Abstract

A novel snapshot hyperspectral imager is introduced for ocean color (OC) applications and its capabilities are demonstrated. The instrument provides hyperspectral radiance images with a wide field-of-view (FOV) and short exposure time, which is valuable for the direct characterization of the wind-roughened surface in various illumination conditions and wind speeds. Uncertainties in the total(Lt), sky (Ls) and derived water-leaving (Lw)radiances at viewing angles of 20–60° are determined as a function of wind speed together with associated correlation coefficients and variances of the sea surface reflectance coefficient ρ. Estimated Lw uncertainties can partially explain the inaccuracy of satellite retrievals in the blue bands in the coastal waters. It is shown that in above-water measurements in no-glint conditions with viewing and azimuth angles of 40° and 90°, respectively, for both Lt(λ) and Ls(λ) the impact of FOV is minimal at least up to measured W = 5.7 m/s for full-angle FOV of 4° and larger. Implications of uncertainties for the derivation of water leaving radiance in above-water ship-borne and AERONET-OC measurements are discussed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Multi-spectral remote sensing reflectance data from Ocean Color (OC) satellites are suitable for the retrieval of important water parameters such as concentration of chlorophyll-a, absorption and backscattering coefficients, but they often do not have appropriate spatial and spectral resolution in some applications, such as characterization of the bottom, detection of underwater objects and depth retrieval. Hyperspectral measurements with proper resolution can significantly improve the accuracy of retrievals in complex coastal and inland waters, and are particularly useful in shallow waters where bathymetric and bottom make-up information maps can be retrieved [1].

Development of hyperspectral imagers and applications of hyperspectral imagery to coastal and optically shallow waters has attracted increasing attention. Some example airborne sensors include [2]: AVIRIS, Ocean PHILLS and CASI instruments, and the satellite-borne Hyperion imager. Applications range from validation [3] to mapping and classification of corals [4], extraction of bathymetry and bottom types [5] as well as algorithm development [6,7]. Recent systems include the HICO instrument on the International Space Station [8] and a new generation NASA airborne imager PRISM [9] with multiple applications, which demonstrate the efficacy of hyperspectral imaging [10]. In NASA’s Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission [11] it is expected that the main sensor will be a hyperspectral imager, so different aspects of hyperspectral sensing and processing including atmospheric correction [12,13], surface characterization, skylight correction and advanced retrieval algorithms are especially important and require novel approaches.

Until recently, advances in hyperspectral imaging were generally constrained to improvements in signal-to-noise ratio, or increases of cross-track or spectral resolution through substitution of newer generations of focal plane arrays. However the basic design still required physically moving or scanning the instrument to achieve along-track information, the so-called “push-broom” mode of operation. The recent development of “snapshot” mode hyperspectral imagers eliminates this difficulty, and while such instruments have their own disadvantages, measurements can be made from non-moving platforms, ships, etc., providing an abundance of new data and capabilities [14].

In OC applications, the accuracy of retrievals of water parameters depends on the quality of the estimated remote sensing reflectance (Rrs). One of the significant uncertainties in this estimation is associated with the characterization of the ocean surface, especially in windy conditions, and removal of the sky component reflected from this surface. For satellite applications, such reflectance is included in the atmospheric correction algorithm, specifically in the calculation of the Rayleigh and aerosol components [15–17]. For ship-borne measurements, the reflectance coefficient of skylight from the sea surface (ρ) is pre-calculated for specific geometries, which are recommended for such observations [18,19]. In all these cases, the impact of the wind-roughened surface on the radiance is estimated based on statistics of Cox and Munk [20], who measured wave slopes as a function of the wind speed. This approach is included in multiple scalar [21] and vector [16,22–26] radiative transfer models and allows simulation of the mean radiance spectra for differing wind speeds and various atmospheric and water conditions. Such models, however, do not estimate the variability of the radiance spectra and corresponding uncertainties in measurements of the water leaving radiance (orRrs) in windy conditions. Several factors drive these uncertainties. Typically, for in situ Ocean Color measurements, Cox-Munk statistics (derived from an approximate wind speed measurement) are the only available indicator of the instantaneous sea state. The reflectance coefficient, ρ, depends strongly on knowledge of the sea state, but also significantly on wavelength, aerosol characteristics and polarization effects, which are not routinely measured [24,27–31]. Related uncertainties can affect the quality of the near surface measurements and atmospheric correction [32]. That includes data from AERONET-OC stations [33], which are based on above water measurements from ocean platforms and are widely used for the validation of satellite sensors.

The goal of this paper is to demonstrate the capabilities of a new snapshot hyperspectral imager for applications of interest to the ocean color community, including characterization of the ocean surface, estimation of the uncertainties associated with above water radiometric measurements and derived water leaving radiances.

This paper is broken down as follows: Section 2 introduces the imager, Section 3 describes our uncertainty model for water-leaving radiance, Section 4 describes the in situ data collected with the imager, Section 5 combines uncertainty model with the spatial and spectral information of the imager to analyze the sources of uncertainty in the derivation of Rrs, Section 6 discusses the implications of the results to above-water, AERONET-OC and satellite retrievals, and Section 7 concludes the work.

2. Instrumentation and calibration

As was mentioned before, hyperspectral imagers which were thus far used in ocean studies were primarily based on a push-broom method of data acquisition, with hyperspectral and cross track data recorded in one CCD scan and with the along track dimension added through the movement of the system. Some instruments attempt to circumvent this requirement through addition of a rotatable mirror, however this is only a partial solution; the resultant system requires additional time to complete a scan, and becomes polarization sensitive.

The Cubert company (Germany) recently developed a robust imaging spectrometer UHD285 (Fig. 1) with no moving parts which permits acquisition of the entire spectral cube in the visible/NIR part of the spectrum. Internally, after light from the scene passes through the objective lens, it is divided by a 50:50 cubic non-polarizing beam splitter. One-half is directed to a photo-detector matrix for acquisition of a panchromatic image in the 450-1000 nm wavelength range with a spatial resolution of 1000x1000 pixels. The other half of the beam is modified by a microlens array, collimated, spectrally split using a prism, and finally focused on a second detector matrix. After processing with Cubert’s proprietary algorithm, 138 spectral channels with 4 nm spacing are available in a 50x50 pixel image. It was found that the instrument has some polarization sensitivity; however, these effects were not taken into account in the current study.

 figure: Fig. 1

Fig. 1 Snapshot hyperspectral imager Cubert UHD285: (a) general view, (b) on the tripod at the ocean platform.

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The entire system can collect images with a frame rate of up to 20 cubes/s and 14 bit digitization. The weight of the instrument is about 3kg and it has dimensions of 280 mm in length and 100 mm in diameter, which makes it suitable for various field measurements.

Since a prism is used as the dispersive element in the imager, the spectral bandwidth strongly depends on the wavelength [34], Fig. 2(a). To illustrate the effects on the measurements, Fig. 2(b) shows a spectrum of a Spectralon plate under clear-sky conditions taken by a GER-1500 spectroradiometer with 1.5 nm resolution (SpectraVista, NY), compared with the same spectra measured by center pixel of the UHD285 imager. Near Fraunhofer lines or other pronounced absorption peaks, there can be deviations (as with most spectrometers), but the effect becomes much more pronounced as the wavelength increases.

 figure: Fig. 2

Fig. 2 Integration of the spectra by the imager: (a) spectral bandwidths, (b) comparison with GER spectrum.

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The non-scanning feature eliminates the necessity of the continual movement required by push-broom imagers. This new approach opens the possibility for continuous observations from elevated on-shore locations, and from ocean platforms, as well as from appropriately positioned helicopters. The method can therefore be used for monitoring fast changing features and processes in the ocean and on the surface for any desired period of time, at video frame rates. A UHD285 imager was recently acquired by the Optical Remote Sensing Laboratory at CCNY, where it underwent additional laboratory calibration and was used in field measurements of ocean waters from several platforms. A typical integration time for ocean observations with the imager is 20-50 ms, which means that the images represent an average state of the ocean surface, and are unable to capture fine-scale wave structure, which would require integration times below 1ms [35].

