Estimating particle composition and size distribution ... - OSA Publishing

Estimating particle composition and size distribution from polarized water-leaving radiance Alberto Tonizzo,1,* Alex Gilerson,1 Tristan Harmel,1 Amir Ibrahim,1 Jacek Chowdhary,2 Barry Gross,1 Fred Moshary,1 and Sam Ahmed1 1

Optical Remote Sensing Laboratory, The City College of The City University of New York, New York, New York 10031, USA

2

Department of Applied Physics and Mathematics, Columbia University, New York, New York 10025, USA *Corresponding author: [email protected] Received 3 March 2011; revised 26 May 2011; accepted 16 June 2011; posted 1 July 2011 (Doc. ID 143587); published 1 September 2011

The sensitivity of the polarization of water-leaving radiance to the microphysical parameters of oceanic hydrosols, specifically to the real part of the bulk refractive index (nbulk ) and to the hyperbolic slope of the Junge-type particle size distribution (PSD, ξ) is analyzed using in situ measurements of the underwater polarized light, in both Case I and Case II waters, and multiple scattering computations. Based on comparisons of experimental and simulated data, estimations of the real part of the refractive index and of the slope of the PSD are given. The study yielded results that generally agreed with expectations and that have accuracies comparable to previously published techniques. The analysis also demonstrates that the inclusion of polarization in addition to traditional radiance measurements can be expected to provide complementary information on the nature of particle populations in the ocean. © 2011 Optical Society of America OCIS codes: 010.0280, 010.4450, 010.5620, 120.5410, 120.5630.

1. Introduction

Solar radiation is initially unpolarized when entering the Earth’s atmosphere. Solar photons are then scattered by aerosols and atmospheric molecules, refracted and reflected at the atmosphere–ocean interface, and further scattered by hydrosols and water molecules. As a result of these interactions, solar radiation becomes partially polarized. Polarization of light in the atmosphere has been used as a tool for gaining information on aerosol optical properties that could not have been obtained by studying the scalar radiance alone (see, for example, [1] and references therein). In the atmosphere, polarization mainly comes from single scattering, so that angular features of the phase function are mapped directly onto the polarized radiance. Features in single scattering can be readily identified in the angular 0003-6935/11/255047-12$15.00/0 © 2011 Optical Society of America

distribution of the degree of (linear) polarization (DOP) [2]. In the ocean, features tend to be washed out due to the presence of multiple scattering by hydrosols [3]. In the open ocean (Case I waters), most particles are organic particles (both living and nonliving), covarying with chlorophyll concentration. These suspended particles have a weak effect on the underwater DOP because of usually low concentrations and low refractive indices [4]. Underwater polarization is, therefore, mainly driven by Rayleigh scattering by water molecules resulting in a relatively simple pattern, i.e., with maximal DOP between ∼0:6 and ∼0:8 (depending on the wavelength) occurring around a 90° scattering angle [5]. However, in Case II waters, inorganic particles, having a relative refractive index much higher than chlorophyllic particles, can significantly change the DOP of the water-leaving radiance. More than 40 years ago, Timofeeva [6] anticipated the importance of polarization for gaining additional information on the suspended particles in the ocean. 1 September 2011 / Vol. 50, No. 25 / APPLIED OPTICS

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Timofeeva and her co-workers conducted measurements both in the sea and in milky solutions in the laboratory, which enabled an extensive study of the variations of the DOP with the zenith and azimuth angle, optical depth, and wavelength. Timofeeva also discovered the existence of neutral points analogous to those found in the sky [7] and illustrated the effect of the optical properties of milky solutions on the orientation of the e-vector [8]. Far more recently, Chami et al. [9,10] and Loisel et al. [11], and, very recently, Lotsberg and Stamnes [12] showed how polarized water-leaving radiance depends on the properties of marine particulates and exploited the information embedded in the polarized upwelling radiation to retrieve compositions and concentrations of suspended particulates. Chami et al. studied the variations of the DOP (at the Brewster angle) with water turbidity and proposed an empirical algorithm to estimate the concentration of inorganic particles [10]. The investigation suggested that the observed variability of the magnitude of the DOP in the red region of the visible spectrum (i.e., 650 nm) is highly correlated with the concentration of suspended particles. Loisel et al. [11] showed that the polarized remote sensing reflectance from the POLarization and Directionality of the Earth’s Reflectances (POLDER-2) sensor can be used to assess the composition of the suspended particles in absence of aerosols and over relatively high scattering waters, such as those typically found in coastal areas or in the presence of a phytoplankton bloom. Lotsberg et al. used the T-matrix method of Mishchenko et al. [13] to compute the underwater polarized backscattered light for suspended particles having various Junge-type size distributions, asphericities, and refractive indices. They observed that the hydrosol Mueller matrices are mostly affected by variations of the real part of the refractive index. It is in this context that we attempt to apply the results of both experimental and simulated observations to systematically retrieve complementary information on the in-water suspended particles (specifically, the real part of the refractive index and the size distribution) that cannot be obtained with methods that only analyze the scalar radiance. This study is focused on the comparison between the measured and calculated spectral and angular variations of the DOP. Analyzing the DOP instead of the individual components of the Stokes vector has the advantage that the DOP is weakly dependent on calibration, because the DOP itself is a ratio. This means that only relative rather than absolute values of the water-leaving radiance are needed, and therefore the DOP can be measured very accurately because it is a relative measure. In Section 2 we outline the experimental procedure and the technique used in the analysis of field data. In Section 3 we describe the coupled atmosphere– ocean radiative transfer model and discuss the dependence of the calculated DOP of the water-leaving radiance on the composition, i.e., refractive index 5048

