In the IOCCG Report Series:
1. Minimum Requirements for an Operational Ocean-Colour Sensor for the Open
Ocean (1998).
2. Status and Plans for Satellite Ocean-Colour Missions: Considerations for Complementary Missions (1999).
3. Remote Sensing of Ocean Colour in Coastal, and Other Optically-Complex,
Waters (2000).
4. Guide to the Creation and Use of Ocean-Colour, Level-3, Binned Data Products(2004).
5. Remote Sensing of Inherent Optical Properties: Fundamentals, Tests of Algorithms, and Applications (2006).
6. Ocean-Colour Data Merging (2007).
7. Why Ocean Colour? The Societal Benefits of Ocean-Colour Technology (2008).
8. Remote Sensing in Fisheries and Aquaculture (2009).
9. Partition of the Ocean into Ecological Provinces: Role of Ocean-Colour Radiometry (2009).
10. Atmospheric Correction for Remotely-Sensed Ocean-Colour Products (this volume).

Disclaimer: The contents of this report are solely the opinions of the authors, anddo not constitute a statement of policy, decision, or position on behalf of any of
the space agencies or other organizations mentioned, or the governments of any
country.

The printing of this report was sponsored and carried out by the National Oceanicand Atmospheric Administration (NOAA, USA), which is gratefully acknowledged.

Reports and Monographs of the International
Ocean-Colour Coordinating GroupAn Affiliated Program of the Scientific Committee on Oceanic Research (SCOR)An Associated Member of the Committee on Earth Observation Satellites (CEOS)

IOCCG Report Number 10, 2010

Atmospheric Correction for Remotely-Sensed OceanColour Products

Edited by:
Menghua Wang, NOAA/NESDIS Center for Satellite Applications and Research,
USA

Report of an IOCCG working group on Comparison of Atmospheric Correction Algorithms, chaired by Menghua Wang, and based on contributions from (in alphabeticalorder):David Antoine

Laboratoire d’Oceanographie de Villefranche, France

Pierre-Yves Deschamps

Laboratoire d’Optique Atmospherique, France

Robert Frouin

Scripps Institution of Oceanography, UCSD, USA

Hajime Fukushima

Tokai University, Japan

Howard R. Gordon

University of Miami, USA

André MorelLaboratoire d’Oceanographie de Villefranche, France

Jean-Marc Nicolas

Laboratoire d’Optique Atmospherique, France

Menghua Wang

NOAA/NESDIS Center for Satellite Applications and Research, USA

Series Editor: Venetia Stuart

Correct citation for this publication:
IOCCG (2010). Atmospheric Correction for Remotely-Sensed Ocean-Colour Products.
Wang, M. (ed.), Reports of the International Ocean-Colour Coordinating Group, No.
10, IOCCG, Dartmouth, Canada.

The International Ocean-Colour Coordinating Group (IOCCG) is an internationalgroup of experts in the field of satellite ocean colour, acting as a liaison andcommunication channel between users, managers and agencies in the ocean-colour
arena.
The IOCCG is sponsored by the Canadian Space Agency (CSA), Centre Nationald’Etudes Spatiales (CNES, France), Department of Fisheries and Oceans (Bedford
Institute of Oceanography, Canada), European Space Agency (ESA), GKSS ResearchCentre (Geesthacht, Germany), National Institute for Space Research (INPE, Brazil),
Indian Space Research Organisation (ISRO), Japan Aerospace Exploration Agency(JAXA), Joint Research Centre (JRC, EC), Korean Ocean Research and Development
Institute (KORDI), National Aeronautics and Space Administration (NASA, USA), National Oceanic and Atmospheric Administration (NOAA, USA), and Second Instituteof Oceanography (SIO), China.

http: //www.ioccg.org

Published by the International Ocean-Colour Coordinating Group,
P.O. Box 1006, Dartmouth, Nova Scotia, B2Y 4A2, Canada.
ISSN: 1098-6030 ISBN: 978-1-896246-61-1©IOCCG 2010
Printed by the National Oceanic and Atmospheric Administration (NOAA), USA

Contents

1 Introduction

1

1.1 The IOCCG Atmospheric Correction Working Group . . . . . . . . . . . .

1

1.2 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22 Atmospheric Correction Algorithm Description

5

2.1 The SeaWiFS/MODIS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.2 The MERIS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.3 The OCTS/GLI Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 The POLDER Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Simulated Testing Data Set

15

3.1 The TOA Atmospheric Path Radiance . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Radiative-Transfer Code . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 Aerosol Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 The Ocean Water Radiance Contributions . . . . . . . . . . . . . . . . . . 16
3.2.1 Case-1 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2 Case-2 Water Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 The TOA Radiance Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Comparison Results

23

4.1 The Open Ocean (Case-1 Waters) . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.1 Ocean-Colour Parameters . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Aerosol Optical Thickness Results . . . . . . . . . . . . . . . . . . . 25
4.2 The Coastal Ocean Region (Case-2 Waters) . . . . . . . . . . . . . . . . . . 28
4.2.1 Sediment-Dominated Waters . . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 Yellow Substance-Dominated Waters . . . . . . . . . . . . . . . . . 31
4.3 Strongly-Absorbing Aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3.1 Comparison Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3.2 Effects of Vertical Distribution of Absorbing Aerosol . . . . . . . 34
4.4 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4.1 Case-1 Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4.2 Case-2 Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4.3 Cases with Strongly-Absorbing Aerosols . . . . . . . . . . . . . . . 38
i

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Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

5 Algorithm Validations from In Situ Data
5.1 The NOMAD Data Set for Algorithm Evaluation for Global Oceans . . .
5.2 The BOUSSOLE In Situ Data Set for Algorithm Evaluation . . . . . . . . .
5.3 Some Validation Results for OCTS/GLI . . . . . . . . . . . . . . . . . . . .
5.4 The SIMBAD(A) In situ Data Set for POLDER Algorithm Evaluation . . .

39
39
40
41
41

6 Conclusions and Recommendations

43

Appendices
A Details of the POLDER Algorithm
47
A.1 Radiometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
A.2 Aerosol Model Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
A.3 Dealing with the ‘Black-Pixel Assumption’ . . . . . . . . . . . . . . . . . . 48
A.4 Aerosol Optical Thickness Inversion . . . . . . . . . . . . . . . . . . . . . . 49
A.5 Dealing with Absorbing Aerosols . . . . . . . . . . . . . . . . . . . . . . . . 50
A.6 Atmospheric Correction of Ocean-Colour Bands (443, 490, and 565 nm) 50
A.7 Sun Glint Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
A.8 Whitecap Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
B Other Atmospheric Correction Algorithms
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Spectral Matching Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3 Spectral Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . .
B.4 The SWIR Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.5 Neural Network Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53
53
54
55
55
56

C Atmospheric Diffuse Transmittance59
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
C.2 Formal Definition of Diffuse Transmittance . . . . . . . . . . . . . . . . . 60
D Ocean Bidirectional Reflectance Distribution Function
D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2 Ocean Surface Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3 In Water BRDF Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3.1 The f -Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3.2 The Q-Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3.3 The Ratio f /Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3.4 The Corrective Term (f /Q)Eff . . . . . . . . . . . . . . . . . . . . .
D.3.5 Additional Comments . . . . . . . . . . . . . . . . . . . . . . . . . .

63
63
64
65
67
68
68
69
69

References

71

Acronyms

77

Chapter 1
Introduction
Menghua Wang, André Morel and Howard R. Gordon

1.1

The IOCCG Atmospheric Correction Working GroupThe IOCCG established the atmospheric correction working group (ACWG) because
atmospheric correction is a key procedure in remote sensing of ocean colour. It is
important to have quantitative evaluations and comparisons of the performanceof various atmospheric correction algorithms used to derive global ocean-colour
products from operational ocean-colour sensors. The primary objective of the
IOCCG ACWG was to quantify the performance of the various existing operational
atmospheric correction algorithms so that data users can have a better pictureof how data products derived from various ocean-colour satellite sensors can becompared and/or possibly merged. A number of ocean-colour sensors designed
to produce global ocean-colour products have been successfully launched in recent years: the Ocean Color Temperature Scanner (OCTS) from NASDA (now JAXA)
and CNES’s Polarization and Directionality of the Earth’s Reflectances (POLDER)-1(both launched on 17 August 1996), NASA’s Sea-Viewing Wide Field-of-View Sensor(SeaWiFS) (launched on 1 August 1997), NASA’s Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra (launched on 18 December 1999), ESA’s Medium
Resolution Imaging Spectrometer (MERIS) (launched on 1 March 2002), NASA’s
MODIS on Aqua (launched on 4 May 2002), the Global Imager (GLI) from NASDA(now JAXA) and POLDER-2 from CNES (both launched on 14 December 2002). In
addition, POLDER-3 on PARASOL was launched on 18 December 2004, and can beused for deriving ocean-colour products. SeaWiFS, MODIS-Aqua, and MERIS havebeen providing global ocean-colour products continuously since their launch, whileboth GLI and POLDER-2 unfortunately ended their missions on 24 October 2003 due
to a sudden failure of the spacecraft power system. A complete list of ocean-colour
satellite sensors, including some experimental ones, can be found in the IOCCG
website at: http://www.ioccg.org/sensors_ioccg.html.
In this report, four operational atmospheric correction algorithms are discussed,
and their performances for various cases are compared. These include algorithms for
SeaWiFS and MODIS-Aqua (Gordon and Wang, 1994a; Gordon, 1997), MERIS (Antoine
1

2

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

and Morel, 1999), the Ocean Colour and Temperature Scanner (OCTS) and GLI from
NASDA/JAXA (Fukushima et al., 1998), and POLDER. Scientists and investigators
who are primarily responsible for development of these four atmospheric correction
algorithms comprised the IOCCG ACWG, and are also the authors of this report.
In the past decade or so, significant efforts have been made by space agencies
for validating global ocean-colour products, particularly for routine ocean-colour
products from SeaWiFS, MODIS, and MERIS. Consequently, various algorithms havebeen updated, modified, and refined. At the same time, significant progress has
been made in the development of other approaches for atmospheric correction,
particularly dealing with cases for strongly-absorbing aerosols and waters with
non-negligible near-infrared (NIR) ocean contributions. Therefore, another objectiveof the ACWG was to provide the ocean community with an overview of the current
status of atmospheric correction algorithm development, including a more complete
list of references for those who are interested in the details. Some outstanding
issues are also discussed.
In this report, overviews of the various atmospheric correction algorithms used
for global ocean-colour data processing are provided. The performance of thevarious algorithms is compared using common simulated data sets, mainly foropen ocean (Case-1) waters and for non- or weakly-absorbing aerosols (generally
present in the open ocean). It should be noted that these four operational algorithms
are designed specifically for Case-1 waters and non- or weakly-absorbing aerosols.
Examples from coastal Case-2 waters (sediment-dominated and yellow-substancedominated waters) and from strongly-absorbing aerosols are also provided anddiscussed. Overviews are also provided of some other approaches developed inrecent years for regional applications, in particular, for dealing with turbid coastal
waters and strongly-absorbing aerosol issues (see Appendix B). In addition, comparison results for deriving aerosol optical thickness data are presented. Aerosol
optical property data are a by-product of the atmospheric correction of ocean-colour
products. The question of whether or not the various algorithms meet predefinedrequirements were considered to be outside the scope of this report. For this reason,
the report focuses only on intercomparisons between the various algorithms.

1.2

Brief History

Very likely, the first systematic measurements of the colour of the sea from aircraft,
carried out at the end of the sixties, were those of George L. Clarke, Gifford C. Ewing,
and Carl J. Lorenzen (Clarke, et al., 1970). The remote spectroscopy of the lightbackscattered from the sea in coastal waters near Woods Hole, and in offshore
waters from the Sargasso Sea across Georges Bank, demonstrated the possibility ofdetecting the chlorophyll concentration within the upper layers. Measurements fromaltitudes ranging from 152 to 3050 m showed the effect of increasing ‘airlight’ onIntroduction•

3

the upward radiance received by the sensor, and thus the need for an ‘atmosphericcorrection’ (Austin, 1974; Clarke and Ewing, 1974). It was soon realized that theatmospheric path radiance (the atmospheric signal) was largely dominant comparedto the marine signal in the visible part of the spectrum.
Simultaneously, field measurements of upward and downward spectral irradiance, Eu (λ) and Ed (λ), respectively, were performed by John E. Tyler and Raymond
C. Smith in different water bodies (Tyler and Smith, 1970). Thereafter, systematic
determinations of the same radiometric quantities were made during the SCOR
WG-15 Discoverer 1970 Expedition (Tyler, 1973), and allowed the diffuse attenuation coefficients, Kd (λ), and the irradiance reflectance, R(λ) = Eu (λ)/Ed (λ), to becomputed. The interpretation of this reflectance, a basic quantity in ocean-colour
science, was given in the frame of radiative transfer (Gordon et al., 1975) and also
in terms of optically-significant substances present in the water (Morel and Prieur,
1977; Smith and Baker, 1978).
The problem of removing the atmospheric and surface effects from satellite
imagery of the ocean was examined (Gordon, 1978; Gordon and Clark, 1980; Morel,1980), and the technique developed for that purpose (Gordon, 1980) was thenimplemented into the NASA processing system used with the NIMBUS-7 Coastal
Zone Color Scanner (CZCS) sensor. The problem encountered with this sensor was
the absence of an appropriate channel in the near-infrared (NIR) portion of thespectrum where the open ocean can be considered as black, so that the detectedsignal can be assumed to be of purely atmospheric origin. As a replacement, the
CZCS band at 670 nm was used along with the assumption that the marine radianceat this wavelength, Lw (670), was negligible, or if not, that it could be iteratively
derived based on an empirical relationship between Lw (670) and the chlorophyll
concentration (Smith and Wilson, 1981; Bricaud and Morel, 1987), or based ona priori knowledge when the chlorophyll content is sufficiently low (clear water
concept) (Gordon and Clark, 1981). Such a solution, applicable to Case-1 waters
fails when turbid, highly reflective, coastal waters are under consideration. Thisparticular situation continues to represent a difficult problem.
During the CZCS era, the atmospheric contribution was predicted (and removed)
based on the single scattering approximation. Within such an approach, the Rayleighscattering by air molecules can be considered separately, and computed in theabsence of the aerosol, whereas the aerosol scattering contribution can also becomputed separately in the absence of molecules (Gordon and Morel, 1983). Later in
the CZCS mission, and also for the present ocean-colour sensors, this simplifying
assumption was abandoned. The coupling of the scattering by aerosol molecules
was addressed (Gordon and Wang, 1994a), as well as the effect of polarization on themagnitude of the atmospheric contribution (Gordon et al., 1988a). The new schemes
for the atmospheric correction, such as those presented in this report, include these
improvements, together with the consideration and selection of various types ofaerosols.

4•

Atmospheric Correction for Remotely-Sensed Ocean-Colour ProductsChapter 2
Atmospheric Correction Algorithm Description
Howard R. Gordon, David Antoine, Hajime Fukushima, Menghua Wang,
Robert Frouin, André Morel, Pierre-Yves Deschamps and Jean-Marc
NicolasIn this document, the reflectance ρ(λ), is defined at a given wavelength λ, to berelated to the radiance L(λ) through ρ(λ) = π L(λ)/{F0 (λ) cos θ0 }, where F0 (λ) isthe extraterrestrial solar irradiance and θ0 is the solar-zenith angle. Radiance andreflectance are interchangeable based on this definition.
The purpose of the atmospheric correction for the remote retrieval of ocean
properties is to remove the atmospheric and surface effects from the signal measured by the satellite-sensor, thereby deriving the radiances coming from the ocean
waters. For the ocean-atmosphere system, the top-of-atmosphere (TOA) radiance
Lt (λ) can be partitioned linearly into various distinct physical contributions:
Lt (λ) = Lr (λ)+La (λ)+Lra (λ)+t(λ)Lwc (λ)+T (λ)Lg (λ)+t(λ)t0 (λ) cos θ0 [Lw (λ)]N ,(2.1)
where Lr (λ) is the radiances due to scattering by the air molecules (Rayleigh scattering in the absence of aerosols), La (λ) is the scattering by aerosols (in the absenceof air molecules), Lra (λ) is the multiple interaction term between molecules andaerosols, Lwc (λ) and Lg (λ) are the components of radiance due to whitecaps on thesea surface and the specular reflection of direct sunlight off the sea surface (sunglitter), respectively, and [Lw (λ)]N is the normalized water-leaving radiance dueto photons that penetrate the sea surface and are backscattered out of the water.
The relationship between [Lw (λ)]N and the actual water-leaving radiance, Lw (λ),
propagating in a direction toward the sensor is given in Appendix D. The quantities
t0 (λ) and t(λ) are the diffuse transmittances of the atmosphere from the sun to
the surface and from the surface to the sensor, respectively (Appendix C). T (λ) isthe direct transmittance from the surface to the sensor. Note that Equation 2.1 isvalid when the target is large spatially, i.e., effects of the target environment canbe neglected. The goal of the atmospheric correction is to retrieve the normalized
water-leaving radiance [Lw (λ)]N accurately from the spectral measurements of the
TOA radiance Lt (λ) at the satellite altitude. We can further define the TOA atmospheric path radiance (including both contributions from atmosphere scattering and
5

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Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

surface reflection) as
Lpath (λ) = Lr (λ) + La (λ) + Lra (λ).

(2.2)

It should be noted that Lpath includes any and all-multiple reflections from theFresnel reflection of the air-sea interface. The principal challenge in atmosphericcorrection is the estimation and removal of Lpath (λ) from Lt (λ). In Case-1 waters,
Lpath (λ) contributes about 90% of the TOA radiance in the blue and green, and ahigher fraction in the red. The estimation of the diffuse transmittances is next inthe order of importance. The main difficulty with its estimation is that it depends
on the angular distribution of the radiance just beneath the sea surface. Lg (λ) canbe rendered as small as desired by avoiding the region surrounding the specular
image of the sun, and Lwc (λ) can be estimated from surface wind speed.
In the last two decades, various atmospheric correction algorithms have beendeveloped and used to derive global ocean-colour products for the following satellite
ocean-colour sensors: OCTS (1996-1997), POLDER-1 (1996-1997), SeaWiFS (1997present), MODIS-Terra (1999-present), MODIS-Aqua (2002-present), MERIS (2002present), GLI (2002-2003), and POLDER-2 (2002-2003). These algorithms all use
standard radiative transfer methods to compute and remove Lr (λ) from Lt (λ).
This computation requires an estimate of the surface atmospheric pressure (andin some implementations, the surface wind speed is also used). The remaining
part of Lpath (λ) is estimated from Lt (λ) in the NIR wavelengths, where [Lw (λ)]N is
negligible, providing La (λ) + Lra (λ) in the NIR. Based on La (λ) + Lra (λ) in the NIR,
an estimate is made of La (λ) + Lra (λ) in the visible (VIS). The principal difference
between the atmospheric correction algorithms for the various sensors listed above
is in the details of how the estimate of La (λ) + Lra (λ) in the VIS is made fromthe estimate of La (λ) + Lra (λ) in the NIR. These algorithms are described in thefollowing sections.

