Calibration and validation of a generic multisensor …Calibration and validation of a generic...

Remote Sensing of Environment 114 (2010) 854–866

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Remote Sensing of Environment

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Calibration and validation of a generic multisensor algorithm for mapping of totalsuspended matter in turbid waters

B. Nechad ⁎, K.G. Ruddick, Y. Park 1

Royal Belgian Institute for Natural Sciences (RBINS), Management Unit of North Sea Mathematical Model (MUMM), 100, Gulledelle 1200 Brussels, Belgium

⁎ Corresponding author.E-mail address: [email protected] (B. Nechad)

1 Now at CSIRO Land and Water.

0034-4257/$ – see front matter © 2009 Elsevier Inc. Aldoi:10.1016/j.rse.2009.11.022

a b s t r a c t
a r t i c l e i n f o
Article history:Received 2 March 2009Received in revised form 10 November 2009Accepted 30 November 2009

Keywords:Total Suspended Matter concentration (TSM)Bio-optical algorithmTSM algorithm calibrationHyperspectral calibrationSatellite derived TSM

Mapping of total suspended matter concentration (TSM) can be achieved from space-based optical sensorsand has growing applications related to sediment transport. A TSM algorithm is developed here for turbidwaters, suitable for any ocean colour sensor including MERIS, MODIS and SeaWiFS. Theory shows that use ofa single band provides a robust and TSM-sensitive algorithm provided the band is chosen appropriately.Hyperspectral calibration is made using seaborne TSM and reflectance spectra collected in the southernNorth Sea. Two versions of the algorithm are considered: one which gives directly TSM from reflectance, theother uses the reflectance model of Park and Ruddick (2005) to take account of bidirectional effects.Applying a non-linear regression analysis to the calibration data set gave relative errors in TSM estimationless than 30% in the spectral range 670–750 nm. Validation of this algorithm for MODIS and MERIS retrievedreflectances with concurrent in situ measurements gave the lowest relative errors in TSM estimates, lessthan 40%, for MODIS bands 667 nm and 678 nm and for MERIS bands 665 nm and 681 nm. Consistency of theapproach in a multisensor context (SeaWiFS, MERIS, and MODIS) is demonstrated both for single point timeseries and for individual images.

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1. Introduction

Mapping of total suspended matter concentration (TSM) fromsatellites and airborne imagery has become a valuable tool for marinescientists to assess andmonitor suspended sedimentdistribution,whichis a key element of water quality in coastal areas. Remote sensing (RS)data have been used in various ways: combined with in situmeasurements to draw up sediment transport maps e.g. van Raaphorstet al. (1998), as input boundary conditions and validation data tosediment transport models by Fettweis and Van den Eynde (2003),assimilated in transport models by Vos and Gerritsen (1997) and Blaaset al. (2007), or used in the light forcing of an ecosystem model e.g.Lacroix et al. (2007). With the continuous optimisation of satellitecapabilities e.g. improvement of wavelengths used for MODIS after theSeaWiFS experiment as described in Esaias et al. (1998), themore bandsand higher spatial resolution of the MERIS instrument, and thedevelopment of algorithms for retrieval of water constituents, theaccuracy and reliability of RS products is increasing. A historicaloverview of TSM algorithm evolution from 1974 to 2005 is given inAcker et al. (2005).

TSM algorithms were first designed for open ocean waters as afunction of chlorophyll a (CHL) concentration, as established in Morel(1980), Sturm(1980) andViollier andSturm(1984), because suspended

solids in the deep sea consist mainly of plankton and associated organicdetrital matter. The form commonly adopted for CHL algorithms andinherited by TSM algorithms is a reflectance band ratio, characterizingthe high CHL absorption around 440 nm and low absorption in 550 nm.However, as underlined by Tassan (1993), CHL and TSM do not co-varyin coastal waters because of the presence of particles arising from re-suspension, shore erosion or river discharge, making the blue:greenband ratio algorithms unsuitable for TSM retrieval.

Curran et al. (1987) and Novo et al. (1989) investigated the form ofthe relationship between TSM and reflectance in coastal waters andshowed that single band algorithms may be adopted where TSMincreases with increasing reflectance. A variation of these relationswith viewing geometry was observed by Novo et al. (1989). Empiricalcalibration of different data sets followed during the last decade,establishing log-linear models as function of reflectance or radiance inthe visible range. Calibration has been made using variously:laboratory TSM and reflectance data by Chen et al. (1991), with insitu reflectances over the Rhône river plume by Forget and Ouillon(1998) and with MODIS 645 nm-reflectance over Tampa Bay by Huet al. (2004). Non-linear equations have been tested by Myint andWalker (2002) for TSM and AVHRR data, concluding that the bestmodel is a linear one with AVHRR channel 2 (725 nm–1100 nm) withnon-linear models being better adapted for shorter wavelengths.

Although these models might be efficiently applied to satelliteimages concurrent with calibration data sets, their accuracy may bereduced outside the conditions of the calibration data set because ofthe empirical basis. Semi-analytical approaches have overcome such a

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855B. Nechad et al. / Remote Sensing of Environment 114 (2010) 854–866

limitation with models based on physical knowledge of therelationship between reflectance and TSM. The reflectance model ofGordon et al. (1988) used for open sea waters and validated for inlandturbid waters by Dekker et al. (1997), has been intensively used toretrieve TSM in estuarine e.g. Stumpf and Pennock (1989) and Dekkeret al. (1998), in coastal and deep waters by Van Der Woerd et al.(2000), Van Der Woerd and Pasterkamp (2004) and Eleveld et al.(2008). In very turbid waters Doxaran et al. (2002, 2003) used a NIRband ratiomodel to remove the effects of particle size distribution andof the bidirectional variation of the remote sensed reflectance.

Analytical approaches have been developed since the last decadeaiming to solve the reflectance model with water constituents as theunknowns, by parameterization of specific IOPs (inherent opticalproperties) e.g. Forget et al. (1999), Lahet et al. (2000) and Haltrin andArnone (2003). Vasilkov (1997) used non-linear least squareregression, with parameterization of particle backscattering coeffi-cient and coloured dissolved organic matter (CDOM) absorption.Multi-spectrum multi-component analytical retrieval algorithms areemerging, where the reflectance spectrum is inverted to derivesimultaneously TSM, phytoplankton pigment and CDOM, e.g: Hoo-genboom et al. (1998) and Sterckx and Debruyn (2004) using matrixinversion of the reflectance model and Schiller and Doerffer (1999)used a neural network technique. The multi-component models (e.g.TSM, CHL and CDOM) generally use hyperspectral information or atleast many bands in the visible range, to discriminate eachcomponent.

In the present study a single band algorithm for TSM retrievalbased on a reflectance model is developed (Section 2) and calibrated(Section 3) using seaborne reflectance and TSM measurementscollected in the southern North Sea area. A second version of thealgorithm is calibrated using the reflectance model of Park andRuddick (2005) to take into account the bidirectional effects(Sections 2.1 and 2.2). Unlike the papers available in literature up tonow, this TSM algorithm innovates by its hyperspectral calibration, itsstrong theoretical basis and its simple application to multiple oceancolour sensors. The hyperspectral calibration is used to identify thebest spectral interval for TSM retrieval from remote sensed reflec-tance, while the semi-empirical approach takes into account assump-tions on spatial and temporal variability of specific IOPs, whose impacton TSM estimation are discussed in “Web Appendix 1 — Theoreticalerror of estimates”, hereafter referred to as WA1. The results of thegeneric hyperspectral calibration and the specific calibration forMERIS, MODIS and SeaWiFS sensors are presented (Section 4). Theresults of the calibration using the reflectance model of Park andRuddick (2005) are presented in “Web Appendix 2 — BRDF algorithmvariant”, denoted byWA2 and themethod to remove outliers from thecalibration dataset is given in “Web Appendix 3 — Treating outliers inregression analysis” (WA3). Validation of the algorithm is carried outusing MERIS and MODIS imagery (Section 5) and model errors areassessed using in situ matchups. TSM time series from the MERISstandard product using the neural network technique Schiller andDoerffer (1999) and from MODIS and SeaWiFS using the currentalgorithm are shown (Section 6). The performance of the single bandalgorithm is demonstrated with TSM concentration maps retrievedfrom the three ocean colour sensors (Section 7). Finally conclusionssynthesize the method and the results and consider future possibil-ities of TSM retrieval in a synergistic multisensor perspective(Section 8).

