Use of a neuro-variational inversion for retrieving oceanic ... - CiteSeerX

Neural Networks 19 (2006) 178–185 www.elsevier.com/locate/neunet

2006 Special issue

Use of a neuro-variational inversion for retrieving oceanic and atmospheric constituents from satellite ocean colour sensor: Application to absorbing aerosols Julien Brajard a,*, Ce´dric Jamet b, Cyril Moulin b, Sylvie Thiria a a

IPSL/LOCEAN (ex LODyC), BC 100, T45-55, 4 Place Jussieu, 75252 Paris Cedex, France b IPSL/LSCE, Bat. 712, 91191 Gif-sur-Yvette Cedex, France

Abstract This paper presents a new development of the NeuroVaria method. NeuroVaria computes relevant atmospheric and oceanic parameters by minimizing the difference between the observed satellite reflectances and those computed from radiative transfer simulations modelled by artificial neural networks. Aerosol optical properties are computed using the Junge size distribution allowing taking into account highly absorbing aerosols. The major improvement to the method has been to implement an iterative cost function formulation that makes the minimization more efficient. This implementation of NeuroVaria has been applied to sea-viewing wide field-of-view sensor (SeaWiFS) imagery. A comparison with in situ measurements and the standard SeaWiFS results for cases without absorbing aerosols shows that this version of NeuroVaria remains consistent with the former. Finally, the processing of SeaWiFS images of a plume of absorbing aerosols off the US East coast demonstrate the ability of this improved version of NeuroVaria to deal with absorbing aerosols. q 2006 Elsevier Ltd. All rights reserved. Keywords: Ocean colour; Variational inversion; NeuroVaria; Multilayer perceptron; Atmospheric correction; Absorbing aerosols; Satellite; Cost function

1. Introduction Ocean colour sensors on board satellites measure the solar radiation reflected in its direction (reflectance) by the ocean and the atmosphere at several wavelengths in the visible and near infrared (NIR) spectra. In the blue, this reflectance is affected for about 90% by air molecules and aerosols in the atmosphere and for about 10% by water molecules and phytoplankton cells in the ocean. This weak but detectable signal is used to estimate the chlorophyll a concentration (chl-a). Coastal Zone Color Scanner (CZCS), which has been launched in 1978, has been the first space-borne sensor to provide global maps of chl-a. Several sensors with improved characteristics have been launched since, e.g. SeaWiFS in 1997, POLDER in 1996 and 2003, MODIS in 1999 and 2002, or MERIS in 2002. The basic principle of the data processing has not changed since the late 1970s. The atmospheric * Corresponding author. Tel.: C33 1 44 27 23 41. E-mail addresses: [email protected] (J. Brajard), cjamet@ cea.fr (C. Jamet), [email protected] (C. Moulin), sylvie.thiria@lodyc. jussieu.fr (S. Thiria).

0893-6080/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.neunet.2006.01.015

contribution of the top-of-atmosphere (TOA) reflectance is first estimated from red and NIR bands. This atmospheric contribution is then extrapolated to blue and green bands, and is removed from the TOA measurement to get the waterleaving reflectance. The chl-a is then computed through a biooptical algorithm that most of the time relies on the ratio of blue–green water-leaving reflectance. This approach is well suited to open ocean waters and to clear atmospheres. There is, however, an increasing interest for accurate estimates of chl-a in more complex situations such as turbid coastal waters or in the presence of absorbing aerosols in the atmosphere, which cannot be handled by such standard algorithms. Indeed, standard methods fail when facing absorbing aerosols because they use only the near-infrared part of the spectrum to estimate the aerosol optical properties, and thus are not able to detect absorbing aerosols at all. A first version of the algorithm described here, denoted NeuroVaria, has been presented in Jamet, Thiria, Moulin, and Crepon (2005) and validated in Brajard, Jamet, Moulin, and Thiria (in press) in the presence of low absorbing aerosols. In this paper, we describe the modifications that we applied to NeuroVaria in order to address the critical issue of retrieving oceanic constituents in the presence of absorbing aerosols. The principle of NeuroVaria was inspired by the ‘Spectral Matching Algorithm’ (SMA) presented

