Howard R. Gordon and G. Chris Boynton, "Radiance—irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters," Appl. Opt. 36, 2636-2641 (1997)
A full multiple-scattering algorithm for inverting upwelling radiance
(Lu) or
irradiance
(Eu) and
downwelling irradiance (Ed)
profiles in homogeneous natural waters to
obtain the absorption (a) and backscattering
(bb)
coefficients is described and tested with simulated data. An attractive
feature of the algorithm is that it does not require precise knowledge of the
scattering phase function of the medium. For the Eu – Ed algorithm, tests suggest that
the error in the retrieved a should usually be
≲1%, and the error in bb ≲10–20%. The performance of
the Lu
–Ed
algorithm is not as good because it is more sensitive to the scattering phase
function employed in the inversions; however, the error in
a is usually still small, i.e., ≲3%. When
the algorithm is extended to accommodate the presence of a
Lambertian-reflecting bottom, the retrievals of a are
still excellent, even when the presence of the bottom significantly influences
the upwelling light field; however, the error in bb can be
large.
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Here 0° and 60° mean the source
is the Sun at solar zenith angles of 0° and 60°, respectively;
D indicates totally diffuse radiance incident upon the
surface.
δa and δbb are the
errors in the retrieved values of a and
bb,
respectively.
Here 0° and 60° mean the source
is the Sun at solar zenith angles of 0° and 60°, respectively; D indicates totally diffuse radiance incident upon the surface.
δa and δbb are the errors in the retrieved values of a and bb, respectively.
Here the Petzold phase function is used to create the pseudodata,
and a HG with g = 0.85 is used in the retrievals.
Here 0° and 60° mean the source is the Sun
at solar zenith angles of 0° and 60°, respectively.
δa and δbb are the
errors in the retrieved values of a and bb, respectively.
Table 5
Test of
the
Lu–Ed
Algorithm with a Correct and Incorrect
P(Θ) used in the Inversiona
ω0
AB
zB = 3.00 m
zB = 4.75 m
Correct P(Θ)
Incorrect P(Θ)
Correct P(Θ)
Incorrect P(Θ)
δa (%)
δbb (%)
δa (%)
δbb (%)
δa (%)
δbb (%)
δa (%)
δbb (%)
0.20
0.25
+0.0
+34.3
-1.0
+37.5
+0.3
+8.9
+0.2
+8.3
0.20
0.50
-1.3
+55.5
-2.4
+81.3
+0.2
+11.0
+0.1
+18.8
0.20
1.00
-3.3
+127.6
-0.0
+17.5
+0.3
+19.7
-0.7
+23.0
0.60
0.25
-0.2
-0.7
-2.3
+4.3
+0.4
+0.6
-1.6
-0.9
0.60
0.50
-0.3
+2.7
-2.0
+3.0
-0.5
+5.1
-1.5
-0.5
0.60
1.00
+1.3
+15.3
-2.0
-1.1
-0.4
+2.4
-2.8
+5.8
0.80
0.25
+0.1
+0.3
-2.9
+6.0
+0.2
+1.0
-1.5
-3.2
0.80
0.50
-1.2
+9.2
-4.8
+19.5
-0.5
+4.1
-3.0
+2.2
0.80
1.00
+7.9
-52.2
-1.6
+3.1
-0.7
+4.0
+1.4
-14.7
The solar zenith angle is 0°, the bottom depth is zB,
and the bottom albedo is AB.
Tables (5)
Table 1
Test of
the Eu – Ed
Algorithm with a Correct and Incorrect
P(Θ) used in the Inversion
Here 0° and 60° mean the source
is the Sun at solar zenith angles of 0° and 60°, respectively;
D indicates totally diffuse radiance incident upon the
surface.
δa and δbb are the
errors in the retrieved values of a and
bb,
respectively.
Here 0° and 60° mean the source
is the Sun at solar zenith angles of 0° and 60°, respectively; D indicates totally diffuse radiance incident upon the surface.
δa and δbb are the errors in the retrieved values of a and bb, respectively.
Here the Petzold phase function is used to create the pseudodata,
and a HG with g = 0.85 is used in the retrievals.
Here 0° and 60° mean the source is the Sun
at solar zenith angles of 0° and 60°, respectively.
δa and δbb are the
errors in the retrieved values of a and bb, respectively.
Table 5
Test of
the
Lu–Ed
Algorithm with a Correct and Incorrect
P(Θ) used in the Inversiona
ω0
AB
zB = 3.00 m
zB = 4.75 m
Correct P(Θ)
Incorrect P(Θ)
Correct P(Θ)
Incorrect P(Θ)
δa (%)
δbb (%)
δa (%)
δbb (%)
δa (%)
δbb (%)
δa (%)
δbb (%)
0.20
0.25
+0.0
+34.3
-1.0
+37.5
+0.3
+8.9
+0.2
+8.3
0.20
0.50
-1.3
+55.5
-2.4
+81.3
+0.2
+11.0
+0.1
+18.8
0.20
1.00
-3.3
+127.6
-0.0
+17.5
+0.3
+19.7
-0.7
+23.0
0.60
0.25
-0.2
-0.7
-2.3
+4.3
+0.4
+0.6
-1.6
-0.9
0.60
0.50
-0.3
+2.7
-2.0
+3.0
-0.5
+5.1
-1.5
-0.5
0.60
1.00
+1.3
+15.3
-2.0
-1.1
-0.4
+2.4
-2.8
+5.8
0.80
0.25
+0.1
+0.3
-2.9
+6.0
+0.2
+1.0
-1.5
-3.2
0.80
0.50
-1.2
+9.2
-4.8
+19.5
-0.5
+4.1
-3.0
+2.2
0.80
1.00
+7.9
-52.2
-1.6
+3.1
-0.7
+4.0
+1.4
-14.7
The solar zenith angle is 0°, the bottom depth is zB,
and the bottom albedo is AB.