In this study, sea surface skylight spectral reflectance ρ(λ) was retrieved by means of the non-linear spectral optimization method and a bio-optical model. The spectral variability of ρ(λ) was found to be mainly influenced by the uniformity of the incident skylight, and a model is proposed to predict the ρ(λ) spectral dependency based on skylight reflectance at 750 nm. It is demonstrated that using the spectrally variable ρ(λ), rather than a constant, yields an improved agreement between the above-water remote sensing reflectance Rrs(λ) estimates and concurrent profiling ones. The findings of this study highlight the necessity to re-process the relevant historical above-water data and update ocean color retrieval algorithms accordingly.
© 2013 Optical Society of America
Spectral remote sensing reflectance Rrs(λ) is a fundamental hydro-optical property, and is the basis of the bio-optical model, ocean color algorithm, and vicarious calibration of satellite sensors . The above-water method [2–7] is one of the most widely adopted methods for in situ Rrs(λ) estimation. In this scheme, spectral radiance of the ocean Lt(λ) and skylight Lsky(λ) is measured by the spectroradiometer(s) with suitable observation geometry, to avoid the effect of the sun glint and platform shadow on the light field . After data quality control, such as abandoning the data contaminated by the residual sun glint, the spectral water-leaving radiance Lw(λ) is estimated as follows:
ρ(λ) depends on the sky radiance distribution, sea state (indexed by wind speed), sun position, observation geometry, and wavelength, as well as the field of view (FOV) of the spectroradiometer, and is not usually equal to the Fresnel coefficient of the wind roughened sea surface . As the Lsky(λ) usually dominates Lw(λ), especially in the shorter wavelengths and less turbid waters under clear sky, the influence of adopted ρ(λ) values on the estimates of Lw(λ) and Rrs(λ) is direct and significant, and the accurate determination of ρ(λ) is the most important issue for the above-water method [8–12]. Nevertheless, due to its intricate nature, the determination (or even an experienced guess) of the justified ρ(λ) value is quite difficult.
In the routine data processing procedure, ρ(λ) is commonly regarded as wavelength independent, although its spectral variability has been mentioned occasionally. Mobley suggested adopting the constant of 0.028 under an overcast sky, and determining the values from a look-up table of the wind speed, solar zenith angle (SZA) and viewing geometry for the clear sky condition . For clear open ocean, ρ values can also be estimated by assuming a null water leaving signal at 750 nm, which may not always be applicable even to all Case 1 waters. There have been other attempts towards the accurate ρ(λ) estimates using polarization information [8, 13], or decomposing the skylight signal into the Rayleigh and aerosol contributions .
Recently, Lee et al.  found that ρ(λ) had obvious spectral dependence and could vary by 5 (8) times in the visible (up to NIR) bands. Based on observations at two example sites in clear and turbid waters, respectively, they demonstrated the feasibility of ρ(λ) and Rrs(λ) estimates, by using the spectral optimization-based method.
The aims of this paper are to (1) understand the spectral variability of ρ(λ) and the underlying factors; and (2) quantify the effect of inaccurate ρ values, especially ignoring its spectral variability, on the Rrs(λ) estimation and ocean color retrievals. First, ρ(λ) was retrieved by the spectral optimization method and bio-optical model (described in the “Model” section) from in situ data (described in the “Data” section) over turbid coastal waters. Subsequently, the ρ(λ) spectral variability was characterized in terms of its dependence on the uniformity of the skylight distribution. Then, Rrs(λ) estimates from the optimization-derived ρ(λ) and the spectrally constant ρ values were compared with the concurrent profiling ones (regarded as “sea truth”). Finally, the implications of ρ(λ) spectral variability was discussed.
