Remote Sensing of Environment 115 (2011) 1617–1631

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Remote Sensing of Environment

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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, 06904 Sophia Antipolis, Franceb Université Pierre et Marie Curie-Paris6, Laboratoire d'Océanographie de Villefranche, 06230 Villefranche-sur-Mer, Francec CNRS, Laboratoire d'Océanographie de Villefranche, 06230 Villefranche-sur-Mer, Franced Université du Québec à Rimouski, Département de Biologie, Chimie et Géographie, 300 allée des Ursulines, Rimouski, Qc, Canada G5L 3A1

⁎ Corresponding author at: Present address: Laboratoireet Industriels, 38000 Grenoble, France. Tel.: +33 4 76 82

E-mail address: doron@hmg.inpg.fr (M. Doron).

0034-4257/$ – see front matter © 2011 Elsevier Inc. Aldoi:10.1016/j.rse.2011.01.015

a b s t r a c t

a r t i c l e i n f o

Article history:Received 9 December 2009Received in revised form 18 January 2011Accepted 24 January 2011Available online 5 April 2011

Keywords:Ocean colorNear-infraredReflectanceSatellite dataIn situ dataTurbidityCoastalSuspended particulate matter

The optical properties of natural waters beyond the visible range, in the near-infrared (NIR, 700–900 nm),have received little attention because they are often assumed to bemostly determined by the large absorptioncoefficient of pure water, and because of methodological difficulties. It is now growingly admitted that the NIRrepresents a potential optical source of unambiguous information about suspended sediments in turbidwaters, thence the need for better understanding the NIR optical behaviour of such waters. It has recentlybeen proposed (Ruddick et al., Limnology and Oceanography. 51, 1167–1179, 2006) that the variability in theshape 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 inthe NIR does vary in turbid to extremely turbid waters. Space-borne ocean reflectance data were collectedusing 3 different sensors (SeaWiFS, MODIS/Aqua and MERIS) over the Amazon, Mackenzie and Rio de la Plataturbid river plumes during extremely clear atmospheric conditions so that reliable removal of gas and aerosoleffects on reflectance could be achieved. In situ NIR reflectance data were collected in different Europeanestuaries where extremely turbid waters were found. In both data sets, a flattening of the NIR reflectancespectrum with increasing turbidity was observed. The ratio of reflectances at 765 nm and 865 nm, forinstance, varied from ca. 2 down to 1 in our in situ data set, while a constant value of 1.61 had been proposedbased on theory in a previous study. Radiative transfer calculations were performed using a range of realisticvalues for the seawater inherent optical properties, to determine the possible causes of variations in the shapeof the NIR reflectance spectrum. Based on these simulations, we found that the most significant one was thegradual increase in the contribution of suspended sediments to the color of surface waters, which often leadsto the flattening of the reflectance spectrum. Changes in the scattering and absorption properties of particlesalso contributed to variations in the shape of the NIR surface ocean reflectance spectrum. The impact of suchvariations on the interpretation of ocean color data is discussed.

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1. Introduction

The apparent optical properties (AOPs) of marine waters beyondthe visible domain, in the near-infrared (NIR, 700–900 nm), are oftenassumed to be nearly constant and to be only determined by theoptical properties of pure seawater. This is because the absorptioncoefficient of water gets very high with increasing wavelength. Forinstance, when calculating the heating rate resulting from theabsorption of solar radiation in the upper ocean, Morel and Antoine(1994) set the vertical diffuse attenuation coefficient, Kd(λ) (m−1),constant above 740 nm (see Table 1 for a list of symbols andsubscripts). Furthermore, NIR water-leaving reflectance (ρw, dimen-sionless), specular reflection at sea surface excluded, is generallyassumed to be null in open ocean waters when estimating the

contribution of the atmosphere to the ocean reflectance measuredfrom the top of atmosphere by satellite sensors e.g. Gordon andWang(1994). While the above assumptions are very appropriate for mostopen ocean waters, it has been known for a long time by thoseworking in marine optics that the apparent optical properties ofseawater do in fact vary in the NIR, especially reflectance, when theamount of suspended particles becomes significant (e.g. Morel &Gordon, 1980; Bricaud & Morel, 1987). This happens mostly duringstrong phytoplankton blooms (Siegel et al., 2000), and in coastalwaters where bottom sediments get re-suspended and/or particlesare transported by rivers (e.g. Doxaran et al., 2002a, 2002b). WhenNIR ρw is large enough to be measurable, it provides unambiguousinformation about the concentration of suspended particles (Doxaranet al., 2006). The drawback is that high NIR ρw prevents atmospherefrom being readily distinguished from the ocean in the signalmeasured from top of atmosphere by satellite sensors. Both thoseopposing aspects of the problem call for improved knowledge aboutthe variability of NIR reflectance and for a clear understanding of the

Table 1List of notations.

Symbol Description Unit

AOT Aerosol optical thickness Dimensionlessa (λ) Absorption coefficient m−1

b (λ) Scattering coefficient m−1

bb (λ) Backscattering coefficient m−1

b̃b ch λð Þ Backscattering efficiency for thechlorophyll (in the IOCCG dataset)

Dimensionless

b̃b dm λð Þ Backscattering efficiency for thedetrital matter (in the IOCCG dataset)

Dimensionless

b*SPM Mass-specific scattering coefficient for SPM m2 g−1

c (λ) Beam attenuation coefficient m−1

Ed (λ,z) Downward plane irradiance at the depth z W m−2 nm−1

Eu (λ,z) Upward plane irradiance at the depth z W m−2 nm−1

Kd (λ) Vertical diffuse attenuation coefficient m−1

Lu(λ,θs,θv, ΔΦ, z)

Upwelling radiance in the viewingdirection (below the surface)

W m−2 sr−1 nm−1

Lw(λ,0+) Water-leaving radiance in the viewingdirection (above the surface)

W m−2 sr−1 nm−1

Lwn Normalized water-leaving radiance W m−2 sr−1 nm−1

NIR Near-infraredQ Bidirectionality factor DimensionlessR(λ) Irradiance reflectance just below

the surface (0−)Dimensionless

Rrs (λ) Above-surface remote-sensing reflectance (0+)Rrs λ; θs; θv;ΔΦð Þ = Lw 0þ ;λ;θs ;θv ;ΔΦð Þ

Ed 0þ ;λð Þsr−1

rrs (λ) Below-surface remote-sensing reflectance (0−) sr−1

SSPM Spectral slope of aSPM nm−1

SPM Suspended particulate matter g m−3

t Diffuse atmospheric transmittance Dimensionlessαa Angström coefficient DimensionlessΔΦ Difference of azimuth between the solar

zenith angle and the viewing zenith angle°

Δλ Waveband width for the satellite oceancolor sensors

nm

ε Spectral dependence of aerosol reflectance Dimensionlessλ1 Wavelength in the NIR: λ1=779 (Δλ=15)

for MERIS, λ1=765 (Δλ=40) for SeaWiFSand λ1=748 (Δλ=10) for MODIS

nm

λ2 Wavelength in the NIR: λ2=865 (Δλ=20)for MERIS, λ2=865 (Δλ=40) for SeaWiFSand λ2=869 (Δλ=15) for MODIS

nm

ρa Aerosol reflectance (contributionof the atmosphere)

Dimensionless

ρRay Rayleigh reflectance (contributionof the atmosphere)

Dimensionless

ρrc Rayleigh-corrected reflectance=ρTOA−ρRay DimensionlessρTOA Top Of Atmosphere reflectance Dimensionlessρw Water-leaving reflectance Dimensionlessθs Solar zenith angle °θv Viewing zenith angle °ωp Single-scattering albedo for SPM Dimensionless

m

Index orsymbol

Signification

No subscript Totalw Waterˆ Estimated variable, e.g. ρ̂w

1618 M. Doron et al. / Remote Sensing of Environment 115 (2011) 1617–1631

causes. Recently, a few studies provided the first reliable data oninherent optical properties (IOPs, absorption and scattering coeffi-cients) of marine particles in the NIR (Tassan & Ferrari, 2003; Stramskiet al., 2007; Doxaran et al., 2007). There is now a need for betterunderstanding how those IOPs combine in the ocean to form AOPssuch as reflectance in the NIR.

While it is well known that the magnitude of NIR ρw does varylargely 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 ρw spectrum.Ruddick et al. (2006) recently showed that the shape of the ρwspectrum in turbid waters is quite constant in the NIR because theshape of the seawater absorption spectrum mostly determines it.

Their conclusions were based on careful measurements of the ρwspectrum in turbid coastal waters. The data set used by Ruddick et al.(2006) (27 ρw spectra of high quality from their database of 188) ishowever very small because of the difficulty of achieving good above-water in situ reflectance measurements (Hooker & Morel, 2003),especially in the NIR. If confirmed, the finding of a constant shape ofthe ρw spectrum, so-called by Ruddick et al. (2006) “similarityspectrum”, greatly simplifies the interpretation of NIR ρw. It could beused in the inversion of reflectance, both for removing theatmospheric contribution to the remotely sensed reflectance (e.g.Ruddick et al., 2000) and for retrieving the concentrations or IOPs ofthe substances contained in seawater (e.g. Moore et al., 1999).

