Spectral variability of sea surface skylight reflectance and its effect on ocean color

Ting-Wei Cui; Qing-Jun Song; Jun-Wu Tang; Jie Zhang

doi:10.1364/OE.21.024929

1. Introduction

Spectral remote sensing reflectance R_rs(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 [1]. The above-water method [2–7] is one of the most widely adopted methods for in situ R_rs(λ) estimation. In this scheme, spectral radiance of the ocean L_t(λ) and skylight L_sky(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 [4]. After data quality control, such as abandoning the data contaminated by the residual sun glint, the spectral water-leaving radiance L_w(λ) is estimated as follows:

L_{w} (λ) {=L}_{t} (λ) - ρ (λ) L_{sky} (λ) .

where ρ(λ) is the (effective) sea surface skylight reflectance (factor). Then, with the incident spectral irradiance just above the sea surface E_d(0⁺, λ) directly measured or estimated from the measured spectral radiance L_p(λ) of a well-calibrated plaque (the spectral reflectance ρ_p(λ) of which is known), R_rs(λ) is calculated as follows:

R_{rs} (λ) = \frac{L_{w} (λ)}{E_{d} (0^{+}, λ)} = \frac{[L_{t} (λ) - ρ L_{sky} (λ)] ρ_{p}}{π L_{p} (λ)} .

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 [4]. As the L_sky(λ) usually dominates L_w(λ), especially in the shorter wavelengths and less turbid waters under clear sky, the influence of adopted ρ(λ) values on the estimates of L_w(λ) and R_rs(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 [4]. 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 [14].

Recently, Lee et al. [1] 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 R_rs(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 R_rs(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, R_rs(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.

2. Model

In the condition of ignoring the sun glint, foam and white cap, spectral upwelling radiance L_t(λ) measured from the angular geometry (θ, φ) comprises the spectral water-leaving radiance L_w(λ, θ, φ) and the skylight radiance L_sky(λ) reflected by the sea surface, which includes the skylight coming from the specular direction (θ’ = θ, φ), F(θ, φ)L_sky(λ, θ’, φ), as well as that from all the other directions Δ(θ, φ) [1]:

L_{w} (λ, θ, ϕ) \approx L_{t} (λ, θ, ϕ) - F (θ, ϕ) L_{sky} (λ, θ^{'}, ϕ) - Δ (θ, ϕ) .

or in terms of reflectance:

R_{rs} (λ, θ, ϕ) \approx T_{rs} (λ, θ, ϕ) - F (θ, ϕ) S_{rs} (λ, θ^{'}, ϕ) - Δ (θ, ϕ) .

where F(θ, φ) is the known Fresnel reflectance of the sea surface for the specific observing geometry, and

T_{r s} (λ) = \frac{L_{t} (λ) ρ_{p} (λ)}{π L_{p} (λ)} .

S_{r s} (λ) = \frac{L_{s k y} (λ) ρ_{p} (λ)}{π L_{p} (λ)} .

For any wavelength, T_rs(λ) and S_rs(λ) are directly determined from measurements usually made with θ = 40° from the nadir and φ = 135° from the sun plane, and only R_rs(λ) and Δ are unknown.

R_rs(λ) can be modeled by the following bio-optical model [15]

R_{rs} (λ) \approx \frac{0.5 r_{rs} (0^{-}, λ)}{1 - 1.5 r_{rs} (0^{-}, λ)} .

where r_rs(0^-, λ) is the subsurface remote sensing reflectance.

r_{rs} (0^{-}, λ) = \frac{L_{u} (0^{-}, λ)}{E_{d} (0^{-}, λ)} = g_{w} \frac{b_{b w} (λ)}{a_{t} (λ) + b_{b} (λ)} + g_{p} \frac{b_{b p} (λ)}{a_{t} (λ) + b_{b} (λ)} .

where g_w and g_p are the model parameters [16].

g_{p} (λ) = G_{0} {1 - G_{1} \exp [- G_{2} \frac{b_{b p} (λ)}{a_{t} (λ) + b_{b} (λ)}]} .

