Remote Sensing of Environment

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1 Remote Sensing of Environment 115 (2011) Contents lists available at ScienceDirect Remote Sensing of Environment journal homepage: Spectral variations in the near-infrared ocean reflectance Maéva Doron a,b,c,, Simon Bélanger d, David Doxaran b,c, Marcel Babin b,c a ACRI-ST, 260 route du Pin Montard, B.P. 234, Sophia Antipolis, France b Université Pierre et Marie Curie-Paris6, Laboratoire d'océanographie de Villefranche, Villefranche-sur-Mer, France c CNRS, Laboratoire d'océanographie de Villefranche, Villefranche-sur-Mer, France d Université du Québec à Rimouski, Département de Biologie, Chimie et Géographie, 300 allée des Ursulines, Rimouski, Qc, Canada G5L 3A1 article info abstract Article history: Received 9 December 2009 Received in revised form 18 January 2011 Accepted 24 January 2011 Available online 5 April 2011 Keywords: Ocean color Near-infrared Reflectance Satellite data In situ data Turbidity Coastal Suspended particulate matter The optical properties of natural waters beyond the visible range, in the near-infrared (NIR, nm), have received little attention because they are often assumed to be mostly determined by the large absorption coefficient of pure water, and because of methodological difficulties. It is now growingly admitted that the NIR represents a potential optical source of unambiguous information about suspended sediments in turbid waters, thence the need for better understanding the NIR optical behaviour of such waters. It has recently been proposed (Ruddick et al., Limnology and Oceanography. 51, , 2006) that the variability in the shape of the surface ocean reflectance spectrum in the NIR is negligible in turbid waters. In the present study, we show, based on both in situ and remote sensing data, that the shape of the ocean reflectance spectrum in the NIR does vary in turbid to extremely turbid waters. Space-borne ocean reflectance data were collected using 3 different sensors (SeaWiFS, MODIS/Aqua and MERIS) over the Amazon, Mackenzie and Rio de la Plata turbid river plumes during extremely clear atmospheric conditions so that reliable removal of gas and aerosol effects on reflectance could be achieved. In situ NIR reflectance data were collected in different European estuaries where extremely turbid waters were found. In both data sets, a flattening of the NIR reflectance spectrum with increasing turbidity was observed. The ratio of reflectances at 765 nm and 865 nm, for instance, varied from ca. 2 down to 1 in our in situ data set, while a constant value of 1.61 had been proposed based on theory in a previous study. Radiative transfer calculations were performed using a range of realistic values for the seawater inherent optical properties, to determine the possible causes of variations in the shape of the NIR reflectance spectrum. Based on these simulations, we found that the most significant one was the gradual increase in the contribution of suspended sediments to the color of surface waters, which often leads to the flattening of the reflectance spectrum. Changes in the scattering and absorption properties of particles also contributed to variations in the shape of the NIR surface ocean reflectance spectrum. The impact of such variations on the interpretation of ocean color data is discussed Elsevier Inc. All rights reserved. 1. Introduction The apparent optical properties (AOPs) of marine waters beyond the visible domain, in the near-infrared (NIR, nm), are often assumed to be nearly constant and to be only determined by the optical properties of pure seawater. This is because the absorption coefficient of water gets very high with increasing wavelength. For instance, when calculating the heating rate resulting from the absorption of solar radiation in the upper ocean, Morel and Antoine (1994) set the vertical diffuse attenuation coefficient, K d (λ) (m 1 ), constant above 740 nm (see Table 1 for a list of symbols and subscripts). Furthermore, NIR water-leaving reflectance (ρ w, dimensionless), specular reflection at sea surface excluded, is generally assumed to be null in open ocean waters when estimating the Corresponding authorat: Presentaddress: Laboratoiredes Ecoulements Géophysiques et Industriels, Grenoble, France. Tel.: ; fax: address: doron@hmg.inpg.fr (M. Doron). contribution of the atmosphere to the ocean reflectance measured from the top of atmosphere by satellite sensors e.g. Gordon and Wang (1994). While the above assumptions are very appropriate for most open ocean waters, it has been known for a long time by those working in marine optics that the apparent optical properties of seawater do in fact vary in the NIR, especially reflectance, when the amount of suspended particles becomes significant (e.g. Morel & Gordon, 1980; Bricaud & Morel, 1987). This happens mostly during strong phytoplankton blooms (Siegel et al., 2000), and in coastal waters where bottom sediments get re-suspended and/or particles are transported by rivers (e.g. Doxaran et al., 2002a, 2002b). When NIR ρ w is large enough to be measurable, it provides unambiguous information about the concentration of suspended particles (Doxaran et al., 2006). The drawback is that high NIR ρ w prevents atmosphere from being readily distinguished from the ocean in the signal measured from top of atmosphere by satellite sensors. Both those opposing aspects of the problem call for improved knowledge about the variability of NIR reflectance and for a clear understanding of the /$ see front matter 2011 Elsevier Inc. All rights reserved. doi: /j.rse