2. Theory

The aim of this section is to derive the mathematical form of themodel allowing TSM concentration, S, to be estimated from the water-leaving reflectance defined by:

ρwðλÞ = πRrsðλÞ ð1Þ

where Rrs is the remote sensing reflectance at wavelength λ (dropped

hereafter for simplicity): Rrs =L0+wE0+d

, Lw0+ and Ed0+ are respectively the

water-leaving radiance, corrected for air–sea interface reflection, andthe downward irradiance just above the sea surface. S is first relatedto the ratio of total backscattering bb to total absorption a,ω′b = bb

a . Twoalternative approaches are then offered here. In the first approach theinherent optical property ωb′ is estimated from water-leaving reflec-tance by inversion of the reflectancemodel of Park and Ruddick (2005).In the second approach, the simple first order analytical reflectancemodel of Gordon et al. (1988) is used. It is assumed in thesemodels thatbottom effects do not contribute to water-leaving reflectance (opticallydeep water column).

2.1. Inherent optical property model

For the purposes of deriving a total suspended matter retrievalalgorithm, ωb′ is most conveniently divided into the contributions tobackscatter and absorption from particles (both non-algal and algal)and all other non-particle optically-active substances (essentially thepure water molecules and coloured dissolved organic matter):

ω′b =bbp + bbnpap + anp

ð2Þ

where the subscripts p and np denote the particle and non-particlecontributions. A number of assumptions and approximations regard-ing these inherent optical properties (IOPs) are then made in order torelate S directly to ωb′. The validity of these assumptions is obviouslycrucial to the accuracy of the consequent retrieval algorithm and isassessed in detail in the error analysis of WA1. Starting with the mostimportant, these assumptions are as follows:

1. Particulate backscatter is assumedproportional to TSM concentrationvia the constant TSM-specific particulate backscatter coefficient, bbp⁎:

bbp = b*bpS ð3Þ

This is themost important of the 4 assumptionsmade regarding IOPssince natural variability of bbp⁎ will give a direct, linear error to Sretrieval. Both specific-scattering studied in Babin et al. (2003a) andthe scattering:backscattering ratio examined by Boss et al. (2004) areknown to vary in relationwith space or time variations of particle sizeand composition, and bbp⁎ is expected to be significantly differentbetween algae and non-algae particles (as well as being variablewithin these two groups). If the natural variability of bbp⁎ could becharacterised in someway a priori, then itmaybe possible to improveon this assumption. The quantification of the errors associated withdifferences in bbp⁎ between algae and non-algae particles is given inWA1, Section I.1.

2. Space and time variabilities of non-particulate absorption, anp isassumed to be negligible. For validity of this assumption in areas ofhigh CDOM absorption, e.g. coastal waters with river plumes, it isnecessary to choose the wavelength for retrieval such that the purewater absorption is dominant. The impact of variability of anp onretrieval errors is quantified in WA1, Section I.2.

3. Particulate absorption is assumed proportional to TSM concentrationvia the constant TSM-specific particulate absorption coefficient, ap⁎:

ap = a*pS: ð4Þ

It iswell known that there is considerable variability in ap⁎ as stressedby Babin et al. (2003b), both in magnitude and spectral variation,according to the size and composition of particles. This is particularlysignificant when comparing algae particles with non-algae particles.However, the impact of this variability on retrieval accuracy can be

856 B. Nechad et al. / Remote Sensing of Environment 114 (2010) 854–866

limited provided wavelengths for retrieval are suitably chosen suchthat purewater is the dominant absorbing component. The impact ofvariability of ap⁎ on retrieval errors is quantified in WA1, Section I.3.

4. Non-particulate backscatter is assumed negligible, bbnp=0. For allbut the clearest water, backscatter in the green, red and nearinfrared is dominated by particulates. The impact of neglecting bbnpis quantified in WA1, section I.4.Using these four assumptions Eq. (2) can be simply rewritten as:

S = Aω′b

1−ω′b = C½gm−3� ð5Þ

where the calibration coefficients A and C are given by:

A =anp

b*bp½gm−3� ð6Þ

C =b*bp

a*p½dimensionless�: ð7Þ

Eq. (5) expresses a linear relationship between S and ωb′ for low ωb′

and the asymptotic limit ofωb′→bbp⁎ /ap⁎ as S→∞. For this asymptoticlimit the backscatter to absorption ratio and the reflectance are deter-mined only by the type of particles and not by their concentration —

the optical “saturation” phenomenon in Bowers et al. (1998). Thisindicates that quantitative retrieval of S is no longer reliable beyonda certain concentration for a specified wavelength. This should beavoidedby choosing a retrievalwavelengthwith sufficientlyhighpurewater absorption, using longer red or near infrared wavelengths forwater with higher S. If this asymptotic regime is avoided then (5) canbe understood easily by the linear approximation:

S≈Aω′b½gm−3� ð8Þ

2.2. Bidirectional reflectance model

Park and Ruddick (2005) describe amodel of reflectance as functionof ωb′ taking into account the bidirectional variation of reflectance asfunction of sun and viewing geometry, which may be of order 10% inturbid waters. This model expresses ρw as a fourth order polynomialfunction of ωb′ chosen to fit as well as possible the simulations of aradiative transfermodel for a wide range of conditions and in particularallowing non-linear variation of ρw as function of ωb′.

2.3. Alternative reflectance model

An alternative, simpler approach can be developed for inversiondirectly from ρw, which ignores the bidirectional variation and uses asimplified reflectance model, based on a first order version of themodel of Gordon et al. (1988):

rrs =f ′

Qbb

a + bb=

f ′

Qω′

b

1 + ω′b

ð9Þ

where rrs is the subsurface remote sensing reflectance, f ′ is a varyingdimensionless factor set by Morel and Gentili (1991) and Q is the ratioof subsurface upwelling irradiance to the subsurface upwellingradiance in the viewing direction. The subsurface reflectance can berelated to the water-leaving reflectance by:

ρw = πℜrrs ð10Þ

whereℜ represents reflection and refraction effects at the sea surface,as described in Morel and Gentili (1996). Combining Eqs. (9) and (10)

and taking a typical value of f ′/Q=0.13 for sediment-dominatedwaters in Loisel and Morel (2001) and ℜ = 0:529 from Morel andGentili (1996) gives:

ρw = γω′

b

1 + ω′b

!orω′

b =ρw

γ−ρwð11Þ

where γ = πℜf ′ =Q≈0:216. When combinedwithmodel (5) relatingωb′ to TSM concentration, S, this gives:

S = Aρ ρw1−ρw = C ρ ½gm−3� ð12Þ

where

Aρ = A= γ½gm−3�andCρ = γC = ð1 + CÞ½dimensionless�: ð13Þ

This reflectance-based algorithm is algebraically equivalent toEq. (4) of Stumpf et al. (1993) and is obviously very similar to the ωb

′

based algorithm (5). It requires calibration of the parameters Aρ andCρ. Since the calibration and validation of the two algorithms haveshown very similar results – this is discussed later in this paper – thereflectance-based algorithm is the focus of the main paper while themodel calibration for the ωb′ based algorithm is given in WA2.

