biogeo-optics: particle optical properties and the partitioning of the spectral scattering...

Biogeo-optics: particle optical properties and thepartitioning of the spectral scattering coefficient

of ocean waters

Robert H. Stavn1,* and Scott J. Richter2

1Department of Biology, The University of North Carolina at Greensboro, Greensboro, North Carolina 27402, USA2Department of Mathematics and Statistics, The University of North Carolina at Greensboro,

Greensboro, North Carolina 27402, USA

*Corresponding author: [email protected]

Received 1 October 2007; revised 22 March 2008; accepted 14 April 2008;posted 14 April 2008 (Doc. ID 87627); published 7 May 2008

We propose a direct method of partitioning the particulate spectral scattering coefficient of the marinehydrosol based on the concurrent determination of the concentrations of particulate mineral and organicmatter (the total mass of optically active scattering material exclusive of water) with the particulatespectral scattering coefficient. For this we derive a Model II multiple linear regression model. The multi-ple linear regression of the particulate spectral scattering coefficient against the independent variables,the concentrations of particulate inorganic matter and particulate organic matter, yields their mass-specific spectral scattering cross sections. The mass-specific spectral scattering cross section is simplythe particle scattering cross section normalized to the particle mass, a fundamental optical efficiencyparameter for the attenuation of electromagnetic radiation [Absorption and Scattering of Light by SmallParticles, (Wiley-Interscience, 1983), pp. 80–81, 289]. It is possible to infer the optical properties of thesuspended matter from the mass-specific spectral scattering cross sections. From these cross sections wepartition the particulate spectral scattering coefficient into its major components. © 2008 OpticalSociety of America

OCIS codes: 010.4450, 010.4458, 290.5850, 280.1415, 280.4991, 010.4455.

1. Introduction

The scattering coefficient of the marine hydrosol isboth the source of remote sensing information aboutthe ocean and the basis for mechanistic inversion al-gorithms. Such algorithms invert the remote sensingreflectance to retrieve concentrations of materials ofinterest: suspended sediments, chlorophyll, organicmatter, and suspended organic detritus [1]. Theabsorption coefficient of the marine hydrosol is rou-tinely coupled with the scattering coefficient to gen-erate such remote sensing inversion algorithms [2].The absorption coefficient is partitioned by variousmethods into absorption due to phytoplankton,yellow substance, and organic detritus to give more

information about the materials dissolved and sus-pended in the marine hydrosol [3,4]. It is thus rou-tine to partition the hydrosol absorption coefficientin ocean optics but not the scattering and backscat-tering coefficients.

The hydrosol scattering coefficient is occasionallypartitioned into a molecular water component anda vaguely defined category called “suspended parti-cles.” The problem with this approach is that sus-pended particulate matter can be broadly classifiedinto inorganic matter (often terrigenous) and organicmatter (some terrigenous, but usually autochtho-nous). The two broad categories of suspendedparticulates have different indices of refraction,essentially nonoverlapping according to availabletheoretical calculations [5], and therefore rather dif-ferent scattering coefficients. There are, however,

0003-6935/08/142660-20$15.00/0© 2008 Optical Society of America

2660 APPLIED OPTICS / Vol. 47, No. 14 / 10 May 2008

very few data on the refractive index of nonliving or-ganic particles. The differing scattering coefficientsgenerate rather different effects on the remote sen-sing reflectance because the mineral matter, withits relatively high index of refraction, dominatesthe optical scattering process. This factor is most pro-nounced in coastal ocean waters and the program weare developing in biogeo-optics will make contribu-tions to coastal ocean remote sensing algorithmsby the accurate partitioning of the hydrosol scatter-ing coefficient. As we get further away from thecoastline and approach the continental shelf break,the mineral matter will tend to become seasonal inits effects [6,7].The biogeo-optical approach, though most impor-

tant for the coastal ocean, can also be a factor in theopen ocean, usually assumed bio-optical in nature,when dust storms deposit mineral matter [8–10]. Ad-ditionally during blooms both in the open ocean andnear-coastal waters, coccolithophores shed quantita-tive amounts of CaCO3 lith plates, easily visible tosatellites, that radically alter the open ocean opticalenvironment [11]. Chlorophyll concentration in theopen ocean, typically assumed to covary with the con-centration of suspended organic matter, is used to es-timate the particle scattering coefficient where themajority of the suspended particles are organic innature [12,13]. However, recent modeling work im-plicates suspended mineral matter as a factor inthe scattering coefficient of the open ocean [14] suchas under the above-enumerated conditions.The ability to partition the particulate scattering

and backscattering coefficients becomes very impor-tant in the coastal region where the presence ofsuspended sediment renders chlorophyll retrievalalgorithms based on the absorption and backscatter-ing coefficients nearly useless and very limitedgeographically [15–18]. Furthermore retrieving theconcentration of the mineral matter itself is very im-portant as the issues of erosion and loss of the coastalshoreline, the concomitant loss of protective, produc-tive wetlands, and the possible roles of suspendedsediments in adsorption of nutrients and pollutantsbecome more important.Various indirect methods to partition the particu-

late scattering coefficient have been proposed. Stavnand Keen [19] and Keen and Stavn [20] did this onthe basis of a biogeo-optical model in which themajority of hydrosol absorption was ascribed to chlor-ophyll or CDOM while total scattering was ascribedprimarily to mineral matter. This particular ap-proach works best when the mineral matter is sus-pended quartz or calcite particles. Absorption bymineral matter [21] is easily factored in. The parti-tioning of the particle scattering coefficient camefrom knowledge of the total particle scattering coef-ficient and the calculation of the mineral concentra-tion from physical models of sediment resuspension.The concentration and the particle size distribution(PSD) obtained from the model were utilized in Miecalculations to estimate the mineral particle scatter-

ing coefficient. Additionally, complex nonlinear opti-mizations have been performed utilizing informationon the remote sensing reflectance and the concentra-tions of major inorganic and organic suspended par-ticulates of the aquatic and marine hydrosol [18].Another indirect method is to estimate the particlescattering coefficient from Kirk [22] relations utiliz-ing the diffuse exponential decay coefficient K . Thenthe estimated total particle scattering coefficient ismultiply regressed with the concentration of sus-pended mineral matter and chlorophyll concentra-tion to get mass-specific mineral optical scatteringcross sections [15,23] and thus a partitioning of theindirectly determined particulate scattering co-efficient. There have been attempts to build up ascattering coefficient of the marine hydrosol by esti-mating scattering cross sections for major particu-late components, multiplying the cross sections byestimated particle concentrations and assumed sizedistributions, and adding them together to get a scat-tering coefficient [24]. Overall this method is soundand well-considered. It does require extensive knowl-edge of the optical particle types, their concen-trations, and their PSDs. At this point their assump-tions about the PSD of oceanic particulates arequestionable [25]. The modeling accomplished so fardoes yield approximate relations that are testablehypotheses about the interaction of particle opticalproperties and bulk optical properties.

We consider the partitioning of the particle scatter-ing coefficient first by reviewing the theory of particleoptical properties and the particle scattering crosssection as they relate to the bulk particulate scatter-ing coefficient. Then we discuss the mass-specificparticle scattering cross section as a simple functionof the single particle scattering cross section. Fromthe biogeo-optical mode of analysis, we propose a di-rect method of partitioning the particulate scatteringcoefficient. The method utilizes concurrent informa-tion on the mass concentration of suspended mineralmatter, the particulate inorganic matter (PIM), themass concentration of suspended organic matter,the particulate organic matter (POM), and the totalparticulate scattering coefficient. The concentrationsof PIM and POM are determined by the loss on igni-tion (LOI) technique [26], while the total particulatescattering coefficient is determined by theWET LabsAC 9m or a similar instrument. The concentrationsof PIM and POM are regressed against the totalparticle scattering coefficient. The partial regressioncoefficients from this multiple linear regression arethen mass-specific scattering cross sections for thePIM and the POM. When the correlation betweenthese three field variables is not high (for example,R2

≈ 0:40), the interpretation of the partial regres-sion slopes becomes ambiguous. There are thentwo possible regression slopes per independent vari-able. In univariate Model II regression (one inde-pendent variable and one dependent variable), thesolution to this problem is to use the geometric meanof the two possible regression slopes as a best esti-

10 May 2008 / Vol. 47, No. 14 / APPLIED OPTICS 2661

mate of that slope. We generalize the univariateModel II regression to the multivariate case andillustrate it with data from the northern Gulf ofMexico of both relatively high and relatively lowcorrelation between the particulate scattering coeffi-cient and PIM and POM. Finally we utilize the infor-mation on the mass-specific scattering cross sectionsand the PIM and POM concentrations to partitionthe total particle scattering coefficient into the scat-tering coefficient of the suspended mineral particlesand the scattering coefficient of the suspended organ-ic particles. This fundamental direct partitioning ofthe scattering coefficient can be subdivided evenfurther as knowledge of the optics and concentra-tions of individual mineral and organic componentsbecomes available from laboratory studies and fromoceanographic field exercises [14,27].