J. Brajard et al. / Neural Networks 19 (2006) 178–185

by Chomko and Gordon (1998). It proposes a new way to process ocean colour images by using neural network modelling to retrieve in one step both atmospheric and marine parameters from the whole TOA spectrum. The main advantage of such approach is to deal with complex situations such as absorbing aerosols or turbid waters. In Section 2, we present the radiative transfer equation, the aerosol models and the bio-optical algorithm we chose. Then the general method and the modifications of NeuroVaria are explained. Finally, the new version of NeuroVaria is compared to in situ data and to SeaWiFS products not only in the presence of non and weakly absorbing aerosols in the Mediterranean Sea but also in the presence of absorbing aerosols off US east coast. 2. Modelling the radiative transfer equation Ocean colour sensors measure the TOA reflectance at several wavelengths. Using ancillary information (e.g. wind speed, atmospheric pressure, etc.), this reflectance can be corrected for contributions of the molecular (Rayleigh) scattering, of oxygen and water-vapor absorption, and of sun glint and whitecaps perturbations, to obtain a corrected reflectance rCOR. This reflectance is composed of three unknown terms due to the aerosols (rA) in the atmosphere and the phytoplankton in the ocean (rw), i.e. rCOR ðlÞ Z rA ðlÞ C tðlÞ rw ðlÞ

(1)

where t is the diffuse transmittance of the atmosphere. This term accounts for the attenuation of the water-leaving reflectance during its atmospheric pathway toward the satellite (Gordon, 1997). Both rA(l) and t(l) depend on the sun and the viewing geometry, on the aerosol optical thickness at 865 nm, which characterizes the aerosol concentration in the atmospheric column, and on an aerosol model defined by its refractive index mZmrKimi and its size distribution. The aerosol model we use is determined by the Junge power-law size distribution (Eq. (2)) 8 K; D0 ! D% D1 ; > > > > > > < 0 1nC1 dN (2) Z D dD > K @ 1 A ; D1 ! D% D2 ; > > D > > > : 0; DO D2 where dN is the number of particles per unit of volume with diameters between D and DCdD, K is a normalization constant, D0, D1 and D2 are constant physical parameters. This Junge power-law, which poorly models the real aerosol size distribution, offers two main advantages for our purpose: the size distribution depends only on one continuous parameter n and it allows to simulate realistic atmospheric reflectance rA (Junge, 1958) even for absorbing aerosols. The goal of the atmospheric correction is to retrieve precise values of rA(l) and t(l) to obtain the water-leaving reflectance rw(l) which is related to the phytoplankton. We performed simulations of

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Table 1 Range of the input parameters of the direct radiative transfer model: rA(l,n,mr,mi,t), t(l,n,mr,mi,t), rw(l,b0,C) Parameters

Min value

Max value

n mr mi t qs qv df C b0

2 1.33 0 0.05 0 0 0 0.03 0

4.5 1.5 0.04 0.35 60 60 360 3 60

rA(l) and t(l) by using transfer radiative models where aerosols are represented by the Junge law described in Chomko and Gordon (1998) and we stored them into LookUp-Tables (LUT) where the values of n range from 2 to 4.5 by steps of 0.5, mi2{0; 0.001; 0.003; 0.01; 0.03; 0.04} and mr2{1.33; 1.50}. The three angles defining the observation geometry range from 08 to 608 for the sun zenith angle and the viewing zenith angle and from 08 to 3608 for the difference between the sun and the viewing azimuth angle (see Table 1). The LUT contains more than 2 millions simulations of rA(l) and t(l). A first difference with the initial NeuroVaria method (Jamet et al., 2005) is that we account for absorbing aerosols defining by a larger range of mi values up to 0.04 instead of 0.003 in the initial version. The method is applied to SeaWiFS which has eight wavelengths in the visible and in the NIR: 412, 443, 490, 510, 555, 670, 765, 865 nm. The water-leaving reflectance rw in Eq. (1) is almost not dependent on the geometry, and is thus assumed to be only a function of two oceanic parameters: the pigment concentration C (roughly close to the chl-a concentration) and the scattering particulate parameter b0 according to the bio-optical model described in Gordon et al. (1988). The simulated rw(l) are stored in another LUT that contains 1400 simulated values corresponding to C values ranging from 0.03 to 3 mg mK3 with a logarithmic step, and b0 values ranging from 0.12 to 0.45 in steps of 0.03. This model is limited to the study of case 1 waters, whose optical properties are determined by the water itself and the phytoplankton concentration and their immediate detrital material (Gordon et al., 1983). These waters represent most of the world ocean waters. Moreover, the model is accurate for moderate pigment concentrations, prohibiting its use for eutrophic waters (CO3 mg mK3). Note that the accuracy of the bio-optical model is better for C!1 mg mK3. This will have an impact on our results, especially in the presence of blooms. The objective of NeuroVaria is thus to find a set of aerosol and oceanic parameters that lead to (rACtrw) values that best match the measured rCOR at all wavelengths. In Section 3, we present the general method NeuroVaria. 3. Variational inversion The variational inversion (Jamet et al., 2005) whose diagram is described in Fig. 1 is based on the iterative