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and size distribution of the suspended particles. In Section 4 we report the angular and spectral variations of the DOP for various types of waters and compare experimental and simulated results. The comparison of radiative transfer simulations with in situ measurements allows us to estimate the hydrosols’ microphysical parameters. 2. Optical Instruments and Methods

The quantities required for radiative transfer computations are the absorption coefficient, the scattering coefficient, and the phase matrix, Pðθsca Þ, where θsca is the scattering angle (θsca ¼ 0° for light scattered exactly in the forward direction). The absorption and scattering coefficients can be measured in situ with existing commercial instrumentation. Absorption and backscattering coefficients can also be routinely retrieved from above-water measurements with a variety of techniques, e.g., the widely adopted quasi-analytical algorithm [14]. In our field measurements, absorption and attenuation of all inwater constituents except water itself were measured with an ac-s or an ac-9 (WET Labs), recording data in the wavelength range of 412 to 715 nm [15]. Backscattering measurements were made with an ECO BB9 (WET Labs) at seven wavelengths in the visible (between 412 and 715 nm) [16]. Particle size distributions (PSDs) were obtained using the LISST100X (Sequoia Scientific): the scattering intensities recorded at 670 nm by the 32 rings of the laser in situ scattering and transmissometry (LISST) were mathematically inverted to obtain the PSD [17]. Underwater polarized radiance measurements were obtained using a custom-built polarimeter [18]; see Fig. 1. It consists of three HyperOCR radiance sensors (Satlantic) mounted on a scanning system controlled by an underwater electric stepper motor (Newmark Systems). Four buoys are necessary to

Fig. 1. (Color online) The underwater polarimeter in clear oceanic 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 Erich Schlegel).

float the instrument away from the ship to avoid shadowing effects and maintain a constant instrumentation depth even in rough sea conditions. The sensors’ windows are positioned along the pivot axis of the motor; in this way, the signal recorded by each sensor is always detected and integrated for the same volume of water. The stepper motor rotates the sensors in a specific local meridian plane (considered the reference plane) following a preset table of zenith viewing angles established by the user. The azimuth orientation of the instrument is controlled manually by means of two telescopic poles extending from the deck of the research vessel. A fourth HyperOCR sensor records above-water downwelling irradiance for normalization purposes. Data are acquired through customized software (NI LabVIEW) that automatically controls the rotation of the electric stepper motor synchronized with the data acquisition of the hyperspectral sensors. For each angular position, 10 to 15 recordings are taken by each sensor. Each recording has a minimum integration time of 8 ms and a maximum integration time of 2048 ms. The three radiance sensors have a linear polarizer (Edmund Optics) in front of each sensor window. The orientations of the linear polarizers are at 0°, 90°, and 45° with respect to a reference axis. After the addition of the polarizers, an absolute calibration was performed on the sensors using standard radiometric techniques. An integrating sphere (OL Series 455 Calibration Standard, Optronic Laboratories) with known radiance characteristics was used to create a uniform light field. The immersion coefficient for the system “polarizer plus sensor” in water was also determined following the procedure described by Zibordi [19]. From the values of radiance obtained by the HyperOCRs (I 0° , I 90° , and I 45° ), the elements I, Q, U of the Stokes vector S and the DOP can be obtained [2]: Tχ ½I þ Q cosð2αÞ þ U sinð2αÞ; 2 α ¼ 0°; 90°; 45°;

Iα ¼

ð1Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q2 þ U 2 ; ð2Þ DOP ¼ I where T is the transmission of the linear polarizer placed in front of each hyperspectral sensor and χ is its polarization efficiency. The underwater DOP at a constant depth of 1 m is obtained over the entire visible part of the spectrum (in the range of 400 to 750 nm at approximately 3 nm resolution). From Eq. (2) it is obvious that if each system’s “polarizer plus sensor” is indistinguishable from the other two (apart from the orientation of the linear polarizer), then an absolute calibration of each sensor is not necessary. That is the main advantage of analyzing the DOP instead of obtaining the absolute values of the individual Stokes components. In the following discussion, the circular component V of the Stokes vector is assumed to be negligible in comparison with

the other Stokes components, as confirmed by numerous experimental and simulated data [20,21]. To compare experimental data with results of the radiative transfer code [22], underwater polarized radiance measurements must be propagated to the appropriate above-water level values. The model, having been developed for remote sensing applications, gives as output the Stokes vector of the waterleaving radiance (which is one of the scattering contributions in which the radiation field is decomposed; see Section 3). The change in the state of polarization of the underwater radiance refracted out through the water–air interface of a flat water surface can be described by the following transmission matrix [22]: 2μ twai ¼ 2 TF ðμt ðμÞÞ m ðλÞ TF ðμt ðμÞÞ¼

