Idea Transcript
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:1
OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in Case 1 waters (“Clear Waters Ocean Colour Products” or “CWOC”) DOCUMENT REF: DELIVERABLE REF:
S3L2SD03C10LOVATBD SD03C
VERSION:
2.2
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
David ANTOINE
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:2
Document Signature Table Name
Function
Company
D. Antoine
OLCI Expert
Consultant
O. Fanton d’Andon
OLCI coordinator
ACRIST
Approved
L. Bourg
OLCI expert
ACRIST
Released
O. Fanton d’Andon
OLCI coordinator
ACRIST
Prepared
Signature
Date July 13, 2010
Change record Issue
Date
Description
2.0
March 30, 2010
Version 2 for CDR delivery
2.1
April 10, 2010
Minor Updates
2.2
July 13, 2010
Change pages
Version 2.2 for CDR delivery
Clarified list of products in Section 3.3.1
Distribution List Organisation
To
ESA
Philippe Goryl, Alessandra Buongiorno and Carla Santella
EUMETSAT
Vincent FournierSicre and Vincenzo Santacesaria
CONSORTIUM PARTNERS
ARGANS, ACRIST, RAL, Brockmann Consult, ElsagDatamat
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:3
Table of content 1. INTRODUCTION .............................................................................................................. 6 1.1 PURPOSE AND SCOPE ........................................................................................................ 6 1.2 ACRONYMS ....................................................................................................................... 6 1.3 SYMBOLS ........................................................................................................................... 7 1.4 ALGORITHM IDENTIFICATION .......................................................................................... 8 2. ALGORITHM OVERVIEW ............................................................................................. 9 2.1 OBJECTIVES ....................................................................................................................... 9 3. ALGORITHM DESCRIPTION ..................................................................................... 10 3.1 THEORETICAL DESCRIPTION .......................................................................................... 10 3.1.1 The chlorophyll concentration, Chl ................................................................... 10 3.1.2 The diffuse attenuation coefficient at 490 nm, Kd(490) .................................. 12 3.1.3 The total absorption and backscattering coefficients (a and bb) ................... 13 3.1.4 Can the CDOM absorption coefficient (ag) be derivable?.............................. 18 3.1.5 Alternative approach: the GSM algorithm ....................................................... 20 3.2 ERROR ESTIMATES .......................................................................................................... 23 3.2.1 Semiempirical algorithm .................................................................................... 23 3.2.2 GSM algorithm ..................................................................................................... 24 3.3 SUMMARY OF RECOMMENDATIONS ............................................................................... 26 3.3.1 Products ................................................................................................................. 26 3.3.2 Pixelbypixel error estimates ............................................................................. 27 4. ASSUMPTIONS AND LIMITATIONS....................................................................... 28 4.1 ASSUMPTIONS ................................................................................................................ 28 4.2 CONSTRAINTS, LIMITATIONS.......................................................................................... 28 5. REFERENCES.................................................................................................................... 29 6. APPENDIX: B BW COMPUTATION .............................................................................. 31
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:4
List of Figures
Figure 1: Adapted from Fig. 6 of Morel 2007: Ratios ρ 2,5 , ρ 3,5 , ρ 4,5 of reflectances at 443, 490, and 510 nm (indices 2, 3, and 4) to the reflectance at 560 nm (indice 5), as a function of the Chlorophyll concentration. The corresponding algorithms making use of only 2 wavelengths are denoted OC2Me443, OC2Me490, and OC2Me510. The envelope of these three curves (maximum band ratio technique) forms the currently used MERIS algorithm, denoted OC4Me. The ρ is the log 10 of the maximum of the 3 (ρ 2,5 , ρ 3,5 , ρ 4,5 ) ratios ............................................................................................... 11 Figure 2: Adapted from Fig. 7 of Morel 2007: “ The maximum band ratio technique, represented by the curve reproduced from Fig. 6, is compared to recent measurements of irradiance reflectance, made at sea during the following cruises: Bencal (Benguela current, 2002), Biosope, (SouthEast Pacific,2004), Aopex, (Western Mediterranean Sea, 2004).” ............................................................... 11 Figure 3: reproduced from Morel et al. (2007a): validation of the OK2555 algorithm against the NOMAD in situ data set (Werdell and Bailey, 2005) .............................................................. 13 Figure 4: Validation of the proposed IOP algorithm against the synthetic data set of IOCCG (IOCCG, 2006). The four panels are for total absorption and total backscattering at two wavelengths. The parameters of a linear regression on the logtransformed data are provided in each panel. Here Kd and R are taken from the synthetic data set so they are independent quantities ............................................................................................................................................. 15 Figure 5: Validation of the proposed IOP algorithm against the in situ data set of IOCCG (IOCCG, 2006). The four panels are for total absorption at four wavelengths (no backscattering measurements in the IOCCG data set). Here, Kd has been derived from Chl before entering into the algorithm (no Kd data within the IOCCG in situ data base). The parameters of a linear regression on the logtransformed data are provided in each panel. Note: data from the Chesapeake bay and its vicinity (experiment name: “LMERTIES”), suspected of having been collected in Case 2 waters, have been removed from the data base....................................................................................................................................................... 16 Figure 6: Validation of the proposed algorithm for the particulate backscattering coefficient, against in situ data from the BOUSSOLE site (Antoine et al., 2006; hydroscatII instrument), the Plumes and Blooms site (Kostadinov et al., 2007; hydroscatVI instrument), and the NOMAD v2 data set (Werdell and Bailey, 2005; various instrument). The parameters of a linear regression on the logtransformed data are provided. The shaded area corresponds to