2.1

The SeaWiFS/MODIS Algorithm

Gordon and Wang (1994a) developed the basic SeaWiFS/MODIS atmospheric correction algorithm. Its performance was then validated through simulations, and after
launch, through direct application of the algorithms to SeaWiFS and MODIS imagery
and comparison with in situ data (McClain et al., 2004; Wang, et al., 2005; Bailey
and Werdell, 2006; Zibordi, et al., 2006). Using Equation 2.1, the procedure for the
SeaWiFS/MODIS atmospheric correction can be described as follows:
v the Rayleigh radiance Lr (λ) is computed from the Rayleigh lookup tables thatwere prepared using the vector radiative transfer theory (all polarization effects
included) with inputs of the solar-sensor geometry, atmospheric pressure, andwind speed (Gordon et al., 1988a; Gordon and Wang, 1992; Wang, 2002; 2005);
v the whitecap radiance Lwc (λ) is modelled using input of the sea surface windspeed (Gordon and Wang, 1994b; Frouin, et al., 1996; Moore et al., 2000);

Atmospheric Correction Algorithm Description•

7v the TOA sun glint radiance T (λ)Lg (λ) is mostly masked out and residual
contamination is corrected based on a model of sea surface slope distribution(Cox and Munk, 1954; Wang and Bailey, 2001);v the fact that [Lw (λ)]N is negligible in the NIR (for the open ocean), can beused to estimate the combination La (λ) + Lra (λ) in the NIR bands, and aerosol
modelling can be used to extrapolate it from the NIR to the visible bands; andfinallyv t0 (λ) and t(λ) are estimated (Yang and Gordon, 1997) and used to compute[Lw (λ)]N in the visible wavelengths.
The derived [Lw (λ)]N spectra data are then used as inputs for all of the ocean
bio-optical products from ocean-colour sensors.
To account for the multiple-scattering effect on La (λ)+Lra (λ), which depends on
the aerosol properties and increases as the aerosol concentration increases, realistic
aerosol models are required. A set of 12 aerosol models from, or derived from, thework of Shettle and Fenn (1979) are used for the SeaWiFS/MODIS data processing(Shettle and Fenn, 1979; Gordon and Wang, 1994a; Wang et al., 2005). Specifically,
these 12 aerosol models are:v the ‘Oceanic’ model with a relative humidity (RH) of 99% (denoted O99),
v the ‘Maritime’ model with a RH of 50%, 70%, 90%, and 99% (denoted M50, M70,
M90 and M99),v the ‘Coastal’ model with a RH of 50%, 70%, 90%, and 99% (denoted C50, C70,
C90, and C99), andv the ‘Tropospheric’ model with a RH of 50%, 90%, and 99% (denoted T50, T90,
and T99).
These 12 aerosol models represent non- or weakly-absorbing aerosols. The singlescattering albedo at 865 nm varies from 0.930 for the T50 model, to 1.0 for the O99
model, while the Ångström exponent between wavelengths 510 and 865 nm changes
from -0.087 for the O99 model to 1.53 for the T50 model.
These aerosol models are used to compute lookup tables (LUTs) for computing
La (λ) + Lra (λ). Briefly, for each aerosol model radiative transfer, computations arecarried out to determine Lpath (λ) as a function of the aerosol optical thickness τa (λ),
for a variety of sensor-sun geometries. For these computations the sea surface isassumed to be flat and free of whitecaps. The computations are carried out using
scalar radiative transfer (Gordon and Wang, 1994a) or more recently, complete
vector radiative transfer (Wang, 2006a). The appropriate Lr is then subtracted from
Lpath yielding La (λ) + Lra (λ), or equivalently, ρa (λ) + ρra (λ). For a given geometry,ρa (λ) + ρra (λ) is then fit to a fourth order polynomial in the single-scattered aerosol
reflectance ρas (λ), i.e.,234
ρa + ρra = aρas + bρas
+ cρas+ dρas
,

(2.3)

8

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

where a, b, c and d are constants,ρas (λ) ≡ωa (λ)τa (λ) pa (λ)ωa (λ)τa (λ) [Pa (λ, α+ ) + Pa (λ, α− ) [r (θ) + r (θ0 )]]≡4 cos θ cos θ0
4 cos θ cos θ0(2.4)
cos α± = ± cos θ cos θ0 + sin θ sin θ0 cos(φ − φ0 ),(2.5)

Pa is the aerosol scattering phase function at the appropriate scattering angle, θand φ are the polar and azimuth angles of the sensor’s view of the sea surface, θ0 ,and φ0 are the solar zenith and azimuth angles, and r is the Fresnel reflectance forthe indicated incidence angle (in air). The LUTs contain a, b, c and d constants for alarge number of viewing-sun geometries and for values of τa (λ) up to 0.8.
The procedure for estimating La (λ) + Lra (λ) or ρa (λ) + ρra (λ) is to estimate
this quantity in the NIR first, assuming negligible [Lw (λ)]N in that region of thespectrum for the open oceans. Using the aerosol LUTs, the sensor-measured spectral
variation of ρa (λ) + ρra (λ) at the two NIR bands can be used to estimate ρas (λ) for
the same two bands. As ρas (λ) is related directly to the aerosol phase function,
single scattering albedo, and optical thickness, it can be computed directly for eachaerosol model. It is then possible to select the most appropriate aerosol models forwhich the computed radiances are best matched with the measured values. Thisis accomplished by comparing the measured value of the single scattering epsilon(SSE) with those computed for each model (Gordon and Wang, 1994a; Wang and
Gordon, 1994; Wang, 2004). SSE is denoted (λi , λj ), where λi and λj are the two
NIR wavelengths, and(λi , λj ) ≡ρas (λi )ωa (λi )τa (λi )pa (λi )=.
ρas (λj )ωa (λj )τa (λj )pa (λj )(2.6)

This approach was used (and is still used today) because the SSE depends only on
the aerosol model, and not on the aerosol optical thickness. Based on the derived
SSE values in the NIR bands, the two most appropriate aerosol models (from theset of 12 models) are retrieved and used for estimation of the aerosol effects in thevisible bands La (λ) + Lra (λ). Therefore, the normalized water-leaving radiance inthe visible wavelengths [Lw (λ)]N can be derived through Equation 2.1.
For Case-2 waters, where the assumption that [Lw (λ)]N is negligible in the NIR
may be violated, the procedure is to:v use the derived [Lw (λ)]N to estimate [Lw (λ)]N in the NIR,v use this estimate of [Lw (λ)]N in the NIR to provide a new estimate of ρa (λ) +ρra (λ) in the NIR, andv use this as above to estimate ρa (λ) + ρra (λ) and hence [Lw (λ)]N in the visible.
This latter procedure can be iterated as many times as required for convergence.
For this report, we have implemented the Siegel et al. (2000) algorithm to estimate
the NIR ocean contributions in Case-2 waters.

Atmospheric Correction Algorithm Description

2.2

•

9

The MERIS Algorithm

Basic principles for the MERIS atmospheric correction scheme are described in Antoine and Morel (1998), and the practical implementation and tests are developed in
Antoine and Morel (1999), as described below. In this multiple scattering algorithm,
the path reflectance is derived globally to perform the atmospheric correction, instead of separately assessing ρa (λ) and ρr (λ). It is therefore based on the following
decomposition of the total reflectance at the top of atmosphere level (ρt (λ)):ρt (λ) = ρpath (λ) + t(λ)ρw (λ),(2.7)

where ρpath (λ) is the atmospheric path reflectance and t(λ) is the diffuse transmittance along the pixel-to-sensor path (approximated as per Gordon et al., 1983). The
reflectance ρpath is formed by all photons reaching the TOA after one or several
scattering events in the atmosphere, with the exception of those that entered theocean.
It was shown that the [ρpath /ρr ] ratios are monotonic and unique functions ofτa for a given aerosol and geometry (Antoine and Morel, 1998). Such functions allow
an aerosol type to be identified among several predefined models, by using LUTs
generated from radiative transfer simulations. These LUTs contain the coefficientsof the quadratic relationship between the ratio [ρpath /ρr ] and τa , for several aerosol
models, geometries, and wavelengths. A quadratic expression is used to account forthe saturating behavior of the [ρpath /ρr ] versus τa relationship for large values of
τa . For moderate τa values (<∼0.5) linearity between [ρpath /ρr ] and τa is actuallyobserved (for non-absorbing aerosols).
The scheme starts with computing [ρpath /ρr ] at two wavelengths in the NIR(λNIR1 and λNIR2 , where there is no marine signal), where ρpath is measured by thesensor and ρr is pre-computed. Because multiple scattering effects depend on theaerosol type, several values of τa (λNIR1 ) correspond to the value of [ρpath /ρr ] at
λNIR1 , each one being associated with a given aerosol model. This set of τa (λNIR1 )values is converted into the equivalent set at λNIR2 , using the spectral attenuation coefficients of each aerosol. Several values of the ratio [ρpath /ρr ] at λNIR2 correspondto these τa (λNIR2 ) values; they differ according to the aerosol type. Comparing thisset of values to the actual [ρpath /ρr ] ratio at λNIR2 allows the two aerosol models
that most closely bracket the actual [ρpath /ρr ] ratio to be selected. The remaining
steps of the algorithm rest on the assumption that the mixing ratio derived in thisway, is invariable with wavelength (Gordon and Wang, 1994a). It is then possible toestimate [ρpath /ρr ] for the visible wavelengths from its values at λNIR2 and λNIR1 ,provided that the relationships with τa have been previously established for theappropriate wavelengths. Atmospheric correction of the visible observations is
obtained by multiplying the ratio [ρpath /ρr ] by ρr , leading to ρpath , and, by difference with ρt , to the marine reflectance. The aerosol optical thickness is obtainedat each wavelength as the weighted average of the two values corresponding to10•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

the two bracketing aerosol models, again using the mixing ratio obtained from the
NIR bands. The accuracy of reflectance in the blue wavebands of such a multiple
scattering algorithm has been shown to be about ±0.002.
The algorithm implementation used for the present inter-comparison exercise
is described in Antoine and Morel (1999). The radiative transfer computations
needed to produce the necessary LUTs were performed with a scalar version of
the Matrix Operator Method (MOM) code (Fell and Fischer, 2001). The more recent
implementation into the ESA operational processing environment is somewhat
different. It still uses aerosol models from Shettle and Fenn (1979), but with a set of
12 aerosol models similar to the one used in the SeaWiFS processing. The Rayleighand aerosol LUTs are now generated from a successive order of scattering radiativetransfer code including polarization (Deuze et al., 1989).
This ‘Case-1 water algorithm’ (assumption of no marine signal in the NIR) is
applied over all water types, after application of a specific procedure (Moore et al.,1999), which removes the marine signal, if any, in the NIR bands.
A specific feature has been implemented in addition to the reference scheme for
non-absorbing aerosols, which allows absorbing aerosols to be detected using theobservations at 510 nm and assumptions about the marine signal at this wavelength(Nobileau and Antoine, 2005). When the presence of blue-absorbing aerosols isrevealed by this test, atmospheric correction is based on the dust models proposedby (Moulin et al., 2001a). This unique feature of the MERIS atmospheric corrections
is not further discussed here (but see Nobileau and Antoine, 2005; Antoine andNobileau, 2006).

2.3

The OCTS/GLI Algorithm

The OCTS/GLI algorithm shares its theoretical basis with that of SeaWiFS, although
the implementation of the algorithm has some differences. The theoretical aspectof the algorithm is described in Fukushima et al. (1998), while the implementation
details can be found in the NASDA-EOC (1997) document.
In the reflectance-based expression, the satellite-observed radiance ρt (λ) is
modelled as:
ρt (λ) = ρr (λ) + ρa (λ) + ρra (λ) + t(λ)t0 (λ)[ρw (λ)]N ,(2.8)

where ρr (λ) is Rayleigh reflectance, ρa (λ) is the reflectance that would be observed
if the atmosphere consisted of aerosol particles only, ρra is the Rayleigh-aerosol interaction term, [ρw (λ)]N is the normalized water-leaving reflectance (i.e., ρw (λ)/t0 (λ)),
and t0 (λ)(t(λ)) is the transmittance between sun and the ocean surface (between
satellite and the ocean surface). Note that, for simplicity, sun glitter reflectance andwhitecap reflectance are omitted from the equation.

Atmospheric Correction Algorithm Description•

11

The transmittance t(λ) (or similarly t0 (λ)) is expressed as a product of Rayleightransmittance tr (λ), absorptive gaseous transmittance toz (λ) and aerosol transmittance ta (λ), where tr (λ) and toz (λ) are easily given. In the OCTS algorithm, ta ismodelled as:ta (λ) = exp [− {1 − ωa (λ)η(λ)} τa / cos θ] ,(2.9)
where ωa is the aerosol single scattering albedo, η is the aerosol forward scattering
probability, and θ is the satellite zenith angle. In the evaluation of ta , the OCTS
algorithm assumes η is unity while ωa is determined through the atmosphericcorrection process.
In Equation 2.8, ρr (λ) is determined accurately by theory. Assuming that[ρw (λ)]N in the NIR bands are negligible, ρa (λ) + ρra (λ) can be obtained in the NIR
bands. Following the standard scheme for ocean-colour atmospheric correction
described in this report, the OCTS algorithm, in essence, estimates ρa (λ) + ρra (λ)
in the visible bands based on the observed ρa (λ) + ρra (λ) in the red and NIR bands(i.e. 670 and 865 nm).
Similar to the SeaWiFS algorithm, a set of 10 aerosol models are defined (theSeaWiFS algorithm uses 12 models). The first 9 models are: ‘Tropospheric’ models
with a RH of 50%, 80% and 90%, ‘Coastal’ models with the same set of RH, and‘Maritime’ models with a RH of 50%, 80%, and 98%, all defined based on the aerosol
models described in Shettle and Fenn (1979). The last one, ‘Asian dust’ aerosol isdefined based on the ground-level observation in an Asian dust event (Nakajima etal., 1989), although the model was rarely used because of its extremely low epsilon
values, i.e. Equation 2.6
The method for estimating ρa (λ) + ρra (λ) in the visible bands from the NIR
observed aerosol reflectance is almost the same as for the SeaWiFS algorithm, butinstead of relating ρa (λ) + ρra (λ) to ρas (λ), it is assumed that ρa (λ) + ρra (λ) for
each aerosol model M, wavelength, and scan geometry, can be given as a function ofaerosol optical thickness, τa , as follows:ρa (M, λ) + ρra (M, λ) = a1 (M, λ, θ, θ0 , ∆φ)τa (M, λ)+a2 (M, λ, θ, θ0 , ∆φ)τa2 (M, λ)(2.10)+a3 (M, λ, θ, θ0 , ∆φ)τa3 (M, λ),where θ and θ0 are satellite-zenith and solar-zenith angles, respectively, and ∆φ issatellite azimuth angle relative to sun. LUTs are generated for ai (M, λ, θ, θ0 , ∆φ) for
every few degrees of θ, θ0 , ∆φ for an appropriate set of τa values for every aerosol
type M, by conducting a series of radiative transfer simulation with the Rstar5b
code (Nakajima and Tanaka, 1988). In processing actual satellite data, the values ofai for given θ, θ0 , ∆φ are derived from 3-dimensional Lagrangian interpolation of
the table entries.
In addition to the aerosol LUTs, auxiliary aerosol lookup tables are used forsingle scattering albedo, extinction coefficient (Kext ), and phase function for every

12•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

aerosol model M, in addition to a Rayleigh reflectance lookup table, which was
generated through a series of vector radiative transfer simulations.
Given ρa (λ) + ρra (λ) at 670 and 865 nm bands, the algorithm calculates aerosol
optical thickness, τa , at these bands, assuming each one of the aerosol models
by solving the cubic Equation 2.10. Then, a model-wise ratio of τa (M, 670) toτa (M, 865), orτA (670)γE (670, 865) =,(2.11)τA (865)
where ‘E’ denotes ‘estimated’ is calculated to produce ‘average γE ’. This γE iscompared with ‘theoretical γ’ for each modelγT (M, 670, 865) =Kext (M, 670),
Kext (M, 865)

(2.12)

and a pair of aerosol models which have the closest γT to γE average is selected.
Using the aerosol lookup table for ai in Equation 2.10, ρa (λ) + ρra (λ) values for theselected two aerosol models are obtained for each visible band and used for interpolation to determine the final ρa (λ) + ρra (λ) to estimate tt0 ρw . The aerosol single
scattering albedo ωa , which is necessary for evaluation of aerosol transmittance, isdetermined from the aerosol model pair selected for that pixel. This completes the
pixel-wise OCTS atmospheric correction.
The GLI algorithm is based on the OCTS algorithm described above but with someenhancements. The earlier version (Version 1.5) of the GLI atmospheric correction
algorithm has a slightly different aerosol model set with no Asian dust model
included. It incorporates a bio-optical model and a neural network (Tanaka et al.,2004) to determine iteratively the magnitude of [ρw (λNIR )]N , which considers theeffect of inorganic suspended matter as well as phytoplankton. Version 2.1 of thisalgorithm introduces an empirical iterative scheme for absorptive aerosol correction.
The algorithm description can be found in NASDA-EOC (2004) and Toratani et al.
(2007), while Murakami et al. (2006) and Fukushima et al. (2007) evaluated theperformance of the algorithm in comparison with in situ data.

2.4

The POLDER Algorithm

The general idea of the algorithm is to use spectral bands in which ocean reflectanceis very low to assess aerosol quantity (optical thickness) and quality (Ångström
coefficient and model). This information is then extrapolated to ocean-colour bands
to correct the TOA signal from atmospheric perturbations. As in Gordon and Wang
(1994a), the aerosol inversion relies on models developed by Shettle and Fenn (1979).
In situations of eutrophic or Case-2 waters, the algorithm takes into account the
non-negligible ocean reflectance in the red. The algorithm also deals with absorbing
aerosols by exploiting directional information. These features, however, were not
implemented to produce the results discussed in Chapters 4 and 5 of this report.

Atmospheric Correction Algorithm Description•

13

The core of the algorithm is a two-step iterative process. In the first step, theaerosol model is determined for a given optical thickness. In the second step, theoptical thickness is computed for the model inverted in the first step. Because ofmultiple scattering effects, the two steps are run twice. The atmospheric correctionof the ocean-colour bands is then carried out using the aerosol model and optical
thickness inverted in the previous steps. Specific operations are implemented forsun-glint and whitecap correction and are discussed in detail in Appendix A.
Aerosols families are defined to deal with absorbing aerosols, ranging from a
non-absorbing aerosol family to a highly absorbing one. The idea is to run the coreof the algorithm for each family (one family is made of 12 aerosol models), and thento select the family that best fits directional observations.
The algorithm relies heavily on exact simulation of the TOA radiances for eachpixel and viewing direction, and for multiple geophysical conditions, including
polarization effects from molecules and aerosols scattering. The simulations are
CPU-consuming and are incompatible with global data set processing. For thatreason, lookup tables are computed beforehand. The simulated data are then linearlyinterpolated over multiple variables (solar and sensor viewing angles, aerosol models,
optical thicknesses).
Solar zenith angle, view zenith angle and relative azimuth angle are available foreach pixel and each viewing direction in the Level-1 product. Precision is sufficientfor the solar zenith angle (there is a lapse of about four minutes between the first andthe last sequence for an observed spot on Earth from POLDER), but for the viewing
zenith angle and relative azimuth angle a fine geometric registration correction iscomputed for each band, to account for the small lapse of 0.306 seconds between
measurements in the two different bands. The measurements are then associatedwith a geometry exactly defined by a triplet [θ0 (i), θ(λj , i), φ(λj , i)], where λj is the
wavelength of band j, and i is the index of viewing direction. Further details of the
POLDER algorithm are provided in Appendix A.

14•

Atmospheric Correction for Remotely-Sensed Ocean-Colour ProductsChapter 3
Simulated Testing Data Set
Menghua Wang, Howard R. Gordon and André MorelTo test the various atmospheric correction algorithms, a pseudo-TOA data set was
generated using the radiative-transfer simulation for the ocean-atmosphere system.
In generating the TOA data set, it was assumed that the radiative-transfer processes
for ocean and atmosphere are decoupled, i.e., processes such as photons scatteredfrom ocean water then scattered back into the water, and backscattered out again,
are ignored. Therefore, the TOA atmospheric path radiance and water-leaving
radiance can be computed separately. For a fair comparison, the radiative-transfer
code for generating pseudo-TOA atmospheric path radiance is different from all
the codes used for generating the lookup tables for the atmospheric correction
algorithms.

3.1

The TOA Atmospheric Path Radiance

3.1.1

Radiative-Transfer CodeThe forward Monte-Carlo vector radiative-transfer code was used to generate the
TOA atmospheric path radiance Lpath (λ) as in Equation 2.2. The forward MonteCarlo code was developed by Ding and Gordon based on their backward Monte-Carlocode (Ding and Gordon, 1994) and subsequently modified to include the polarization
effects. Typically, the Monte-Carlo code can produce the TOA path radiance within
an uncertainty of <∼0.1%. The simulations were carried out for a two-layer planeparallel atmosphere (PPA) model with 78% of molecules occupying the top layer(aerosols mixed with 22% of molecules confined in the bottom layer), overlying aflat Fresnel-reflecting ocean surface (black ocean). The PPA model is generally valid
for the solar and sensor zenith angles <∼80◦ , and the effects of the aerosol vertical
distribution on results of the atmospheric correction are negligible for non- andweakly-absorbing aerosols. The TOA atmospheric path radiances, Lpath (λ), were
simulated to include polarization effects. For each Monte-Carlo run, 15 million
photons were used to reduce the noise. Results show that, using the 15 million
photons, the random noise in the Monte-Carlo simulation is generally within ∼0.05%.
In addition, the Monte-Carlo results were compared with those from the vector
15

16

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

successive order of scattering (SOS) code (Gordon and Wang, 1992) for various cases.
They generally agreed with one another to within ∼0.3%, and differences in thereflectance within ∼5×10−4 .

3.1.2

Aerosol Models

The ‘Maritime’ aerosol model with a RH of 80% (M80) was used for generating thepseudo-TOA atmospheric path radiance Lpath (λ). The M80 model (not used in thelook-up tables generated by the various algorithms) represents weakly-absorbing
aerosols in the open ocean with a single-scattering albedo of 0.99 at 865 nm. The
aerosol optical thickness (at 865 nm) used for the M80 model is 0.05, 0.1, and 0.2.
In addition, the ‘Urban’ model from Shettle and Fenn (1979), with a RH of 80% (U80),
was used for Lpath (λ) generation to test the algorithm performance for strongly
absorbing aerosols. For the U80 model, the single-scattering albedo was 0.75, andan aerosol optical thickness of 0.1 was used (at 865 nm). Table 3.1 summarizes
all the parameters and models used for computation of the TOA atmospheric pathradiances, Lpath (λ).
Table 3.1 Parameters and models for generating the TOA atmospheric pathradiance Lpath (λ).
Radiative Transfer Code

Forward Monte-Carlo (Vector)
Two-layer plane-parallel atmosphere with 78%

Atmospheric Model

molecules at the top and aerosols mixed with 22%
molecules at the bottom

Ocean Surface
Photons used for EachA flat Fresnel-reflecting ocean surface
15 million

Monte-Carlo Run
Aerosol Models

Maritime RH=80%, Urban RH=80%

Aerosol Optical Thickness

M80: 0.05, 0.1, and 0.2; U80: 0.1

at 865 nm

3.2

Wavelengths (nm)412, 443, 490, 555, 670, 708, 765, 779, 865

Solar-Zenith Angles

0◦ , 45◦ , 60◦ , 65◦ , 70◦ , 78◦

Sensor-Zenith Angles

5◦ , 25◦ , 45◦ , 55◦ , 65◦

Relative Azimuth Angle

90◦

The Ocean Water Radiance Contributions

The ocean radiance contributions for both the Case-1 and Case-2 waters, which wereused for the pseudo-TOA radiance computations ([Lw (λ)]N component in Equation
2.1, or equivalently [ρw (λ)]N ), are described below.