1 4mðλÞμ

3 2 2 2 0 0 t2 ∥ ðμÞþt⊥ ðμÞ t∥ ðμÞ−t⊥ ðμÞ 7 6 2 2 2 0 0 7 6 t∥ ðμÞ−t2 ⊥ ðμÞ t∥ ðμÞþt⊥ ðμÞ 7; 6 0 0 0 2t∥ ðμÞt⊥ ðμÞ 5 4 0 0 0 2t∥ ðμÞt⊥ ðμÞ 2

ð3Þ where 2mðλÞμ 2mðλÞμ ; t⊥ ðμÞ ¼ ; μ þ mðλÞμt mðλÞμ þ μt qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μt ðμÞ ¼ 1 þ ðμ2 − 1Þm2 ðλÞ; μ ¼ j cosðθt Þj; t∥ ðμÞ ¼

ð4Þ

and where mðλÞ ¼ 1:34 is the index of refraction of seawater (supposed to be constant with wavelength) and θt ¼ arcsinðm sinðθi ÞÞ, with θi being the angle of incidence (from below) measured from the vertical and t ∥ ðμÞ and t ⊥ ðμÞ are the Fresnel transmission coefficients for the polarization parallel and perpendicular to the scattering plane (the asterisk indicates illumination from below; see [22] for details). The assumption of a flat water surface is justified by the fact that the effect of waves on polarized waterleaving radiance is known to be weak [23]. If the Stokes vectors of the incident (from below) and transmitted (i.e., refracted) light are Si and St , then St ¼ twai · Si :

ð5Þ

The DOP of the transmitted light, DOPt , is then given by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q2t þ U 2t ; DOPt ¼ It

ð6Þ

where I t , Qt , and U t are the Stokes components of the transmitted light. The above procedure assumes that the DOP for upwelling light inside Snell’s window 1 September 2011 / Vol. 50, No. 25 / APPLIED OPTICS

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measured at a depth of 1 m is a good approximation for the DOP just below water, as verified by complementary radiative transfer calculations [24]. 3. Radiative Transfer Computations

In this section, our aim is to show the sensitivity of the DOP of the water-leaving radiance to changes of microphysical properties of suspended particles. For this purpose, we performed radiative transfer computations for the coupled atmosphere–ocean system. An accurate description of the radiative transfer code based on the adding–doubling method can be found in Chowdhary et al. [25] Here we will give only the details necessary for our specific situation. In this work, we will limit our analysis to the principal 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 angles that can be observed above water and includes any range of scattering angles found in any other viewing geometry. Figure 2(a) shows the range of observable scattering angles for an in-plane viewing geometry; see Fig. 2(b). As a consequence, data recorded outside the main scattering plane can be related to the data presented here as long as they are analyzed as a function of the scattering angle (different viewing geometries correspond to the same scattering angle): this is commonly done in atmospheric polarimetry. The angular plots of the DOP will show its dependence on the above-water viewing angle, θv , and

Fig. 2. (a) In-water scattering angle versus above-water viewing angle, θv , and Sun elevation, θSun . θv ¼ 0° corresponds to an observer looking along the nadir direction and θv ¼ 90° corresponds to the horizontal directions. (b) Geometry of observation and relevant angles. The thick gray lines indicate the borders of Snell’s window. 5050