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:5
the usual range over which inversion methods are validated, clearly showing that validation for clear waters was missing up to now. ......................................................................................... 17 Figure 7: Validation of the proposed ag algorithm against the in situ data set of IOCCG (IOCCG, 2006). The four panels are for CDOM absorption at four wavelengths. Here, ap has been derived from Chl following Bricaud et al. (1998). The parameters of a linear regression on the logtransformed data are provided in each panel. ............................................................ 19 Figure 8: Adapted from Fig. 11 of Maritorena et al. 2009. Matchups statistics for the three GSM merged products, Chl (left), CDM (centre) and bbp (right). The colour of each matchup point indicates which satellite data sources were used for that point (green: SeaWiFS only, red: AQUA only, yellow: MERIS only, light blue: AQUA+MERIS, purple: SeaWiFS+MERIS, black: SeaWiFS+AQUA, dark blue: SeaWiFS+AQUA+MERIS). .................................................. 22 Figure 9: (from Wang et al., in preparation, IOCCG report #10): 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) [L w ()]N at 443 nm, (b) [L w ()]N at 490 nm, (c) ratio [L w (443)] N /[L w (555)] N , and (d) ratio [L w (490)] N /[L w (555)] N . These results are for the M80 aerosols with aerosol optical thickness of 0.1 at 865 nm and for open ocean (Case1) water with pigment concentration of 0.1 mg/m3. Air mass is for the sunpixel plus pixelsatellite paths). ........................................................................................................ 24 Figure 10: Adapted from Fig. 9 of Maritorena et al. 2009. Comparisons of the predicted and actual uncertainties using the NOMAD data set (upper left: Chl; upper right: CDM; lower left: bbp. If the predicted uncertainties are accurate, about 2/3 of the data points should be below the 1:1 line. The centred variables (retrieval/error; lower right panel) show a normal distribution for CHL (circles) and bbp (stars) while the CDM (triangles) distribution departs from normal (curve). .......................................................................................................................... 25
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:6
1. INTRODUCTION 1.1 Purpose and scope This Algorithm Theoretical Basis document (ATBD) is written for the Ocean and Land Colour Imager (OLCI) of the Earth Observation Mission Sentinel3 of the European Space Agency (ESA). The purpose of this document is to lay out algorithms for the OLCI ocean colour products in Case 1 waters. As much as possible, basic principles of the algorithm and the description of their various segments will refer to publications in the peerreviewed scientific literature. When such literature exists, minimum information will be provided here for the sake of clarity, and the reader will be referred to the relevant literature for further information.
1.2 Acronyms ATBD
Algorithm Theoretical Basis Document
CDOM
Colored Dissolved Organic Matter
ENVISAT
Environmental Satellite
ESA
European Space Agency
LOV
Laboratoire d'Océanographie de Villefranche
MERIS
Medium Resolution Imaging Spectrometer
NASA
National Aeronautics & Space Administration
nLw
Normalized Waterleaving radiance
NOMAD
NASA bioOptical Marine Algorithm Data set
OC
Ocean Color
OLCI
Ocean and Land Color Imager
PnB
Plumes and Blooms (Biooptics time series in the Santa Barbara Channel)
SeaWiFS
Seaviewing Wide Fieldofview Sensor
Sentinel3
Third series of “sentinel” (ESA satellites)
TOA
Top of Atmosphere
UV
Ultra Violet
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:7
1.3 Symbols Symbol
definition
Dimension / units
Geometry, wavelengths, others λ Wavelength θs Sun zenith angle (µs = cos(θs)) θv Satellite viewing angle (µv = cos(θv)) ∆φ Azimuth difference between the sunpixel and pixelsensor half vertical planes Chl
Chlorophyll concentration
nm degrees degrees degrees mg m
3
Radiometry and Apparent Optical properties (AOPs) F0(λ) L(λ,θs,θv,∆φ) Ed(z) Eu(z) Ed(0+) 
R(λ, 0 )
Mean extraterrestrial spectral irradiance
W m nm
2
1
Radiance Downward irradiance at depth z
W m nm sr W m2 nm1
2
1
Upward irradiance at depth z
W m2 nm1
Downward irradiance just above the sea surface
W m2 nm1
1
Diffuse reflectance at null depth, or irradiance ratio (Eu / Ed) dimensionless (upward and downward irradiances, respectively)
Kd(λ)
Diffuse attenuation coefficient for the downward plane
m
1
m
1
irradiance Kw(λ) f f' µd Q(λ,θs,θv,∆φ)
ρw(λ) [ρw]N(λ)
Contribution of seawater to Kd(λ) 
Ratio of R(0 ) to (bb/a); subscript 0 when θs = 0
dimensionless

Ratio of R(0 ) to (bb/(a+bb)); subscript 0 when θs = 0
dimensionless
Average cosine of the downward irradiance
dimensionless 
Factor describing the bidirectional character of R(λ, 0 ) Q = Eu / Lu. Subscript 0 when θs = θv = 0,
sr
Waterleaving reflectance (i.e., π Lw / Ed(0+))
dimensionless
Normalised waterleaving reflectance (i.e., the reflectance if there were no atmosphere, and for θs = θv = 0)
dimensionless Inherent optical properties (IOPs) a(λ) aw(λ) aph(λ) or af(λ) ag(λ) or acdom(λ)
Total absorption coefficient
m
1
Water absorption coefficient
m
1
Phytoplankton absorption coefficient
m
1
CDOM absorption coefficient
m
1
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:8
Coloured detrital material absorption coefficient
m
1
Total backscattering coefficient
m
1
bbw(λ)
Water backscattering coefficient
m
1
bbp(λ)
Particulate backscattering coefficient
m
1
acdm(λ) bb(λ)
Airwater interface ℜ(θ )
Geometrical factor, accounting for all refraction and reflection dimensionless effects at the airsea interface (Morel and Gentili, 1996) (1 − ρ ) (1 − ρ F (θ ' ) ) ℜ(θ ' ) = (subscript 0 when θ’ = 0) n2 (1 − r R ) where n is the refractive index of water ρF(θ) is the Fresnel reflection coefficient for incident angle θ ρ is the mean reflection coefficient for the downward irradiance at the sea surface r is the average reflection for upwelling irradiance at the waterair interface
dimensionless dimensionless dimensionless
θ’ is the refracted viewing angle (θ’ = sin1(n.sin(θv)))
degrees
td(λ,θs)
Upward diffuse atmospheric transmittance (pixeltosensor)
dimensionless
ts(λ,θs)
Downward global atmospheric transmittance (Ed(0+) / F0 µs) dimensionless
Others
dimensionless
1.4 Algorithm identification This algorithm is identified under reference “SD03C10” in the Sentinel3 OLCI documentation. In this document, it will be referred to as “CWOC”, standing for “ClearWater Ocean Colour Products”.