Simulated Testing Data Set

3.2.1

•

17

Case-1 Water

Representative normalized water-leaving reflectance spectra for Case-1 waters were
derived using a semi-analytic model (Gordon, et al., 1988b). Briefly, in the Gordon etal. (1988b) model the normalized water-leaving reflectance [ρw (λ)]N is given by
(1 − ρ)(1 − ρ̄)1R[ρw (λ)]N = π
,
(3.1)
2
m
(1 − r R) Q
where ρ is the Fresnel reflectance of the sea surface at normal incidence, ρ̄ is theFresnel reflectance for irradiance from the sun and sky, m is the refractive index
of water, R is the irradiance reflectance just beneath the surface, r is the waterto-air surface reflectance for diffuse light (r ≈ 0.48), and Q = Eu /Lu , with Eu the
upwelling irradiance just beneath the sea surface and Lu the upwelling radiancein the same position propagating toward the zenith. A nominal value of Q is π ,the value assuming a totally diffuse upwelling light field. The quantity R/Q can be
related to the inherent optical properties of the water throughbb
R≈ 0.0949,
Q
a + bb

(3.2)

where the absorption coefficient of the medium is given by a = aw + ac and thebackscattering coefficient by bb = (bb )w + (bb )c , where the subscripts ‘w’ and‘c’ refer to water and its constituents, respectively. It has been shown (Gordon,
et al., 1975) that the sum a + bb can be related to the attenuation coefficient of
downwelling irradiance K just beneath the water surface throughK ≈ 1.16(a + bb ),

(3.3)

R
bb
≈ 0.11 .
Q
K

(3.4)

so Equation 3.2 becomes

In the Gordon et al. (1988b) model, K is divided according to K = Kw + KC + Kys ,where the subscripts ‘w’, ‘C’, and ‘ys’ stand for water, chlorophyll, and yellow
substance, respectively. Although this separation is not quite correct because K
cannot be rigorously summed over constituents, Gordon (1989) has neverthelessshown that for most purposes this approximation is a valid approximation. The
spectral values of Kw are taken from Smith and Baker (1978) and KC from Smithand Baker (1981). Kys is taken to be zero here. This is equivalent to assuming thatany background yellow substance is accounted for in KC .
The backscattering coefficient of the constituents (phytoplankton) is written as(bb )c = A(λ)C B(λ) ,(3.5)

where C is the chlorophyll concentration. The coefficients A(λ) and B(λ) werechosen in a manner that provided the best fit to the spectral radiance data collected

18•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Productsby Clark (1981). Given these quantities, R/Q in Equation 3.2 is determined as afunction of C. Then assuming Q = π (the value for a totally diffuse upwelling lightfield), R is determined for the computation of (1 − r R). These are then inserted
into Equation 3.1 providing [ρw (λ)]N as a function of C. Figure 3.1a shows thenormalized water-leaving reflectance [ρw (λ)]N as a function of the wavelength forchlorophyll concentrations of 0.03, 0.1, 0.3, and 1.0 mg/m3 . These spectra should
be representative of those in typical Case-1 waters and sufficiently accurate for the
purpose of this atmospheric correction study.

3.2.2

Case-2 Water Examples

Two examples of the ocean contributions from Case-2 waters, which correspond to
typical sediment-dominated and yellow substance dominated waters, are used forthe pseudo-TOA radiance computations.
The first example corresponds to sediment-dominated Case-2 waters. It isderived from actual irradiance measurements (upward and downward irradiances
just below the surface, Eu and Ed ), which were performed at a station off Cap
Corveiro (Morocco-Mauritania, Station #16, 16 March 1974 at 17◦ 03 W, 21◦ 47.5 N,
water depth 37 m) during the CINECA-5 cruise (Cooperative Investigation of the NE
Central Atlantic, a sub-program of the CUEA, Coastal Upwelling Ecosystems Analysis).
The high particle load resulted from the re-suspension of bottom sediments due towave action generated by strong trade winds. The scattering coefficient, b(λ), at 550
nm was between 3.1 and 3.9 m−1 , and the chlorophyll concentration ranged from
1.1 to 1.9 mg m−3 . Such turbid milky waters were encountered along this arid coast
within a strip delimited by the shoreline and the 40 or 50 m isobaths (Morel, 1982).
The second example is typical of yellow substance dominated Case-2 water. The
irradiance ratio, R = Eu /Ed , was determined in Saanich inlet (Sidney, Vancouver
Island, BC, Canada) on 7 August 1979. The water was dark brownish, almost blackwith b(550) around 1.2 m−1 and chlorophyll about 4.5 mg m−3 . The high yellow
substance content of terrigenous origin originated from the drainage of the forest
soil.
For both examples, the irradiance reflectance, R(λ), was transformed into normalized water-leaving reflectance [ρw (λ)]N = R(λ)F0 (λ)(<0 /Q0 ) (see Appendix D).
Figure 3.1b provides the normalized water-leaving reflectance [ρw (λ)]N as a function of the wavelength for sediment-dominated water observed off the Mauritaniancoast and yellow substance-dominated water acquired from an inlet in Vancouver
Island. Table 3.2 summarizes model and data used for computations of the ocean
normalized water-leaving reflectance [ρw (λ)]N (or radiance [Lw (λ)]N ).

Simulated Testing Data Set•

Figure 3.1 Examples of the ocean normalized water-leaving reflectance[ρw (λ)]N as a function of the wavelength for (a) Case-1 waters for chlorophyll concentrations of 0.03, 0.1, 0.3, and 1.0 mg/m3 and (b) Case-2 waters
for sediment-dominated water observed off the Mauritanian coast, and yellow
substance-dominated water acquired from an inlet in Vancouver Island, respectively. Note that reflectance values at 749, 765 and 865 nm are null for the
Case-1 waters.

19

20

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Table 3.2

Parameters for generating ocean normalized water-leaving radiance [Lw (λ)]N .
Case-1 Waters

Case-2 Waters

Model data: Gordon et al. (1988b)

Two examples from measurements

semianalytic model

3.3

Chlorophyll concentrations:

Sediment-dominated:

0.03, 0.1, 0.3, and 1.0 mg/m3

Data from the Mauritanian coast

Black ocean assumed for

Yellow substance-dominated:wavelengths > 670 nm

Data from an inlet in Vancouver Island

The TOA Radiance Data Set

With the simulated TOA atmospheric path radiance Lpath (λ) and the modelled(or observed) ocean water contributions [Lw (λ)]N , the TOA radiance Lt (λ) as inEquation 2.1 can be computed by ignoring both Lwc (λ) and Lg (λ) terms, i.e.,
Lt (λ) = Lr (λ) + La (λ) + Lra (λ) + t(λ)t0 (λ) cos θ0 [Lw (λ)]N ,(3.6)

where terms t0 (λ) and t(λ) are calculated according to Yang and Gordon (1997)
with appropriate aerosol models (M80 or U80). The contributions of Lwc (λ) andLg (λ) are ignored because the algorithm performance comparisons are focusing on
the aerosol corrections. In addition, the term Lg (λ) is generally masked out, while
the Lwc (λ) contribution was found to be less important than originally expected(Gordon and Wang, 1994b; Moore et al., 2000).
Figure 3.2 shows some examples of the simulated TOA reflectance ρt (λ) as afunction of the wavelength for various cases. Figure 3.2a provides examples ofthe simulated ρt (λ) for three typical water types, i.e., Case-1 water with a chlorophyll concentration of 0.1 mg/m3 , sediment-dominated water (Case-2), and yellow
substance-dominated water (Case-2), for the M80 aerosols with aerosol optical
thickness at 865 nm (τa (865)) of 0.1, while Figures 3.2b–d provide the TOA totalreflectance ρt (λ) and the Rayleigh reflectance contribution ρr (λ), as well as a moredetailed reflectance contribution partition for each of these three cases. These
are all for a case of the solar-zenith angle of 60◦ , sensor-zenith angle of 45◦ , andrelative-azimuth angle of 90◦ . The right side of Figures 3.2b–d show the scale forthe reflectance ratio value indicated in the plot. For example, results in Figure 3.2b
show that, for the case of the M80 model with τa (865) of 0.1 and with chlorophyll
concentration of 0.1 mg/m3 , the TOA atmospheric path reflectance ρpath (λ) contributes about 93.6%, 90.2%, 87.9%, 89.2%, 94.5% and 98.7% in the TOA reflectancefor wavelengths at 412, 443, 490, 510, 555, and 670 nm, respectively. In other words,
the corresponding TOA water-leaving reflectance t(λ)ρw (λ) contributes about 6.4%,
9.8%, 12.1%, 10.8%, 5.5%, and 1.3% in the TOA reflectance at these wavelengths. On
the other hand, for the sediment-dominated waters, Figure 3.2c shows that the
TOA water-leaving reflectance contributes about 5.8%, 11.8%, 26.3%, 30.6%, 39.0%,

•Figure 3.2 Examples of the simulated TOA reflectance ρt (λ) (testing data set) as a function of the wavelength for the M80
aerosol model with τa (865) of 0.1 and for (a) cases with both Case-1 and Case-2 waters, (b) Case-1 water with chlorophyll
concentration of 0.1 mg/m3 , (c) Case-2 with sediment-dominated waters, and (d) Case-2 with yellow substance-dominatedwaters. Plots (b)–(d) also present results of ratio values for ρpath (λ)/ρt (λ) and ρr (λ)/ρt (λ) (scaled on the right side).

Simulated Testing Data Set

21

22

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

16.4%, 8.2%, 3.7%, 3.0%, and 2.4% in the TOA reflectance for wavelengths at 412,
443, 490, 510, 555, 670, 708, 765, 779, and 865 nm, respectively, while for theyellow substance-dominated waters Figure 3.2d shows that these values are reduced dramatically to 0.2%, 0.4%, 1.2%, 1.7%, 3.6%, 5.3%, 3.8%, 1.5%, 1.2%, and 1.0%,
respectively.
Results in Figure 3.2 demonstrate that the ocean contributions comprise onlya small portion of the sensor-measured signals in the visible wavelengths. Thisis especially the case for the waters dominated by yellow substances. Therefore,
for such waters sufficiently accurate atmospheric correction in the blue and green
bands is extremely difficult, if not impossible. Results in Figure 3.2 also indicate theimportance of the vicarious calibration for ocean-colour remote sensing. It requires
a calibration accuracy of ∼0.1%. Examples of the Case-2 waters in Figure 3.2c andFigure 3.2d also show that the NIR black ocean assumption is not valid for theseocean waters (Siegel, et al., 2000; Wang and Shi, 2005).
The simulated TOA reflectance ρt (λ) (or radiance Lt (λ)) spectra are used as inputs for testing the performance of the various atmospheric correction algorithms.

Chapter 4
Comparison Results
Menghua Wang, David Antoine, Robert Frouin, Howard R. Gordon,
Hajime Fukushima, André Morel, Jean-Marc Nicolas and Pierre-Yves
Deschamps

With inputs of the pseudo-TOA reflectance ρt (λ) for various atmosphere and oceancases, the performance of various atmospheric correction algorithms is evaluated.
Specifically, results are compared with the ‘true’ normalized water-leaving radiance[Lw (λ)]N at 443, 490, and 555 nm, and radiance ratio values of [Lw (443)]N /[Lw (555)]N and [Lw (490)]N /[Lw (555)]N for Case-1 (Table 4.1) and Case-2 (Table
4.2) waters. Some example results of the retrieved aerosol optical thickness (AOT)
data from the four algorithms for typical Case-1 waters are also provided anddiscussed in the following sections. Note that [Lw (λ)]N data at 412 nm are notincluded because POLDER does not have a 412 nm band.
True water parameters for Case-1 waters.

Table 4.1

Case-1 Water with Pigment Concentration C in mg/m3

Parameter

0.03

0.1

0.3

1.0

[Lw (443)]N †

2.309

1.668

0.761

0.333

†

1.510

1.398

0.886

0.483

[Lw (555)]N †

0.283

0.335

0.344

0.306

[Lw (490)]N /[Lw (555)]N

8.174

4.978

2.212

1.088

[Lw (490)]N /[Lw (555)]N

5.344

4.173

2.574

1.578

[Lw (490)]N†−2

Units mW cm

−1

µm

−1

sr

4.1

The Open Ocean (Case-1 Waters)

4.1.1

Ocean-Colour Parameters

Figure 4.1 provides some examples of the results of algorithm performance for atypical Case-1 water with maritime aerosols. Results in Figure 4.1 are ratio values(derived/true) of various ocean-colour parameters as a function of the air mass,23

•

Figure 4.1 Ratio values (derived/true) of various ocean-colour parameters as a function of the air mass from atmosphericcorrection algorithms of SeaWiFS/MODIS, MERIS, OCTS/GLI, and POLDER for (a) [Lw (λ)]N at 443 nm, (b) [Lw (λ)]N at 490 nm,(c) ratio [Lw (443)N /[Lw (555)]N , and (d) ratio [Lw (490)]N /[Lw (555)]N . These results are for the M80 aerosols with aerosol
optical thickness of 0.1 at 865 nm and for open ocean (Case-1) water with pigment concentration of 0.1 mg/m3 .

24
Atmospheric Correction for Remotely-Sensed Ocean-Colour ProductsComparison Results

25

True water parameters for Case-2 waters.

Table 4.2

ParameterCase-2 Waters
Sediment

Yellow SubstanceDominated Water

Dominated Water

†

2.053

0.061

[Lw (490)]N †

3.619

0.123

[Lw (555)]N †

3.650

0.224

[Lw (443)]N /[Lw (555)]N

0.562

0.272

[Lw (490)]N /[Lw (555)]N

0.991

0.550

[Lw (443)]N

†

•

−2

Units mW cm

−1

µm

−1

sr

which is defined as air mass = 1/ cos θ0 + 1/ cos θ, from atmospheric correction algorithms of SeaWiFS/MODIS, MERIS, OCTS/GLI, and POLDER, respectively. Figures 4.1aand Figure 4.1b are for the ratio of the derived normalized water-leaving radiance[Lw (λ)]N at wavelengths of 443 and 490 nm, while Figure 4.1c and Figure 4.1d are
the radiance ratio values of [Lw (443)]N /[Lw (555)]N and [Lw (490)]N /[Lw (555)]N ,respectively. These results are for the M80 aerosols with aerosol optical thicknessof 0.1 at 865 nm and for open ocean water (Case-1) with a chlorophyll concentrationof 0.1 mg/m3 . Results show that, overall, all four atmospheric correction algorithms
performed quite well for cases with moderate air mass values. Some quantitative
comparisons in statistics for typical open ocean cases are also provided in Table
4.3, which shows the mean and standard deviation (STD) values of the ratio (derived/true) values for various ocean-colour parameters ([Lw (λ)]N at wavelengths of443, 490, and 555 nm, as well as radiance ratios for [Lw (443)]N /[Lw (555)]N and[Lw (490)]N /[Lw (555)]N ). The mean and STD values were derived for Case-1 waters
with a chlorophyll concentration of 0.1 mg/m3 and for cases with air mass values< 5.5. They are for the M80 aerosols with AOT at 865 nm of 0.05, 0.1, and 0.2. As
expected, cases with large AOTs (e.g., 0.2) generally have larger uncertainties in thederived water-leaving radiance data. We have only listed results for various aerosol
optical thicknesses with a global average chlorophyll concentration for open oceans
because results of atmospheric correction depend strongly on the aerosol properties.
Uncertainties for other Case-1 waters can be easily computed from Table 4.1 andTable 4.3, as the error in atmospheric correction is independent of [Lw (λ)]N , e.g.,
ratio values for [Lw (443)]N with C = 0.03 mg/m3 are closer to 1 than those with
C = 0.1 mg/m3 , but ratios are lower for cases with C = 0.3 and 1.0 mg/m3 .

4.1.2

Aerosol Optical Thickness Results

In deriving the ocean-colour parameters from satellite-measured radiance spectra(as discussed in Chapter 2), the aerosol radiance contributions in the visible must be
estimated accurately and removed (atmospheric correction). Therefore, ocean-colour

26•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Figure 4.2 Ratio values (derived/true) of the AOT data at 865 nm as a functionof the air mass from atmospheric correction algorithms of (a) SeaWiFS/MODIS,MERIS, OCTS/GLI, and POLDER and (b) comparison of the derived ratio in the
AOT data for using the scalar and vector aerosol lookup tables (including
polarization effects). These results are for the M80 aerosols with an aerosol
optical thickness of 0.1 at 865 nm and for open ocean (Case-1) water with achlorophyll concentration of 0.1 mg/m3 .

Comparison Results•

27

Table 4.3 Statistics (mean and standard deviation) for Case-1 water for various
AOT data.
C=0.1

Mean Ratio of Derived/True Value ± STD

3

mg/m
Parameterand for

SeaWiFS/MODIS

MERIS

OCTS/GLIPOLDERτa (865)[Lw (443)]N[Lw (490)]N

0.05

0.968±0.025

0.971±0.030

1.014±0.028

0.933±0.053

0.10

0.966±0.027

0.998±0.047

1.036±0.067

0.940±0.044

0.20

0.944±0.048

1.022±0.101

1.053±0.121

0.923±0.055

0.05

0.975±0.018

0.983±0.022

0.989±0.018

0.948±0.040

0.10

0.977±0.017

1.001±0.042

1.004±0.046

0.952±0.032

0.20

0.961±0.037

1.017±0.089

1.009±0.086

0.930±0.046

0.05

0.961±0.034

0.995±0.043

0.946±0.038

0.919±0.060

0.10

0.955±0.043

1.020±0.083

0.978±0.033

0.906±0.069

0.20

0.923±0.113

1.062±0.190

1.019±0.104

0.846±0.114[Lw (443)]N /0.05

1.008±0.019

0.976±0.022

1.073±0.057

1.016±0.018[Lw (555)]N

0.10

1.013±0.026

0.981±0.034

1.060±0.055

1.041±0.036

0.20

1.035±0.098

0.973±0.064

1.034±0.054

1.104±0.098[Lw (490)]N /0.05

1.016±0.020

0.988±0.023

1.047±0.044

1.033±0.028[Lw (555)]N

0.10

1.025±0.033

0.985±0.037

1.028±0.038

1.055±0.050

0.20

1.055±0.113

0.969±0.069

0.993±0.043

1.113±0.109

0.05

1.130±0.091

1.107±0.057

1.015±0.035

0.970±0.019

1.139±0.065

1.008±0.032

1.026±0.023

1.108±0.053

0.963±0.030

0.994±0.004[Lw (555)]N†

1.036±0.016
τa (865)0.10

1.075±0.034
1.042±0.022†
1.061±0.024

0.20†

1.043±0.018†

Use the vector aerosol lookup tables.

satellite sensors can also give access to aerosol optical properties, in particular AOT.
Figure 4.2 displays examples of evaluation results for the derived AOT. Figure 4.2a
provides the resulting ratio values in the retrieved AOT (derived/true) from thefour algorithms as a function of the air mass for a maritime aerosol (M80 model)
with the AOT of 0.1 at 865 nm, and for Case-1 ocean water with a chlorophyll
concentration of 0.1 mg/m3 . Some relatively larger errors for the case with air
mass ∼2 likely resulted from the effect of the glint contamination. Results in Figure
4.2a show that the AOT data derived from the POLDER and OCTS/GLI algorithms
are quite accurate with uncertainties within ∼5%, while both the SeaWiFS/MODIS
and MERIS algorithms over-estimated the AOT data with uncertainties of ∼10% for
SeaWiFS/MODIS and ∼15% for the MERIS algorithms. Overestimation of the AOT
data for the SeaWiFS/MODIS algorithm (probably also for the MERIS algorithm) is
partly due to the use of the scalar aerosol lookup tables, which do not include

28•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

polarization effects (Wang, 2006a). Note that the pseudo data were generated using
the vector RTE. POLDER has used the vector aerosol lookup tables for the dataprocessing in retrievals of ocean colour and aerosol parameters. Results in Figure
4.2b show that using the vector aerosol lookup tables, which include polarization
effects, the SeaWiFS/MODIS-derived AOT data are improved, with uncertainties
usually within ∼5%, which is consistent with the results from Wang (2006a). Some
detailed discussions for effects of the polarization on the other aerosol models, forexample the T80 model, can be found in Wang (2006a).
Statistics (mean and STD) comparison results for the AOT at 865 nm of 0.05,
0.1, and 0.2 for the four operational algorithms, as well as for the SeaWiFS/MODIS
algorithm using the vector aerosol lookup tables are presented in Table 4.3 (the lastrow). The OCTS/GLI and POLDER algorithms produced AOT products with uncertainties usually within ∼3% (Table 4.3). Both SeaWiFS/MODIS and MERIS operationalalgorithms overestimate the AOT product for the M80 aerosols. With the vector
aerosol lookup tables, however, the SeaWiFS/MODIS algorithm not only improves
the bias error in the derived AOT, but also the noise error (STD values) is reduced
significantly. It is worth noting that even though the AOT data are overestimatedby SeaWiFS/MODIS and MERIS algorithms, both algorithms still derived accurate
ocean-colour products. Wang (2006a) found that for aerosols with spectrally flat
SSE (or Ångström exponent), e.g., maritime aerosols, ocean colour products can still
be derived accurately even though the AOT data are overestimated. However, foraerosols with significant spectral variation in SSE, e.g., tropospheric aerosols, errors
in the AOT data will result in relatively large uncertainties in the ocean colour products (Wang, 2006a). Thus, the comparison of AOTs does not necessary allow one
to evaluate and compare the performance of the different atmospheric correction
algorithms. Note that, for the open ocean, aerosols often exhibit spectrally flat SSE,
while in coastal regions, aerosols with large spectral variation SSE are usually the
case.

4.2

The Coastal Ocean Region (Case-2 Waters)

4.2.1

Sediment-Dominated Waters

Sample results for a Case-2 sediment-dominated water are shown in Figure 4.3.
Presented similarly to Figure 4.1, this figure shows ratio values (derived/true) ofvarious ocean-colour parameters as a function of the air mass for atmosphericcorrection algorithms of SeaWiFS/MODIS, MERIS, OCTS/GLI, and POLDER, and fora sediment-dominated Case-2 water as shown in Figure 3.1b. Figures 4.3a andb are for the ratio (derived/true) of the derived [Lw (λ)]N at wavelengths of 443
and 490 nm, while Figures 4.3c and d are the ratio (derived/true) of parameters[Lw (443)]N /[Lw (555)]N and [Lw (490)]N /[Lw (555)]N , respectively. Overall all
four atmospheric correction algorithms underestimated the [Lw (λ)]N values in the•Figure 4.3 Ratio values (derived/true) of various ocean-colour parameters as a function of the air mass from atmosphericcorrection algorithms of SeaWiFS/MODIS, MERIS, OCTS/GLI, and POLDER for (a) [Lw (λ)]N at 443 nm, (b) [Lw (λ)]N at 490 nm,(c) ratio [LW (443)]N /[LW (555)]N , and (d) ratio [Lw (490)]N /[Lw (555)]N . These results are for the M80 aerosols with aerosol
optical thickness of 0.1 at 865 nm and for a sediment-dominated Case-2 water.