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), the wind speed is set at 5 m=s, and the solar elevation (θSun ) is equal to 30°, which allows covering a broad range of scattering angles without confining the analysis to a restricted situation [i.e., sunrise or sunset; see Fig. 2(a)]. The viewing angle varies from −85° to 85°, with a 5° step, 0° being the nadir direction and 90° is the horizontal direction. The observer’s position is just above the ocean surface. The outputs of the radiative transfer code that we consider are only the polarized components of the water-leaving radiation, which means that there is neither Sun nor sky glint contamination. For realistic conditions, the reflected sky or sunlight can also be removed as long as enough knowledge of the downwelling radiance exists [26]. We assume that the ocean body consists of one layer with an optical thickness of 10 with no bottom. It is well known that the linear polarization of scattered light decreases with increasing the concentration of scatterers (see, for example, [2]). This is due to the fact that multiple scattered photons exhibit very low linear polarization. Here we want to investigate the effect of particle compositions and size distributions on the angular and spectral variations of the DOP of the water-leaving radiance. We therefore pick a typical Case II water situation with given total absorption, a and total scattering, b, coefficients [2] (as they would be measured by an ac-s or an ac-9), and we vary the size distribution and the bulk refractive index for the calculation of the normalized phase matrix, Pðθsca Þ. The coefficients a and b are used as inputs in the radiative transfer code. Fixing the total absorption and scattering coefficients of the water body does not, in fact, exclude the substantial variability of hydrosols compositions, because the absorption and scattering coefficients of each water component combined in different ways can lead to the same total absorption and total scattering coefficients (because of their additive property) [27]. This peculiarity of the optical properties is advantageous because our analysis is intended as a research tool for examining the effects on the DOP of variations of the particles composition and size distribution for given a and b. The information obtained through the analysis of the polarized signal is used as complementary information to retrieve physical properties that are not routinely retrieved with standard inversion algorithms. The computations we have made assume only variations of the real part of the bulk refractive index, i.e., for the imaginary part of the bulk refractive index nbulk;i ¼ 0. The imaginary part of the refractive index is introduced in the radiative transfer computations through the total (without the water contribution) absorption coefficient, a. The total (without the water contribution) scattering coefficient, b, is also introduced in the radiative transfer computations. Figure 3

Fig. 3. Total absorption and total scattering coefficients (without the water contributions) used in the radiative transfer computations.

shows total absorption and total scattering coefficients (without the water contribution) used in the radiative transfer calculations. These values of the absorption/scattering coefficients, as stated above, are appropriate for many Case II waters [28]. The bulk refractive index of the suspended particles is varied between 1.02 [29] and 1.22 [30] (0.02 initial step increment, then linearly interpolated). A power-law (or Junge-type) number size distribution is chosen for the oceanic particulates, i.e., nðrÞ ¼ kr−ξ ;

ð7Þ

where nðrÞ is the fractional number density at radius r. The constant k is chosen such that Z

∞ 0

nðrÞdr ¼ 1:

ð8Þ

Power-law PSDs have the advantage that they have only one varying parameter and usually show a good fit with experimental measurements, even when multiple types of particles are present [31]. Particle diameters have been chosen between 0.02 and 100 μm, capturing the size range of realistic marine particles [32]. The slope of the PSDs is varied between 3.5 and 4.5 [33] (0.1 initial step increment, then linearly interpolated). For all possible combinations of (ξ, nbulk ), the Stokes components I, Q, and U (at wavelengths: 412, 440, 488, 510, 532, 555, 650, 676, and 715 nm) of the water-leaving light are calculated. The DOP is given by Eq. (8) for each wavelength and viewing angle. Because the Stokes parameter U is null in the principal scattering plane, it is common to consider the signed DOP (this is the quantity that we analyze in our study): DOP ¼ −

Q : I

ð9Þ

Figure 4 shows the DOP versus scattering angle and bulk refractive index, nbulk , for slopes of the size

distribution, ξ, equal to 3.5, 4, and 4.5, and for wavelengths (λ) equal to 440, 510, and 650 nm (blue, green, and red, respectively). Analogously, Fig. 5 shows the DOP versus scattering angle and ξ for nbulk equal to 1.02, 1.12, and 1.22 and for wavelengths equal to 440, 510, and 650 nm. Comparison of Figs. 4 and 5 shows that the DOP is less sensitive to the size distribution than it is to the bulk refractive index. The contour borders in Fig. 5 are mostly vertical, thus showing a relatively weak variability of the DOP with the slope of the size distribution. We can anticipate that this will lead to a bigger uncertainty in the retrieval of ξ from the analysis of the DOP. The exception is the red band, 650 nm, especially for increasing values of the refractive index. The changes in the physical properties, both the size distribution and the refractive index, of the suspended particles are, indeed, more pronounced in the red region of the spectrum, because Rayleigh scattering (by water molecules) dominates in the blue. Another feature common to both Figs. 4 and 5 is the lack of sensitivity of the DOP in the backscattering direction to ξ and nbulk . In fact, the DOP for spherical particles is identically equal to zero at θsca ¼ 180°. For the position of the maximum of the DOP, the strongest influence can be found, again, by varying the value of the bulk refractive index, while changes in the slope of the size distribution have a minor or insignificant influence. 4. Application of Modeled Results to Measurements A. Retrieval Method

In this section, we compare the measurements of the DOP with the radiative transfer simulations. Estimates of the bulk refractive index, nbulk , and the slope of the PSD, ξ, are then given based on the comparisons. For these purposes, underwater polarized radiance measurements are first propagated to the corresponding above-water values, using Eq. (11), then compared with the results of the radiative transfer simulations. The variables of the computational model are nbulk (the bulk refractive index), ξ (the slope of the PSD), a (the total absorption coefficient, not including any water contribution), b (the total scattering coefficient, again, not including any water contribution), θs (the Sun elevation), and the wind speed. The Sun elevation and wind speed are readily obtainable quantities; total absorption and total attenuation coefficients are measured with an ac-s or an ac-9; the bulk refractive index and the slope of the PSD are varied until the simulated DOP (DOPcalc ) matches the measured DOPt . The retrieval technique is based on a simple least-squares fit method, in which for each value of nbulk the value of ξ is chosen to minimize the root-mean-squared difference (RMSD), i.e., 1 September 2011 / Vol. 50, No. 25 / APPLIED OPTICS

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Fig. 4. (Color online) Color contour diagrams of the DOP versus viewing (and scattering) angle and bulk refractive index for a Junge-type size distribution with hyperbolic slope ξ ¼ 3:5, 4, 4.5; λ ¼ 440, 510, and 650 nm.