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:9
2. ALGORITHM OVERVIEW 2.1 Objectives The objective is to derive several ocean colour products from the spectrum of the normalised waterleaving reflectances.
The following products are to be derived here:
The chlorophyll concentration, Chl, expressed in units of mg (Chl) m3.
The diffuse attenuation coefficient for downward irradiance at 490 nm, K d (490), expressed in units of m1.
The total absorption and backscattering coefficients, a and b b , expressed in units of m1.
The CDOM absorption coefficient, expressed in units of m1.
The proposed algorithms are from Morel et al. (2006; 2007a) (see also the latest version of the MERIS ATBD 2.9 for the chlorophyll concentration), and from Maritorena et al. (2002). Note: the products presented here are all derived from various combinations of the fully normalized waterleaving reflectances. The latter are actually the main ocean colour product above Case 1 waters. There is no need to describe them in this document, however; they are simply the output of the atmospheric correction algorithm, for which a specific ATBD exists [SD03CO7].
David ANTOINE
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:10
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
3. ALGORITHM DESCRIPTION 3.1 Theoretical Description 3.1.1 The chlorophyll concentration, Chl The proposed algorithm is the “OC4Me” maximumbandratio (MBR) semianalytical algorithm developed by Morel et al. (2007a). (cf. O'Reilly et al., 1998 for a more general description of such algorithms) It is the latest version of the MERIS pigment index algorithm, which is fully described in 1
the MERIS ATBD 2.9 and in Morel et al. (2007a). A brief reminder is provided here: OC4Me is a polynomial based on the use of a semianalytical model, itself based on the analysis of AOPs measured in situ over the past decades in various oceanic regions (Morel 1988; Morel and Maritorena, 2001). It is expressed as: n
h ] =l∑ Ai ( l 1 oρ0 i , j )gx l o1 [C 0 g
(1)
x =0
where ρ i,j is the ratio of the irradiance reflectance, R, at band i (λ i ) to the irradiance reflectance at band j (λ j ). The value of this ratio is the maximum found among the 3 ratios formed with the following bands: 560 nm for λ j , and 443 or 490 or 510 nm for λ i . In Eq. (1), n is equal to 4. Figures 1 and 2 show how the algorithm behaves. The “A” coefficients to be used are (Morel et al., 2007a):
A0
A1
A2
A3
A4
0.4502748
−3.259491
3.522731
−3.359422
0.949586
Because this algorithm uses R and the MERIS atmospheric correction provides directional reflectances, ρw, a conversion is needed as follows:
ρ Q R= w πℜ The Q factor is from Morel et al., 2002 (it is chlorophylldependent so an iterative procedure is needed similarly as in Morel and Gentili, 1996). 1
Latest version available at http://envisat.esa.int/instruments/meris/pdf/
(2)
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:11
The ℜ geometrical factor merges all reflection / refraction effects at the airsea interface. It is defined as (Morel and Gentili, 1996): (1 − ρ ) (1 − ρ F (θ ' ) ) ℜ(θ ' ) = (subscript 0 when θ’ = 0) (3) n2 (1 − r R ) where n is the refractive index of water
ρF(θ) is the Fresnel reflection coefficient for incident angle θ ρ is the mean reflection coefficient for the downward irradiance at the sea surface r is the average reflection for upward irradiance at the waterair interface
θ’ is the refracted viewing angle (θ’ = sin1(n sin(θv))) In Eq. (3), the dependence of ρ and R on θ s are neglected. This dependence was recently shown significant for low sun elevations by Wang (2006). It is here proposed to include this effect, which can be done easily by adding one more dimension to the ℜ lookup tables currently in use.
Figure 1: Adapted from Fig. 6 of Morel 2007: Ratios ρ 2,5 , ρ 3,5 , ρ 4,5 of reflectances at 443, 490, and 510 nm (indices 2, 3, and 4) to the reflectance at 560 nm (indice 5), as a function of the Chlorophyll concentration. The corresponding algorithms making use of only 2 wavelengths are denoted OC2Me443, OC2Me490, and OC2Me510. The envelope of these three curves (maximum band ratio technique) forms the currently used MERIS algorithm, denoted OC4Me. The ρ is the log 10 of the maximum of the 3 (ρ 2,5 , ρ 3,5 , ρ 4,5 ) ratios
Figure 2: Adapted from Fig. 7 of Morel 2007: “ The maximum band ratio technique, represented by the curve reproduced from Fig. 6, is compared to recent measurements of irradiance reflectance, made at sea during the following cruises: Bencal (Benguela current, 2002), Biosope, (SouthEast Pacific,2004), Aopex, (Western Mediterranean Sea, 2004).”
Recommendation: use the OC4Me algorithm, and include a θ s dependence in the ℜ lookup table.