Comparison Results

29

30

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

visible (e.g., at wavelengths of 443 and 490 nm) due to the incorrect assumption
in the estimation of the NIR ocean contributions. The biased error in the derived[Lw (λ)]N gets worse with the decrease of the wavelength, for example in the blue
bands, because the extrapolation error in the aerosol contribution (biased high)increases with increase of wavelength difference from the NIR band. However, theradiance ratio values were derived relatively accurately for all four algorithms, inparticular, for the parameter [Lw (490)]N /[Lw (555)]N . The coherent errors in thederived [Lw (490)]N and [Lw (555)]N cancel each other in the corresponding ratio
value. This suggests that, for the current four operational atmospheric correction
algorithms, it may be better to use the normalized water-leaving radiance ratios(particularly for [Lw (490)]N /[Lw (555)]N ) for deriving the water properties for
sediment-dominated Case-2 waters.
Table 4.4 Statistics (mean and standard deviation) for Case-2 sedimentdominated water for various AOT data.
Case-2

Mean Ratio of Derived/True Value ± STD

Sediment
Parameter

Water andfor

SeaWiFS/MODIS

MERIS

OCTS/GLIPOLDER

0.05

0.874±0.027

0.778±0.057

0.904±0.047

0.749±0.062

0.10

0.878±0.028

0.748±0.065

0.933±0.080

0.771±0.059

0.20

0.869±0.043

0.650±0.182

0.956±0.116

0.768±0.057

0.05

0.942±0.012

0.880±0.037

0.940±0.021

0.873±0.026

0.10

0.945±0.011

0.848±0.030

0.939±0.030

0.880±0.023

0.20

0.942±0.016

0.770±0.059

0.923±0.038

0.873±0.023

0.05

0.961±0.008

0.911±0.033

0.928±0.007

0.901±0.014

0.10

0.961±0.007

0.875±0.032

0.914±0.006

0.902±0.014

0.20

0.959±0.007

0.796±0.048

0.885±0.011

0.894±0.014[Lw (443)]N /0.05

0.909±0.021

0.853±0.039

0.974±0.050

0.831±0.056[Lw (555)]N

0.10

0.913±0.024

0.856±0.082

1.021±0.088

0.854±0.053

0.20

0.906±0.039

0.820±0.238

1.081±0.134

0.858±0.051[Lw (490)]N /0.05

0.980±0.005

0.966±0.010

1.013±0.021

0.968±0.013[Lw (555)]N

0.10

0.983±0.006

0.970±0.025

1.027±0.033

0.976±0.011

0.20

0.983±0.011

0.968±0.066

1.043±0.045

0.976±0.011

τa (865)[Lw (443)]N[Lw (490)]N[Lw (555)]N

Some statistics results for sediment-dominated Case-2 waters are presented inTable 4.4 for the M80 aerosols with the AOT at 865 nm of 0.05, 0.1, and 0.2. Resultsin Table 4.4 show that, for the sediment-dominated Case-2 water with the AOT
of 0.1, errors in the derived [Lw (443)]N , [Lw (490)]N , and [Lw (555)]N from fouralgorithms vary from ∼7-25%, ∼5-15%, and ∼4-10%, respectively, while the derived[Lw (443)]N /[Lw (555)]N and [Lw (490)]N /[Lw (555)]N change from ∼2-15% and∼2-3%, respectively. Thus, errors in the radiance ratios are reduced significantly. For

Comparison Results•

31

the ratio of [Lw (490)]N /[Lw (555)]N , all four algorithms produced results within
5% for all three AOT values.

4.2.2

Yellow Substance-Dominated Waters

As one would expect, for the yellow substance-dominated waters, deriving thenormalized water-leaving radiance accurately from satellite sensor measurements isextremely difficult, particularly for [Lw (λ)]N values at the short visible wavelengths.
Not only are there non-negligible ocean contributions at the NIR bands (Figure 3.1b),
but the ocean signals in the visible bands are also very small, compared with the[Lw (λ)]N spectra over open oceans (Case-1 waters) and sediment-dominated Case-2
waters. For example, the [Lw (λ)]N at 443 nm for typical open ocean, sedimentdominated, and yellow substance-dominated water are about 1.668, 2.053, and0.061 mW cm−2 µm−1 sr−1 respectively (Tables 4.1 and 4.2), corresponding to thecontributions of the sensor-measured TOA signal of about 9.8%, 11.8%, and 0.4%,
respectively (Section 3.3).
Table 4.5 Statistics (mean and standard deviation) for Case-2 yellowsubstance-dominated water for various AOT data.
Case-2

Mean Ratio of Derived/True Value ± STD

YellowParameter

sub Water
and for

SeaWiFS/MODIS

MERIS

OCTS/GLIPOLDER

0.05

0.676±1.397

0.274±1.027-0.763±0.620-2.749±1.707

0.10

0.482±1.695

2.979±2.601

0.501±1.581-8.324±0.908

0.20

0.774±1.721

5.407±5.656

2.142±3.251-8.036±0.993

0.05

1.097±0.500

0.480±0.281

0.298±0.178-0.498±0.581

0.10

1.071±0.670

1.448±0.820

0.714±0.533-2.794±0.283

0.20

1.228±0.567

2.264±1.923

1.243±1.071-2.750±0.353

0.05

1.159±0.189

0.703±0.109

0.681±0.027

0.413±0.150

0.10

1.140±0.275

0.971±0.173

0.748±0.060-0.412±0.073

0.20

1.175±0.168

1.175±0.512

0.860±0.187-0.418±0.106[Lw (443)]N /0.05

0.404±1.499

0.386±1.543-1.146±0.919-10.370±12.002[Lw (555)]N

0.10

0.046±1.889

2.759±2.163

0.524±1.927

20.462±1.669

τa (865)[Lw (443)]N[Lw (490)]N[Lw (555)]N

0.20

0.502±1.598

2.793±5.086

1.932±2.697

19.837±2.585[Lw (490)]N /0.05

0.896±0.398

0.665±0.388

0.432±0.249-2.263±3.430[Lw (555)]N

0.10

0.832±0.514

1.401±0.592

0.913±0.586

6.877±0.599

0.20

1.003±0.414

1.377±1.554

1.288±0.764

6.773±0.785

In this exercise, the [Lw (λ)]N at 490 nm for the yellow-substance type of water is0.123 mW cm−2 µm−1 sr−1 , compared with values of 1.398 and 3.619 mW cm−2 µm−1
sr−1 for typical open ocean (Case-1) and sediment type waters. With this in mind,

32•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Figure 4.4 Ratio values (derived/true) of various ocean-colour parameters as
a function of the air mass from atmospheric correction algorithms of SeaWiFS/MODIS, MERIS, and OCTS/GLI, for (a) [Lw (λ)]N at 490 nm and (b) ratio[Lw (490)]N /[Lw (555)]N . These results are for the M80 aerosols with aerosol
optical thickness of 0.1 at 865 nm and for a yellow substance-dominated Case-2
water. Note POLDER results are out of scale and are not shown in here.

Comparison Results•

33

we have only shown the comparison results for [Lw (λ)]N at 490 nm (Figure 4.4a)and the normalized water-leaving radiance ratio of [Lw (490)]N /[Lw (555)]N (Figure4.4b). The plot scales are also considerably enlarged (from −5 to 5) in Figure 4.4,
compared with those in Figure 4.1 and Figure 4.3. Note that the POLDER results are
not shown in Figure 4.4 because they are all outside the scale (see Table 4.5).
Statistics (mean and STD) comparison results for a yellow substance-dominatedwater and for various AOT values are summarized in Table 4.5. Results show
significantly large errors in the derived [Lw (443)]N , as well as for the parameter [Lw (443)]N /[Lw (555)]N , from all four algorithms. Conversely, errors for[Lw (λ)]N at wavelengths of 490 and 555 nm are reduced, compared with thatfor the blue bands. The sensor-derived [Lw (490)]N , [Lw (555)]N , and ratio results of [Lw (490)]N /[Lw (555)]N may still be used with caution for retrieval ofproperties from yellow substance dominated waters. The relationships between
the water-leaving radiance parameters and water properties for the Case-2, yellow
substance-dominated waters are certainly different from the Case-1 waters.

4.3

Strongly-Absorbing Aerosols

4.3.1

Comparison Results

Figure 4.5 and Table 4.6 provide algorithm comparison results for the stronglyabsorbing aerosols (U80 model) combined with a typical open ocean Case-1 water.
The U80 aerosol particles are very strongly absorbing with the single-scattering
albedo values of 0.783, 0.782, 0.781, 0.774, 0.762, and 0.748 for wavelengthsof 443, 490, 555, 765, and 865 nm, respectively. Figure 4.5a shows comparison results for the ratio (derived/true) of sensor-derived [Lw (λ)]N at the wavelength of 443 nm, while Figure 4.5b shows the comparison results for the ratioof [Lw (443)]N /[Lw (555)]N . The pseudo-TOA radiance data were simulated witha two-layer atmosphere (aerosols in the bottom) for the U80 model with the AOT
of 0.1 at 865 nm, overlying a clear, open ocean, Case-1 water (chlorophyll = 0.1
mg/m3 ). Obviously, for this strongly-absorbing aerosol case, all four algorithms
fail badly at deriving accurate [Lw (λ)]N , i.e., the derived [Lw (λ)]N in the visible issignificantly biased low (Figure 4.5a) with mean errors from the four algorithms
of about 35 − 60% (Table 4.6). However, the radiance ratio values are not that bad,particularly for the parameter [Lw (443)]N /[Lw (555)]N . Indeed, results in Table
4.6 show that mean errors in the derived [Lw (443)]N /[Lw (555)]N are all within∼10%. Thus, the radiance ratio values of [Lw (443)]N /[Lw (555)]N may still be used

34•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

for deriving reasonable chlorophyll concentration values even though the [Lw (λ)]Nvalues are not very accurate.
Table 4.6 Statistics (mean and standard deviation) for strongly absorbing
aerosols (U80) with Case-1 water.
C=0.1

Mean Ratio of Derived/True Value ± STD

mg/m3
Parameterand for

SeaWiFS/MODIS

MERIS

OCTS/GLIPOLDERτa (865)[Lw (443)]N

0.10

0.438±0.201

0.556±0.104

0.535±0.140

0.432± 0.232[Lw (490)]N

0.10

0.561±0.161

0.654±0.082

0.627±0.111

0.563±0.181[Lw (555)]N

0.10

0.383±0.276

0.602±0.170

0.567±0.195

0.469±0.257[Lw (443)]N /0.10

1.077±0.597

0.975±0.210

0.995±0.200

0.885±0.188

0.10

1.416±1.134

1.154±0.254

1.214±0.376

1.327±0.770[Lw (555)]N[Lw (490)]N /[Lw (555)]N

The effects of the strongly-absorbing aerosols over Case-2 waters can be understood and explained by plotting the TOA reflectance ratio [ρt − ρr ](λ, 865) =[ρt (λ) − ρr (λ)]/[ρt (865) − ρr (865)] as a function of the wavelength for various
cases. Figure 4.6a compares [ρt − ρr ](λ, 865) values for M80 (weakly-absorbing) andU80 (strongly-absorbing) aerosols with three different ocean waters, i.e., a typicalclear Case-1 water mass, sediment-dominated Case-2 water, and yellow substancedominated Case-2 water. For a typical clear Case-1 water mass, the derived [Lw (λ)]Nin the visible bands would be significantly underestimated (Figure 4.5a) with a nonor weakly-absorbing aerosol (e.g., M80 in Figure 4.6a) for estimation of the aerosol
radiance contributions, i.e., as shown in Figure 4.6a the [ρt − ρr ](λ, 865) values atthe visible are larger for the M80 model than the U80 model, leading to overestimation of aerosol radiance contribution and underestimation of the ocean radiance
contributions. Similar cases are also shown for the two Case-2 waters in Figure
4.6a. However, underestimations of [Lw (λ)]N values are even worse due to ocean
contributions at the NIR bands (combined problems for turbid waters in Figure
4.3 and Figure 4.4 and strongly-absorbing aerosols in Figure 4.5). Furthermore,another difficulty in dealing with this issue of strongly-absorbing aerosols, is thatthe aerosol radiance contributions depend on the aerosol vertical distribution, which
is discussed further in the following section.

4.3.2

Effects of Vertical Distribution of Absorbing Aerosol

The effect of the vertical distribution of absorbing aerosols on the satellite-derived[Lw (λ)]N values can be demonstrated through the results in Figure 4.6b, whichshows results of the TOA reflectance ratio as a function of the wavelength, for astrongly-absorbing aerosol (U80) with aerosol vertical distributions of two-layer

Comparison Results•

Figure 4.5 Ratio values (derived/true) of various ocean-colour parameters as
a function of the air mass from atmospheric correction algorithms of SeaWiFS/MODIS, MERIS, OCTS/GLI, and POLDER for (a) [Lw (λ)]N at 443 nm and(b) ratio [Lw (443)]N /[Lw (555)]N . These results are for the U80 (stronglyabsorbing) aerosols with aerosol optical thickness of 0.1 at 865 nm and foropen ocean (Case-1) water with a chlorophyll concentration of 0.1 mg/m3 .

35

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Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Figure 4.6 Reflectance ratio of [ρt (λ) − ρr (λ)]/[ρt (865) − ρr (865)] as a function of the wavelength for various cases, demonstrating the effects of stronglyabsorbing aerosols. (a) Comparison results of M80 (weakly absorbing) and U80(strongly-absorbing) aerosols for Case-1 and Case-2 waters and, (b) aerosol
vertical effects for strongly-absorbing aerosols (U80) compared with aerosol
vertical distributed as two-layer and one-layer atmospheric models.

Comparison Results•

37

and one-layer atmospheric models. The two-layer model has been used for allcomputations in this report and the one-layer model is for aerosols (U80) uniformly
mixed with molecules (Rayleigh). This is for a typical Case-1 water and for an
AOT at 865 nm (U80) of 0.1. Thus, the only difference in computing two casesof [ρt − ρr ](λ, 865) in Figure 4.6b is their different vertical distributions. At the
NIR wavelengths, the two cases give exactly the same [ρt − ρr ](λ, 865), while atthe visible wavelengths (particularly at the blue bands) [ρt − ρr ](λ, 865) values are
considerably different (with the one-layer model having significantly lower values)(Figure 4.6b). These results indicate that, for strongly-absorbing aerosols, the TOA
aerosol radiance is strongly dependant upon the aerosol vertical distribution, andthis information cannot be obtained from the NIR measurements. Therefore, toderive ocean-colour products accurately over strongly absorbing aerosols such as
dust and smoke, information about aerosol vertical distribution is required. Suchinformation can be obtained from LIDAR measurements, or possibly from passive
measurements in the oxygen A-band (Dubuisson et al., 2009).

4.4

Brief Summary

Algorithm performance evaluations from the comparison results presented in Sections 4.1 to 4.3 of this report are summarized briefly below.

4.4.1

Case-1 Waters

For the open ocean, Case-1 waters, all four operational algorithms performed reasonably well. For a typical open ocean and atmosphere case, the algorithms for MERIS,
OCTS/GLI, SeaWiFS/MODIS, and POLDER produced mean errors of [Lw (λ)]N in thevisible to within 2%, 4%, 5%, and 9% respectively, while for the radiance ratio values([Lw (443)]N /[Lw (555)]N ) and [Lw (490)]N /[Lw (555)]N ), mean errors for MERIS,
SeaWiFS/MODIS, POLDER, and OCTS/GLI were within 2%, 2%, 6%, and 6% respectively.
On the other hand, the SeaWiFS/MODIS algorithm consistently produced resultswith the lowest noise (STD) errors among the four operational algorithms.
Both POLDER and OCTS/GLI produced excellent aerosol optical thickness products, while SeaWiFS/MODIS and MERIS overestimated the AOT data. For a typicalcase, the mean errors in the derived AOT for POLDER, OCTS/GLI, SeaWiFS/MODIS,and MERIS are about 3%, 4%, 8%, and 14% respectively. With the use of vector aerosol
lookup tables, the mean error in the derived AOT for SeaWiFS/MODIS algorithm canbe reduced to 4%, in addition to a considerably reduced noise (STD) error.

4.4.2

Case-2 Waters

For the coastal region Case-2 waters, all four operational algorithms produced somesignificant errors in deriving ocean-colour products, particularly for the yellow

38•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

substance-dominated waters. For a sediment-dominated Case-2 water and a typicalmaritime atmosphere, mean errors in [Lw (λ)]N for wavelengths 443, 490, and 555
nm for SeaWiFS/MODIS, OCTS/GLI, POLDER, and MERIS ranged from 4–12%, 7–10%,
10–23% and 13–25%, respectively, while the mean errors in [Lw (443)]N /[Lw (555)]N
and [Lw (490)]N /[Lw (555)]N for OCTS/GLI, SeaWiFS/MODIS, POLDER, and MERIS
are 2–3%, 2–9%, 2–15%, and 3–14% respectively. It should be noted that all four
operational algorithms can produce [Lw (490)]N /[Lw (555)]N accurately with meanerrors of ∼2%. Again, the SeaWiFS/MODIS algorithm produced the lowest noise
errors in the derived ocean-colour products.
However, for yellow substance dominated Case-2 waters, all four algorithms
performed poorly, particularly [Lw (λ)]N in the short blue bands. On the other
hand, satellite-derived [Lw (λ)]N at 490 and 555 nm, as well as radiance ratio of[Lw (490)]N /[Lw (555)]N may still be useful for retrieval of some water property
products from the CDOM-type waters (e.g, some results from SeaWiFS/MODIS).

4.4.3

Cases with Strongly-Absorbing Aerosols

For the strongly-absorbing aerosol (U80) case, all four operational algorithms significantly underestimated the derived [Lw (λ)]N values in the visible. Indeed, for atypical open ocean case (the most favorable ocean condition for algorithm performance) and with AOT of 0.1 at 865 nm, all four operational algorithms essentially
failed to produce reasonable [Lw (λ)]N values, with mean errors in [Lw (λ)]N ranging
from around -35% to -60%. However, algorithms can still produce good or reasonable radiance ratio values, particularly for the parameter [Lw (490)]N /[Lw (555)]N ,therefore chlorophyll concentrations. In fact, the mean errors in the derived[Lw (490)]N /[Lw (555)]N for OCTS/GLI, MERIS, SeaWiFS/MODIS, and POLDER are
0.5%, 2.5%, 7.7% and 12.5%, respectively, which are accurate enough for producing
reasonable chlorophyll products, at least for low or moderate chlorophyll, where
the ratio rapidly evolves as a function of chlorophyll.

Chapter 5
Algorithm Validations from In Situ Data
Menghua Wang, Hajime Fukushima, Robert Frouin, David Antoine,
Howard R. Gordon and André Morel

The atmospheric correction algorithms discussed in this report have been implemented into the corresponding data processing systems for producing the global
ocean-colour products from various satellite ocean-colour sensors. Supported by
the corresponding agencies and countries, there has been a significant effort inacquiring ocean-colour in situ data (see Mueller and Fargion, 2002; Werdell et al.,
2003; Werdell and Bailey, 2005), for validating the ocean-colour products producedby the satellite ocean-colour sensors SeaWiFS, MODIS, MERIS, OCTS/GLI, and POLDER(see Shimada et al., 1998; Bailey et al., 2000; Wang et al., 2005; Bailey and Werdell,
2006; Murakami et al., 2006; Zibordi, et al., 2006; Antoine et al., 2008). For thecurrent operational SeaWiFS, MODIS, and MERIS global ocean-colour missions, there
has been a continuous effort for algorithm evaluation and refinement through in situ
data validation and global satellite ocean-colour data analyses (e.g. Wang, 2000; Patt,
et al., 2003; McClain et al., 2004; Antoine et al., 2008). In fact, SeaWiFS has undergone
five major reprocessings of the entire data set. Each reprocessing has addressed
the data quality issues that are related to the sensor calibration, instrument navigation, data masks and flags, and retrieval algorithms. In addition, from 1997—2003,
the NASA Sensor Inter-calibration and Merger for Biological and Interdisciplinary
Oceanic Studies (SIMBIOS) Project (McClain et al., 2002) has played a leading role in
the international ocean community to define and document a series of in situ dataacquisition strategies and methodologies to ensure consistency in the in situ datacollection for satellite algorithm evaluation and validation. The next section briefly
describes a number of validation studies for SeaWiFS, MODIS, MERIS, OCTS/GLI, and
POLDER data products.

5.1

The NOMAD Data Set for Algorithm Evaluation for Global
OceansUsing the NASA bio-Optical Marine Algorithm Data set (NOMAD), Werdell and Bailey(2005) and Bailey and Werdell (2006) evaluated the SeaWiFS-derived ocean-colour
39

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Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

products for both global oceans and ocean regions with deep water (usually open
oceans). Their results show that over open oceans the mean ratio values (SeaWiFS
vs. in situ) of SeaWiFS-derived [Lw (λ)]N at wavelengths of 412, 443, 490, 510, and555 nm are 1.030, 0.962, 0.956, 0.975, and 0.976, respectively. However, for the
global oceans (including coastal regions), these ratio values are reduced to 0.905,
0.915, 0.918, 0.918, and 0.915, respectively. These results are consistent withthe simulation results of the SeaWiFS/MODIS algorithm performance discussed inprevious sections in this report, showing better algorithm performance over the
open ocean (Case-1 waters). It should be noted that the SeaWiFS/MODIS algorithm is
not designed for Case-2 coastal waters, resulting in large uncertainties for satellite
match-ups (particularly for [Lw (λ)]N in the blue), as has been reported by Feng etal. (2008) for coastal waters along the northeast coast of the U.S. and Mélin et al.
(2007) for a coastal site in the northern Adriatic Sea.