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Nθ X Nλ u 1 X RMSDðnbulk ; ξÞ ¼ t ½DOPt ðθv;k ; λj ; nbulk ; ξÞ − DOPcalc ðθv;k ; λj ; nbulk ; ξÞ2 : N θ N λ k¼1 j¼1

In Eq. (10), λj ¼ 412, 440, 488, 510, 532, 555, and 650 nm, which gives N λ ¼ 7 (the ac-9 bands centered at 676 and 715 nm are not used because they are contaminated by chlorophyll a fluorescence, not included in the radiative transfer model), and θv;k varies from θmax − 10° to θmax þ 10° (5° step increments; θmax is the viewing angle corresponding to the maximal DOPt ), which gives N θ ¼ 5. This means that the main criterion for agreement between measurements and computations is the goodness of the fit to the positive polarization maximum. This angular interval was chosen because it corresponds to the range of the largest spectral variability in the DOP (which therefore enables the highest accuracy in the retrieval of parameters). It is implicitly assumed in Eq. (10) that the estimated value of nbulk is an average value over the visible wavelengths 412, 440, 488, 510, 532, 555, and 650 nm. This is justified by the fact 5052


ð10Þ

that the spectral variations of the bulk refractive index were found to fall within the retrieval error. The contour diagram in Fig. 6 presents an example of the behavior of the RMSD as a function of nbulk and ξ for one of the stations that will be considered in the following section. The RMSD (which appears to be monomodal) reaches its absolute minimum for nbulk ¼ 1:14 and ξ ¼ 3:5. Figure 6 clearly shows that variations of the bulk refractive index have a significant influence on the DOP, while the variations of the PSD have a relatively minor influence (i.e., the variability of the RMSD along the horizontal axis is small). Nonetheless, the correct value of ξ is retrieved, as confirmed by the match with the values extracted from the particulate attenuation spectrum and the LISST measurements (shown in the following section).

Fig. 5. (Color online) Color contour diagrams of the DOP versus viewing (and scattering) angle and hyperbolic slope for hydrosols with bulk refractive index nbulk ¼ 1:02, 1.12, 1.22; λ ¼ 440, 510, and 650 nm.

B.

Examples of Retrieval

In situ measurements of the underwater polarization were carried out at 12 locations, including near-theshore (Chesapeake Bay, New York Bight, and Long Island Sound) and off-shore sites (the Gulf of Mexico and Atlantic Ocean); see Table 1. To illustrate the

Fig. 6. (Color online) Color contour diagram of the RMSD versus nbulk and ξ. The solid lines are the initial outputs of the radiative transfer computations, which are then linearly interpolated with respect to nbulk and ξ.

sensitivity of the DOP to the particles refractive index and size distributions, we select three survey stations, characterized by substantially different waters. For the first station (representative of a “Case I” water type), measurements were conducted approximately 20 nautical miles east of Virginia Beach, Va. (73° 30.9554 W, 36° 53.7833 N, θs ¼ 55°, on August 17 2009, 11 a.m., 1:5 m=s winds); for the second station (“Case II-Coastal”), near the entrance of Chesapeake Bay, Va. (75° 52.4573 W, 36° 53.7833 N, θs ¼ 63°, August 20 2009, 2 p.m., 4:0 m=s winds); for the third station (“Case II—Coastal high [NAP]” water) in the Upper New York Bight, N.Y. (74° 02.596 W, 40° 37.020 N, θs ¼ 62°, July 15 2009, 10 a.m., 3:0 m=s winds). For all cases, the sky was very clear and cloudless; i.e., the maximal recorded aerosol optical depths were 0.020, 0.016, and 0.011 at 440, 510, and 650 nm, respectively [given by remotely sensed data provided by the MODIS (Aqua) satellite]. Because the inputs for the radiative transfer computations are the measured total absorption and total scattering coefficients, there is no need to calculate the concentrations of dissolved and particulate components using the equations of a bio-optical model. This 1 September 2011 / Vol. 50, No. 25 / APPLIED OPTICS