In the present study, we revisit the problem of the variations in theshape of the NIR seawater reflectance spectrum in turbid waters. Thiswork was triggered by coincidental observations of significant

variations in theρw 765ð Þρw 865ð Þ ratio within data from the ocean color

satellite sensor SeaWiFS collected over turbid waters of the BeaufortSea (plume of the Mackenzie River). Those measurements wererecordedwhen the load of aerosols was exceptionally low. The aerosoloptical thickness at 865 nm [AOT(865), dimensionless] was lowerthan 5.2×10−2 for data from the MERIS sensor for instance. Suchatmospheric conditions allowed very reliable atmospheric correctionsto be made even using a very simple approach, so that the ρw datacould be considered as sea-truth. We extended our analysis to datacollected with the MODIS/Aqua (MODerate Resolution ImagingSpectroradiometer) and MERIS (MEdium Resolution Imaging Spec-trometer) sensors, and to the area of the Amazon and Rio de la Plataplume to cover differing observational geometries and seawateroptical properties. Additionally, we present reflectance data obtainedin situ in the highly turbid waters of the Elbe (Germany), Gironde(France) and Tamar (UK) estuaries to extend the range of suspendedparticulate 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 theρw 765ð Þρw 865ð Þ

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 (ArcticCanadian Basin, around latitude 70° North, longitude 135° West). Thesatellite imagery was considered during the summer months whenthe ice cover is minimal in the Arctic Ocean and the limit of theicepack 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 arethe months between July and October, supposedly with the clearestatmospheres. The Rio de la Plata River plume is located in theSouthern Atlantic (around latitude 35° South and longitude 52°West).

2.2. Ocean color data from the sensors MERIS, SeaWiFS and MODIS/Aqua

We selected MERIS, SeaWiFS and MODIS/Aqua images over theMackenzie River, the Amazon River and the Rio de la Plata Riverplumes and surrounding oceanic waters, for the clearest atmosphericconditions observed during summer in the recent years. Due to thehigh latitude of the Beaufort Sea, the ocean color sensors can see thezone twice a day. The properties of the atmosphere were retrievedwith confidence over the oceanic clear-water pixels using the standardprocessing chain (Gordon &Wang, 1994; Antoine & Morel, 1999). Forinstance, over the Amazon, AOT(865) was below 8.6×10−2, while

Fig. 1. A red–green–blue composite image of a SeaWiFS scene, captured above theBeaufort Sea in the North of Canada, 21st of June 1998. The image is obtained using theradiances at the top of atmosphere (without corrections, Level 1 data). Image courtesyof the NASA.

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over the Mackenzie, it was below 5.2×10−2 for the MERIS data. Weassumed that the optical properties of the atmosphere did not varysignificantly at local scale, and used those properties found over a clearoffshorewater to perform local atmospheric corrections to retrieve theNIR water-leaving reflectances with a great accuracy (the practicaldetails are provided below).

The fact that the NIR water-leaving reflectances are not negligibleabove turbid waters has long been recognised (for instance Mundayand Alfoldi (1979) for remotely sensed data) and different approacheshave been developed to overcome this problem. For instance, in Hu etal. (2000), the aerosol type applied above a given turbid zone is takenfrom the nearest clear-water area. Then, to derive the aerosolreflectance, it is necessary to assume a constant shape for the NIRwater-leaving reflectance spectrum, which is obviously not appropri-ate here for studying the variability of the latter. Wang et al. (2007)proposed an alternative approach based on reflectances in theshortwave infrared (SWIR, 1240 and 2130 nm), where the oceanreflectance signal can be safely assumed to be negligible even overturbid waters. It consists of achieving a pre-atmospheric correction toremove the contribution of the ocean to the Rayleigh-corrected top-of-atmosphere reflectance, at 748 nm and 869 nm. Standard atmo-spheric corrections using the latter two wavelengths can then bemade safely. In this approach, no assumption on the ratio of NIRwater-leaving reflectances is required. The spectral extrapolation ofaerosol 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 SeaWiFStreatment 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) inthe sense that we apply NIR atmosphere properties from adjacentareas, but different in the sense that we extrapolate not only theaerosol type, but also the aerosol concentration which allows us not tomake any assumption about the spectral shape of water-leaving

reflectance as in Hu et al. (2000). To make this approach valid, weselect ocean color scenes for which the atmosphere is very clear andhomogeneous over large scales (see below).

We now describe in details the steps that allow us using ocean colorremote sensing as a robust mean to measure spectral dependency ofwater-leaving reflectance in theNIR. As an example, we described thosesteps for the processing of a SeaWiFS image acquired on June 21st 1998at around 22:00 UTC (Fig. 1).

2.2.1. Step 1: determination of spectral aerosol optical thickness abovethe turbid plume

SeaWiFS L1a data with local-area-coverage (LAC) are first processedto level 2using standard atmospheric correction algorithms (hereinafterdenoted as STD_AC) implemented in the SeaWiFS Data AnalysisSoftware (SeaDAS version 5.1.3; program msl12 version 5.7.1). TheSTD_AC uses the black pixel assumption in the NIR (Gordon & Wang,1994) over clearwaters,while an iteration scheme to retrieve thewater-leaving radiance in NIR is used over turbid or highly productive waters(Patt et al., 2003). Output parameters of the L1a-to-L2 includenormalized water-leaving reflectance at all eight bands, spectral AOT,spectral dependence of aerosol reflectance (ε, dimensionless), andatmospheric input parameters from NCEP as interpolated to fit theSeaWiFS grid (zonal and meridional wind vectors and humidity). Acareful analysis of these output and a visual inspection of the RGB image(Fig. 1) allow us to determine the aerosol properties over the turbidplume.

Fig. 2 shows the spatial distribution of AOT(865) over theMackenzie shelf and the adjacent Beaufort Sea. Aerosol propertiesobserved above clear waters (cf Fig. 1) were relatively constant overlarge space scales (N1000 km2; boxes 1 and 2 in Fig. 2) with extremelylow AOT(865), typically b0.024. 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 ofAOT(865) and ε in box 4 (highly turbid area) was twice as large as thatabove clear waters. Moderate anticyclonic winds (5 to 10 m s−1),dominated by East–North–East direction over the eastern part of theMackenzie shelf (Fig. 2 and Table 2), most likely transported towardsthe turbid plume aerosols with properties similar as those observedover clear waters, thus reducing the possibility to find continentalaerosols in that area. Over the turbid plume, we therefore assume thatthe aerosol properties are those observed near the coast of CapeBathurst (box 2), i.e. AOT(865) of 0.02 and epsilon of 1.184.

Interestingly, our results suggest that the STD_AC remainssensitive to water turbidity, despite its iterative scheme for retrievingthe water-leaving signal in the NIR (Patt et al., 2003), and given the 1)offshore to inshore wind conditions, 2) spatial homogeneity of aerosolproperties over a large area above clear waters located just North-Eastof the turbid plume, and 3) spatial heterogeneity of aerosol propertiesretrieved above highly turbid waters.

2.2.2. Step 2: re-processing ocean color datawith known aerosol propertiesTo estimate the water-leaving reflectances in the NIR part of the

spectrum, the SeaWiFS L1a data were reprocessed using the multiple-scattering with fixed aerosol optical thickness option in the SeaDASmsl12 program (hereinafter denoted as CTE_TAU). When using thatoption, the user needs to specify the AOT for each SeaWiFS bands,which will be applied to every cloud-free pixels of the scene. In theexample presented here, AOT varies from 0.020 at 865 nm to 0.049 at412 nm.

Fig. 3 and Table 3 compare, as an example, the water-leavingreflectance at 555 nm obtained using both STD_AC and CTE_TAUschemes, respectively. The difference between the two products is ingeneral b10%, except for highly turbid waters (box 4) where CTE_TAUproduced higher nLw of about 0.44 mW cm−2 nm−1 sr−1 (13.4%)than STD_AC.

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 greyarrows. The areas where aerosol properties and wind characteristics were calculated (Table 2) are shown as red boxes.

1620 M. Doron et al. / Remote Sensing of Environment 115 (2011) 1617–1631

A similar protocol was applied to the other SeaWiFS, MODIS/Aquaand MERIS images. In the latter case, the geographical coordinates ofoffshore pixels located in clear waters were found by eye inspectionand using the BEAM software (http://www.brockmann-consult.de/cms/web/beam). We also verified that the low values of ρa(865) hadlow spatial variability and that there was no flag on Case I chlorophyllproduct. The coordinates of coastal pixels located inside the turbidplume of the river are used to define imaginary trajectories(transects) between clear and turbid waters, that represent a gradientof turbidity. During the standard processing chain from level 1A tolevel 2, the entire set of aerosol properties for clear pixels is extractedand is used to perform atmospheric corrections for the entire transectwith constant aerosol properties. A summary of the satellite images,considered in the present study together with the locations of offshoreand coastal pixels is presented in Table 4.

Fig. 4 illustrates the very low contribution of the aerosol to thetotal signal in a selected scene from the ocean color images. Because ofsuch atmospheric conditions, the error in retrieved ρw over turbidwaters due to our atmospheric corrections was very low (seeAppendix A for details).

Recently Wang et al. (2009) showed, in a validation study for theSWIR algorithm, that the water-leaving radiance quality from SWIRalgorithm is similar to theNIRderivedwater-leaving radiance evenwith

Table 2Statistics on aerosols, as obtained using standard AC algorithm, and winds above clearand turbid waters from different areas (16.5×16.5 km2 boxes, or 15×15 pixels) shownin Fig. 2 (average±1 standard deviation). Data obtained for the SeaWiFs scene the 21stof June 1998.

