Solar radiation is initially unpolarized when enter-ing the Earth’s atmosphere. Solar photons are thenscattered by aerosols and atmospheric molecules, re-fracted and reflected at the atmosphere–ocean inter-face, and further scattered by hydrosols and watermolecules. As a result of these interactions, solarradiation becomes partially polarized. Polarizationof light in the atmosphere has been used as a toolfor gaining information on aerosol optical propertiesthat could not have been obtained by studyingthe scalar radiance alone (see, for example, [1] andreferences therein). In the atmosphere, polarizationmainly comes from single scattering, so that angularfeatures of the phase function are mapped directlyonto the polarized radiance. Features in singlescattering can be readily identified in the angular
distribution of the degree of (linear) polarization(DOP) [2]. In the ocean, features tend to be washedout due to the presence of multiple scattering by hy-drosols [3]. In the open ocean (Case I waters), mostparticles are organic particles (both living and non-living), covarying with chlorophyll concentration.These suspended particles have a weak effect onthe underwater DOP because of usually low concen-trations and low refractive indices [4]. Underwaterpolarization is, therefore, mainly driven by Rayleighscattering by water molecules resulting in arelatively simple pattern, i.e., with maximal DOPbetween ∼0:6 and ∼0:8 (depending on the wave-length) occurring around a 90° scattering angle [5].However, in Case II waters, inorganic particles, hav-ing a relative refractive index much higher thanchlorophyllic particles, can significantly change theDOP of the water-leaving radiance.
More than 40 years ago, Timofeeva [6] anticipatedthe importance of polarization for gaining additionalinformation on the suspended particles in the ocean.
Timofeeva and her co-workers conducted measure-ments both in the sea and in milky solutions in thelaboratory, which enabled an extensive study of thevariations of the DOP with the zenith and azimuthangle, optical depth, and wavelength. Timofeeva alsodiscovered the existence of neutral points analogousto those found in the sky [7] and illustrated the effectof the optical properties of milky solutions on the or-ientation of the e-vector [8]. Far more recently, Chamiet al. [9,10] and Loisel et al. [11], and, very recently,Lotsberg and Stamnes [12] showed how polarizedwater-leaving radiance depends on the propertiesof marine particulates and exploited the informationembedded in the polarized upwelling radiation to re-trieve compositions and concentrations of suspendedparticulates. Chami et al. studied the variations ofthe DOP (at the Brewster angle) with water turbidityand proposed an empirical algorithm to estimate theconcentration of inorganic particles [10]. The inves-tigation suggested that the observed variability ofthe magnitude of the DOP in the red region of thevisible spectrum (i.e., 650nm) is highly correlatedwith the concentration of suspended particles. Loiselet al. [11] showed that the polarized remote sensingreflectance from the POLarization and Directionalityof the Earth’s Reflectances (POLDER-2) sensor canbe used to assess the composition of the suspendedparticles in absence of aerosols and over relativelyhigh scattering waters, such as those typically foundin coastal areas or in the presence of a phytoplanktonbloom. Lotsberg et al. used the T-matrix method ofMishchenko et al. [13] to compute the underwater po-larized backscattered light for suspended particleshaving various Junge-type size distributions, as-phericities, and refractive indices. They observedthat the hydrosol Mueller matrices are mostly af-fected by variations of the real part of the refractiveindex.
It is in this context that we attempt to applythe results of both experimental and simulated ob-servations to systematically retrieve complementaryinformation on the in-water suspended particles(specifically, the real part of the refractive indexand the size distribution) that cannot be obtainedwith methods that only analyze the scalar radiance.This study is focused on the comparison between themeasured and calculated spectral and angular varia-tions of the DOP. Analyzing the DOP instead of theindividual components of the Stokes vector has theadvantage that the DOP is weakly dependent oncalibration, because the DOP itself is a ratio. Thismeans that only relative rather than absolute valuesof the water-leaving radiance are needed, and there-fore the DOP can be measured very accurately be-cause it is a relative measure.
In Section 2 we outline the experimental procedureand the technique used in the analysis of field data.In Section 3 we describe the coupled atmosphere–ocean radiative transfer model and discuss the de-pendence of the calculated DOP of the water-leavingradiance on the composition, i.e., refractive index
and size distribution of the suspended particles.In Section 4 we report the angular and spectralvariations of the DOP for various types of watersand compare experimental and simulated results.The comparison of radiative transfer simulationswith in situ measurements allows us to estimate thehydrosols’ microphysical parameters.