2. Particle Optical Properties: Theory

We wish to demonstrate that the mass-specific spec-tral scattering cross section of the suspended parti-culate mineral or organic matter is a simplefunction of the fundamental optical properties ofan individual particle. Gordon and Du [28], Bohrenand Huffman [29], andMcCartney [30] point out thatthe fundamental scattering interaction of a particlewith electromagnetic radiation is the differentialscattering cross section dσðθÞ=dΩ. Here dσ is thecross sectional area of the incoming wave front thatis diverted into angle θ, the angular trajectory ofradiant power scattered by a particle from a wavefront or reference beam, and dΩ is the solid anglesubtended by the radiant power scattered into thattrajectory. The total scattering cross section of theparticle, σ, is obtained from the following integral:

σ ¼ 2πZ π

0

�dσðθÞdΩ

�sin θdθ;

which then represents the total cross sectional areaof the particle that is actively interacting with andscattering power from an incoming wave front of elec-tromagnetic radiation. If the incoming wave front isof unit energy per square meter, then σ is numeri-cally equal to the total radiant power scattered bythe single particle [30] in all directions. And, ofcourse, the scattering cross section is a function ofwavelength, which we have not emphasized to keepthe notation simple. The scattering activity of asingle particle is related to the bulk scattering coeffi-cient per unit volume of a hydrosol containing a givenconcentration of these particles [28] by

bpðλÞ ¼Xi

σiðλÞNi; ð1Þ

where, assuming that the summation in Eq. (1) is fortwo particle types, mineral and organic (i ¼ 2), bpðλÞis the particle scattering coefficient at wavelength λper unit volume of hydrosol, and Ni is the number ofparticles of species i per m3. Furthermore assuming

the mineral and organic particles are each of one sizeand composition, the two particle types each possessa particle scattering cross section and

bmðλÞ ¼ σmðλÞNm; ð2Þ

boðλÞ ¼ σoðλÞNo; ð3Þ

where bmðλÞ is the mineral particle scattering coeffi-cient at wavelength λ per unit hydrosol volume, σmðλÞis the single particle scattering cross section atwavelength λ of the suspended mineral particles ofconcentration Nm particles m−3, boðλÞ is the organicparticle scattering coefficient at wavelength λ perunit hydrosol volume, and σoðλÞ is the single particlescattering cross section at wavelength λ of the sus-pended organic particles of concentration No parti-cles m−3. The particle scattering coefficient is thenpartitioned into mineral and organic particle compo-nents:

bpðλÞ ¼ bmðλÞ þ boðλÞ: ð4Þ

The particle number concentration, or density, is re-lated to the particle mass concentration by

Nm ¼ VTm=νm;

where VTm is the volume proportion of the total sus-pended mineral particles in a cubic meter of hydrosoland νm is the volume of a single mineral particle.Note that VTm is therefore dimensionless [5]. Thus

PIM ¼ ρmVTm ¼ Nmρmνm; ð5Þwhere ρm is the density or mass per unit volume(gm−3) of the mineral particle, and PIM is the massconcentration or total mass of the mineral particlesin a unit volume of hydrosol, so

Nm ¼�

1ρmνm

�PIM; bmðλÞ ¼

�σmðλÞρmνm

�PIM;

σPIMðλÞ ¼σmðλÞρmνm

; ð6Þ

in the simplest case. Thus the spectral mass-specificscattering cross section is simply the spectral parti-cle scattering cross section normalized to the particlemass if there is only one type and size of mineral par-ticle in suspension. And if the particle mass happensto be 1:0 × 10−12 g, reasonable for a clay particle, theparticle scatter cross section, σmðλÞ, will be numeri-cally equal to the mass-specific normalized particlescatter cross section, σPIMðλÞ. Bohren and Huffman[29] emphasize that the mass-specific scatteringcross section of a particle is one of the fundamental


optical parameters in the interaction of a particlewith an electromagnetic field. We note here that anincrease in size of the assumed single type of mineralparticle, as reflected in an increase in νm in Eq. (6),will cause a decrease in σPIMðλÞ. Conversely a de-crease in size of the assumed mineral particle willresult in an increase in σPIMðλÞ. Furthermore a rela-tively large particle will exhibit no spectral slope inthe mass-specific scattering cross section because theparticle scattering coefficient will have no spectralslope. Smaller particles will, of course, demonstratea spectral slope in the mass-specific scattering crosssection.We must note that the relationships between the

dry organic matter POM and the optical propertiesof suspended organic particles, assumed of one sizeand type, are strictly analogous to the above-delineated relations for an assumed single type ofsuspended mineral particle, but they are not identi-cal. The determination of PIM, with due regard forthe structural water relations of clay minerals,results in a mineral residue with known density[5]. However, the determination of the POM by dryweight of suspended matter filtered from a seawatersample and differencing it with the ash weight of thesuspended matter is a determination of only theorganic mass component of the suspended organicparticle. The water component of the suspended or-ganic particle is driven off in the drying step. Thusthe POM volatiles cannot be related directly to ρ0,the wet weight density of the suspended organicmatter. Wet weight density of organics is related todry organic matter density by

ρo ¼ ρdof do þ ρwf w;

where ρdo is the dry organic mass density of the or-ganic particle, f do is the volume fraction of dry organ-ic matter in the organic particle, ρw is the density ofwater, and f w is the volume fraction of water in theorganic particle. The mass-specific scattering crosssection for POM is then

σPOMðλÞ ¼σoðλÞ

ρdof doνo: ð7Þ

In analogy with the relations for a suspended miner-al particle, σPOMðλÞ is the organic particle scatteringcross section, σoðλÞ, normalized to the dry organicmass of the suspended particle. In the case of the or-ganic particle, we can also state that an increase inthe size of the particle will result in a decrease in thevalue for σPOMðλÞ, while a decrease in the size of theorganic particle will result in an increase in the valuefor σPOMðλÞ if f do does not change. The tone of theabove derivations for optical relations of mineraland organic particles was strongly inspired by thework of Bricaud and Morel [31].It is rare to find suspended mineral and organic

particles existing in just one size class, one exceptionbeing a heavy bloom of a single phytoplankton spe-

cies. The major classes of suspended particles existin PSDs. If we consider organic and mineral matteras the two major classes of suspended particles, westart to generalize Eqs. (6) and (7) with the particledensities for the two major classes. For suspendedmineral particles, then, Eq. (6) becomes

σPIMðλÞ ¼1ρm

Xi

Xj

½σmðλÞ�ijðvmÞij

; ð8Þ

or

σPIMðλÞ ¼1ρm

Xi

Xj

½σmðλÞ�ijðNmÞijðVTmÞij

; ð9Þ

where ρm is the average density of all mineral matterand the summations are over the ith mineral speciesand the jth size class, or volume, of that mineral spe-cies. The relative contribution of each component inthe summations is then a function of the size distri-bution associated with each component. However,the densities of the suspended organic particles willvary depending on the concentration of water in theorganic particle. Thus Eq. (7) for suspended organicparticles becomes

σPOMðλÞ ¼1ρdo

Xi

Xj

½σoðλÞ�ijðf doÞijðνoÞij

; ð10Þ

or

σPOMðλÞ ¼1ρdo

Xi

Xj

½σoðλÞ�ijðNoÞijðf doÞijðVToÞij

: ð11Þ

The reasoning applied to the organic fraction of thesuspended matter, again, is analogous but not iden-tical with that applied to the mineral fraction of thesuspended particulates. The organic dry density, ρdo,applied in Eqs. (10) and (11), is nearly constant. How-ever, its role in Eqs. (10) and (11) is modified by itsvolume fraction, f do, contribution to the density ofthe entire organic particle. In theory the volume frac-tion of dry organic matter in the particle can vary[5,32] from possibly 0.2 to 1.0. As yet there are nodirect observations of organic particles containingvirtually no water, so the volume fraction is probablycloser to the lower end of the theoretical range. Thereis, then, at least one more variable in the descriptionof the mass-specific scattering cross section of sus-pended organic particles than is the case with sus-pended mineral particles; this can increase thevariability of organic mass-specific scattering crosssections. When considering the PSD of these compo-nents, the individual components each exhibit alognormal distribution [33–35]. One method of sum-ming the lognormal distributions of all componentparticles yields a PSD model containing two compo-nent particle types in the ocean [36–38]. The two


component model proposes one particle component ofsmall diameter, as with clay particles, and one com-ponent of larger diameter, such as algal cells ororganic detritus. In coastal regions such a two com-ponent model can be tested by the mineral-organiccomponent partition presented in Eqs. (8)–(11). Inprinciple, then, the mass-specific spectral opticalscattering cross sections provide valuable con-straints, based on fundamental optical properties,on inferences regarding size distributions of the sus-pended matter. Various PSDs have been proposed forsuspended matter [19] and all of these can be testedwith the above-delineated relations.We applied an average density of all the individual

mineral particle species in Eqs. (8) and (9). The sum-mation terms in those equations then give us aweighted mean particle scattering cross section anda weighted mean particle volume for a mean mineralparticle. The concept of a mean particle to representa PSD has a long history [39]. Determining a meandensity for mineral particles is relatively easy—wecalculate a mean mineral particle density, ρm, of2:6� 0:15 × 106 gm−3 from Babin et al. [5]. The situa-tion for suspended organic particles is more compli-cated [5,32]. The volume of a cell can contain 80%water or more, while a particle of organic detritusprobably contains much less water [5,32]. Thereare at least two possible average dry organic massdensities. Babin et al. [5] and Morel and Ahn [40] de-termined an organic dry mass density for algal or-ganic matter of 1:38 × 106 gm−3 from data in [32].However, much of the suspended POM is degrada-tion products from living cells. We propose an aver-age dry mass density for detrital organic matter fromthe average of the dry densities for cellulose [32]:1:48� 0:15 × 106 gm−3. The algal dry mass densityvalue could be used in studies of ocean areas whereit is known that living cells are a dominant compo-nent of the organic mass, and the organic detritaldry mass density could be used in studies of areaswhere organic detritus is dominant. The two densi-ties can be utilized in situations where the partition-ing of the organic mass is known.We can investigate the bulk optical properties of

the marine hydrosol when we have knowledge ofthe individual particle optical properties and theiraverages. For example, Gordon and Du [28], utilizingthe discrete dipole approximation, were able to cal-culate the particle spectral scattering cross sectionof the double crenulated disk-shaped calcium carbo-nate lith plates of the coccolithophore Emilianahuxleyi. Coccolithophores are a very important com-ponent of the phytoplankton of the open ocean andoften the nearshore waters [11,41]. There is greatinterest in the contribution of E. huxleyi to the ocea-nic carbon budget. The aggregations of lith platesfrom coccolithophore blooms are visible in satelliteimages, so they are a significant factor in the opticalproperties of the marine hydrosol. We can predict themass-specific scattering coefficient of small detachedliths in the open ocean utilizing the Gordon and Du

[28] results and Eq. (6). We used 2:71 × 106 gm−3 forthe density of CaCO3, 0:616 μm3 for the averagevolume of a lith plate, and the spectral particle crosssections calculated by Gordon and Du [28] and illu-strated in their Fig. 7. The mass-specific mineralscattering cross section of a region of the open oceandominated by detached liths from a coccolith bloom isshown in Fig. 1. This shows that the spectral mass-specific scattering cross section of a small mineralparticle such as a lith plate varies from ∼1:4m2 g−1in the blue end of the spectrum to ∼0:6m2 g−1 in thered end of the spectrum. The value of σPIMð555Þ ≈0:98m2 g−1, approximately 60% of the numericalvalue of the lith plate particle scattering cross sec-tion. As previously noted, σmðλÞ ≈ σPIMðλÞ for smallmineral particles. The wavelength dependence ofthis optical parameter is λ−n, where we determinedn to be approximately 1.8. We expect the wavelengthdependence to lessen as the particle increases in size.

