Characterization of radiance from the ocean surface by hyperspectral imaging

: 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 ( ) t L , sky ( ) s L and derived water-leaving ( ) w L 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 w L 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 ( ) t L λ and ( ) s L 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.


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 ( ) rs R .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][16][17].For ship-borne measurements, the reflectance coefficient of skylight from the sea surface (ρ) is precalculated 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][23][24][25][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 rs R ) 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][28][29][30][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 rs R , Section 6 discusses the implications of the results to above-water, AERONET-OC and satellite retrievals, and Section 7 concludes the work.

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/ the objective directed to a nm waveleng beam is modi focused on a 138 spectral c that the instru into account i The entire digitization.T length and 10 Since a p strongly depe measurements taken by a G compared wit Fraunhofer lin spectrometers The non-s push-broom i from elevated positioned he features and p frame rates.Laboratory at field measure ocean observa average state would require

Theory an
The related th main paramet the surface of where ( Viewing angl and the sensor l field deploym aperture.For la a switch betw f light in the co 2. Integration of th spectrum.For above surface ocean observations, assuming that Sun glint is avoided and there are no whitecaps, ( , , ) L θ ϕ λ is determined from ( , , ) ( , , ) ( , , , , , ) ( , , ), where ( , , ) L θ ϕ λ is the total upwelling radiance leaving the ocean surface, with a typical relative solar azimuth angle of 90 . 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][30][31]38,39] and is thus wavelength dependent.Generally ρ is 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][44][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 ( ABS τ ) and scattering ( MOL τ ) optical depths, depolarization ratio, and an aerosol or hydrosol (represented by a 4x4 single-scattering Mueller matrix, single scattering albedo, and optical depth, SOL τ ).
The Stokes vectors corresponding to the radiance arriving at the sensor from the water body ( t L ) and the sky ( s L ) 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 ( R τ ) and 100% of the ozone optical thickness ( 3 O τ ), a middle layer containing the remaining 35% of R τ and the full aerosol optical thickness, and the last layer with 0.26% of R τ 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 A τ 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 2 iso σ of the isotropic slope distribution related to the wind speed W at 12.5 m above the surface level is determined as [20] 2 0.003 0.00512 0.004.
The VRT program does not simulate uncertainties of t L , w L and ρ .Including 1-sigma uncertainties into the nomenclature, we now have , , , , where the ( , , )   v v θ ϕ λ parameters have been omitted for clarity, and t σ , w σ , s σ and ρ σ 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 [ where all covariance terms are included.The partial derivatives may be computed simply, resulting in 1 Substituting the computed derivatives into Eq.
(5) and simplifying, yields In the above equation, 2 w σ has been replaced with 2 0 w σ , 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 2 0 w σ , 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 , the variance of the water leaving signal would then be In this equation 2 w σ characterizes the variance of w L in the process of w L retrieval from above surface measurements, depends on all components in Eq. (7a) and as such can be very different from 2 0 w σ .Additional relationships regarding 2 0 w σ and 2 w σ from Eqs. ( 6) and (7a) will be further given in Section 5.1.
Let us assume that ρ σ in 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 w L 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 2 , and through the subtraction of Eq. (7b) from (7a) and considering a weak correlation between ρ and s L , we can estimate the effect of the assumption as where t r ρ is the correlation coefficient for t L and ρ .Thus a preliminary relationship between t σ and ρ σ in Eq. (7c) can be established.
Using data from the imager we can quantify components w σ , t σ , s σ , ts σ 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 t r ρ exceeds 1.In these cases, t r ρ 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 w L using Eq. ( 2), as is done for above water measurements and in the satellite atmospheric correction models.
Since ρ σ cannot be determined from Eq. ( 7), additional relationships based on Eq. ( 3) [20] were utilized to find a dependence of ρ σ on the wind speed and viewing geometry.
starting with the isotropic mean-square wave slope as a function of wind speed, 2 iso σ , the Gaussian probability density function describing the slope distribution,