2.4. Model calibration — asymptotic limit Cρ parameter

From the discussion of Section 2.1 extended to the alternativemodel described in Section 2.3, it is clear that the two calibrationparameters Aρ and Cρ have very different importance: any errors incalibration of Cρ have no impact in the linear regime where thealgorithm will mainly be used. For this reason, Cp is calibrated using“standard” IOP data as described in this section, leaving the seabornereflectance measurements for calibration of Aρ alone, as described inSection 3. Thus Cρ is computed from Eqs. (7) and (13) as follows:

1) the mass-specific absorption of TSM is derived from ap⁎λ=ap⁎443e(− slopeNAP(λ− 443)) where slopeNAP=0.0123 nm−1 andap⁎443=0.036 m2g−1 is an average of the specific absorptionof non-algal particles published in Babin et al. (2003b);

2) the mass-specific backscattering of TSM is related to the mass-specific particle scattering, bp⁎, through bbp⁎ λ=0.02 bp⁎λ. The 0.02value was derived from the measurements of turbid harbourwater data by Petzold in Mobley (1994). Similar values of 0.016and 0.018 were found by Lubac and Loisel (2007) (his Table 3)from in situ measurements of backscattering and scattering ofparticles at 650 nm respectively in detritus and sediment-dominated waters in the North Sea. The specific particulatescattering can be split into spectrally-constant and wavelength-varying factors: bbp⁎ λ=0.02 bp⁎

555bpλ/bp555. The bbp⁎ spectrum is

then estimated using bp⁎555=0.51 m2g−1, a typical value forcoastal waters given in Babin et al. (2003a) and using the values ofbpλ/bp555 tabulated in Babin et al. (2003a) for all regions (Atlantic,

Mediterranean sea case 1 and case 2 waters, North Sea, Baltic seaand the Channel), with linear interpolation between tabulatedwavelengths.

The computed Cρ factor is given in Table 1 every 2.5 nm forwavelengths ranging from 520 nm to 885 nm and in Table 2 forMERIS, MODIS and SeaWiFS bands. Note that for shorter wavelengthsCλb600nm

ρis arbitrarily set to C600nm

ρ=14.49·10−2, to avoid saturation

of the model. In fact, the algorithm is not well-suited to use ofwavelengths less than 600 nm as discussed later.

Algorithm (12) then has a single free calibration parameter, Aρ,which is obtained from non-linear regression analysis using reflectanceand TSM data as described in the next section.

Table 1The Cρ coefficients as computed from literature (see text for details) and interpolated toevery 2.5 nm. In the range λb600 nm, the computed values shown in italic font are notused, but Cρ=14.49 10−2 is used instead to avoid the saturation of the TSM model.

λ (nm) 102

Cρ102 Cρ

replacedλ(nm)

102

Cρλ(nm)

102

Cρλ(nm)

102Cρ

600.0 14.49 700.0 18.64 800.0 20.78602.5 14.61 702.5 18.72 802.5 20.80605.0 14.72 705.0 18.79 805.0 20.82607.5 14.83 707.5 18.86 807.5 20.85610.0 14.94 710.0 18.92 810.0 20.87612.5 15.04 712.5 18.98 812.5 20.89615.0 15.14 715.0 19.04 815.0 20.91617.5 15.24 717.5 19.13 817.5 20.92

520.0 9.29 14.49 620.0 15.33 720.0 19.22 820.0 20.94522.5 9.47 14.49 622.5 15.42 722.5 19.30 822.5 20.96525.0 9.65 14.49 625.0 15.51 725.0 19.37 825.0 20.97527.5 9.82 14.49 627.5 15.60 727.5 19.44 827.5 20.99530.0 9.99 14.49 630.0 15.68 730.0 19.51 830.0 21.00532.5 10.15 14.49 632.5 15.81 732.5 19.57 832.5 21.01535.0 10.31 14.49 635.0 15.94 735.0 19.63 835.0 21.03537.5 10.46 14.49 637.5 16.07 737.5 19.68 837.5 21.04540.0 10.61 14.49 640.0 16.19 740.0 19.73 840.0 21.05542.5 10.76 14.49 642.5 16.30 742.5 19.78 842.5 21.06545.0 10.90 14.49 645.0 16.41 745.0 19.83 845.0 21.07547.5 11.03 14.49 647.5 16.51 747.5 19.88 847.5 21.08550.0 11.17 14.49 650.0 16.61 750.0 19.92 850.0 21.09552.5 11.30 14.49 652.5 16.74 752.5 19.96 852.5 21.10555.0 11.43 14.49 655.0 16.86 755.0 20.00 855.0 21.11557.5 11.67 14.49 657.5 16.97 757.5 20.03 857.5 21.12560.0 11.89 14.49 660.0 17.08 760.0 20.07 860.0 21.13562.5 12.11 14.49 662.5 17.19 762.5 20.10 862.5 21.14565.0 12.32 14.49 665.0 17.28 765.0 20.13 865.0 21.15567.5 12.52 14.49 667.5 17.38 767.5 20.21 867.5 21.16570.0 12.71 14.49 670.0 17.47 770.0 20.28 870.0 21.17572.5 12.89 14.49 672.5 17.56 772.5 20.34 872.5 21.19575.0 13.06 14.49 675.0 17.64 775.0 20.40 875.0 21.20577.5 13.23 14.49 677.5 17.75 777.5 20.45 877.5 21.21580.0 13.39 14.49 680.0 17.88 780.0 20.50 880.0 21.22582.5 13.55 14.49 682.5 17.99 782.5 20.54 882.5 21.23585.0 13.70 14.49 685.0 18.10 785.0 20.59 885.0 21.24587.5 13.84 14.49 687.5 18.21 787.5 20.62590.0 13.98 14.49 690.0 18.30 790.0 20.66592.5 14.12 14.49 692.5 18.40 792.5 20.69595.0 14.24 14.49 695.0 18.48 795.0 20.72597.5 14.37 14.49 697.5 18.57 797.5 20.75

Table 2The Cρ coefficients for MERIS, MODIS and SeaWiFS central wavelengths. In the range λ(nm)b600 nm, the computed values shown in italic font are not used, but Cρ

(λb600 nm)=14.49·10−2 is used instead to avoid the saturation of the TSM model.

Sensors central bands λ (nm) 10 Cρ

MODIS 531 14.49 (10.05)MODIS 551 14.49 (11.22)MODIS HIRES, SeaWiFS 555 14.49 (11.43)MERIS 560 14.49 (11.89)MERIS 620 15.33MODIS HIRES 645 16.41MERIS 665 17.28MODIS 667 17.36SeaWiFS 670 17.47MODIS 678 17.74MERIS 681 17.92MERIS 708 18.87MODIS 748 19.88MERIS 760 20.07MERIS 753 19.97SeaWiFS 765 20.13MERIS 778 20.46MODIS HIRES 858 21.12MERIS, SeaWiFS 865 21.15MODIS 869 21.16MERIS 885 21.24


Finally, to account for measurement and model errors, Eq. (11) ismodified by adding a second coefficient Bρ:

S =Aρρw

1� ρw = Cρ + Bρ: ð14Þ

In theory, perfectly particle-free waters with S=0 would have anon-zero reflectance because of the backscatter of pure water andbubbles, suggesting a slightly negative value for Bρ. In practice, thecalibration datasets (see next section) may have errors associatedwith both measurements of reflectance and TSM, which may becomecritical for low reflectance and low TSM. The extra degree of freedomafforded by the Bρ coefficient allows for all such factors and avoids theproblems associated with forcing a regression line through the origin.For the satellite data application Bρ is set to zero because the satellitesensor and processing will probably have different measurementerrors from the calibration data.

3. Method

3.1. Model calibration

Non-linear regression analysis is used to find the optimalparameter Aρ in Eq. (14) that gives the best fit to TSM and ρwmeasurements.