Thus the mass-specific scattering cross section issimply the fundamental particle optical scatteringcross section normalized by the mass of the mineralparticle or the dry organic mass of an organic parti-cle. There is the potential for the mass-specific scat-tering cross section to be used to invert remotesensing reflectance to determine the mass concentra-tion of particulate matter [18]. However, the com-plexities of the coastal optical field are great [42],and much work will need to be done to effect thisgoal. In addition this optical parameter provides

Fig. 1. (Color online) Spectral mass-specific scattering cross sec-tions of suspended coccolith lith plates from data and calculationsof Gordon and Du [28].


valuable constraints on attempts to determine thenature of PSDs that will be used to investigate thedynamics of particulates in the coastal ocean. Therewill be applications in the open ocean as well.

3. Materials and Methods

We have two sets of field data for this study, one col-lected at Mobile Bay, Alabama, 20–24 May 2002, bythe Naval Research Laboratory–Stennis SpaceCenter for a total of 24 field stations. The samplingarea extended from inside Mobile Bay out to thecoastal barrier islands: Dauphin Island and PetitBois Island. The sampling stations followed theMobile River sediment plume out of the bay androughly along the coast and barrier islands endingup in open water. The other data set was collectedat Southwest Pass, Mississippi River mouth, 29–30July and 1–2 August 2003, by NASA–Stennis SpaceCenter for a total of 16 field stations. The samplingstations extended from within Southwest Pass andthe Mississippi River plume out to the Gulf of Mexicointo relatively clear water. The samples were surfacesamples collected in the first 0:5m of depth for pos-sible future investigation of scattering propertiesand remote sensing algorithms.The particulate scattering coefficient, bpðλÞ, was

obtained for the two study areas with a WET LabsAC 9m at wavelengths 412, 440, 488, 510, 532, 555,650, 676, and 715nm. The AC-9s were attached to aCTD-rosette with several 6 l Niskin bottles, which al-lowed the collection of water samples concurrentwith the collection of AC-9 data from the instrumentattached to the rosette.The concurrent water samples collected from the

CTD-rosette were subjected to the standard gravi-metric LOI technique [26] of filtering a water sampleunder vacuum onto a prewashed, preweighed glassfiber filter, drying, weighing, ashing, and weighingagain. This protocol yields estimates of PIM andPOM. The filters were of the 47mm Whatman GF/Fvariety. Each stage of the technique is repeated untilthe weights obtained are constant. The filter andsample are initially dried at 103°C for 2h andweighed to constancy. Then the sample is ashed at550°C for 15 min and weighed to constancy. The in-itial weight provides total suspended solids (TSS)concentration and the ashed weight provides PIMconcentration. The POM is obtained from the differ-ence (TSS − PIM). An important aspect of the tech-nique is to run process-control filters treated identi-cally with sample filters except that deionized wateris filtered rather than the water sample. Glass fiberfilters tend to be fragile, and loss of filter mass duringtreatment must be accounted for [43]. Barillé-Boyeret al. [44] point out that the LOI method for deter-mining POM has difficulties when inorganic matteris dominated by clay minerals. The ignition stepdrives off structural water from the clay mineralmatrix, requiring correction factors for both the esti-mated mass of PIM and for the estimated massof POM. Average clay mineral proportions for these

samples were obtained from Doyle and Sparks [45]for Mobile Bay, Alabama, and Johnson and Kelley[46] for the mouth of the Mississippi River and theBarillé-Boyer, et al. [44] corrections then applied. An-other source of error is salt retention by glass fiberfilters. This will cause an overestimation of the TSSmass [47]. We have also recently determined that thesalt retention on glass fiber filters is a function of thesalinity of the sample—highly variable in coastalwaters. We applied salt retention correction factorsthat we determined as a function of salinity.

We determined mineral and organic particle mass-specific scattering cross sections by partitioning thetotal suspended particle spectral scattering coeffi-cient, Eq. (4), using multiple linear regression withPIM and POM data. We have shown that the mineralspectral scattering coefficient, bmðλÞ, and the organicparticle spectral scattering coefficient, boðλÞ, can beexpressed in terms of the mass-specific spectral scat-tering cross section and the total mass concentrationof the particle type, Eqs. (5)–(7). The mass-specificscattering cross sections are, then, the partial regres-sion coefficients or slopes of the multiple regressionof bpðλÞ with PIM and POM data [15,48–50]:

bpðλÞ ¼ gðλÞ þ σPIMðλÞPIMþ σPOMðλÞPOM: ð12Þ

Equation (12) is a standard multiple regressionequation that includes a term for the intercept, ex-pressed here as gðλÞ, on the dependent variable axis(particulate scattering coefficient axis) [50,51]. ThegðλÞ intercept term is the value of bpðλÞ when bothPIM and POM ¼ 0. Thus gðλÞ should not differ signif-icantly from 0. If this is not the case, the interceptvalue can give insight into possible problems withthe determination of the PIM and POM values. Thecorrelations, or strengths of association, between thevariables of Eq. (12) were determined by Model Imultiple linear regression [50–53]. However, leastsquares regression, or Model I-type regression, doesnot apply strictly to field data collected without di-rect control of independent variables by the investi-gator [53,54]. Correlations obtained in this way arevalid, however [53]. Therefore Model II regressionhas been proposed for univariate regressions (one de-pendent variable and one independent variable) toobtain the best estimate of regression slopes fromfield observations not under direct experimental con-trol [53,54]. The problem of obtaining the optimal re-gression slope becomes acute when there is relativelylow, but still significant, correlation of the uncon-trolled field variables adversely affecting the slopeestimates [53]. This will show up in the attempt toobtain the estimates of σPIMðλÞ and σPOMðλÞ fromModel I multiple linear regression. Thus we proposehere a generalization of Model II regression to themultivariate case to obtain the best estimates ofσPIMðλÞ and σPOMðλÞ.

We will briefly describe the application of Model IIregression to three variables, which is relevant to theeffort to obtain the best slope or partial regression


coefficient estimates for the mass-specific opticalscattering cross sections. To simplify the extensionof Model II regression to three variables, we expressthe equation in terms of principal components ana-lysis and apply it first to the Model II regressionof two variables, the well-known univariate regres-sion, of a dependent variable, y2, on an independentvariable, y1. We utilize the reduced major axis or geo-metric meanmethod throughout. Let �y1 and �y2 be thesample means, and s1 and s2 be the sample standard

deviations of y1 and y2, respectively. Let a01 ¼�a011

a012

�

and a02 ¼�a021

a022

�be the eigenvectors associated with

the eigenvalues, λ0 ¼�λ01λ02

�, of the correlation ma-

trix, R ¼�

1 r12r21 1

�, where r12 is the correlation be-

tween y1 and y2. Then the Model II regressionequation can be written as

y2 ¼��y2 þ

�s2s1

��a021

a022

��y1

�þ�s2s1

��−a021

a022

�y1; ð13Þ

which has slope ð− a021a022

Þðs2s1Þ. When using the correlationmatrix for two variables, the magnitudes of theeigenvector components a0

21 and a022 will always be

the same, and thus the slope estimator reduces tothe reduced major axis estimator, � s2

s1.

The univariate equation can be extended to threevariables as

y3 ¼��

a031

a033

��s3s1

��y1 þ

�a032

a033

��s3s2

��y2 þ �y3

�

þ�−a031

a033

��s3s1

�y1 þ

�−a032

a033

��s3s2

�y2; ð14Þ

where a0ij represents the jth component of the ith ei-

genvector from the correlation matrix, ð− a031

a033Þðs3s1Þ is

the conditional slope associated with y1, andð− a0

32a033Þðs3s2Þ is the conditional slope associated with

y2. Note that unlike the two variable case, the ratioof eigenvector elements will usually not equal 1, andthus the slope estimates do not reduce to the ratio ofsample standard deviations. Thus the optimum esti-mates of the mass-specific optical scattering crosssections, Eqs. (6) and (7), are

σ̂PIMðλÞ ¼�−a031

a033

��s3s1

�; ð15Þ

σ̂POMðλÞ ¼�−a032

a033

��s3s2

�; ð16Þ

where s3 is the standard deviation of bpðλÞ, s1 is the

standard deviation of PIM, s2 is the standard devia-tion of POM, and a0

ij represents the jth component ofthe ith eigenvector from the correlation matrix.

When we have the estimates of the mass-specificoptical scattering cross sections, Eqs. (15) and (16),we are then able to partition the spectral particlescattering coefficient bpðλÞ into the spectral scatter-ing coefficient of mineral matter, bmðλÞ, and the spec-tral scattering coefficient of organic matter, boðλÞ, ata given station. All that is required is to multiply theestimate of σPIMðλÞ by PIM at a given station andmultiply the estimate of σPOMðλÞ by POM at thatstation.

4. Results

The values of bpðλÞ, PIM, and POM for the two datasets were as follows. In Mobile Bay bpðλÞ varied from0.90 to 20:6m−1 across the wavelength spectrum,PIM varied from 1.59 to 22:24mg l−1, and POMvaried from 0.17 to 3:08mg l−1. In Southwest PassbpðλÞ varied from 0.58 to 11:4m−1 across the wave-length spectrum, PIM varied from 0.05 to 9:53mg l−1,and POM varied from 0.18 to 1:89mg l−1.

