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 $\left(R_{rs}\right)$. 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 (or$R_{rs}$) 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 $R_{rs}$, 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.

 

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 $\approx 1.5$ 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.

 

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 (ZenithLite^TM, SphereOptics GmbH) with the radiances measured by the GER spectroradiometer, which recently underwent spectral and radiometric calibration at the manufacturer.

 

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 $R_{rs}$ just above the surface of the ocean [36]:

For above surface ocean observations, assuming that Sun glint is avoided and there are no whitecaps, $L_w({\theta }_v,{\phi }_v,\lambda )$ is determined from

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 (${\tau }_{ABS}$) and scattering (${\tau }_{MOL}$) optical depths, depolarization ratio, and an aerosol or hydrosol (represented by a 4x4 single-scattering Mueller matrix, single scattering albedo, and optical depth, ${\tau }_{SOL}$).

The Stokes vectors corresponding to the radiance arriving at the sensor from the water body ($L_t$) and the sky ($L_s$) 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 (${\tau }_R$) and 100% of the ozone optical thickness (${\tau }_{O_3}$), a middle layer containing the remaining 35% of ${\tau }_R$ and the full aerosol optical thickness, and the last layer with 0.26% of ${\tau }_R$ 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 ${\tau }_A$ and Angstrom coefficient $\gamma$ 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 ${\sigma }_{iso}^2$ of the isotropic slope distribution related to the wind speed W at 12.5 m above the surface level is determined as [20]

The VRT program does not simulate uncertainties of $L_t$, $L_w$ and $\rho$. Including 1-sigma uncertainties into the nomenclature, we now have

In the above equation, ${\sigma }_w^2$ has been replaced with ${\sigma }_{w0}^2$, 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 ${\sigma }_{w0}^2$, 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 $L_w=L_t-\rho L_s$, the variance of the water leaving signal would then be

In this equation ${\sigma }_w^2$characterizes the variance of $L_w$in the process of $L_w$retrieval from above surface measurements, depends on all components in Eq. (7a) and as such can be very different from ${\sigma }_{w0}^2$ . Additional relationships regarding ${\sigma }_{w0}^2$ and ${\sigma }_w^2$ from Eqs. (6) and (7a) will be further given in Section 5.1.

Let us assume that ${\sigma }_{\rho }$in Eq. (7a) is small and $\rho$ almost constant for a given measurement at a specific viewing angle. This is the typical practice for estimation of $L_w$ 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

Using data from the imager we can quantify components ${\sigma }_w$, ${\sigma }_t$, ${\sigma }_s$,${\sigma }_{ts}$ 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 $r_{t\rho }$ exceeds 1. In these cases, $r_{t\rho }$ was clamped to a value of 1.

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

Since ${\sigma }_{\rho }$ cannot be determined from Eq. (7), additional relationships based on Eq. (3) [20] were utilized to find a dependence of ${\sigma }_{\rho }$ on the wind speed and viewing geometry. starting with the isotropic mean-square wave slope as a function of wind speed, ${\sigma }_{iso}^2$, the Gaussian probability density function describing the slope distribution, $f(x|{\sigma }_{iso}^2)$, is given by

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 ${\theta }_{facet}>90°$, which is of course unphysical. For this calculation, the sky radiance is assumed to be isotropic, since skylight influence upon $\rho$ is accounted for separately through the ${\sigma }_s$ and ${\sigma }_{s\rho }$ terms. In this work we limit the VA to ${\theta }_v\le 60°$, 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 ${\displaystyle \underset{-\infty }{\overset{\infty }{\int }}f(x)dx\equiv 1}$.

Given the probability distribution, and the corresponding unpolarized Fresnel coefficients${\rho }_F({\theta }_{facet})$, we may then estimate the variance of the reflectance coefficient ${\sigma }_{\rho }^2$ for a given angle and wind speed by

Figure 4 illustrates the variation of ${\sigma }_{\rho }$ as a function of VA, and the coefficient of variation ${\sigma }_{\rho }/\rho$ for wind speeds of 2, 5, and 8 m/s.

 

Fig. 4 Standard deviation ${\sigma }_{\rho }$ and a coefficient of variation ${\sigma }_{\rho }/\rho$ 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, ${\sigma }_{\rho }$ is shown in Fig. 4(a). The value is small at ${\theta }_v$ = 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 ${\sigma }_{\rho }$ 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 $\rho$ 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 ${\sigma }_{t\rho }$ 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 (${\theta }_v=40°$) and at 40° from zenith for sky observations (${\theta }_v=140°$). 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 $\rho =0.028$ for W = 5 m/s and $\rho =0.024$ 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.

 

Fig. 5 Water IOPs and remote sensing reflectance spectra from the studied sites: (a) particulate + CDOM absorption ‘a_pg’ and attenuation ‘c_pg’, (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 $R_{rs}$ 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 $L_t$, $L_s$ and derived by Eq. (2) $L_w$ 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 ${\phi }_v$ are given for ${\theta }_v=40°$ 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 ${\theta }_v$ and ${\phi }_v$ 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 $L_w$ here and below from measured $L_t$ and $L_s$ spectra was calculated based on Eq. (2) with the $\rho$ coefficient from [18], except Fig. 7 where $L_w$was determined from VRT by subtracting above surface radiances computed for fully absorbing ocean.