2 1618 M. Doron et al. / Remote Sensing of Environment 115 (2011) Table 1 List of notations. Symbol Description Unit AOT Aerosol optical thickness Dimensionless a (λ) Absorption coefficient m 1 b (λ) Scattering coefficient m 1 b b (λ) Backscattering coefficient m 1 b b ch ðλþ Backscattering efficiency for the Dimensionless chlorophyll (in the IOCCG dataset) b b dm ðλþ Backscattering efficiency for the Dimensionless detrital matter (in the IOCCG dataset) b * SPM Mass-specific scattering coefficient for SPM m 2 g 1 c (λ) Beam attenuation coefficient m 1 E d (λ,z) Downward plane irradiance at the depth z W m 2 nm 1 E u (λ,z) Upward plane irradiance at the depth z W m 2 nm 1 K d (λ) Vertical diffuse attenuation coefficient m 1 L u (λ,θs, Upwelling radiance in the viewing Wm 2 sr 1 nm 1 θv, ΔΦ, z) direction (below the surface) L w (λ,0 + ) Water-leaving radiance in the viewing Wm 2 sr 1 nm 1 direction (above the surface) L wn Normalized water-leaving radiance W m 2 sr 1 nm 1 NIR Near-infrared Q Bidirectionality factor Dimensionless R(λ) Irradiance reflectance just below Dimensionless the surface (0 ) R rs (λ) Above-surface remote-sensing reflectance (0 + ) sr 1 R rs ðλ; θ s; θ v; ΔΦÞ = Lw ð 0þ ;λ;θs;θv;δφþ E d ð0 þ ;λþ r rs (λ) Below-surface remote-sensing reflectance (0 ) sr 1 S SPM Spectral slope of a SPM nm 1 SPM Suspended particulate matter g m 3 t Diffuse atmospheric transmittance Dimensionless α a Angström coefficient Dimensionless ΔΦ Difference of azimuth between the solar zenith angle and the viewing zenith angle Δλ Waveband width for the satellite ocean nm color sensors ε Spectral dependence of aerosol reflectance Dimensionless λ 1 Wavelength in the NIR: λ 1 =779 (Δλ =15) nm for MERIS, λ 1 = 765 (Δλ=40) for SeaWiFS and λ 1 =748 (Δλ=10) for MODIS λ 2 Wavelength in the NIR: λ 2 =865 (Δλ =20) nm for MERIS, λ 2 = 865 (Δλ=40) for SeaWiFS and λ 2 =869 (Δλ=15) for MODIS ρ a Aerosol reflectance (contribution Dimensionless of the atmosphere) ρ Ray Rayleigh reflectance (contribution Dimensionless of the atmosphere) ρ rc Rayleigh-corrected reflectance =ρ TOA ρ Ray Dimensionless ρ TOA Top Of Atmosphere reflectance Dimensionless ρ w Water-leaving reflectance Dimensionless θs Solar zenith angle θv Viewing zenith angle ω p Single-scattering albedo for SPM Dimensionless m Index or symbol No subscript w ˆ Signification Total Water Estimated variable, e.g. ˆρ w causes. Recently, a few studies provided the first reliable data on inherent optical properties (IOPs, absorption and scattering coefficients) of marine particles in the NIR (Tassan & Ferrari, 2003; Stramski et al., 2007; Doxaran et al., 2007). There is now a need for better understanding how those IOPs combine in the ocean to form AOPs such as reflectance in the NIR. While it is well known that the magnitude of NIR ρ w does vary largely with turbidity far beyond 750 nm (Doxaran et al., 2002a, 2002b; Sydor et al., 2002), and not necessarily in extreme conditions, less is known about variations in the shape of the NIR ρ w spectrum. Ruddick et al. (2006) recently showed that the shape of the ρ w spectrum in turbid waters is quite constant in the NIR because the shape of the seawater absorption spectrum mostly determines it. Their conclusions were based on careful measurements of the ρ w spectrum in turbid coastal waters. The data set used by Ruddick et al. (2006) (27 ρ w spectra of high quality from their database of 188) is however very small because of the difficulty of achieving good abovewater in situ reflectance measurements (Hooker & Morel, 2003), especially in the NIR. If confirmed, the finding of a constant shape of the ρ w spectrum, so-called by Ruddick et al. (2006) similarity spectrum, greatly simplifies the interpretation of NIR ρ w. It could be used in the inversion of reflectance, both for removing the atmospheric contribution to the remotely sensed reflectance (e.g. Ruddick et al., 2000) and for retrieving the concentrations or IOPs of the substances contained in seawater (e.g. Moore et al., 1999). In the present study, we revisit the problem of the variations in the shape of the NIR seawater reflectance spectrum in turbid waters. This work was triggered by coincidental observations of significant variations in the ρ wð765þ ratio within data from the ocean color ρ w ð865þ satellite sensor SeaWiFS collected over turbid waters of the Beaufort Sea (plume of the Mackenzie River). Those measurements were recorded when the load of aerosols was exceptionally low. The aerosol optical thickness at 865 nm [AOT(865), dimensionless] was lower than for data from the MERIS sensor for instance. Such atmospheric conditions allowed very reliable atmospheric corrections to be made even using a very simple approach, so that the ρ w data could be considered as sea-truth. We extended our analysis to data collected with the MODIS/Aqua (MODerate Resolution Imaging Spectroradiometer) and MERIS (MEdium Resolution Imaging Spectrometer) sensors, and to the area of the Amazon and Rio de la Plata plume to cover differing observational geometries and seawater optical properties. Additionally, we present reflectance data obtained in situ in the highly turbid waters of the Elbe (Germany), Gironde (France) and Tamar (UK) estuaries to extend the range of suspended particulate matter covered by the study of Ruddick et al. (2006). Radiative transfer calculations are conducted to interpret the observed trends. Finally, the impact of the variability in the ρ wð765þ ρ w ð865þ ratio on atmospheric corrections is assessed. 2. Material and methods 2.1. The study areas: the turbid plumes of three large rivers, Mackenzie, Amazon and Rio de la Plata The Mackenzie River plume is located in the Beaufort Sea (Arctic Canadian Basin, around latitude 70 North, longitude 135 West). The satellite imagery was considered during the summer months when the ice cover is minimal in the Arctic Ocean and the limit of the icepack is far from our region of interest (see Fig. 1 for an example). The Amazon River plume is located in the tropical Atlantic Ocean (around latitude 0, longitude 50 West). The periods of interest are the months between July and October, supposedly with the clearest atmospheres. The Rio de la Plata River plume is located in the Southern Atlantic (around latitude 35 South and longitude 52 West) Ocean color data from the sensors MERIS, SeaWiFS and MODIS/Aqua We selected MERIS, SeaWiFS and MODIS/Aqua images over the Mackenzie River, the Amazon River and the Rio de la Plata River plumes and surrounding oceanic waters, for the clearest atmospheric conditions observed during summer in the recent years. Due to the high latitude of the Beaufort Sea, the ocean color sensors can see the zone twice a day. The properties of the atmosphere were retrieved with confidence over the oceanic clear-water pixels using the standard processing chain (Gordon & Wang, 1994; Antoine & Morel, 1999). For instance, over the Amazon, AOT(865) was below , while