3.2. Dataset

A large set of 441 water-leaving reflectances was collected from2001 to 2006, from the Research Vessels Belgica and Zeeleeuw, overthe Southern North Sea (Fig. 1). The ρw spectra were recorded using asystem of three Trios spectro-radiometers with 2.5 nm resolutioncovering the spectral range [350 nm–950 nm] and following theprotocol described in Ruddick et al. (2006), based on the NASAprotocols (see Mueller et al. (2000)). From this dataset are selectedonly reflectances with standard deviation of 5 successive measure-ments of reflectance to average reflectance ratio less than 25%, giving101 spectra. A second selection excludes 29 in situ TSM andreflectances recorded during satellite overpasses — these will beused later as validation data (see locations in Fig. 1 of MERISmatchupsas blue plus symbols, MODIS and SeaWiFSmatchups as red circles andblack squares for calibration data). This gives two non-overlapping

Fig. 1. 72 Locations of TSM and reflectance measurements used for TSM algorithmcalibration are plotted as black squares, the special stations 230 (51.308°N, 2.84°E) and330 (51.420°N, 2.83°E) are respectively plotted as red and blue flags. TSM measure-ments used for validation purposes are: 21 plotted as green triangles and used withseaborne validation, 24 matchups plotted as red circles and used with MODISoverpasses and 10 matchups with MERIS overpasses are plotted as blue circles. (Forinterpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)


sets of 72 and 29 ρw spectra, shown in Fig. 2a respectively used forcalibration and validation purposes. Table 3 lists the sky and seaconditions during in situ measurements: sky radiance measuredabove the sea surface and the ratio sky radiance:downwellingirradiance above the sea surface at 750 nm, are respectively denotedby Lsky and Lsky/Ed. 50% of data taken was under clear skies with cloudcover less than 3/8, and Lskyb20 mW/m2/nm/sr. 90% of the data wascollected in a calm sea state with 5.4 ms−1 and 0.3 m average windspeed and wave height.

The 72 reflectances are convoluted with the MERIS, MODIS andSeaWiFS sensor response functions to derive the band-weightedreflectance data as follows:

ρKw =∫

ΔK

ρwðλÞσðλÞ dλ

∫ΔK

σðλÞdλð15Þ

where the reflectance ρwK is computed for each band K with a bandwidthΔK using the respective spectral responses σ (λ) of each sensor;an example of this convolution is presented in Fig. 2b and shows littledifference between the band-weighted and central-wavelengthapproaches.

72 TSMmeasurementsweremade concurrentlywith the reflectancemeasurements. The water samples were taken between 0.5 m and 3 mdepth, and TSMwasmeasuredwith the gravimetricmethodwith a pre-ashed GF/F filter following the procedure described in Tilstone et al.(2003), based on van der Linde (1998). TSMmeasurements range from1.24 gm−3 to 110.27 gm−3, with a standard deviation of 23.35 gm−3

and an average value of 26.16 gm−3. As reported in Table 3, 50% of TSMsamples are less than 20.5 gm−3 and 90% do not exceed 60 gm−3.

3.3. Calibration by non-linear regression analysis

For the N=72 seaborne measurements of TSM, denoted by Si andband-weighted reflectances ρwi,k, i=1…N, and k=1…Kwhere K is thenumber of bands for a given sensor (k will be dropped hereafter forbrevity), model estimates are denoted by S̑i and the mean value of

Fig. 2. a) Reflectance spectra recorded by the Trios system, b) the reflectance measuredat station 130 (51.270°N, 2.90°E) on July 10th 2003 and convoluted with, respectivelyMERIS, MODIS and SeaWiFS response functions plotted respectively by squares, circlesand triangles.

TSM measurements by S ̅. The residual or error sum of squares, SSE,and the coefficient of multiple determination, R2, are definedrespectively by:

SSE = ∑N

i=1ðSi−

⌢SiÞ2 andR2 = 1−SSE = ∑

N

i=1ðSi−

�S Þ2: ð16Þ

R2 indicates the fraction of variance in the observations set (Si) that isexplained by the regression model and may vary from 0 to 1. If R2=1then the curve fits all data points. The coefficient A that minimizesSSE, corresponding to the highest R2, is selected for our algorithmcalibration. However, since the variance of Si increases with increasingρwi , the log-transformed TSM data are more likely to stabilize thisvariance as indicated in Kleinbaum et al. (1998) (its section“Transformations” page 220). As reported by Eisma and Kalf (1979)TSM are log-normally distributed for the Southern North Sea and theNorth Sea area. Hence, SSE and R2 defined in Eq. (16) are rewritten toexpress the log-transformation:

SSElog = ∑N

i=1½logðSiÞ− logðS⌢iÞ�2

R2 = 1− SSElog

∑N

i=1logðSiÞ−∑

N

j=1logðSjÞ=N

" #2

8>>>>>>><>>>>>>>:

ð17Þ

Since the contribution of certain couples (TSM, ρwi ) hugely increasesthe SSElog value, it is necessary to study the distribution of residuals todetermine which observations are to be considered as “outliers” andshould be removed from the dataset. To objectively identify outliers thestatistical jackknife residual defined by Kleinbaum et al. (1998) (inchapter 12: “Regression Diagnostics”) is examined for each observation(see WA3). 4 outliers were then rejected leading to 68 observations asinput to the regression analysis. As an example, Fig. 3 shows as dashedlines the TSM models for 6 MERIS bands, using 72 reflectance and TSMdata and as solid lineswhen using 68 data. The effect of outlier removal issignificant in the low TSM range with an improvement of the Rρ

2

coefficient of 5% to 8%. Highly scattered points around the regressioncurves of models at longer wavelengths λ≥760 nm are noticeable forTSM values less than 10 gm−3, mainly due to the lower precision inmeasurement of low reflectances. This regression analysis is applied bothfor individual bands specific to MERIS, MODIS and SeaWiFS and for ageneric sensor with any wavelength from 520 nm to 885 nm at 2.5 nmintervals.

3.4. Validation data set

After calibration (Section 4), the reflectance dataset of 29 stationswith the corresponding measurements of TSM used for validation(Section 5) is further subsetted and used as follows:

a) after removal of 8 measurements in suboptimal sun conditions, 21seaborne reflectances, measured under cloud cover being 0/8, areused as validation data set in Section 5.1,

b) satellite reflectance measurements are used as validation data inSection 5.2with thematchup subsets of 10 (MERIS) and 24 (MODIS)out of 29 seaborne measurements. With respect to method a) thisadds errors in TSM retrieval due to atmospheric correction anddifferent satellite and in situ sampling scales. 10MERIS images wereacquired concurrently with seaborne measurements in the BelgianandNorthSeawaters from2002 to2006, andprocessedwith the2ndreprocessingversion2005 (MERISQualityWorkingGroup, 2005). 24MODIS matchups (acquired within one hour of satellite overpass)were collectedandprocessedwith theSeaDAS5.2 softwareusing theturbid water atmospheric correction option of Ruddick et al. (2000).Only 6 SeaWiFSmatchups couldbe collected from theperiod of 2001

Table 3The distribution of in situ measurements of TSM used for the calibration and CHL, sky and sea condition parameters during field measurement (see text for details).

Parameter Mean Standard deviation Minimum Percentile 50% Percentile 75% Percentile 90% Maximum

TSM (g−3) 26.2 23.4 1.2 20.5 36.2 57.0 110.3CHL (µg/l) 10.0 9.1 0.2 8.0 13.6 18.1 52.3Wind (m/s) 5.4 3.5 0.0 4.5 7.3 9.5 16.2Cloud cover (/8) 4 3 0 3 8 8 8Lsky (mW/m2/nm/sr) 32.3 29.0 4.7 19.4 44.5 67.7 129.8Lsky/Ed (100/sr) 0.1 0.1 0 0 0.2 0.3 0.4Water depth (m) 15.4 9.3 0.9 13 16.9 28.8 43.5Wave height (m) 0.3 0.3 0 0.2 0.4 0.7 2.0


to 2004 over the Belgianwaters, and so were not used for validationpurposes.

Water-leaving reflectances are extracted around matchup stations(using a 3×3 and 5×5 box respectively for MERIS and MODIS data)and TSM estimates are then derived using Eq. (11).