2. Optical Instruments and Methods
The quantities required for radiative transfer com-putations are the absorption coefficient, the scatter-ing coefficient, and the phase matrix, PðθscaÞ, whereθsca is the scattering angle (θsca ¼ 0° for light scat-tered exactly in the forward direction). The absorp-tion and scattering coefficients can be measuredin situ with existing commercial instrumentation.Absorption and backscattering coefficients can alsobe routinely retrieved from above-water measure-ments with a variety of techniques, e.g., the widelyadopted quasi-analytical algorithm [14]. In our fieldmeasurements, absorption and attenuation of all in-water constituents except water itself were mea-sured with an ac-s or an ac-9 (WET Labs), recordingdata in the wavelength range of 412 to 715nm [15].Backscattering measurements were made with anECO BB9 (WET Labs) at seven wavelengths in thevisible (between 412 and 715nm) [16]. Particle sizedistributions (PSDs) were obtained using the LISST-100X (Sequoia Scientific): the scattering intensitiesrecorded at 670nm by the 32 rings of the laser in situscattering and transmissometry (LISST) were math-ematically inverted to obtain the PSD [17].
Underwater polarized radiance measurementswere obtained using a custom-built polarimeter [18];see Fig. 1. It consists of three HyperOCR radiancesensors (Satlantic) mounted on a scanning systemcontrolled by an underwater electric stepper motor(Newmark Systems). Four buoys are necessary to
Fig. 1. (Color online) The underwater polarimeter in clearoceanic waters. For this deployment, a fourth radiance sensor(measuring circular polarization, not discussed in this analysis)was installed on the scanning system (photo courtesy of ErichSchlegel).
float the instrument away from the ship to avoid sha-dowing effects andmaintain a constant instrumenta-tion depth even in rough sea conditions. The sensors’windows are positioned along the pivot axis of themotor; in this way, the signal recorded by each sensoris always detected and integrated for the same vo-lume of water. The stepper motor rotates the sensorsin a specific local meridian plane (considered the re-ference plane) following a preset table of zenith view-ing angles established by the user. The azimuthorientation of the instrument is controlled manuallyby means of two telescopic poles extending from thedeck of the research vessel. A fourth HyperOCR sen-sor records above-water downwelling irradiance fornormalization purposes. Data are acquired throughcustomized software (NI LabVIEW) that automati-cally controls the rotation of the electric steppermotor synchronized with the data acquisition ofthe hyperspectral sensors. For each angular position,10 to 15 recordings are taken by each sensor. Eachrecording has a minimum integration time of8ms and a maximum integration time of 2048ms.The three radiance sensors have a linear polarizer(Edmund Optics) in front of each sensor window. Theorientations of the linear polarizers are at 0°, 90°,and 45° with respect to a reference axis. After the ad-dition of the polarizers, an absolute calibration wasperformed on the sensors using standard radiometrictechniques. An integrating sphere (OL Series 455Calibration Standard, Optronic Laboratories) withknown radiance characteristics was used to createa uniform light field. The immersion coefficient forthe system “polarizer plus sensor” in water was alsodetermined following the procedure described byZibordi [19]. From the values of radiance obtainedby the HyperOCRs (I0°, I90°, and I45°), the elementsI, Q, U of the Stokes vector S and the DOP can beobtained [2]:
; ð2Þwhere T is the transmission of the linear polarizerplaced in front of each hyperspectral sensor and χis its polarization efficiency. The underwater DOPat a constant depth of 1m is obtained over the entirevisible part of the spectrum (in the range of 400 to750nm at approximately 3nm resolution). FromEq. (2) it is obvious that if each system’s “polarizerplus sensor” is indistinguishable from the other two(apart from the orientation of the linear polarizer),then an absolute calibration of each sensor is notnecessary. That is the main advantage of analyzingthe DOP instead of obtaining the absolute values ofthe individual Stokes components. In the followingdiscussion, the circular component V of the Stokesvector is assumed to be negligible in comparison with
the other Stokes components, as confirmed bynumerous experimental and simulated data [20,21].