We determined the Model I partial regression coef-ficients (slopes) for the two data sets and the strengthof the association between the two independent vari-ables, PIM and POM, and the dependent variable,bpðλÞ. Themost highly correlated data set, the resultsfrom the Naval Research Laboratory Mobile Baycruise, showed 0:86 ≤ R2

≤ 0:94 across the spectrumfrom 412 to 715nm for the analysis including the 24field stations. The data set of lower correlation, theresults from the NASA Southwest Pass cruise,showed 0:58 ≤ R2

≤ 0:68 across the same spectrumfor the analysis including the 16 field stations. TheF-test of significance of these R2 values resulted inp-values <0:005 for all wavelengths of SouthwestPass and even smaller p-values for Mobile Bay. In ad-dition the individual Model I partial regression coef-ficients were investigated for statistical significanceby a two-sided t-test at the 0.05 significance level[52]. The mineral and organic partial regression coef-ficients for Mobile Bay were significant at this level.For Southwest Pass, however, although the mineralpartial regression coefficients were significant at thislevel, the organic partial regression coefficients werenot statistically significant at the 0.05 level.

For Mobile Bay the Model I partial regression coef-ficients and standard errors for suspended mineralmatter are plotted in Fig. 2 along with the ModelII partial regression coefficients. The Model I andModel II coefficients track each other closely andthe Model II partial regression coefficients sit com-fortably inside the standard error limits of theModel I partial regression coefficients. Similar plotsfor the suspended organic matter of Mobile Bay arein Fig. 3. The partial regression coefficients for or-ganic matter also track each other closely, and theModel II coefficients fall easily within the standarderror limits of the Model I coefficients. The mineralModel II coefficients are uniformly larger than the


mineral Model I coefficients, while the organic ModelII coefficients are uniformly smaller than the organicModel I coefficients.

At Southwest Pass the Model I partial regressioncoefficients and standard errors for suspendedmineral matter are plotted in Fig. 4 along with theModel II mineral partial regression coefficients.The similar plots for the suspended organic matterof Southwest Pass are shown in Fig. 5. In this casethe Model II mineral partial regression coefficientsfall outside the standard error limits of the ModelI mineral coefficients, are uniformly larger thanthe Model I coefficients, and show a spectral slopenot evident in the Model I coefficients. The organicModel II partial regression coefficients lie withinthe broad standard error range of theModel I organicpartial regression coefficients and are uniformlysmaller than the Model I organic partial regressioncoefficients. The standard error limits of the Model Iorganic partial regression coefficients span zero forsome of the wavelengths.

We partitioned the particle spectral scatteringcoefficients into spectral scattering coefficients formineral particles and spectral scattering coefficientsfor organic particles, multiplying the mass concen-tration of mineral or organic matter at a particularfield station by its respective mass-specific scatteringcross section (partial regression coefficient). The par-titioned particle spectral scattering coefficients for

Fig. 2. (Color online) Spectral mass-specific optical scatteringcross sections of suspended mineral matter in Mobile Bay, Alaba-ma. Model I-type multiple regression results with standard errorsplotted along with the estimates from the Model II-type multipleregression. In the figure legend s[PIM] represents σ½PIM� and s[POM] represents σ½POM�.

Fig. 3. (Color online) Spectral mass-specific optical scatteringcross sections of suspended organic matter in Mobile Bay, Alaba-ma. Model I-type multiple regression results with standard errorsplotted along with the estimates from the Model II-type multipleregression. In the figure legend s[PIM] represents σ½PIM� and s[POM] represents σ½POM�.

Fig. 4. (Color online) Spectral mass-specific optical scatteringcross sections of suspended mineral matter at Southwest Pass,Mississippi River, Louisiana. Model I-type multiple regression re-sults with standard errors plotted along with the estimates fromthe Model II-type multiple regression. In the figure legend s[PIM]represents σ½PIM� and s[POM] represents σ½POM�.


Station 23-s01 in Mobile Bay are plotted in Fig. 6.The partitioned particle spectral scattering coeffi-cients for Station AC3-13 at Southwest Pass areplotted in Fig. 7. In both field sites the particulatespectral scattering due to mineral scattering domi-nates the particulate organic spectral scattering:by a factor of 4 in Mobile Bay (see Fig. 6) and a factorof 20 to 30 at Southwest Pass (see Fig. 7).We investigated the efficiency of the Model I and

Model II spectral partial regression coefficients in re-constructing the spectral particle scattering coeffi-cients at each station of the field exercises. Thesum of the calculated mineral and organic spectralscattering coefficients should equal the particle spec-tral scattering coefficients measured at each station.A series of plots covers the ranges of particle concen-trations utilized here. High particle concentrationwas defined as 6:87–22:24mg l−1 of PIM for MobileBay and 6:01–9:53mg l−1 of PIM for Southwest Pass.Medium particle concentration was defined as 5:00–6:86mg l−1 of PIM for Mobile Bay and 1:22–3:76mg l−1 of PIM for Southwest Pass. Low particleconcentration was defined as 1:59–4:65mg l−1 of PIMfor Mobile Bay and 0:05–1:12mg l−1 of PIM forSouthwest Pass. We defined the concentrations interms of PIM because this material tended to domi-nate the scattering process in these coastal regions.All stations relatively high in suspended mineral

matter for Mobile Bay and Southwest Pass havethe reconstructed spectral particle scattering curves

Fig. 5. (Color online) Spectral mass-specific optical scatteringcross sections of suspended organic matter at Southwest Pass,Mississippi River, Louisiana. Model I-type multiple regression re-sults with standard errors plotted along with the estimates fromthe Model II-type multiple regression. In the figure legend s[PIM]represents σ½PIM� and s[POM] represents σ½POM�.

Fig. 6. (Color online) Partitioned total particle spectral scatteringcoefficient from station 23s01, Mobile Bay, Alabama. The sus-pended mineral spectral particle scattering coefficient (bm) andthe suspended organic spectral particle scattering coefficient (bo)indicated.

Fig. 7. (Color online) Partitioned total particle spectral scatteringcoefficient from station AC3-13, Southwest Pass, MississippiRiver, Louisiana. The suspended mineral spectral particle scatter-ing coefficient (bm) and the suspended organic spectral particlescattering coefficient (bo) indicated.


plotted against the measured spectral particle scat-tering curves in Figs. 8 and 9, respectively. In MobileBay the spectral particle scattering curves recon-structed from Model II [see Fig. 8(a)] and Model I[see Fig. 8(b)] multiple regressions tend to agree,but the Model I reconstructions [see Fig. 8(b)] maydeviate more from the measured spectral scatteringcoefficients than do the Model II reconstructions. Allof the Model II curves agree closely with the mea-sured spectral scattering values with the exceptionof two stations. In this case the maximum deviationfrom the field data curves was 25%. At SouthwestPass the spectral particle scattering curves recon-structed from the Model II [see Fig. 9(a)] spectralparticle scattering cross sections are in closer agree-ment with the field data at all stations but one [seeFig. 9(b)]. Here themaximum deviation of thatModelII curve from the field data curve was 40%.All stations at a medium level of suspended miner-

al matter have their particle spectral scattering re-constructions from Model I and Model II plottedagainst the measured particle spectral scatteringcurves in Figs. 10 and 11. In Mobile Bay we see thatthe reconstructions of the particle spectral scatteringcurves fromModel II [see Fig. 10(a)] and Model I [seeFig. 10(b)] are in close agreement in their relation tothe measured particle scattering values. In bothcases only three stations are not in close agreementwith the measured spectral scattering coefficients. Inthis case the maximum deviation of the model curves

from the field data curves was 42%. At SouthwestPass the Model II [see Fig. 11(a)] reconstructedcurves are in closer agreement with the measuredscattering values than the Model I [see Fig. 11(b)]curves. One station in Fig. 11(b) has Model II valuesnot in close agreement with the field data. In thiscase the maximum deviation of the Model II curvefrom the field data curve was 50%.

All stations relatively low in concentration of sus-pended mineral matter with particulate spectralscattering reconstructions from Model I and ModelII are plotted against themeasured values in Figs. 12and 13. In Mobile Bay the Model II [see Fig. 12(a)]spectral particle scattering curve reconstructionsare in better agreement with the measured valuesthan the Model I [see Fig. 12(b)] values. The maxi-mum deviation of the reconstructed curves fromthe field data curves [see Fig. 12(a)] was 20%. AtSouthwest Pass the Model II [see Fig. 13(a)] recon-structed curves tend to show closer agreement withthe field data curves with one exception. At thisrather low concentration of suspended matter, the re-constructions are less efficient at tracking the mea-sured values. The maximum deviation of theaberrant Model II curve from the field data rangeswas 70%.

5. Discussion

We have directly partitioned the spectral particlescattering coefficient with a Model II-type multiple

Fig. 8. (Color online) Comparison of particle spectral scattering coefficients for stations of high suspended mineral concentrations(PIM ¼ 6:87–22:24mg l−1), Mobile Bay, Alabama. Particle spectral scattering coefficients reconstructed from mass-specific spectral scat-tering cross sections and PIM and POM. (a) Reconstructed particle spectral scattering coefficients utilizing Model II-type mass-specificspectral scattering cross sections plotted against measured particle spectral scattering coefficients. (b) Reconstructed particle spectralscattering coefficients utilizing Model I-type mass-specific spectral scattering cross sections plotted against measured particle spectralscattering coefficients.


regression method utilizing measured data relevantto the theory of particle scattering. This multiple re-gression generates mass-specific scattering crosssections, which can then be used to determine thescattering coefficient for both suspended mineralsand organic particulates. The mass-specific scatter-ing cross section converts the mass concentrationof mineral or organic matter to the scattering coeffi-cient of suspended minerals or suspended organicmatter. In addition we have demonstrated that themass-specific scattering cross section is a simplefunction of the fundamental optical properties ofthe suspended particles, and it thus provides infor-mation about the nature of the suspended particlesthemselves. The mass-specific scattering cross sec-tions determined in this way are statistical averagesand subject to the limitations of the method of deri-vation and calculation.The multiple regression method of determining

the mass-specific scattering cross sections of mineraland organic matter rests on a few assumptions. Wepresume, for example, that suspended mineral mat-ter has the same composition at each station and theonly difference between stations is that the con-centration varies, not the composition. Thus thesuspended mineral matter is simply “diluted” or

“concentrated” in a conservative manner betweenstations. If the composition does vary, the mass-spe-cific cross sections determined are spatial averagesover various compositions of suspended mineral mat-ter, and the mass-specific scattering cross sectionwould not necessarily apply strictly to a given sta-tion. Furthermore significant layering of particletypes will impact the analysis similarly. Partitioningthe stations and depths into meaningful groupings ofmaterials will allow separate multiple regressionanalyses and the mass-specific scattering cross sec-tions can then be compared. A strong gradient inthe variables always helps in a regression analysis,and we had this in these data sets. If there is signif-icant phytoplankton growth over the period of sam-pling and the phytoplankton is the major componentof the organic matter, the variation in the concentra-tion of organic matter would not be conservative, andthis would adversely affect the interpretation ofany mass-specific organic scattering cross sectionsdetermined.