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:12
3.1.2 The diffuse attenuation coefficient at 490 nm, Kd(490) The diffuse attenuation coefficient for the downward plane irradiance at wavelength λ and at a given depth z is defined as: K d (λ ) = − [1/ Ed ( z , λ ) ][ dEd ( z , λ ) / dz ]
or K d (λ ) = − d [lnEd ( z , λ ) ] / dz
(3)
Many realisations of this coefficient are possible, as a function of the depth range over which it is computed. It can be a local coefficient around a given small depth interval between any depths z1 and z2: l o[Ed ( z1g, λ ) / Ed ( z 2 , λ )] K d (λ ) = − (5) z 2 − z1 It can be computed for the upper layer defined from below the surface (0) to a given depth z: l o E d (gz) / E d (0 − ) Kd = − (6) z It can also be an Edweighted average value computed over a certain depth z, e.g.,
[
]
the 1% light level (Kirk, 2003): z
K d ,a v(λ ) =
∫K
d
( z , λ ) Ed ( z , λ )d z (7)
0
z
∫E
d
( z , λ )d z
0
Practically speaking, the Kd's found in in situ data bases are essentially of the second category. The reason is simply that measuring properly Ed(z) at sea requires that the irradiance sensor is placed at a depth where the irradiance fluctuations due to surface waves are small enough (or even absent). This depth can be as large as ~30 meters in clear waters. Then this Ed(z) measurement is combined with the downward irradiance measured above the surface after it is multiplied by the transmission across the airsea interface, which provides Ed(0), in order to get Kd as per Eq (6) above. It is proposed here to use the “OK2560” algorithm proposed by Morel et al. (2007a). It is based on the 490560 reflectance ratio (see Fig. 3) and has the form: n
K d (4 ) =9K w (40 ) +91
∑ Ax (
x =0
00
1l
ρo40
x , 59 g) 60
(8)
where Kw(490) is 0.0166 m1, ρ490,560 is the ratio of the irradiance reflectances at 490 and 560 nm, and the n+1=5 coefficients Ax have the values :
David ANTOINE
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:13
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
A0
A1
A2
A3
A4
0,82789
1,64219
0,90261
1,62685
0,088504
Conversion from directional reflectances to irradiance reflectances is as per Eq. (2). Recommendation: use the OK2560 algorithm to determine Kd(490).
Figure 3: reproduced from Morel et al. (2007a): validation of the OK2555 algorithm against the NOMAD in situ data set (Werdell and Bailey, 2005)
3.1.3 The total absorption and backscattering coefficients (a and bb) Many algorithms have been proposed to derive inherent optical properties (IOPs), particularly the total absorption coefficient (at) and the total backscattering coefficients (bb), from various AOPs (very often from Rrs or from R and Kd). It is out of scope here to enter into these details, and the reader is referred to the comprehensive review by Gordon (2002) and to the IOCCG report N°5 (IOCCG, 2006). In particular, the results of the intercomparison presented in the IOCCG report don't reveal one algorithm as performing significantly better than the others (whatever their degree of complexity). Therefore, it is proposed here to use a simple approach, as proposed by Morel et al. (2006); see their Eq. (10) to (13). This approach combines two equations (Gordon, 1989; Gordon et al., 1975; Morel and Gentili, 2004): Kd(λ) = 1.0395 [a(λ) + bb(λ)] / µd
(9)
R(λ) = f' bb(λ) / [a(λ) + bb(λ)]
(10)
and
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:14
which leads to a(λ) = 0.962 Kd(λ) µd(λ, θs, Chl) x [1 – R(λ) / f'(λ, θs, Chl)]
(11)
bb(λ) = 0.962 Kd(λ) µd(λ, θs, Chl) x [R(λ) / f'(λ, θs, Chl)]
(12)
where the dependence of f' and µd on the sun zenith angle and Chl is explicitly introduced. These two parameters are taken from precomputed lookup tables, following Morel et al. (2002). To operate Eqs (11) and (12) Kd(555) is derived from an algorithm similar to the OK2560 but adapted to λ=555 nm and R(555) is derived from ρw(555) through Eq. (2). Because Chl is needed to operate Eqs 11 and 12, this algorithm would be applied after the Chl algorithm. It must be stressed, however, that the nominal application of such a method needs independent Kd and R estimates, which is the case when using in situ data. When applying the same method in the remote sensing context, the sole quantity available directly is ρw, whereas Kd is derived from a reflectance ratio (Eq. 8). It is no longer a quantity independent from R. The performance of the algorithm is, therefore, expected to be affected in this case (this is a general statement valid for any type of IOP inversion algorithm using the remote sensing signal). This scheme has been tested in order to assess its performance as compared to other methods and as compared to in situ data. The synthetic and the in situ data bases previously used by the IOCCG working group on IOP algorithms (IOCCG, 2006) have been used here, as well as backscattering measurements from the BOUSSOLE site (Antoine et al., 2006), the “Plumes and Blooms” site (Kostadinov et al., 2007), and the NOMAD V2 data set (Werdell and Bailey, 2005). The results are provided in Figs. 4 to 7 below. Figure 4 shows that the proposed algorithm is working well when applied to synthetic data. More importantly, Figure 5 still shows good performances when the same algorithm is applied to independent in situ data (only for absorption). Total absorption tends to be underestimated by the algorithm; this needs to be confirmed or invalidated through additional validation exercises (using, e.g., NOMAD). It is, therefore, proposed to use Eqs 11 and 12 to derive total absorption at 443 nm.
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:15
Figure 4: Validation of the proposed IOP algorithm against the synthetic data set of IOCCG (IOCCG, 2006). The four panels are for total absorption and total backscattering at two wavelengths. The parameters of a linear regression on the logtransformed data are provided in each panel. Here Kd and R are taken from the synthetic data set so they are independent
quantities
Figure 6 shows good results for the derivation of bbp in the green. It is, therefore, proposed to derive the total backscattering coefficient in the 560 nm green band. This coefficient is usually produced at 443 nm, the accuracy of which being likely affected by the presence of the large phytoplankton absorption in mesoto eutrophic Case 1 waters. In oligotrophic waters, the respective contributions of particles and seawater to the total backscattering is largely unbalanced to the advantage of seawater (the backscattering coefficient of seawater at 443 nm is 2.45 10
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:16
3 m1). The signal to be retrieved (b ) is therefore small and the uncertainty on its bp
derivation is large. These two disadvantages are largely suppressed at 560 nm. Atmospheric correction errors are also much lower in the green than they are in the blue.