In our measurements, the system was used with an additional lens in front of the imager, which increased the FOV to 40°. The sophistication of the imager calibration can be seen from Fig. 3, where only two wavelengths are shown. Similar matrices are generated for all 138 wavelengths of the imager. This calibration was carried out through the comparison of radiances reflected from a white Lambertian plate standard (ZenithLiteTM, SphereOptics GmbH) with the radiances measured by the GER spectroradiometer, which recently underwent spectral and radiometric calibration at the manufacturer.

 figure: Fig. 3

Fig. 3 Calibration matrices for the imager at 530 and 750 nm.

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For initial field deployments, dark measurements were conducted by manually placing a cap over the aperture. For later deployments, a filter wheel was installed in front of the imager to automate a switch between dark and object measurements, which resulted in small shadowing of light in the corners of the instrument.

3. Theory and modeling

The related theory was discussed in details elsewhere [31] but is briefly repeated here. The main parameter of interest in the field of OC is the remote sensing reflectance Rrs just above the surface of the ocean [36]:

Rrs(θv,φv,λ)=Lw(θv,φv,λ)/Ed(λ),
where Lw(θv,φv,λ) is the water leaving radiance, Ed(λ) is the downwelling irradiance, θv,φv are the viewing (VA) and azimuth angles respectively and λ is the wavelength. Viewing angles are measured from nadir and the azimuth angle is equal to 0° when the Sun and the sensor are in opposition.

For above surface ocean observations, assuming that Sun glint is avoided and there are no whitecaps, Lw(θv,φv,λ) is determined from

Lt(θv,φv,λ)=Lw(θv,φv,λ)+ρ(θv,φv,λ,W,AOT,)Ls(πθv,φv,λ),
where Lt(θv,φv,λ) is the total upwelling radiance leaving the ocean surface, with a typical relative solar azimuth angle of ϕv=90° or ϕv=135° [18]. For a flat ocean surface, the ρ coefficient is the Fresnel coefficient defined by the viewing angle [37] and the indices of refraction of the air and water. In the presence of ocean waves it is a function of many parameters, including wind speed, illumination-viewing conditions, aerosol optical thickness (AOT), polarization, dispersion of seawater, and Sun glint [29–31,38,39] and is thus wavelength dependent. Generally ρis the integral of reflections from individual wave facets, so it additionally depends on the FOV and the integration time of the sensor. For satellite observations at the top of atmosphere (TOA), surface effects are included in both the Rayleigh component (calculated independently of aerosol parameters) and in the radiances for aerosol models [16,40,41].

In this work, the RayXP vector radiative transfer code (VRT) [25] was used in RT closure with the measurements from the imager. This code was successfully benchmarked against other VRT codes [25,42], polarimetric measurements of the atmosphere-ocean system [43–45] and surface effects for wind roughened surface [31]. The code allows the stratification of the atmosphere and ocean in horizontally homogeneous (plane parallel) layers, which are characterized by molecular absorption (τABS) and scattering (τMOL) optical depths, depolarization ratio, and an aerosol or hydrosol (represented by a 4x4 single-scattering Mueller matrix, single scattering albedo, and optical depth, τSOL).

The Stokes vectors corresponding to the radiance arriving at the sensor from the water body (Lt) and the sky (Ls) were computed from the simulations of the atmosphere-ocean system assuming a set of the following plane-parallel homogeneous layers. The first three layers are dedicated to the atmosphere (described top to bottom) with the first one representing 64.74% of the total Rayleigh optical thickness (τR) and 100% of the ozone optical thickness (τO3), a middle layer containing the remaining 35% of τR and the full aerosol optical thickness, and the last layer with 0.26% of τR between the sensor and the ocean surface. The aerosol single scattering albedo was assumed 0.99 for all simulations. Aerosols are usually absorbing in the coastal areas and that can be the reason for some discrepancies. Rayleigh optical thickness values were the same as the ones used for MODIS products (0.098 at 550 nm). The middle layer containing aerosols was defined as consisting of a mixture of 79.6% sea salt, 19.9% dust and 0.5% soot by volume with a relative humidity of 60% [29]. The total aerosol optical thickness τA and Angstrom coefficient γ used for simulations were from Microtops II (Solar Light, PA) measurements. The oceanic layer, including hydrosols, was composed simply of one homogenous, optically thick water layer at which IOPs were measured (i.e. 0.5m underneath the water surface). The hydrosol single scattering albedo was calculated from the particulate absorption and attenuation. A Rayleigh depolarization factor of 0.039 was applied to account for the molecular anisotropy of water molecules [46]. Isotropic Cox-Munk slope distributions [20] were assumed for all simulations based on average anemometer wind speed (W) measurements. The variance σiso2 of the isotropic slope distribution related to the wind speed W at 12.5 m above the surface level is determined as [20]

σiso2=0.003+0.00512W±0.004.

The VRT program does not simulate uncertainties of Lt, Lw and ρ. Including 1-sigma uncertainties into the nomenclature, we now have

Ls±σs,Lt±σt,Lw±σw,ρ±σρ,
where the (θv,φv,λ) parameters have been omitted for clarity, and σt, σw, σs and σρ are the standard deviations of the total, water leaving and sky radiances, and reflectance coefficient, respectively. The full uncertainty equation for the total radiance (assuming lack of glint and foam in Eq. (2)) is given as [47]
σt2=[LtLwLtLsLtρ][σw2σwsσwρσwsσs2σsρσwρσsρσρ2][LtLwLtLsLtρ],
where all covariance terms are included. The partial derivatives may be computed simply, resulting in LtLw=1, LtLs=ρ and Ltρ=Ls. Substituting the computed derivatives into Eq. (5) and simplifying, yields

σt2=σw02+ρ2σs2+Ls2σρ2+2ρLsσsρ+2ρσws+2Lsσwρ.

In the above equation, σw2 has been replaced with σw02, for contrast with an alternate formulation below. This equation identifies components which contribute to the variance of the total signal emanating from the ocean surface, and includes σw02, which is due to the natural variability of the upwelling radiance under the surface and its propagation through the wind-roughened water-air interface.

If we use Eq. (2) in the form of Lw=LtρLs, the variance of the water leaving signal would then be

σw2=σt2+ρ2σs2+Ls2σρ2+2ρLsσsρ2ρσts2Lsσtρ.

In this equation σw2characterizes the variance of Lwin the process of Lwretrieval from above surface measurements, depends on all components in Eq. (7a) and as such can be very different from σw02 . Additional relationships regarding σw02 and σw2 from Eqs. (6) and (7a) will be further given in Section 5.1.

Let us assume that σρin Eq. (7a) is small and ρ almost constant for a given measurement at a specific viewing angle. This is the typical practice for estimation of Lw in situ. In actuality, this is only a valid assumption under conditions of very low wind speed, homogenous sky, viewing angles near nadir, and solar angles near the horizon where the contribution of Sun glitter is small. Then

σw2σt2+ρ2σs22ρσts,
and through the subtraction of Eq. (7b) from (7a) and considering a weak correlation between ρ and Ls, we can estimate the effect of the assumption as
Ls2σρ22Lsσtρorσρ2rtρσt/Ls,
where rtρ is the correlation coefficient for Lt and ρ. Thus a preliminary relationship between σt and σρ in Eq. (7c) can be established.

Using data from the imager we can quantify components σw, σt, σs,σts as well as corresponding correlation coefficients in Eq. (7) to estimate realistic uncertainties in measurements of these parameters and contributions to the total signals. Due to the assumptions made, sometimes the value of rtρ exceeds 1. In these cases, rtρ was clamped to a value of 1.

As noted above, assumption of the constant coefficient ρ corresponds to typical cases of derivation of the water leaving radiance Lw using Eq. (2), as is done for above water measurements and in the satellite atmospheric correction models.