The mass-specific spectral scattering cross sec-tions (spectral partial regression coefficients) forModel I-type and Model II-type multiple regressionsfrom Mobile Bay are comparable (see Figs. 2 and 3).This is assured by the relatively high correlations of

Fig. 9. (Color online) Comparison of particle spectral scattering coefficients for stations of high suspended mineral concentrations(PIM ¼ 6:01–9:53mg l−1), Southwest Pass, Mississippi River mouth. Particle spectral scattering coefficients reconstructed from mass-specific spectral scattering cross sections and PIM and POM. (a) Reconstructed particle spectral scattering coefficients utilizing ModelII-type mass-specific spectral scattering cross sections plotted against measured particle spectral scattering coefficients. (b) Reconstructedparticle spectral scattering coefficients utilizing Model I-type mass-specific spectral scattering cross sections plotted against measuredparticle spectral scattering coefficients.


the Mobile Bay data [53,55]. A very high correlationwould probably show essentially no difference be-tween the spectral optical scattering cross sectionsdetermined by either method of multiple regression.An interesting trend shown in Figs. 2 and 3 is thatthe Model II-type estimates for the mass-specificmineral spectral scattering cross sections are greaterthan the Model I-type estimates while the opposite istrue for the mass-specific spectral scattering crosssections for organic matter. In the univariate regres-sion (one dependent variable and one independentvariable) it is known that the Model II regressionslope is greater than the Model I regression slope[53,55]. However, we see a new trend arising in theModel II-type multivariate regression. The Model IIpartial regression slope for organic matter, the sec-ond independent variable, is less than the Model Ipartial regression slope—to our knowledge thishas not been previously reported for Model II re-gressions.The estimate of mass-specific spectral scattering

cross sections for Southwest Pass (see Figs. 4 and5) came out differently because of the lower correla-tions of the spectral particle scattering coefficientand the mineral and organic concentrations. Herethe Model II mineral mass-specific spectral scatter-ing cross sections were also greater in magnitudethan the Model I estimates; however, they werelocated outside the standard error band of the Model

I estimates (see Fig. 4). These Model II estimates forSouthwest Pass are comparable in magnitude to theModel II estimates for Mobile Bay, and these ModelII estimates also exhibit a spectral slope that is notevident in the Model I mineral mass-specific scatter-ing estimates for Southwest Pass (see Figs. 2 and 4).ThusModel II multiple regression exhibits aspects ofthe data from Southwest Pass that are lost in theModel I multiple regression. The Model II estimatesof the suspended organic spectral optical scatteringcross sections lie below the Model I estimates of thespectral optical scattering cross sections but withinthe standard error limits. The variance of the spec-tral organic optical scattering cross sections is veryhigh with estimates that occasionally span zero atthe shorter wavelengths. It is not surprising thatthe Model II estimates fall within the large standarderror band of the Model I spectral optical scatteringcross sections—the very large variances of the organ-ic scattering cross sections render them nonsignifi-cant statistically. Recall the potential for largevariances in organic mass-specific scattering crosssections indicated in Eqs. (10) and (11). The largevariances come about by the variability of the watercontent of organic particles leading to greatly differ-ent densities of organic particles.

We did individual analyses for each day of theMobile Bay data sampling period. There were morestations per day in the Mobile Bay data set, so better

Fig. 10. (Color online) Comparison of particle spectral scattering coefficients for stations of medium suspended mineral concentrations(PIM ¼ 5:00–6:86mg l−1), Mobile Bay, Alabama. Particle spectral scattering coefficients reconstructed from mass-specific spectral scatter-ing cross sections and PIM and POM. (a) Reconstructed particle spectral scattering coefficients utilizing Model II-type mass-specific spec-tral scattering cross sections plotted against measured particle spectral scattering coefficients. (b) Reconstructed particle spectralscattering coefficients utilizing Model I-type mass-specific spectral scattering cross sections plotted against measured particle spectralscattering coefficients.


statistical conclusions could be drawn from them.The mass-specific scattering coefficients for mineralmatter and organic matter on each day all over-lapped the standard error limits established for theentire 24 station data set. The only difference wasthat in the analyses for each day, the organic mass-specific scattering cross sections were often nonsigni-ficant at the 0.05 level—the organic matter alwayshaving a larger standard error for the mass-specificcoefficients than the suspended mineral matter. Itwould appear that the mineral matter did not changesignificantly in composition over the five-day periodof sampling and the geographic sampling range of in-side Mobile Bay out to the barrier islands. Organicmatter, of course, will have greater opportunities toviolate the assumption of conservative dilution orconcentration that the mineral matter appears to fol-low. The conservative assumption would be violatedwith significant patchy or pulsating phytoplanktongrowth over an extended time period or an extendedgeographic range. Organic matter concentrations ofprimarily organic detritus would be expected to varymore conservatively.We feel that the values reported and analyzed

above are the first direct determinations of mass-specific scattering cross sections obtained from mea-sured field data of particulate scattering and massconcentrations of suspended mineral and organicparticles. Earlier work had supplied plausible ap-

proximations to the mass-specific scattering crosssections (often called mass-specific scattering coeffi-cients), but their limitations made them approxi-mations only and not direct determinations. For ex-ample, to obtain an approximation of σPIMðλÞ, thebpðλÞ coefficient would be regressed directly againstPIM [23] or bpðλÞ would be regressed directly againstTSS [5]. Thus no attempt is made to partition bpðλÞ ineither case or to partition TSS in the second case, sothe contribution of suspended organic matter to theparticle scattering coefficient is ignored in both casesand subsumed into the mineral particle scatteringcross section. However, the regression of bpðλÞagainst TSS has also been assumed to be an estimateof σPOMðλÞ in open ocean waters away from coastalinfluence (subsuming the contribution of suspendedminerals under organics) [5]. Furthermore the beamtransmittance coefficient, c, (the sum of the hydrosolabsorption and scattering coefficients) has been as-sumed to be a measure of particle scattering andthen regressed against TSS to provided approxima-tions of σPIMðλÞ or σPOMðλÞ depending on whether thewater being sampled was coastal or open ocean [56].The problems of confounding one major suspendedcomponent with another are obvious as we shall see.

Examples of the above-mentioned order-of-magni-tude approximations come from Babin et al. [5] witha report of σPIMð555Þ ≈ 0:5m2 g−1 and σPOMð555Þ ≈1:0m2 g−1 and essentially no or small spectral varia-

Fig. 11. (Color online) Comparison of particle spectral scattering coefficients for stations of medium suspended mineral concentrations(PIM ¼ 1:22–3:76mg l−1), Southwest Pass, Mississippi River mouth. Particle spectral scattering coefficients reconstructed from mass-specific spectral scattering cross sections and PIM and POM. (a) Reconstructed particle spectral scattering coefficients utilizing ModelII-type mass-specific spectral scattering cross sections plotted against measured particle spectral scattering coefficients. (b) Reconstructedparticle spectral scattering coefficients utilizing Model I-type mass-specific spectral scattering cross sections plotted against measuredparticle spectral scattering coefficients.


Fig. 12. (Color online) Comparison of particle spectral scattering coefficients for stations of low suspended mineral concentrations(PIM ¼ 1:56–4:65mg l−1), Mobile Bay, Alabama. Particle spectral scattering coefficients reconstructed from mass-specific spectral scatter-ing cross sections and PIM and POM. (a) Reconstructed particle spectral scattering coefficients utilizing Model II-type mass-specific spec-tral scattering cross sections plotted against measured particle spectral scattering coefficients. (b) Reconstructed particle spectralscattering coefficients utilizing Model I-type mass-specific spectral scattering cross sections plotted against measured particle spectralscattering coefficients.

Fig. 13. (Color online) Comparison of particle spectral scattering coefficients for stations of low suspended mineral concentrations(PIM ¼ 0:05–1:12mg l−1), Southwest Pass, Mississippi River mouth. Particle spectral scattering coefficients reconstructed from mass-specific spectral scattering cross sections and PIM and POM. (a) Reconstructed particle spectral scattering coefficients utilizing ModelII-type mass-specific spectral scattering cross sections plotted against measured particle spectral scattering coefficients. (b) Reconstructedparticle spectral scattering coefficients utilizing Model I-type mass-specific spectral scattering cross sections plotted against measuredparticle spectral scattering coefficients.