3 M. Doron et al. / Remote Sensing of Environment 115 (2011) reflectance as in Hu et al. (2000). To make this approach valid, we select ocean color scenes for which the atmosphere is very clear and homogeneous over large scales (see below). We now describe in details the steps that allow us using ocean color remote sensing as a robust mean to measure spectral dependency of water-leaving reflectance in the NIR. As an example, we described those steps for the processing of a SeaWiFS image acquired on June 21st 1998 at around 22:00 UTC (Fig. 1). Fig. 1. A red green blue composite image of a SeaWiFS scene, captured above the Beaufort Sea in the North of Canada, 21st of June The image is obtained using the radiances at the top of atmosphere (without corrections, Level 1 data). Image courtesy of the NASA. over the Mackenzie, it was below for the MERIS data. We assumed that the optical properties of the atmosphere did not vary significantly at local scale, and used those properties found over a clear offshore water to perform local atmospheric corrections to retrieve the NIR water-leaving reflectances with a great accuracy (the practical details are provided below). The fact that the NIR water-leaving reflectances are not negligible above turbid waters has long been recognised (for instance Munday and Alfoldi (1979) for remotely sensed data) and different approaches have been developed to overcome this problem. For instance, in Hu et al. (2000), the aerosol type applied above a given turbid zone is taken from the nearest clear-water area. Then, to derive the aerosol reflectance, it is necessary to assume a constant shape for the NIR water-leaving reflectance spectrum, which is obviously not appropriate here for studying the variability of the latter. Wang et al. (2007) proposed an alternative approach based on reflectances in the shortwave infrared (SWIR, 1240 and 2130 nm), where the ocean reflectance signal can be safely assumed to be negligible even over turbid waters. It consists of achieving a pre-atmospheric correction to remove the contribution of the ocean to the Rayleigh-corrected topof-atmosphere reflectance, at 748 nm and 869 nm. Standard atmospheric corrections using the latter two wavelengths can then be made safely. In this approach, no assumption on the ratio of NIR water-leaving reflectances is required. The spectral extrapolation of aerosol reflectance is however performed over a long spectral interval, which can introduce significant uncertainties (see also Shi and Wang (2007)). Patt et al. (2003), based on a study by Stumpf et al. (2003) proposed a method currently implemented in the standard SeaWiFS treatment chain, but we will see a limit below in a practical case. Here, we adopted an approach similar to that of Hu et al. (2000) in the sense that we apply NIR atmosphere properties from adjacent areas, but different in the sense that we extrapolate not only the aerosol type, but also the aerosol concentration which allows us not to make any assumption about the spectral shape of water-leaving Step 1: determination of spectral aerosol optical thickness above the turbid plume SeaWiFS L1a data with local-area-coverage (LAC) are first processed to level 2 using standard atmospheric correction algorithms (hereinafter denoted as STD_AC) implemented in the SeaWiFS Data Analysis Software (SeaDAS version 5.1.3; program msl12 version 5.7.1). The STD_AC uses the black pixel assumption in the NIR (Gordon & Wang, 1994) over clear waters, while an iteration scheme to retrieve the waterleaving radiance in NIR is used over turbid or highly productive waters (Patt et al., 2003). Output parameters of the L1a-to-L2 include normalized water-leaving reflectance at all eight bands, spectral AOT, spectral dependence of aerosol reflectance (ε, dimensionless), and atmospheric input parameters from NCEP as interpolated to fit the SeaWiFS grid (zonal and meridional wind vectors and humidity). A careful analysis of these output and a visual inspection of the RGB image (Fig. 1) allow us to determine the aerosol properties over the turbid plume. Fig. 2 shows the spatial distribution of AOT(865) over the Mackenzie shelf and the adjacent Beaufort Sea. Aerosol properties observed above clear waters (cf Fig. 1) were relatively constant over large space scales (N1000 km 2 ; boxes 1 and 2 in Fig. 2) with extremely low AOT(865), typically b Comparing to clear waters, AOT(865) values above moderately and highly turbid waters (boxes 3 and 4) were significantly higher (Table 2). In addition, spatial variability of AOT(865) and ε in box 4 (highly turbid area) was twice as large as that above clear waters. Moderate anticyclonic winds (5 to 10 m s 1 ), dominated by East North East direction over the eastern part of the Mackenzie shelf (Fig. 2 and Table 2), most likely transported towards the turbid plume aerosols with properties similar as those observed over clear waters, thus reducing the possibility to find continental aerosols in that area. Over the turbid plume, we therefore assume that the aerosol properties are those observed near the coast of Cape Bathurst (box 2), i.e. AOT(865) of 0.02 and epsilon of Interestingly, our results suggest that the STD_AC remains sensitive to water turbidity, despite its iterative scheme for retrieving the water-leaving signal in the NIR (Patt et al., 2003), and given the 1) offshore to inshore wind conditions, 2) spatial homogeneity of aerosol properties over a large area above clear waters located just North-East of the turbid plume, and 3) spatial heterogeneity of aerosol properties retrieved above highly turbid waters Step 2: re-processing ocean color data with known aerosol properties To estimate the water-leaving reflectances in the NIR part of the spectrum, the SeaWiFS L1a data were reprocessed using the multiplescattering with fixed aerosol optical thickness option in the SeaDAS msl12 program (hereinafter denoted as CTE_TAU). When using that option, the user needs to specify the AOT for each SeaWiFS bands, which will be applied to every cloud-free pixels of the scene. In the example presented here, AOT varies from at 865 nm to at 412 nm. Fig. 3 and Table 3 compare, as an example, the water-leaving reflectance at 555 nm obtained using both STD_AC and CTE_TAU schemes, respectively. The difference between the two products is in general b10%, except for highly turbid waters (box 4) where CTE_TAU produced higher nl w of about 0.44 mw cm 2 nm 1 sr 1 (13.4%) than STD_AC.