At each band of each of these sensors, the seaborne TSM and sensor-retrieved TSM (respectively denoted by Si

meas and Sisens, i=1, N)

are used to compute the root-mean-square-error (RMSE), correlationin the logarithmic space, r, and mean relative error, εr, defined by

εr = 1N ∑

N

i=1

jSmeasi −Ssensi jSmeasi

. Analysis of TSM product errors is addressed

in term of uncertainties of reflectance measurements, of the validity ofcalibration assumptions and of atmospheric correction errors.

4. Results of calibration

Table 4 lists the computed Aρ, Bρ and Rρ2 coefficients for all

wavelengths from 520 nm to 885 nm every 2.5 nm. The best curvefitting coefficient Rρ2=82.9% is obtained in the NIR spectral range at

Fig. 3. Non-linear regression curve for MERIS at 6 selected bands (560, 620, 681, 708,760 and 865 nm), superimposed on the scatter plot of 72 TSM versus ρw data (squares).The dashed lines show the regression analysis curves resulting from the use of the 72observations and the solid lines come from regression analysis applied to 68observations (dropping out the 4 outliers drawn as filled symbols).

710 nm as shown in Fig. 3. Fig. 4 shows the Aρ (λ) spectrumnormalized at λ=780 nm. Strikingly this spectrum has the sameshape as the pure water absorption, aw (λ), in the red and NIR range.Aρ=A/γ being proportional to the ratio of non-particulate absorptionto the specific particulate backscatter (6), the good match betweenthe normalized Aρ and aw suggests that: a) the contribution of CDOMabsorption is indeed negligible in this spectral range, b) the specificbackscatter of particles and the term γ = πℜf ′=Q are spectrally quiteflat. The fact that laboratory measurements of pure water absorptioncan be reproduced here by measuring only seaborne reflectance andTSM and using the theoretical model (11) is a very strong argumentsupporting this algorithm.

One significant difference between the normalized Aρ and awspectra is seen at 670 nm where chlorophyll a absorption enhancesthe particulate absorption. A second difference is seen near 762 nmwhere the seaborne reflectance measurements are known to be lessreliable because of narrow band atmospheric oxygen absorption.Except within these special spectral ranges and provided that CDOMabsorption is negligible, the Eqs. (6) and (13) combined with theresult Aρ

Aρ780 nm ≈ awa780 nmw

allow the specific backscatter coefficient in thered to NIR spectral range, to be estimated as follows:

bbp*red;NIR =

anpγAρ ≈

a780w

γAρ780 ð18Þ

Using aw780=2.69 m−1, this gives bbp⁎ red,NIR≈6.83 10−3 m2g−1.

The following section presents the errors in TSM retrieval due toassumption of non-variability of bbp⁎ to assess how inaccurate thiscalibrated algorithm may be when applied to different water types.

4.1. Regionality

Calibration of an algorithm with a dataset from a specific regionobviously raises the question of generality: can the same algorithm beapplied to a different region where suspended particulate matter mayhave a very different composition (refractive index, density) or sizedistribution? Is it possible to have a general, global algorithm forretrieval of marine properties such as total suspended matter or is itnecessary to have local algorithms tailored to specific regions/seasons? Such questions of algorithm generality/regionality havestimulated a number of efforts to measure specific inherent opticalproperties (SIOP) and characterise their variability, e.g. Babin et al.(2003a,b) and Berthon et al. (2008). If this SIOP variability can beparameterised as function of retrievable parameters (e.g. TSM,chlorophyll a) or of other known parameters (e.g. salinity, temper-ature, water depth, etc.) then regional improvements of generalalgorithms could be achieved.

The detailed analysis of the algorithm assumptions given in I.1-4(WA1) indicates the circumstances in which the present algorithmmay lack generality or require region-specific adaptation. Thistheoretical analysis shows low sensitivity to factors such as mass-specific particulate absorption — section I.3 in WA1. Similarly there islow sensitivity to coloured dissolved organic matter absorption. As an

Table 4Aρ (gm−3), Bρ (gm−3) and Rρ

2 coefficients for a generic narrow band TSM algorithm for wavelengths ranging from 520 nm to 885 nm.

λ (nm) Aρ Bρ Rρ2 % λ (nm) Aρ Bρ Rρ

2 % λ (nm) Aρ Bρ Rρ2 % λ (nm) Aρ Bρ Rρ

2 %

600.0 155.61 2.87 68.6 700.0 445.11 1.13 82.5 800.0 1596.41 1.58 77.5602.5 162.61 2.90 70.0 702.5 468.13 1.15 82.6 802.5 1573.61 1.61 77.7605.0 174.82 2.83 71.1 705.0 493.65 1.16 82.8 805.0 1562.74 1.63 77.8607.5 184.42 2.69 71.9 707.5 526.68 1.15 82.9 807.5 1552.21 1.64 77.7610.0 191.73 2.66 72.4 710.0 561.94 1.23 82.9 810.0 1548.63 1.65 77.7612.5 198.36 2.54 72.9 712.5 606.12 1.19 82.9 812.5 1552.99 1.65 77.8615.0 203.69 2.53 73.2 715.0 649.78 1.25 82.7 815.0 1570.74 1.64 77.6617.5 208.81 2.52 73.6 717.5 708.16 1.17 82.5 817.5 1613.05 1.59 77.7

520.0 167.69 2.83 53.8 620.0 213.55 2.42 73.9 720.0 774.27 1.17 82.2 820.0 1664.01 1.65 77.3522.5 161.48 2.87 53.8 622.5 217.73 2.42 74.2 722.5 861.11 1.16 82.0 822.5 1763.64 1.58 76.6525.0 162.17 2.72 53.8 625.0 221.78 2.42 74.4 725.0 966.39 1.12 81.7 825.0 1867.44 1.60 75.9527.5 155.27 2.89 53.7 627.5 225.15 2.42 74.7 727.5 1086.85 1.07 81.2 827.5 1996.74 1.60 74.7530.0 148.37 2.97 53.7 630.0 229.45 2.32 74.9 730.0 1229.15 1.02 80.4 830.0 2125.12 1.72 73.4532.5 147.68 2.87 53.7 632.5 234.85 2.30 75.3 732.5 1374.86 0.98 79.5 832.5 2267.88 1.71 72.1535.0 140.09 3.07 53.7 635.0 239.94 2.29 75.6 735.0 1491.46 1.06 78.5 835.0 2379.77 1.80 70.8537.5 138.71 2.99 53.7 637.5 245.08 2.28 75.9 737.5 1592.19 1.09 77.6 837.5 2481.42 1.83 69.7540.0 130.43 3.21 53.7 640.0 249.96 2.26 76.2 740.0 1664.72 1.14 76.7 840.0 2543.56 1.92 68.5542.5 129.74 3.11 53.7 642.5 254.60 2.24 76.5 742.5 1725.83 1.12 76.1 842.5 2601.28 1.93 67.7545.0 122.15 3.32 53.7 645.0 253.51 2.32 76.7 745.0 1754.77 1.22 75.6 845.0 2646.87 2.00 67.0547.5 121.46 3.23 53.9 647.5 260.09 2.20 77.0 747.5 1781.18 1.24 75.3 847.5 2697.96 2.00 66.4550.0 120.77 3.14 53.9 650.0 268.95 2.17 77.2 750.0 1804.05 1.27 75.0 850.0 2719.82 2.08 65.8552.5 113.17 3.44 54.0 652.5 280.36 2.14 77.6 752.5 1815.54 1.27 74.5 852.5 2780.02 2.03 65.4555.0 111.79 3.35 53.9 655.0 289.29 2.10 77.9 755.0 1822.38 1.28 74.3 855.0 2814.06 2.12 64.8557.5 104.89 3.60 53.8 657.5 307.78 1.96 78.2 757.5 1789.22 1.30 74.6 857.5 2870.40 2.11 64.2560.0 104.20 3.47 53.7 660.0 327.84 1.91 78.5 760.0 1750.72 1.34 74.7 860.0 2905.11 2.21 63.8562.5 97.30 3.74 53.5 662.5 342.56 1.84 78.7 762.5 1736.96 1.39 74.9 862.5 2924.54 2.28 63.1565.0 97.99 3.62 53.4 665.0 355.85 1.74 78.9 765.0 1795.66 1.38 75.5 865.0 2971.93 2.30 62.7567.5 91.78 3.92 53.3 667.5 374.11 1.61 79.1 767.5 1851.11 1.41 75.3 867.5 3016.31 2.32 61.9570.0 93.16 3.74 53.3 670.0 384.11 1.44 79.4 770.0 1894.33 1.37 75.3 870.0 3050.06 2.40 61.2572.5 89.02 3.97 53.5 672.5 391.38 1.26 79.7 772.5 1889.64 1.43 75.3 872.5 3104.12 2.45 60.7575.0 93.16 3.72 54.1 675.0 401.61 1.09 80.0 775.0 1866.93 1.47 75.1 875.0 3161.90 2.46 60.0577.5 93.16 3.78 55.2 677.5 403.49 1.04 80.4 777.5 1834.05 1.53 75.2 877.5 3199.96 2.58 59.1580.0 95.92 3.74 56.7 680.0 408.84 0.82 80.7 780.0 1802.62 1.57 75.3 880.0 3251.89 2.65 58.4582.5 98.68 3.73 57.8 682.5 400.68 0.87 81.0 782.5 1787.56 1.50 75.5 882.5 3318.38 2.65 57.6585.0 80.74 4.34 54.3 685.0 396.87 0.84 81.3 785.0 1760.19 1.54 75.7 885.0 3388.53 2.68 56.6587.5 84.19 4.37 56.6 687.5 394.57 0.85 81.5 787.5 1724.54 1.59 76.0590.0 93.85 4.08 59.1 690.0 394.20 0.90 81.7 790.0 1701.46 1.54 76.3592.5 109.72 3.58 61.9 692.5 402.74 0.96 81.9 792.5 1667.30 1.58 76.6595.0 124.91 3.26 64.5 695.0 414.72 1.02 82.1 795.0 1646.43 1.53 76.9597.5 138.02 3.14 66.8 697.5 430.21 1.08 82.3 797.5 1619.05 1.56 77.3