tion in all waters investigated. Then Bowers andBinding [23] reported σPIMð555Þ ≈ 0:4m2 g−1 from in-vestigations in the Irish Sea along with a peculiardrop in σPIMðλÞ in the blue region of the spectrum.It is possible to explain this by strong absorptionin the blue region of the light spectrum as reportedfor some suspended minerals [27,57], but the indirectdetermination of bpðλÞ in their study remains aproblem in this interpretation. Furthermore regres-sing PIM against the total particle scattering coeffi-cient, bpðλÞ, confounds the organic scatteringcontribution to bpðλÞ with the mineral contribution.We report σPIMð555Þ ≈ 0:69m2 g−1 in Mobile Bayand σPIMð555Þ ≈ 0:60m2 g−1 in Southwest Pass (seeFigs. 2 and 4). Our results for σPOMð555Þ indicate thatit can be both higher and lower than 1:0m2 g−1 (seeFigs. 3 and 5). We demonstrate a spectral depen-dency for σPIMðλÞ in both cases and σPOMðλÞ in MobileBay (see Figs. 2–4). However, in Southwest PassσPOMðλÞ does not exhibit a spectral curve (see Fig. 5).The order-of-magnitude approximations reported byothers are in rough accord with these direct determi-nations, but they lack the spectral detail we havebeen able to observe.One major benefit of the mass-specific spectral

scattering cross sections determined from multipleregression analysis of the particle spectral scatteringcoefficient and the mineral and organic matter con-centrations is the ability to partition the spectral par-ticle scattering coefficient into its components: thespectral scattering coefficient of suspended mineralmatter and the spectral scattering coefficient of sus-pended organic matter. The spectral scattering coef-ficients for mineral matter and organic matter areshown in Figs. 6 and 7, and they are different forMobile Bay and Southwest Pass. In Mobile Bay the

spectral scattering coefficient for mineral matter isapproximately four times the value of the spectralscattering coefficient for organic matter. In South-west Pass the mineral spectral scattering coefficientis approximately 20–30 times the value of organicmatter. In either area the mineral contribution tototal scattering is considerable (Mobile Bay) to anorder-of-magnitude more (Southwest Pass) than thescatter contribution of suspended organic matter.Clearly the mineral matter will dominate the remotesensing signal and more so in the Southwest Pass.There are obvious implications here for remote sen-sing algorithms. The stations shown in Figs. 6 and 7were at the maximum for suspended matter concen-tration and particle spectral scattering for each fieldsampling area so that the Mobile Bay stations hadapproximately three times as much suspended mat-ter as the Southwest Pass stations. To our knowledgea direct determination of the spectral scattering coef-ficient for suspended organic matter in mineraldominated coastal areas has not been previously ac-complished.

An important issue is the efficiency of our multipleregressions in reconstructing the field data curves ofparticle spectral scattering coefficients for individualsampling stations. The partitioned particle spectralscattering coefficients, determined for all stationsof the two areas sampled, were used to reconstructthe particle spectral scattering coefficients. For thosestations high in suspended matter concentration (seeFigs. 8 and 9) the Model II reconstructions are goodand comparable with the field data. The deviation ofModel I reconstructions tends to be higher both forMobile Bay and Southwest Pass [see Figs. 8(b) and9(b)]. For stations of medium concentration of sus-pended matter (see Figs. 10 and 11), the reconstruc-

Table 1. Notation

Parameter Value

λ Light wavelength in vacuum (nm)bw Molecular water volume scattering coefficient (m−1)bp Particle volume scattering coefficient (m−1)bm Mineral particle volume scattering coefficient (m−1)bo Organic particle volume scattering coefficient (m−1)Nm Number of mineral particles in a unit volume of seawater (number m−3)No Number of organic particles in a unit volume of seawater (number m−3)PIM Dry weight per unit volume of seawater (gm−3)POM Dry weight per unit volume seawater (gm−3)TSS Particle dry weight per unit volume seawater (gm−3)f do Volume of dry organic matter per unit volume of organic particle (dimensionless)f w Volume of seawater per unit volume of organic particle (dimensionless)ρw Density of pure seawater (×106 gm−3)ρm Density of suspended mineral particles (×106 gm−3)ρo Density of suspended organic particles (×106 gm−3)ρdo Density of dry POM (×106 gm−3)σm Scattering cross section for mineral particle (m2 particle−1)σo Scattering cross section for organic particle (m2 particle−1)

σPIM Mass-specific scattering cross section for mineral particle (m2 g−1)σPOM Mass-specific scattering cross section for organic particle (m2 g−1)νm Volume of mineral particle (m3)VTm Total volume of mineral particles per unit volume of seawater (dimensionless)


tions are less efficient with Model II reconstructionsgenerally better at both sample areas [see Figs. 10(a)and 11(a)]. At the low end of suspended particulatematter, the Model II reconstruction for Mobile Bay isquite good, the maximum deviation recorded being20% [see Fig. 12(a)]. The reconstructions for South-west Pass are adequate with Model II tending to clo-ser agreement and one station considered aberrant[see Figs. 13(a) and 13(b)]. As we might expect fromour discussions of Model I and Model II regressions,the relatively highly correlated values of Mobile Bayshow reasonable agreement between theModel I andModel II reconstructions. In the Southwest Pass re-constructions, generated from relatively lower corre-lations, the Model I values consistently deviate morefrom the field data curves than the Model II recon-structions. So the multiple regressions utilized inthis report are most efficient at reconstructing fielddata when the concentration of suspended matter ishigh and least efficient at very low concentrations. Atthe very low concentrations of suspended matter, weare approaching the limits of accuracy of the LOItechnique and of the AC-9 meter. The water sampleswith the highest concentration of mineral matter inthese studies contain significant amounts of clays.Isphording et al. [58] have pointed out that claysare predominant in Mobile Bay but are largely pre-cipitated in the bay and do not make it out to theopen water. It is quite likely that the qualitative com-position of the low suspended matter stations dif-fered from the qualitative composition of the highsuspended matter stations. There was a greaternumber of low suspended matter stations at South-west Pass. The general pattern was to encounter lowsuspended matter as we were further away fromshore. This would encourage the flocculation and set-tling of mineral matter out of the water column andthere would be a higher concentration of biogenicmineral matter: siliceous tests from diatoms and cal-cium carbonate liths from coccolithophores [11,41].Biogenic mineral detritus is usually of larger dia-meter than minerogenic clays and would thus makea smaller contribution to the mass-specific mineralscattering cross section, Eq. (5). Thus the smallermineral particles are to be expected for the high con-centrations of PIM, and they will make the dominantcontribution to the average mineral scattering crosssection. This would explain the higher values of thereconstructed spectral scattering coefficients in thestations with a lower concentration of suspendedmineral particles.The other major benefit of determining the mass-

specific particle scattering cross sections is that wecan make inferences about the nature and propertiesof the suspended particles in addition to partitioningthe particle spectral scattering coefficient. We canmake many simple predictions. For example, anyspectral slope for both σPIMðλÞ and σPOMðλÞ will be in-dicative of the domination of the particle suite bysmaller particles since the mass-specific scatteringcross sections are simply normalized particle scatter-

ing cross sections. This is demonstrated from the cal-culation of the spectral mass-specific scattering crosssection of coccolithophore liths, which can be consid-ered a typical small mineral particle (see Fig. 1). Aspectral slope to the scattering cross section of smallparticles is a general prediction of optical theory[12,28–30]. We pointed out earlier that considera-tions of the mean densities of the suspended particu-lates allow some simplification of the mass-specificscattering cross section functions. We proposed thatthe mean density of mineral matter is approximately2:6 × 106 gm−3 and the mean dry density of particu-late dry organic matter is approximately 1:48 ×106 gm−3 for organic detritus and 1:38 × 106 gm−3

for living organic particulates. So for particles of com-parable size and scattering cross section, consideringthe relations of Eqs. (6) and (10), we expect the mass-specific scattering coefficient for organic matter to be,at a minimum, twice that of the mineral particle. Ifthe organic particles have a high concentration ofwater, the ratio would be even higher. This is alsoone of the general predictions from the studies ofBabin et al. [5]. If the mass-specific scattering crosssection for the two particle classes is the same, wemay infer that the average organic particle is at leasttwice the volume of the mineral particle. The volumeof the average organic particle would be even greater,relative to the average inorganic particle, if themass-specific scattering cross section of organic matter isless than that of the mineral particle. And, conver-sely, application of known optical properties for sus-pended particles allows the prediction of the mass-specific scattering cross section for a known particlein the environment. We have already demonstratedthis in connection with the optical properties deter-mined by Gordon and Du [28] for suspended lithplates (see Fig. 1).

The simple above-considerations can be greatlyexpanded by important new work investigating theoptical properties of suspended mineral matter boththeoretically and experimentally [24,27,57]. The par-ticle scattering cross section is a function of both par-ticle size and the complex refractive index [29].Woźniak and Stramski [24] havemade theoretical in-vestigations of the mass-specific scattering cross sec-tion considering variations in the real and imaginaryparts of the complex refractive index and the size dis-tribution. They assumed a Jungian size distributionfor the suspended particles—questionable [19,37,38]but this does provide a qualitative approximation ofparticle suites dominated by either small or largeparticles. They reconfirmed the relations concerningparticle size and the spectral slope of the mass-specific scattering cross section. That is, relative in-crease in particle size causes a decrease in spectralslope. However, they also demonstrated a loss inspectral slope of a small particle dominated distribu-tion, a relatively high mass-specific scattering crosssection, if the particle has a significant absorptioncoefficient, a relatively large imaginary coefficient ofthe complex refractive index. In addition they de-


monstrated that the magnitude of the mass-specificscattering cross section can decrease with a decreasein the real part of the complex refractive index withno change in spectral slope.Consider the nature of the particles in Mobile Bay

given the results of theoretical analyses, the Model IImultiple regressions, and the latest experimentalwork [14,57]. The mineral particles in Mobile Bay(see Fig. 2) exhibit a spectral mass-specific scatteringcross section that is in remarkable agreement withresults of laboratory analysis of suspended clays re-ported by Stramski et al. [57]. Suspensions of illiteand montmorillonite exhibit spectral slopes for themass-specific scattering cross sections very similarto what we report for σPIMðλÞ calculated from theModel II multiple regression (see Fig. 2). They reportσPIMð550Þ ≈ 0:70–0:82m2 g−1 for illite and montmor-illonite, which compares with the σPIMð550Þ ≈0:695m2 g−1 that we report for Mobile Bay. The stan-dard error for σPIMð550Þ at Mobile Bay easily encom-passes the above-values reported by Stramski et al.[57]. In addition illite and montmorillonite areknown common constituents of the suspended claysof the northern Gulf of Mexico [45,46]. Thus we haveevidence for small, clay-size particles in the sus-pended mineral component of Mobile Bay. That theorganic particles in Mobile Bay (see Fig. 3), withσPOMð555Þ ≈ 1:25m2 g−1, are also relatively small isattested to by the spectral slope of the mass-specificspectral scattering cross section. The spectral slopefor the organic mass-specific scattering cross sectionscompares favorably with the spectral slopes for thespectral scattering cross sections reported byStramski et al. [14] for picophytoplankton. The valueof σPOMð555Þ reported here can be easily duplicatedwith the typical scattering cross sections and spheri-cal equivalent diameters of picophytoplankton [14]substituted into Eq. (10) utilizing the mean organicmatter densities reported here. With σPOMð555Þbeing about twice the magnitude of σPIMð550Þ, it ispossible that the mean volume of organic particlesin Mobile Bay could be comparable to the meanvolume of the mineral particles as would be the casewith picophytoplankton and the density of the miner-al particles being about twice the density of theorganic particles as predicted from Eqs. (9) and(10) and the mean densities proposed in this paper.In Southwest Pass the nature of the suspended