Since σρ cannot be determined from Eq. (7), additional relationships based on Eq. (3) [20] were utilized to find a dependence of σρ on the wind speed and viewing geometry. starting with the isotropic mean-square wave slope as a function of wind speed, σiso2, the Gaussian probability density function describing the slope distribution, f(x|σiso2), is given by

f(x|σiso2)=(2πσiso2)1/2exp(x22σiso2),
where x is the slope. For calculation of the Fresnel coefficients, the slopes are converted to viewing angles (θn, the angle between zenith and the instantaneous “facet” normal direction) by θn=tan1(x), and the incidence angle upon the facet (θfacet) which would produce a reflection observable at a viewing angle of θv is determined by θfacet=θv+θn.

This simplified view ignores wave shadowing and multiple scattering by wave surfaces. These effects become significant at large VAs, where due to the simplification the possibility exists that θfacet>90°, which is of course unphysical. For this calculation, the sky radiance is assumed to be isotropic, since skylight influence upon ρ is accounted for separately through the σs and σsρ terms. In this work we limit the VA to θv60°, which are anyhow the angles of interest for ocean color and largely mitigate the problem, but still may produce some small amounts of shadowing at the fringes of the slope distribution. Such angles are omitted from the calculation (since we are not accounting for multiple scattering by wave surfaces), but when this occurs f(x) is renormalized in order to maintain the requirement that f(x)dx1.

Given the probability distribution, and the corresponding unpolarized Fresnel coefficientsρF(θfacet), we may then estimate the variance of the reflectance coefficient σρ2 for a given angle and wind speed by

σρ2(θv,σiso2)=f(x)ρF2dx(f(x)ρFdx)2.

Figure 4 illustrates the variation of σρ as a function of VA, and the coefficient of variation σρ/ρ for wind speeds of 2, 5, and 8 m/s.

 figure: Fig. 4

Fig. 4 Standard deviation σρ and a coefficient of variation σρ/ρ as a function of viewing angle for 2, 5, and 8 m/s wind speeds.

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The standard deviation of the sea surface reflectance, σρ is shown in Fig. 4(a). The value is small at θv = 20° and lower, but rises to about 0.01 for the typical case of 40° and 5m/s winds, which is a variability of about 35%, Fig. 4(b). If we consider that the CV represents the 1-sigma variation, the 3-sigma variation is over 100%, which clearly shows that σρ is the significant factor in the overall uncertainty budget, and becomes more so as the wind speed and viewing angle increases.

It should be noted that the distribution of ρ is not Gaussian [29], but the uncertainty propagation framework [47] described by Eq. (5) intrinsically assumes that all errors and uncertainties are Gaussian in nature. Without explicitly running Monte Carlo simulations to determine the exact distribution of all variables involved, all estimates of uncertainties given in this work are assumed to be Gaussian.

With all other terms now known, the spectra of covariances σtρ and corresponding correlation coefficients were determined from Eq. (7c).

4. Field measurements

Above water observations were carried out from three coastal platforms: a) a 150-m long platform (Steeplechase pier, 40.5702° N, 73.9834° W) located in Brooklyn, NY; b) an offshore platform (Long Island Sound Coastal Observatory, LISCO, 40.9545° N, 73.3418° W) located 2 miles offshore from Northport, NY, and c) a 500-m long pier (US Army Corps of Engineers Field Research Facility (FRF), 36.1833° N, 75.7464° W) located in Duck, NC. Platform heights above mean sea level were 7m, 4m and 8m and bottom depth were 5 m, 15 m and 6 m, respectively. Total 14 measurements are considered in the processing with wind speed in the range of 3.0-5.7 m/s, Sun zenith angle SZA = 43-69°, AOT(440) = 0.198-0.452.

The imager was installed on a tripod as shown in Fig. 1(b), with its optical axis oriented at 40° from nadir for the observations of the water surface (θv=40°) and at 40° from zenith for sky observations (θv=140°). The relative solar azimuth angle was fixed at 90° or 270°, depending on measurement conditions. The imager’s 40° FOV covered the range of viewing angles from 20° to 60° with respect to nadir (water-viewing) and zenith (sky-viewing). In the each measurement cycle, water and sky observations were complemented by measurements of the downwelling irradiance using a Spectralon white plate, and measurements of the dark noise. At the same time spectral data from the water, sky and the plate were acquired by a GER-1500 spectroradiometer, AOT was measured by a Microtops Sun-photometer at wavelengths 380, 500, 675, 870 and 1020 nm. Inherent Optical Properties (IOPs) of water were measured in situ using an ac-s instrument (WET Labs, OR), except for the Brooklyn Pier, where water samples were measured in the CCNY laboratory using the same instrument. To obtain the appropriate measured IOPs from the ac-s system, correction of pure water, temperature, salinity, and scattering dependencies [48,49] were performed in the processing. Absorption of CDOM spectra was not measured directly for experiments at the FRF but was retrieved based on spectra measured by the GER-1500 instrument using a general coastal waters relationship which considers the phytoplankton and mineral absorption [50]. The GER-1500 spectra were corrected for the sky reflectance [18] with the reflectance coefficient ρ=0.028 for W = 5 m/s and ρ=0.024 for low wind conditions. Examples of the IOPs and remote sensing reflectance spectra measured at all three sites are shown in Fig. 5. Wind speed was measured by a handheld anemometer at NY sites and by permanently installed anemometers at the FRF in Duck.

 figure: Fig. 5

Fig. 5 Water IOPs and remote sensing reflectance spectra from the studied sites: (a) particulate + CDOM absorption ‘apg’ and attenuation ‘cpg’, (b) remote sensing reflectance from GER. Data are shown for the Brooklyn Pier, 5/03/17, LISCO platform, 08/24/17, FRF Pier on 10/11/17 and 10/15/17.

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The chlorophyll-a concentration [Chl-a] was estimated to be 3.0 mg/m3 at the LISCO site and 14.0 mg/m3 at the Duck site. Water IOPs and Rrs were highly variable and changed about five times depending on the water composition.

5. Results of measurements and comparison with VRT simulations

5.1 Radiance spatial distribution, estimation of uncertainties

The main advantage of the imager is the availability of the radiance spatial distribution over the FOV for each wavelength. The example of such data for three wavelengths for Lt, Ls and derived by Eq. (2) Lw is shown in Fig. 6 for the experiments from the FRF platform demonstrating radiance variability and opening the possibility for the statistical analysis of the radiance fluctuations both spectrally and spatially. Azimuth viewing angles φv are given for θv=40° with values slightly different for other viewing angles. Corresponding panchromatic water and sky images are shown at the bottom of Fig. 6. It should be noticed that sky radiance has strong azimuth dependence. Coordinates θv and φv are shown for the center of the image; small differences in the scales at the different parts of the image were not taken into account. In all derivations of Lw here and below from measured Lt and Ls spectra was calculated based on Eq. (2) with the ρ coefficient from [18], except Fig. 7 where Lwwas determined from VRT by subtracting above surface radiances computed for fully absorbing ocean.

 figure: Fig. 6

Fig. 6 (a) Pixel-to-pixel variability of Lt, Ls (left to right) for three different wavelengths: 450, 550 and 650 nm (top to bottom) and Lw calculated using Eq. (2), (b) corresponding panchromatic images of water surface and (c) sky.

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 figure: Fig. 7

Fig. 7 Comparison of measurements and simulations for mean: (a)Lt, (b)Ls and (c) derived Lw at the FRF, 10/11/17. The insets denote the ROIs used throughout the rest of this work.

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Measured spectra for the whole range of viewing angles 20-60° were compared with VRT simulations. In such matchups mean spectra in the regions of interests (ROIs) corresponding to different VA as shown in Fig. 7, and their simulated counterparts were compared. Each ROI had 4° in zenith direction and 40° in azimuth direction.