Figure 5: Validation of the proposed IOP algorithm against the in situ data set of IOCCG
(IOCCG, 2006). The four panels are for total absorption at four wavelengths (no backscattering measurements in the IOCCG data set). Here, Kd has been derived from Chl before entering into the algorithm (no Kd data within the IOCCG in situ data base). The parameters of a linear regression on the logtransformed data are provided in each panel. Note: data from the Chesapeake bay and its vicinity (experiment name: “LMERTIES”), suspected of having been collected in Case 2 waters, have been removed from the data base.
David ANTOINE
SENTINEL3 OPTICAL PRODUCTS AND ALGORITHM DEFINITION OLCI Level 2 Algorithm Theoretical Basis Document Ocean Colour Products in case 1 waters
Ref: S3L2SD03 C10LOVATBD Issue: 2.2 Date: July 13, 2010 Page:17
Figure 6: Validation of the proposed algorithm for the particulate backscattering coefficient,
against in situ data from the BOUSSOLE site (Antoine et al., 2006; hydroscatII instrument), the Plumes and Blooms site (Kostadinov et al., 2007; hydroscatVI instrument), and the NOMAD v2 data set (Werdell and Bailey, 2005; various instrument). The parameters of a linear regression on the logtransformed data are provided. The shaded area corresponds to the usual range over which inversion methods are validated, clearly showing that validation for clear waters was missing up to now.
In clear waters, getting accurate particulate backscattering coefficients, bbp, requires accurate determination of the backscattering by seawater itself, bbw. A recent analysis by Twardowski et al (2007) provided a refined computation for bbw (used to produce the results shown in Fig. 6 here). Their recommendations should be followed, which means that the water temperature (SST) and salinity (SSS) should be known to determine bbw. Sufficiently accurate climatologies exist for these two parameters so there is no need to determine their actual values to compute bbw when processing OLCI data (for instance a 1psu difference in SSS for SST=20°C ends up with a 1 105 m1 difference in bbw at 555 nm). More realistic values could be incorporated, however, and at least for SST, when reprocessing the data (e.g., weekly global products for SST such as the ones provided by the GHRSST project). Recommendation: use the Morel et al. (2006) approach (Eqs. 11 & 12 here) to derive total absorption and total backscattering coefficients. Follow Twardowski et al. (2007)
David ANTOINE
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to determine bbw (to get bbp) and Morel et al. (2007b) to determine aw (to get at – aw, i.e., the sum ap + acdom). Data sources for SST and SSS to be discussed / selected during algorithm implementation. 3.1.4 Can the CDOM absorption coefficient (ag) be derivable? The uncertainty on absorption by CDOM is known to be a major problem in the derivation of the chlorophyll concentration, for instance. An accurate determination of ag would be, therefore, a significant advance in the retrieval of OC products in Case 1 waters. A better separation of the influence of CDOM and phytoplankton in the absorption budget is also important to improve the modelling of primary production. Deriving ag is, however, far from easy, because the deconvolution of the effects of Chl and CDOM is largely impeded by their intermingled influences in the blue part of the e.m. spectrum. Nonalgal particles also intervene. Once the total absorption coefficient is known (see above), it is feasible in theory to decompose it into several components and the associated “partialcoefficients” corresponding to various opticallysignificant quantities. This is feasible by virtue of the additive character of IOPs, so that one can write: a(λ) = aw(λ) + aφ(λ) + anap(λ) + ag(λ)
(13)
where aw(λ) is the absorption coefficient of sea water, aφ(λ) is the absorption coefficient of phytoplankton, anap(λ) is the absorption coefficient of nonalgal particles, and ag(λ) is the absorption coefficient of coloured dissolved organic matter (also called gelbstoff, hence the “g” subscript). The sum of aφ(λ) plus anap(λ) is denoted ap(λ), standing for the absorption coefficient of all particles. The error budget that could be derived from each component depends on the wavelength, because the relative importance of the different components is varying dramatically with wavelength.
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Figure 7: Validation of the proposed ag algorithm against the in situ data set of IOCCG
(IOCCG, 2006). The four panels are for CDOM absorption at four wavelengths. Here, ap has been derived from Chl following Bricaud et al. (1998). The parameters of a linear regression on the logtransformed data are provided in each panel.
Roughly speaking, it is illusory to derive ag(λ) with an acceptable accuracy for λ>500 nm, and it is best to derive aφ(λ) in the vicinity of phytoplankton absorption peaks. Here, the feasibility to derive ag(412) from a(412) has been examined, because (1) ag increases exponentially in the blue, (2) water absorption is small at 412 nm, and (3)
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the particle absorption is not at its maximum (in other words, the relative contribution of ag to the total absorption budget is larger). The operation to perform is: ag(λ) = a(λ)  [aw(λ) + ap(λ)]
(14)
The difficulty is the unavailability of a direct estimate of ap(λ). The use of an empirical relationship between ap(412) and Chl has been tested, following Bricaud et al. (1998). By doing so, it is assumed that the uncertainty on the Chlderived particle absorption is still low enough for ag(412) to be derived meaningfully. This approach has been tested on the IOCCG in situ data set and the results are presented in Fig. 7. An acceptable accuracy is only obtained at 412 nm. It seems, therefore, possible to derive the absorption coefficient of the coloured dissolved organic matter through this technique. A much thorough validation is still needed, however, to definitely conclude on the appropriateness of this approach. A data base of CDOM absorption measurements should be assembled for that purpose. It will rely in particular on data presently collected at BOUSSOLE, and on any other available data sets (e.g., NOMAD), provided that their quality is appropriate. Recommendation: combine the total absorption, at, as derived from the KdR inversion algorithm (Morel et al., 2006: Eqs. 11 & 12 here), the Chlderived ap from Bricaud et al. (1998) and aw derived as per Morel et al. (2007b) to determine acdom(412) = at(412) – aw(412)  ap(412). 3.1.5 Alternative approach: the GSM algorithm The algorithms proposed above are independent one from each other, so that the various products are separately determined from the waterleaving reflectance spectrum derived after atmospheric correction. This solution has one advantage, which is precisely to have independent estimates of each parameter, i.e., the possible error on one of them doesn't transfer as an error on the others. This solution also has some disadvantages, among which is the impossibility to derive an error estimate on each determination of the geophysical parameters. In other words, there is no possible pixelbypixel uncertainty estimate. The nature of these algorithms only allows an overall uncertainty to be assessed (in general though the comparison with in situ data). Another approach is therefore proposed here, which consists of a simultaneous determination of the inherent optical properties and derived parameters (chlorophyll