In the condition of ignoring the sun glint, foam and white cap, spectral upwelling radiance Lt(λ) measured from the angular geometry (θ, φ) comprises the spectral water-leaving radiance Lw(λ, θ, φ) and the skylight radiance Lsky(λ) reflected by the sea surface, which includes the skylight coming from the specular direction (θ’ = θ, φ), F(θ, φ)Lsky(λ, θ’, φ), as well as that from all the other directions Δ(θ, φ) :
Rrs(λ) can be modeled by the following bio-optical model 16].16].
at(λ) is the seawater total spectral absorption coefficient, which can be decomposed into pure seawater absorption aw(λ), phytoplankton absorption aph(λ), colored dissolved organic matter and detritus absorption adg(λ).17]; S = 0.015 nm−1.
bb(λ), bbw(λ) and bbp(λ) are total, pure seawater and particle spectral backscattering coefficients.1]. In Eqs. (7)-(14), only bbp(440), adg(440) and aph(440) are unknown.
An objective function is defined as follows:Eq. (4) and from Eq. (7). represents the average of an array between λ1 and λ2. Err is then a function of 4 variables (bbp(440), adg(440), aph(440), and Δ) for optically deep waters, and they are derived numerically when Err reaches a minimum – spectral optimization [15, 18]. Rrs(λ) is therefore computed by applying this numerically derived Δ to Eq. (4). Then ρ (λ) is obtained.
The optimization-derived Rrs(λ) and ρ(λ) are referred to as RrsOpt(λ) and ρOpt(λ).
3.1 General condition
The in situ data, of which there are a total of 78, were acquired in August and September, 2003 in the Yellow Sea (YS) and East China Sea (ECS), covering diverse ocean and atmosphere conditions from relatively clean to moderately turbid waters, calm to roughened sea surfaces, and clear to overcast sky [See Fig. 1(a) for the sites of geographic distribution]. Above-water and in-water profiling optical measurements for the apparent optical properties were performed concurrently almost at each site. AC-S and HS-6 were operated to measure at(λ) and bbp(λ). Discrete water samples were collected for the measurements of aph(λ), colored dissolved organic matter (CDOM) absorption ag(λ), detritus absorption ad(λ), as well as the concentrations of ocean color constituents. adg(λ) was calculated as the sum of ad(λ) and ag(λ), and the average and standard deviation of S values in the study area were 0.015 ± 0.003 nm−1. Aerosol optical depth was measured by a sunphotometer CIMEL CE317. The statistics of the major parameters are shown in Table 1.
3.2 Above-water optical measurement
Above-water optical measurements  were made by a well-calibrated field spectroradiometer with the nominal 8° FOV (ASD, Inc., model FieldSpec) and reference plaque following the NASA ocean optics protocols . The spectroradiometer was operated in the viewing direction of θ = 40° from the nadir or zenith and φ = 135° from the sun plane. The plaque was held horizontally and exposed to the sun and sky in a position free from any shading, and the radiance sensor view was normal to the center of the plaque, the bidirectional (BRDF) properties of which were accurately characterized.
Three independent measurements were performed, each including 15 scans of Lt(λ), Lsky(λ) and Lp(λ), respectively with the integration time of 100~200 milliseconds. The outliers were identified as those scans exceeding the average plus or minus 2 times the standard deviation and removed from the sequential scans. The largest Lt(λ) scans were abandoned due to the possible residual effect of sun glint or foam. The remaining scans were averaged. Ed(0+, λ) was estimated from Lp(λ).
To be comparable with concurrent in-water radiometric measurements, the bidirectional effect of upwelling light field was corrected with the look-up table method proposed by Morel et al. (2002).
As an index of the cloud coverage and thus the degree of skylight uniformity, skylight remote sensing reflectance at 750 nm was computed, Srs(750) = Lsky(750)/Ed(0+,750), which is as low as about 0.02 under clear sky (non-uniform skylight), and up to over 0.3 under overcast sky (uniform skylight) .
3.3 Profiling optical measurement
Simultaneous in-water optical profile measurements were performed to obtain independent Rrs(λ) estimates, by a calibrated multispectral Optical Profiler (Satlantic, Inc., model SPMR) following the NASA ocean-optics protocols . The instrument was deployed at least 20 m away from the stern to avoid ship shadow disturbance [21, 22] and lowered at the speed of about 0.4 m/s. Incident spectral irradiance Ed(0+, λ) was measured simultaneously with a deck cell to normalize the in-water profiles, accounting for the changes in cloud cover during the cast. Replicate measurements were performed three times at each site. The self-shading effect of the in-water radiometric data was corrected .