All atmospheric (τR,τA,τO3, etc.) and water parameters (IOPs and hydrosol Mueller matrices) were used as input parameters for RayXP and data cubes were produced, which match the spectral and spatial resolution of the imager (50x50x113). For this study we limited the wavelength range to 450-900 nm. Results of the comparison for the FRF measurements at W = 5.6 m/s are shown in Fig. 7 demonstrating a good match for all viewing angles. Some mismatch after 750nm is probably due to the large bandwidths in the imager in this part of the spectra (Fig. 2), while simulations were carried out for the central wavelengths. Comparison were similar also for the other wind speeds thus showing that the average radiances can be well simulated by VRT, which properly takes into account effects of wind-roughened surface. For most stations, the spectra from the imager at θv=40°matched well the spectra measured by GER instrument with some discrepancies due to the bandwidth differences shown in Fig. 2. Figure 7 mostly demonstrates consistency of matchups between VRT and imager radiances simultaneously for all viewing angles from the same IOP and sky data inputs. Slight differences can be due to uncertainty in input parameters like aerosol and hydrosol scattering matrices, which led to slightly elevated backscattering in simulations.

The advantage of the imager is that in addition to the mean values, variability of the radiances can be also estimated. Spectra of mean radiance values (shown here as Lt and Ls), standard deviations σt and σs for the water and sky data and corresponding ratios σt/Lt and σs/Ls for each viewing angle and averaged over FOV, for the case with wind speed W = 5.6 m/s are shown in Fig. 8. All values were calculated based on the ROIs’ configuration shown in Fig. 7. Because of the strong gradient of Lsin the azimuth direction σswas determined from 5x5 pixel boxes, which was then averaged over ROI.

 figure: Fig. 8

Fig. 8 Mean radiances Lt and Ls, standard deviations σt and σs for the water and sky data and corresponding ratios σt/Lt and σs/Ls for FRF station with wind speed W = 5.6 m/s.

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Obviously all radiance values depend on the downwelling irradiance but in Fig. 8 absolute values are presented.

From Fig. 8 and similar data from other stations, σt/Lt is typically 5-15% depending on the viewing angle and noticeably increasing to 20-30% in the NIR with typically lowest values at 40° or smaller VA. σs/Ls is about 2-5% with a slight increase in the NIR. The contribution of different components in Eq. (7) were evaluated and as an example, measured and calculated spectra are presented for the same station in Fig. 9. In most cases σw is equal or close to σt. The ρ2σs2 term was very small and is not shown in Fig. 9. Ls2σρ2=2Lsσtρ is comparable with other terms for VA = 20-40° and becomes much higher at VA = 50-60° where assumption of small σρ becomes inaccurate. But both parts of the equation probably remain similar, which makes σwσt.

 figure: Fig. 9

Fig. 9 Spectra of the main components from Eq. (7) for FRF station at different viewing angles in (mW/cm2/μm/sr)2. Bottom right figure is the Ls2σρ2=2Lsσtρ term. The value of σw is determined in the assumption of constant ρ for all pixels in the same VA.

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The correlation coefficients rtρ and rtsfor three stations are given in Table 1 for VA = 20-40° showing large variability as a function of viewing angle, wavelength and wind speed. Some inaccuracies in calculations of rtρ could arise from the assumption of small σρ in Eq. (7), which also resulted in |r|>1 in two cases shown as |r|=1.0in the table.

Tables Icon

Table 1. Correlation coefficientsrtρ and rts for three stations

Analysis of data for all available stations resulted in the coefficient of variation (CV) σw/Lwas a function of wind speed as shown in Fig. 10. The ratio is in the range of 3-8% for most of viewing angles with increase to 6-20% in the NIR and higher for VA = 60° and small increase towards short wavelengths.

 figure: Fig. 10

Fig. 10 The coefficient of variation for water-leaving radiance (σw/Lw) as a function of wind speed and viewing angle: 470nm, 550nm, 650nm and 850nm (left to right). σw is determined in the assumption of constant ρ for all pixels in the same VA.

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As discussed above, ρ2σs2term is typically very small in comparison with other components in Eq. (7) and similar ones in Eq. (6), also in Eq. (6) σw and σsare uncorrelated, which makes2ρσws0, a weak correlation can be expected between reflectance coefficient and sky radiance, so 2ρLsσsρterm can be also omitted. Then Eq. (6) can be rewritten as

σt2=σw02+Ls2σρ2+2Lsσwρ.
The main effect of sky glint comes from Ls2σρ2 term but preliminary data analysis (omitted here for brevity) showed that covariance term also plays significant role depending on the viewing angle, which results in the partial mitigation of the sky glint; additional studies are required for a proper characterization of the σw02 and σwρ covariance.

Although the imager is unable to acquire data below 450 nm, we can estimate propagation of σw/Lwto the blue part of the spectrum. As shown in Fig. 9, σwσtand according to Eq. (10) at least partially proportional to σρLs. Then we can write

σwLwLsLw=LsEd(LwEd)1=LsEdRrs.

In the open ocean, since the spectral shapes of the skyLs/Ed and remote sensing reflectance Rrs are similar, the uncertainty for wavelengths near 400 nm will be only slightly higher than that of 450 nm. In the coastal waters, Rrsdecreases rapidly till 400 nm. These effects are explained in Fig. 11 (for typical open ocean and coastal water spectra not acquired in this study) where Ls/Lw remains almost the same for the open ocean and increases towards the blue in the coastal waters. The result is a higher uncertainty σw/Lwin the blue wavelengths in the coastal waters. It is expected that the actual increase of σw/Lwcan be smaller than shown in Fig. 11 because of contributions of other terms in Eq. (10) beyondLs2σρ2. These results are consistent with the spectra of Rrsvariations measured in Chesapeake Bay and Florida waters [53], Fig. 12. The σw/Lwratio also increases towards the NIR part of the spectrum and even normalized sky radiance is small, this ratio can be partially responsible for the increase of uncertainties in the NIR as shown in Fig. 10.

 figure: Fig. 11

Fig. 11 (a) Normalized sky radiance spectrum,(b) Rrs and (c) their ratio for the open ocean and coastal waters.

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 figure: Fig. 12

Fig. 12 (a) Lt and (b) Ls measured at 40° and 140° viewing angles as a function of FOV. The pink boxes in the image indicate saturated pixels which were excluded from the processing.

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5.2 Field of view considerations in above water measurements

Instruments which are used for Lt and Ls measurements above water have different FOV, ranging from about 1° (SeaPRISM) to greater than 20° (fiber optic sensors), so it is important to determine the dependence of Lt and Ls on the FOV and how it affects the mean radiances and their fluctuations in variable surface and sky conditions. Lt and Ls were measured at 40° and 140° viewing angles respectively, with a full-angle FOV (θFOV) up to 35° were calculated using the following expression:

Lt,s(λ,ΩFOV)=1ΩFOVΩFOVLi(λ)dΩFOV',
where Lt,s is the radiance for water and sky (Lt and Ls, respectively), ΩFOV is the solid angle corresponding to the conical FOV and Li is the radiance for each individual pixel within the FOV. Example of the spectra for different FOVs is shown for W = 4.5 m/s in Fig. 12 with the corresponding images and analyzed areas. It can be clearly seen that in the wide range of θFOV=0.8°31.2° for the moderate wind speed there is very small dependence of radiance on the FOV for both Lt and Ls for the whole spectra.

To provide more information on the FOV radiance dependence, variability of radiance Lt at 530 nm was analyzed for measurements from the FRF platform at W = 4.5 m/s. Results are shown in Fig. 13(a) for 18 different pixels along the diagonal of the image, for which FOVs up to θFOV=13.6° were tested. Lt_FOV radiance is normalized to the mean radiance Lt_mean determined from the 9 radiances (from the center pixel of study and ±4 pixels closest to it along the horizontal line). It can be seen that starting with θFOV=4° there is no noticeable dependence on the FOV where Lt_FOV/Lt_mean deviations are inside ±3%, while smaller FOV provide less stable results. Analysis of sky measurements, Fig. 13(b), resulted in the same preferred FOV range where Ls_FOV/Ls_mean deviations are inside ±2%. Statistics are presented only for one water and one sky image, but results were similar for many stations with different conditions with most stable results for θFOV=47°. The highest deviations are at θFOV=0.82.4°, which are most likely underestimated due to stray light from adjacent pixels causing increased pixel-to-pixel covariance and therefore reducing the deviations.

 figure: Fig. 13

Fig. 13 Variability of Lt_FOV/Lt_mean and Ls_FOV/Ls_mean ratio for different θFOV, W = 4.5 m/s (Duck 14:37): (a) for water radiance, (b) for sky radiance.