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Fig. 1. Description of the variational algorithm: x is the set of control parameters to adjust, y is the set of spectral reflectance (either observed or calculated) and J is the cost function.

minimization of a dedicated cost function J by adjusting relevant atmospheric and oceanic parameters (n, mi, t, b0, C), which are the control parameters. We used a gradient method, which computes the partial derivatives of this function with respect to these control parameters by using an adjoint code. There are several problems to face to calibrate the variational inversion. 3.1. The parameters initialization A major difficulty of the variational inversion comes from the initial conditions, which must be close enough from their real values to reach the global minima of the cost function. So we have to set the initial values of the inputs parameters. † The three aerosol parameters n, mr and t are initialized with a dedicated multi-layer perceptron (MLP) inverting the observations in the NIR. A previous work (Jamet, Moulin, & Thiria, 2004) has shown that this initialization provides an accurate first guess, † The other parameters are initialized at arbitrary constant: miZ0.001, b0Z0.285 and CZ0.2.

3.2. The direct model The direct model allows the computation of rCOR at each wavelength for any parameter value. As shown previously, the output values of the direct model rCOR can easily be determined knowing rA, t and rw. In order to obtain continous derivable functions for rCOR, the LUT is modelled using three multi-layer Perceptrons (MLPs). Fig. 2 shows how the three MLPs (MLP-A for rA, MLP-t for t and MLP-O for rw) are used to estimate the output rCOR of the direct model. The global function rCOR is highly non-linear with respect to the different input parameters (especially n and the geometry). A subset of 100,000 randomly selected examples from the LUT provides the learning dataset to train the three MLPs needed, the test dataset is made by randomly extracting 5000 examples from the LUT, independent of the learning database. Table 1 shows the range of input parameters we used. The architecture of these MLPs and the performance on the test set are shown in Table 2. 3.3. The adjoint code As seen in Fig. 2, the model output rCOR is computed through interconnected MLPs, which forms a modular graph

Fig. 2. Architecture of the rCOR computation using MLP-A, MLP-t and MLPO; C and b0 are the oceanic parameters, n, mi and t are the aerosol parameters, and qs, qv, df are the geometry of the considered pixel. The parameters that are framed are the control parameters during the variational inversion.

(each MLP is a module). The determination of the adjoint is thus straightforward with a gradient backpropagation through this modular graph and the MLPs (Bishop, 1995) (the implementation of the direct model and the adjoint code is realized by using a dedicated software called YAO). 3.4. The parameter adjustement The parameter adjustment is made with the help of a minimizer provided by Institut National de Recherche en Informatique et en Automatique (INRIA). The algorithm, called M2QN1, takes parameter boundaries into account and uses the BFGS (Broyden–Fletcher–Goldfarb–Shanno) formula at each iteration (Gilbert & Lemarchal, 1989). Note that in this case, the adjoint calculation is an ill-posed problem because the solution is multi-valuated. To avoid local minima of the cost function during the minimization, the calculation of the first guess for aerosol parameters must be accurate. After the presentation of the general method already described in Jamet et al. (2005), we focus in Section 4 on the second main improvement of the first version of NeuroVaria (the first was the change of aerosol models for direct

Table 2 Architecture (number of layers and neurons) and performance in terms of RMS of the MLPs modelling the direct model: MLP-A for rA, MLP-t for t and MLPO for rw

No. of inputs Neurons first hidden layer Neurons second hidden layer Outputs RMS error