example, for part of the calibration dataset region, the data of Astorecaet al. (2006) suggests that CDOM absorption at 443 nm is less than 1/m and the analysis of section I.2 in WA1 shows that such CDOMabsorption will give an error of less than 6% for wavelengths higherthan 700 nm. This is reinforced by the striking practical demonstra-tion (Fig. 4) that the pure water absorption spectrum can be deducedfrom the algorithm calibration coefficient just from measurements ofreflectance and TSM. The theoretical basis of the present approach forretrieving particulate backscatter coefficient from water-leaving re-flectance is thus quite general. As shown in I.1 (WA1) issues ofregionality of the TSM retrieval will become critical when thealgorithm is applied to situations where the TSM-specific particulate

Fig. 4. The Aρ calibration coefficient for wavelengths ranging from 600 nm to 885 nmand normalized at 780 nm (bold line) superimposed to the pure water absorptionnormalized at 780 nm using data from Kou et al. (1993) for λN751 nm (light line) anddata from Buiteveld et al. (1994) for 500 nmbλb800 nm (dashed line).

backscatter coefficient is different from the effective average bb⁎ ofwaters of the calibration dataset.

For the case of mass-specific particulate backscatter there are a fewmultispectral datasets available where backscatter is deduced fromscattering at one or more angles. Loisel et al. (2009) report bb⁎532nm

values of 0.0065±0.0025 m2g−1 in the coastal waters of FrenchGuiana. Snyder et al. (2008) report mass-specific backscatter at630 nm of up to about 0.025 m2g−1 for particulate organic matter atthe LEO-15 site but highly variable values at other sites down to lessthan 0.001 m2g−1 with large but not systematic differences betweenthe organic and inorganic fractions. Considerable multispectral data isavailable for TSM-specific particulate scattering. In a large dataset fora variety of European waters Babin et al. (2003a) found bp⁎

555nm of


2 coefficients for the MERIS-TSM algorithm for bands560 nm to 881 nm.

MERIS band λ (nm) Aρ Bρ Rρ2%

560 104.66 3.48 53.7620 212.13 2.47 73.8665 352.61 1.74 78.9681 406.89 0.83 80.8708 537.05 1.15 82.9753 1810.76 1.27 74.6760 1762.97 1.30 74.7778 1827.06 1.50 75.3865 2972.34 2.27 62.7885 3365.00 2.70 56.7


2 coefficients for the MODIS-TSM algorithm for bands551 nm to 869 nm.

MODIS band λ (nm) Aρ Bρ Rρ2%

551 122.01 3.22 53.9555 112.18 3.34 53.9645 258.85 2.21 76.8667 362.09 1.65 79.1678 400.75 1.02 80.4748 1768.59 1.21 75.4858 2846.89 2.15 64.3869 3031.49 2.29 61.9

Fig. 5. TSM (gm−3) derived from seaborne reflectance versus in situ TSM (gm−3),retrieved from reflectance using MERIS bands centered at 665 (with Aρ and Bρ given inTable 5), 681 nm, 708 and 753 nm.


similar average value (0.42–0.56 m2g−1) for each of the case 2 regionsconsidered (Mediterranean, Baltic, Channel, and North Sea). An averagebbp/bp ratio of 0.019 from Petzold (1972) would imply bbp⁎

555nm ofbetween 0.008 and 0.011 m2g−1 from thesemeasurements. However,within each region very large variability (geometric standarddeviation of 2 implying a typical variability of a factor 0.5–2.0 aboutthe mean) was found. Finally variability of mass-specific particulatebackscatter is well known for the simpler single-wavelength OBS(Optical Backscatter Sensor) instruments typically used in sedimenttransport studies and it is known that variability of particle size intime even for a single location can be significant, as underlined byDowning (2006).

These measurements for other regions suggest that there is likelyto be at least as much variability of bbp⁎ within any single region asthere is variability between different geographical regions. The“region” considered in the calibration dataset here may seem smallgeographically but does contain already a high diversity of particlecompositions and sizes including resuspended mineral particles aswell as high chlorophyll a phytoplankton blooms — see Section 3.2.The quest for regional tailoring of globally-applicable algorithms hasled Doerffer (2006) to propose that the standard MERIS neuralnetwork-based TSM product could be regionally adapted if reliableestimates of bp⁎ are available for a region. A similar approach isproposed here for application of this algorithm to other regions. Ifreliable estimates of bbp⁎ are available then these can be used to scalethe coefficients provided by Table 3, taking advantage of thetheoretical framework and functional form for TSM retrieval devel-oped here.

Finally, calibration of Cρ is made using published values for SIOPs,which may not be valid for other regions. However, provided theasymptotic limit of the algorithm is avoided the results are not at allsensitive to Cρ. Since the reflectance model also becomes unreliablenear the asymptotic limit, it is recommended that the wavelength forretrieval be optimised to avoid the high reflectance regime and thusavoid all such problems.

4.2. Satellite TSM algorithms

Tables 5–7 show the model coefficients respectively for MERIS,MODIS and SeaWiFS bands. The higher values of Rρ2 and lower valuesof B found in Table 5 and the generally lower dispersion of dataaround the best-fit curves for 681 nm and 708 nm in Fig. 3 suggest


2 coefficients for the SeaWiFS TSM algorithm for bands555 nm to 865 nm.

SeaWiFS band λ (nm) Aρ Bρ Rρ2%

555 111.80 3.34 53.9670 373.79 1.47 79.4765 1824.86 1.34 75.1865 2983.56 2.22 62.7

that these wavelengths are best-suited for TSM retrieval for thisdataset. The reasons may be explained as follows:

1. at shorter wavelengths higher variability of anp is likely to be aproblem (especially because of CDOM absorption — see Section I.2in WA1), giving greater scatter of data and lower Rρ2.

2. variability of TSM-specific particulate absorption may also be asource of model error (see the discussion in Section I.3 in WA1) atshorter wavelengths.