4 1620 M. Doron et al. / Remote Sensing of Environment 115 (2011) Fig. 2. Aerosol optical thickness at 865 nm obtained using SeaDAS standard level 1a to level 2 data processing (SeaWiFS data; June 21st 1998). Wind vectors are shown as grey arrows. The areas where aerosol properties and wind characteristics were calculated (Table 2) are shown as red boxes. A similar protocol was applied to the other SeaWiFS, MODIS/Aqua and MERIS images. In the latter case, the geographical coordinates of offshore pixels located in clear waters were found by eye inspection and using the BEAM software ( cms/web/beam). We also verified that the low values of ρ a (865) had low spatial variability and that there was no flag on Case I chlorophyll product. The coordinates of coastal pixels located inside the turbid plume of the river are used to define imaginary trajectories (transects) between clear and turbid waters, that represent a gradient of turbidity. During the standard processing chain from level 1A to level 2, the entire set of aerosol properties for clear pixels is extracted and is used to perform atmospheric corrections for the entire transect with constant aerosol properties. A summary of the satellite images, considered in the present study together with the locations of offshore and coastal pixels is presented in Table 4. Fig. 4 illustrates the very low contribution of the aerosol to the total signal in a selected scene from the ocean color images. Because of such atmospheric conditions, the error in retrieved ρ w over turbid waters due to our atmospheric corrections was very low (see Appendix A for details). Recently Wang et al. (2009) showed, in a validation study for the SWIR algorithm, that the water-leaving radiance quality from SWIR algorithm is similar to the NIR derived water-leaving radiance even with Table 2 Statistics on aerosols, as obtained using standard AC algorithm, and winds above clear and turbid waters from different areas ( km 2 boxes, or pixels) shown in Fig. 2 (average±1 standard deviation). Data obtained for the SeaWiFs scene the 21st of June AOT(865) ε Zonal wind (+ = W to E) Meridional wind (+ = S to N) Box ± ± ± ±0.03 Box ± ± ± ±0.06 Box ± ± ± ±0.01 Box ± ± ± ±0.04 longer extrapolation. They showed that the uncertainty caused by the noise of the SWIR bands and the long extrapolation in the NIR is small in comparison to the water-leaving radiance at NIR. A comparison of the remotely-sensed water-leaving reflectances obtained with either a) atmospheric corrections assuming a clear atmosphere with regional characteristics (our approach) or b) the SWIR atmospheric corrections (Wang et al., 2007) was made for a MODIS/Aqua image (captured the 6th of August 2004 above the Beaufort Sea). It was possible for the MODIS/Aqua sensor, because it has the adequate wavelength to perform SWIR In situ measurements The 2005 and 2006 RSFLUX field campaigns were conducted in different turbid estuarine and coastal waters around Europe. We here focus on data gathered in the Elbe (Germany, October 2005), Gironde (France, October 2005 and March 2006) and Tamar (UK, October 2005) estuaries. Simultaneous measurements of the above-surface remotesensing reflectance R rs (sr 1 ) and concentration of total suspended material within surface waters were achieved. To determine the concentration of suspended particulate matter (SPM, in g m 3 ), a known volume of the surface water sample was filtered through preweighted Whatman GF/F filters. Filters stored at 80 C were then dried 24 h at 65 C to obtain the dry weight (van Der Linde, 1998). The R rs signal is defined (see Eq. 1, and Morel and Mueller (2002)) as the ratio of the water-leaving radiance L w (in W m 2 sr 1 nm 1 ) to downwelling irradiance just above the water surface E d (0 + ) (in W m 2 nm 1 ). R rs ðλ; θ s ; θ v ; ΔΦÞ = L w 0 þ ; λ; θ s ; θ v ; ΔΦ E d ð0 þ ; λþ where λ is the wavelength (in nm), θ s, θ v, ΔΦ are respectively the solar zenith angle, the viewing zenith angle and the azimuth difference between the sun and viewing directions (all three in ). ð1þ

5 M. Doron et al. / Remote Sensing of Environment 115 (2011) Fig. 3. Normalized water-leaving radiance at 555 nm A) (top panel) as obtained using the standard atmospheric correction for SeaWiFS (noted STD_AC, following Gordon and Wang (1994)and Patt et al. (2003)) and B) (bottom panel) as obtained using constant aerosol properties above the scene. In this case, the optical properties of the aerosol are the ones obtained for a region located in clear waters (box 2). This method is noted CTE_TAU in the text. Hyperspectral ( nm) radiometric measurements were carried out in the estuaries, using two Trios RAMSES-ARC radiance sensors (7 field of view) and one Trios RAMSES-ACC-VIS irradiance sensor. E d (0 + ) was measured directly with the irradiance sensor pointing the zenith and placed at the top of the ship to avoid any shadow effect. L w was calculated from above-water upwelling radiance measurements (total radiance L t ) corrected for surface reflection effects by substraction of a certain percentage ρ of the measured sky radiance signal (L s ). L t was measured pointing the first radiance sensor towards the sea surface with an angle of 35 with the nadir and an azimuth angle of 137 with the Sun. L s was measured pointing, simultaneously, the second radiance sensor towards the sky with an angle of 35 to zenith and the same azimuth angle. Radiance measurements were recorded every five seconds during two minutes, and then averaged over this time period. The water leaving radiance signal, L w, was finally calculated following Eq. (2) (more details on these in situ measurements can be found in Doxaran et al. (2007)). L w = L t ρl s Based on ρ values calculated by Mobley (1999) for different cloud cover and sea surface roughness conditions, a spectrally flat ρ value of 0.02 was adopted in the NIR. To assess the R rs uncertainties due to inaccuracy on the selected ρ factor, ρ values of 0.01 and 0.03 (i.e., 0.02±50%, ð2þ

6 1622 M. Doron et al. / Remote Sensing of Environment 115 (2011) Table 3 Comparison of normalized water-leaving radiance at 555 nm as obtained using STD_AC (Fig. 3, top panel) and CTE_TAU (Fig. 3, bottom panel) schemes for four selected areas shown in Fig. 3 (average±1 standard deviation). Data obtained for the SeaWiFS scene the 21st of June STD_AC (mw cm 2 nm 1 sr 1 ) CTE_TAU (mw cm 2 nm 1 sr 1 ) Box ± ± ( 9.1) Box ± ± (9.3%) Box ± ± (4.2%) Box ± ± (13.4%) a 100 (CTE_TAU STD_AC)/STD_AC. Absolute (and relative a ) difference (mw cm 2 nm 1 sr 1 )(%) respectively) were also considered. The resulting variations induced on the R rs (765)/R rs (865) ratio proved to be smaller than ±6%. Consequently, the same decrease of R rs (765)/R rs (865) for increasing R rs (865) values was systematically obtained independently of the correction for surface reflection effects applied to radiometric measurements. Based on results obtained by Mobley (1999), the case of wavelength-dependent ρ factors should be considered when the sky is clear blue or overcast. This was done in the study published by Doxaran et al. (2004) where above-water and in-water reflectance measurements were used to quantify