MLP-A

MLP-t

MLP-O

8 35

7 19

3 8

20

11

6

1 2.4!10K3

1 4.19!10K5

1 7.61!10K4

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computations): the introduction of a new cost function which allows us to use NeuroVaria for absorbing aerosols. 4. The new cost function The cost function J is a quadratic function, which cal depends on the observed robs cor , the computed rcor and the control parameters to be retrieved. Here, the dimension of the observation vector robs cor is 8, corresponding to the eight wavelengths. The general form of the cost function is shown in Eq. (3). The ai and bi represent the weights for the different terms of the cost function, xj are the control parameters ð2fv; mi ; t; b0 ; C gÞ; xeb are the first guesses for j these parameters. So the cost junction is defined by the following equation: JZ

8 X iZ1

cal 2 ai ðrobs COR ðli ÞKrCOR ðli ÞÞ C

X

2 bj ðxj Kxeb j Þ

(3)

j

The weight coefficients are considered as variability indexes of the terms of the cost function J. They are different for each wavelength and depend on the control parameters. NeuroVaria uses a pseudo-relaxation technique: several successive minimizations are proceeding to take into account the specificities of J. Two sets of parameters are controlled during distinctive phases: † mi, b0 and C constitute the first set. These parameters have a strong impact on the visible part of the signal (from 412 to 555 nm), and have no accurate first guess. These sets of parameters are those we are most interested in. † n, t and mi constitute the second set. These parameters have a strong impact on all spectral bands. n, t can be quite accurately initialized from the near-infrared bands (from 670 to 865 nm) (Jamet et al., 2004) and will be improved further during the minimizing process. The variational inversion is processed by considering five independent minimizing cycles, with alternatively one of the two sets of parameters being controlled. We, therefore, consider two different cost functions JA and JB for the minimizations depending on the two control parameter sets. JA is related to the set (mi, b0 and C) and JB to the set (n, t and mi). The first minimization is done with the set (mi, b0 and C) corresponding to the cost function JA. After several steps, we switched the cost function and the set of parameters to JB and to (n, t and mi). Then, we stopped the minimization to change for JA and (mi, b0 and C). This switch is done five times in a row. Table 3 sums up the minimization process. At each step, the cost function is associated with its specific weights coefficient ai. The values of the bi used in JA and JB increase from one minimizing cycle to another. They have been determined after experiments using synthetic datasets. We discuss here, the different aspects considered to determine the weights coefficients ai:

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Table 3 Minimizing cycle in NeuroVaria Minimizing cycle

Cost function

Control parameters

1 2 3 4 5

JA JB JA JB JA

{mi; b0; C} {n; t; mi} {mi; b0; C} {n; t; mi} {mi; b0; C}

(1) The black ocean assumption. This study is limited to case I waters, and non-eutrophic waters, so we can assume that ocean is ‘black’ in the near-infrared (lR670 nm) (Siegel, Wang, Maritorena, & Robinson, 2000), implying that r w (lR670)Z0 and so rCOR (lR670 nm)ZrA (lR670 nm). This allows us to set the weights coefficients for the NIR bands of the cost function JA to very small values (because the control parameters have almost no impact for these wavelengths) and to very strong values for the cost function JB for the opposites reasons. Note that the weights coefficients at 670 nm are small because there is a residual rw signal at this wavelength that is not taken into account by the models used in NeuroVaria. (2) The coloured dissolved organic matter. These matters, also called yellow substances, are not explicitly accounted for by the present bio-optical model. Their major impacts are at 412 nm (Bricaud, Morel, & Prieur, 1981). So, because of this potential noise, the weights of JA at 412 nm are set to very small values. (3) The typical shape of rw. The bio-optical model gives a typical shape of rw with a strong variability at 443 and 490 nm and a weak variability at 555 nm. So the weights of JA are taken at high values for 443 and 490 nm. At 555 nm, we know that rw is almost constant, so the variability of rCOR at this wavelengths is mainly due to the atmosphere, therefore the weight of JB at 555 nm is strong. From these assumptions, the weight coefficients can be fixed. Table 4 gives the values chosen for the weights coefficients ai for the cost functions JA and JB. We have presented the main improvements of NeuroVaria. These modifications had to be compared first with in situ and the previous version and then applied to images showing events with absorbing aerosols.