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via its absorption coefficient in the blue, the particulate backscattering coefficient at 443 nm, and the absorption by coloured detrital matter at 443 nm), and which is able to provide a pixelbypixel uncertainty estimate. This is the socalled “GSM” semianalytical algorithm (for “Garver, Siegel and Maritorena”; Garver and Siegel, 1997; Maritorena et al., 2002; Maritorena and Siegel, 2005). The inputs to this model are the spectral normalized waterleaving radiances (LwN(λ)) (i.e., the full spectrum is used from 412 nm to the red). The GSM model is briefly described below (essentially taken from IOCCG, 2006). It is based on the quadratic relationship between the remotesensing reflectance (Rrs) and the absorption and backscattering coefficients (Gordon et al., 1988):
where g1(= 0.0949) and g2(= 0.0794) are geometrical factors. The absorption coefficient, a(λ), is decomposed into aw(λ) (seawater), aph(λ) (phytoplankton), and adg(λ) (coloured detrital and dissolved material, CDM). Similarly bb(λ), is partitioned into backscattering by seawater, bbw(λ), and by suspended particulates, bbp(λ). The nonwater absorption and scattering terms are parameterized as a known shape with an unknown magnitude:
where a*ph(λ) is the chlorophylla specific absorption coefficient, S is the spectral slope for CDM absorption (Bricaud et al., 1981, 1998), Y is the power law exponent for bbp, and λ0 is a scaling wavelength (443 nm). S, Y and a*ph(λ) are set to constant values. For aph(λ), adg(λ), and bbp(λ), the unknown magnitudes are the chlorophylla concentration (Chl), the detritus/gelbstoff absorption coefficient, adg(443), and the particulate backscatter coefficient, bbp(443), respectively. GSM validation results are shown in Fig. 8 with MERIS, SeaWiFS, and MODIS (in situ data from NOMAD data set for the 19972003 time period and additional data from the SeaBASS archive for the 20032007 period).
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Figure 8: Adapted from Fig. 11 of Maritorena et al. 2009. Matchups statistics for the three GSM merged products, Chl (left), CDM (centre) and bbp (right). The colour of each matchup point indicates which satellite data sources were used for that point (green: SeaWiFS only, red: AQUA only, yellow: MERIS only, light blue: AQUA+MERIS, purple: SeaWiFS+MERIS, black: SeaWiFS+AQUA, dark blue: SeaWiFS+AQUA+MERIS).
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3.2 Error estimates 3.2.1 Semiempirical algorithm For the semiempirical algorithms proposed in section 3.1, there is no possible pixelbypixel uncertainty (error) estimate. An average uncertainty can be derived from the comparison with in situ data, typically providing the slope and intercept of a regression, and the associated coefficient of regression and root mean square error. Numbers are not provided here because they depend on the data base that is used for this assessment. Such an approach can be global or regionalized to some extent (see Dwell et al., 2009). This will have to be discussed among the Sentinel3 group and an agreement found on which data base has to be used to produce such numbers. The reader is referred also to the MERIS ATBD 2.9 for some discussions about the uncertainties inherent to such algorithms (Morel and Antoine, 2007). Another approach could be tested, however, where some kind of quality indicator could be derived on a pixelbypixel basis. The approach would rely on the fact that the ratio of reflectances at 490 and 560 nm is one of the parameters that is retrieved with the best accuracy. This is illustrated on Fig. 9, from the results of an intercomparison of atmospheric correction algorithms performed under the auspices of the IOCCG (chair M. Wang). It is clear from this figure that the ratio of reflectances at 490 to 560 nm is better retrieved than the reflectances themselves, and that the uncertainty in this ratio is often within 5%. The same results, i.e., the band at 490 nm being better retrieved than others, are also obtained from validation with respect to in situ data bases (e.g., Antoine et al., 2008). The logic would be to recompute the various reflectances from this band ratio using a semianalytical reflectance model (e.g., Morel and Maritorena, 2001), and to derive an average relative difference between this reconstructed reflectance spectrum and the spectrum available after atmospheric correction of the satellite measurements. Large values of this average difference may result from a variety of situations, including in particular large errors in atmospheric corrections or inappropriateness of the semianalytical reflectance model. The combination of this quality indicator with other science flags may also provide some insight about the behaviour of the algorithms in varied situations. This approach has not been tested up to now. It could be tested using existing MERIS data.
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Figure 9: (from Wang et al., in preparation, IOCCG report #10): 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) [L w (λ)] N at 443 nm, (b) [L w (λ)] N at 490 nm, (c) ratio [L w (443)] N /[L w (555)] N , and (d) ratio [L w (490)] N /[L w (555)] N . These results are for the M80 aerosols with aerosol optical thickness of 0.1 at 865 nm and for open ocean (Case1) water with pigment concentration of 0.1 mg/m3. Air mass is for the sunpixel plus pixelsatellite paths).
3.2.2 GSM algorithm Concerning the GSM algorithm, error estimates can be provided on a pixelbypixel basis (from Maritorena et al., Remote Sensing of Environment, submitted). This paper presents the outcomes of the ESA GlobColour project to what concern error estimates based on the use of the GSM (or even GSMlike) algorithms. For any “semianalytical” inversion technique, a minimisation is done between a “reference spectrum model” and the observed model by iterating on values of freeparameters. The invaluable advantage is that, providing error estimates on inputs and appropriated minimisation technique, the fitting procedure provides, mathematically, the range of uncertainties of inversion and, by this, the three IOP presented above, as well as their uncertainties. This potential for providing error bars has been extensively explored during GlobColour and some consolidated results are presented below.
