Radiative transfer model for the computation of radiance and polarization in an ocean–atmosphere system: polarization properties of suspended matter for remote sensing

Malik Chami, Richard Santer, and Eric Dilligeard

Malik Chami, Richard Santer, and Eric Dilligeard

^{}The authors are with the Unité Propre de Recherche de l’Enseignement Superieur Associee, Centre National de la Recherche Scientifique 8013, Ecosystème Littoraux et Côtiers, Laboratoire Interdisciplinaire des Sciences de l’Environnement, Université du Littoral Côte d’Opale, 32 avenue Foch, 62930 Wimereux, France.

Malik Chami, Richard Santer, and Eric Dilligeard, "Radiative transfer model for the computation of radiance and polarization in an ocean–atmosphere system: polarization properties of suspended matter for remote sensing," Appl. Opt. 40, 2398-2416 (2001)

A radiative transfer code termed OSOA for the ocean–atmosphere
system that is able to predict the total and the polarized signals has
been developed. The successive-orders-of-scattering method is
used. The air–water interface is modeled as a planar
mirror. Four components grouped by their optical properties, pure
seawater, phytoplankton, nonchlorophyllose matter, and yellow
substances, are included in the water column. Models are validated
through comparisons with standard models. The numerical accuracy of
the method is better than 2%; high computational efficiency is
maintained. The model is used to study the influence of
polarization on the detection of suspended matter. Polarizing
properties of hydrosols are discussed: phytoplankton cells exhibit
weak polarization and small inorganic particles, which are strong
backscatterers, contribute appreciably to the polarized
signal. Therefore the use of the polarized signal to extract the
sediment signature promises good results. Also, polarized radiance
could improve characterization of aerosols when open ocean waters are
treated.

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Computation of Diffuse Downward and Upward Irradiances
Just Below the Surface by Use of the Actual Petzold Phase Function and
the Corresponding Truncated Function for Three Chlorophyll Contents for
Case I Watersa

Chlorophyll a (mg m^{-3})

Downward Irradiance

Upward Irradiance

Truncation

Exact

ΔE/E (%)

Truncation

Exact

ΔE/E (%)

0.5

0.09652

0.09697

+0.46

0.18448

0.18381

-0.36

1

0.13584

0.13640

+0.41

0.26177

0.26061

-0.44

2

0.18281

0.18352

+0.39

0.35524

0.35348

-0.49

Hemispherical Downward Irradiance

Hemispherical Upward Irradiance

0.5

0.29295

0.29321

+0.09

0.39777

0.39645

-0.33

1

0.40732

0.40745

+0.03

0.55744

0.55514

-0.41

2

0.54294

0.54295

+0.002

0.74852

0.74505

-0.46

The solar zenith angle is 30°, and the
wavelength is λ = 560 nm. Also shown is the hemispherical
irradiance computed for each case and the relative error
ΔE/
E = E_{exact} -
E_{truncated}/E_{exact}, where
E is the irradiance in percent.

Table 2

Order of Convergence for the Scattering Order of the
Zeroth Order (s = 0) Fourier Series Term and for
the Fourier Series Expansion (θ
_{
0
}
=
30°)
a

Order of

Case Number

(1)

(2)

(3)

(4)

(5)

(6)

Scattering (s = 0)

9

19

23

10

20

25

Fourier series

3

23

23

3

23

33

The six cases listed correspond to those
enumerated in Subsection 3.C.

Table 3

Bidirectional Reflectance (in percent) Above the Ocean
Surface, ρ_{w}
(0
^{
+
}
), for a Solar
Zenith Angle of θ
_{
0
}
= 30° and a Nadir
View
a

Radiative Transfer Model

Case Number

(1)

(2)

(3)

(4)

(5)

OSOA scalar

2.38

0.405

0.530

2.54

0.630

(9)

(38)

(42)

(9)

(38)

Hydrolight

2.37

0.425

0.566

2.58

0.656

(68)

(434)

(433)

(711)

(436)

Δρ/ρ (%)

0.4

-4.9

-6.8

-1.6

-4.1

Calculations were made with the scalar
version of the OSOA code and with the Hydrolight model. The
corresponding computation time (in seconds) is given in parentheses
for the given case. The relative difference Δρ/ρ =
(ρ_{OSOA} -
ρ_{Hydrolight})/ρ_{OSOA} is also
given. The five cases listed correspond to those enumerated in
Subsection 3.C.

Table 4

Computations of Diffuse Irradiance for Conservative
Casesa

Problem

Optical Depth

Number of Scattering Events n

Accuracy (%)

Pure seawater

5

582

1.8

30

8587

1.7

Sediments

5

382

1.7

30

3352

1.7

The degree of accuracy expresses the
relative difference between an ideal conservation result and the sum of
the irradiances computed with the OSOA. The number of scattering
events n required for the computation is indicated for each
case.