AOT(865) ε Zonal wind(+ = W to E)

Meridional wind(+ = S to N)

Box 1 0.018±0.002 1.225±0.004 −5.95±0.13 −0.76±0.03Box 2 0.020±0.003 1.184±0.003 −5.35±0.12 0.03±0.06Box 3 0.027±0.002 1.080±0.001 −8.55±0.07 −3.10±0.01Box 4 0.048±0.006 1.238±0.005 −7.66±0.22 −3.90±0.04

longer extrapolation. They showed that the uncertainty caused by thenoise of the SWIR bands and the long extrapolation in theNIR is small incomparison to the water-leaving radiance at NIR. A comparison of theremotely-sensed water-leaving reflectances obtained with either a)atmospheric corrections assuming a clear atmosphere with regionalcharacteristics (our approach) or b) the SWIR atmospheric corrections(Wang et al., 2007) was made for a MODIS/Aqua image (captured the6th of August 2004 above the Beaufort Sea). It was possible for theMODIS/Aqua sensor, because it has the adequatewavelength toperformSWIR.

2.3. In situ measurements

The 2005 and 2006 RSFLUX field campaigns were conducted indifferent turbid estuarine and coastal waters around Europe. We herefocus on data gathered in the Elbe (Germany, October 2005), Gironde(France, October 2005 andMarch 2006) and Tamar (UK, October 2005)estuaries. Simultaneous measurements of the above-surface remote-sensing reflectance Rrs (sr−1) and concentration of total suspendedmaterial within surface waters were achieved. To determine theconcentration of suspended particulate matter (SPM, in g m−3), aknown volume of the surface water sample was filtered through pre-weighted Whatman GF/F filters. Filters stored at −80 °C were thendried 24 h at 65 °C to obtain the dry weight (van Der Linde, 1998).

The Rrs signal is defined (see Eq. 1, and Morel and Mueller (2002))as the ratio of the water-leaving radiance Lw (in W m−2 sr−1 nm−1)to downwelling irradiance just above the water surface Ed(0+)(in W m−2 nm−1).

Rrs λ; θs; θv;ΔΦð Þ = Lw 0þ;λ; θs; θv;ΔΦ

� �Ed 0þ;λð Þ ð1Þ

where λ is the wavelength (in nm), θs, θv,ΔΦ are respectively the solarzenith angle, the viewing zenith angle and the azimuth differencebetween the sun and viewing directions (all three in °).

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 andWang(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 onesobtained for a region located in clear waters (box 2). This method is noted CTE_TAU in the text.

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Hyperspectral (380–950 nm) radiometric measurements werecarried out in the estuaries, using two Trios RAMSES-ARC radiancesensors (7° field of view) and one Trios RAMSES-ACC-VIS irradiancesensor. Ed(0+) was measured directly with the irradiance sensorpointing the zenith and placed at the top of the ship to avoid anyshadow effect. Lw was calculated from above-water upwellingradiance measurements (total radiance Lt) corrected for surfacereflection effects by substraction of a certain percentage ρ of themeasured sky radiance signal (Ls). Lt was measured pointing the firstradiance sensor towards the sea surface with an angle of 35° with thenadir and an azimuth angle of 137° with the Sun. Ls was measuredpointing, simultaneously, the second radiance sensor towards the sky

with an angle of 35° to zenith and the same azimuth angle. Radiancemeasurements were recorded every five seconds during twominutes,and then averaged over this time period. The water leaving radiancesignal, Lw, was finally calculated following Eq. (2) (more details onthese in situ measurements can be found in Doxaran et al. (2007)).

Lw = Lt−ρLs ð2Þ

Based on ρ values calculated by Mobley (1999) for different cloudcover and sea surface roughness conditions, a spectrallyflatρvalue of 0.02was adopted in the NIR. To assess the Rrs uncertainties due to inaccuracyon the selected ρ factor, ρ values of 0.01 and 0.03 (i.e., 0.02±50%,

Table 3Comparison 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 shownin Fig. 3 (average±1 standard deviation). Data obtained for the SeaWiFS scene the 21st of June 1998.

STD_AC(mW cm−2 nm−1 sr−1)

CTE_TAU(mW cm−2 nm−1 sr−1)

Absolute (and relativea) difference(mW cm−2 nm−1 sr−1)(%)

Box 1 0.22±0.02 0.20±0.02 −0.02 (−9.1)Box 2 0.43±0.17 0.47±0.16 0.04 (9.3%)Box 3 1.18±0.14 1.23±0.14 0.05 (4.2%)Box 4 3.15±0.27 3.59±0.42 0.44 (13.4%)

a 100×(CTE_TAU−STD_AC)/STD_AC.

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respectively) were also considered. The resulting variations induced onthe Rrs(765)/Rrs(865) ratio proved to be smaller than±6%. Consequently,the samedecrease of Rrs(765)/Rrs(865) for increasing Rrs (865) valueswassystematically obtained independently of the correction for surfacereflection effects applied to radiometric measurements. Based on resultsobtained by Mobley (1999), the case of wavelength-dependent ρ factorsshouldbe consideredwhen the sky is clear blueor overcast. Thiswasdonein the study published by Doxaran et al. (2004) where above-water andin-water reflectance measurements were used to quantify surfacereflection effects. Doxaran et al. (2004) showed that these surfacereflection effects on above-water Ltmeasurements are very limitedwhenconsidering spectral reflectance ratios. Consequently, imperfect correc-tions of surface reflection effects cannot explain the flattening of the ρw(765)/ρw (865) ratio. The in situ data set is especially interesting for ourstudy because it covers highly turbidwaters, beyond the range covered byour satellite data set.

Morel et al. (2002) explicitly detailed the calculation ofthe normalized water-leaving radiance Lwn (λ, θs, θv, ΔΦ) (in W m−2

nm−1 sr−1), originally introduced by Gordon and Clark (1981) from Rrs,measured above the interface, see Eq. (3).

Lwn λð Þ = Lwn λ; θs; θv;ΔΦð Þ = Rrs λ; θs; θv;ΔΦð ÞF0 λð Þ ð3Þ

where F0 λð Þ is the solar irradiance at the top of the atmosphere at themean Sun–Earth distance (in W m−2 nm−1). Gordon and Wang(1994) introduced the water-leaving reflectance ρw (dimensionless,see Eq. 4), which is notably used in the MERIS processing chain.

ρw = πRrs ð4Þ

For the sake of consistency, all the data presented in this paper areexpressed in terms of ρw, hence the SeaWiFS and MODIS/Aqua data

Table 4List 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 theoffshore pixels

Location of thecoastal pixels

SeaWiFS 21st June 1998 69.231°N 69.09°N138.15°W −136.71°W

SeaWiFS 6th August 2004 70.798°N 69.84°N133.853°W 134.85°W

SeaWiFS 22nd August 2003 2.762°N 1.682°N47.173°W 49.479°W

MODIS/Aqua 6th August 2004 70.802°N 69.839°N133.85°W 134.856°W

MODIS 21st August 2003 3.468°N 2.175°N48.287°W 49.854°W

MERIS 2nd September 2003 35.698°S 35.218°S54.835°W 56.920°W

MERIS 27th April 2004 35.619°S 34.916°S53.385°W 57.235°W

MERIS 4th June 2007 35.707°S 34.866°S53.294°W 56.484°W

MERIS 10th June 2007 35.996°S 35.447°S53.278°W 56.484°W

are converted from Lwn to ρw and the in situ data are converted fromRrs to ρw, to allow comparisons.

Unfortunately, there are no match-ups between the satellitemeasurements and in situ measurements to assess the quality of ourwater-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 onassumptions and our interpretation (see discussion in Results—Alternative interpretation section)and ii) a very clear andhomogeneousatmosphere over large area and over both turbid and clear waters.Obviously, the chance to find “a perfect scene” matching in situmeasurements was extremely small. In situ measurements in the NIRare very difficult to perform and their accuracy would have been worsein less turbid waters than is shown. Therefore, the in situ and satellitedata are complementary: satellite data for highly turbid waters and insitu data for extremely turbid waters.

2.4. Radiative transfer simulations

Radiative transfer simulations were conducted using the radiativetransfer code Hydrolight© (version 4.2, Sequoia Scientific Inc.,Redmond WA, USA, Mobley (1994)), modified to include the NIRspectral domain (up to 1000 nm, beta-version). The calculations wereperformed for different NIR couples of wavebands to simulate thethree ocean color sensors considered here: λ1=779 nm (band width,Δλ: 15 nm) and λ2=865 nm (Δλ: 20 nm) for MERIS, λ1=765 nm(Δλ: 40 nm) and λ2=865 nm (Δλ: 40 nm) for SeaWiFS, λ1=748 nm(Δλ: 10 nm) and λ2=869 nm (Δλ: 15 nm) for MODIS/Aqua. In turbidwaters and in the NIR, the influence of absorption by phytoplanktonand colored dissolved organic matter (CDOM) can be considered asnegligible (Babin & Stramski, 2002). Moreover, to assess theirassumption on the existence of the similarity spectrum in the NIR

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), respectivelydenoted ρTOA, ρa, ρw and ρR. Spectra are shown for two turbid pixels in the transectextracted from the SeaWiFS image taken on the 21st June 1998 above the Beaufort Sea.For pixel 1, ρw(865)=0.0278 and for pixel 2, ρw(865)=0.0208.