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Figure 10: Adapted from Fig. 9 of Maritorena et al. 2009. Comparisons of the predicted and actual uncertainties using the NOMAD data set (upper left: Chl; upper right: CDM; lower left: bbp. If the predicted uncertainties are accurate, about 2/3 of the data points should be below the 1:1 line. The centred variables (retrieval/error; lower right panel) show a normal distribution for CHL (circles) and bbp (stars) while the CDM (triangles) distribution departs from normal (curve).
The requested qualification of inputs (as well as model uncertainties) has been done through GlobColour and propagation of error through LevenbergMarquardt minimisation procedure has allowed production of reliable error bars at least for Chla and for bbp. For CDM the propagation of uncertainties has proven to be less reliable and points toward a requested adaptation of the reference reflectance spectrum. Fig. 10 shows the results for all three parameters (see the three first panels) of the retrieved error estimates wrt to actual error obtained through matchup analysis. Scatter plots for which (visually) two third of the actual error is under the 1/1 line of error estimates, indicate a satisfactory estimates of the error (as assumed to follow a normal probability function). The three normalised distribution function have been reported on the fourth panel (bottom right) and theoretically should be comparable
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to the normalised centred density probability function which is also sketched. Good correlation between this theoretical shape and the ones obtained for Chla and bbp (while CDM deserves some attention) indicates that this approach is the one to be followed for the implementation of the OLCI L2 processing.
3.3 Summary of recommendations 3.3.1 Products The list of products is: • Pigment index (Chl) (OC4Me algorithm) • Kd(490) (OK2560 algorithm) •
bbp(560) (Morel et al., 2006 algorithm)
•
acdom(412) (Morel et al., 2006 algorithm)
•
aphy(443) (GSM algorithm)
•
bbp(443) (GSM algorithm)
•
acdm(443) (GSM algorithm)
The marine reflectances in all visible bands (ρw(λ)) are obviously part of the product list as well (it is just not clear whether they are considered as the final products of the atmospheric correction, and so to be listed in the CWAC ATBD, or as the first basic ocean colour product, to be listed in this ATBD).
“Pigment index” (Chl): use the OC4Me algorithm, and include a θ s dependence in the ℜ lookup table. Derive Chl also from the GSM algorithm (Garver and Siegel, 1997; Maritorena et al., 2002; Maritorena and Siegel, 2005). Kd(490): use the OK2560 algorithm (Morel et al. 2007a). IOPs: At λ = 560 nm only: use the Morel et al. (2006) approach (Eqs. 11 & 12 here) to derive the total backscattering coefficient (bb). Follow Twardowski et al. (2007) to determine bbw (see appendix) so that bbp is obtained as bb  bbw. Data sources for SST and SSS to be discussed / selected during algorithm implementation. At λ = 412 nm only: combine the total absorption, at, as derived from the KdR inversion algorithm (Morel et al., 2006: Eqs. 11 & 12 here), the Chlderived ap from Bricaud et al. (1998) and aw derived as per Morel et al. (2007b) to determine acdom = at – aw  ap. In parallel, use the GSM (Garver and Siegel, 1997; Maritorena et al., 2002; Maritorena and Siegel, 2005) to get aph, bbp and acdm, at λ = 443 nm.
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3.3.2 Pixelbypixel error estimates Semiempirical algorithms: both the Chl and the Kd(490) algorithms proposed here rely on the Morel and Maritorena (2001) semianalytical model (MM01). Therefore, they follow this global average algorithm. The approach described here (section 3.2.1) will provide an indication about how far from the average model each pixel is. Would the water optical properties behave exactly as in MM01 (as a function of Chl) and the atmospheric correction error be null, the reconstructed reflectance spectra should be equal to the one derived from the TOA signal after atmospheric correction. Therefore, the average difference proposed in section 3.2.1 will conceal the effects of atmospheric correction errors and deviation of optical properties from the MM01 model. GSM algorithm: proceed as described in section 3.2.2 of this ATBD.
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4. ASSUMPTIONS AND LIMITATIONS 4.1 Assumptions Pixelbypixel error estimates of the water leaving reflectance (each marine band) are available as input.
4.2 Constraints, limitations The algorithms proposed here are valid above Case 1 waters, which means that they cannot provide reliable results when applied over Case 2 waters that would not have been identified as such (in particular turbid Case 2 waters). The same comment is valid for any other “nonnominal” conditions of applications, including but not being limited to, coccolithophorid blooms, residual, nonidentified, sun glint, noncorrected adjacency effects, cloud shadows and unidentified thin clouds. For the chlorophyll concentration, the reader is referred more specifically to Morel (2007a) and the MERIS ATBD 2.9 for a detailed discussion of the assumptions and limitations related to the OC4Me algorithm. For the Kd algorithm, the reader is referred more specifically to Morel et al. (2007a) for a detailed discussion about the OK2560 algorithm. A possible limitation of the GSM algorithm lies in the range of variability of the data bases used for its optimization. It is known that GSM isn’t totally optimized for clear oceanic waters. This is under study and an improved version optimized for a larger range of trophic states is under development.