surface reflection effects. Doxaran et al. (2004) showed that these surface reflection effects on above-water L t measurements are very limited when considering spectral reflectance ratios. Consequently, imperfect corrections of surface reflection effects cannot explain the flattening of the ρ w (765)/ρ w (865) ratio. The in situ data set is especially interesting for our study because it covers highly turbid waters, beyond the range covered by our satellite data set. Morel et al. (2002) explicitly detailed the calculation of the normalized water-leaving radiance L wn (λ, θ s, θ v, ΔΦ) (inwm 2 nm 1 sr 1 ), originally introduced by Gordon and Clark (1981) from R rs, measured above the interface, see Eq. (3). L wn ðλþ = L wn ðλ; θ s ; θ v ; ΔΦÞ = R rs ðλ; θ s ; θ v ; ΔΦÞF 0 ðλþ where F 0 ðλþis the solar irradiance at the top of the atmosphere at the mean Sun Earth distance (in W m 2 nm 1 ). Gordon and Wang (1994) introduced the water-leaving reflectance ρ w (dimensionless, see Eq. 4), which is notably used in the MERIS processing chain. ρ w = πr rs For the sake of consistency, all the data presented in this paper are expressed in terms of ρ w, hence the SeaWiFS and MODIS/Aqua data ð3þ ð4þ are converted from L wn to ρ w and the in situ data are converted from R rs to ρ w, to allow comparisons. Unfortunately, there are no match-ups between the satellite measurements and in situ measurements to assess the quality of our water-leaving reflectance retrieval. The criteria for the perfect scene were: i) very turbid waters far from the coast to avoid adjacency effect (i.e. N4 5 km from the coast), which would have put serious doubt on assumptions and our interpretation (see discussion in Results Alternative interpretation section) and ii) a very clear and homogeneous atmosphere over large area and over both turbid and clear waters. Obviously, the chance to find a perfect scene matching in situ measurements was extremely small. In situ measurements in the NIR are very difficult to perform and their accuracy would have been worse in less turbid waters than is shown. Therefore, the in situ and satellite data are complementary: satellite data for highly turbid waters and in situ data for extremely turbid waters Radiative transfer simulations Radiative transfer simulations were conducted using the radiative transfer code Hydrolight (version 4.2, Sequoia Scientific Inc., Redmond WA, USA, Mobley (1994)), modified to include the NIR spectral domain (up to 1000 nm, beta-version). The calculations were performed for different NIR couples of wavebands to simulate the three ocean color sensors considered here: λ 1 =779 nm (band width, Δλ: 15 nm) and λ 2 =865 nm (Δλ: 20 nm) for MERIS, λ 1 =765 nm (Δλ: 40 nm) and λ 2 =865 nm (Δλ: 40 nm) for SeaWiFS, λ 1 =748 nm (Δλ: 10 nm) and λ 2 =869 nm (Δλ: 15 nm) for MODIS/Aqua. In turbid waters and in the NIR, the influence of absorption by phytoplankton and colored dissolved organic matter (CDOM) can be considered as negligible (Babin & Stramski, 2002). Moreover, to assess their assumption on the existence of the similarity spectrum in the NIR Table 4 List of the scenes used in the present study, with the locations of the offshore pixels, from which are derived the atmospheric properties and the location of the turbid pixel. Sensor Date Location of the offshore pixels Location of the coastal pixels SeaWiFS 21st June N N W W SeaWiFS 6th August N N W W SeaWiFS 22nd August N N W W MODIS/Aqua 6th August N N W W MODIS 21st August N N W W MERIS 2nd September S S W W MERIS 27th April S S W W MERIS 4th June S S W W MERIS 10th June S S W W Fig. 4. Line plots of the spectral values of the following reflectances: top-of-atmosphere (black), Rayleigh (light blue), aerosol (red) and water-leaving (green), respectively denoted ρ TOA, ρ a, ρ w and ρ R. Spectra are shown for two turbid pixels in the transect extracted from the SeaWiFS image taken on the 21st June 1998 above the Beaufort Sea. For pixel 1, ρ w (865) = and for pixel 2, ρ w (865)=

7 M. Doron et al. / Remote Sensing of Environment 115 (2011) for turbid waters, Ruddick and collaborators performed comprehensive radiative transfer simulations with the same code Hydrolight (Ruddick et al., 2006), and determined the sensitivity of their results to the presence of other constituents such as colored dissolved organic matter (CDOM) or phytoplankton. They showed that these constituents have a low impact on the resulting ratio of ρ wð765þ. The total ρ w ð865þ absorption coefficient a (in m 1 ) and the total scattering coefficient b (in m 1 ) were therefore taken here as the sum of contributions by pure seawater (a w and b w ) and by suspended particulate matter (a SPM and b SPM ). The a w (λ) and b w (λ) values were taken from Kou et al. (1993) and following Morel (1974), respectively. The coefficients a SPM and b SPM were related to the concentration of suspended particulate matter (SPM; gm 3 ), and SPM was varied in such a way that b SPM (865) covered the range from 1 to 300 m 1 for each set of other IOPs. b SPM a SPM + b SPM ) The single scattering albedo ω p for SPM (defined as ω p = is used to constrain the relation (Eq. 5) betweenb SPM (865) and a SPM (865), using the results of Stramski et al. (2007). 1 ω p b SPM ð865þ a SPM ð865þ = ω p The relationship between a SPM (λ) and a SPM (865) is given by Eq. (6) where S SPM (nm 1 ) is the spectral slope of a SPM (λ): a SPM ðλþ = a SPM ð865 Þe S SPMðλ 865Þ The spectral variations of b SPM (λ) were assumed to follow a λ n law with n being a dimensionless factor (Eq. 7). The relationship between b SPM (λ) and SPM is given by Eq. (8) where b SPM (555) is the mass-specific scattering coefficient for the suspended particulate matter (in m 2 g 1 ). λ n b SPM ðλþ = b SPM ð865þ ð7þ 865 b SPM ð555þ = b SPMð 555 Þ SPM ð8þ ð5þ ð6þ In the above equations, the parameters are ω p, n, S SPM, and b SPM (555), and the only undetermined variable is SPM. The values of ω p, n, S SPM, and b SPM (555) were given the following values based on previously published studies. Stramski et al. (2007) observed the value of ω p to vary between 0.96 and 1 in the NIR for various types of mineral particles, including highly absorbing ones. We adopted in the present study the following values: 0.98, 0.99 and for ω p. The results from the study of Babin et al. (2003), showed an average of nm 1 for the value of S SPM. In the study of Stramski et al. (2007), the values of S SPM are reported between and nm 1. The slopes of the absorption by detritus (suspended particulate matter mostly from organic origin) are found to be between and nm 1 with a mean of nm 1, in the study of Roesler et al. (1989). Here, to cover the range reported in the literature, S SPM was given the values of either 0.006, 0.012, or nm 1. The values of n have been studied theoretically and with measurements and are expected to range from 0 in coastal waters (Roesler & Perry, 1995; Roesler & Boss, 2003) to 2 in clear oceanic waters (Bricaud & Morel, 1986; Morel, 1988; Maritorena et al., 2002). A recently published paper (Doxaran et al., 2007) showed the spectral slope of the particle scattering coefficient to be around 0.4 in coastal waters and to range between 