To compare experimental data with results of theradiative transfer code [22], underwater polarizedradiance measurements must be propagated to theappropriate above-water level values. The model,having been developed for remote sensing applica-tions, gives as output the Stokes vector of the water-leaving radiance (which is one of the scatteringcontributions in which the radiation field is decom-posed; see Section 3). The change in the state ofpolarization of the underwater radiance refractedout through the water–air interface of a flat watersurface can be described by the following transmis-sion matrix [22]:
and where mðλÞ ¼ 1:34 is the index of refraction ofseawater (supposed to be constant with wavelength)and θt ¼ arcsinðm sinðθiÞÞ, with θi being the angle ofincidence (from below) measured from the verticaland t�∥ðμÞ and t�⊥ðμÞ are the Fresnel transmissioncoefficients for the polarization parallel and perpen-dicular to the scattering plane (the asterisk indicatesillumination from below; see [22] for details). The as-sumption of a flat water surface is justified by thefact that the effect of waves on polarized water-leaving radiance is known to be weak [23]. If theStokes vectors of the incident (from below) and trans-mitted (i.e., refracted) light are Si and St, then
St ¼ t�wai · Si: ð5Þ
The DOP of the transmitted light, DOPt, is thengiven by
where It,Qt, andUt are the Stokes components of thetransmitted light. The above procedure assumes thatthe DOP for upwelling light inside Snell’s window
measured at a depth of 1m is a good approximationfor the DOP just below water, as verified by comple-mentary radiative transfer calculations [24].
3. Radiative Transfer Computations
In this section, our aim is to show the sensitivity ofthe DOP of the water-leaving radiance to changes ofmicrophysical properties of suspended particles. Forthis purpose, we performed radiative transfer com-putations for the coupled atmosphere–ocean system.An accurate description of the radiative transfer codebased on the adding–doubling method can be foundin Chowdhary et al. [25] Here we will give only thedetails necessary for our specific situation.
In this work, we will limit our analysis to the prin-cipal scattering plane (in which φ, the azimuth angle,is equal to zero and 180°). The choice of φ ¼ 0=180°maximizes the range of in-water scattering anglesthat can be observed above water and includes anyrange of scattering angles found in any other viewinggeometry. Figure 2(a) shows the range of observablescattering angles for an in-plane viewing geometry;see Fig. 2(b). As a consequence, data recorded outsidethe main scattering plane can be related to the datapresented here as long as they are analyzed as afunction of the scattering angle (different viewinggeometries correspond to the same scattering angle):this is commonly done in atmospheric polarimetry.The angular plots of the DOP will show its depen-dence on the above-water viewing angle, θv, and
the in-water scattering angle, θsca (see Figs. 4, 5,and 8).
The atmosphere is assumed to be purely molecular(molecular depolarization factor equal to 0.0279), thewind speed is set at 5m=s, and the solar elevation(θSun) is equal to 30°, which allows covering a broadrange of scattering angles without confining the ana-lysis to a restricted situation [i.e., sunrise or sunset;see Fig. 2(a)]. The viewing angle varies from −85° to85°, with a 5° step, 0° being the nadir direction and�90° is the horizontal direction. The observer’s posi-tion is just above the ocean surface. The outputs ofthe radiative transfer code that we consider are onlythe polarized components of the water-leaving radia-tion, which means that there is neither Sun nor skyglint contamination. For realistic conditions, thereflected sky or sunlight can also be removed as longas enough knowledge of the downwelling radianceexists [26].
We assume that the ocean body consists of onelayer with an optical thickness of 10 with no bottom.It is well known that the linear polarization of scat-tered light decreases with increasing the concentra-tion of scatterers (see, for example, [2]). This is due tothe fact that multiple scattered photons exhibit verylow linear polarization. Here we want to investigatethe effect of particle compositions and size distribu-tions on the angular and spectral variations of theDOP of the water-leaving radiance. We therefore picka typical Case II water situation with given total ab-sorption, a and total scattering, b, coefficients [2] (asthey would be measured by an ac-s or an ac-9), andwe vary the size distribution and the bulk refractiveindex for the calculation of the normalized phasematrix, PðθscaÞ. The coefficients a and b are usedas inputs in the radiative transfer code. Fixing thetotal absorption and scattering coefficients of thewater body does not, in fact, exclude the substantialvariability of hydrosols compositions, because the ab-sorption and scattering coefficients of each watercomponent combined in different ways can lead tothe same total absorption and total scattering coeffi-cients (because of their additive property) [27]. Thispeculiarity of the optical properties is advantageousbecause our analysis is intended as a research toolfor examining the effects on the DOP of variationsof the particles composition and size distributionfor given a and b. The information obtained throughthe analysis of the polarized signal is used as comple-mentary information to retrieve physical propertiesthat are not routinely retrieved with standardinversion algorithms.