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5. REFERENCES Antoine, D. M. Chami, H. Claustre, F. D'Ortenzio, A. Morel, G. Bécu, B. Gentili, F. Louis, J. Ras, E. Roussier, A.J. Scott, D. Tailliez, S. B. Hooker, P. Guevel, J.F. Desté, C. Dempsey and D. Adams. 2006, BOUSSOLE : a joint CNRSINSU, ESA, CNES and NASA Ocean Color Calibration And Validation Activity. NASA Technical memorandum N° 2006  214147, 61 pp. Bricaud, A., Morel, A. and L. Prieur (1981). Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains, Limnology and Oceanography, 26, 4353. Bricaud, A., Morel, A., Babin, M., Allali, K., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (Case 1) waters: analysis and implications for biooptical models. Journal of Geophysical Research 103, 31033–31044. Garver, S.A. and 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: 18,60718,625. Gordon, H.R., 1989. Can the LambertBeer law be applied to the diffuse attenuation coefficient of ocean water? Limnology and Oceanography 34, 1389–1409. Gordon, H.R. (2002). Inverse Methods in hydrologic optics. Oceanologia 44: 958. Gordon, H.R., 2005, Normalized waterleaving radiance: revisiting the influence of surface roughness, Appl. Opt. 44, 241248. Gordon, H.R., Brown, O.B., Jacobs, M.M., 1975. Computed relations between inherent and apparent optical properties of a flat homogeneous ocean. Applied Optics 14, 417–427. Gordon H.R. and A. Morel, 1983. Remote assessment of ocean color for interpretation of satellite visible imagery. Edité par R.T. Barber, C.N.K. Mooers, M.J. Bowman and B. Zeitzschel, Lecture notes on coastal and estuarine studies, 4, 114 pp. IOCCG (2006). Remote Sensing of Inherent Optical Properties: Fundamentals, Tests of Algorithms, and Applications. Lee, Z.P. (ed.), Reports of the International OceanColour Coordinating Group, No. 5, IOCCG, Dartmouth, Canada. Kostadinov T., D.A. Siegel, S. Maritorena, and N. Guillocheau, 2007, Ocean color observations and modelling for an optically complex site: Santa barbara channel, california, USA, J. Geophys. Res., 112, C07011, doi:10.1029/2006JC003526. Maritorena S., D.A. Siegel & A. Peterson. 2002. Optimization of a SemiAnalytical Ocean Colour Model for Global Scale Applications. Applied Optics. 41(15): 27052714. Maritorena, S. and D.A. Siegel. 2005. Consistent Merging of Satellite Ocean Colour Data Sets Using a BioOptical Model. Remote Sensing of Environment, 94(4): 429440.
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Maritorena, S., O. Hembise Fanton d’Andon, A. Mangin & D.A. Siegel. 2009. Merged Ocean Color Data Products Using a BioOptical Model: Characteristics, Benefits and Issues. Remote Sensing of Environment, submitted Morel A., 1988. Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters). J. Geophys. Res., 93, 1074910768. Morel A. and D. Antoine, 2007, MERIS ATBD 2.9, available at : http://envisat.esa.int/instruments/meris/pdf/ Morel A., D. Antoine, and B. Gentili, 2002. Bidirectional reflectance of oceanic waters: accounting for the Raman emission and varying particle scattering phase function. Appl. Opt.41, 62396306 Morel A. and B. Gentili, 1996. Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the the remotesensing problem. App. Opt., 35, 48504862. Morel A. and B. Gentili, 2004. Radiation transport within oceanic (Case 1) waters. J. Geophys. Res., 109, C06008, doi:10.1029/2003JC002259. Morel, A., Gentili, B., Chami, M., and J. Ras (2006) Biooptical properties of high chlorophyll Case 1 waters, and of yellowsubstance dominated Case 2 waters. DeepSea Research I, 53, 14391559. Morel, A., Huot, Y., Gentili, B., Werdell, P.J., Hooker, S.B. and B.A. Franz (2007a). Examining the consistency of products derived from various ocean color sensors in open ocean (Case 1) waters in the perspective of a multisensor approach. Remote Sensing of Environment, 111, 6988. Morel, A., Gentili, B., Claustre, H., Babin, M., Bricaud, A., Ras, J., and F. Tieche (2007b) Optical properties of the "clearest" natural waters, Limnology and Oceanography, 52(1), 217229 Morel, A., and S. Maritorena (2001). Biooptical properties of oceanic waters: A reappraisal. Journal of Geophysical research, 106, 77637780. Morel A. and L. Prieur, 1977. Analysis of variations in ocean color. Limnol. Oceanogr., 22, 709722. O'Reilly J. E., S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru and C. R. McClain. 1998. Ocean Color Chlorophyll Algorithms for SeaWiFS. Journal of Geophysical Research, 103(C11): 24,93724,953. Twardowski, M. S., Claustre, H., Freeman, S. A., Stramski, D., and Huot, Y.: Optical backscattering properties of the “clearest” natural waters, Biogeosciences, 4, 1041– 1058, 2007, http://www.biogeosciences.net/4/1041/2007/. Wang, M. (2006), "Effects of ocean surface reflectance variation with solar elevation on normalized waterleaving radiance," Appl. Opt., 45, 41224128. Werdell, P.J., and Bailey, S.W. (2005). An improverd insitu biooptical data set for ocean color algorithm development and satellite data product validation. Remote Sensing of Environment, 98: 122140.
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6. Appendix: b bw computation Computation of bbw as per Twardowski et al. (2007) (Eqs. 13 and Table 1) and references therein: Parameters: k = Boltzmann constant, 1.38054 10−23 J K−1 δ = 0.051 (depolarization ratio). SST is seasurface temperature, in °C SSS is seasurface salinity, in psu λ is the wavelength in nm. Equations: n_wat = 1.3247 + 3.3 103 λ2 3.2 107 λ4  2.5 106 SST2 isothermal_compress = (5.062271  0.03179 SST + 0.000407 SST2) 1010 comp1 = (0.000156 λ + 1.5989) 1010 comp2 = (1.61857  0.005785 SST) 1010 n_pressure_derivative = (comp1 comp2) / 1.5014 101 βw(90) =
2 π 2 k (SST + 273) n _ wat 2 (λ 10
−9 4
)
n _ pressure _ derivative 2
isothermal _ compress
(6 + 6 δ) (6 − 7 δ)
bwat = [ 16 π / 3 ] βw(90) [ (1/2) ((2+ δ) / (1+ δ)) ] bw = bwat (1 + 0.3 (SSS / 37)) bbw = bw / 2 Values of bbw for two bands and two SSTSSS configurations, for verification:
SST = 20°C, SSS = 38 psu SST = 30°C, SSS = 36 psu
λ = 442 nm 0.004586 m1 0.00443253 m1
λ = 555 nm 0.00178731 m1 0.00172748 m1