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6. Implications for field measurements, AERONET-OC and satellite observations

In above water measurements from ships at 40° and 140° viewing angles, as it was shown previously [31], the mean value of the reflectance coefficient ρ depends on the wind speed, wavelength, AOT and polarization effects. This impact can be minimized if AOT is measured and spectral ρ calculated accordingly. The coefficient of variation for water-leaving radiance (σw/Lw) is expected to be about 3-8% with increase to 6-20% in the NIR at θv=40° and W < 6 m/s. According to Eq. (11) and Fig. 11 it is expected that σw/Lw remains approximately the same in the open ocean with increasing Rrstowards the blue end of the spectrum and increases in the coastal waters with decrease of Rrscausing larger measurement uncertainties. This trend was verified in the preliminary manner by us with the imager sensitive in the blue wavelength range and by AERONET-OC data and should be further validated. Partially the errors can be made smaller by increasing the number of measurements; however, this can often be associated with additional effects of the ship movements and instantaneous changes in sky and water conditions.

AERONET-OC measurements are carried out by SeaPRISM instruments at 40° and 140° viewing angles for the water and sky radiance respectively with an integration time of about 80 ms and a FOV of 1.2° [33]. An azimuth angle of ± 90° is always maintained to minimize Sun glint. Additional data filtering by eliminating cases with standard deviations σt greater than certain threshold is applied to reduce further Sun glint effects [51]. Instruments are positioned on the stable platforms in the ocean, which are not sensitive to the wave perturbations, so the increased number of measurements is expected to bring Lt closer to the mean value Lt_mean. Lw is then determined based on Eq. (2) with the ρ coefficient from [18], which was calculated without taking into account impacts of polarization and AOT. Estimations of σw/Lw from Fig. 10 and σt/Lt from Fig. 8 at θv=40° are generally consistent with the AERONET-OC results based on data from several platforms [52]. While for θv=40° σρ/ρ0.35 (see Fig. 4) (if ρ=0.028is assumed), which is substantially higher than other estimations of σρ/ρ calculated based on different reasons of ρ variability [52], these effects are probably mitigated by the covariance terms in Eq. (7).

In the current processing, Lt is taken to be the average of the lowest 2 out of 11 measurements, denoted asLt_REL, which typically has a value between Lt_mean and Lt'=Ltσt. Data from the imager show that Lt' can be smaller than Lt_mean for θv=40° depending on the wind speed and SZA. Further dedicated studies are probably necessary to determine possible improvements of Lw retrieval. This includes application of a proper ρ coefficient, which is preferably determined by VRT with aerosol parameters measured by the same AERONET-OC station. It is expected that in the new version of AERONET-OC processing ρ will be calculated taking into account aerosol and polarization effects [Zibordi, private communications].

It can be expected that standard deviations similar to σt(λ) spectra determined in this work can characterize the uncertainties of the radiance at the TOA LTOA(λ), which are due to the effects of the ocean surface. In accordance with Eq. (11) and Fig. 11, σw/Lwis larger in the blue bands in the coastal waters than in the open ocean, which will contribute to the uncertainties of Lw andRrs, derived from satellite observations. The uncertainties can be even further amplified by the dependence of ρ on AOT discussed in [31] with AOT very variable in coastal waters and not determined accurately enough in the atmospheric correction process.

Snapshot hyperspectral imagers like the one presented in this paper, which preferably covers the whole wavelength range of OC interest in at least 380-900 nm should be a suitable choice for the validation of the discussed effects in various water an atmospheric conditions.

7. Conclusions

A novel hyperspectral imager is introduced for OC applications in coastal waters and its advantages over non-imaging spectroradiometers and push broom imagers are discussed. The instrument provides hyperspectral radiance distribution with a wide FOV and short exposure time, which is valuable for the direct characterization of the wind-roughened surface in various illumination conditions and wind speeds. Spectra of standard deviations for the radiance from the water and the sky at the viewing angles 20-60° are accurately determined and their ratios to the corresponding mean radiances are evaluated, showing that the coefficients of variation σt(λ)/Lt(λ) for water and σs(λ)/Ls(λ) for the sky measurements can be in the range of 3-20% depending on the viewing angle, wind speed and wavelength.

The minimal values of σt(λ)/Lt(λ) are typically around viewing angle of 40°or smaller VA. The coefficients of variation σw(λ)/Lw(λ) is in the range of 3-8% for most cases and can reach 10-25% for VA = 60° at 470 nm. It is expected that σw(λ)/Lw(λ) is higher in the blue bands in coastal waters, which at least partially explains typically inaccurate satellite retrieval of Lw in blue bands in such areas, where values of Lw are few times smaller than in the open ocean. Significant part of uncertainties comes from the variability of ρ coefficient from the windy surface (or its equivalent value from VRT calculations for TOA). It was found that σρ/ρ can be about 35% at 40° and W = 5 m/s and about 100% at higher wind speed and VA = 60°. The uncertainties can be amplified by the dependence of ρ on AOT [31]. Thus accurate determination of the ρ coefficient, which takes into account polarization effects and impact of AOT is critical to the calculation of the water leaving radiance Lw(λ), however, most of uncertainties come from the changes of wave slopes in windy conditions and can be unavoidable.

Further measurements with the imager in open ocean water conditions with different ocean states are suggested to analyze differences in surface effects between the near shore and open ocean areas, which can be directly relevant to satellite data processing in terms of atmospheric correction and retrieval algorithms.

Funding

National Aeronautics and Space Administration (NASA), Ocean Biology and Biochemistry program (NNX16AR46G); National Oceanic and Atmospheric Administration (NOAA), Joint Polar Satellite System Calibration/validation program and ESSRST Center (NA16SEC4810008); Office of Naval Research (ONR) (N00014-16-1-2555).

Acknowledgments

This research was performed while Robert Foster held an NRC Research Associateship award at the U.S. Naval Research Laboratory in Washington, DC. The authors are grateful for two anonymous reviewers whose suggestions significantly improved the quality of the paper. We thank Eder Herrera for processing auxiliary data.