3. The optical saturation at higher TSM and the associated theoreticalmodel uncertainty is also problematic especially for λb600 nm (e.g.560 nmmodel in Fig. 3). Such saturation has also been observed forTSMN30 gm−3 by Eleveld et al. (2008) using SeaWiFS band 555 nm.

4. At wavelengths longer than 710 nm the accurate measurement ofreflectance becomes more difficult — see the uncertainty analysisin Web Appendix 2 of Ruddick et al. (2006).

It is interesting to note that a similar conclusion regarding optimalwavelength was drawn by Ouillon et al. (2008) who tested empiricalalgorithms using a set of in situ reflectances and turbidity data collectedin different water types in New Caledonia, Cuba and Laucala Bay (Fiji).

5. Validation

5.1. TSM retrieved from seaborne reflectance measurements

Fig. 5 shows scatter plots of the 21 TSM retrieved from seabornereflectances versus seaborne TSM measurements. Corresponding statis-tics are given in Table 8. Reflectances are taken at MERIS bands 665 nm,708 nm and 753 nm. Relative errors range from 33% at 753 nm to 46% at620 nm (Table 8). At wavelengths λN708 nm, the algorithm showslower relative errors εr≤36% and RMSE about 10 gm−3 to 12 gm−3.2% to 7% of relative errors comes from errors in TSM estimates in thelower range (TSMb10 gm−3) at longer wavelengths λN708 nm. This ismainly due to the higher relative errors occurring for low reflectancemeasurement, in clearer waters, at longer wavelengths.

5.2. Satellite retrieved TSM

Fig. 6 presents the scatterplot of MERIS-derived TSM fromreflectances at bands a) 665 nm and b) 708 nm versus seabornemeasured TSM showing also the linear regression line (solid line),with related statistics reported in Table 9. The algorithm for the

Table 8RMSE, εr and r2 of TSM estimates using seaborne reflectance taken at MERIS bands and using (14) with Aρ and Bρ given in Table 5 (grey numbers), and setting Bρ=0. The slope andintercept of the regression line between in situ TSM and seaborne reflectance-derived TSM, shown as solid line in left Fig. 5, are also listed.

λ (nm) RMSE gm−3 εr% all TSM εr% TSMN10 gm−3 r2% Slope Intercept

620 15.51 14.92 46.1 41.9 53.9 50.1 89.1 88.7 0.94 1.15 0.34 −0.51665 12.79 12.42 42.1 39.6 50.0 47.4 89.8 89.3 0.96 1.12 0.23 −0.38681 12.85 12.65 41.2 39.4 49.6 48.3 90.0 89.9 0.99 1.06 0.12 −0.16708 13.44 13.21 38.2 35.5 44.3 42.6 89.9 89.6 0.99 1.09 0.11 −0.29753 12.15 12.21 33.0 31.7 35.1 34.6 88.1 87.8 0.89 0.98 0.30 −0.09778 12.11 12.15 33.4 32.0 35.2 34.6 88.4 88.0 0.90 1.02 0.29 −0.20865 11.15 11.66 34.6 32.7 35.6 34.6 86.4 85.7 0.77 0.92 0.64 −0.01885 11.05 11.84 35.9 33.3 36.1 35.4 85.7 84.8 0.71 0.88 0.80 0.06


708 nm band exhibits the highest correlation factor, r2=93.4%.MERIS standard TSM product generated by neural network inversionof the full water-leaving reflectance spectrum of Schiller and Doerffer(1999) versus seaborne TSM matchups in Fig. 7a shows a very similarscatter plot to that of the single band algorithm using MERISreflectance at 665 nm (Fig. 6a). Fig. 7b confirms this high correlation(up to 98.8%). However the data set is too small to be conclusive.

The TSM algorithm applied to MODIS imagery showed goodcorrelation up to 80.9% (Table 10), between band 667 nmderived TSMand in situ TSM (Fig. 8) and low relative errors 37%. This is mainly dueto a better atmospheric correction of water-leaving reflectance atband 667 nm than at longer wavelengths (the relative error inreflectance retrieval is 29% at 667 nm against 44% at 748 nm and thehighest correlation between seaborne and satellite reflectances is93.24% found at band 667 nm). Moreover, an error in satellitereflectance retrieval, due to an error in the estimation of the aerosolpath reflectance in the near infrared, ρamNIR, gives a proportional error inTSM estimates and errors less than 1 mg−3 from band 710 nm andabout 2.7 mg−3 at longer wavelengths, for each error of ρamNIR=0.005(see WA1, Section II).

The MODIS-derived total backscattering coefficient at band667 nm, denoted by bb

667, was computed using three algorithmsimplemented in the SeaDAS version 5.2 software: the semi-analyticalalgorithms of Carder et al. (2003), the quasi-analytical model of Leeet al. (2005) and the Garver–Siegel–Maritorena (GSM01) semi-analytical algorithm described in Maritorena et al. (2002). While allthree algorithms give a reasonably linear fit to the TSM derived usingthe present approach, the slope of the fit which corresponds to thespecific backscattering coefficient is noticeably different (Fig. 9).Comparison with MODIS-derived TSM concentrations exhibits thehigh correlations 90.7%, 85.4% and 83.1% respectively with Carder, Leeand GSM01 methods. The specific backscattering coefficient, comput-ed as the ratio of these backscatter coefficients to the corresponding insitu TSM concentrations shows average values of bb⁎

667=0.0041,0.0086 and 0.0096 m2g−1 from the respective algorithms above. TheGSM01 algorithm gave negative backscatter values at 2 stations andhigher specific backscattering coefficient. The values above are withinthe range of backscattering coefficients found in literature, derived

Fig. 6. MERIS-TSM (gm−3) versus in situ TSM(gm−3), retrieved from reflectance usinga) single band 665 nm and b) 708 nm algorithm, applying (14), with Aρ and Bρ given inTable 5.

from values of particle scattering and the backscatter slope, forexample bb⁎

665=0.009 m2g−1 derived from Gohin et al. (2005)bb⁎

555=0.015 m2g−1 interpolated at 665 nm, using Babin et al.(2003a), Bowers and Binding (2006) gives bb⁎665=0.0058 m2g−1.

6. TSM time series

Fig. 10a and b shows TSM products extracted from satellite imagesover the two locations in the Belgian waters indicated in Fig. 1. Theseproducts are:

– TSM standard product from MERIS images taken from 2003 to2006,

– TSM retrieved from MODIS bands 667 nm and 748 nm, from June2002 to end 2006,

– TSM from SeaWiFS bands 670 nm and 765 nm, with images fromJanuary 2002 to end 2004.

MODIS and SeaWiFS reflectances were converted into TSM usingEq. (12) with Aρ coefficients respectively listed in Tables 6 and 7 andCρ given in Table 2. The Bρ coefficients of Table 2 are specific to themeasurement errors of the reflectance and TSM data used forcalibration. Since there is no reason to suppose that the satellite-derived reflectances will have similar errors to the in situ reflectancemeasurements, Bρ is set to zero for the satellite applications.

Although different atmospheric correction and TSM retrievalalgorithms are used for each sensor, they present strong similaritiesin the time variations of TSM. Both figures show the seasonal variationof TSM with good agreement between the 3 sensors. High TSM valuesare encountered during October–February, due to strong windscausing more re-suspension. The spatial distribution of TSM is alsovery similar: similar TSM amplitudes are retrieved from the 3 sensorswith equivalent gradient between near-shore (station 230) and off-shore (station 330) locations.

7. TSM maps from MERIS, MODIS and SeaWiFS

An example of the TSM algorithm application to 3 different sensorsis presented in this section. Fig. 11 shows TSM maps generated fromMERIS, MODIS and SeaWiFS image taken on the 9th of September

Table 9RMSE, εr and r2 of TSM estimates using MERIS reflectance and (14), with Aρ and Bρ

given in Table 5. The slope and intercept of regression line between in situ TSM andMERIS-TSM, shown as solid line in left Fig. 6, are also listed.