 

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.

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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.

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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 (${\tau }_R,{\tau }_A,{\tau }_{O_3}$, 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 ${\theta }_v=40°$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 $L_t$ and $L_s$), standard deviations ${\sigma }_t$ and ${\sigma }_s$ for the water and sky data and corresponding ratios ${\sigma }_t/L_t$ and ${\sigma }_s/L_s$ 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 $L_s$in the azimuth direction ${\sigma }_s$was determined from 5x5 pixel boxes, which was then averaged over ROI.

 

Fig. 8 Mean radiances $L_t$ and $L_s$, standard deviations ${\sigma }_t$ and ${\sigma }_s$ for the water and sky data and corresponding ratios ${\sigma }_t/L_t$ and ${\sigma }_s/L_s$ 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, ${\sigma }_t/L_t$ 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. ${\sigma }_s/L_s$ 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 ${\sigma }_w$ is equal or close to ${\sigma }_t$. The ${\rho }^2{\sigma }_s^2$ term was very small and is not shown in Fig. 9. $L_s^2{\sigma }_{\rho }^2=2L_s{\sigma }_{t\rho }$ is comparable with other terms for VA = 20-40° and becomes much higher at VA = 50-60° where assumption of small ${\sigma }_{\rho }$ becomes inaccurate. But both parts of the equation probably remain similar, which makes ${\sigma }_w\approx {\sigma }_t$.

 

Fig. 9 Spectra of the main components from Eq. (7) for FRF station at different viewing angles in ${(mW/c{m}^2/\mu m/sr)}^2$. Bottom right figure is the $L_s^2{\sigma }_{\rho }^2=2L_s{\sigma }_{t\rho }$ term. The value of ${\sigma }_w$ is determined in the assumption of constant $\rho$ for all pixels in the same VA.

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The correlation coefficients $r_{t\rho }$ and $r_{ts}$for 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 $r_{t\rho }$ could arise from the assumption of small ${\sigma }_{\rho }$ in Eq. (7), which also resulted in $\left|r\right|>1$ in two cases shown as $\left|r\right|=1.0$in the table.

Table 1. Correlation coefficients$r_{t\rho }$ and $r_{ts}$ for three stations

View Table

Analysis of data for all available stations resulted in the coefficient of variation (CV) ${\sigma }_w/L_w$as 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.

 

Fig. 10 The coefficient of variation for water-leaving radiance (${\sigma }_w/L_w$) as a function of wind speed and viewing angle: 470nm, 550nm, 650nm and 850nm (left to right). ${\sigma }_w$ is determined in the assumption of constant $\rho$ for all pixels in the same VA.

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As discussed above, ${\rho }^2{\sigma }_s^2$term is typically very small in comparison with other components in Eq. (7) and similar ones in Eq. (6), also in Eq. (6) ${\sigma }_w$ and ${\sigma }_s$are uncorrelated, which makes$2\rho {\sigma }_{ws}\approx 0$, a weak correlation can be expected between reflectance coefficient and sky radiance, so $2\rho L_s{\sigma }_{s\rho }$term can be also omitted. Then Eq. (6) can be rewritten as

Although the imager is unable to acquire data below 450 nm, we can estimate propagation of ${\sigma }_w/L_w$to the blue part of the spectrum. As shown in Fig. 9, ${\sigma }_w\approx {\sigma }_t$and according to Eq. (10) at least partially proportional to ${\sigma }_{\rho }^{}{L}_s^{}$. Then we can write

In the open ocean, since the spectral shapes of the sky$L_s/E_d$ and remote sensing reflectance $R_{rs}$ are similar, the uncertainty for wavelengths near 400 nm will be only slightly higher than that of 450 nm. In the coastal waters, $R_{rs}$decreases 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 $L_s/L_w$ remains almost the same for the open ocean and increases towards the blue in the coastal waters. The result is a higher uncertainty ${\sigma }_w/L_w$in the blue wavelengths in the coastal waters. It is expected that the actual increase of ${\sigma }_w/L_w$can be smaller than shown in Fig. 11 because of contributions of other terms in Eq. (10) beyond$L_s^2{\sigma }_{\rho }^2$. These results are consistent with the spectra of $R_{rs}$variations measured in Chesapeake Bay and Florida waters [53], Fig. 12. The ${\sigma }_w/L_w$ratio 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.

 

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

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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.