The computations we have made assume only var-iations of the real part of the bulk refractive index, i.e.,for the imaginary part of the bulk refractive indexnbulk;i ¼ 0. The imaginary part of the refractive indexis introduced in the radiative transfer computationsthrough the total (without thewater contribution) ab-sorption coefficient, a. The total (without the watercontribution) scattering coefficient, b, is also intro-duced in the radiative transfer computations.Figure3
Fig. 2. (a) In-water scattering angle versus above-water viewingangle, θv, and Sun elevation, θSun. θv ¼ 0° corresponds to an obser-ver looking along the nadir direction and θv ¼ �90° corresponds tothe horizontal directions. (b) Geometry of observation and relevantangles. The thick gray lines indicate the borders of Snell’s window.
shows total absorption and total scattering coeffi-cients (without thewater contribution) used in the ra-diative transfer calculations. These values of theabsorption/scattering coefficients, as stated above,are appropriate for many Case II waters [28].
The bulk refractive index of the suspended parti-cles is varied between 1.02 [29] and 1.22 [30] (0.02initial step increment, then linearly interpolated).A power-law (or Junge-type) number size distribu-tion is chosen for the oceanic particulates, i.e.,
nðrÞ ¼ kr−ξ; ð7Þ
where nðrÞ is the fractional number density at radiusr. The constant k is chosen such that
Z∞
0nðrÞdr ¼ 1: ð8Þ
Power-law PSDs have the advantage that theyhave only one varying parameter and usually showa good fit with experimental measurements, evenwhen multiple types of particles are present [31].Particle diameters have been chosen between 0.02and 100 μm, capturing the size range of realistic mar-ine particles [32]. The slope of the PSDs is varied be-tween 3.5 and 4.5 [33] (0.1 initial step increment,then linearly interpolated). For all possible combina-tions of (ξ, nbulk), the Stokes components I, Q, and U(at wavelengths: 412, 440, 488, 510, 532, 555, 650,676, and 715nm) of the water-leaving light are cal-culated. The DOP is given by Eq. (8) for each wave-length and viewing angle. Because the StokesparameterU is null in the principal scattering plane,it is common to consider the signed DOP (this is thequantity that we analyze in our study):
DOP ¼ −QI: ð9Þ
Figure 4 shows the DOP versus scattering angleand bulk refractive index, nbulk, for slopes of the size
distribution, ξ, equal to 3.5, 4, and 4.5, and forwavelengths (λ) equal to 440, 510, and 650nm (blue,green, and red, respectively). Analogously, Fig. 5shows the DOP versus scattering angle and ξ fornbulk equal to 1.02, 1.12, and 1.22 and for wave-lengths equal to 440, 510, and 650nm.
Comparison of Figs. 4 and 5 shows that the DOP isless sensitive to the size distribution than it is to thebulk refractive index. The contour borders in Fig. 5are mostly vertical, thus showing a relatively weakvariability of the DOP with the slope of the size dis-tribution. We can anticipate that this will lead to abigger uncertainty in the retrieval of ξ from the ana-lysis of the DOP. The exception is the red band,650nm, especially for increasing values of the refrac-tive index. The changes in the physical properties,both the size distribution and the refractive index,of the suspended particles are, indeed, more pro-nounced in the red region of the spectrum, becauseRayleigh scattering (by water molecules) dominatesin the blue. Another feature common to both Figs. 4and 5 is the lack of sensitivity of the DOP in the back-scattering direction to ξ and nbulk. In fact, the DOPfor spherical particles is identically equal to zero atθsca ¼ 180°. For the position of the maximum of theDOP, the strongest influence can be found, again, byvarying the value of the bulk refractive index, whilechanges in the slope of the size distribution have aminor or insignificant influence.
4. Application of Modeled Results to Measurements
A. Retrieval Method
In this section, we compare the measurements of theDOP with the radiative transfer simulations.Estimates of the bulk refractive index, nbulk, and theslope of the PSD, ξ, are then given based on the com-parisons. For these purposes, underwater polarizedradiance measurements are first propagated to thecorresponding above-water values, using Eq. (11),then compared with the results of the radiativetransfer simulations. The variables of the computa-tional model are nbulk (the bulk refractive index), ξ(the slope of the PSD), a (the total absorption coeffi-cient, not including any water contribution), b (thetotal scattering coefficient, again, not includingany water contribution), θs (the Sun elevation), andthe wind speed. The Sun elevation and wind speedare readily obtainable quantities; total absorptionand total attenuation coefficients are measured withan ac-s or an ac-9; the bulk refractive index and theslope of the PSD are varied until the simulated DOP(DOPcalc) matches the measured DOPt. The retrievaltechnique is based on a simple least-squares fitmethod, in which for each value of nbulk the valueof ξ is chosen to minimize the root-mean-squared dif-ference (RMSD), i.e.,
Fig. 3. Total absorption and total scattering coefficients(without the water contributions) used in the radiative transfercomputations.
