.6 REMOTE SENSING REFLECTANCE
2.6.1 Deep water
The ratio of upwelling radiance to downwelling irradiance, R rs (Ȝ) = L u (Ȝ) / E d (Ȝ), is
called remote sensing reflectance (Mobley, 1994). It is an AOP and can be
parameterized the same as R(Ȝ) (Albert and Mobley, 2003):
R rs
− (Ȝ) = f rs · ω b (Ȝ).
(17)
Alternately, R rs
− can be calculated as R rs
− (Ȝ) = R(Ȝ) / Q, where R(Ȝ) is either calculated
using eq. (14) or imported from file, and Q ≡ E u / L u is treated as a parameter with a
default value of 5 sr. A parameterization of the factor f rs , which can be applied to both
deep and shallow waters, was found by Albert and Mobley (2003):
(
)
2
3
0.4021
0.1098
0.0512 1 4.6659
7.8387
5.4571
1
1
.
cos '
cos '
rs
b
b
b
v
s u n
f
§
·§
·
=
⋅ +
⋅
−
⋅
+
⋅
⋅ +
⋅ +
¨
¸¨
¸
©
¹©
¹
(18)
Parameters of f rs are ω b of eq. (8), the sun zenith angle in water, ș’ sun , and the viewing
angle in water, ș’ v . Alternately, f rs can be calculated as f rs = f / Q.
2.6.2 Shallow water
For shallow water, the following parameterization is chosen (Albert and Mobley,
2003):
(
)
{
}
[
]
(
)
{
}
B
uB
d
b
rs
B
uW
d
rs
sh
rs
z
)
(
k
)
(
K
exp
)
(
R
0389
.
1
z
)
(
k
)
(
K
exp
1576
.
1
1
)
(
R
)
(
R
⋅
λ
+
λ
−
⋅
λ
⋅
+
⋅
λ
+
λ
−
⋅
−
⋅
λ
=
λ
−
−
(19)
The first term on the right-hand side is the reflectance of a water layer of thickness z B ,
the second term the contribution of the bottom. Bottom reflectance R
b
rs (Ȝ) is calculated
using eq. (22). K d , k uW and k uB account for attenuation within the water layer and are
calculated using eqs. (5), (9), and (10), respectively.
2.6.3 Above the surface
Above the surface, the user can select one of the following parameterizations:
,
)
(
R
)
(
R
Q
1
)
(
R
n
)
1
)(
1
(
)
(
R
surf
rs
rs
rs
2
w
L
rs
λ
+
λ
⋅
⋅
σ
−
λ
⋅
σ
−
σ
−
=
λ
−
−
−
−
(20a)
,
)
(
R
)
(
R
1
)
(
R
Q
n
)
1
)(
1
(
)
(
R
surf
rs
2
w
L
rs
λ
+
λ
⋅
σ
−
λ
⋅
⋅
σ
−
σ
−
=
λ
−
−
(20b)
.
)
(
R
)
(
R
1
)
(
R
n
)
1
)(
1
(
)
(
R
surf
rs
rs
2
w
L
rs
λ
+
λ
⋅
σ
−
λ
⋅
σ
−
σ
−
=
λ
−
−
−
(20c)
ω
ω
ω
ș
ș
89
Inverse Modeling of Spectral Measurements