Table 4 ai Weight coefficients considered for the cost function JA and JB for all spectrum Wavelength (nm)

ai for JA

ai for JB

412 443 490 510 555 670 765 865

10 50 200 200 200 0 1 1

40 40 40 40 800 30 200 800

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J. Brajard et al. / Neural Networks 19 (2006) 178–185 0.2

NeuroVaria v1 NeuroVaria v2

0.025

τ NeuroVaria

ρw(443) NeuroVaria

NeuroVaria v1 NeuroVaria v2

0.02 0.015

0.1

0.05

0.01 0.005

0.15

0.01

0.015

0.02

0.025

ρw(443) insitu

0

0

0.05

0.1

0.15

0.2

τ insitu

Fig. 3. Scatter plot of t (upper panel) and rw(443) (lower panel) retrieved by the two version of NeuroVaria (the initial version v1 (*) and the new version v2 ($)) versus t and rw in situ, respectively. Solid lines are the lines of slope 1. Dash–dotted lines are the linear fits for the initial version results and dotted lines are the linear fits for the new version results.

5. Validation of NeuroVaria The former version of NeuroVaria has been validated for clear atmospheric situations (Brajard et al., in press) using in situ data performed in the Mediterranean in the framework of two campaigns, NORBAL and SARHYGOL. During these two campaigns, the aerosol optical thickness t(865) (hereafter t) and the water-leaving reflectances rw(443) were measured regularly. It has been shown (Brajard et al., in press) that the initial version of NeuroVaria performs better than the standard SeaWiFS algorithm. Given the importance of the changes applied to NeuroVaria, we briefly show here that the new version remains of high quality. The NORBAL and SARHyGOL measurements took place in the Gulf of Lion in 2000 in the Mediterranean Sea (Deschamps, Fougnie, Frouin, Lecomte, & Verwaerde, 2004). No absorbing aerosol has been noticed for these measurements. The mean and the variance of in situ data are computed for each set of measurement corresponding to 1 day and one localization. The points for which less than three measurements are available are rejected to assure a sufficient confidence in the values. The mean and the variance of NeuroVaria retrievals are computed over a square of 3!3 pixels centered on the in situ measurements. Only 14 matches are available for comparison. Fig. 3 (bottom t top rw(443)) presents the comparison between the initial NeuroVaria retrieval (v1) and the new version (v2) presented in this paper. Both versions present similar results: the relative error for the retrieval of rw(443) is 17.7% for the first version and 13.7% for the new version (SeaWiFS presents a relative error of 37.1% for the same validation points). The over-estimation of t that has been noticed for the first version of NeuroVaria with a relative error of 120.7% is increased. The relative error for the t retrieval in the new version of NeuroVaria is 180.0%. This is probably due to the fact that the Junge models of aerosols can introduce a bias into the estimation of t in comparison with the Gordon aerosol models (Gordon & Wang, 1994) used in the previous version. But even with an overestimation of t, the atmospheric reflectance rA can be obtained with accuracy and allows retrieving with the same accuracy as the water-leaving reflectance rw.

Fig. 4. chl-a (mg mK3) retrieved for 3rd April 1998 with Neurovaria (top) and the SeaWiFS algorithm (bottom). The two methods show the same variations of chl-a in term of spatial structures especially in the region of the spring bloom. It shows that Neurovaria is consistent for clear atmosphere.

J. Brajard et al. / Neural Networks 19 (2006) 178–185

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Fig. 5. chl-a (mg mK3) retrieved for 6th October 1997 with absorbing aerosols (top) and for 8th October 1997 without absorbing aerosols (bottom). The left column is the NeuroVaria processing, the right column is the SeaWiFS processing. The SeaWiFSstandard algorithm fails to obtain the same patterns and the same concentrations for both days whereas the NeuroVaria processing shows a good retrieval of the chlorophyll-a patterns. It indicates that Neurovaria is able to perform atmospheric correction when there are absorbing aerosols events.

6. Comparison with the SeaWiFS in presence of weakly and absorbing aerosols 6.1. Results with a clear atmosphere We first compared SeaWiFS and NeuroVaria chl-a retrieval in the western part of the Mediterranean Sea (between Spain and Morocco) on the 3rd of April, 1998.