Table 5

Bidirectional Reflectance (in percent) Above the Ocean
Surface, ρ_{w}
(0
^{
+
}
), for a Solar
Zenith Angle of θ
_{
0
}
= 30° and a Nadir
View
a

OSOA Version

Case Number

(1)

(2)

(3)

(4)

(5)

OSOA scalar

2.38

0.405

0.530

2.54

0.630

(9)

(38)

(42)

(9)

(38)

OSOA vector

2.43

0.417

0.554

2.31

0.577

(69)

(161)

(495)

(77)

(319)

Δρ/ρ (%)

2.1

2.9

4.3

-10.0

-9.2

Calculations were made with the scalar
and the vector versions of the OSOA. The corresponding computation
time (in seconds) is given in parentheses for the given case and
code version. Relative differences Δρ/ρ =
ρ_{vector} -
ρ_{scalar}/ρ_{vector} are also given. The
five listed cases correspond to those enumerated in Subsection 3.C.

Tables (5)

Table 1

Computation of Diffuse Downward and Upward Irradiances
Just Below the Surface by Use of the Actual Petzold Phase Function and
the Corresponding Truncated Function for Three Chlorophyll Contents for
Case I Watersa

Chlorophyll a (mg m^{-3})

Downward Irradiance

Upward Irradiance

Truncation

Exact

ΔE/E (%)

Truncation

Exact

ΔE/E (%)

0.5

0.09652

0.09697

+0.46

0.18448

0.18381

-0.36

1

0.13584

0.13640

+0.41

0.26177

0.26061

-0.44

2

0.18281

0.18352

+0.39

0.35524

0.35348

-0.49

Hemispherical Downward Irradiance

Hemispherical Upward Irradiance

0.5

0.29295

0.29321

+0.09

0.39777

0.39645

-0.33

1

0.40732

0.40745

+0.03

0.55744

0.55514

-0.41

2

0.54294

0.54295

+0.002

0.74852

0.74505

-0.46

The solar zenith angle is 30°, and the
wavelength is λ = 560 nm. Also shown is the hemispherical
irradiance computed for each case and the relative error
ΔE/
E = E_{exact} -
E_{truncated}/E_{exact}, where
E is the irradiance in percent.

Table 2

Order of Convergence for the Scattering Order of the
Zeroth Order (s = 0) Fourier Series Term and for
the Fourier Series Expansion (θ
_{
0
}
=
30°)
a

Order of

Case Number

(1)

(2)

(3)

(4)

(5)

(6)

Scattering (s = 0)

9

19

23

10

20

25

Fourier series

3

23

23

3

23

33

The six cases listed correspond to those
enumerated in Subsection 3.C.

Table 3

Bidirectional Reflectance (in percent) Above the Ocean
Surface, ρ_{w}
(0
^{
+
}
), for a Solar
Zenith Angle of θ
_{
0
}
= 30° and a Nadir
View
a

Radiative Transfer Model

Case Number

(1)

(2)

(3)

(4)

(5)

OSOA scalar

2.38

0.405

0.530

2.54

0.630

(9)

(38)

(42)

(9)

(38)

Hydrolight

2.37

0.425

0.566

2.58

0.656

(68)

(434)

(433)

(711)

(436)

Δρ/ρ (%)

0.4

-4.9

-6.8

-1.6

-4.1

Calculations were made with the scalar
version of the OSOA code and with the Hydrolight model. The
corresponding computation time (in seconds) is given in parentheses
for the given case. The relative difference Δρ/ρ =
(ρ_{OSOA} -
ρ_{Hydrolight})/ρ_{OSOA} is also
given. The five cases listed correspond to those enumerated in
Subsection 3.C.

Table 4

Computations of Diffuse Irradiance for Conservative
Casesa

Problem

Optical Depth

Number of Scattering Events n

Accuracy (%)

Pure seawater

5

582

1.8

30

8587

1.7

Sediments

5

382

1.7

30

3352

1.7

The degree of accuracy expresses the
relative difference between an ideal conservation result and the sum of
the irradiances computed with the OSOA. The number of scattering
events n required for the computation is indicated for each
case.

Table 5

Bidirectional Reflectance (in percent) Above the Ocean
Surface, ρ_{w}
(0
^{
+
}
), for a Solar
Zenith Angle of θ
_{
0
}
= 30° and a Nadir
View
a

OSOA Version

Case Number

(1)

(2)

(3)

(4)

(5)

OSOA scalar

2.38

0.405

0.530

2.54

0.630

(9)

(38)

(42)

(9)

(38)

OSOA vector

2.43

0.417

0.554

2.31

0.577

(69)

(161)

(495)

(77)

(319)

Δρ/ρ (%)

2.1

2.9

4.3

-10.0

-9.2

Calculations were made with the scalar
and the vector versions of the OSOA. The corresponding computation
time (in seconds) is given in parentheses for the given case and
code version. Relative differences Δρ/ρ =
ρ_{vector} -
ρ_{scalar}/ρ_{vector} are also given. The
five listed cases correspond to those enumerated in Subsection 3.C.