5.2

The BOUSSOLE In Situ Data Set for Algorithm Evaluation

Using the in situ data from a deep, clear ocean site in the northwestern Mediterranean
Sea (BOUSSOLE site) from September 2003 to October 2006, Antoine et al. (2008)
evaluated algorithm performances for deriving ocean-colour products from SeaWiFS,
MODIS-Aqua, and MERIS. Some AOT results were also included in the study. Theirevaluation results show that the mean ratio values (satellite vs. in situ) for the
SeaWiFS-derived normalized water-leaving reflectance [ρw (λ)]N at wavelengths 412,
443, 490, 510, 555 nm are 0.92, 1.00, 0.97, 0.95, and 0.90 respectively, while mean
ratios for the MODIS-Aqua [ρw (λ)]N at wavelengths 412, 443, 488, 551 nm are
0.90, 0.99, 0.95, and 0.88, respectively. The MERIS-derived [ρw (λ)]N results show
some significant over-estimations in the blue bands, with ratio values of 1.60, 1.32,
1.16, 1.22, and 1.21 for [ρw (λ)]N at wavelengths of 412, 443, 490, 510, and 560
nm respectively. Similar overestimation results have also been reported for MERIS
data in a comparison study by Zibordi et al. (2006) for a coastal site in the northern
Adriatic Sea. The overestimation of the MERIS-derived [ρw (λ)]N products, however,is most likely due to the lack of on-orbit vicarious calibration, which is necessary,and has been employed by both SeaWiFS and MODIS. The introduction of such avicarious calibration is currently underway for MERIS. In addition, this study also
showed that both SeaWiFS and MODIS-Aqua derived [ρw (λ)]N products show similar
noise errors, which are lower (particularly in the blue bands) than those from MERIS.
On the other hand, the AOT comparison results (Antoine, et al., 2008) showthat SeaWiFS-derived AOT data are overestimated, compared with the ground-based
measurements. The AOT over-estimations are consistent with results of Wanget al. (2005), and as was discussed earlier in this report, the derived AOT data
can be improved with the use of the vector aerosol lookup tables that include thepolarization effects (Wang, 2006a).

Algorithm Validations from In Situ Data

5.3

•

41

Some Validation Results for OCTS/GLIFor OCTS, in situ water-leaving radiance data were collected through international
and interagency collaboration (Shimada et al., 1998) at about 500 stations, but
under rather stringent match-up conditions only 11 remained and were used forvalidation studies. The standard deviation of the [Lw (λ)]N estimate against in
situ data was about +100% for the 412–520 nm bands, and about +400% for the
550 nm band with significantly large bias, which was understood to be related tocalibration offset of the OCTS instrument, and not necessarily from the atmosphericcorrection algorithm. For GLI validation, Murakami et al. (2006) examined 435[Lw (λ)]N data, again obtained through international and domestic collaboration,
including nearly 300 data measurements collected by SIMBAD/SIMBADA hand-heldradiometers (Deschamps et al., 2004). The results (Murakami, et al., 2006) show thatthe median absolute percentage differences (MedPD) between GLI and in situ data
were 14.1–35.7% for [Lw (λ)]N at 380–565 nm using the ‘Version 2.1’ GLI atmosphericcorrection algorithm (Toratani et al., 2007) where an empirical absorptive aerosol
correction was implemented. However, Fukushima et al. (2007) compared theperformance of algorithm Version 2.1 vs. Version 1.5, and the performance of thetwo was rather similar, suggesting that aerosol absorption is not a factor in theobserved [Lw (λ)]N error.

5.4

The SIMBAD(A) In situ Data Set for POLDER Algorithm
Evaluation

Using SIMBAD, and the advanced SIMBADA field radiometers (Deschamps et al.,2004), above-water marine reflectances were measured in various oceans duringcruises of opportunity, and compared with POLDER-1 and -2 estimates. In Case-1
waters, the comparison statistics were as follows: for POLDER-1, the bias between
estimated and measured values was 0.001 at 443 nm (167 match-ups), 0.0019 at
490 nm (97 match-ups), and 0.0005 at 560 nm (167 match-ups). The corresponding
standard deviations were 0.0051, 0.0035, and 0.0018, respectively (Fougnie, 1998).
For POLDER-2 the values, obtained with 101 match-ups were -0.0021, -0.0028, and-0.0025 respectively for the bias, and 0.0048, 0.0041, and 0.0038 for the standard
deviation (see http://smsc.cnes.fr/POLDER/SCIEPROD/oc_pr.htm). The POLDER-2 performance falls short of the accuracy requirement of 0.001–0.002 in the blue inoligotrophic waters (Gordon, 1997). The POLDER-3 estimates were evaluated using
underwater radiometric measurements at the BOUSSOLE site during 2005 and 2006
(186 match-ups), which resulted in a standard deviation of 0.0019 at 490 nm and
0.0009 at 565 nm (Steinmetz, 2008). This was obtained after correction of the
POLDER-3 radiance for residual stray light in the optical system. Note that the
POLDER-3 spectral band centered on 443 nm, which has a high dynamic range, is42•Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

not used for ocean-colour purposes, but for cloud detection.

Chapter 6
Conclusions and Recommendations
Menghua Wang, Howard R. Gordon, David Antoine, Robert Frouin André
Morel, Hajime Fukushima and Pierre-Yves Deschamps

Several conclusions are evident from this algorithm comparison exercise, the mostimportant of which is the good performance of the algorithms in Case-1 waters(comprising the bulk of the global oceans), with assumption of realistic maritime
aerosol models. Although several conclusions below address improvements recommended for atmospheric correction, these are required only for a small portionof the global oceans, i.e., mainly areas near the coast with high concentrations of
dissolved organic matter and/or suspended sediments, or areas influenced by windblown dust or urban pollution. In general, the atmospheric correction algorithms
for global ocean-colour data processing can be considered highly successful. Listed
below are the specific conclusions reached from this algorithm comparison exercise.

v For open ocean Case-1 waters with maritime aerosols, all four operational
atmospheric correction algorithms generally performed well in deriving the[Lw (λ)]N spectra and radiance ratio values. Thus, over open oceans, oceancolour radiance products can be derived accurately in most cases from satellite
remote sensors. However, some in situ validation results show that further improvements in the data product are still required and are possible, particularly
for [Lw (λ)]N in the blue.
v For a sediment-dominated Case-2 water with typical maritime aerosols, allfour operational algorithms produced slightly larger errors in the [Lw (λ)]Nin the blue bands, mainly due to an incorrect estimation of the NIR ocean
contributions. The [Lw (λ)]N in the longer visible wavelengths (e.g. 555 nm),and radiance band ratio values can be retrieved accurately. Since the [Lw (λ)]N
spectra for the sediment-dominated waters are highest in the green-red wavelengths, it is suggested that the satellite-derived [Lw (λ)]N and radiance ratioat the longer visible bands are used for retrieval of sediment-dominated water
optical and biological properties.
v For a yellow substance-dominated Case-2 water, all four operational algorithms performed poorly, particularly for the [Lw (λ)]N in the blue band. It
43

44

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

is extremely difficult (if not impossible) to derive accurate [Lw (λ)]N in theblue because radiance signals in that region of the spectrum are very low for
CDOM-type waters (strong absorption). In addition, the derived [Lw (λ)]N in
the blue contains very significant noise errors. However, the [Lw (λ)]N in theblue should be used to obtain CDOM absorption information (i.e., to distinguish it from phytoplankton absorption), even though the blue radiance isdifficult to derive accurately. The spectral shape of [Lw (λ)]N , i.e., ratios, could
be helpful for deriving the water property for yellow substance dominatedwaters.

v All four operational algorithms failed to produce accurate [Lw (λ)]N spectrain the visible wavelengths for a strongly-absorbing aerosol (U80). Satellitederived [Lw (λ)]N values are significantly underestimated, with the mean errorin [Lw (λ)]N ranging from around −35% to −60%. However, the radianceratio, in particular [Lw (490)]N /[Lw (555)]N , is still reasonably accurate forthe retrieval of ocean chlorophyll concentrations. For accurate retrieval of the[Lw (λ)]N spectra data over a strongly absorbing aerosol, one must (i) identify
the presence of the strongly-absorbing aerosols and (ii) acquire the aerosol
vertical distribution, for example from LIDAR measurements.
v Errors in the derived [Lw (λ)]N spectra from the various atmospheric correction algorithms are spectrally correlated, as was demonstrated in this report.
Consequently, the resulting errors in radiance band ratios (e.g. [Lw (490)]N /[Lw (555)]N ) are reduced. It is recommended that radiance band ratios should
be used preferentially for deriving ocean optical and biological properties.
v The aerosol product (that is, aerosol optical thickness) is a by-product ofocean-colour data processing (atmospheric correction). Results show that the
AOT data over the oceans can be derived accurately using the vector aerosol
lookup tables, with errors within ∼5%. It was also demonstrated that the ocean[Lw (λ)]N spectra can be derived accurately using the scalar aerosol lookup
tables, even though there are some slightly larger over estimations in thederived AOT data.
v Future development of ocean-colour remote sensing will require considerable
efforts in retrieving ocean-colour products in the coastal ocean regions, wherewaters are not only Case-2 types, but the aerosols are often strongly absorbing(depending on the region). Some regional algorithms and approaches areuseful in dealing with coastal complex ocean waters, for example the spectral
matching algorithm, the spectral optimization algorithm, and neural network
approaches. Furthermore, in order to deal with significant ocean contributionsin the NIR bands in turbid waters, future satellite sensors will require SWIR
bands with high signal-to-noise characteristics for measurement of optical

Conclusions and Recommendations•

45

and biological properties in coastal and inland turbid waters. In dealing withthe strongly-absorbing aerosols, it is first necessary to detect the presence ofthe strongly-absorbing aerosols (e.g. using measurements in the UV bands
where the TOA signal is very sensitive to the aerosol absorption), and then to
derive the aerosol vertical profile (for example, from LIDAR measurements)
with sufficient accuracy for atmospheric correction.

46•

Atmospheric Correction for Remotely-Sensed Ocean-Colour ProductsAppendix A
Details of the POLDER Algorithm
Robert Frouin, Pierre-Yves Deschamps and Jean-Marc Nicolas

A.1

Radiometric Model

After radiometric calibration, POLDER Level-1 data are in the form of TOA normalized radiance, defined for each band j and direction i as:
Rmea (λj , i) = π Lmea (λj , i)/F0 (λj )(A.1)

where Lmea is the measured radiance. The TOA normalized radiance, after corrections for gaseous absorption and scattering/absorption by stratospheric aerosols(made just after cloud masking), is expressed as:
Rt (λj , i) = Rmol (λj , i) + Rgm (λj , i) + Raer (λj , i) + Rga (λj , i) + To (λj , i)T (λj , i)Rg+

to (λj , i)t(λj , i) cos θ0 {[ρw (λj , i)]N + [ρwc (λj )]N },1 − S(λj ){[ρw (λj , i)]N + [ρwc (λj )]N }(A.2)

where Rmol accounts for multiple scattering by molecules, Rgm accounts for coupling terms between molecules and photons reflected on a rough sea surface, Raeraccounts for multiple scattering by aerosols and by molecules plus aerosols, Rga
accounts for coupling terms between aerosols and photons reflected on a roughsurface, and S is the spherical albedo of the atmosphere (accounts for successive
photon interactions with surface, then atmosphere, and again surface). In order
to include multiple scattering on both molecules and aerosols (coupling), Raer iscomputed as Raer = Rtot − Rmol , where Rtot is the total (aerosol + molecule) scattering
term. This decomposition allows one to adjust the molecular term by sea-surfacepressure without modifying the aerosol term. It should be noted that Equation A.2
is only exact when the surface reflectance above the air-sea interface (water body +whitecaps) is isotropic.

A.2

Aerosol Model Inversion

The first step of the process is first the evaluation of the spectral dependence of theobserved aerosol signal in the red and NIR part of the spectrum, and then of the
47

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Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

model which can be associated with that spectral dependence, including multiple
scattering effects. First a corrected normalized radiance, Rcor , is computed from thenormalized radiance Rt in each band j (j = 4, 5, 6 with λ4 = 670 nm, λ5 = 765 nm,
λ6 = 865 nm) and each viewing direction i:
Rcor (λj , i) = Rt (λj , i) − Rmol (λj , i) − Rgm (λj , i) − To (λj , i)T (λj , i)Rg
= Raer (λj , i) + Rga (λj , i) +to (λj , i)t(λj , i) cos θ0 [ρwc (λj )]N
1 − S(λj )[ρwc (λj )]N(A.3)

Then a weighted spectral dependence measured over all viewing directions is computed:
X ARcor (670, i) + (1 − A)Rcor (765, i)
=
,
(A.4)
Rcor (865, i)iwhere A is a variable weighting factor taking values in the range 0–1. For POLDER-1,
A is set to 1 because the noise affecting the 765 nm band is too high and would
strongly affect the retrieved marine reflectance. In parallel, the same computation iscarried out for each aerosol model in the lookup table database:mod =X ARmod (670, i) + (1 − A)Rmod (765, i)
Rmod (865, i)

i

(A.5)

where Rmod (λj , i) is linearly interpolated on four variables (θ0 , θ, φ, τa ).
Comparison of  and mod yields two models x and y such that x <  < y .
The distance dx is also computed:dx = − xy − x(A.6)

The 12 aerosol models have been organized in growing mod order and selected sothat their mod values never cross each other for the geometries generally observed.
The model that best fits the observation is coded as a real number, denoted Xdx ,between 1 and 12.
A specific procedure has been developed for very clear observations. In suchsituations, the spectral dependence is highly unpredictable because the denominatorin Equation A.4 is very small. The aerosol model is set to a fixed value (C90) forvery low aerosol loadings to prevent adding noise in the final estimates (marinereflectance and chlorophyll concentration). A threshold is applied to Rcor for eachdirection, and when a direction is below the threshold, the spectral dependence isforced to the value of the fixed model. For POLDER-1, the threshold accounts for an
aerosol optical thickness of about 0.05.

A.3

Dealing with the ‘Black-Pixel Assumption’

Aerosol model inversion relies on the hypothesis of a black ocean from 670 nm to865 nm. It has been demonstrated that this is not true for eutrophic and Case-2

Details of the POLDER Algorithm•

49waters, where absorption of pure water is counter-balanced by scattering of particles(organic or inorganic). Thus the contribution of marine reflectance generally leads tooverestimation of the aerosol Ångström coefficient. The computation of the marinereflectance is necessary prior to aerosol inversion, which in turn is necessary tocompute marine reflectance correctly. Solutions currently developed rely on an
iterative process (Siegel et al., 2000) or on spatial homogeneity of aerosols versus
water heterogeneity (Ruddick et al., 2000).
In the operational algorithm, where computation time should be minimized, asimple solution has been developed, based on an empirical relationship between
marine reflectance at 565 and 670 nm. This solution, first developed for CZCS
by Viollier et al. (1980), has been shown to work reasonably well for waters thatcan be observed at POLDER spatial resolution, including high sedimentation andcoccolithophorid bloom situations. Problems arise potentially over waters highly
charged with yellow substances, where the algorithm will not work correctly.
The hypothesis that a linear relationship exists between marine reflectance at
565 and 670:
[ρw (670)]N = a[ρw (565)]N + b,

(A.7)

where a ∼0.20 and b ∼-0.0005. Using that relationship, a new weighted spectral
dependence is computed:=

X A[Rcor (670, i) − aRcor (565, i) + b] + (1 − A)Rcor (765, i)
i

Rcor (865, i)

,

(A.8)

where the marine contributions at 565 and 670 nm cancel each other out.

A.4

Aerosol Optical Thickness Inversion

The second step of the process is the inversion of the aerosol optical thickness fromobservations. The corrected radiance Rcor (865) is used in all viewing directions. For
each direction and each tabulated optical thickness, Rmod (865, i, τa ) is interpolated
for four variables (θ0 , θ, φ, Xdx ) in the pre-computed lookup table. The arithmetic
mean over all viewing directions is computed for Rmod and Rcor and the aerosol
optical thickness τa is then given by:τa =X [hRmod (865, τa2 )i − hRcor (865)i]τa1 + [hRcor (865)i − hRmod (865, τa1 )i]τa2hRmod (865, τa2 )i − hRmod (865, τa1 )i(A.9)
where hRmod (865), τa1 i and hRmod (865), τa2 i are the simulated radiances for aerosol
model Xdx (determined in the first step; see above) and for the tabulated aerosol
optical thicknesses τa1 and τa2 that give simulated radiances surrounding thecorrected radiance hRcor (865)i.

,

50

•

A.5

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Dealing with Absorbing Aerosols

Absorption by aerosols is a difficult problem to solve because its main impact
is observed in the very bands used for ocean-colour applications, i.e. in shortwavelengths, because molecular scattering is maximum at these wavelengths, andbecause the absorption effect is proportional to the level of the signal. Near infrared
information, therefore, cannot be readily extrapolated to the visible part of thespectrum. One solution using the multi-directionality capability of the POLDER
instrument has been developed to deal with such absorbing aerosols. It relies on thechange of absorption efficacy with molecular scattering and air mass changes. The
aerosol absorption effect varies almost linearly with molecular scattering radiancemultiplied by air mass, irrespective of aerosol altitude. The slope of the linear
relation is related to the efficacy of aerosol absorption.
These characteristics have been implemented in the operational algorithm using
the aerosol family concept. An aerosol family is a set of models (12) with consistentabsorption. The core of the algorithm is played for each family, and the slope
defined above is computed for each family. The family that leads to the slope
nearest to zero is selected for final atmospheric correction.

A.6

Atmospheric Correction of Ocean-Colour Bands (443, 490,
and 565 nm)

After having gone through the two steps described above twice for each family (i.e.,
one iteration), the aerosol model, optical thickness, and family inverted from thatprocess are used to compute surface marine reflectance from the corrected TOA
normalized radiances.
First, for each viewing direction a NIR equivalent corrected radiance, Re , iscomputed as a weighted mean over the three red and NIR bands:
Re (i) =a670 Rcor (670, i) + a765 Rcor (765, i) + a865 Rcor (865, i)
a670 + a765 + a865

(A.10)

where a670 , a765 , and a865 are the weights given to each band. For POLDER-1, owing
to the noise considerations mentioned above, a765 is equal to zero and a670 and a865
are equal to 0.5. Then for each ocean-colour band j (j = 1, 2, 3 with λ1 = 443nm,
λ2 = 490nm, λ3 = 565nm) the spectral dependence of the aerosol radiance, e , isinterpolated on five variables (θ0 , θ, φ, Xdx , τa ) in the lookup table:
a670 + a765 + a865.
a670 Rcor (670, i) + a765 Rcor (765, i) + a865 Rcor (865, i)(A.11)
When computing the lookup table for e , geometric conditions, i.e., the triplet(θ0 , θ, φ), these are supposed to be identical for each band. Within a POLDER
e (λj , i) = Rmod (λj , i)

Details of the POLDER Algorithm•

51

measurement sequence (i.e., a set of viewing directions), however, the measurements
are not made simultaneously in all the spectral bands because of the specific designof the POLDER instrument. A fine correction on e is therefore necessary. The
correction factor is defined by:∆R(λj , i) =P (γ λj ,i ) cos θ 765,i,
P (γ 765,i ) cos θ λj ,i(A.12)

where P (γ λj ,i ) and P (γ 765,i ) are the values of the phase function of model Xdx
for scattering angles γ λj ,i and γ 765,i , respectively, and cos θ λj ,i and cos θ 765,i are
the cosine of the viewing zenith angle of bands at λj and 765 nm, respectively,
for viewing direction i. In this correction, the band at 765 nm is considered as
representative of the three red and NIR bands (670, 765, and 865 nm) used in theatmospheric correction scheme.
The correction term that accounts for aerosol contribution in each ocean-colour
band j(j = 1, 2, 3) is then easily computed as follows:
Raer (λj , i) = e (λj , i)Re (λj , i)∆R(λj , i).

(A.13)

This allows one to estimate the contribution Rw of the water body to Rt , i.e., the lastterm in Equation A.2:
Rw (λj , i) = Rt (λj , i) − Rmol (λj , i) − Rgm (λj , i) − T0 (λj , i)T (λj , i)Rg − Ratm (λj , i).
(A.14)
Finally the marine reflectance is obtained for each viewing direction i in each oceancolour band j:[ρw (λj , i)]N =A.7

Rw (λj , i)
− [ρwc (λj )]Ncos θ0 t0 (λj , i)t(λj , i) + S(λj )Rw (λj , i)

(A.15)Sun Glint Correction

For a given POLDER pixel, 12 or 13 viewing directions are available. A couple ofdirections are highly contaminated by sun-glint and are thus rejected. Still some ofthe directions considered as sun-glint free are slightly contaminated. The correction
term for those directions is T0 T Rg . The sun glint reflectance, Rg , is considered
spectrally flat and computed as a function of wind speed, U , using the Cox and
Munk (1954) model:
π P (Z(U ))Rf (γ)
Rg (θ0 , θ, φ, U ) =(A.16)
4 cos4 β cos θ0where Rf is the reflection coefficient at the air-sea interface for the scattering angleγ, β is the wave inclination, and P (Z(U )) is the Gaussian slope distribution as given
by Cox and Munk (1954). Surface wind speed is obtained from meteorological data.
The correction is applied for Rg < 0.005. For higher Rg values the model is notprecise enough (due to uncertainties on surface wind speed, intrinsic variability ofFresnel reflection on a rough surface).

52

•

A.8

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Whitecap Correction

When sea surface agitation becomes important, generally for a wind speed above 8m/s, the air-sea interface can be contaminated by whitecaps (Koepke, 1984; Monahan
and O’Muircheartaigh, 1986). An empirical relationship between surface density ofwhitecaps and wind speed has been provided by these authors and is widely used:
Swc = 2.95 × 10−6 U 3.52

(A.17)

where Swc is the fraction of the sea surface covered with whitecaps and U is expressed in m/s. Whitecap reflectance has been measured in situ and its mean value
is generally considered to be equal to 0.22 in the visible. More recently in situ or
aircraft measurements (Frouin, et al., 1996; Moore, et al., 2000; Nicolas et al., 2001)
have indicated that whitecap reflectance cannot be considered as spectrally flat in
the visible and NIR region.
Therefore, in the algorithm the model used for whitecap reflectance is:[ρwc (λj )]N = 0.22wc (λj )Swc

(A.18)

where wc (λj ) is a spectral whitecap coefficient defined for each band from 443
to 865 nm. Surface wind speed to compute Swc comes from meteorological data,
and a wind speed threshold of 8 m/s is used below which whitecap reflectance isneglected.
In the algorithm aerosol optical inversion module, if Rcor (865) < 0 and whitecap
reflectance used in Equation A.3 is not 0, then ρwc is progressively lowered until
Rcor (865) becomes positive. If Rcor (865) is still negative, no aerosol correction andno whitecap correction are made (but the pixel can still be rejected later in theprocessing line).