In Eq. (10), λj ¼ 412, 440, 488, 510, 532, 555, and650nm, which gives Nλ ¼ 7 (the ac-9 bands centeredat 676 and 715nm are not used because they arecontaminated by chlorophyll a fluorescence, not in-cluded in the radiative transfer model), and θv;k var-ies from θmax − 10° to θmax þ 10° (5° step increments;θmax is the viewing angle corresponding to the max-imal DOPt), which givesNθ ¼ 5. This means that themain criterion for agreement between measure-ments and computations is the goodness of the fitto the positive polarization maximum. This angularinterval was chosen because it corresponds to therange of the largest spectral variability in the DOP(which therefore enables the highest accuracy inthe retrieval of parameters). It is implicitly assumedin Eq. (10) that the estimated value of nbulk is an aver-age value over the visible wavelengths 412, 440, 488,510, 532, 555, and 650nm. This is justified by the fact
that the spectral variations of the bulk refractiveindex were found to fall within the retrieval error.
The contour diagram in Fig. 6 presents an exampleof the behavior of the RMSD as a function of nbulk andξ for one of the stations that will be considered in thefollowing section. The RMSD (which appears to bemonomodal) reaches its absolute minimum fornbulk ¼ 1:14 and ξ ¼ 3:5. Figure 6 clearly shows thatvariations of the bulk refractive index have a signif-icant influence on the DOP, while the variations ofthe PSD have a relatively minor influence (i.e., thevariability of the RMSD along the horizontal axisis small). Nonetheless, the correct value of ξ is re-trieved, as confirmed by the match with the valuesextracted from the particulate attenuation spectrumand the LISST measurements (shown in the follow-ing section).
Fig. 4. (Color online) Color contour diagrams of the DOP versus viewing (and scattering) angle and bulk refractive index for a Junge-typesize distribution with hyperbolic slope ξ ¼ 3:5, 4, 4.5; λ ¼ 440, 510, and 650nm.
In situmeasurements of the underwater polarizationwere carried out at 12 locations, including near-the-shore (Chesapeake Bay, New York Bight, and LongIsland Sound) and off-shore sites (the Gulf of Mexicoand Atlantic Ocean); see Table 1. To illustrate the
sensitivity of the DOP to the particles refractiveindex and size distributions, we select three surveystations, characterized by substantially differentwaters.
For the first station (representative of a “Case I”water type), measurements were conducted approxi-mately 20nautical miles east of Virginia Beach, Va.(73° 30.9554W, 36° 53.7833 N, θs ¼ 55°, on August 172009, 11 a.m., 1:5m=s winds); for the second station(“Case II-Coastal”), near the entrance of ChesapeakeBay, Va. (75° 52.4573 W, 36° 53.7833 N, θs ¼ 63°,August 20 2009, 2 p.m., 4:0m=s winds); for the thirdstation (“Case II—Coastal high [NAP]” water) in theUpper New York Bight, N.Y. (74° 02.596 W, 40°37.020 N, θs ¼ 62°, July 15 2009, 10 a.m., 3:0m=swinds). For all cases, the sky was very clear andcloudless; i.e., the maximal recorded aerosol opticaldepths were 0.020, 0.016, and 0.011 at 440, 510, and650nm, respectively [given by remotely sensed dataprovided by the MODIS (Aqua) satellite]. Becausethe inputs for the radiative transfer computationsare the measured total absorption and total scatter-ing coefficients, there is no need to calculate the con-centrations of dissolved and particulate componentsusing the equations of a bio-optical model. This
Fig. 5. (Color online) Color contour diagrams of the DOP versus viewing (and scattering) angle and hyperbolic slope for hydrosols withbulk refractive index nbulk ¼ 1:02, 1.12, 1.22; λ ¼ 440, 510, and 650nm.
Fig. 6. (Color online) Color contour diagram of the RMSD versusnbulk and ξ. The solid lines are the initial outputs of the radiativetransfer computations, which are then linearly interpolated withrespect to nbulk and ξ.
greatly enhances the validity and accuracy of theradiative transfer calculations. In the following, abio-optical model is only used to obtain estimatesof the water components.