particles is apparently indeterminate in the Model Imultiple regression analysis. The mineral mass-specific spectral scattering cross sections are sub-stantially larger in the Model II analysis than inthe Model I multiple regression analysis (see Fig. 4).This is evidence that the mineral particle size is sub-stantially smaller in Southwest Pass than would beindicated by the Model I analysis. And further evi-dence for this is that there is clearly a spectral slope[12,27,57,59] for the Model II mass-specific mineralspectral scattering cross sections while none is evi-dent for Model I. The σPIMð550Þ ≈ 0:60m2 g−1 forSouthwest Pass from Model II falls a bit below the

values reported for illite and montmorillonite, butthe spectral slope appears to be comparable. Thiscould be evidence for a mineral array of small clay-size particles at Southwest Pass with an admixtureof claylike material of a real refractive index lowerthan that for illite and montmorillonite into the sus-pended clay particles [24,57]. The nature of the or-ganic particles at Southwest Pass is indicated by theσPOMð555Þ ≈ 0:32m2 g−1 (Model II), which is indica-tive of a suite of large particles. The lack of a spectralslope to the mass-specific scattering cross section ofthe organic particles mirrors the lack of a spectralslope to the scattering cross sections of large nano-phytoplankton as reported by Stramski et al. [14].The value of σPOMð555Þ reported here is easily dupli-cated utilizing the spectral scattering cross sectionsand spherical equivalent diameters for typical nano-phytoplankton [14] and Eq. (10) with the meanvalues of organic particle density proposed here.Additionally further evidence that the organic parti-cles are large phytoplankton comes from the dips inthe mass-specific spectral scattering coefficient at425nm and 676nm (see Fig. 5) also reported in thetheoretical calculations of Stramski et al. [14] illus-trating the effects of anomalous dispersion [60] onphytoplankton scattering cross sections caused byphytoplankton absorption bands. It is worth keepingin mind that the uncertainty limits for the organicmatter at Southwest Pass are rather wide.

6. Conclusion

In summary we have performed a successful parti-tion of the spectral scattering coefficient at studysites in the northern Gulf of Mexico utilizing mass-specific scattering cross sections. We have delineatedthe quantitative contribution of suspended mineraland organic matter to the particulate scattering coef-ficient. With this partition we add to the arsenal ofoptical tools for studying the ocean environment andthe dynamics of the suspended particulates that playsuch a critical role in the elemental and biogeochem-ical cycles of the ocean. The total scattering coeffi-cient and its partitions give us information aboutthe suspended matter load and its major constitu-ents. Themass-specific scattering cross sections havethe real potential to give us information about theprobable mean particle size, possibly the underlyingsize distributions, and the variations in the complexrefractive index of the suspended particulates.

There are several reasons for the variations in theefficiency of the multiple regression analysis inreconstructing the particle spectral scattering coeffi-cients from field data. We are proposing improve-ments to the efficiency and accuracy of thisprocedure. Given the dominance of suspended PIMin its effect on the particulate spectral scatteringcoefficient and therefore the remote sensing reflec-tance, we must obtain more information about thenature of this material in the coastal ocean. We needto know the percentile of the clay component ofthe suspended mineral matter in order to apply the


Barillé-Boyer et al. [44] corrections in the most effi-cient manner. This can be done relatively easily androutinely with x-ray diffraction analysis on the fieldsamples collected from the CTD rosettes. In thisstudy we were forced to deal with averages of claycomposition over an entire region rather than havingdetailed knowledge of the clay composition of indivi-dual station samples. Qualitative characterization ofliving suspended POM is probably done as well asany particle characterization now being attempted[6,13,14]. However, there is still little knowledge ofparticulate organic detritus. For example, the rela-tive water concentration of living and nonlivingorganic particulates is particularly sparse. Amongpossibilities for characterizing the detrital organicparticulates are determining carbon isotope ratiosfor ascertaining whether detrital carbon particulatescame from C3 or C4 plants. Thus the variance we ob-serve in our present sets of data is due partly to op-tical differences that are not accounted for in thegrossest determinations of PIM and POM. When in-dividual samples can be ascertained to be of similarmaterials or of differing materials, it will then be pos-sible to partition the results of a research cruise intogroups of samples that would be utilized to generatemore accurate mass-specific particle scattering crosssections. Other forms of multivariate analyses suchas principle components analysis would help togroup data on particulate scattering coefficients,PIM, and POM into discrete similar groups thatcould then be analyzed by the Model II multiplelinear regression method.The mass-specific cross sections that we can now

obtain, averages of the two major suspended compo-nents, are certainly useful, but better and more accu-rate mass-specific cross sections will be forthcomingwhen the nature of suspended particulates is wellcategorized: quartz, opal, carbonates, clays, and thevarious forms of suspended organic matter. Thebiogeo-optical program continues work and effortsalong the lines of multicomponent optical modelsstarted decades ago [18]. The efforts to improve thedetermination and characterization of mass-specificscattering cross sections all involve determining thenature of the individual components of the two majorclasses of suspended particulate matter. To this endit is encouraging that there is much activity in recentyears to better characterize the optical properties ofsuspended mineral matter [11,21,24,27,28,38,41,57]and suspended organic matter [3,6,14,31,32,40,61–63]. The effort to fully characterize the optical prop-erties of the significant optically active componentsin the sea has been termed the reductionist approach[57]. The complete solution of Eqs. (8)–(11) is defi-nitely the purview of the reductionist approach. Itis clear that the completion of the biogeo-optical pro-gram of ocean optics, the recognition and investiga-tion of the optical effects of the major components ofsuspended particulates, requires the reductionistapproach.

The SAS code used to determine the Model II par-tial regression coefficients may be obtained fromScott J. Richter.

R. H. Stavn acknowledges the valuable discussionson regression with C. C. Trees, Center for Hydro-Optics and Remote Sensing, San Diego State Univer-sity. D. Stramski, Marine Physical Laboratory,Scripps Institution of Oceanography, University ofCalifornia at San Diego, submitted a detailed, andmost helpful, review of this manuscript. We acknowl-edge the valuable support of a Research AssignmentLeave from the University of North Carolina atGreensboro; a National Research Council ResearchAssociateship through NASA, Applied SciencesDirectorate, Stennis Space Center; a summer fellow-ship from the American Society of Engineering Edu-cation through Naval Research Laboratory, Code7323, Coastal and Marginal Seas Section, StennisSpace Center; the early support from ONR grantN00014-97-0812; and the Naval Research LabProject 0601153N to R. W. Gould, Jr., PredictingCoastal Bio-optical Response to Atmospheric/Oceanographic Forcing, Stennis Space Center.

References1. R. W. Gould Jr., R. A. Arnone, and M. Sydor, “Absorption, scat-

tering, and remote-sensing reflectance relationships in coastalwaters: testing a new inversion algorithm,” J. Coast. Res. 17,328–341 (2001).

2. M. Sydor, R. W. Gould, R. A. Arnone, V. I. Haltrin, and W.Goode, “Uniqueness in remote sensing of the inherent opticalproperties of ocean water,” Appl. Opt. 43, 2156–2162 (2004).

3. J. S. Cleveland, “Regional models for phytoplankton absorp-tion as a function of chlorophyll a concentration,” J. Geophys.Res. 100, 13333–13344 (1995).

4. R. W. Gould Jr. and R. A. Arnone, “Three-dimensional model-ing of inherent optical properties in a coastal environment:coupling ocean colour imagery and in situ measurements,”Int. J. Remote Sens. 19, 2141–2159 (1998).

5. M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski,“Light scattering properties of marine particles in coastal andopen ocean waters as related to the particle mass concentra-tion,” Limnol. Oceanogr. 48, 843–859 (2003).

6. R. E. Green, H. M. Sosik, and R. J. Olson, “Contributions ofphytoplankton and other particles to inherent optical proper-ties in New England continental shelf waters,” Limnol. Ocea-nogr. 48, 2377–2391 (2004).

7. R. E. Green and H. M. Sosik, “Analysis of apparent propertiesand ocean color models using measurement of seawater con-stituents in New England continental shelf surface waters,”J. Geophys. Res. 109, C03026, doi:10.1029/2003JC001977(2004).

8. D. Antoine, A. Morel, and H. Claustre, “Some peculiarities ofcase 1 waters optical properties in the northwestern Mediter-ranean Sea,” presented at the ASLO/TOS Ocean ResearchConference, Honolulu, Hawaii, USA, 15–20 February 2004.

9. H. Claustre, A. Morel, S. B. Hooker, M. Babin, D. Antoine, K.Oubelkheir, A. Bricaud, K. Leblanc, B. Quéguiner, and S. Mar-itorena, “Is desert dust making oligotrophic waters greener?,”Geophys. Res. Lett. 29, 1469, doi:10.1029/2001GL014056(2002).

10. C. Moulin, C. E. Lambert, F. Dulac, and U. Dyan, “Control ofatmospheric export of dust from North Africa by the NorthAtlantic oscillation,” Nature 387, 691–694 (1997).


11. W. M. Balch, P. M. Holligan, S. G. Ackleson, and K. J. Voss,“Biological and optical properties of mesoscale coccolithophoreblooms in the Gulf of Maine,” Limnol. Oceanogr. 36, 629–643(1991).

12. R. W. Gould Jr., R. A. Arnone, and P. M. Martinolich, “Spectraldependence of the scattering coefficient in case 1 and case 2waters,” Appl. Opt. 38, 2377–2383 (1999).