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greatly enhances the validity and accuracy of the radiative transfer calculations. In the following, a bio-optical model is only used to obtain estimates of the water components. Phytoplankton, color-dissolved organic matter (CDOM), and nonalgal particle (NAP) absorption spectra are fitted into the total absorption spectra, recorded with an ac-s or an ac-9 (WET Labs), using the equations of the bio-optical model described by Zhou et al. [34] but taking into account the observations of Ciotti et al. [35] for phytoplankton absorption. Simultaneously, a similar procedure was followed to fit the scattering spectra of phytoplankton and NAP into the total scattering spectra. As a result, we retrieved [Chl] and [NAP] as well as the absorption coefficient of CDOM at 412 nm, i.e., aCDOM (412 nm). The hyperbolic slope of the particulate attenuation spectrum (γ) was used to estimate the slope of the PSD (ξ) using the inversion model of Boss et al. [36]. When fitting a spectrum using the equations of the bio-optical model (typically using a nonlinear least-squares method), particular care has to be given to the choice of the initial conditions or “first guess” [37]. If realistic initial conditions are chosen, the retrieved quantities (i.e., concentrations of dissolved and particulate components) can be considered as a reasonable approximation of the properties of a water medium. Nonetheless, the retrieved values of the concentration of the particulate matter must be treated with care, as particulate specific absorption coefficients might vary substantially from one location to another [38]. Table 1 shows the relevant retrieved quantities for the different types of water. The left panels in Fig. 7 show both the data obtained with the LISST-100X and the PSDs used in the computations (for clarity, modeled PSD values corresponding to particle diameters smaller than 0:5 μm are not shown). Equation (7) is fitted into LISST data using the slope obtained from the particulate attenuation spectrum (γ ¼ ξ − 3). The only unknown in this case is the normalization constant k. Only LISST data corresponding to size (diameter) classes between 12 and 100 μm are considered in Table 1.

Concentrations and Inherent Optical Properties Estimated from the Absorption/Scattering Spectra for the Sites Considered in this Study

Site/Station 1 “Case I” 2 “Case II—Coastal” 3 “Case II—Coastal high [NAP]” 4 5 6 7a 8a 9 10 11 12 a

the fitting, because small size class data are not considered reliable because of instrumentation/retrieval problems [39]. In the larger size classes, data deviate from the power-law approximation and are also not considered in the computations. Even if only size classes between 12 and 100 μm are used in the analysis, there are still small but noticeable differences between the experimental data and the fitted curves because of the presence of different modes. However, using, for example, a lognormal PSD for each mode would introduce several other parameters that would then need to be varied in order to fit the experimental DOP. In light of these considerations, the power-law approximation was therefore considered to be a reasonable compromise and approximation for the waters under investigation and yielded a satisfactory fit with the LISST measurements. Figure 8 shows the DOPt and the computations for the stations selected as representative of three different water types. In all cases, good agreement between measurements and radiative transfer computations is observed. In Fig. 8(a) (“Case I”), the DOPt reaches maximal values of 0.56 in the blue (440 nm), 0.52 in the green (510 nm), and 0.63 in the red (650 nm) 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 is the one expected for phytoplankton particles, i.e., particles with a high water content [29], which are the majority of the particles found in Case I waters. The retrieved value of the slope of the particle size distribution is consistent with what is obtained from the particulate attenuation spectrum (and from the inversion of LISST measurements), i.e., 3.866. In Fig. 8(b) (“Case II—Coastal”), the DOPt reaches maximal values of 0.25 in the blue (440 nm), 0.20 in the green (510 nm), and 0.26 in the red (650 nm) at a 120° in-water scattering angle. The substantial decrease of the amount of polarized light for all bands is due to the higher concentrations of scatterers, both organic (phytoplankton) and inorganic (NAP). The shift of the position of the maximum DOPt is influenced by the increased nbulk , due to the presence of inorganic particles (which were absent in the station

Location Atlantic Ocean (East of Virginia Beach, Va.) Upper New York Bight, N.Y. Chesapeake Bay, Va. Long Island Sound, N.Y. Long Island Sound, N.Y. Kingsborough Marina, N.Y. Gulf of Mexico (East of Corpus Christi, Tex.) Gulf of Mexico (East of Corpus Christi, Tex.) Sandy Hook Bay, N.J. Lower New York Bight, N.J. Lower New York Bight, N.J. Upper New York Bight, N.Y.

[Chl] 1:2 μg=literðlÞ 11:3 μg=l 8:1 μg=l 15:4 μg=l 18:0 μg=l 57:4 μg=l 0:20 μg=l 0:12 μg=l 7:2 μg=l 4:1 μg=l 4:5 μg=l 9:4 μg=l

[NAP]

aCDOM ð412 nmÞ

γ

0 3:0 mg=l 8:4 mg=l 8:1 mg=l 8:0 mg=l 8:8 mg=l 0 0 7:3 mg=l 5:9 mg=l 4:8 mg=l 15:9 mg=l

0:195 m−1

0.866 1.163 0.486 0.751 0.926 0.343 1.109 1.188 0.996 1.003 1.217 0.905

The ac-9 (WET Labs) was run without a prefilter, measuring both particulate and dissolved matter at once.