The spectral diffuse attenuation coefficient for downwelling irradiance and upwelling radiance, Kd(λ) and KLu(λ) were calculated [see Fig. 1(b) for Kd(490) histogram] from a linear regression between the depth z and logarithm transformed Ed(z, λ) and Lu(z, λ) over a depth interval of 3~10 m, which varied with the wavelength. Lu(z, λ), was extrapolated with KLu(λ) to estimate Lu(0-, λ) and further across the sea surface to determine the spectral water-leaving radiance.
3.4 Radiometric calibration of radiometers
The absolute calibration of the radiometers was made in the optics lab of National Ocean Technology Center (NOTC) of China. The total calibration uncertainty was estimated to be within 4%.
With the two successive calibrations made before and after the field campaign, the radiometric stability of the radiometers over the experimental time period was estimated to be within 2-3%. During the cruise, the SeaWiFS Quality Monitor (Satlantic, Inc., SQM-II) was also used to monitor the radiometric stability of the radiometers once every 2-3 days.
Assuming that sources of uncertainties from laboratory inter-calibration and the changes in sensors sensitivity with time are additive , the overall inter-comparison uncertainty between the two sensors (FieldSpec and SPMR) was estimated to be about 5%.
Under the clear or partly cloudy sky with smaller Srs(750) values (with an average of 0.03 ± 0.03 sr−1, N = 39), the spectra variability of each ρOpt(λ) curve is obvious over the visible and near infrared domain [Fig. 2(a)], with the average of the coefficient of variation (CV, the ratio of standard deviation to the average) of 15 ± 8% (in a range of 3~35%). For the majority cases, ρOpt(λ) increases towards longer wavelengths, and the absolute percentage increment Q [defined in Eq. (18)] from 400 to 700 nm reaches 35 ± 27%.
Under mostly cloudy or overcast sky (cloud coverage over 90%), corresponding to the higher Srs(750) values (with an average of 0.33 ± 0.08 sr−1, N = 39), spectra of ρOpt(λ) are almost flat [Fig. 2(b)]. The CV of each ρOpt(λ) curve is less than ~2%.
The ρOpt(λ) spectral variability may be attributed to the difference in the spectral components of skylight contained in Trs(λ) and Srs(λ). Under clear or partly cloudy sky with the non-uniform skylight distribution, Srs(λ) is usually rich blue as a result of the dominated contribution from Rayleigh scattering; whereas, Trs(λ) comprises upwelling radiance from all directions, including even the sun and near horizon directions. Compared to skylight from zenith, radiances from these directions are richer in the longer wavelengths . Under overcast sky, the skylight distribution tends to be uniform, and the difference in the spectral components of skylight in Trs(λ) and Srs(λ) will diminish to vanish, thus leading to the low spectral variation of ρOpt(λ).
Note that for the overcast conditions the ρ values indeed vary in a relatively broad range of 0.0204~0.0332, with an average of 0.0245 ± 0.0029, which is slightly lower than the suggested constant of 0.028 .
A model that relates CV of ρ(λ) and Srs(750) is proposed to characterize the effect of the skylight distribution on the spectral variability of sea surface skylight reflectance [Fig. 3(a)]Fig. 3(b)].
To independently validate the optimization-retrieved ρOpt(λ) and its spectral variability, ρ(λ) is computed directly (referred to as ρMea(λ)) by Eq. (16) with RrsSPMR(λ) from the in-water measurement, and Trs(λ) and Srs(λ) from the above-water measurement. The calculation was made at the 7 discrete SPMR nominal bands from 412 to 565 nm, excluding longer wavelengths as in the profiling Rrs(λ) estimates there may be inherent with large uncertainties because of strong water attenuation (absorption).