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for turbid waters, Ruddick and collaborators performed comprehen-sive radiative transfer simulations with the same code Hydrolight(Ruddick et al., 2006), and determined the sensitivity of their resultsto the presence of other constituents such as colored dissolved organicmatter (CDOM) or phytoplankton. They showed that these constitu-

ents have a low impact on the resulting ratio ofρw 765ð Þρw 865ð Þ. The total

absorption coefficient a (in m−1) and the total scattering coefficient b(in m−1) were therefore taken here as the sum of contributions bypure seawater (aw and bw) and by suspended particulate matter (aSPMand bSPM). The aw(λ) and bw(λ) values were taken from Kou et al.(1993) and followingMorel (1974), respectively. The coefficients aSPMand bSPM were related to the concentration of suspended particulatematter (SPM; g m−3), and SPM was varied in such a way that bSPM(865) covered the range from 1 to 300 m−1 for each set of other IOPs.

The single scattering albedoωp for SPM (defined asωp = bSPMaSPM + bSPM

)is used to constrain the relation (Eq. 5) between bSPM (865) and aSPM(865), using the results of Stramski et al. (2007).

aSPM 865ð Þ =1−ωp

� �bSPM 865ð Þωp

ð5Þ

The relationship between aSPM(λ) and aSPM(865) is given by Eq. (6)where SSPM (nm−1) is the spectral slope of aSPM(λ):

aSPM λð Þ = aSPM 865ð Þe�SSPM λ−865ð Þ ð6Þ

The spectral variations of bSPM (λ) were assumed to follow a λ−n

law with n being a dimensionless factor (Eq. 7). The relationshipbetween bSPM (λ) and SPM is given by Eq. (8) where b⁎SPM (555) is themass-specific scattering coefficient for the suspended particulatematter (in m2 g−1).

bSPM λð Þ = bSPM 865ð Þ λ865

� �−n

ð7Þ

bSPM 555ð Þ = b⁎SPM 555ð Þ⁎SPM ð8Þ

In the above equations, the parameters are ωp, n, SSPM, and b⁎SPM(555), and the only undetermined variable is SPM. The values of ωp, n,SSPM, and b⁎SPM(555) were given the following values based onpreviously published studies.

Stramski et al. (2007) observed the value of ωp to vary between0.96 and 1 in the NIR for various types of mineral particles, includinghighly absorbing ones. We adopted in the present study the followingvalues: 0.98, 0.99 and 0.999 for ωp.

The results from the study of Babin et al. (2003), showed anaverage of 0.0123 nm−1 for the value of SSPM. In the study of Stramskiet al. (2007), the values of SSPM are reported between 0.004 and0.009 nm−1. The slopes of the absorption by detritus (suspendedparticulate matter mostly from organic origin) are found to bebetween 0.006 and 0.014 nm−1 with a mean of 0.011 nm−1, in thestudy of Roesler et al. (1989). Here, to cover the range reported in theliterature, SSPM was given the values of either 0.006, 0.012, or0.024 nm−1.

The values of n have been studied theoretically and withmeasurements and are expected to range from 0 in coastal waters(Roesler & Perry, 1995; Roesler & Boss, 2003) to 2 in clear oceanicwaters (Bricaud & Morel, 1986; Morel, 1988; Maritorena et al., 2002).A recently published paper (Doxaran et al., 2007) showed the spectralslope of the particle scattering coefficient to be around 0.4 in coastalwaters and to range between 0 and 1.We gave n the value of 0, 0.3, 0.6or 1, which is a robust assumption in the NIR according to theliterature mentioned above.

The average value of b⁎SPM(555) is reported to be 0.51 m2 g−1 byBabin et al. (2003) in European coastal waters and was used in thepresent study only to provide an estimation of SPM associated withbSPM (865).

The scattering phase function for particles was taken from Mobleyet al. (1993) who derived it on the basis of the measurements byPetzold (1972). The Fournier–Forand 1% phase function (Fournier &Forand, 1994) was also tested in the case of MERIS and for the solarzenith angle of 50°. All IOPs were set constant with depth. Thefluorescence inelastic scattering is not taken into account since thechlorophyll fluoresces strongly around 685 nm. The fluorescenceband width is around 25 nm wide (Mobley, 1994) and is out of thespectral domain considered here. Siegel et al. (2000) found that forchlorophyll concentrations greater than 0.5 mg m−3, and reasonablesolar zenith angles, the error of not including the Raman scatteringprocess is less than 5% in the estimation of the water-leavingreflectances in the NIR. They concluded that Raman scattering is notimportant 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 Amazonrivers. 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 ameanwind speedof 4 m s−1. For each simulation,we extracted Ed(0+)and Lw(θs, θv, ΔΦ) for different observational geometries. The resultsare expressed in terms of water-leaving reflectance, ρw followingEq. (9).

ρw λ; θs; θv;ΔΦð Þ = πLw λ; θs; θv;ΔΦð ÞEd λ;0þð Þ ð9Þ

Radiative transfer calculations were performed at the NIR wave-lengths listed above for thedifferent sensors, for two solar zenith angles,for combinations of the values given toωp, n, and SSPM and for ten valuesof bSPM (865) between 1 and 300 m−1.

3. Results and discussion

3.1. The satellite data over the Beaufort Sea

Fig. 1 shows an example of an ocean color scene captured bySeaWiFS during a very clear day (21st of June 1998) over the BeaufortSea. The image is an RGB composite obtained with three wavelengthsin the visible using data at the level 1 (top-of-atmosphere reflec-tances). That day, there were no clouds, and the plume of theMackenzie River was extending relatively far offshore, up to tens ofkilometres. The turbidity of the water was gradually decreasing frominshore to offshore. Other scenes captured by other sensors and forother “clear” days present similar features.

The aerosol content for the clear images above the Beaufort Sea wasvery low. Indeed, the observed aerosol reflectances are among thelowest obtainable in typical oceancolor processing. For instance, aboveaCase 1 pixel, the retrieved ρa (865) was 0.0034 and 0.0049 for the twoscenes considered with the MERIS sensor (respectively the 21st of July2003 and the 6th of August 2004), and 0.0012 for the SeaWiFS scene ofthe 21st of June 1998. Such low values are consistent with the in situmeasurements made in this area by the AERONET network at stationBarrow (http://aeronet.gsfc.nasa.gov/cgi-bin/webtool_opera_v2_new?stage=3&region=Alaska_and_Canada&state=Alaska&site=Barrow).From 1997 to 2007, the mean AOT(870) was 0.049 with a standarddeviation of 0.062. The median was 0.034 and values lower than 0.02were often observed (58 values out of 254).

Fig. 4 shows the relative importance of the Rayleigh, aerosol, andwater-leaving reflectances in the composition of the top-of-atmospheresignal for two pixels, one moderately turbid with ρw (865)=5.2.10−3 and one very turbid pixel with ρw (865)=2.3.10−2, in the

Fig. 6. Scatterplot of the water-leaving reflectance ρw (λ1) versus ρw (λ2) obtainedabove the Beaufort Sea for the same date, the 6th of August 2004, with three differentocean color sensors. The wavelengths are λ1=779 and λ2=865 nm for MERIS,λ1=765 and λ2=865 nm for SeaWiFS, and λ1=748 and λ2=869 nm for MODIS/Aqua. The (Moore et al., 1999) curve shows the relationship between the tworeflectances proposed in their study to perform atmospheric corrections above turbidwaters. The similarity spectrum lines (ratio of ρw (λ1)/ρw (λ2) in the NIR) are plottedaccording to Ruddick et al. (2006) (noted R06 in the legend). The slopes of the lines (seetheir 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”).

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SeaWiFS scene of the 21st of June 1998. The level of aerosolreflectances is very low compared with the water-leaving one, evenin the NIR. We believe that, in those images, an error in the estimationof aerosol reflectance by atmospheric correction can only have a smallimpact on the retrieval of the water-leaving reflectances of turbidwaters, even in the NIR portion of the spectrum (see Appendix A fordetails). Our remotely sensed data can therefore be almost consideredas sea-truth.

Data shown in the Fig. 5 were captured above the Beaufort Sea bythe SeaWiFS sensor for different clear days and treated foratmospheric correction as presented in the Material and methodssection. For each scene considered, a rectangular sub-scene of theimage was sampled and the scatterplot represents ρw (765) versus ρw(865). We observed a clear trend in the water-leaving reflectances inthe NIR (Fig. 5). Systematically, for increasing turbidity, or equiva-lently, increasing ρw (865), the increasing ρw (765) progressivelydeviates from a straight line, which would be expected if thereflectance spectrum had a constant shape as suggested by Ruddicket 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 ρw (765)/ρw(865) for the SeaWiFS sensor by Ruddick et al. (2000, 2006),respectively.