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References

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  1. C. Giardino, V. E. Brando, P. Gege, N. Pinnel, E. Hochberg, E. Knaeps, I. Reusen, R. Doerffer, M. Bresciani, F. Braga, S. Foerster, N. Champollion, and A. Dekker, “Imaging spectrometry of inland and coastal waters: state of the art, achievements and perspectives” (Serv. Geophys., 2018). https://doi.org/10.1007/s10712-018-9476-0
  2. C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, R. P. Reid, E. M. Louchard, and A. Gleason, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44(17), 3576–3592 (2005).
    [Crossref] [PubMed]
  3. C. Davis, J. Bowles, R. Leathers, D. Korwan, T. V. Downes, W. Snyder, W. Rhea, W. Chen, J. Fisher, P. Bissett, and R. A. Reisse, “Ocean PHILLS hyperspectral imager: design, characterization, and calibration,” Opt. Express 10(4), 210–221 (2002).
    [Crossref] [PubMed]
  4. E. J. Hochberg and M. J. Atkinson, “Spectral discrimination of coral reef benthic communities,” Coral Reefs 19(2), 164–171 (2000).
    [Crossref]
  5. H. M. Dierssen, R. C. Zimmerman, R. A. Leathers, T. V. Downes, and C. O. Davis, “Ocean color remote sensing of seagrass and bathymetry in the Bahamas Banks by high resolution airborne imagery,” Limnol. Oceanogr. 48(1part2), 444–455 (2003).
    [Crossref]
  6. J. C. Sandidge and R. J. Holyer, “Coastal bathymetry from hyperspectral observations of water radiance,” Remote Sens. Environ. 65(3), 341–352 (1998).
    [Crossref]
  7. Z. P. Lee, K. L. Carder, R. F. Chen, and T. G. Peacock, “Properties of the water column and bottom derived from Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data,” J. Geophys. Res. 106(C6), 11639–11651 (2001).
    [Crossref]
  8. R. L. Lucke, M. Corson, N. R. McGlothlin, S. D. Butcher, D. L. Wood, D. R. Korwan, R. R. Li, W. A. Snyder, C. O. Davis, and D. T. Chen, “Hyperspectral Imager for the Coastal Ocean: instrument description and first images,” Appl. Opt. 50(11), 1501–1516 (2011).
    [Crossref] [PubMed]
  9. P. Mouroulis, B. Van Gorp, R. Green, M. Eastwood, D. Wilson, B. Richardson, and H. Dierssen, “The Portable Remote Imaging Spectrometer (PRISM) Coastal Ocean Sensor,” in Imaging and Applied Optics Technical Papers, OSA Technical Digest (online) (Optical Society of America, 2012), paper RM2E.5.
    [Crossref]
  10. A. A. Gitelson, B.-C. Gao, R.-R. Li, S. Berdnikov, and V. Saprygin, “Estimation of chlorophyll-a concentration in productive turbid waters using a Hyperspectral Imager for the Coastal Ocean – the Azov Sea case study,” Environ. Res. Lett. 6(2), 024023 (2011).
    [Crossref]
  11. PACE Science Definition Team, “Pre-Aerosol, Clouds, and ocean Ecosystem (PACE) mission science definition team report,” http://decadal.gsfc.nasa.gov/ .
  12. A. Ibrahim, B. Franz, Z. Ahmad, R. Healy, K. Knobelspiesse, B.-C. Gao, C. Proctor, and P.-W. Zhai, “Atmospheric correction for hyperspectral ocean color retrieval with application to the Hyperspectral Imager for the Coastal Ocean (HICO),” Remote Sens. Environ. 204, 60–75 (2018).
    [Crossref]
  13. D. R. Mishra and I. Ogashawara, Bio-Optical Modeling and Remote Sensing of Inland Waters (Elsevier, 2017), pp. 69–100.
  14. C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).
  15. H. R. Gordon and M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. I: The Rayleigh-scattering component,” Appl. Opt. 31(21), 4247–4260 (1992).
    [Crossref] [PubMed]
  16. H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33(3), 443–452 (1994).
    [Crossref] [PubMed]
  17. M. Wang, “The Rayleigh lookup tables for the SeaWiFS data processing: accounting for the effects of ocean surface roughness,” Int. J. Remote Sens. 23(13), 2693–2702 (2002).
    [Crossref]
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2018 (5)

A. Ibrahim, B. Franz, Z. Ahmad, R. Healy, K. Knobelspiesse, B.-C. Gao, C. Proctor, and P.-W. Zhai, “Atmospheric correction for hyperspectral ocean color retrieval with application to the Hyperspectral Imager for the Coastal Ocean (HICO),” Remote Sens. Environ. 204, 60–75 (2018).
[Crossref]

C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).

A. Gilerson, C. Carrizo, R. Foster, and T. Harmel, “Variability of the reflectance coefficient of skylight from the ocean surface and its implications to Ocean Color,” Opt. Express 26(8), 9615–9633 (2018).
[Crossref] [PubMed]

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
[Crossref]

M. Zhang, C. Hu, J. Cannizzaro, D. English, B. B. Barnes, P. Carlson, and L. Yarbro, “Comparison of two atmospheric correction approaches applied to MODIS measurements over North American waters,” Remote Sens. Environ. 216, 442–455 (2018).
[Crossref]

2017 (3)

2016 (1)

2015 (3)

H. Aasen, A. Burkart, A. Bolten, and G. Bareth, “Generating 3D hyperspectral information with lightweight UAV snapshot cameras for vegetation monitoring: From camera calibration to quality assurance,” J. Photog. Remote Sens. 108, 245–259 (2015).
[Crossref]

P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
[Crossref] [PubMed]

C. D. Mobley, “Polarized reflectance and transmittance properties of windblown sea surfaces,” Appl. Opt. 54(15), 4828–4849 (2015).
[Crossref] [PubMed]

2014 (1)

M. Gergely and G. Zibordi, “Assessment of AERONET-OC Lwn uncertainties,” Metrologia 51(1), 40–47 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (2)

R. L. Lucke, M. Corson, N. R. McGlothlin, S. D. Butcher, D. L. Wood, D. R. Korwan, R. R. Li, W. A. Snyder, C. O. Davis, and D. T. Chen, “Hyperspectral Imager for the Coastal Ocean: instrument description and first images,” Appl. Opt. 50(11), 1501–1516 (2011).
[Crossref] [PubMed]

A. A. Gitelson, B.-C. Gao, R.-R. Li, S. Berdnikov, and V. Saprygin, “Estimation of chlorophyll-a concentration in productive turbid waters using a Hyperspectral Imager for the Coastal Ocean – the Azov Sea case study,” Environ. Res. Lett. 6(2), 024023 (2011).
[Crossref]

2010 (4)

Z. Ahmad, B. A. Franz, C. R. McClain, E. J. Kwiatkowska, J. Werdell, E. P. Shettle, and B. N. Holben, “New aerosol models for the retrieval of aerosol optical thickness and normalized water-leaving radiances from the SeaWiFS and MODIS sensors over coastal regions and open oceans,” Appl. Opt. 49(29), 5545–5560 (2010).
[Crossref] [PubMed]

A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1931–1946 (2010).
[Crossref]

Z. Lee, Y.-H. Ahn, C. Mobley, and R. Arnone, “Removal of surface-reflected light for the measurement of remote-sensing reflectance from an above-surface platform,” Opt. Express 18(25), 26313–26324 (2010).
[Crossref] [PubMed]

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7–8), 1025–1040 (2010).
[Crossref]

2009 (1)

G. Zibordi, F. Mélin, J. F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

2008 (1)

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

2006 (2)

2005 (1)

2003 (1)

H. M. Dierssen, R. C. Zimmerman, R. A. Leathers, T. V. Downes, and C. O. Davis, “Ocean color remote sensing of seagrass and bathymetry in the Bahamas Banks by high resolution airborne imagery,” Limnol. Oceanogr. 48(1part2), 444–455 (2003).
[Crossref]

2002 (2)

2001 (3)

2000 (1)

E. J. Hochberg and M. J. Atkinson, “Spectral discrimination of coral reef benthic communities,” Coral Reefs 19(2), 164–171 (2000).
[Crossref]

1999 (2)

1998 (1)

J. C. Sandidge and R. J. Holyer, “Coastal bathymetry from hyperspectral observations of water radiance,” Remote Sens. Environ. 65(3), 341–352 (1998).
[Crossref]

1995 (1)

1994 (1)

1992 (1)

1976 (1)

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[Crossref]

1954 (1)

Aasen, H.

H. Aasen, A. Burkart, A. Bolten, and G. Bareth, “Generating 3D hyperspectral information with lightweight UAV snapshot cameras for vegetation monitoring: From camera calibration to quality assurance,” J. Photog. Remote Sens. 108, 245–259 (2015).
[Crossref]

Ahmad, Z.

A. Ibrahim, B. Franz, Z. Ahmad, R. Healy, K. Knobelspiesse, B.-C. Gao, C. Proctor, and P.-W. Zhai, “Atmospheric correction for hyperspectral ocean color retrieval with application to the Hyperspectral Imager for the Coastal Ocean (HICO),” Remote Sens. Environ. 204, 60–75 (2018).
[Crossref]

Z. Ahmad, B. A. Franz, C. R. McClain, E. J. Kwiatkowska, J. Werdell, E. P. Shettle, and B. N. Holben, “New aerosol models for the retrieval of aerosol optical thickness and normalized water-leaving radiances from the SeaWiFS and MODIS sensors over coastal regions and open oceans,” Appl. Opt. 49(29), 5545–5560 (2010).
[Crossref] [PubMed]

C. D. Mobley, J. Werdell, B. Franz, Z. Ahmad, and S. Bailey, Atmospheric Correction for Satellite Ocean Color Radiometry (Goddard Space Flight Space Center, 2016).