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5.2 Field of view considerations in above water measurements

Instruments which are used for $L_t$ and $L_s$ 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 $L_t$ and $L_s$ on the FOV and how it affects the mean radiances and their fluctuations in variable surface and sky conditions. $L_t$ and $L_s$ were measured at 40° and 140° viewing angles respectively, with a full-angle FOV (${\theta }_{FOV}$) up to 35° were calculated using the following expression:

To provide more information on the FOV radiance dependence, variability of radiance $L_t$ 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 ${\theta }_{FOV}=13.6°$ were tested. $L_{t\_FOV}$ radiance is normalized to the mean radiance $L_{t\_mean}$ determined from the 9 radiances (from the center pixel of study and $\pm 4$ pixels closest to it along the horizontal line). It can be seen that starting with ${\theta }_{FOV}=4°$ there is no noticeable dependence on the FOV where $L_{t\_FOV}/L_{t\_mean}$ deviations are inside $\pm 3\%$, while smaller FOV provide less stable results. Analysis of sky measurements, Fig. 13(b), resulted in the same preferred FOV range where $L_{s\_FOV}/L_{s\_mean}$ deviations are inside $\pm 2\%$. 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 ${\theta }_{FOV}=4-7°$. The highest deviations are at ${\theta }_{FOV}=0.8-2.4°$, which are most likely underestimated due to stray light from adjacent pixels causing increased pixel-to-pixel covariance and therefore reducing the deviations.

 

Fig. 13 Variability of $L_{t\_FOV}/L_{t\_mean}$ and $L_{s\_FOV}/L_{s\_mean}$ ratio for different ${\theta }_{FOV}$, 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 $\rho$ depends on the wind speed, wavelength, AOT and polarization effects. This impact can be minimized if AOT is measured and spectral $\rho$ calculated accordingly. The coefficient of variation for water-leaving radiance (${\sigma }_w/L_w$) is expected to be about 3-8% with increase to 6-20% in the NIR at ${\theta }_v=40°$ and W < 6 m/s. According to Eq. (11) and Fig. 11 it is expected that ${\sigma }_w/L_w$ remains approximately the same in the open ocean with increasing $R_{rs}$towards the blue end of the spectrum and increases in the coastal waters with decrease of $R_{rs}$causing 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 ${\sigma }_t$ 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 $L_t$ closer to the mean value $L_{t\_mean}$. $L_w$ is then determined based on Eq. (2) with the $\rho$ coefficient from [18], which was calculated without taking into account impacts of polarization and AOT. Estimations of ${\sigma }_w/L_w$ from Fig. 10 and ${\sigma }_t/L_t$ from Fig. 8 at ${\theta }_v=40°$ are generally consistent with the AERONET-OC results based on data from several platforms [52]. While for ${\theta }_v=40°$ ${\sigma }_{\rho }/\rho \approx 0.35$ (see Fig. 4) (if $\rho =0.028$is assumed), which is substantially higher than other estimations of ${\sigma }_{\rho }/\rho$ calculated based on different reasons of $\rho$ variability [52], these effects are probably mitigated by the covariance terms in Eq. (7).

In the current processing, $L_t$ is taken to be the average of the lowest 2 out of 11 measurements, denoted as$L_{t\_REL}$, which typically has a value between $L_{t\_mean}$ and $L_t^{\text{'}}=L_t-{\sigma }_t$. Data from the imager show that $L_t^{\text{'}}$ can be smaller than $L_{t\_mean}$ for ${\theta }_v=40°$ depending on the wind speed and SZA. Further dedicated studies are probably necessary to determine possible improvements of $L_w$ retrieval. This includes application of a proper $\rho$ 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 $\rho$ will be calculated taking into account aerosol and polarization effects [Zibordi, private communications].

It can be expected that standard deviations similar to ${\sigma }_t(\lambda )$ spectra determined in this work can characterize the uncertainties of the radiance at the TOA $L_{TOA}(\lambda )$, which are due to the effects of the ocean surface. In accordance with Eq. (11) and Fig. 11, ${\sigma }_w/L_w$is larger in the blue bands in the coastal waters than in the open ocean, which will contribute to the uncertainties of $L_w$ and$R_{rs}$, derived from satellite observations. The uncertainties can be even further amplified by the dependence of $\rho$ 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 ${\sigma }_t(\lambda )/L_t(\lambda )$ for water and ${\sigma }_s(\lambda )/L_s(\lambda )$ 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 ${\sigma }_t(\lambda )/L_t(\lambda )$ are typically around viewing angle of 40°or smaller VA. The coefficients of variation ${\sigma }_w(\lambda )/L_w(\lambda )$ 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 ${\sigma }_w(\lambda )/L_w(\lambda )$ is higher in the blue bands in coastal waters, which at least partially explains typically inaccurate satellite retrieval of $L_w$ in blue bands in such areas, where values of $L_w$ are few times smaller than in the open ocean. Significant part of uncertainties comes from the variability of $\rho$ coefficient from the windy surface (or its equivalent value from VRT calculations for TOA). It was found that ${\sigma }_{\rho }/\rho$ 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 $\rho$ on AOT [31]. Thus accurate determination of the $\rho$ coefficient, which takes into account polarization effects and impact of AOT is critical to the calculation of the water leaving radiance $L_w(\lambda )$, 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.