The comparison (Table 2 and Fig. 4) indicates the difference (indexed by MAPD) between ρOpt(λ) and ρMea(λ) are <20% from 412 to 555 nm. If we confine the comparison to the relatively clear waters (Kd(490) < 0.2 m−1) observed with local SZA between 30 and 60 deg under which conditions the more robust and reliable profiling Rrs(λ) estimates may generally be expected and achieved, a closer match (<15%) can be found (the numbers in parentheses of Table 2).
Furthermore, the spectral variability found from ρOpt(λ) is also confirmed by the CV values of ρMea(λ); for the clear (or partly cloudy) and overcast (or mostly cloudy) sky subsets, CV values of ρMea(λ) at the seven discrete bands from 412 to 565 nm are 35 ± 26% and 3 ± 9%, respectively. Note that the CV values here are calculated based on ρMea(λ) at the seven discrete SPMR bands, and thus are not directly comparable in magnitude with that based on hyperspectral ρOpt(λ) from 350 to 780 nm).
Optimization-derived RrsOpt(λ) is shown in Fig. 5, which indicates a broad range of turbidity in the study area.
For the coastal waters with Kd(490) up to 1 m−1, the agreement (<20%) in the blue and green bands is achieved between RrsOpt (λ) and the concurrent RrsSPMR(λ) (Fig. 6 and Table 3), which is better than that between RrsSPMR(λ) and RrsConst(λ), as estimated from spectrally invariable ρ values according to wind speed and SZA . The comparisons at sites (N = 10) from relatively clear waters (Kd(490)<0.2 m−1) under favorable observation conditions (30°<SZA<60° and stable light field) show a better agreement (see the numbers in parenthesis in Table 3).
Figure 7 illustrates the effect of ρ values on Rrs(λ) estimate under the overcast or clear sky. Under overcast conditions [Fig. 7(a)], due to the low spectral dependence of ρ(λ), the effect of choosing different ρ values on Rrs(λ) is mainly on the Rrs(λ) curve magnitude; whereas under clear sky [Fig. 7(b)], the difference in the spectral shape of above-water Rrs(λ) is noticeable, especially in the blue (<500 nm) and red bands (>600 nm).
Table 4 shows the effect of ρ value variation on above-water Rrs(λ) band ratios, commonly used by empirical ocean color algorithms [25–29], which indicates that band ratios based on Rrs(670) or Rrs(412) may have MAPD of about 10%.
Sea surface skylight reflectance ρ(λ) is the widely regarded as the most important source of the uncertainties in above-water Rrs(λ) estimation. The spectral dependence of ρ(λ), which is generally ignored in the commonly adopted data processing methods, has been proven here to be significant under the non-uniform skylight distribution (e.g. clear sky or scattered clouds). For the uniform sky condition under which ρ(λ) has little spectral dependence, the ρ values are found to vary in a relatively broad range around the generally adopted constant (0.028). Therefore, the traditional method of ρ estimation may lead to significant uncertainties in the Rrs(λ) retrievals (especially in the blue and red spectral domain), possibly with its genuine spectral shape being altered to some extent. It might be necessary to re-process the historical above-water data and systematically evaluate the possible ocean color consequences. The established ocean color algorithms, especially those for the retrieval of chlorophyll-a and CDOM concentrations [27, 31, 32], which usually rely on the blue bands, must be re-tuned using the re-processed Rrs(λ). The uncertainty of the satellite radiometric products might also require re-assessment, as this type of activity mainly deals with data acquired under clear sky, when significant spectral variability of ρ(λ) usually exists.
The spectral optimization-based method appears applicable to the turbid coastal waters of YS and ECS (Kd(490) and SPM up to 1.95 m−1 and 20 mg/L, respectively, for our data set) and capable of deriving reasonable and reliable estimates of both Rrs(λ) and ρ(λ) under various environmental conditions (see Table 1). Except for the unique ability of handling with ρ(λ) spectral variability, the advantage of this method is that it derives all the retrievals solely from the direct above-water measurement quantities, relying on neither the concurrent wind speed data nor the null NIR water-leaving radiance assumption. In addition, with little subjective or empirical factors involved in the retrievals, site-consistent Rrs(λ) estimates can be safely achieved. It would be a qualified candidate among the methods for the routine above-water data processing or historical data re-processing. Nevertheless, it should be noted that, for certain turbid waters with unique bio-optical characteristics, such as the highly turbid waters dominated by suspended sediment, algal blooms (coccolithophore), oil film-covered waters, etc., its applicability must be carefully evaluated, especially for the empirical relationships and the statistical regression-derived model parameters.