This general trend was further examined for transects (instead ofrectangular sub-scenes) in Mackenzie, Amazon and Rio de la PlataRivers plumes and for SeaWiFS, MODIS/Aqua and MERIS sensors. Thetransects were made of a succession of contiguous pixels along astraight line going from oceanic Case 1 waters offshore to increasinglyturbid waters inshore. For each pixel in the transect, we extracted thewater-leaving reflectances at two wavelengths in the NIR: λ1=779and λ2=865 nm for MERIS, λ1=765 and λ2=865 nm for SeaWiFS,and λ1=748 and λ2=869 nm for MODIS. Fig. 6 shows the scatterplotof ρw (λ1) versus ρw (λ2) for the three sensors (MERIS, SeaWiFS andMODIS/Aqua) above the Beaufort Sea, on the same day (6th of August2004). Due to the high latitude of the Beaufort Sea, the MODIS/Aquasensor can see the zone twice a day. The data points form a trend withvery low scatter that departs from a straight line for the larger valuesof ρw (λ2). The ρw (λ2) values extend over different ranges for thedifferent sensors because of the different thresholds used by eachstandard 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 ρw (765) versus ρw (865) fromdifferent SeaWiFS images taken above the Beaufort Sea at various dates (as written inthe legend). The data were extracted on rectangular subscenes. A polynomial fit wascalculated for this data set and the equation of the bold red line is P(x)=−13.64x2+2.003 x-0.00117. The constant values of the ratio ρw (765)/ρw (865) proposed byRuddick et al. (2000, 2006), respectively 1.72 and 1.611, are depicted as straight lines.

instance, the flag is based on a combination of thresholds and look-uptables (http://envisat.esa.int/handbooks/meris/toc.htm). For SeaWiFSand MODIS/Aqua, the standard cloud or ice flag is set when the NIRalbedo (i.e., 865 and 870 nm respectively) is larger than 2.7%. For thepurpose of this study, however, the threshold was increased to 3.5% inorder to increase the number of pixels in very turbid waters. Thequantity ρw (λ1) is always larger than ρw (λ2) because the absorptioncoefficient of pure seawater is nearly twice as large at λ2 than at λ1

(e.g. 2.71 m−1 at 779 nm and 4.61 m−1 at 865 nm according to Kou etal. (1993)). The three different sensors show a very good agreementover common ranges. On the same figure, the relationships betweenρw (λ1) and ρw (λ2) proposed by previously published studies areplotted. In the one proposed by Moore et al. (1999), the ratio ρw (λ1)/ρw (λ2) decreases very slightly with increasing turbidity. In thesimilarity spectrum in the NIR for turbid waters; Ruddick et al. (2006)propose a constant value of the ρw (λ1)/ρw (λ2) ratio for varyingturbidity, hence a straight line in Fig. 6. Note that this constant valuedepends on the sensor because of their different spectral character-istics, and also on whether it was originally derived from in situmeasurements or radiative transfer simulations. Our satellite dataclearly show a trend different from what they proposed. Lavender(1996) reports laboratory experiments in a tank, where measure-ments of reflectances below water, R(865) and R(750.5) (dimension-less), were performed for varying levels of turbidity and various typesof supended particulate matter. The values of R(865) were up to 0.1.Mostmeasurements weremadewith SPM b600 g m−3 but a fewwerefor SPM as high as 1200 g m−3. The ratio of the two reflectances in theNIR 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 ρw (λ1)/ρw (λ2) ratio as afunction of ρw (λ2) for the same data as in Fig. 6. Some discrepanciesbetween the sensors appear more clearly than in Fig. 6. They areprobably due to differences between measured wavebands by thedifferent sensors.

Fig. 7. Scatterplot of the water-leaving reflectance ρw (λ1)/ρw (λ2) versus ρw (λ2)obtained above the Beaufort Sea for the same date, the 6th of August 2004, with threedifferent ocean color sensors. The wavelengths are λ1=779 and λ1=865 nm forMERIS, λ1=765 and λ2=865 nm for SeaWiFS, and λ1=748 and λ2=869 nm forMODIS. TheMoore et al. (1999) curve shows the relationship proposed in their study toperform atmospheric corrections above turbid waters. The similarity spectrum lines(ratio of ρw (λ1)/ρw (λ2) in the NIR) are plotted in reference to the study of Ruddick etal. (2006), noted R06 in the legend. The height of the lines depend on the sensor (valuesreported from their Table 3) because of their different spectral characteristics, and alsoon whether it is based on in situ measurements (lines noted “experimental”: 1.98 and1.82 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. Comparison between the water-leaving reflectances obtained with localatmospheric 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 BeaufortSea (6th of August 2004). A) Scatterplot of the water-leaving reflectance ρw (λ1) versusρw (λ2); B) scatterplot of the water-leaving reflectance ρw (λ1)/ρw (λ2) versus ρw (λ2).

Fig. 9. Scatterplot of the water-leaving reflectance ρw (λ1)/ρw (λ2) versus ρw (λ2)obtained above the Amazon and Rio de la Plata turbid plumes for different dates, withthree different ocean color sensors. The wavelengths are λ1=779 and λ2=865 nm forMERIS, λ1=765 and λ2=865 nm for SeaWiFS, and λ1=748 and λ2=869 nm forMODIS.

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Fig. 8 shows the results of the comparison of the water-leavingreflectances obtained either with our local atmospheric corrections(when the atmosphere is very clear) or with the SWIR method (Wanget al., 2007) for a MODIS/Aqua image located above the Beaufort Sea.Fig. 8A shows the scatterplot of ρw(λ1) versus ρw(λ2) for the twomethods and the reflectances are in very good agreement. Fig. 8B shows

the ratio ofρw λ1ð Þρw λ2ð Þ versus ρw(λ2) 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 thespectra when the turbidity increases. This comparison confirms thegood quality of the retrieval of the water-leaving reflectances with ourmethod and its consistency with the SWIR approach.

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, weobserved the same general trend for the reflectances in the NIR asabove the Beaufort Sea (Fig. 9). We obtained these data for the threedifferent sensors and for two different locations, in addition fromwhat was observed above the Beaufort Sea. This highlights the factthat our results are neither region-dependent, nor sensor-dependent.Although the trend for a flattening of the water-leaving spectra in theNIR is clearly seen in a variety of situations detailed above, somevariations in the reflectance ratio can be seen. This happens whenconsidering the data for different days for the same sensor, such as inFig. 5 (SeaWiFS data for the Beaufort Sea) or for different sensors onthe 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 sensorsabove two locations as in Fig. 9 (Rio de la Plata and Amazon, for thethree sensors). Part of the variations in the reflectance ratio may bedue to some residual error in atmospheric corrections. We however

believe that this effect is negligible given the successful validation wepresented for our atmospheric correction scheme, and given howsystematic the observed trend is over various dates, sites and sensors.

3.3. In situ observations of the NIR ρw(λ) spectrum in highly turbid waters

Our in situ measurements were achieved in estuaries where SPMvaried from 8 to 2500 g m−3. The obtained ρw values in the NIR varied

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between 0.02 and 0.18 at 765 nm, and between 0.01 and 0.16 at865 nm. The maximum values are around one order of magnitudelarger than the water-leaving reflectances obtained with the space-borne ocean color sensors in this study. Fig. 10 shows the variations inρw (765)/ρw (865) versus ρw (865) for the different estuaries.Although the data points exhibit significant scatter, they depict aclear trend with ρw (765)/ρw (865) decreasing from around 1.6 for ρw(865)=0.03, to around 1 for ρw (865)=0.15. This result obtained fordifferent European turbid waters confirms for larger turbidities thetrend revealed by the satellite data set: the ratio ρw (765)/ρw (865) isnot constant as it decreases with increasing turbidity.

3.4. Simulated variations in the ratio ρw (765)/ρw (865)

While Ruddick et al. (2006) suggest that, as a first approximation,the shape of the NIR ρw(λ) spectrum, and hence the ρw (λ1)/ρw (λ2)ratio, can be assumed constant in turbidwaters, their radiative transfersimulations do show that this is valid only over an intermediate rangeof turbidity (see their Fig. 4). For very clear waters (ρw (λ2) lower than10−4), the variations in the ρw (λ1)/ρw (λ2) ratio mostly result from ashift frommolecular to particle scattering with increasing turbidity. Itdecreases from more than 2.1 down to around 1.8. For moderatelyturbid to turbid waters (say, ρw (λ2) between 10−4 and 10−2), the ρw(λ1)/ρw (λ2) ratio varies little, between 1.73 and 1.84. For extremelyturbid waters (say ρw (λ2) between 10−2 and 10−1), the value of theratio ρw (λ1)/ρw (λ2) decreases significantly (down to 1.5).

Fig. 10. A) Scatterplot of ρw (765) versus ρw (865) and B) scatterplot of ρw (765)/ρw(865) versus ρw (865) for in situ measurements gathered during the RSFlux campaigns,in very turbid and extremely turbid waters. The reflectance ratio decreases forincreasing turbidity. The constant values of the ratio ρw (765)/ρw (865) proposed byRuddick et al. (2006), i.e. 1.611, are depicted as a straight line.