0 and 1. We gave n the value of 0, 0.3, 0.6 or 1, which is a robust assumption in the NIR according to the literature mentioned above. The average value of b SPM (555) is reported to be 0.51 m 2 g 1 by Babin et al. (2003) in European coastal waters and was used in the present study only to provide an estimation of SPM associated with b SPM (865). The scattering phase function for particles was taken from Mobley et al. (1993) who derived it on the basis of the measurements by Petzold (1972). The Fournier Forand 1% phase function (Fournier & Forand, 1994) was also tested in the case of MERIS and for the solar zenith angle of 50. All IOPs were set constant with depth. The fluorescence inelastic scattering is not taken into account since the chlorophyll fluoresces strongly around 685 nm. The fluorescence band width is around 25 nm wide (Mobley, 1994) and is out of the spectral domain considered here. Siegel et al. (2000) found that for chlorophyll concentrations greater than 0.5 mg m 3, and reasonable solar zenith angles, the error of not including the Raman scattering process is less than 5% in the estimation of the water-leaving reflectances in the NIR. They concluded that Raman scattering is not important to the modelling of the NIR reflectances. The calculations were made for solar zenith angles of 50 and 30, which are respectively representative for the Mackenzie and Amazon rivers. The sky model is taken from RADTRAN (Gregg & Carder, 1990) with a standard oceanic set of parameters for a clear atmosphere (visibility of 30 km). The ocean atmosphere interface was set for a mean wind speed of 4 m s 1. For each simulation, we extracted E d (0 + ) and L w (θ s, θ v, ΔΦ) for different observational geometries. The results are expressed in terms of water-leaving reflectance, ρ w following Eq. (9). ρ w ðλ; θ s ; θ v ; ΔΦÞ = πl w ðλ; θ s ; θ v ; ΔΦÞ E d ðλ; 0 þ Þ Radiative transfer calculations were performed at the NIR wavelengths listed above for the different sensors, for two solar zenith angles, for combinations of the values given to ω p, n,ands SPM and for ten values of b SPM (865) between 1 and 300 m Results and discussion 3.1. The satellite data over the Beaufort Sea Fig. 1 shows an example of an ocean color scene captured by SeaWiFS during a very clear day (21st of June 1998) over the Beaufort Sea. The image is an RGB composite obtained with three wavelengths in the visible using data at the level 1 (top-of-atmosphere reflectances). That day, there were no clouds, and the plume of the Mackenzie River was extending relatively far offshore, up to tens of kilometres. The turbidity of the water was gradually decreasing from inshore to offshore. Other scenes captured by other sensors and for other clear days present similar features. The aerosol content for the clear images above the Beaufort Sea was very low. Indeed, the observed aerosol reflectances are among the lowest obtainable in typical ocean color processing. For instance, above a Case 1 pixel, the retrieved ρ a (865) was and for the two scenes considered with the MERIS sensor (respectively the 21st of July 2003 and the 6th of August 2004), and for the SeaWiFS scene of the 21st of June Such low values are consistent with the in situ measurements made in this area by the AERONET network at station Barrow ( stage=3&region=alaska_and_canada&state=alaska&site=barrow). From 1997 to 2007, the mean AOT(870) was with a standard deviation of The median was and values lower than 0.02 were often observed (58 values out of 254). Fig. 4 shows the relative importance of the Rayleigh, aerosol, and water-leaving reflectances in the composition of the top-of-atmosphere signal for two pixels, one moderately turbid with ρ w (865)= and one very turbid pixel with ρ w (865)= ,inthe ð9þ

8 1624 M. Doron et al. / Remote Sensing of Environment 115 (2011) SeaWiFS scene of the 21st of June The level of aerosol reflectances is very low compared with the water-leaving one, even in the NIR. We believe that, in those images, an error in the estimation of aerosol reflectance by atmospheric correction can only have a small impact on the retrieval of the water-leaving reflectances of turbid waters, even in the NIR portion of the spectrum (see Appendix A for details). Our remotely sensed data can therefore be almost considered as sea-truth. Data shown in the Fig. 5 were captured above the Beaufort Sea by the SeaWiFS sensor for different clear days and treated for atmospheric correction as presented in the Material and methods section. For each scene considered, a rectangular sub-scene of the image was sampled and the scatterplot represents ρ w (765) versus ρ w (865). We observed a clear trend in the water-leaving reflectances in the NIR (Fig. 5). Systematically, for increasing turbidity, or equivalently, increasing ρ w (865), the increasing ρ w (765) progressively deviates from a straight line, which would be expected if the reflectance spectrum had a constant shape as suggested by Ruddick et al. (2006). The slopes of the lines drawn on Fig. 5, 1.72 and 1.61, correspond to the proposed constant values for the ratio ρ w (765)/ρ w (865) for the SeaWiFS sensor by Ruddick et al. (2000, 2006), respectively. This general trend was further examined for transects (instead of rectangular sub-scenes) in Mackenzie, Amazon and Rio de la Plata Rivers plumes and for SeaWiFS, MODIS/Aqua and MERIS sensors. The transects were made of a succession of contiguous pixels along a straight line going from oceanic Case 1 waters offshore to increasingly turbid waters inshore. For each pixel in the transect, we extracted the water-leaving reflectances at two wavelengths in the NIR: λ 1 =779 and λ 2 =865 nm for MERIS, λ 1 =765 and λ 2 =865 nm for SeaWiFS, and λ 1 =748 and λ 2 =869 nm for MODIS. Fig. 6 shows the scatterplot of ρ w (λ 1 ) versus ρ w (λ 2 ) for the three sensors (MERIS, SeaWiFS and MODIS/Aqua) above the Beaufort Sea, on the same day (6th of August 2004). Due to the high latitude of the Beaufort Sea, the MODIS/Aqua sensor can see the zone twice a day. The data points form a trend with very low scatter that departs from a straight line for the larger values of ρ w (λ 2 ). The ρ w (λ 2 ) values extend over different ranges for the different sensors because of the different thresholds used by each standard processing chain to flag pixels as a bright non-water target (i.e. cloud or ice). In the case of the MERIS processing chain, for Fig. 5. Scatterplot of the water-leaving reflectances ρ w (765) versus ρ w (865) from different SeaWiFS images taken above the Beaufort Sea at various dates (as written in the legend). The data were extracted on rectangular subscenes. A polynomial fit was calculated for this data set and the equation of the bold red line is P(x)= 13.64x x The constant values of the ratio ρ w (765)/ρ w (865) proposed by Ruddick et al. (2000, 2006), respectively 1.72 and 1.611, are depicted as straight lines. Fig. 6. Scatterplot of the water-leaving reflectance ρ w (λ 1 ) versus ρ w (λ 2 ) obtained above the Beaufort Sea for the same date, the 6th of August 2004, with three different ocean color sensors. The wavelengths are λ 1 =779 and λ 2 =865 nm for MERIS, λ 1 =765 and λ 2 =865 nm for SeaWiFS, and λ 1 =748 and λ 2 =869 nm for MODIS/ Aqua. The (Moore et al., 1999) curve shows the relationship between the two reflectances proposed in their study to perform atmospheric corrections above turbid waters. The similarity spectrum lines (ratio of ρ w (λ 1 )/ρ w (λ 2 ) in the NIR) are plotted according to Ruddick et al. (2006) (noted R06 in the legend). The slopes of the lines (see their Table 3) depend on the sensor because of their different spectral characteristics, and also on whether it is based on in situ measurements (lines noted experimental ) or on radiative transfer simulations (lines noted theoretical ). instance, the flag is based on a combination of thresholds and look-up tables ( For SeaWiFS and MODIS/Aqua, the standard cloud or ice flag is set when the NIR albedo (i.e., 865 and 870 nm respectively) is larger than 2.7%. For the purpose of this study, however, the threshold was increased to 3.5% in order to increase the number of pixels in very turbid waters. The quantity ρ w (λ 1 ) is always larger than ρ w (λ 2 ) because the absorption coefficient of pure seawater is nearly twice as large at λ 2 than at λ 1 (e.g m 1 at 779 nm and 4.61 m 1 at 865 nm according to Kou et al. (1993)). The three different sensors show a very good agreement over common ranges. On the same figure, the relationships between ρ w (λ 1 ) and ρ w (λ 2 ) proposed by previously published studies are plotted. In the one proposed by Moore et al. (1999), the ratio ρ w (λ 1 )/ ρ w (λ 2 ) decreases very slightly with increasing turbidity. In the similarity spectrum in the NIR for turbid waters; Ruddick et al. (2006) propose a constant value of the ρ w (λ 1 )/ρ w (λ 2 ) ratio for varying turbidity, hence a straight line in Fig. 6. Note that this constant value depends on the sensor because of their different spectral characteristics, and also on whether it was originally derived from in situ measurements or radiative transfer simulations. Our satellite data clearly show a trend different from what they proposed. Lavender (1996) reports laboratory experiments in a tank, where measurements of reflectances below water, R(865) and R(750.5) (dimensionless), were performed for varying levels of turbidity and various types of supended particulate matter. The values of R(865) were up to 0.1. Most measurements were made with SPM b600 g m 3 but a few were for SPM as high as 1200 g m 3. The ratio of the two reflectances in the NIR showed a similar trend as observed in our in situ data set: decrease of the ratio R(750.5)/R(865) when R(865) increases. Fig. 7 shows the variations in the ρ w (λ 1 )/ρ w (λ 2 ) ratio as a function of ρ w (λ 2 ) for the same data as in Fig. 6. Some discrepancies between the sensors appear more clearly than in Fig. 6. They are probably due to differences between measured wavebands by the different sensors.

9 M. Doron et al. / Remote Sensing of Environment 115 (2011) Fig. 7. Scatterplot of the water-leaving reflectance ρ w (λ 1 )/ρ w (λ 2 ) versus ρ w (λ 2 ) obtained above the Beaufort Sea for the same date, the 6th of August 2004, with three different ocean color sensors. The wavelengths are λ 1 =779 and λ 1 =865 nm for MERIS, λ 1 =765 and λ 2 =865 nm for SeaWiFS, and λ 1 =748 and λ 2 =869 nm for MODIS. The Moore et al. (1999) curve shows the relationship proposed in their study to perform atmospheric corrections above turbid waters. The similarity spectrum lines (ratio of ρ w (λ 1 )/ρ w (λ 2 ) in the NIR) are plotted in reference to the study of Ruddick et al. (2006), noted R06 in the legend. The height of the lines depend on the sensor (values reported from their Table 3) because of their different spectral characteristics, and also on whether it is based on in situ measurements (lines noted experimental : 1.98 and 1.82 for MODIS and MERIS) or on radiative transfer simulations (lines noted theoretical : 1.61, 1.64 and 1.69 SeaWiFS, MODIS and MERIS, respectively). Fig. 8 shows the results of the comparison of the water-leaving reflectances obtained either with our local atmospheric corrections (when the atmosphere is very clear) or with the SWIR method (Wang et al., 2007) for a MODIS/Aqua image located above the Beaufort Sea. Fig. 8A shows the scatterplot of ρ w (λ 1 ) versus ρ w (λ 2 )forthetwo methods and the reflectances are in very good agreement. Fig. 8B shows the ratio of ρ wðλ 1 Þ ρ w ðλ 2 Þ versus ρ w(λ 2 ) for both methods. Again, the ratio of reflectances and their trend can be superimposed for the two methods. Both datasets show a very clear trend where there is a flattening of the spectra when the turbidity increases. This comparison confirms the good quality of the retrieval of the water-leaving reflectances with our method and its consistency with the SWIR approach. Fig. 8. Comparison between the water-leaving reflectances obtained with local atmospheric corrections (our method, in blue) and obtained with the SWIR method (Wang et al. (2007), in red). The data is from a MODIS/Aqua image above the Beaufort Sea (6th of August 2004). A) Scatterplot of the water-leaving reflectance ρ w (λ 1 ) versus ρ w (λ 2 ); B) scatterplot of the water-leaving reflectance ρ w (λ 1 )/ρ w (λ 2 ) versus ρ w (λ 2 ). believe that this effect is negligible given the successful validation we presented for our atmospheric correction scheme, and given how systematic the observed trend is over various dates, sites and sensors In situ observations of the NIR ρ w (λ) spectrum in highly turbid waters Our in situ measurements were achieved in estuaries where SPM varied from 8 to 2500 g m 3. The obtained ρ w values in the NIR varied 3.2. The satellite data over the Amazon River and Rio de la Plata River Above the Amazon River and Rio de la Plata River plumes, we observed the same general trend for the reflectances in the NIR as above the Beaufort Sea (Fig. 9). We obtained these data for the three different sensors and for two different locations, in addition from what was observed above the Beaufort Sea. This highlights the fact that our results are neither region-dependent, nor sensor-dependent. Although the trend for a flattening of the water-leaving spectra in the NIR is clearly seen in a variety of situations detailed above, some variations in the reflectance ratio can be seen. This happens when considering the data for different days for the same sensor, such as in Fig. 5 (SeaWiFS data for the Beaufort Sea) or for different sensors on the same area for the same day, for instance in Fig. 7 (all sensors, Beaufort Sea), or for two types of atmospheric corrections as in Fig. 8 (SWIR and our method, for the Beaufort Sea) or for different sensors above two locations as in Fig. 9 (Rio de la Plata and Amazon, for the three sensors). Part of the variations in the reflectance ratio may be due to some residual error in atmospheric corrections. We however Fig. 9. Scatterplot of the water-leaving reflectance ρ w (λ 1 )/ρ w (λ 2 ) versus ρ w (λ 2 ) obtained above the Amazon and Rio de la Plata turbid plumes for different dates, with three different ocean color sensors. The wavelengths are λ 1 =779 and λ 2 =865 nm for MERIS, λ 1 =765 and λ 2 =865 nm for SeaWiFS, and λ 1 =748 and λ 2 =869 nm for MODIS.