Ahmed, S.

A. Gilerson, E. Herrera, Y. Klein, R. Foster, B. Gross, R. Arnone, and S. Ahmed, “Characterization of aerosol parameters over ocean from the Ocean Color satellite sensors and AERONET-OC data,” Proc. SPIE 10422, 104220H (2017).

T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Opt. 51(35), 8324–8340 (2012).
[Crossref] [PubMed]

Ahmed, S. A.

Ahn, Y.-H.

Arnone, R.

Atkinson, M. J.

E. J. Hochberg and M. J. Atkinson, “Spectral discrimination of coral reef benthic communities,” Coral Reefs 19(2), 164–171 (2000).
[Crossref]

Bailey, S.

C. D. Mobley, J. Werdell, B. Franz, Z. Ahmad, and S. Bailey, Atmospheric Correction for Satellite Ocean Color Radiometry (Goddard Space Flight Space Center, 2016).

Banner, M. L.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Bareth, G.

H. Aasen, A. Burkart, A. Bolten, and G. Bareth, “Generating 3D hyperspectral information with lightweight UAV snapshot cameras for vegetation monitoring: From camera calibration to quality assurance,” J. Photog. Remote Sens. 108, 245–259 (2015).
[Crossref]

Barnard, A. H.

Barnes, B. B.

M. Zhang, C. Hu, J. Cannizzaro, D. English, B. B. Barnes, P. Carlson, and L. Yarbro, “Comparison of two atmospheric correction approaches applied to MODIS measurements over North American waters,” Remote Sens. Environ. 216, 442–455 (2018).
[Crossref]

Berdnikov, S.

A. A. Gitelson, B.-C. Gao, R.-R. Li, S. Berdnikov, and V. Saprygin, “Estimation of chlorophyll-a concentration in productive turbid waters using a Hyperspectral Imager for the Coastal Ocean – the Azov Sea case study,” Environ. Res. Lett. 6(2), 024023 (2011).
[Crossref]

Berthon, J. F.

G. Zibordi, F. Mélin, J. F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Bevan, A.

A. Bevan, Statistical Data Analysis for the Physical Sciences, (Cambridge University, 2013).

Bissett, P.

Bissett, W. P.

Bolten, A.

H. Aasen, A. Burkart, A. Bolten, and G. Bareth, “Generating 3D hyperspectral information with lightweight UAV snapshot cameras for vegetation monitoring: From camera calibration to quality assurance,” J. Photog. Remote Sens. 108, 245–259 (2015).
[Crossref]

Bowles, J.

C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).

C. Davis, J. Bowles, R. Leathers, D. Korwan, T. V. Downes, W. Snyder, W. Rhea, W. Chen, J. Fisher, P. Bissett, and R. A. Reisse, “Ocean PHILLS hyperspectral imager: design, characterization, and calibration,” Opt. Express 10(4), 210–221 (2002).
[Crossref] [PubMed]

Bowles, J. H.

Brady, P.

Brady, P. C.

P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
[Crossref] [PubMed]

Budak, V. P.

A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1931–1946 (2010).
[Crossref]

Burkart, A.

H. Aasen, A. Burkart, A. Bolten, and G. Bareth, “Generating 3D hyperspectral information with lightweight UAV snapshot cameras for vegetation monitoring: From camera calibration to quality assurance,” J. Photog. Remote Sens. 108, 245–259 (2015).
[Crossref]

Burton, S.

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
[Crossref]

Butcher, S. D.

Cairns, B.

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
[Crossref]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[Crossref] [PubMed]

Cannizzaro, J.

M. Zhang, C. Hu, J. Cannizzaro, D. English, B. B. Barnes, P. Carlson, and L. Yarbro, “Comparison of two atmospheric correction approaches applied to MODIS measurements over North American waters,” Remote Sens. Environ. 216, 442–455 (2018).
[Crossref]

Carder, K. L.

Z. P. Lee, K. L. Carder, R. F. Chen, and T. G. Peacock, “Properties of the water column and bottom derived from Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data,” J. Geophys. Res. 106(C6), 11639–11651 (2001).
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Carlson, P.

M. Zhang, C. Hu, J. Cannizzaro, D. English, B. B. Barnes, P. Carlson, and L. Yarbro, “Comparison of two atmospheric correction approaches applied to MODIS measurements over North American waters,” Remote Sens. Environ. 216, 442–455 (2018).
[Crossref]

Carrizo, C.

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
[Crossref]

C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).

A. Gilerson, C. Carrizo, R. Foster, and T. Harmel, “Variability of the reflectance coefficient of skylight from the ocean surface and its implications to Ocean Color,” Opt. Express 26(8), 9615–9633 (2018).
[Crossref] [PubMed]

P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
[Crossref] [PubMed]

Cetinic, I.

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
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A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1931–1946 (2010).
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Foster, R.

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A. Gilerson, C. Carrizo, R. Foster, and T. Harmel, “Variability of the reflectance coefficient of skylight from the ocean surface and its implications to Ocean Color,” Opt. Express 26(8), 9615–9633 (2018).
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A. Gilerson, E. Herrera, Y. Klein, R. Foster, B. Gross, R. Arnone, and S. Ahmed, “Characterization of aerosol parameters over ocean from the Ocean Color satellite sensors and AERONET-OC data,” Proc. SPIE 10422, 104220H (2017).

R. Foster and A. Gilerson, “Polarized transfer functions of the ocean surface for above-surface determination of the vector submarine light field,” Appl. Opt. 55(33), 9476–9494 (2016).
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A. Ibrahim, B. Franz, Z. Ahmad, R. Healy, K. Knobelspiesse, B.-C. Gao, C. Proctor, and P.-W. Zhai, “Atmospheric correction for hyperspectral ocean color retrieval with application to the Hyperspectral Imager for the Coastal Ocean (HICO),” Remote Sens. Environ. 204, 60–75 (2018).
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C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).

A. Gilerson, C. Carrizo, R. Foster, and T. Harmel, “Variability of the reflectance coefficient of skylight from the ocean surface and its implications to Ocean Color,” Opt. Express 26(8), 9615–9633 (2018).
[Crossref] [PubMed]

A. Gilerson, E. Herrera, Y. Klein, R. Foster, B. Gross, R. Arnone, and S. Ahmed, “Characterization of aerosol parameters over ocean from the Ocean Color satellite sensors and AERONET-OC data,” Proc. SPIE 10422, 104220H (2017).

R. Foster and A. Gilerson, “Polarized transfer functions of the ocean surface for above-surface determination of the vector submarine light field,” Appl. Opt. 55(33), 9476–9494 (2016).
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T. Harmel, A. Gilerson, A. Tonizzo, J. Chowdhary, A. Weidemann, R. Arnone, and S. Ahmed, “Polarization impacts on the water-leaving radiance retrieval from above-water radiometric measurements,” Appl. Opt. 51(35), 8324–8340 (2012).
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Gilerson, A. A.

P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
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A. A. Gilerson, J. Stepinski, A. I. Ibrahim, Y. You, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, B. Russell, M. E. Cummings, P. Brady, S. A. Ahmed, and G. W. Kattawar, “Benthic effects on the polarization of light in shallow waters,” Appl. Opt. 52(36), 8685–8705 (2013).
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G. Zibordi, F. Mélin, J. F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
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C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).

Gordon, H. R.

Gray, D.

C. Carrizo, A. Golovin, A. El-Habashi, R. Foster, D. Gray, J. Bowles, and A. Gilerson, “Ocean surface characterization using snapshot hyperspectral polarimetric imager,” Proc. SPIE 10631, 1063107 (2018).

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
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A. Gilerson, E. Herrera, Y. Klein, R. Foster, B. Gross, R. Arnone, and S. Ahmed, “Characterization of aerosol parameters over ocean from the Ocean Color satellite sensors and AERONET-OC data,” Proc. SPIE 10422, 104220H (2017).