The aerosol optical thickness was low everywhere during that day, allowing us to validate this new NeuroVaria version on a case with clear atmospheric conditions. Note that the NeuroVaria chl-a is deduced from the NeuroVaria water-leaving reflectance rw(l) through the OC4V4 biooptical model (O’Reilly et al., 1998) to have a consistency in the results. The two chl-a maps are presented in Fig. 4. The same spatial structures of chlorophyll-a concentration

Fig. 6. t retrieved for the 6th October 1997 with absorbing aerosols (top) and for the 8th October 1997 without absorbing aerosols (bottom). Studies have shown that for this region, high aerosol thickness values t correspond to an absorbing aerosol plume, which is visible on the upper image. The bottom image shows a clear atmosphere with a small optical thickness.

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are found. In the Gulf of Lion, South of France, a bloom of phytoplankton appears with strong values of chl-a. This bloom is well retrieved by both algorithms. However, the bloom is less intense with NeuroVaria, likely because of the low variability of the bio-optical model we used for the pigment concentration less than 1 mg mK3. Nevertheless, this test shows that NeuroVaria performs well for standard atmospheric conditions. 6.2. Results with an absorbing aerosol event The second case (6th and 8th October 1997) corresponds to the comparison between 2 days. One day present an absorbing aerosol event and for the following one, the atmosphere is clear. Fig. 5 presents processing for the two orbits off the east coast of USA by the SeaWiFS and NeuroVaria algorithms. In this region and for this period, the state of the ocean is stable (see Chomko and Gordon, 1998) and therefore the oceanic constituents, such as the chlorophyll-a, are almost the same for the two selected days. On 6th October 1997, an absorbing aerosol event has been identified (see Chomko and Gordon, 1998) whereas the atmosphere is clear for 8th October (see the aerosol optical thickness retrieved by NeuroVaria for these 2 days in Fig. 6). These 2 days are therefore a good test to evaluate the performance of our algorithm in the presence of absorbing aerosols. The 8th October image is the reference image, since the sky is clear, and we expect to obtain the same chl-a patterns and concentrations for the 2 days. On the right column of Fig. 5, one can see the SeaWiFS standard product for 6th of October at the top and the 8th of October at the bottom. The SeaWiFS standard algorithm fails to obtain the same patterns and the same concentrations for both days. For 6th of October, the concentrations are weaker and the specific chl-a pattern is not well retrieved. It is certainly due to the failure of the atmospheric correction on the 6th October (upper panel) because of absorbing aerosols. On the left side of the same figure, the NeuroVaria processing shows a good retrieval of the chlorophyll-a patterns with almost the same concentrations for the two selected days and the specific pattern is correctly retrieved with the same shape at the same location. It indicates that NeuroVaria is able to perform atmospheric correction when there are absorbing aerosols events. This shows that the new NeuroVaria algorithm can now handle non- and absorbing aerosols in the same time. 7. Conclusions This article presents the evolution of an original method to process ocean colour imagery. It is a combination of neural network techniques and variational inversion. This method allows retrieving simultaneously the aerosol optical properties and the oceanic constituents by taking into account the whole spectrum. The new features of the method enable to take into account the absorbing aerosols

and to use all the information given by the whole spectrum through the cost function. This new version has been validated with in situ data in the Gulf of Lion in the Mediterranean Sea and compared to the previous version showing a slight improvement in the atmospheric correction algorithm, especially for the water-leaving reflectance. A processing of two images on the east coast of the USA shows that NeuroVaria allows retrieving oceanic constituents under absorbing aerosols conditions where the standard SeaWiFS algorithm fails. This is the main improvement of the method. But the work needs to be validated with in situ data and then will be applied to various regions with aerosol events as the east of India. Acknowledgements The authors thank, for providing their in situ data: H. Claustre (DYFAMED), A. Bricaud and JGOFS-France (PROSOPE), A. Petrenko (SARHYGOL), G.L. Liberti and P.Y. Deschamps (NORBAL). We thank C. Sorror for developing and providing assistance on the software YAO, ACRIst for their support, Michel Crepon for his help in the redaction of this article and H.R. Gordon for providing the synthetical database (LUT).

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