For given sets of IOPs, our radiative transfer simulations showsimilartrends in ρw (λ1)/ρw (λ2) versus ρw (λ2) as described above, whenincreasing turbidity through increasing bSPM(865). In Fig. 11A, for thesake of clarity, we only show the simulation results for the MERISwavebands, for a solar angle of 50°, a viewing angle of 30° and anazimuth angle of 135°, together with our satellite observations fordifferent sensors. Note that the simulation results obtained for the othersensors and for various observational geometries (not shown) producesimilar trends. Noticeable differences are observedbetween theρw (λ1)/ρw (λ2) versus ρw (λ2) relationships obtained for the different sets ofIOPs used here (different combinations of ωp and n; Fig. 11A). At thelower values of ρw (λ2), the differences between ρw (λ1)/ρw (λ2) versusρw (λ2) curves result mostly from changes in the spectral slope of theparticle scattering coefficient (n) (Fig. 11A). As ρw (λ2) increases, theclusters of ρw (λ1)/ρw (λ2) versus ρw (λ2) curves for given n valuesdiverge and, at extreme turbidity, cover a wide range of ρw (λ1)/ρw (λ2)ratios, from down to ca. 0.8 for ωp=0.98 (most absorbing particles) tomore than 1.4 for ωp=0.999 (less absorbing particles). For ρw (λ2)b0.01, assuming minimum particle absorption (ωp=0.999) and varyingn from 0 to 1 is sufficient to simulate the range of variations in ρw (λ1)/ρw (λ2) as observed from satellites (data points also shown in Fig. 11A).Note that part of this variability in satellite data is due to the differentvalues of λ1 and λ2 for the different sensors. For ρw (λ2) N0.02, ourradiative transfer calculations can be reconciled with our reflectanceobservations only when assuming more significant absorption in theNIR (ωp=0.99). When ρw (λ2) are the largest for satellite data, greaterconfidence can be put on the value of the ratio, as explained in theMaterial and methods section. In that case, the value of the ratio for allthe sensors seems to converge. For intermediate values of 0.005bρw(λ2)b0.015, there ismore scatterbetween the sensors. This fact couldbedue to the specific data treatment processes for instance. In the future, itcould be worthwhile to investigate more closely to the phenomena,either to the sensor or to the water column optics. Fig. 11B shows thesame results as in Fig. 11A, but as a function of the concentration of SPMon a linear scale instead of ρw (λ2) on a log scale, to provide a bettersense of the variability of NIR reflectance spectral shape with changingturbidity. The concentration of SPM is obtained from bSPM (865) andEqs. (7) and (8).

Additional simulations for the MERIS sensor and the illuminatinggeometry of 50°were conductedwith the Fournier–Forand 1% particlescattering phase function (Fournier & Forand, 1994; Haltrin, 1998).Naturally, since the backscattering efficiency is lower than for thePetzold phase function (Petzold, 1972), the reflectances in the NIR arelower for a given level of turbidity. This has the effect of translatingthe curves to the left (towards lower values of ρw (λ2)) in a coordinatesystem as in Fig. 11A, but the variations of the ratio of the NIRreflectances presented the same behaviour than for the Petzold phasefunction (not shown).

3.5. Alternative interpretations

It was demonstrated above that the trends we observed in ρw(λ1)versus ρw(λ2) (Figs. 5–9) do not result from spurious atmosphericcorrections (see Material and methods, Fig. 4 and Appendix A). Twoother phenomena may be put forward to explain those trends asalternatives to the interpretation developed in the previous section:the adjacency effect resulting from the proximity of the coast, and thetemperature effect on the pure seawater absorption coefficient.

The adjacency effect is the process through which a photonreflected from a surface adjacent to a targeted pixel is scattered by theatmosphere between the sensor and the target, blurring the sharpboundary between the coast and the sea. Numerical simulations wereperformed using the Second Simulation of the Satellite Signal in theSolar Spectrum (6S) radiative transfer code (available online at http://www-loa.univ-lille1.fr/SOFTWARE/Msixs/msixs_gb.html, Vermote etal. (1997)) to simulate ρTOA in the presence of adjacency effect for the

Fig. 11. A) Scatterplot of the water-leaving reflectance ρw (λ1)/ρw (λ2) versus ρw (λ2) inlogarithmic scale. The satellite data is obtained above the Beaufort Sea for the 6th ofAugust 2004, and the line plots are obtained through radiative transfer simulations. Thebold line is from Ruddick et al. (2006), the thin lines are our simulations. The mainvariations in the optical properties are n, the spectral dependency of the particlescattering coefficient (in λ−n) and the single-scattering albedo ωp. The simulations areable to reproduce the trend in the satellite data set. B) Line plots of our radiative transfersimulations versus SPM, where SPM is calculated from Eqs. (6) and (7), to give an orderof magnitude of the turbidity associated to ρw (865).

Fig. 12. Scatterplot of the sea surface temperature (SST, in °C) derived from AVHRR data(data courtesy from NOAA) versus the water-leaving reflectances at 865 nm over theMackenzie River plume (obtained from the SeaWiFS imagery), for the 21st June of 1998.

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SeaWiFS NIR bands (for details see Bélanger et al. (2007)). Toillustrate the impact of the adjacency effect for a typical pixelconsidered in the present study, calculations were made for a pixellocated at 5 km from the land. The nearest land surface surroundingthe targeted water pixel has a reflectance of 0.145 and 0.19 at 765 and865 nm, respectively, in the Mackenzie River plume area. In thisexample, the adjacency effect increases the ρTOA in the NIR bands byb0.0007, which is very low. In our satellite dataset, for the 6th August2004, the first pixels considered were located at 7 km from the coastfor the SeaWiFS image, at 8.5 and 2.5 km for the MODIS/Aqua images,

for instance. We therefore believe that the adjacency effect had anegligible effect on our results.

Let us now examine the possible effect of seawater temperature onthe shape of the reflectance spectrum in the NIR. ρw(NIR) is stronglydependent upon the pure seawater absorption coefficient aw(λ)because the latter dominates total absorption in the NIR. In turn, aw(λ) is sensitive to the water temperature, particularly at somewavelengths in the NIR (Pegau et al., 1997; Sullivan et al., 2006; Hollis,2002). This is why seawater temperature may affect our reflectanceobservations. To assess this effect in the particular case of theMackenzie River plume, generally warmer than the adjacent ArcticOcean seawater (close to 0 °C in this area), we examined AVHRR datataken on the same day as one SeaWiFS scene (20th June 1998),although the water column temperature may be somewhat over-estimated due to a skin effect. Temperature in the Beaufort Sea mayreach 10 °C at that time of the year (Lavoie et al., 2009). Our seasurface temperature measurements (SST, in °C) were obtained duringnight time, whereas ocean color is measuredwith daylight conditions.We nevertheless put in relation those two data sources, assuming thatthe river plume system under study is large and spatially stableenough to show the same characteristics in a 12-hour interval. Fig. 12shows the scatterplot of SST versus ρw(865) for a rectangular sub-scene. For turbid waters where 0.01bρw(865)b0.03, the changes inthe temperature are lower than 3 °C. In their study, Ruddick et al.(2006) showed that a 12 °C decrease in the water temperature gavean increase of 9% and 6% respectively in ρw (740) and ρw (840). A 3 °Cchange in the temperature should then be equivalent to a 0.7% changein the ratio. This value of 0.7%, compared to the large deviationsobtained in our satellite dataset, shows that a temperature effectcannot reasonably be responsible for the trend in the ratio ρw (765)/ρw (865) observed in the satellite data set over the Mackenzie Riverplume.

3.6. Impact of using the similarity spectrum instead of the real value of theratioρw (λ1)/ρw (λ2), on the estimation of thewater-leaving reflectances inthe visible

The finding of a constant shape of the ρw spectrum, or “similarityspectrum”, could be exploited to remove the atmospheric contribu-tion from the top-of-atmosphere reflectance sensed over turbidwaters, as suggested by Ruddick et al. (2006). Ruddick et al. (2000)had indeed already proposed an efficient method to performatmospheric corrections for the SeaWiFs imagery over turbid waterswhich extends the standard algorithm. To solve a simple set ofequations, Ruddick et al. (2000) assume that 1) the ratio of themultiple-scattering and aerosol-Rayleigh scattering reflectance at 765and 865 nm is spatially homogeneous at least over the subscene ofinterest and this ratio is taken as a calibration parameter, fixed for

1628 M. Doron et al. / Remote Sensing of Environment 115 (2011) 1617–1631

each image, and 2) the ratio of water-leaving reflectances normalizedby the sun–sea atmospheric transmittance at 765 and 865 nm isassumed to be spatially homogeneous at least over the subscene ofinterest and is as well taken as a calibration parameter. The similarityspectrum is an extension of the second assumption of the method,since it sets the ratio of the water-leaving reflectances in the NIR as aconstant for all images (Ruddick et al., 2006).

We showed earlier in the present study, with different data sets, thatincreasing turbidities and their associated IOPs had an impact in theNIRreflectance spectrum for turbid waters, and led to systematic deviationsfrom the similarity spectrum. In the present subsection,wewent furtherand estimate what would be the error committed in the estimation ofwater-leaving reflectances in the visible for turbid waters if using thesimilarity spectrum to perform atmospheric corrections. For thisestimation, we considered, as in the Ruddick et al. (2000) method thatthe ratio of the multiple-scattering and aerosol-Rayleigh scatteringreflectance at 765 and 865 nm is known byothermeans andwe focusedon the error committed only doing the similarity spectrum assumption.

For this purpose, we considered realistic IOPs spectra of non-Case Iwaters, proposed by the International Ocean Color CoordinatingGroup (IOCCG, http://www.ioccg.org/groups/OCAG_data.html),which consists in assemblages of phytoplankton, detrital matter anddissolved organic matter (gilvin), with their associated spectralabsorption and scattering coefficients. We “added” suspendedparticulate matter (through its absorption coefficient, its scatteringcoefficient and its scattering spectral slope n) to obtain samples withthree different levels of turbidity. The details of the calculations aregiven in Appendix B. The ρw spectra were calculated for each set ofIOPs using Hydrolight© (version 4.2) extended to the NIR.