Gu, Y.

P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
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M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
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He, S.

Healy, R.

A. Ibrahim, B. Franz, Z. Ahmad, R. Healy, K. Knobelspiesse, B.-C. Gao, C. Proctor, and P.-W. Zhai, “Atmospheric correction for hyperspectral ocean color retrieval with application to the Hyperspectral Imager for the Coastal Ocean (HICO),” Remote Sens. Environ. 204, 60–75 (2018).
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A. Gilerson, E. Herrera, Y. Klein, R. Foster, B. Gross, R. Arnone, and S. Ahmed, “Characterization of aerosol parameters over ocean from the Ocean Color satellite sensors and AERONET-OC data,” Proc. SPIE 10422, 104220H (2017).

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M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
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Hu, C.

M. Zhang, C. Hu, J. Cannizzaro, D. English, B. B. Barnes, P. Carlson, and L. Yarbro, “Comparison of two atmospheric correction approaches applied to MODIS measurements over North American waters,” Remote Sens. Environ. 216, 442–455 (2018).
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Hu, Y.

M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
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P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7–8), 1025–1040 (2010).
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Ibrahim, A.

A. Ibrahim, B. Franz, Z. Ahmad, R. Healy, K. Knobelspiesse, B.-C. Gao, C. Proctor, and P.-W. Zhai, “Atmospheric correction for hyperspectral ocean color retrieval with application to the Hyperspectral Imager for the Coastal Ocean (HICO),” Remote Sens. Environ. 204, 60–75 (2018).
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M. Ottaviani, R. Foster, A. Gilerson, A. Ibrahim, C. Carrizo, A. El-Habashi, B. Cairns, J. Chowdhary, C. Hostetler, J. Hair, S. Burton, Y. Hu, M. Twardowski, N. Stockley, D. Gray, W. Slade, and I. Cetinic, “Airborne and shipborne polarimetric measurements over open ocean and coastal waters: intercomparisons and implications for spaceborne observations,” Remote Sens. Environ. 206, 375–390 (2018).
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P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
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Ibrahim, A. I.

Josset, D. B.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7–8), 1025–1040 (2010).
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G. Zibordi, F. Mélin, J. F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
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A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1931–1946 (2010).
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A. Gilerson, E. Herrera, Y. Klein, R. Foster, B. Gross, R. Arnone, and S. Ahmed, “Characterization of aerosol parameters over ocean from the Ocean Color satellite sensors and AERONET-OC data,” Proc. SPIE 10422, 104220H (2017).

Klyukov, D. A.

A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1931–1946 (2010).
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P. C. Brady, A. A. Gilerson, G. W. Kattawar, J. M. Sullivan, M. S. Twardowski, H. M. Dierssen, M. Gao, K. Travis, R. I. Etheredge, A. Tonizzo, A. Ibrahim, C. Carrizo, Y. Gu, B. J. Russell, K. Mislinski, S. Zhao, and M. E. Cummings, “Open-ocean fish reveal an omnidirectional solution to camouflage in polarized environments,” Science 350(6263), 965–969 (2015).
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Figures (13)

Fig. 1
Fig. 1 Snapshot hyperspectral imager Cubert UHD285: (a) general view, (b) on the tripod at the ocean platform.
Fig. 2
Fig. 2 Integration of the spectra by the imager: (a) spectral bandwidths, (b) comparison with GER spectrum.
Fig. 3
Fig. 3 Calibration matrices for the imager at 530 and 750 nm.
Fig. 4
Fig. 4 Standard deviation σ ρ and a coefficient of variation σ ρ / ρ as a function of viewing angle for 2, 5, and 8 m/s wind speeds.
Fig. 5
Fig. 5 Water IOPs and remote sensing reflectance spectra from the studied sites: (a) particulate + CDOM absorption ‘apg’ and attenuation ‘cpg’, (b) remote sensing reflectance from GER. Data are shown for the Brooklyn Pier, 5/03/17, LISCO platform, 08/24/17, FRF Pier on 10/11/17 and 10/15/17.
Fig. 6
Fig. 6 (a) Pixel-to-pixel variability of L t , L s (left to right) for three different wavelengths: 450, 550 and 650 nm (top to bottom) and L w calculated using Eq. (2), (b) corresponding panchromatic images of water surface and (c) sky.
Fig. 7
Fig. 7 Comparison of measurements and simulations for mean: (a) L t , (b) L s and (c) derived L w at the FRF, 10/11/17. The insets denote the ROIs used throughout the rest of this work.
Fig. 8
Fig. 8 Mean radiances L t and L s , standard deviations σ t and σ s for the water and sky data and corresponding ratios σ t / L t and σ s / L s for FRF station with wind speed W = 5.6 m/s.
Fig. 9
Fig. 9 Spectra of the main components from Eq. (7) for FRF station at different viewing angles in ( m W / c m 2 / μ m / s r ) 2 . Bottom right figure is the L s 2 σ ρ 2 = 2 L s σ t ρ term. The value of σ w is determined in the assumption of constant ρ for all pixels in the same VA.
Fig. 10
Fig. 10 The coefficient of variation for water-leaving radiance ( σ w / L w ) as a function of wind speed and viewing angle: 470nm, 550nm, 650nm and 850nm (left to right). σ w is determined in the assumption of constant ρ for all pixels in the same VA.
Fig. 11
Fig. 11 (a) Normalized sky radiance spectrum,(b) Rrs and (c) their ratio for the open ocean and coastal waters.
Fig. 12
Fig. 12 (a) L t and (b) L s measured at 40° and 140° viewing angles as a function of FOV. The pink boxes in the image indicate saturated pixels which were excluded from the processing.
Fig. 13
Fig. 13 Variability of L t _ F O V / L t _ m e a n and L s _ F O V / L s _ m e a n ratio for different θ F O V , W = 4.5 m/s (Duck 14:37): (a) for water radiance, (b) for sky radiance.

Tables (1)

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Table 1 Correlation coefficients r t ρ and r t s for three stations

Equations (14)

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R r s ( θ v , φ v , λ ) = L w ( θ v , φ v , λ ) / E d ( λ ) ,
L t ( θ v , φ v , λ ) = L w ( θ v , φ v , λ ) + ρ ( θ v , φ v , λ , W , A O T , ) L s ( π θ v , φ v , λ ) ,
σ i s o 2 = 0.003 + 0.00512 W ± 0.004.
L s ± σ s , L t ± σ t , L w ± σ w , ρ ± σ ρ ,
σ t 2 = [ L t L w L t L s L t ρ ] [ σ w 2 σ w s σ w ρ σ w s σ s 2 σ s ρ σ w ρ σ s ρ σ ρ 2 ] [ L t L w L t L s L t ρ ] ,
σ t 2 = σ w 0 2 + ρ 2 σ s 2 + L s 2 σ ρ 2 + 2 ρ L s σ s ρ + 2 ρ σ w s + 2 L s σ w ρ .
σ w 2 = σ t 2 + ρ 2 σ s 2 + L s 2 σ ρ 2 + 2 ρ L s σ s ρ 2 ρ σ t s 2 L s σ t ρ .
σ w 2 σ t 2 + ρ 2 σ s 2 2 ρ σ t s ,
L s 2 σ ρ 2 2 L s σ t ρ or σ ρ 2 r t ρ σ t / L s ,
f ( x | σ i s o 2 ) = ( 2 π σ i s o 2 ) 1 / 2 exp ( x 2 2 σ i s o 2 ) ,
σ ρ 2 ( θ v , σ i s o 2 ) = f ( x ) ρ F 2 d x ( f ( x ) ρ F d x ) 2 .
σ t 2 = σ w 0 2 + L s 2 σ ρ 2 + 2 L s σ w ρ .
σ w L w L s L w = L s E d ( L w E d ) 1 = L s E d R r s .
L t , s ( λ , Ω F O V ) = 1 Ω F O V Ω F O V L i ( λ ) d Ω F O V ' ,

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