Appendix B
Other Atmospheric Correction Algorithms
Howard R. Gordon, Menghua Wang and Robert Frouin

B.1

Introduction

There has been significant progress in developing other approaches for atmosphericcorrection, in particular, in dealing with cases for either the strongly-absorbing
aerosols and/or waters with non-negligible NIR ocean contributions. These algorithms are used regionally, and are not the focus of this report. Brief descriptions ofthese algorithms are provided below.
The algorithms described in Sections 2.1 to 2.4 are applicable only in the presenceof non-absorbing or weakly-absorbing aerosols (used for global ocean-colour dataprocessing). They cannot produce acceptable results in the presence of stronglyabsorbing aerosols. In addition, they all require that ρw (λ) be negligible in the
NIR bands. These conditions are not always met. Two observations (Gordon, 1997)
indicate how the algorithm is confounded in the presence of strongly-absorbing
aerosols:
1. Although aerosol absorption can seriously reduce ρa (λ) + ρra (λ) in the visible,
it is not possible on the basis of the observed TOA radiance in the NIR toinfer the presence of aerosol absorption, because the spectral variation of
ρa (λ) + ρra (λ) in the NIR depends mostly on the aerosol’s size distribution;
and2. The vertical distribution of strongly-absorbing aerosols profoundly influences
their TOA reflectance in the visible (especially in the blue) but not in the NIR.
In the case of a mineral aerosol such as Saharan dust transported over large
distances over the ocean by the winds, there is the additional complicationthat the dust is coloured, i.e., the absorption properties of the material itself
vary strongly with the wavelength.
The fact that the absorption properties cannot be determined on the basis of
the observations of ρa (λ) + ρra (λ) in the NIR means that observations in the visible
are required as well. However, in the visible (especially in the blue) ρw (λ) can besignificant, and cannot be estimated a priori. This suggests that the retrieval of
ρw (λ) and the atmospheric correction (retrieval of ρa (λ) + ρra (λ)) must be carried
53

54

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

out simultaneously. As retrieval of ρa (λ) + ρra (λ) in the existing algorithm requires
aerosol models, retrieval of ρw (λ) will require an optical model of the ocean. Twoalgorithms, based on simultaneous determination of oceanic and atmospheric properties that show promise in dealing with absorbing aerosols, have been developedby Gordon and co-workers (Gordon et al., 1997; Chomko and Gordon, 1998).
The requirement for ρw (λ) ≈ 0 in the NIR fails in turbid coastal waters. A
remedy is to base atmospheric correction on spectral bands at longer wavelengths,
where the absorption of water is greater than in the NIR and the correspondingρw (λ) is smaller: the shortwave infrared (SWIR) (Wang and Shi, 2005; Wang, 2007).
In addition, the neural network approach for deriving ocean-colour products forregional applications also show some good results (Jamet et al., 2005; Brajard et al.,2006), in particular, for coastal regions with Case-2 waters (Schroeder et al., 2007).

B.2

Spectral Matching Algorithm

The ‘spectral matching algorithm’ (SMA) is described in detail in Gordon et al., (1997).
In this algorithm, the properties of the ocean and the atmosphere are retrieved simultaneously. Briefly, assuming that [ρw (λNIR )]N = 0, ρt (λNIR ) − ρr (λNIR ) provides
ρa (λNIR ) + ρra (λNIR ). Given an aerosol model (the ith ) one can find the value of the(i)aerosol optical depth, τa (λNIR ), that reproduces ρa (λNIR ) + ρra (λNIR ). Then from(i)(i)
τa (λNIR ) and the model ρa (λj ) + ρra (λj ) can be determined as well τa (λj ) for all(i)spectral bands λj . This provides the quantity ρw (λj ), retrieved assuming that the
ith aerosol model is correct. At this point the Gordon et al. (1988b) two-parametermodel of the Case-1 water-leaving reflectance that uses the pigment concentration, Cand a pigment-related scattering parameter at 550 nm, b0 , is employed to computeρw (λj ) for a discrete set of values of C and b0 that fall within the typical range ofvariation. The residual
2
(i)
ρ
(λ
)
−
ρ
(λ
)
w
w
j
j

 ,
j=1
ρw (λj )0δ(i, C, b ) =

Xn

(B.1)

where n is the number of visible wavelengths, is then computed for each modeland set of ocean parameters. The set of parameters i, C, and b0 , that yield thesmallest δ(i, C, b0 ) is chosen as the best, i.e., the solution the problem; however, as
it is unlikely that the ‘correct’ model is one of the set of candidates, Gordon et al.,(1997) suggested averaging for the ten best retrievals (ten retrievals with the lowest
values of δ(i, C, b0 )) to obtain the retrieved ocean and aerosol parameters. Extensive
tests using simulated pseudo data with strongly-absorbing aerosols suggest that
this approach is capable of excellent retrievals in the presence of either weakly- or
strongly-absorbing aerosols. Of particular importance is the fact that the algorithm
has no difficulty indicating the presence of strongly-absorbing aerosols. The algorithm can also incorporate vertical structure by having candidate models with any

Other Atmospheric Correction Algorithms•

55

prescribed vertical structure. An important feature of this algorithm is that it can be
configured to use the same LUTs as the standard algorithm, and therefore could be
run concurrently. An unattractive feature of the algorithm is that it requires realistic
aerosol models to effect the correction, i.e., the better the models approximate thereal aerosol, the better the parameter retrievals. Obviously the results also dependon the quality of the ocean model.
Moulin et al. (2001a, 2001b) and Banzon et al. (2004) applied this method toimagery contaminated with Saharan dust, much improving the retrievals of C.

B.3

Spectral Optimization Algorithm

The ‘spectral optimization algorithm’ (SOA) is described in detail in Chomko and Gordon (1998). As in the spectral matching algorithm, the properties of the ocean andthe atmosphere are retrieved simultaneously. In contrast to the spectral matchingalgorithm, no attempt is made to use realistic aerosol models, i.e., aerosol models aredescribed by the overly-simple power-law size distributions (number between r andr + dr ∝ r −(υ+1) ) are employed to derive the aerosol properties. Briefly, for a given
value of the parameter υ, assuming the particles are spherical, and ignoring theaerosol vertical distribution for the moment, the aerosol reflectance ρa (λ) + ρra (λ)
only depends on the real (mr ) and imaginary (mi ) parts of the aerosol refractive
index and τa (λNIR ). The values of mr and mi are assumed to be independent of
λ, so such a model will apply to wavelength-independent absorbing aerosols only,
e.g., carbonaceous. As in the spectral matching algorithm, the water contribution to
the TOA reflectance depends on the parameters C, and b0 , through the Gordon etal. (1988b) reflectance model. Standard optimization procedures are then used todetermine the values of these parameters using an equation similar to Equation B.1,
i.e., minimizing δ(υ, τa , mr , mi , C, b0 ), where τa = τa (λNIR ).
Application to SeaWiFS imagery off the U.S. east coast has been presented by
Chomko and Gordon (2001). The algorithm showed consistent retrieved water
properties between days with turbid and clear atmospheres. The algorithm was
improved by Chomko et al. (2003) by replacing the bio-optical model with a morerobust model (Garver and Siegel, 1997; Maritorena et al., 2002) and showed excellent
retrievals of both C and the absorption by detrital material. It was further modified
by Kuchinke et al. (2009a; 2009b) for application to Case-2 waters.

B.4

The SWIR Algorithm

For dealing with the turbid waters in the coastal regions, where there are often significant ocean contributions in the NIR bands, Wang (2007) proposed an atmosphericcorrection algorithm using the shortwave infrared (SWIR) bands. At the SWIR wavelengths, ocean water has much stronger absorption than that at the NIR bands (Hale56•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

and Querry, 1973), thus the black ocean assumption is generally valid at the SWIR
bands, even for very turbid ocean waters. The algorithm basically operates in thesame way as that of Gordon and Wang (1994a), but the two NIR bands (e.g. MODIS
748 and 869 nm) are replaced with two SWIR bands (e.g. MODIS 1240 and 2130 nm)
for atmospheric correction. Wang et al. (2009) evaluated the performance of the
SWIR algorithm using both MODIS data and in situ measurements, and Wang and
Shi (2005) and Wang et al. (2007) demonstrated applications for extremely turbid
waters in various coastal regions. In addition, ocean-colour products derived fromthe SWIR-based atmospheric correction have been shown to have various important
applications, such as studying storm-driven phytoplankton blooms (Shi and Wang,2007; Liu et al., 2009) and storm-induced sediment re-suspension (Shi and Wang,2008), storm-water runoff plume detection (Nezlin, et al. 2008), inland fresh water
monitoring and management (Wang and Shi, 2008), and flood-driven river plumedynamics (Shi and Wang, 2009). With the SWIR method, NIR ocean contributions
can also be derived accurately and used for retrieval of ocean properties such as
sediment concentration.

B.5

Neural Network Approach

Atmospheric correction using the neural network approach has also shown promising results. In contrast to standard approaches, but in line with spectral matchingand optimization algorithms, the correction is not based on decoupling atmosphericand oceanic effects, and it takes into account all the spectral information in themeasurements. The neural network methodology is used either to model the radiation transfer in the ocean-atmosphere system (direct modelling), or to achievea mapping between top-of-atmosphere measurements and bottom-of-atmospherereflectance or geophysical parameters (inverse modelling). The basic advantages ofneural networks are exploited, namely their good approximation properties, theirrobustness to noise, and their rapidity of execution. However, the neural network
approach requires realistic training data sets (usually regionally dependent) for thealgorithm tuning, and it may be difficult to produce accurate global ocean-colour
products.
In the neuro-variational method proposed by Jamet et al. (2005) and refined byBrajard et al. (2006), the TOA signal is modelled by the use of multi-layer perceptrons. One perceptron is used for atmospheric reflectance, one for water reflectance,and one for atmospheric transmittance. Atmospheric and oceanic parameters affecting the measured signal, namely aerosol index of refraction, size distribution, andoptical thickness, chlorophyll-a concentration, and hydrosol scattering, are retrieved
using a variational inversion scheme. The distance between observed reflectance andthat calculated at several wavelengths is minimized, the control parameters being
the oceanic and atmospheric parameters. An iterative cost function formulation

Other Atmospheric Correction Algorithms•

57

and minimization phases, controlled separately by oceanic and atmospheric parameters, allows one to handle absorbing aerosols. A limited evaluation against in situ
measurements has demonstrated acceptable chlorophyll-a concentration retrievals,consistent with standard SeaWiFS results.
In the inverse model parameterization developed for MERIS and described in
Schroeder et al. (2007), the TOA signature, solar and viewing geometries, andenvironmental data (surface pressure and wind speed) are used as data entry in a
fully connected, forward-feed, neural network. The output data are the spectral
bottom-of-atmosphere reflectance and, as a by-product, aerosol optical thickness.
Situations of Case-2 waters were simulated and used in the determination of the freeparameters of the network, which makes an algorithm adapted to those opticallycomplex waters. For the marine reflectance product, a mean absolute percentage
error of 18% in the spectral range 412—710 nm was obtained in comparisons within situ measurements. The improvement in accuracy was substantial in the blue partof the spectrum when neural network estimates were compared with the standard
MERIS Level-2 marine reflectance product.
In the function field methodology proposed by Pelletier and Frouin (2006) andFrouin and Pelletier (2007), the TOA reflectance vectors, after correction for molecular effects, are considered as explanatory variables conditioned by the angular
geometry. The inverse problem, therefore, is viewed as a collection of similar inverse
problems, continuously indexed by the angular variables. The solution is in theform of a field of non-linear regression models over the set of permitted values forthe angular variables. Each value of the field is a regression model that performs a
direct mapping of the TOA reflectance to the chlorophyll-a concentration (Pelletierand Frouin, 2006) or the marine reflectance (Frouin and Pelletier, 2007). The selectedmodels, for reasons of approximation theory, are fields of shifted ridge functions.
The fields constructed on synthetic data for Case-1 waters are robust to noise, theyhandle situations of weakly and strongly-absorbing aerosols well, and the retrievals
are accurate in both oligotrophic and productive waters. The methodology was applied successfully to satellite imagery, but needs to be further tested and evaluatedagainst in situ measurements. Extension to the retrieval of other variables such as
yellow substance absorption and sediment concentration, is possible.
In the algorithm proposed by Gross-Colzy et al. (2007a), the satellite reflectanceis first decomposed into principal components. The components sensitive to theocean signal are then combined to retrieve the principal components of the marinereflectance. This allows a reconstruction of the marine reflectance and, therefore,
an estimate of the marine reflectance. Neural network methodology is used toapproximate the non-linear functions that relate the useful principal components
of satellite reflectance to the principal components of marine reflectance. Keeping
only the ocean-sensitive principal components of satellite reflectance reduces theinfluence of the atmosphere, making the non-linear mapping accurate. The algorithm
performs atmospheric correction in the presence of a wide range of aerosol contents

58•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

and types, including absorbing mixtures, for the full range of water properties (Case1 and Case-2), and marine reflectance is retrieved with good theoretical accuracy.
By operating with principal components, the algorithm is minimally influenced bybiases in radiometric calibration (only inter-band calibration needs to be accurate),making it well adapted to provide consistency across sensors and continuity in thequality of the marine reflectance (Gross-Colzy et al., 2007b).

Appendix C
Atmospheric Diffuse Transmittance
Howard R. Gordon, Pierre-Yves Deschamps, Menghua Wang and Robert
FrouinC.1

Introduction

In the remote sensing of ocean colour, we are interested in the water-leaving radiance
Lw (θ, φ), i.e. the component of the radiance leaving the sea surface that wastransmitted through the interface from below the ocean surface. The radiancejust below the sea surface is Lu (θ 0 , φ), where θ 0 and θ are related by the law ofrefraction, i.e., sin θ = m sin θ 0 . Lw (θ, φ) and Lu (θ 0 , φ) are related by
Lw (θ, φ) =Tf (θ, θ 0 )Lu (θ 0 , φ),
m2

(C.1)

where Tf (θ, θ 0 ) is the Fresnel reflectance of the air-sea interface. This is not the
only component of the upward radiance just above the sea surface: the sky radiance Lsky (π − θ, φ) will be Fresnel-reflected upward by the sea surface adding
Lsky (π − θ, φ)[1 − Tf (θ, θ 0 )] to the upward radiance just above the sea surface.
Note that Lsky (π − θ, φ) is the totality of sky radiance, i.e., it includes any andall-multiple reflections from the interface. The total radiance just above the sea
surface Lw(total) (θ, φ) is
Lw(total) (θ, φ) = Lsky (π − θ, φ)[1 − Tf (θ, θ 0 )] + Lw (θ, φ).

(C.2)

If the sea surface is rough, the first term is replaced by an integral over solid angle,
as is the right-hand-side of Equation C.1. These are related to the radiance measured
at the top of the atmosphere Lt (θ, φ) by
Lt (θ, φ) = Lpath (θ, φ) + t(θ, φ)Lw(total) (θ, φ),(C.3)

where Lpath (θ, φ) is the path radiance, i.e., the radiance generated by scattering
within the atmosphere along the path of sight and t(θ, φ) is usually referred to as
the diffuse transmittance. Writing this out in detail, we have
Lt (θ, φ) = Lpath (θ, φ)+t(θ, φ)Lsky (π −θ, φ)[1−Tf (θ, θ 0 )]+t(θ, φ)Lw (θ, φ). (C.4)
59

60

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

In the Gordon and Wang (1994a) atmospheric correction scheme the path radianceis defined to include sky radiance reflected from the interface, i.e.,
0
LGW
path (θ, φ) = Lpath (θ, φ) + t(θ, φ)Lsky (π − θ, φ)[1 − Tf (θ, θ )].

(C.5)

The Gordon-Wang lookup tables for LGW
path (θ, φ) were generated by solving the radiative transfer equation for an atmosphere illuminated from the top by the sun andbounded by a Fresnel-reflecting interface over a totally absorbing medium, i.e., any
photons penetrating the interface are lost. Thus, if there are photons incident bothfrom the sun and from beneath the surface (actually reflected upward from beneaththe water surface) in the Gordon-Wang definition,
Lt (θ, φ) = LGW
path (θ, φ) + t(θ, φ)Lw (θ, φ).

C.2

(C.6)

Formal Definition of Diffuse Transmittance

Using Equations C.2 and C.3, the diffuse transmittance can be defined as   L(TOA)
ξ̂
w
  ,
t ξ̂ =
Lw ξ̂
(TOA)

(C.7)

where Lw (ξ̂) is the radiance leaving the surface in the direction ξ̂, Lw(ξ̂) isthe radiance originating in the water and exiting the TOA in the direction ξ̂, ξ̂ =
ˆ k̂ areî sin θ cos φ + jˆsin θ sin φ + k̂ cos θ is in the propagation direction, and î, j,
Cartesian unit vectors. Yang and Gordon (1997) provided a rigorous framework
based on the reciprocity principle in which to compute t(ξ̂). They showed thatt(ξ̂) is not just a function of the atmospheric properties, but also depends on the
angular distribution of Lw (ξ̂) itself. In general, this distribution is unknown. If it
were known, the procedure for computing t(ξ̂) would be straightforward: consider
the atmosphere bounded by a Fresnel-reflecting, but totally transparent ocean,
introduce a radiance Lw (ξ̂) with the appropriate angular distribution just above(TOA)
the sea surface, and compute the radiance leaving the TOA, Lw(ξ̂). In practicesimplifying assumptions have been used to effect this computation. Gordon andWang (1994a) assume that the upwelling radiance just beneath the sea surface Lu (ξ̂)
is uniform, i.e., independent of direction, while the POLDER team (University of Lille)
assume that Lw (ξ̂) is uniform. The resulting t(ξ̂), and hence the retrieved value of
Lw (ξ̂), will depend on which assumption is employed. When either Lu (ξ̂) or Lw (ξ̂)
are assumed to be uniform, the associated t(ξ̂) will be denoted by t ∗ (ξ̂). In reality,
however, neither Lu (ξ̂) nor Lw (ξ̂) are completely uniform.
Yang and Gordon (1997) show that when Lu (ξ̂) is uniform, t(ξ̂) (denoted by t ∗to differentiate it from t) can be computed from



~B−
Ed ρ
∗(GW ) t−ξ̂0 =(C.8)
F0 ξ̂0 • n̂T Tf ξ̂0Atmospheric Diffuse Transmittance

•

61

 
~B̄− is the downward irradiance at a position just below the sea surface
where Ed ρ
~B̄ , when the TOA is illuminated with the solar beam (irradiancespecified by ρF0 )

propagating in the direction ξ̂0 . The POLDER team computation of t ξ̂ is given byt∗(U L)

−ξ̂0 =

~B+
Ed ρ



F0 ξ̂0 • n̂T

(C.9)


~B+ is the downward irradiance at a position just above the sea surface
where Ed ρ
~B+ , when the TOA is illuminated with the solar beam (irradiance F0 )specified by ρ
propagating in the direction ξ̂0 . For completeness,  we provide  the associatedequations valid for any angular distribution of Lu ξ̂ and Lw ξ̂0 :

t (GW ) −ξ̂0 =



1





t (UL) −ξ̂0 =Z

 
F0 ξ̂0 • n̂T Tf ξ̂01
F0 ξ̂0 • n̂Tξ̂ • n̂TZξ̂ • n̂T L1






 Lu ρ ~B− , −ξ̂ dΩ ξ̂~B− , ξ̂L1 ρ~B− , −ξ̂0Lu ρ
(C.10)

 Lu ρ
 ~B+ , −ξ̂ dΩ ξ̂~B+ , ξ̂ρ
~B+ , −ξ̂0Lu ρ

(C.11)


~B± , ξ̂ is radiance just above (+) or just beneath (−) the sea surface
where L1 ρ
when the TOA is illuminated with the solar beam (irradiance F0 ) propagating in the
direction ξ̂0 . Over all, the integrations are in the downward direction of ξ̂. Given
either Lu (ξ) just below the water surface, or Lw (ξ) just above the water surface,exact values of the diffuse transmittance in any direction can be obtained fromthese equations. Figure C.1 provides example results for the ratio of t (U L) /t (GW )as a function of the solar (or sensor) zenith angle for wavelengths of 443 and 555
nm and for the M80 aerosols with the AOT at 865 nm of 0.1 and 0.2. Results in
Figure C.1 show that for θ ≤ 70◦ the difference between t (U L) and t (GW ) are within∼2%. Thus, we have used these relationships (Figure C.1) for making corrections inconversion between two systems in deriving the normalized water-leaving radiance.

62•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Figure C.1 The ratio of the atmospheric diffuse transmittance computed byassuming the upward radiance uniformly distributed just above the surface(t (U L) ) and just below the surface (t (GW ) ) as a function of the solar (or sensor)
zenith angle for wavelengths of 443 and 555 nm and for the M80 aerosols with
the AOT at 865 nm of 0.1 and 0.2.

.

Appendix D
Ocean Bidirectional Reflectance Distribution
Function
André Morel, Howard R. Gordon and Menghua Wang

D.1

Introduction

Developed through a series of papers over many years, the ocean bi-directionalreflectance distribution function (BRDF) of ocean water-leaving radiances has beenstudied by many scientists (Gordon and Clark, 1981; Morel and Gentili, 1991; 1993;
1996; Gordon, 2005; Wang, 2006b). Key in this development is the theoreticalconcept of the normalized water-leaving radiance, defined as the water-leaving
radiance that would be viewed at nadir when the Sun is at the zenith and mean
Earth-Sun distance, with no intervening of atmosphere. The initial definition of thenormalized water-leaving radiance (measured at the wavelength λ and solar-zenith,sensor-zenith, and relative azimuth angles of θ0 , θ, and ∆φ) by Gordon and Clark(1981)F̄0 (λ)dd0

2

Lw (λ, θ0 , θ, ∆φ),t(λ, θ0 ) cos θ0(D.1)
accounts for variations between mean extraterrestrial solar irradiance F̄0 (λ) and(+)
irradiance incident on the sea surface Ed (λ, θ0 ) due to solar zenith angle θ0 ,atmospheric transmittance t(λ, θ0 ), and effects of variations in Earth-Sun distance(d/d0 )2 during the year. Morel et al. (2002) and Morel and Gentili (1991; 1993; 1996)
extended the definition to account for additional effects due to angular variations inreflection and refraction at the sea surface and for the in-water BRDF, introducing aquantity they dubbed the exact normalized water-leaving radiance, [Lw (λ)]Exact, i.e.,N[Lw (λ, θ0 , θ, ∆φ)]N = Lw (λ, θ0 , θ, ∆φ)[Lw (λ)]Exact= [Lw (λ, θ0 , θ, ∆φ)]N
N



(+)
Ed (λ, θ0 )

(f /Q)Eff<0 (λ, τa , W ),<(λ, θ0 , θ, τa , W )(D.2)

where term (f /Q)Eff represents effects of the in-water ocean BRDF (Morel andGentili, 1996), while the term < ratio accounts for angular variations in all effects ofreflection and refraction of radiance at the sea surface. In effect, this representation
separates BRDF effects attributed to the ocean surface (term with < ratio) from
63

64

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

effects associated with the angular distribution of upwelling radiance just beneaththe water surface (Morel and Gentili, 1996)
(
!,
!)

f0 (λ, IOP)f (λ, θ0 , IOP)
(f /Q)Eff =(D.3)
Q0 (λ, IOP)
Q(λ, θ0 , θ, ∆φ, IOP)
which depends on solar-sensor geometry and the ocean inherent optical properties(IOPs). In the above, f is a coefficient that relates ocean upwelling irradiancereflectance to the ocean inherent optical properties and the Q factor is defined asratio of the upwelling irradiance just beneath the ocean surface to the upwellingradiance just beneath the ocean surface (Morel and Gentili, 1996). f0 and Q0 are
defined for f (λ, θ0 = 0, IOP) and Q(λ, θ0 = 0, θ = 0, IOP), respectively. Note that,for a uniform angular distribution of upwelling radiance just beneath the ocean
surface, {(f /Q)Eff } ≡ 1.