The empirical relationships [Eqs. (19)-(20)] are found between the spectral variability of ρ(λ) and the skylight uniformity. Due to the fact that the skylight distribution is intricate and diverse in nature, there will be no clear Srs(750) threshold to determine whether or not ρ(λ) has apparent spectral variability, just as there is no sharp dividing line between Case 1 and Case 2 waters . The approximate value of 0.15sr−1 proposed here is only a rough estimate based on the case study from field data of limited volume. A more idealistic method to comprehensively analyze and document the ρ(λ) spectral variability would be the ocean-atmosphere radiative transfer model, which can fully consider the sea surface roughed by varying wind speeds and diverse conditions of the cloud coverage, wind speed, viewing geometry and ocean optical properties.
For the routine above-water observation setup, it is unavoidable for the sea surface reflected skylight (and sometimes even the residual sun glint) to transfer into the sensor and intermingle with the water-leaving signal, which causes the reliable Rrs(λ) estimation to be severely enslaved to the accurate determination of ρ(λ). Indeed, the sophisticated data processing (such as the spectral optimization here and polarization radiative transfer modeling) for ρ(λ) estimation are incurred to some extent by the deficiency of the observation scheme. The novel above-water observation setup , which effectively blocks the reflected skylight in a mechanical and physical way, seems to be a more ideal method (except for very rough sea conditions), with the ρ estimation being totally avoided and data processing significantly being significantly eased. This promising setup would be a significant improvement over the traditional methods after the effect of self-shading is quantified and minimized.
In this study, sea surface skylight spectral reflectance ρ(λ) in the visible and NIR bands was retrieved by the spectral optimization method and bio-optical model from in situ data. Skylight distribution (influenced by cloud coverage) is found to be main factor in determining the spectral dependence of ρ(λ), which can be predicted by a new model based on Srs(750)≡Lsky(750)/Ed(750). Under overcast or mostly cloudy sky with a uniform skylight distribution (Srs(750)>~0.15sr−1), ρ(λ) shows little spectral variability; under clear or partly cloudy sky with a non-uniform skylight distribution (Srs(750)<~0.15sr−1), ρ(λ) varies significantly with wavelength, and basically increases towards longer wavelengths.
By using the spectrally variable ρ(λ) rather than a constant, the agreement between the above-water estimated Rrs(λ) and concurrent profiling ones is improved. Under non-uniform skylight, ignoring ρ’s spectral dependence may introduce significant uncertainty into Rrs(λ) estimates, especially at the blue and red bands. Even under uniform sky, the ρ values may vary in a broad range, which implies that a pre-defined constant (0.028) may not be universally appropriate. Ocean color algorithms, especially those based on Rrs(412) or Rrs(670), are mostly affected by ρ(λ)-induced uncertainty. It might be necessary to re-process the relevant historical above-water data, and re-tune the parameters of ocean color retrieval algorithms accordingly.
This work is jointly funded by the High-tech Research and Development Program of China (no. 2007AA092102) and Dragon-3 project (ID 10470). The work was performed when Tingwei Cui visited the University of Massachusetts at Boston (UMB), funded by a visiting scholar program co-sponsored by the China Scholarship Council and State Oceanic Administration, and benefited from advice and facilities provided by UMB. We are grateful to Dr. Curtis Mobley for providing his numerical modeling results of the sea surface skylight reflectance. We would like to thank Dr. Zhongping Lee, Jianhua Zhu and Anan Yang for their constructive comments and helpful discussions on the manuscript. We also thank the anonymous reviewers for their critical comments on the manuscript.
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