Phytoplankton, color-dissolved organic matter(CDOM), and nonalgal particle (NAP) absorptionspectra are fitted into the total absorption spectra,recorded with an ac-s or an ac-9 (WET Labs), usingthe equations of the bio-optical model described byZhou et al. [34] but taking into account the observa-tions of Ciotti et al. [35] for phytoplankton absorp-tion. Simultaneously, a similar procedure wasfollowed to fit the scattering spectra of phytoplank-ton and NAP into the total scattering spectra. As aresult, we retrieved [Chl] and [NAP] as well as theabsorption coefficient of CDOM at 412nm, i.e.,aCDOM (412nm). The hyperbolic slope of the particu-late attenuation spectrum (γ) was used to estimatethe slope of the PSD (ξ) using the inversion modelof Boss et al. [36]. When fitting a spectrum using theequations of the bio-optical model (typically using anonlinear least-squares method), particular care hasto be given to the choice of the initial conditions or“first guess” [37]. If realistic initial conditions arechosen, the retrieved quantities (i.e., concentrationsof dissolved and particulate components) can be con-sidered as a reasonable approximation of the proper-ties of a water medium. Nonetheless, the retrievedvalues of the concentration of the particulate mattermust be treated with care, as particulate specific ab-sorption coefficients might vary substantially fromone location to another [38]. Table 1 shows the rele-vant retrieved quantities for the different typesof water.
The left panels in Fig. 7 show both the data ob-tained with the LISST-100X and the PSDs used inthe computations (for clarity, modeled PSD valuescorresponding to particle diameters smaller than0:5 μm are not shown). Equation (7) is fitted intoLISST data using the slope obtained from the parti-culate attenuation spectrum (γ ¼ ξ − 3). The only un-known in this case is the normalization constant k.Only LISST data corresponding to size (diameter)classes between 12 and 100 μm are considered in
the fitting, because small size class data are not con-sidered reliable because of instrumentation/retrievalproblems [39]. In the larger size classes, data deviatefrom the power-law approximation and are also notconsidered in the computations. Even if only sizeclasses between 12 and 100 μm are used in the ana-lysis, there are still small but noticeable differencesbetween the experimental data and the fitted curvesbecause of the presence of different modes. However,using, for example, a lognormal PSD for each modewould introduce several other parameters thatwould then need to be varied in order to fit the ex-perimental DOP. In light of these considerations, thepower-law approximation was therefore consideredto be a reasonable compromise and approximationfor the waters under investigation and yielded a sa-tisfactory fit with the LISST measurements.
Figure 8 shows the DOPt and the computationsfor the stations selected as representative of threedifferent water types. In all cases, good agreementbetween measurements and radiative transfer com-putations is observed. In Fig. 8(a) (“Case I”), theDOPt reaches maximal values of 0.56 in the blue(440nm), 0.52 in the green (510nm), and 0.63 inthe red (650nm) at a 108° in-water scattering angle.The retrieved values of nbulk and ξ are 1.06 and 3.9,respectively. The value of the bulk refractive index isthe one expected for phytoplankton particles, i.e.,particles with a high water content [29], which arethe majority of the particles found in Case I waters.The retrieved value of the slope of the particle sizedistribution is consistent with what is obtained fromthe particulate attenuation spectrum (and from theinversion of LISST measurements), i.e., 3.866.