D.2

Ocean Surface Effects

In Equation D.2, the factor <(λ, θ0 , θ, τa , W ) is given by Morel and Gentili (1996)"#"#
1 − ρ̄f (λ, θ0 , τa , W )1 − ρf (λ, θ, W )<(λ, θ0 , θ, τa , W ) =,(D.4)
1 − r̄ R(λ, θ0 )m2
and <0 (λ, τa , W ) is defined for <(λ, θ0 = 0, θ = 0, τa , W ). ρ̄f (λ, θ0 , τa , W ) andρf (λ, θ, W ) are the surface Fresnel reflectivity for irradiance (from Sun and sky) andradiance, respectively, corresponding to a given spectral wavelength λ, solar-sensor
geometry (θ0 and θ), aerosol optical property (aerosol model and optical thickness
τa ), and surface wind speed W . In Equation D.4, R(λ, θ0 ) is the irradiance reflectancebackscattered from the water just beneath the surface, r̄ is the reflectivity (sphericalalbedo) of upward irradiance by the surface (irradiance incident upward to thesurface from below the interface), and m is the refractive index of water. We
can further define <(λ, θ0 , θ, τa , W ) as a product of functions that are dependent
separately on the solar and viewing angle alone, i.e.,<(λ, θ0 , θ, τa , W ) = <(Sun) (λ, θ0 , τa , W )<(View) (λ, θ, W ),where<(Sun) (λ, θ0 , τa , W ) =and<(View) (λ, θ, W ) =(D.5)

1 − ρ̄f (λ, θ0 , τa , W )1 − r̄ R(λ, θ0 )(D.6)

1 − ρf (λ, θ, W )
.
m2

(D.7)

The first term in Equation D.5, <(Sun) (λ, θ0 , τa , W ), corresponds to the effects of the
air-water interface for the downward irradiance contribution across from above tobeneath the surface, while the second term in Equation D.5, <(View) (λ, θ, W ), is theOcean Bidirectional Reflectance Distribution Function•65

effects of the air-water interface for the upward radiance across from beneath toabove the surface. We can thus re-write Equation D.2 as



(Sun)
(View)

<
(λ,
τ
,
W
)
<
(λ,
W
)
a
Exact
0
0

.
= [Lw (λ, θ0 , θ)]N (f /Q)Eff  (Sun)[Lw (λ)]N<(λ, θ0 , τa , W )R (View) (λ, θ, W )(D.8)◦
Recently, it has been hfound that, for cases with θ0 and θiup to ∼60 , the third(Sun)(λ, τa , W )/<(Sun) (λ, θ0 , τa , W ) , depends only on theterm in Equation D.8, <0
propertiesof the ocean surface andinot the atmosphere (Wang, 2006b), while theh(View)
term <0(λ, W )/R (View) (λ, θ, W ) can be computed accurately with a flat ocean
surface (i.e., independent of the wind speed) (Gordon, 2005). Thus, the effects
in angular variation of the surface reflection and refraction on the normalized
water-leaving radiance (< terms in Equation D.8) can be calculated easily (Gordon,
2005; Wang, 2006b). Figure
h D.1 shows typical cases of two <i terms in Equation
(Sun)
(Sun)
D.8. Figure D.1a shows <0(λ, τa , W )/<(λ, θ0 , τa , W ) (with a flat ocean
surface) as a function of the solar-zenith angle for various wavelengths and for acaseof the M80 model with aerosol
optical thickness of 0.1, while Figure D.1b showshi(View)<0(λ, W )/R (View) (λ, θ, W ) as a function of the sensor-zenith angle for various
wind speeds.

D.3

In Water BRDF Effects

Within a water body, particularly close to the interface, the upward radiance field
is not isotropic, so that a bidirectional reflectance distribution function (BRDF) has
to be taken into account. Simple considerations help explain this non-isotropic
character (see Morel et al., 2002). The first consideration deals with the average
number, ñ, of scattering events undergone by photons before they come back andreach the surface; the second one is related to the shape of the volume scatteringfunction (VSF), particularly the shape of its backward lobe (which is particularly, but
not exclusively, involved in the formation of the backward flux).
Morel and Gentili (1991) showed that ñ is equal to (1 − $)−1 , where $ isthe single scattering albedo (i.e., the ratio (b/c) of the scattering coefficient tothe attenuation coefficient). Therefore, when $ is small enough, single scattering
prevails, and the upward radiance field tends to mimic the backward lobe of the VSF,
centered on the anti-sun direction. If molecular backscattering prevails, with a roundshaped backward lobe, the upward radiance field will thus remain quasi-isotropic.
When non-negligible, the Raman effect with an almost isotropic VSF, acts in the same
direction. Alternatively, if particle backscattering prevails, with a backward peaked
lobe, the radiances coming from the anti-sun direction will be reinforced, so thatthe anisotropy will be increased.
In contrast, when particles are abundant, $ increases, thus ñ may become high(for instance, photons experiencing 5 or 10 successive scattering events before they

66•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Figure D.1 Typical cases of two < terms in Equation D.8 for (a)
(Sun)
[<0
(λ, τa , W )/<(Sun) (λ, θ0 , τa ,hW )] as a function of the solar-zenithangle
i(View)

for various wavelengths and (b) <0(λ, W )/<(View) (λ, θ, W ) as a functionof the sensor-zenith angle for various wind speeds.

Ocean Bidirectional Reflectance Distribution Function•67

can escape toward atmosphere, when $ = 0.8 or 0.9); in such cases (eutrophic waters
or very turbid waters, appropriate wavelengths), the features of the backscattering
lobe are smoothed out by the effect of multiple scattering, so that the upward
light field will tend to be isotropic again (whatever the shape of the VSF). For mostsituations and wavelengths, however, the non-isotropic character of the upward
radiance field will be the general rule.
As initially defined (Equation D.1), the normalized water-leaving radiance is stilla quantity that depends on the observational conditions (through θ0 , θ, ∆φ). To
fully respect the hypothetical geometry at the basis of the normalized water-leaving
radiance (namely, radiance emerging from nadir, and sun at zenith), it was necessary
to introduce a ‘correction’ to account for the in-water BRDF effect. This correction
is represented by (f /Q)Eff in Equation D.2, as made explicit by Equation D.3. A
detailed and illustrated description of the possible variations of the quantities f ,Q, and of their ratio f /Q, are provided by Morel and Mueller (2002), to which thereader is referred for additional information. Briefly, these variations are as follows.

D.3.1

The f -Coefficient

The irradiance reflectance (or irradiance ratio), R, is defined as the ratio of the plane
upward irradiance, Eu , to the plane downward irradiance, Ed , just below the surface:
R = Eu /Ed ; R is related to the IOP, essentially to the backscattering coefficient andthe absorption coefficient, bb and a, respectively. This relationship (wavelength λomitted) is conveniently expressed under a simplified form as R = f [bb /a], where
f is a (dimensionless) coefficient which depends on the illumination conditions,summarized by the sun zenith angle, θ0 , and on all the IOP; therefore it is written
R = f (θ0 , λ, IOP )[bb /a].
For a given λ, and a given set of IOP, f is always minimal when θ0 = 0; it isdenoted f0 in this case and its value amounts to about 1/3 (an historical value).
With increasing θ0 , f increases monotonously, by up to 100% when θ0 exceeds 60◦ .
To the extent that in Case-1 waters, the IOP, including the VSF, can be, on average,
related to the chlorophyll concentration, [Chl] (Morel et al., 2002; Morel and Gentili,2004), f can be regarded as a [Chl] dependent-coefficient (or inversely, [Chl] can be
regarded as a substitute for all IOP when expressing f ).
As a rule, both f0 (θ0 = 0, [Chl], λ) and f (θ0 , [Chl], λ) increase for increasing [Chl].
In total, f0 may exhibit values ranging from 0.28 to 0.45 (according to λ and [Chl]),
whereas f varies within a wider range, from approximately 0.28 to 0.65. Figures
13.5 and 13.6 in Morel and Mueller (2002) display the variations of f as a functionof the three variables (θ0 , λ, [Chl]). They also show the influence of the Raman effecton the f -parameter, which is not negligible especially in very clear waters (i.e., when[Chl] is low, for instance, 0.03 mg m−3 ).

68

•

D.3.2

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

The Q-Coefficient

The Q-Coefficient describes the angular structure of the upward radiance field, as it
stands immediately beneath the surface. It is defined via the relationship between
any upward radiance (Lu ) and the upward plane irradiance, Eu (actually the integralof the upward radiance field), so that
Lu (λ, θ0 , θ, ∆φ, IOP) = Eu (λ, θ0 , IOP)/Q(λ, θ0 , θ, ∆φ, IOP).
Q is expressed as steradian, and would be constant and equal to π (sr), if the
upward radiance field was uniform. In natural waters, values between 2 and 6, or
more, are possible when all (θ − ∆φ) directions are considered. For the upward
directions within the Snell cone, i.e., for the upward radiances oriented in such a
way that they are able to emerge, the range of variations in Q is more restricted. The
particular Q-value, denoted Q0 (λ, IOP), corresponds to both a sun at zenith and a
viewing nadir angle θ = 0 (i.e., when aiming at nadir); Q0 is spectrally rather flat,but depends on [Chl] (a substitute for IOP in Case-1 waters); it increases from about
π to 4.3, when [Chl] goes from 0.03 to 10 mg m−3 (Fig. 13.7 in Morel and Mueller,
2002). If θ0 , the solar zenith angle, increases, but the viewing angle, θ, remains null,
the corresponding function for nadir (denoted Qn )Qn = Q(λ, θ0 , θ = 0, ∆φ = 0, IOP)
also increases when θ0 goes from 0◦ to 60◦ , by 30 to 100% depending on [Chl].

D.3.3

The Ratio f /Q

The particular value f0 (λ, IOP)/Q0 (λ, IOP), which appears in Equation D.3, is builtwith the particular values of both f and Q, pertinent to an observation at nadir
and when the sun is at zenith. This ratio varies within the range 0.075 and 0.120(sr−1 ), or actually within a narrower interval if only the blue and green radiations are
considered. Indeed, the highest values occur for the red wavelengths (> 600 nm),and for the IOP corresponding to the lowest [Chl]; this enhancement is (partly) due
to the influence of the Raman scattering in such waters when λ exceeds 560 nm.
For all geometries and conditions, the ratio f (λ, θ0 , IOP)/Q(λ, θ0 , θ, ∆φ, IOP) isalways larger than f0 (λ, IOP)/Q0 (λ, IOP), and experiences considerable variations
with rather complex geometrical structures (see Fig. 13.10, Morel and Mueller, 2002).
The highest values are always found in the principal plane, either in the direction of
the sun (∆φ = 0) or in the anti-sun (∆φ = π ) direction (depending on the shape of
the VSF, i.e. on [Chl]). As f and Q experience concomitant increases when the solar
zenith angle increases, their ratio is less varying than the two terms themselves. In
total, variations to be expected for f /Q are within the limits 0.08 (low [Chl], blue
wavelengths, high sun, quasi-vertical viewing) and about 0.16 (high [Chl], large sunangle and viewing angle approaching the critical angle).

Ocean Bidirectional Reflectance Distribution Function

D.3.4

•

69

The Corrective Term (f /Q)Eff

Defined above (Equation D.3) as{f0 (λ, IOP )/Q0 (λ, IOP )}/{f (λ, θ0 , IOP )/Q(λ, θ0 , θ, ∆φ, IOP )},this term is always smaller than 1, as the numerator is a minimal value of f /Q.
Since the numerator and denominator (with λ and IOP in common) partly experiencesimilar trends, the variations in the above ratio are thus more limited. In effect,
this corrective term varies approximately between the upper value 1, and 0.6, in theworse conditions of observation (such as high [Chl], slant viewing angle, low sun
elevation).

D.3.5

Additional Comments

All the above f and Q values have been obtained by solving the radiative transfer
equation (RTE) for the coupled atmosphere-ocean system (Morel and Gentili, 1991;
1993; 1996). The numerical solutions of the RTE were obtained through Monte-Carlosimulations and also by using the invariant embedding method i.e. the HYDROLIGHT
code developed by Mobley (1994). Only clear cloudless skies were considered. In
the above expressions, the dependency on the illumination conditions was simply
summarized by a single parameter, namely θ0 , the sun-zenith angle, whilst in
reality these conditions are also determined by the aerosol content (and nature). A
sensitivity study (Fig. 9 in Morel and Gentili, 1996) showed that the influence of
the aerosol optical thickness on f /Q is weak (< 10%) and thus can be neglected.
The same can be said about the wind speed which governs the sea state and surface
slopes, and is of second order effect regarding the upward radiant field.
About the ocean itself, it is important to note that only Case-1 waters withvarying [Chl] have been considered in the computations, because their average IOP
are predictable and can be used as inputs in the RTE computations. Therefore, the
BRDF effects are modelled for these Case-1 waters, and the present BRDF correction
was proposed only for these waters.
The Q and f /Q coefficients have been produced for nadir angles, θ, between◦
1 and 90◦ (17 values), and for 13 values for the azimuth difference (∆φ from0 to 180◦ ). Therefore, the geometrical structure of the entire (2π sr) in-water
upward radiance field is described with a sufficient spatial resolution for efficientinterpolation. This description extending on the half space is more than what isneeded when considering the radiances able to emerge (those within the Snell circle,
with θ ∼48◦ ), or those able to be included within the swath of an orbiting sensor(θ < 35◦ − 40◦ ). A full 2π description of the radiant field, however, is needed whencomparing in-water upward radiance measurements and theoretical predictions,which is the only way of testing the skill of the radiance model.
Such tests were carried out with satisfactory results by using various radiancedistribution camera systems at sea (Voss, 1989; Voss and Chapin, 2005). The first

70•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

successful comparison between experimental and predicted Q-values (Morel et al.,1995) was made in Case-1 water with [Chl] ∼0.3 mg m−3 , at three wavelengths, andwith a sun-zenith angle varying from 32◦ to 80◦ (the historical data from Lake Pend
Oreille, at various depths, were used additionally in this test). In a second series ofcomparisons made at four wavelengths, the variation in the sun zenith angle wasrestricted (28◦ − 40◦ ), whereas the [Chl] range was large (0.14 – 11 mg m−3 ) (Vossand Morel, 2005). Upwelling radiance distributions from several cruises in varied
Case-1 waters ([Chl] from 0.03 to 1.4 mg m−3 ) and with a wide range of solar zenith
angles (0 − 80◦ ), were studied (Voss et al., 2007). From these data, it was shownthat the RMS difference between modelled and measured Lu (θ, ∆φ)/Lu (nadir) wasof the order of 0.03, well within the noise in the data.
It can be concluded that, in Case-1 waters, the bidirectional effect is well understood and can be accurately corrected for. The situation is considerably lessfavorable in Case-2 waters (sediment-dominated or yellow substance dominatedCase-2 waters), despite some preliminary attempts (Loisel and Morel, 2001) whichcannot be generalized. The lack of a reliable prediction and the absence of genericparameterizations for the IOP in such complex waters currently remain a serious
obstacle to further development, except on a case-by-case basis.

References

Antoine D., d’Ortenzio F., Hooker S.B., Becu G., Gentili B., Tailliez D., Scott A.J. (2008). Assessment of
uncertainty in the ocean reflectance determined by three satellite ocean color sensors (MERIS,
SeaWiFS and MODIS-A) at an offshore site in the Mediterranean Sea (BOUSSOLE project). J.
Geophys. Res. 113, C07013, doi: 10.1029/2007JC004472
Antoine D., Morel A. (1998). Relative importance of multiple scattering by air molecules and aerosols
in forming the atmospheric path radiance in the visible and near-infrared parts of the spectrum.
Appl. Opt. 37: 2245-2259
Antoine D., Morel A. (1999). A multiple scattering algorithm for atmospheric correction of remotelysensed ocean color (MERIS instrument): principle and implementation for atmospheres carrying
various aerosols including absorbing ones. Int. J. Remote Sens. 20: 1875-1916
Antoine D., Nobileau D. (2006). Recent increase of the dust load over the Mediterranean Sea, as
revealed from 6 years of ocean color satellite (SeaWiFS) observations. J. Geophys. Res. 111,
D12214, doi: 10.1029/2005JD006795
Austin R.W. (1974). The remote sensing of spectral radiance from below the ocean surface. In: Jerlov
N.G., Nielsen E.S. (Eds.) Optical Aspects of Oceanography. Academic, San Diego, Calif., p 317-344
Bailey S.W., McClain C.R., Werdell P.J., Schieber B.D. (2000). Normalized water-leaving radiance andchlorophyll-a match-up analyses. Report No. Vol. 10, NASA Tech. Memo. 2000-206892, Hooker,
S.B., Firestone, E.R. (Eds.), NASA Goddard Space Flight Center, Greenbelt, Maryland
Bailey S.W., Werdell P.J. (2006). A multi-sensor approach for the on-orbit validation of ocean color
satellite data products. Remote Sens. Environ. 102: 12-23
Banzon V.F., Evans R.E., Gordon H.R., Chomko R.M. (2004). SeaWiFS observations of the Arabian Sea
southwest monsoon bloom for the year 2000. Deep-Sea Res. II 51: 189-208
Brajard J., Jamet C., Moulin C., Thiria S. (2006). Use of a neuro-variational inversion for retrieving
oceanic and atmospheric constituents from satellite ocean color sensor: Application to absorbing
aerosols. Neural Networks 19: 178-185
Bricaud A., Morel A. (1987). Atmospheric correction and interpretation of marine radiances in CZCS
imagery: use of a reflectance model. Oceanologica Acta, SP: 33-50
Chomko R., Gordon H.R. (1998). Atmospheric correction of ocean color imagery: use of the Junge
power-law aerosol size distribution with variable refractive index to handle aerosol absorption.
Appl. Opt. 37: 5560-5572
Chomko R.M., Gordon H.R. (2001). Atmospheric correction of ocean color imagery: test of the spectral
optimization algorithm with SeaWiFS. Appl. Opt. 40: 2973-2984
Chomko R.M., Gordon H.R., Maritorena S., Siegel D.A. (2003). Simultaneous retrieval of oceanic andatmospheric parameters for ocean color imagery by spectral optimization: a validation. Remote
Sens. Environ. 84: 208-220
Clark D.K. (1981). Phytoplankton algorithms for the Nimbus-7 CZCS. In: Gower J.R.F. (ed) Oceanography
from Space. Plenum, New York, p 227-238
Clarke G.K., Ewing G.C., Lorenzen C.J. (1970). Spectra of backscattered light from the sea obtained
from aircraft as a measure of chlorophyll. Science 167: 1119-1121
Clarke G.L., Ewing G.C. (1974). Remote spectroscopy of the sea for biological production studies.
In: Jerlov N.G., Steemann-Nielsen E. (Eds.) Optical aspects of oceanography. Academic Press,
London, New York, p 389-413
Cox C., Munk W. (1954). Measurements of the roughness of the sea surface from photographs of the
sun’s glitter. J. Opt. Soc. Am. 44: 838-850