The comparison between the calculated spectral ρw and the

retrieved ρ̂w in relative difference (ρw−ρ̂w

ρw, dimensionless) was done

for each of the 10 cases: no addition of SPM, addition of SPM to reachSPMtot=10 g m−3 with n=0, 0.5 and 1, addition of SPM to reach

Fig. 13. Line plots of the relative error committed on the water-leaving radiances forturbid waters if the similarity spectrum is used with ρw (765)/ρw (865)=1.689(Ruddick et al., 2006) to perform the atmospheric corrections (see text). Thesimulations are performed with the radiative transfer code Hydrolight©. The inherentoptical properties of 25 realistic samples with average content of phytoplankton(3 mg m−3 of chlorophyll a), proposed by the IOCCG were considered. Additionalsuspended particulate matters were added to this simulated samples (10, 100 and1000 g m−3), with a varying spectral slope of their scattering coefficient (n=0, 0.5 and1). We show the average and standard deviation for the 25 spectra. The relative error islarger with increasing SPM, and with increasing n. It is also largest for blue wavelengthsthan for green wavelengths.

SPMtot=100 g m−3 with n=0, 0.5 and 1 and finally, addition of SPMto obtain SPMtot=300 g m−3 with n=0, 0.5 and 1. Fig. 13 shows themedian for the 25 spectra and the error bar is obtained with thestandard deviation of the 25 samples. Using the similarity spectrumdoes not lead to significant errors when the water is not very turbid.With no addition of turbidity, the maximum error in the visible on thewater-leaving reflectances is 5×10−3, which corresponds to 0.5%. Inthe case where SPMtot=10 g m−3, the maximum difference is 2.5%,which may be acceptable for some applications. The error committedin the estimation of the water-leaving reflectances is larger in the bluethan in the green portion of the spectrum, which is clear for the caseswhere SPMtot=100 g m−3. For the shortest wavelengths in the blue,the relative difference can reach up to 40%. This situation worsens foreven larger turbidity, whatever the value of the n coefficient. Thisexercise showed that the similarity spectrum is convenient to performatmospheric corrections for moderately turbid waters, as in factspecified by Ruddick et al. (2006), but could produce substantialerrors if used in waters with SPMtot superior to 30 g m−3.

4. Conclusion

The use of AOPs, and especially of reflectance, in the blue and greenparts of the spectrum to determine the content of optically significantconstituents in seawater has reached its limits over the last decades. Thisis partly due to the fact that there exist inherent ambiguities in theinterpretation of ocean color (Defoin-Platel & Chami, 2007). Therefore,interest has built up for considering other parts of the spectrum (UV,NIR), and some other optical processes (e.g. fluorescence andpolarization). In this context, the NIR has recently been subject tomuch attention. Various approaches that use NIR reflectance wereproposed to estimate the chlorophyll a concentration in lakes (Gons,1999; Gons et al., 2005; Ruddick et al., 2001; Dall'Olmo& Gitelson, 2005and Dall'Olmo et al., 2005), and SPM in coastal waters (Doxaran et al.,2002a). The estimation of the vertical diffuse attenuation coefficient Kd

and the beam attenuation coefficient c in coastal waters was alsoproposed by Doron et al. (2007), with the use of two reflectances, onebeing located in the NIR. The increasing use of the NIR in marine opticsand related applications stimulated more fundamental studies of theIOPs in this spectral range. For instance, Doxaran et al. (2007),documented the particle scattering coefficient of particles found incoastal waters and showed that n in the NIR varies between 0.1 and 1.2.Stramski et al. (2007) determined both the absorption and scatteringcoefficients of various types of mineral particles that can be found in seawater. The latter study and that of Tassan and Ferrari (2003) suggestthat significant absorption is often observed for marine particles in theNIR, especially in coastal waters.

Ruddick et al. (2006) found based on a sensitivity analysis thatrealistic variations in IOPs have limited impact on the shape of the NIRreflectance spectrum. To some extent, this finding challenged the needfor further documentingNIR IOPs.Here,we found that,whenconsideringa wide range of turbidity such as that found in many river plumes, theshape of the NIR reflectance spectrum does in fact vary significantly.While the use of a similarity spectrum is convenient and certainly validwhen performing quality controls on reflectance measurements, oratmospheric corrections in moderately turbid waters, we showed that itis not the case for more turbid waters. Not only the shape of the particlescattering spectrum has an impact on the shape of NIR reflectance, butalso particle absorption may have too, especially at high turbidities, asshown by the sensitivity analysis performed with the radiative transfersimulations. Our results call for more studies on NIR IOPs of seawaterconstituents. Priority should be given to determine better the absorptioncoefficient of marine particles in the NIR. Also, the wide range of valuesavailable in the current literature suggests that there still existssignificant uncertainty about absorption by pure seawater.

Remotely sensed ocean reflectance was used to document andunderstand thebehaviour ofwater reflectance. Thiswaspossible because

1629M. Doron et al. / Remote Sensing of Environment 115 (2011) 1617–1631

the selected data were collected with exceptionally clear atmospheres.This original approach provides a lot of data of high quality, and oneadditional advantage in using such data is that they are perfectlyconsistent with the ones that are ultimately used in remote sensingapplications. We believe that much more can be done using thisapproach.

Acknowledgements

In situ data sets were obtained in the frame of the RSFlux researchprogram, funded from 2005 to 2007 by a Marie Curie EuropeanReintegration Grant (contract no. 14905) and the Centre Nationald'Etudes Spatiales (CNES — France). The authors thank C. Mobley(Sequoia Scientific) for providing the extended version of Hydrolightincluding the NIR wavelengths. This work has been supportedthrough a PhD fellowship to M. Doron (MD) with a CIFRE contract(Association Nationale de la Recherche Technique). A. Mangin and O.Hembise (ACRI-ST) are thanked for their role in supervising andfunding the thesis work of MD. MD thanks E. Boss, K. Laval, S.Lavender, H. Loisel, Z.-P. Lee and A. Petrenko for their constructivecomments on an earlier version of the manuscript. K. Ruddick isthanked for his fruitful discussions during his stay in Villefranche-sur-Mer. We thank the PI Rick Wagener for its effort in establishing andmaintaining the AERONET Barrow site.

Appendix A

A.1. Estimation of the aerosol content in the atmospheric corrections

The purpose of the atmospheric corrections is to distinguish in thetop-of-atmosphere signal the contributions by the atmosphere andthe water column. The atmospheric reflectance is due to molecules(Rayleigh), aerosol, and coupled molecules–aerosol interactions withlight. The Rayleigh reflectances depend on the atmospheric pressureand are considered as predictable and accurately known in theatmospheric corrections treatments in the ocean color satelliteprocessing chains (Gordon & Wang, 1994; Antoine & Morel, 1999).In particular, the presence of water vapour and other atmosphericgases with their local concentration is taken into account by usingauxiliary data (NCEP for NASA sensors or ECMWF for MERIS). Oncethese molecular effects are taken into account, the largest uncertain-ties remaining in the atmospheric corrections treatment are theaerosol content and spectral behaviour, which are variable on shortscales in time and space. The concentration of the aerosol can beexpressed either with the aerosol reflectance ρa(865) or with theaerosol optical thickness at 865 nm, ΑΟΤ(865) (dimensionless). TheAngström coefficient (dimensionless) describes the spectral depen-dency of the aerosol reflectance and depends on the aerosol type.From these two parameters, the aerosol reflectance ρa can beestimated at all wavelengths. Above oceanic waters, the atmosphericcorrections provide accurate estimation of the aerosol load and type(Gordon &Wang, 1994; Antoine &Morel, 1999), but there is currentlyno consensus on how to perform the atmospheric corrections aboveturbid waters (Pinkerton & Aiken, 1999; Lavender et al., 2005;Ruddick et al., 2000; Stumpf et al., 2003).

A.2. Atmospheric corrections over the transects

The MERIS Case I data was processed using the Antoine and Morel(1999) scheme for atmospheric corrections above Case I waters,which provides the reflectance due to the scattering by the molecules,ρR (R for Rayleigh) and the reflectance due to the aerosol reflectanceρa. The water-leaving reflectances ρw in the turbid plume wereobtained from the top-of-atmosphere reflectances, ρTOA, withEq. (A1), where t is the diffuse atmospheric transmittance (dimen-sionless). All the reflectances ρ are dimensionless. This approach of

not considering the multiple scattering events is valid for clearatmospheres, such as the ones we consider in the present study.

ρw λð Þ = ρTOA λð Þ−ρR λð Þ−ρa λð Þt λð Þ ðA1Þ

TheSeaWiFS andMODIS Level-1datawereprocessed similarly, usingEq. (A1), with the SeaDAS software and the atmospheric correctionswere performed with the Gordon and Wang (1994) scheme, which isrelevant for oceanic waters. The reflectances ρ are obtained from theradiances Lwn (in μW cm−2 sr−1 nm−1) and Eq. (A2), with F0 λð Þ beingthe mean extraterrestrial solar irradiance (here in μW cm−2 nm−1):

ρ =π⁎Lwn

F 0: ðA2Þ

For the SeaWiFS and MODIS imagery, the flag devoted to identifypixels contaminated by the presence of clouds rejects those for whichρw(865) is larger than 2.5%. In this study, a visual inspection of thescene revealed the absence of clouds. We therefore increased thethreshold from 2.5% to 3.5%. Thereby, pixels for highly turbid waterswere not rejected (ρw(865) as large as 0.03). For the MERIS imagery,the standard procedure is applied, and ρw(865) larger than 3.5% mayhappen. Although the fact of modifying the cloud threshold in generalis dangerous, in our present case, it is safe because the location of theturbid plumes is identified and there is no cloud, since the imageshave been chosen carefully for that reason.