In Fig. 8(b) (“Case II—Coastal”), the DOPt reachesmaximal values of 0.25 in the blue (440nm), 0.20 inthe green (510nm), and 0.26 in the red (650nm) ata 120° in-water scattering angle. The substantial de-crease of the amount of polarized light for all bands isdue to the higher concentrations of scatterers, bothorganic (phytoplankton) and inorganic (NAP). Theshift of the position of the maximum DOPt is influ-enced by the increased nbulk, due to the presence ofinorganic particles (which were absent in the station
Table 1. Concentrations and Inherent Optical Properties Estimated from the Absorption/Scattering Spectra for the Sites Considered in this Study
Site/Station Location [Chl] [NAP] aCDOMð412nmÞ γ
1 “Case I” Atlantic Ocean (East of Virginia Beach, Va.) 1:2 μg=literðlÞ 0 0:195m−1 0.8662 “Case II—Coastal” Upper New York Bight, N.Y. 11:3 μg=l 3:0mg=l 0:497m−1 1.163
3 “Case II—Coastal high [NAP]” Chesapeake Bay, Va. 8:1 μg=l 8:4mg=l 1:085m−1 0.4864 Long Island Sound, N.Y. 15:4 μg=l 8:1mg=l 1:340m−1 0.7515 Long Island Sound, N.Y. 18:0 μg=l 8:0mg=l 0:418m−1 0.9266 Kingsborough Marina, N.Y. 57:4 μg=l 8:8mg=l 0:652m−1 0.3437a Gulf of Mexico (East of Corpus Christi, Tex.) 0:20 μg=l 0 0:040m−1 1.1098a Gulf of Mexico (East of Corpus Christi, Tex.) 0:12 μg=l 0 0:030m−1 1.1889 Sandy Hook Bay, N.J. 7:2 μg=l 7:3mg=l 0:341m−1 0.99610 Lower New York Bight, N.J. 4:1 μg=l 5:9mg=l 0:362m−1 1.00311 Lower New York Bight, N.J. 4:5 μg=l 4:8mg=l 0:417m−1 1.21712 Upper New York Bight, N.Y. 9:4 μg=l 15:9mg=l 0:643m−1 0.905
aThe ac-9 (WET Labs) was run without a prefilter, measuring both particulate and dissolved matter at once.
“Case I”). The station is characterized by nbulk ¼ 1:16,typical for inorganic particles, which are abundant inChesapeake Bay. The value for ξ, 4.1, matches the va-lue obtained from the cp spectrum and the LISST(4.163) in this case also.
In Fig. 8(c) (“Case II—Coastal high [NAP]”), theDOPt reaches maximal values of 0.26 in the blue(440nm), 0.20 in the green (510nm), and 0.23 inthe red (650nm) at a 119° in-water scattering angle.The curve corresponding to 412nm is omitted, be-cause the signal in the blue region of the spectrum isdominated by the noise. Even if the values of theDOP in the blue and green are essentially the samein both Figs. 8(b) and 8(c), the DOP in the red is lowerin Fig. 8(c) than in Fig. 8(b). This is another effect ofthe increased amount of multiple scattering due tothe even higher concentration of inorganic particles(compared to the station named “Case II—Coastal”).The retrieved nbulk is 1.14, and ξ is 3.5, which is ex-pected for highly turbid coastal waters containing a
high percentage of large particles [as confirmed bythe particulate attenuation spectrum and the datafrom the LISST(3.486)], typical of this region.
In all cases of Fig. 8, in the backscattering direc-tion, i.e., for negative viewing angles, there is a no-ticeable disagreement between measurements andcalculations; especially for Figs. 8(b) and 8(c) (themeasured polarization is negative and almost spec-trally independent, while the calculated polarizationis positive). We attribute this to the presence of non-spherical scatterers. For spherical particles, in fact,the theory predicts positive rainbow features for thepolarization in the backscattering direction [13].However, these angles are not used in the inversionprocess.
Figure 9 shows the actual measured values ofDOPt versus the calculated values (DOPcalc) from allfield sites. Even if field stations were mostly collectedin coastal areas (i.e., the data points are concentratedin the lower part of the plot), we were able to put
Fig. 7. (Color online) Left panels: PSDs. The solid curve is obtained from LISST measurements, and the dashed line is the result of thefitting. Right panels: absorption spectra of the various water constituents. (a) Case I, (b) Case II—Coastal, (c) Case II—Coastal high [NAP].
together a comprehensive dataset of DOP valueswith a strong correlation between experimentaland calculated results.
C. Retrieval Error Analysis
The retrieved values of the PSD slopes are confirmedby the results derived from LISST measurementsand from the particulate attenuation coefficient, cp,for all cases. With regard to nbulk, we comparedour retrieval of the particulate bulk refractive indexwith the model of Twardowski et al. [33]:
where b̂bp is the particulate backscattering ratio(measured with an ECO BB9, WET Labs) and γ isthe hyperbolic slope of the attenuation spectrum.The wavelength 510nm was used for b̂bp becauseit is these data that have the most stable calibration.In Fig. 10 we plot b̂bp against ξ for selected sites (fromTable 1) that showed variability in both the particu-late backscattering ratio and the estimated slopeof the PSD. Overlaid on this plot are the modeledMie theory estimates for the particulate bulk re-fractive index [Eq. (11)]. Error bars for our retrievalsare shown for b̂bp and ξ. Most of the sites that weinvestigated fall within a narrow range of ξ values(i.e., between 3.8 and 4.2) but cover a wide rangeof b̂bp values (i.e., between 0.008 and 0.035). Excep-tions are sites 3 and 6, which are representativeof stations collected in Chesapeake Bay and inthe marina of Kingsborough College, Brooklyn,
Fig. 8. (Color online) DOPt versus viewing angle and scatteringangle. (a) Case I, (b) Case II—Coastal, (c) Case II—Coastal high[NAP]. The vertical black line indicates the position of the specularreflection of sunlight. Computations are the solid curves.