13. H. Loisel and A. Morel, “Light scattering and chlorophyll con-centration in case 1 waters: a reexamination,” Limnol. Ocea-nogr. 43, 847–858 (1998).

14. D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherentoptical properties of the ocean based on the detailed composi-tion of the planktonic community,” Appl. Opt. 40, 2929–2945(2001).

15. C. E. Binding, D. G. Bowers, and E. G. Mitchelson-Jacob, “Es-timating suspended sediment concentrations in moderatelyturbid waters; the impact of variable particle scattering prop-erties,” Remote Sens. Environ. 94, 373–383 (2005).

16. C. E. Binding, D. G. Bowers, and E. G. Mitchelson-Jacob, “Analgorithm for the retrieval of suspended sediment concentra-tions in the Irish Sea from SeaWiFS ocean colour satelliteimagery,” Int. J. Rem. Sens. 24, 3791–3806 (2003).

17. A. Cunningham, A. Dudek, and D. Mckee, “Comparison of sa-tellite and surface measurements of water leaving radianceand seawater composition in an optically variable shelfsea,” presented at the Eighth International Conference on Re-mote Sensing for Marine and Coastal Environments, Halifax,Nova Scotia, Canada, 17–19 May 2005.

18. R. P. Bukata, J. H. Jerome, K. Ya. Kondratyev, and D. V. Pozd-nayakov,Optical Properties and Remote Sensing of Inland andCoastal Waters (CRC Press, 1995).

19. R. H. Stavn and T. R. Keen, “Suspended minerogenic particledistributions in high-energy coastal environments: optical im-plications,” J. Geophys. Res. Oceans 109, C05005, doi:10.1029/2003JC002098 (2004).

20. T. R. Keen and R. H. Stavn, “Developing a capability to fore-cast coastal ocean optics: minerogenic scattering,” in Proc. 6thInternational Conference on Estuarine and Coastal Modeling,M. Spaulding and A. Blumberg, eds. (ASCE Press, 2000),pp. 178–193.

21. M. Babin and D. Stramski, “Variations in themass-specific ab-sorption coefficient of mineral particles suspended in water,”Limnol. Oceanogr. 49, 756–767 (2004).

22. J. T. O. Kirk, “Dependence of relationships between inherentand apparent optical properties of water on solar altitude,”Limnol. Oceanogr. 29, 350–356 (1984).

23. D. G. Bowers and C. E. Binding, “The optical properties ofmineral suspended particles: a review and synthesis,” Estuar.,Coast. Shelf Sci. 67, 219–230 (2006).

24. S. B. Woźniak and D. Stramski, “Modeling the optical proper-ties of mineral particles suspended in seawater and theirinfluence on ocean reflectance and chlorophyll estimationfrom remote sensing algorithms,” Appl. Opt. 43, 3489–3503(2004).

25. W. A. Snyder, R. A. Arnone, C. O. Davis, W. Goode, R.W. Gould,S. Ladner, G. Lamella, W. J. Rhea, R. Stavn, M. Sydor, and A.Weidemann, “Optical scattering and backscattering by organ-ic and inorganic particulates in U.S. coastal waters,” Appl.Opt. 47, 666–677 (2008).

26. S. R. Pearlman, H. S. Costa, R. A. Jung, J. J. McKeown, and H.E. Pearson, “Solids,” in Standard Methods for the Examina-tion of Water and Wastewater, A. D. Eaton, L. S. Clesceri,and A. E. Greenberg, eds. (American Public Health Associa-tion, 1995), Section 209, pp. 2-53–2-64.

27. D. Stramski, S. B. Woźniak, and P. Flatau, “Optical propertiesof Asian mineral dust suspended in seawater,” Limnol. Ocea-nogr. 49, 749–755 (2004).

28. H. R. Gordon and T. Du, “Light scattering by nonsphericalparticles: application to coccoliths detached from Emilianiahuxleyi,” Limnol. Oceanogr. 46, 1438–1454 (2001).

29. C. F. Bohren and D. R. Huffman, Absorption and Scattering ofLight by Small Particles (Wiley-Interscience, 1983).

30. E. J. McCartney, Optics of the Atmosphere. Scattering byMolecules and Particles (Wiley-Interscience, 1976).

31. A. Bricaud and A. Morel, “Light attenuation and scattering byphytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25,571–580 (1986).

32. E. Aas, “Refractive index of phytoplankton derived from itsmetabolite composition,” J. Plankton Res. 18, 2223 (1996),Table VIII, p. 2341.

33. M. Jonasz and G. Fournier, “Approximation of the size distri-bution of marine particles by a sum of log-normal functions,”Limnol. Oceanogr. 41, 744–754 (1996).

34. C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan,and R. Chesselet, “Log-normal distributions of suspended par-ticles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

35. K. Mahmoud, “Lognormal size distribution of particulatematter,” J. Sediment. Petrol. 43, 1161–1166 (1973).

36. D. Risovic, “Two component model of the sea particle sizedistribution,” Deep-Sea Research, Part I 40, 1459–1473(1993).

37. D. Risovic, “Effect of suspended particulate-size distributionon the backscattering ratio in the remote sensing of seawater,”Appl. Opt. 41, 7092–7101 (2002).

38. F. Peng and S.W. Effler, “Suspendedminerogenic particles in areservoir: light-scattering features from individual particleanalysis,” Limnol. Oceanogr. 52, 204–216 (2007).

39. J. B. Austin, “Methods of representing distribution of particlesize,” Industrial and Engineering Chemistry, AnalyticalEdition 11, 334–339 (1939).

40. A. Morel and Y.-H. Ahn, “Optical efficiency factors of free-living marine bacteria: influence of bacterioplankton uponthe optical properties and particulate organic carbon in ocea-nic waters,” J. Mar. Res. 48, 145–175 (1990).

41. W.M. Balch, D. T. Drapeau, T. L. Cucci, and R. D. Vaillancourt,“Optical backscattering by calcifying algae: separating thecontribution of particulate inorganic and organic carbon frac-tions,” J. Geophys. Res. 104, 1541–1558 (1999).

42. M. Defoin-Platel and M. Chami, “How ambiguous is the in-verse problem of ocean color in coastal waters?,” J. Geophys.Res. Oceans 112, C03004, doi:10.1029/2006JC003847 (2007).

43. R. A. Feely, J. H. Trefry, and B. Monger, “Chapter 1. Particlesampling and preservation,” inMarine Particles: Analysis andCharacterization, D. C. Heard and D. W. Spencer, eds. (Amer-ican Geophysical Union, 1991), pp. 5–22.

44. A.-L. Barillé-Boyer, L. Barillé, H. Massé, D. Razet, and M.Héral, “Correction for particulate organic matter as estimatedby loss on ignition in estuarine ecosystems,” Estuar., Coast.Shelf Sci. 58, 147–153 (2003).

45. L. J. Doyle and T. N. Sparks, “Sediments of the Mississippi,Alabama, and Florida (MAFLA) continental shelf,” J. Sedi-ment. Petrol. 50, 905–916 (1980).

46. A. G. Johnson and J. T. Kelley, “Temporal, spatial, and texturalvariation in the mineralogy of Mississippi river suspended se-diment,” J. Sediment. Petrol. 54, 67–72 (1984).

47. C. C. Trees, “Analytical analysis of the effect of dissolved solidson suspended solids determination,” J. Water Pollut. ControlFed. 50, 2370–2373 (1978).

48. R. W. Gould Jr., R. H. Stavn, M. S. Twardowski, and G. M.Lamela, “Partitioning optical properties into organic and in-organic components from ocean color imagery,” in OceanOptics XVI, S. Ackleson and C. Trees, eds. (Office of NavalResearch CDROM, 2002).

49. N. Jerlov, Marine Optics (Elsevier, 1975).


50. O. J. Dunn and V. A. Clark, Applied Statistics: Analysis ofVariance and Regression (John Wiley, 1974).

51. L. M. Mezei, Practical Spreadsheet Statistics & Curve Fittingfor Scientists and Engineers (Prentice-Hall, 1990).

52. B. F. J. Manly, Multivariate Statistical Methods: A Primer(Chapman & Hall, 2005).

53. W. E. Ricker, “A note concerning Professor Jolicoeur’s com-ments,” J. Fish. Res. Brd. Can. 32, 1494–1498 (1975).

54. E. A. Laws and J. W. Archie, “Appropriate use of regressionanalysis in marine biology,” Mar. Biol. 65, 13–16 (1981).

55. R. R. Sokal and F. J. Rohlf, Biometry. The Principles andPractice of Statistics in Biological Research (W. H. Freeman,1969).

56. E. T. Baker and J. W. Lavelle, “The effect of particle size on thelight attenuation coefficient of natural suspensions,” J. Geo-phys. Res. 89, 8197–8203 (1984).

57. D. Stramski, M. Babin, and S. B. Woźniak, “Variations in theoptical properties of terrigenous mineral-rich particulatematter suspended in seawater,” Limnol. Oceanogr. 52,2418–2433 (2007).

58. W. C. Isphording, F. D. Imsand, and R. B. Jackson, “Fluvialsediment characteristics of the Mobile River Delta,” Trans.Gulf Coast Assoc. Geol. Soc. XLVI, 397–408 (1985).

59. M. Sydor and R. A. Arnone, “Effect of suspended particulateand dissolved organic matter on remote sensing of coastal andriverine waters,” Appl. Opt. 36, 6905–6912 (1997).

60. H. C. van de Hulst, Light Scattering by Small Molecules(Dover, 1981).

61. D. Stramski and C. D. Mobley, “Effects of microbial particleson oceanic optics: a database of single-particle optical proper-ties,” Limnol. Oceanogr. 42, 538–549 (1997).

62. C. D. Mobley and D. Stramski, “Effects of microbial particleson oceanic optics: methodology for radiative transfer modelingand example simulations,” Limnol. Oceanogr. 42, 550–560(1997).

63. D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role ofseawater constituents in light backscattering in the ocean,”Prog. Oceanogr. 61, 27–56 (2004).


biogeo-optics: particle optical properties and the partitioning of the spectral scattering...

Documents