λ (nm) RMSE gm−3 εr% r2% Slope Intercept

620 6.24 87.8 89.3 0.43 1.18665 6.56 70.7 88.8 0.49 0.97681 6.46 49.8 92.1 0.60 0.67708 6.35 54.0 93.4 0.60 0.69753 7.05 65.4 92.1 0.52 0.83778 6.56 65.0 93.2 0.53 0.86865 6.70 84.2 92.2 0.44 1.10885 6.24 87.8 89.3 0.43 1.18

http://dx.doi.org/10.1029/2004JC002275

http://dx.doi.org/10.1029/2004JC002275

Fig. 8. MODIS-derived TSM(gm−3), using reflectances at a) band 667 nm and b)748 nm versus seaborne TSM measurements at 24 locations.

Fig. 9.MODIS retrieved total backscattering at band 667 nm versus TSM (gm−3) over 21validation stations, using the 3 methods GSM01, Carder and Lee (see text for details).Regression lines for the different products are plotted following the same colour code.(For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

Fig. 7. MERIS standard TSM (gm−3) versus a) seaborne measurements of TSM (gm−3)at 10 locations and b) versus TSM (gm−3) derived from ρw at band 665 nm.


2004, respectively at 10:34, 12:54 and 13:00 UTC. The three productswere derived using respectively the reflectance at band681 nm, 667 nmand 670 nm. They show the same patterns of high TSM (N30 gm−3) inthe Belgian coastal area and the eastern English coastal waters near theThames estuary. They also show the very clear waters in the EnglishChannel. In Fig. 12 theMERIS standard TSMproduct (Schiller &Doerffer,1999), is presented for the same day. It is very similar to the one bandTSM product (this was indicated from the 10 MERIS matchups inSection 5.2), with a correlation coefficient of 93.95%. The scatter plot inFig. 12 indicates that, above the range [0–1 gm−3], these two productsare quite equivalent despite the very different inversion technique(single band versus full spectrum). For low concentrations (b1 gm−3)the relative difference between the single band and multispectralproducts becomes significant. In this range the single band approachmay be less appropriate (especially in phytoplankton-dominatedwaters) and a detection limit of 1 gm−3 is suggested for this method.

8. Discussion

A bio-optical algorithm relating TSM concentrations to reflectanceand ωb

′ in turbid waters has been established here based on use of asingle band in the red to NIR spectral range. This generic algorithm,applicable to any ocean colour sensor, is applied here to MERIS,SeaWiFS and MODIS bands. The reflectance-based algorithm wascalibrated using seaborne TSM measurements and reflectances andresults of this calibration were reported here. An equivalent ωb′-basedalgorithm family was also calibrated by converting reflectances to ωb

′,taking into account the sun and viewing angles via the bidirectionalreflectance model of Park and Ruddick (2005). Results of thiscalibration are reported in WA2. The ωb′-based algorithm gave similarperformance to the reflectance-based algorithm (results not shown).

The hyperspectral calibration allowed use of the optimal spectralrange of the reflectance or ωb′ for TSM retrieval, which is locatedbetween 680 nm and 730 nm for the concentrations encounteredhere. The calibration coefficient Aρ (λ) is shown to be strongly relatedto the pure water absorption spectrum except around the chlorophyllabsorption peak. It is striking that laboratory measurements of thepure water absorption coefficient, aw (λ), can be reproduced fromseaborne measurements of reflectance and TSM alone, with atheoretical model providing optical closure. The backscattering

Table 10RMSE, ε and r2 of TSM estimates using MODIS reflectance and (14), with Aρ and Bρ

given in Table 6. The slope and intercept of regression line between in situ TSM andMODIS-TSM, shown as solid line in right Fig. 8 are also listed.

λ (nm) RMSE g−3 εr% r2% Slope Intercept

667 10.98 37.0 80.9 0.91 −0.02678 11.23 38.9 80.2 0.95 −0.13748 12.01 40.7 78.1 0.90 −0.10869 12.74 36.0 79.5 0.77 0.21

coefficient estimated from the spectra of aw (λ), and the calibratedAρ (λ), bbp⁎ =0.0068 m2g−1 in the red and NIR, is within the range ofthe values of bbp⁎ reported so far in literature.

This algorithm is based on the assumption of little or no variabilityof bbp⁎ , which should be appropriate for areas with a horizontally

Fig. 10. TSM time series retrieved from MERIS (green triangles), MODIS (red squares)and SeaWiFS (blue diamonds) imageries taken between 2002 and 2006 for a) station230 and b) station 330. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

Fig. 11. TSM (gm−3) maps derived from a) MERIS, b) SeaWiFS and c) MODIS imagestaken on September 9th 2004 and respectively retrieved using bands 681 nm, 670 nmand 667 nm. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

Fig. 12. Top:MERIS standardTSM(gm−3)mapof September9th2003,bottom:TSM(gm−3)fromMERIS using one band (681 nm) TSM algorithm versus MERIS standard TSM.


homogeneous water composition. The error in TSM estimates due todifferent CDOMabsorptionwas theoretically analysed inWA1 (SectionsA1-4) and is less than 6% using the reflectance around 700 nm. Incontrast with simple Mie theory, a recent study by Boss et al. (2009)shows surprisingly little variability of bbp⁎ with suspended matter sizedistribution and composition.

The calibrated coefficients Aρ and Bρ of Eq. (14), given in Table 4,may be used for any ocean colour sensor with small bandwidths.

The calibrated models are most suitable for moderately turbidwaters (TSMN10 gm−3), where relative errors are less than 30% inTSM estimates, as concluded from the validation of seabornereflectance-derived TSM versus in situ TSM. About 33% relative errorwere found for MERIS-derived TSM in the range TSMN2 gm−3 usingthe algorithm developed here. Higher relative errors for clearer

waters, found from all sensors are thought to be related to the highermeasurement uncertainties for in situ TSM at low concentrations.MODIS-derived TSM exhibits about 40% relative errors, explained bythe additional atmospheric correction error in the satellite reflectanceproduct.

Time series of TSM from MERIS standard TSM and MODIS andSeaWiFS derived TSM (using the single band algorithm) show a goodagreement between satellites products, despite the use of differentatmospheric correction and TSM algorithms.

Although probably inferior to a multispectral inversion approachin low TSM (b1 gm−3) phytoplankton-dominated waters, the presentstudy has the advantage of providing a coherent and robust basis formultisensor mapping of TSM from an incredible variety of satelliteremote sensors.

While the first examples given here are focused on high quality,polar-orbiting, medium resolution ocean colour sensors (SeaWiFS,MODIS, and MERIS), the approach is limited essentially by only theneed for a single atmospherically-corrected red band. Level 3 TSMproducts such as climatology, merged data and long time series ofTSM from different ocean colour missions could benefit from thisunified method of TSM retrieval following IOCCG (2007) recommen-dations and as concluded by Morel et al. (2007). Thus, in amultisensor context, it will be possible to combine the quality ofthese ocean colour sensors with the long time series available fromsensors such as AVHRR, the higher spatial resolution of SPOT andASTER, and the higher temporal resolution of geostationary sensorssuch as SEVIRI e.g. Neukermans et al. (2009).The potential for verysignificant progress in the understanding of TSM distributionsand dynamics at scales down to 15 min and about 10 m is trulyremarkable.


Acknowledgments

This study was funded by the STEREO Programme of the BelgianFederal Science Policy Office in the framework of the BELCOLOUR (SR/00/003) and BELCOLOUR-2 (SR/00/104). The MUMM's Chemistry labis thanked for analysing and providing in situ TSM data. Barbara VanMol and the captain and crew of the Research Vessel Belgica arethanked for their assistance with seaborne measurements. HubertLoisel and Emmanuel Boss are thanked for the discussions on thevariability of the particulate specific backscatter. The NASA OceanColor Product Distribution and SeaDAS teams at GSFC are acknowl-edged for providing and distributing MODIS products, and ESA forMERIS data. Three anonymous reviewers are acknowledged for theircomments on a first version of this paper.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.rse.2009.11.022.

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