5054


0:497 m−1 1:085 m−1 1:340 m−1 0:418 m−1 0:652 m−1 0:040 m−1 0:030 m−1 0:341 m−1 0:362 m−1 0:417 m−1 0:643 m−1

Fig. 7. (Color online) Left panels: PSDs. The solid curve is obtained from LISST measurements, and the dashed line is the result of the fitting. Right panels: absorption spectra of the various water constituents. (a) Case I, (b) Case II—Coastal, (c) Case II—Coastal high [NAP].

“Case I”). The station is characterized by nbulk ¼ 1:16, typical for inorganic particles, which are abundant in Chesapeake Bay. The value for ξ, 4.1, matches the value obtained from the cp spectrum and the LISST (4.163) in this case also. In Fig. 8(c) (“Case II—Coastal high [NAP]”), the DOPt reaches maximal values of 0.26 in the blue (440 nm), 0.20 in the green (510 nm), and 0.23 in the red (650 nm) at a 119° in-water scattering angle. The curve corresponding to 412 nm is omitted, because the signal in the blue region of the spectrum is dominated by the noise. Even if the values of the DOP in the blue and green are essentially the same in both Figs. 8(b) and 8(c), the DOP in the red is lower in Fig. 8(c) than in Fig. 8(b). This is another effect of the increased amount of multiple scattering due to the 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 expected for highly turbid coastal waters containing a

high percentage of large particles [as confirmed by the particulate attenuation spectrum and the data from the LISST(3.486)], typical of this region. In all cases of Fig. 8, in the backscattering direction, i.e., for negative viewing angles, there is a noticeable disagreement between measurements and calculations; especially for Figs. 8(b) and 8(c) (the measured polarization is negative and almost spectrally independent, while the calculated polarization is positive). We attribute this to the presence of nonspherical scatterers. For spherical particles, in fact, the theory predicts positive rainbow features for the polarization in the backscattering direction [13]. However, these angles are not used in the inversion process. Figure 9 shows the actual measured values of DOPt versus the calculated values (DOPcalc ) from all field sites. Even if field stations were mostly collected in coastal areas (i.e., the data points are concentrated in the lower part of the plot), we were able to put 1 September 2011 / Vol. 50, No. 25 / APPLIED OPTICS

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together a comprehensive dataset of DOP values with a strong correlation between experimental and calculated results. C.

Retrieval Error Analysis

The retrieved values of the PSD slopes are confirmed by the results derived from LISST measurements and from the particulate attenuation coefficient, cp , for all cases. With regard to nbulk , we compared our retrieval of the particulate bulk refractive index with the model of Twardowski et al. [33]: Fig. 9. (Color online) Scatterplot of the measured values of DOPt versus the corresponding calculated values (DOPcalc ). N is the total number of comparisons.

^bp ; γÞ ¼ 1 þ b ^bp 0:5377þ0:4867γ2 ð1:4676 þ 2:2950γ 2 nbulk ðb þ 2:3113γ 4 Þ;

ð11Þ

^bp is the particulate backscattering ratio where b (measured with an ECO BB9, WET Labs) and γ is the hyperbolic slope of the attenuation spectrum. ^bp because The wavelength 510 nm was used for b it is these data that have the most stable calibration. ^bp against ξ for selected sites (from In Fig. 10 we plot b Table 1) that showed variability in both the particulate backscattering ratio and the estimated slope of the PSD. Overlaid on this plot are the modeled Mie theory estimates for the particulate bulk refractive index [Eq. (11)]. Error bars for our retrievals ^bp and ξ. Most of the sites that we are shown for b investigated fall within a narrow range of ξ values (i.e., between 3.8 and 4.2) but cover a wide range ^bp values (i.e., between 0.008 and 0.035). Excepof b tions are sites 3 and 6, which are representative of stations collected in Chesapeake Bay and in the marina of Kingsborough College, Brooklyn,

Fig. 8. (Color online) DOPt versus viewing angle and scattering angle. (a) Case I, (b) Case II—Coastal, (c) Case II—Coastal high [NAP]. The vertical black line indicates the position of the specular reflection of sunlight. Computations are the solid curves. 5056


Fig. 10. (Color online) Backscattering ratio as a function of the hyperbolic slope of the PSD. The solid black curves are the results of Mie theory calculations, and each curve represents a different bulk refractive index (between 1.02 and 1.22, at steps of 0.02), from Twardowski et al. [33]. The blue squares are the estimated values using Eq. (11), and the red circles are the estimated values obtained using polarimetric measurements.