71

72

•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Deschamps P.Y., Fougnie B., Frouin R., Lecomte P., Verwaerde C. (2004). SIMBAD: a field radiometer forsatellite ocean color validation. Appl. Opt. 43: 4055-4069
Deuze J.L., Herman M., Santer R. (1989). Fourier series expansion of the radiative transfer equation in
the atmosphere-ocean system. J. Quant. Spectrosc. Radiat. Transfer 41: 483-494
Ding K., Gordon H.R. (1994). Atmospheric correction of ocean-color sensors: effects of the Earth’s
curvature. Appl. Opt. 33: 7096-7106
Dubuisson P., Frouin R., Dessailly D., Duforêt L., Léon J.-F., Voss K., Antoine D. (2009). Estimating thealtitude of aerosol plumes over the ocean from reflectance ratio measurements in the O2 A-band.
Rem. Sens. Environ, 113: 1899-1911
Fell F., Fischer J. (2001). Numerical simulation of the light field in the atmosphere ocean system using
the matrix-operator method. J. Quant. Spectrosc. Radiat. Transfer 69: 351-388
Feng H., Vandemark D., Campbell J.W., Holben B.N. (2008). Evaluation of MODIS ocean color products
at a northeast United States coast site near the Martha’s Vineyard Coastal Observatory. Int. J.
Remote Sens. 29: 4479-4497
Fougnie B. (1998). Contribution of the POLDER satellite sensor to observing ocean color (in French).
Ph.D, No. 2342, University of Lille, France
Frouin R., Pelletier B. (2007). Fields of non-linear regression models for atmospheric correction ofsatellite ocean-color imagery. Remote Sens. Environ. 11: 450-465
Frouin R., Schwindling M., Deschamps P.Y. (1996). Spectral reflectance of sea foam in the visible andnear infrared: In situ measurements and remote sensing implications. J. Geophys. Res. 101(C6):14,361-14,372
Fukushima H., Higurashi A., Mitomi Y., Nakajima T., Noguchi T., Tanaka T., Toratani M. (1998).
Correction of atmospheric effects on ADEOS/OCTS ocean color data: Algorithm description andevaluation of its performance. J. Oceanogr. 54: 417-430
Fukushima H., Toratani M., Murakami H., Deschamps P.Y., Frouin R., Tanaka A. (2007). Evaluation of
ADEOS-II GLI ocean color atmospheric correction using SIMBADA handheld radiometer data. J.
Oceanogr. 63: 533-543
Garver S.A., Siegel D.A. (1997). Inherent optical property inversion of ocean color spectra and its
biogeochemical interpretation: 1. Time series from the Sargasso Sea. J. Geophys. Res. 102:
18,607-18,625
Gordon H.R. (1978). Removal of atmospheric effects rom satellite imagery of the oceans. Appl. Opt.
17: 1631-1636
Gordon H.R. (1980). A preliminary assessment of the NIMBUS-7 CZCS atmospheric correction algorithm
in a horizontally inhomogenous atmosphere. In: Gower J.F.R. (ed) Oceanography from Space.
Plenum Press, New York and London, p 281-294
Gordon H.R. (1989). Can the Lambert-Beer law be applied to the diffuse attenuation coefficient ofocean water. Limnol. Oceanogr. 34: 1389-1409
Gordon H.R. (1997). Atmospheric correction of ocean color imagery in the Earth Observing System era.
J. Geophys. Res. 102: 17,081-17,106
Gordon H.R. (2005). Normalized water-leaving radiance: revisiting the influence of surface roughness.
Appl.Opt. 44: 241-248
Gordon H.R., Brown J.W., Evans R.H. (1988a). Exact Rayleigh scattering calculations for use with the
Nimbus-7 Coastal Zone Color Scanner. Appl. Opt. 27: 862-871
Gordon H.R., Brown O.B., Evans R.H., Brown J.W., Smith R.C., Baker K.S., Clark D.K. (1988b). A
semianalytic radiance model of ocean color. J. Geophys. Res. 93: 10909-10924
Gordon H.R., Brown O.B., Jacobs M.M. (1975). Computed relationship between the inherent andapparent optical properties of a flat homogeneous ocean. Appl. Opt. 14: 417-427
Gordon H.R., Clark D.K. (1980). Atmospheric effects in the remote sensing of phytoplankton pigments.
Boundary-layer Meteorology 18: 299-313
Gordon H.R., Clark D.K. (1981). Clear water radiances for atmospheric correction of coastal zone color
scanner imagery. Appl. Opt. 20: 4175-4180
Gordon H.R., Clark D.K., Brown J.W., Brown O.B., Evans R.H., Broenkow W.W. (1983). Phytoplankton
pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and
CZCS estimates. Appl. Opt. 22: 20-36

References•

73

Gordon H.R., Du T., Zhang T. (1997). Remote sensing of ocean color and aerosol properties: resolving
the issue of aerosol absorption. Appl. Opt. 36: 8670-8684
Gordon H.R., Morel A. (1983). Remote assessment of ocean color for interpretation of satellite visible
imagery: A review, Vol. Springer-Verlag, New York
Gordon H.R., Wang M. (1992). Surface roughness considerations for atmospheric correction of ocean
color sensors. 2: Error in the retrieved water-leaving radiance. Appl. Opt. 31: 4261-4267
Gordon H.R., Wang M. (1994a). Retrieval of water-leaving radiance and aerosol optical thickness over
the oceans with SeaWiFS: A preliminary algorithm. Appl. Opt. 33: 443-452
Gordon H.R., Wang M. (1994b). Influence of oceanic whitecaps on atmospheric correction of ocean-color
sensor. Appl. Opt. 33: 7754-7763
Gross-Colzy L., Colzy F., Frouin R., Henry P. (2007a). A general ocean color atmospheric correction
scheme based on principal component analysis-Part 1: Performance on Case 1 and Case 2
waters. In: Frouin R., Lee Z. (Eds.) Coastal Ocean Remote Sensing. SPIE, Bellingham, WA, doi:
/10.1117/12.738508
Gross-Colzy L., Colzy F., Frouin R., Henry P. (2007b). A general ocean color atmospheric correction
scheme based on principal component analysis-Part 2: Level 4 merging capabilities. In: Frouin
R., Lee Z. (Eds.) Coastal Ocean Remote Sensing, Bellingham Wa, doi: /10.1117/12.738514
Hale G.M., Querry M.R. (1973). Optical constants of water in the 200-nm to 200-µm wavelength region.
Appl. Opt. 12: 555-563
Jamet C., Thiria S., Moulin C., Crépon M. (2005). Use of a neurovariational inversion for retrieving
oceanic and atmospheric constituents from ocean color imagery: A feasibility study. J. Atmos.
Ocean Technol. 22: 460-475
Koepke P. (1984). Effective reflectance of oceanic whitecaps. Appl. Opt. 23: 1816-1824
Kuchinke C.P., Gordon H.R., Franz B.A. (2009). Spectral optimization for constituent retrieval in Case 2
waters I: Implementation and performance. Remote Sens. Environ. 113: 571-587
Kuchinke C.P., Gordon H.R., L. W. Harding J., Voss K.J. (2009). Spectral optimization for constituent
retrieval in Case 2 waters II: Validation study in the Chesapeake Bay. Remote Sens. Environ. 113:
610-621
Liu X., Wang M., Shi W. (2009). A study of a Hurricane Katrina-induced phytoplankton bloomusing satellite observations and model simulations. J. Geophys. Res. 114, C03023, doi:
10.1029/2008JC004934
Loisel H., Morel A. (2001). Non-isotropy of the upward radiance field in typical coastal (Case 2) waters.
Int. J. Remote Sens. 22: 275-295
Maritorena S., Siegel D.A., Peterson A. (2002). Optimization of a semi-analytical ocean color model for
global scale applications. Appl. Opt. 41: 2705-2714
McClain C., Esaias W., Feldman G., Frouin R., Gregg W., Hooker S. (2002). The proposal for the NASASensor Intercalibration and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS)
Program, 1995. Report No. NASA Tech. Memo. 2002-210008, 54pp, NASA Goddard Space Flight
Center, Greenbelt, Maryland, 54 pp
McClain C.R., Feldman G.C., Hooker S.B. (2004). An overview of the SeaWiFS project and strategies for
producing a climate research quality global ocean bio-optical time series. Deep-Sea Res. II 51:
5-42
Mélin F., Zibordi G., Berthon J.F. (2007). Assessment of satellite ocean color products at a coastal site.
Remote Sens. Environ. 110: 192-215
Mobley C.D. (1994). Light and Water: Radiative Transfer in Natural Waters, Academic, New YorkMonahan E.C., O’Muircheartaigh I.G. (1986). Whitecaps and the passive remote sensing of the ocean
surface. Int. J. Remote Sens. 7: 627-642
Moore G.F., Aiken J., Lavender S. (1999). The atmospheric correction of water color and the quantitative
retrieval of suspended particulate matter in Case II waters: application to MERIS. Int. J. Remote
Sens. 20: 1713-1733
Moore K.D., Voss K.J., Gordon H.R. (2000). Spectral reflectance of whitecaps: Their contribution towater-leaving radiance. J. of Geophys. Res. 105: 6493-6499
Morel A. (1980). In-water and remote measuements of ocean color. Boundary-layer Meteorol. 18:
177-201

74•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Morel A. (1982). Optical properties and radiant energy in the waters of the Guinea dome and theMauritanian upwelling area in relation to primary production. Conseil International pour
I’Exploration de la Mer; Rapports et Proces Verbaux 180: 94-107
Morel A., Antoine D., Gentili B. (2002). Bidirectional reflectance of oceanic waters: accounting for
Raman emission and varying particle scattering phase function. Appl. Opt. 41: 6289-6306
Morel A., Gentili B. (2004). Radiation transport within oceanic (case 1) water. J. Geophys. Res. 109:
C06008, doi: 10.1029/2003JC002259
Morel A., Gentili G. (1991). Diffuse reflectance of oceanic waters: its dependence on Sun angle asinfluenced by the molecular scattering contribution. Appl. Opt. 30: 4427-4438
Morel A., Gentili G. (1993). Diffuse reflectance of oceanic waters. II. Bidirectional aspects. Appl. Opt.
32: 6864-6879
Morel A., Gentili G. (1996). Diffuse reflectance of oceanic waters. III. Implication of bidirectionality forthe remote-sensing problem. Appl. Opt. 35: 4850-4862
Morel, A., Mueller, J.L. (2002). Normalized water-leaving radiance and remote sensing reflectance:bidirectional reflectance and other factors. In: Mueller, J.L., Fargion, G.S. (Eds.), Ocean Optics
Protocols for Satellite Ocean Color Sensor Validation, Revision 3, Vol. 2, NASA/TM-2002-210004,
Goddard Space Flight Center, Greenbelt, Maryland, USA, p 183-210
Morel A., Prieur L. (1977). Analysis of variations in ocean color. Limnol. Oceanogr. 22: 709-722
Morel A., Voss K.J., Gentili B. (1995). Bidirectional reflectance of oceanic waters - a comparison ofmodeled and measured upward radiance fields. J. Geophys. Res. 100: 13,143-13,150
Moulin C., Gordon H.R., Chomko R.M., Banzon V.F., Evans R.H. (2001a). Atmospheric correction ofocean color imagery through thick layers of Saharan dust. Geophys. Res. Letters 28: 5-8
Moulin C., Gordon H.R., Banzon V.F., Evans R.H. (2001b). Assessment of Saharan dust absorption in
the visible from SeaWiFS imagery. J. Geophys. Res. 106: 18,239-218,249
Mueller J.M., Fargion G.S. (2002). Ocean Optics Protocols for Satellite Ocean Color Sensor Validation,
Revision 3, Part I & II. Report No. NASA Tech. Memo. 2002-210004, NASA Goddard Space Flight
Center, Greenbelt, Maryland, USA
Murakami H., Sasaoka K., Hosoda K., Fukushima H., Toratani M., Frouin R., Mitchell B.G., Kahru M.,
Deschamps P.Y., Clark D., Flora S., Kishino M., Saitoh S., Asanuma I., Tanaka A., Sasaki H.,
Yokouchi K., Kiyomoto Y., Saito H., Dupouy C., Siripong A., Matsumura S., Ishizaka J. (2006).
Validation of ADEOS-II GLI ocean color products using in situ observations. J. Oceanogr. 62:
373-393
Nakajima T., Tanaka M. (1988). Algorithms for radiative intensity calculations in moderately thickatmospheres using a truncation approximation. J. Quant. Spectrosc. Radiat. Transfer 40: 51-69
Nakajima T., Tanaka M., Yamamoto M., Shiobara M., Arao K., Nakanishi Y. (1989). Aerosol opticalcharacteristics in the yellow sand events observed in May, 1982 at Nagasaki-part II models. J.
Meteor. Soc. Japan 67: 279-291
NASDA-EOC (1997). Advanced Earth Observing Satellite (ADEOS) OCTS data processing algorithm
description, Ver. 2.0.1. http://suzaku.eorc.jaxa.jp/GLI2/adeos/Products/Specifications/
OCTSAlgoPDF.html

NASDA-EOC (2004). GLI ocean algorithm description: Atmospheric correction (OTSK1A), Ver.2.1.
http://suzaku.eorc.jaxa.jp/GLI/ocean/algorithm/index.html

Nezlin N.P., DiGiacomo P.M., Diehl D.W., Jones B.H., Johnson S.C., Mengel M.J., Reifel K.M., Warrick
J.A., Wang M. (2008). Stormwater plume detection by MODIS imagery in the southern California
coastal ocean. Est. Coast. Shelf Sci. 80: 141-152
Nicolas J.M., Deschamps P.Y., Frouin R. (2001). Spectral reflectance of oceanic whitecaps in the visible
and near infrared: Aircraft measurements over open ocean. Geophy. Res. Lett. 28: 4445-4448
Nobileau D., Antoine D. (2005). Detection of blue-absorbing aerosols using near infrared and visible(ocean color) remote sensing observations. Remote Sens. Environ. 95: 368-387
Patt F.S., Barnes R.A., R. E. Eplee J., Franz B.A., Robinson W.D., Feldman G.C., Bailey S.W., Gales J.,
Werdell P.J., Wang M., Frouin R., Stumpf R.P., Arnone R.A., R. W. Gould J., Martinolich P.M.,
Ransibrahmanakul V., O’Reilly J.E., Yoder J.A. (2003). Algorithm updates for the fourth SeaWiFS
data reprocessing. Report No. Vol. 22, NASA Tech. Memo. 2003-206892, Hooker, S.B., Firestone,
E.R. (Eds.), NASA Goddard Space Flight Center, Greenbelt, Maryland, 74 pp

References•75

Pelletier B., Frouin R. (2006). Remote sensing of chlorophyll-a concentration by use of ridge function
fields. Appl. Opt. 45: 784-798
Ruddick K.G., Ovidio F., Rijkeboer M. (2000). Atmospheric correction of SeaWiFS imagery for turbid
coastal and inland waters. Appl. Opt. 39: 897-912
Schroeder T., Behnert I., Schaale M., Fischer J., Doerffer R. (2007). Atmospheric correction algorithm
for MERIS above case-2 waters. Int. J. Remote Sens. 28: 1469-1486
Shettle E.P., Fenn R.W. (1979). Models for the Aerosols of the Lower Atmosphere and the Effects of
Humidity Variations on Their Optical Properties. Report No. AFGL-TR-79-0214, U.S. Air Force
Geophysics Laboratory, Hanscom Air Force Base, Mass.
Shi W., Wang M. (2007). Observations of a Hurricane Katrina-induced phytoplankton bloom in the Gulf
of Mexico. Geophy. Res. Lett. 34(11): L11607
Shi W., Wang M. (2008). Three-dimensional observations from MODIS and CALIPSO for ocean responses to cyclone Nargis in the Gulf of Martaban. Geophy. Res. Lett. 35: L21603, doi:
10.1029/2008GL035279
Shi W., Wang M. (2009). Satellite observations of flood-driven Mississippi River plume in the spring of2008. Geophy. Res. Lett. 36: L07607, doi: 10.1029/2009GL037210
Shimada M., Oaku H., Mitomi Y., Murakami H., Nakamura Y., Ishizaka J., Kawamura H., Tanaka T.,
Kishino M., Fukushima H. (1998). Calibration and validation of the ocean color version-3 productfrom ADEOS OCTS. J. Oceanogr. 54: 401-416
Siegel D.A., Wang M., Maritorena S., Robinson W. (2000). Atmospheric correction of satellite ocean
color imagery: the black pixel assumption. Appl. Opt. 39: 3582-3591
Smith R.C., Baker K.S. (1978). The bio-optical state of ocean waters and remote sensing. Limnol.
Oceanogr. 23: 247-259
Smith R.C., Baker K.S. (1981). Optical properties of the clearest natural waters. Appl. Opt. 20: 177-184
Smith R.C., Wilson W.H. (1981). Ship and satellite bio-optical research in the California Bight. In: Gower
J.F.R. (ed) Oceanography from Space. Plenum Press, New York and London, p 281-294
Steinmetz F. (2008). Study of the correction of atmospheric scattering and sunlight reflected by thewind-ruffled surface for observing ocean color from space (in French). Ph.D, No. 4160, Universityof Lille, France
Tanaka A., Kishino M., Doerffer R., Schiller H., Oishi T., Kubota T. (2004). Development of a neuralnetwork algorithm for retrieving concentrations of chlorophyll, suspended matter and yellow
substance from radiance data of the Ocean Color and Temperature Scanner. J. Oceanogr. 60:
519-530
Toratani M., Fukushima H., Murakami H., Tanaka A. (2007). Atmospheric correction scheme for GLI
with absorptive aerosol correction. J. Oceanogr. 63: 525-532
Tyler J.E. (1973). SCOR Discoverer Expedition, May 1970: data report - measurements of photosynthesis,
available radiant flux and supporting oceanographic data. Unesco-sponsored programmes andpublications, University of California, Scripps Institution of Oceanography, San Diego, USA
Tyler J.E., Smith R.C. (1970). Measurements of spectral irradiance underwater, Vol. Gordon and Breach
Science Publishers, New York, 103 pp
Viollier M., Tanre, D., Deschamps P. Y. (1980). An algorithm for remote sensing of water color fromspace. Boundary Layer Meteorol. 18: 247-267
Voss K.J. (1989). Electro-optic camera system for measurement of the underwater radiance distribution.
Optical Engineering 28: 241-247
Voss K.J., Chapin A.L. (2005). Upwelling radiance distribution camera system, NURADS. Optics Express
13: 4250-4262
Voss K.J., Morel A., Antoine D. (2007). Detailed validation of the bidirectional effect in various Case 1
waters for application to ocean color imagery. Biogeosciences 4: 781-789
Wang M. (2000). The SeaWiFS atmospheric correction algorithm updates. Report No. Vol. 9, NASA Tech.
Memo. 2000-206892, Hooker, S.B., Firestone, E.R. (Eds.), NASA Goddard Space Flight Center,Greenbelt, Maryland
Wang, M. (2002). The Rayleigh lookup tables for the SeaWiFS data processing: Accounting for theeffects of ocean surface roughness. Int. J. Remote Sens. 23: 2693-2702.

76•

Atmospheric Correction for Remotely-Sensed Ocean-Colour Products

Wang M. (2004). Extrapolation of the aerosol reflectance from the near-infrared to the visible: thesingle-scattering epsilon vs multiple-scattering epsilon method. Int. J. Remote Sens. 25: 36373650
Wang M. (2005). A refinement for the Rayleigh radiance computation with variation of the atmosphericpressure. Int. J. Remote Sens. 26: 5651-5663
Wang M. (2006a). Aerosol polarization effects on atmospheric correction and aerosol retrievals inocean color remote sensing. Appl. Opt. 45: 8951-8963
Wang M. (2006b). Effects of ocean surface reflectance variation with solar elevation on normalized
water-leaving radiance. Appl. Opt. 45: 4122-4128
Wang M. (2007). Remote sensing of the ocean contributions from ultraviolet to near-infrared using theshortwave infrared bands: simulations. Appl. Opt. 46: 1535-1547
Wang M., Bailey S. (2001). Correction of the sun glint contamination on the SeaWiFS ocean andatmosphere products. Appl. Opt. 40: 4790-4798
Wang M., Gordon H.R. (1994). A simple, moderately accurate, atmospheric correction algorithm for
SeaWiFS. Remote Sens. Environ. 50: 231-239
Wang M., Knobelspiesse K.D., McClain C.R. (2005). Study of the Sea-Viewing Wide Field-of-View Sensor(SeaWiFS) aerosol optical property data over ocean in combination with the ocean color products.
J. Geophys. Res. 110, D10S06, doi: 10.1029/2004JD004950
Wang M., Shi W. (2005). Estimation of ocean contribution at the MODIS near-infrared wavelengths
along the east coast of the U.S.: Two case studies. Geophy. Res. Lett. 32(13): L13606.1-L13606.5
Wang M., Shi W. (2008). Satellite observed algae blooms in China’s Lake Taihu. Eos Trans. AGU 89:
201-202
Wang M., Son S., Shi W. (2009). Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction
algorithm using SeaBASS data. Remote Sens. Environ. 113: 635-644
Wang M., Tang J., Shi W. (2007). MODIS-derived ocean color products along the China east coastal
region. Geophy. Res. Lett. 34, L06611, doi: 10.1029/2006GL028599
Werdell P.J., Bailey S., Fargion G., Pietras C., Knobelspiesse K., Feldman G., McClain C.R. (2003).
Unique data repository facilitates ocean color satellite validation Eos, Transactions, American
Geophysical Union, 377 pp
Werdell P.J., Bailey S.W. (2005). An improved in-situ bio-optical data set for ocean color algorithm
development and satellite data product validation. Remote Sens. Environ. 98: 122-140
Yang H., Gordon H.R. (1997). Remote sensing of ocean color: assessment of water-leaving radiancebidirectional effects on atmospheric diffuse transmittance. Appl. Opt. 36: 7887-7897
Zibordi G., Mélin F., Berthon J.-F. (2006). Comparison of SeaWiFS, MODIS and MERIS radiometricproducts at a coastal site. Geophy. Res. Lett. 33: L06617, 10.1029/2006GL025778

Acronyms and Abbreviations

ACWG

Atmospheric Correction Working GroupAOT

Aerosol Optical Thickness

BRDF

Bi-directional Reflectance Distribution Function

CNES

Centre National d’Etudes Spatiales

CZCS

Coastal Zone Color Scanner

ESA

European Space Agency

GLI

Global Imager

IOCCG

International Ocean-Colour Coordinating GroupIOP

Inherent Optical Property

JAXA

Japan Aerospace Exploration Agency

LIDAR

Light Detection and Ranging

LOA

Laboratoire d’Optique Atmosphérique

LUTs

Lookup Tables

MERIS

Medium Resolution Imaging Spectrometer

MODIS

Moderate Resolution Imaging Spectroradiometer

MOM

Matrix Operator Method

NASA

National Aeronautics and Space Administration

NASDA

National Space Development Agency of Japan (now JAXA)NIRNear-Infrared

NOMAD

NASA bio-Optical Marine Algorithm Dataset

OCTS

Ocean Color and Temperature Scanner

POLDER

Polarization and Directionality of the Earth’s Reflectances

PPA

Plane-Parallel Atmosphere

RH

Relative Humidity

RTE

Radiative Transfer Equation

RMS

Root Mean Square

SeaWiFS

Sea-viewing Wide Field-of-View Sensor

SSE

Single Scattering Epsilon

SIMBAD

Optical radiometer designed by LOA to validate ocean-colour observations from space

SIMBADA

Advanced SIMBADSIMBIOS

Sensor Intercomparison for Marine Biological and Interdisciplinary Ocean Studies

SMA

Spectral Matching Algorithm

SOA

Spectral Optimization Algorithm

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SOS

Successive Order of Scattering

SSE

Single Scattering Epsilon

STD

Standard Deviation

SWIR

Shortwave Infrared

TOA

Top of Atmosphere

VIS

VisibleVSF

Volume Scattering Function