A.3. Quantification of the uncertainty in our corrections of the aerosolcontent

In the present study, we extracted ocean color data over turbidwaters for very clear days. In these conditions, the relativecontribution to the total signal by the aerosol content is very low asillustrated in Fig. 4. This is the best condition possible to avoid theinfluence of aerosol, the most variable and difficult component toretrieve in the atmosphere, once the Rayleigh, water vapour andatmospheric absorbing gases contribution is identified. But it is stillnecessary to quantify the uncertainty related to our assumption of thehomogeneity of the atmospheric composition above the transect,sometimes over distances as large as tens of kilometres. To do so, weassume that, at the first order, we can have confidence in the top-of-atmosphere reflectances, in the Rayleigh reflectances and in thetransmittances. While doing so, we assume that the aerosol signal isthe main unknown for the kind of transect we consider. The analyticalcalculation of the propagation of the uncertainty U% for ρa can be doneto obtain the uncertainty U′% on the water-leaving reflectance, seeEqs. (A3) and (A4). In Eq. (A3), ρRc is the Rayleigh-correctedreflectance (TOA reflectance minus the Rayleigh reflectance).

ρRc = ρw + ρa = ρw calculated with ρa 1 + U%ð Þð Þ + ρa 1 + U%ð ÞðA3Þ

We can thus estimate ρw(calculated with ρa(1+U%))=ρRc−ρa(1+U%) and the associated uncertainty U′ % for ρw (Eq. A4).

U′% =ρw−ρw calculated with ρa 1 + U%ð Þð Þ

ρw=

U%⁎ρa

ρwðA4Þ

The uncertainty U′ % consequently depends on i) the level ofuncertainty U%, ii) the level of the aerosol reflectance and iii) thewater-leaving reflectance (see Eq. A4). U′ % is larger for lower ρw and larger ρa.

These calculations assume that the transmittances are not affectedby the aerosol content, which is true at a first order: a doubling in ρa (a100% variation) leads to a change in transmittance from 0.98 to 0.975 (a0.5% variation). An approximation of U% is the standard deviation of the

1630 M. Doron et al. / Remote Sensing of Environment 115 (2011) 1617–1631

aerosol content above the subzone located in the Case 1 area, which isvery small in the imageswe considered here. These very low values of U%, lead to high confidence in the resulting values of the water-leavingreflectances. For instance, for the MERIS imagery studied in this paper,the standard deviation is lower than 3%. For these aerosol reflectances,the uncertainty on ρa leads to an uncertainty of around 20% for ρwaround 0.001 and to an uncertainty around 2% for ρw around 0.01. Tokeeponly the reflectances forwhichwe have the greater confidence,wedid not consider the pixels for which ρw (865) is inferior to 0.01.

To go further, we tested on a simulated spectrum the impact of anerror in the estimation of the aerosol content (in ρa (865) or itsspectral slope). A clear atmosphere, such as those we looked for, canbe represented by ρa (865)=0.005 and its spectral slope ε =ρa 779ð Þρa 865ð Þ = 1:1. We tested the impact on the ratio

ρw 779ð Þρw 865ð Þwhen there is

an error in the aerosol reflectances: ρa (865)=0.002, ρa (865)=

0.008 and ε=1.5. When ρw (865)N0.01, the ratioρw 779ð Þρw 865ð Þ calculated

with the error on the aerosol is very close to the actual ratio. Thisresult shows that an error in the aerosol identification cannot beresponsible for the flattening trend observed. Finally, the atmosphericcorrections performed with the SWIR method (Wang et al., 2007)show independently the same trend in the data.

As a summary, with satellite data, the smallest the ρw (865), thelarger the impact of atmospheric corrections. There is then a lowerend where the conclusions are more difficult to draw from the results,but for the present study, we mostly focus on the large values of ρw(865) to draw our conclusions.

Appendix B

In this appendix,we give thedetails of the calculationsperformed forthe paragraph Impact of using the similarity spectrum instead of the realvalue of the ratio ρw (λ1)/ρw (λ2), on the estimation of the water-leavingreflectances in the visible. The goal is to test the sensitivity of the retrievedwater-leaving reflectances in the visible portion of the spectrum if oneuses the similarity spectrumwhen performing atmospheric correctionsabove turbid waters, thus using the method proposed by Ruddick et al.(2000) and the results of Ruddick et al. (2006).

Some 25 realistic samples proposed by the IOCCG with averagecontent of phytoplankton (3 mg m−3 of chlorophyll a) were consid-ered. Their initial content in SPM is obtained through Eq. (7)with b*SPM(555)=0.51 m2 g−1, (Babin et al., 2003) and ranged between 1.2 and5.1 mg m−3. Additional turbidity, to reach the levels of 10, 100 and300 g m−3 was added through the modification of the absorption andscattering coefficients. The IOPs of the additional SPMwere calculatedfor the scattering coefficient with Eqs. (6) and (7) with b*SPM(555)=0.51 m2 g−1, (Babin et al., 2003), andwithn=0, 0.5 or 1, (the rationalefor the choice of the values of n are in the section Radiative transfersimulations). The scattering phase function for particles was takenfrom Mobley et al. (1993) who derived it on the basis of themeasurements by Petzold (1972). The absorption coefficient wasobtained with Eq. (B1), where a*SPM(443)=0.041 m2 g−1, (Babin etal., 2003) and Eq. (6) with SSPM=−0.0123 nm−1.

aSPM 443ð Þ = a⁎SPM 443ð Þ⁎SPM ðB1Þ

For a complete description of the choice of the IOPs in the dataset, seethe document written by the Ocean Color Algorithm Working Group(http://www.ioccg.org/groups/lee_data.pdf). The IOPs (initially givenfor the wavelengths between 400 and 800 nm) were systematicallyextended to 900 nm, to cover the range of the NIR wavelengths of ourinterest. The phytoplankton absorption coefficient aphwas simply set to0 for wavelengths longer than 800 nm. The absorption coefficient forgelbstoff ag (colored dissolved organic matter) was exponentiallydecreasing from the blue to the red, with the two parameters (slope

and absorption coefficient of a reference wavelength) given in thedataset. They were used to extend ag between 800 and 900 nm. Weproceeded similarly for the detritus/mineral absorption coefficient adm.The backscattering term of the phytoplankton bbph is derived from thephytoplankton scattering coefficient bph and the 1% Fournier–Forandfunction. Values of bph are the difference between the phytoplanktonbeam attenuation coefficient cph and aph. The spectral variations of cphfollow a power law of the wavelength with coefficients in the dataset.We calculated cph for wavelengths longer than 810 nm to finallyestimate bph for the same wavebands. The scattering coefficient fordetritus, mineral and others, bdm, follows a power law, which was usedto extend the coefficients to the NIR.

Radiative transfer simulations were performed for the wavelengthsin the visible and in the NIR, for the MERIS wavebands and for a solarzenith angle of 30°, using the Hydrolight software. The obtained water-leaving reflectances ρw were further considered as the “sea-truth”. Totest only the effect of the similarity spectrum, we considered that theRayleigh-corrected reflectances can be obtained with ρRc=ρw+ρa, asthe addition of aerosol reflectances and water-leaving reflectances.Addition of the spectral aerosol reflectance ρa was made for anaverage atmosphere (ρa(865)=0.015, ε = ρa 779ð Þ

ρa 865ð Þ = 1:1 as proposedby Ruddick et al. (2000), which gave an Angström coefficient(dimensionless) αa=−0.91 in the Eq. (B2)).

ρa λð Þ = ρa 865ð Þ λ=865ð Þαa ðB2Þ

The full set of equations with the transmittances due to theatmosphere and the multiple scattering versus the simple scatteringeffect can be found in Ruddick et al. (2000). We neglected the impactof the transmittance through the atmosphere as being of the secondorder (the variations of the transmittance value are very low even forhighly varying type of atmosphere).

With the Rayleigh-corrected reflectances at two wavelengths, thesystem to be solved is the following (Eq. B3), which is a system withfour unknowns and two equations.

ρRc 779ð Þ = ρw 779ð Þ + ρa 779ð ÞρRc 865ð Þ = ρw 865ð Þ + ρa 865ð Þ ðB3Þ

Assuming that α = ρw 779ð Þρw 865ð Þ is known, using the similarity spectrum

for turbid waters and assuming that ε = ρa 779ð Þρa 865ð Þ is an ancillary data, the

system can now be solved.The solution provided the estimations of the water-leaving

reflectances ρ̂w 779ð Þ, ρ̂w 865ð Þ, ρ̂a 779ð Þ and ρ̂a 865ð Þ, as in Eq. (B4).

ρ̂w 865ð Þ = ρRc 779ð Þ−ερRc 865ð Þα−ε

ρ̂w 779ð Þ = αρ̂w 865ð ÞðB4Þ

It is thereby possible to estimatewith Eq. (B2) the spectral ρ̂a in thevisible and to obtain the spectral ρ̂w in the visible by substraction. Wethen compared the initial spectral ρ̂w with their estimates ρ̂w and theirrelative difference for all wavelengths in the visible and NIR:ρw λð Þ− ρ̂ww λð Þ

ρw λð Þ . For each couple of SPMtot and n, there are 25 spectra,

of retrieved water-leaving reflectances ρ̂w and we plot for each casethe result in terms of median and standard deviation (Fig. 13).

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