New York, respectively. These areas were characterized by highly eutrophic waters, dominated by larger particles [40] (indicated by ξ equal to 3.5 and 3.3, respectively). As mentioned in Section 2, for each angular position, 10 to 15 recordings are taken by each sensor. The standard deviation for measurements of the upwelling light inside Snell’s window is between 5% and 10% for calm ocean conditions and could reach 20% (depending on the wavelength) for wind speeds of approximately 8 m=s. This translates into errors as high as 0.01 in estimating nbulk and as high as 0.1 in estimating ξ (Fig. 10). As predicted (Section 3), the relative error in retrieving ξ is larger than the relative error in retrieving nbulk. In the model of Twardowski et al. [33], the uncertainty in the retrieval of nbulk is calculated assuming a 10% error in the measurement of bb, and the uncertainty in the estimation of ξ from the particulate attenuation spectra is 2% (if a Junge-type PSD is assumed), according to Boss et al. [36]; the accuracy of our retrieval of nbulk and ξ is therefore comparable with the techniques of Boss et al. and Twardowski et al. 5. Summary and Conclusions

The analysis of the dependence of the DOP of waterleaving radiance in the Sun’s principal plane as a function of the hydrosols’ composition and size distribution using Mie multiple scattering radiative transfer computations showed that the DOP is strongly influenced by the microphysical parameters of the suspended particles. From results of below-surface polarization measurements in both Case I and Case II waters, we derived the real part of the particulate bulk refractive index (nbulk ) and the slope of the Junge-type size distribution (ξ) by comparing the simulated DOP with the measured DOP. The best fit was found iteratively, by varying both nbulk and ξ until the RMSD reached its minimum. The comparison of the measurements and simulations of the DOP generally showed very good agreement. As a measure of the quality of the match, we looked at the RMSD between the model fits and the polarization measurements. The RMSD was less than 4% in the DOP for points in the vicinity of the maximum of the DOP, for all the cases considered. However, computations and measurements seemed to disagree in the backward-scattering direction, suggesting that the hydrosols consisted of nonspherical particles, which are known to lack rainbow features in polarization. Estimated values of the bulk refractive index and the size distribution were compared with results given by the model of Twardowski et al. and the model of Boss et al., and a satisfactory match was obtained. Based on this study, we found that multiangular polarized water-leaving radiance collected in the visible spectrum is a powerful tool that could be systematically used to gain additional and complementary information on suspended particles. The development of a retrieval algorithm for hydrosol

microphysical and optical properties from polarized water-leaving radiance (without any additional inwater measurements) is planned for the near future. Sensitivities of the method for less clear atmospheric conditions will also be considered. This work was supported by the National Oceanic and Atmospheric Administration and the Office of Naval Research (ONR). We thank George Kattawar, Yu You, Heidi Dierssen, Parrish Brady, and Ioannis Ioannou for valuable discussions. The editor and two anonymous reviewers are acknowledged for the valuable comments on the manuscript. We are grateful to the crews of R/V Connecticut, R/V Fay Slover, R/V Pritchard, and to the Marine Science Institute (University of Texas at Austin) for their support during field operations. We also thank Michael Twardowski, James Sullivan, Scott Freeman, and Heather Groundwater of WET Labs for generously sharing their data. References 1. F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. Mishchenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009). 2. J. E. Hansen and L. D. Travis, “Light-scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974). 3. G. W. Kattawar, “Ocean optics in the near future 5–10 years out, where we’re headed and current challenges,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010. 4. T. Harmel and M. Chami, “Invariance of polarized reflectance measured at the top of atmosphere by PARASOL satellite instrument in the visible range with marine constituents in open ocean waters,” Opt. Express 16, 6064–6080 (2008). 5. A. Tonizzo, A. Ibrahim, J. Chowdhary, A. Gilerson, and S. Ahmed, “Estimating particle composition from the polarized water-leaving radiance,” presented at Ocean Optics XX, Anchorage, Alaska, Sept. 27–Oct. 1 2010. 6. V. A. Timofeeva, “The degree of light polarization in turbid media,” Izv. Atmos. Ocean Phys. 6, 513–522 (1970). 7. V. A. Timofeeva, A. A. Vostroknutov, and L. A. Koveshnikova, “Influence of asymmetrical illumination on the light field inside a turbid medium,” Izv. Atmos. Ocean Phys. 12, 1259–1266 (1966). 8. V. A. Timofeeva, “Plane of vibrations of polarized light in turbid media,” Izv. Atmos. Ocean Phys. 10, 1049–1057 (1969). 9. M. Chami, R. Santer, and E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40, 2398–2416 (2001). 10. M. Chami and D. Mckee, “Determination of biogeochemical properties of marine particles using above water measurements of the degree of polarization at the Brewster angle,” Opt. Express 15, 9494–9509 (2007). 11. H. Loisel, L. Duforet, D. Dessailly, M. Chami, and P. Dubuisson, “Investigation of the variations in the water leaving polarized reflectance from the POLDER satellite data over two biogeochemical contrasted oceanic areas,” Opt. Express 16, 12905–12918 (2008). 12. J. K. Lotsberg and J. J. Stamnes, “Impact of particulate oceanic composition on the radiance and polarization of underwater and backscattered light,” Opt. Express 18, 10432–10445 (2010). 1 September 2011 / Vol. 50, No. 25 / APPLIED OPTICS

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