10 1626 M. Doron et al. / Remote Sensing of Environment 115 (2011) between 0.02 and 0.18 at 765 nm, and between 0.01 and 0.16 at 865 nm. The maximum values are around one order of magnitude larger than the water-leaving reflectances obtained with the spaceborne ocean color sensors in this study. Fig. 10 shows the variations in ρ w (765)/ρ w (865) versus ρ w (865) for the different estuaries. Although the data points exhibit significant scatter, they depict a clear trend with ρ w (765)/ρ w (865) decreasing from around 1.6 for ρ w (865)=0.03, to around 1 for ρ w (865)=0.15. This result obtained for different European turbid waters confirms for larger turbidities the trend revealed by the satellite data set: the ratio ρ w (765)/ρ w (865) is not constant as it decreases with increasing turbidity Simulated variations in the ratio ρ w (765)/ρ w (865) While Ruddick et al. (2006) suggest that, as a first approximation, the shape of the NIR ρ w (λ) spectrum, and hence the ρ w (λ 1 )/ρ w (λ 2 ) ratio, can be assumed constant in turbid waters, their radiative transfer simulations do show that this is valid only over an intermediate range of turbidity (see their Fig. 4). For very clear waters (ρ w (λ 2 ) lower than 10 4 ), the variations in the ρ w (λ 1 )/ρ w (λ 2 ) ratio mostly result from a shift from molecular to particle scattering with increasing turbidity. It decreases from more than 2.1 down to around 1.8. For moderately turbid to turbid waters (say, ρ w (λ 2 ) between 10 4 and 10 2 ), the ρ w (λ 1 )/ρ w (λ 2 ) ratio varies little, between 1.73 and For extremely turbid waters (say ρ w (λ 2 ) between 10 2 and 10 1 ), the value of the ratio ρ w (λ 1 )/ρ w (λ 2 ) decreases significantly (down to 1.5). For given sets of IOPs, our radiative transfer simulations show similar trends in ρ w (λ 1 )/ρ w (λ 2 ) versus ρ w (λ 2 ) as described above, when increasing turbidity through increasing b SPM (865). In Fig. 11A, for the sake of clarity, we only show the simulation results for the MERIS wavebands, for a solar angle of 50, a viewing angle of 30 and an azimuth angle of 135, together with our satellite observations for different sensors. Note that the simulation results obtained for the other sensors and for various observational geometries (not shown) produce similar trends. Noticeable differences are observed between the ρ w (λ 1 )/ ρ w (λ 2 ) versus ρ w (λ 2 ) relationships obtained for the different sets of IOPs used here (different combinations of ω p and n; Fig. 11A). At the lower values of ρ w (λ 2 ), the differences between ρ w (λ 1 )/ρ w (λ 2 ) versus ρ w (λ 2 ) curves result mostly from changes in the spectral slope of the particle scattering coefficient (n) (Fig. 11A). As ρ w (λ 2 ) increases, the clusters of ρ w (λ 1 )/ρ w (λ 2 ) versus ρ w (λ 2 ) curves for given n values diverge and, at extreme turbidity, cover a wide range of ρ w (λ 1 )/ρ w (λ 2 ) ratios, from down to ca. 0.8 for ω p =0.98 (most absorbing particles) to more than 1.4 for ω p =0.999 (less absorbing particles). For ρ w (λ 2 )b 0.01, assuming minimum particle absorption (ω p =0.999) and varying n from 0 to 1 is sufficient to simulate the range of variations in ρ w (λ 1 )/ ρ w (λ 2 ) as observed from satellites (data points also shown in Fig. 11A). Note that part of this variability in satellite data is due to the different values of λ 1 and λ 2 for the different sensors. For ρ w (λ 2 ) N0.02, our radiative transfer calculations can be reconciled with our reflectance observations only when assuming more significant absorption in the NIR (ω p =0.99). When ρ w (λ 2 ) are the largest for satellite data, greater confidence can be put on the value of the ratio, as explained in the Material and methods section. In that case, the value of the ratio for all the sensors seems to converge. For intermediate values of 0.005bρ w (λ 2 )b0.015, there is more scatter between the sensors. This fact could be due to the specific data treatment processes for instance. In the future, it could be worthwhile to investigate more closely to the phenomena, either to the sensor or to the water column optics. Fig. 11B shows the same results as in Fig. 11A, but as a function of the concentration of SPM on a linear scale instead of ρ w (λ 2 ) on a log scale, to provide a better sense of the variability of NIR reflectance spectral shape with changing turbidity. The concentration of SPM is obtained from b SPM (865) and Eqs. (7) and (8). Additional simulations for the MERIS sensor and the illuminating geometry of 50 were conducted with the Fournier Forand 1% particle scattering phase function (Fournier & Forand, 1994; Haltrin, 1998). Naturally, since the backscattering efficiency is lower than for the Petzold phase function (Petzold, 1972), the reflectances in the NIR are lower for a given level of turbidity. This has the effect of translating the curves to the left (towards lower values of ρ w (λ 2 )) in a coordinate system as in Fig. 11A, but the variations of the ratio of the NIR reflectances presented the same behaviour than for the Petzold phase function (not shown) Alternative interpretations Fig. 10. A) Scatterplot of ρ w (765) versus ρ w (865) and B) scatterplot of ρ w (765)/ρ w (865) versus ρ w (865) for in situ measurements gathered during the RSFlux campaigns, in very turbid and extremely turbid waters. The reflectance ratio decreases for increasing turbidity. The constant values of the ratio ρ w (765)/ρ w (865) proposed by Ruddick et al. (2006), i.e , are depicted as a straight line. It was demonstrated above that the trends we observed in ρ w (λ 1 ) versus ρ w (λ 2 )(Figs. 5 9) do not result from spurious atmospheric corrections (see Material and methods, Fig. 4 and Appendix A). Two other phenomena may be put forward to explain those trends as alternatives to the interpretation developed in the previous section: the adjacency effect resulting from the proximity of the coast, and the temperature effect on the pure seawater absorption coefficient. The adjacency effect is the process through which a photon reflected from a surface adjacent to a targeted pixel is scattered by the atmosphere between the sensor and the target, blurring the sharp boundary between the coast and the sea. Numerical simulations were performed using the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative transfer code (available online at www-loa.univ-lille1.fr/software/msixs/msixs_gb.html, Vermote et al. (1997)) to simulate ρ TOA in the presence of adjacency effect for the