( | )
iso f x σ , is given by ( ) where x is the slope.For calculation of the Fresnel coefficients, the slopes are converted to viewing angles ( n θ , the angle between zenith and the instantaneous "facet" normal direction) 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 90 facet θ > °, 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 s σ and sρ σ terms.In this work we limit the VA to 60 v θ ≤ °, 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 Given the probability distribution, and the corresponding unpolarized Fresnel coefficients ( ) ρ θ , we may then estimate the variance of the reflectance coefficient 2 ρ σ for a given angle and wind speed by ( , ) ( ) ( ) .
Figure 4 illustrates the variation of ρ σ as a function of VA, and the coefficient of variation ρ σ ρ for wind speeds of 2, 5, and 8 m/s.
The standard deviation of the sea surface reflectance, ρ σ is shown in Fig. 4(a).The value is small at v θ = 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 ρ σ 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 tρ σ and corresponding correlation coefficients were determined from Eq. (7c).σ 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 the NIR as shown in Fig. 10.

Field of view considerations in above water measurements
Instruments which are used for t L and s L 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 t L and s L on the FOV and how it affects the mean radiances and their fluctuations in variable surface and sky conditions.The p proces

Implica observation
In above wat previously [3 wavelength, A   ) is expected to be about 3-8% with increase to 6-20% in the NIR at 40 v θ = ° and W < 6 m/s.According to Eq. ( 11) and Fig. 11 it is expected that w w L σ remains approximately the same in the open ocean with increasing rs R towards the blue end of the spectrum and increases in the coastal waters with decrease of rs R 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 t σ 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 t L closer to the mean value _ t mean

L
. w L 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 w w L σ from Fig. 10 and t  is assumed), which is substantially higher than other estimations of ρ σ 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, t L is taken to be the average of the lowest 2 out of 11 L λ , which are due to the effects of the ocean surface.In accordance with Eq. ( 11) and Fig. 11, w w L σ is larger in the blue bands in the coastal waters than in the open ocean, which will contribute to the uncertainties of w L and rs R , 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.

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 ( ) ( ) from the windy surface (or its equivalent value from VRT calculations for TOA).It was found that ρ σ 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 ( ) w L 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.
Fig. 1 the oc In our me which increas from Fig. 3, w 138 waveleng radiances ref GmbH) with underwent spe

Fig
Fig. 3.nd modeling heory was disc ter of interest i f the ocean[36] incidence angle upon the facet ( facet θ ) which would produce a reflection observable at a viewing angle of v

Fig. 4 .
Fig. 4. Standard deviation ρ σ and a coefficient of variation ρ σ ρ as a function of viewing angle for 2, 5, and 8 m/s wind speeds.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 ( 40 v θ = °) and at 40° from zenith for Fig. 5 + CDO are sh and 10 The chloro and 14.0 mg/m five times dep 5. Results o 5.1 Radiance The main adv the FOV for e derived by E demonstrating radiance fluct 40 v θ = ° with water and sky has strong az image; small account.In a calculated ba Fig. 7w L at the coeffic .The ratio is in

Fig. 9
Fig. 9. 2 2 s L ρ σ = higher at VA f the equation Fig. 1 speed in the As discus components in which makes and sky radian waters[53], Fig.12.The w w L

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

L
t L and s L were measured at 40° and 140° viewing angles respectively, with a full-angle FOV ( FOV θ ) up to 35° were calculated using the following expression: is the radiance for water and sky ( t L and s L , respectively), FOV Ω is the solid angle corresponding to the conical FOV and i L 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.12with the corresponding images and analyzed areas.It can be clearly seen that in the wide range of 0.8 31.2FOVθ = °− ° for the moderate wind speed there is very small dependence of radiance on the FOV for both t L and s L for the whole spectra.

Fig. 1 m
Fig. 1 m/s (D To provid at 530 nm wa shown in Fig up to FOV θ are generally consistent with the AERONET-OC results based on data from several platforms[52] sky measurements can be in the range of 3-20% depending on the viewing angle, wind speed and wavelength.The minimal values of ( ) ( ) the range of 3-8% for most cases and can reach 10-25% for VA = 60° at 470 nm.It is expected that ( in the blue bands in coastal waters, which at least partially explains typically inaccurate satellite retrieval of w L in blue bands in such areas, where values of w L are few times smaller than in the open ocean.Significant part of uncertainties comes from the variability of ρ coefficient

Table 1 .
depending on the wind speed and SZA.Further dedicated studies are probably necessary to determine possible improvements of w L 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,