Fig. 9. (Color online) Scatterplot of the measured values of DOPt
versus the corresponding calculated values (DOPcalc).N is the totalnumber of comparisons.
Fig. 10. (Color online) Backscattering ratio as a function of thehyperbolic slope of the PSD. The solid black curves are the resultsof Mie theory calculations, and each curve represents a differentbulk refractive index (between 1.02 and 1.22, at steps of 0.02), fromTwardowski et al. [33]. The blue squares are the estimated valuesusing Eq. (11), and the red circles are the estimated values ob-tained using polarimetric measurements.
New York, respectively. These areas were character-ized by highly eutrophic waters, dominated by largerparticles [40] (indicated by ξ equal to 3.5 and 3.3,respectively).
As mentioned in Section 2, for each angular posi-tion, 10 to 15 recordings are taken by each sensor.The standard deviation for measurements of the up-welling light inside Snell’s window is between 5%and 10% for calm ocean conditions and could reach20% (depending on the wavelength) for wind speedsof approximately 8m=s. This translates into errors ashigh as 0.01 in estimating nbulk and as high as 0.1 inestimating ξ (Fig. 10). As predicted (Section 3), therelative error in retrieving ξ is larger than therelative error in retrieving nbulk. In the model ofTwardowski et al. [33], the uncertainty in the retrie-val of nbulk is calculated assuming a 10% error in themeasurement of bb, and the uncertainty in the esti-mation of ξ from the particulate attenuation spectrais 2% (if a Junge-type PSD is assumed), according toBoss et al. [36]; the accuracy of our retrieval of nbulkand ξ is therefore comparable with the techniques ofBoss et al. and Twardowski et al.
5. Summary and Conclusions
The analysis of the dependence of the DOP of water-leaving radiance in the Sun’s principal plane as afunction of the hydrosols’ composition and size distri-bution using Mie multiple scattering radiative trans-fer computations showed that the DOP is stronglyinfluenced by the microphysical parameters of thesuspended particles.
From results of below-surface polarization mea-surements in both Case I and Case II waters, we de-rived the real part of the particulate bulk refractiveindex (nbulk) and the slope of the Junge-type size dis-tribution (ξ) by comparing the simulated DOP withthe measured DOP. The best fit was found iteratively,by varying both nbulk and ξ until the RMSD reachedits minimum. The comparison of the measurementsand simulations of the DOP generally showed verygood agreement. As a measure of the quality of thematch, we looked at the RMSD between the modelfits and the polarization measurements. The RMSDwas less than 4% in the DOP for points in the vicinityof the maximum of the DOP, for all the cases consid-ered. However, computations and measurementsseemed to disagree in the backward-scattering direc-tion, suggesting that the hydrosols consisted of non-spherical particles, which are known to lack rainbowfeatures in polarization.
Estimated values of the bulk refractive index andthe size distribution were compared with results gi-ven by the model of Twardowski et al. and the modelof Boss et al., and a satisfactory match was obtained.
Based on this study, we found that multiangularpolarized water-leaving radiance collected in thevisible spectrum is a powerful tool that could besystematically used to gain additional and comple-mentary information on suspended particles. Thedevelopment of a retrieval algorithm for hydrosol
microphysical and optical properties from polarizedwater-leaving radiance (without any additional in-water measurements) is planned for the near future.Sensitivities of the method for less clear atmosphericconditions will also be considered.
This work was supported by the National Oceanicand Atmospheric Administration and the Office ofNaval Research (ONR). We thank George Kattawar,Yu You, Heidi Dierssen, Parrish Brady, and IoannisIoannou for valuable discussions. The editor and twoanonymous reviewers are acknowledged for the valu-able comments on the manuscript. We are grateful tothe crews of R/V Connecticut, R/V Fay Slover, R/VPritchard, and to the Marine Science Institute(University of Texas at Austin) for their supportduring field operations. We also thank MichaelTwardowski, James Sullivan, Scott Freeman, andHeather Groundwater of WET Labs for generouslysharing their data.
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