where G₀, G₁, and G₂ are constants for the specified light geometry and particle phase function. For the nadir direction and 30° SZA, g_w = 0.113; G₀ = 0.197; G₁ = 0.636; G₂ = 2.552 [16].

a_t(λ) is the seawater total spectral absorption coefficient, which can be decomposed into pure seawater absorption a_w(λ), phytoplankton absorption a_ph(λ), colored dissolved organic matter and detritus absorption a_dg(λ).

a_{t} (λ) = a_{w} (λ) + a_{p h} (λ) + a_{d g} (λ) .

a_{p h} (λ) = {[a_{0} (λ) + a_{1} (λ) \ln [a_{p h} (440)]} a_{p h} (440) .

a_{d g} (λ) = a_{d g} (440) \exp [- S (λ - 440)] .

where a₀(λ) and a₁(λ) are known model parameters [17]; S = 0.015 nm⁻¹.

b_b(λ), b_bw(λ) and b_bp(λ) are total, pure seawater and particle spectral backscattering coefficients.

b_{b} (λ) = b_{b w} (λ) + b_{b p} (λ) .

b_{b p} (λ) = b_{b p} (440) {(\frac{440}{λ})}^{Y} .

Y can be estimated from measured T_rs(λ) and S_rs(λ) [1]. In Eqs. (7)-(14), only b_bp(440), a_dg(440) and a_ph(440) are unknown.

An objective function is defined as follows:

Err = \frac{{\cup_{400}^{675} {{[R}_{r s} (λ) - {\tilde{R}}_{r s} (λ)]}^{2} + \cup_{750}^{800} {{[R}_{r s} (λ) - {\tilde{R}}_{r s} (λ)]}^{2}}^{0.5}}{\cup_{400}^{675} R_{r s} (λ) + \cup_{750}^{800} R_{r s} (λ)} .

with R_rs(λ) from Eq. (4) and

{\tilde{R}}_{r s} (λ)

from Eq. (7).

\cup_{λ_{1}^{}}^{λ_{2}}

represents the average of an array between λ₁ and λ₂. Err is then a function of 4 variables (b_bp(440), a_dg(440), a_ph(440), and Δ) for optically deep waters, and they are derived numerically when Err reaches a minimum – spectral optimization [15, 18]. R_rs(λ) is therefore computed by applying this numerically derived Δ to Eq. (4). Then ρ (λ) is obtained.

ρ (λ) {=[T}_{r s} (λ) - R_{rs} (λ)] / S_{r s} (λ) .

The optimization-derived R_rs(λ) and ρ(λ) are referred to as R_rs^Opt(λ) and ρ^Opt(λ).

3. Data

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 a_t(λ) and b_bp(λ). Discrete water samples were collected for the measurements of a_ph(λ), colored dissolved organic matter (CDOM) absorption a_g(λ), detritus absorption a_d(λ), as well as the concentrations of ocean color constituents. a_dg(λ) was calculated as the sum of a_d(λ) and a_g(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.

Fig. 1 Locations of in situ sampling sites (a) and histogram of K_d(490) measurements (b)

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Table 1. Mean, standard deviation (SD), minimum (Min) and maximum (Max) of the observed parameters

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3.2 Above-water optical measurement

Above-water optical measurements [19] 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 [2]. 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 L_t(λ), L_sky(λ) and L_p(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 L_t(λ) scans were abandoned due to the possible residual effect of sun glint or foam. The remaining scans were averaged. E_d(0⁺, λ) was estimated from L_p(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, S_rs(750) = L_sky(750)/E_d(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) [20].

3.3 Profiling optical measurement

Simultaneous in-water optical profile measurements were performed to obtain independent R_rs(λ) estimates, by a calibrated multispectral Optical Profiler (Satlantic, Inc., model SPMR) following the NASA ocean-optics protocols [2]. 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 E_d(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 [23].

The spectral diffuse attenuation coefficient for downwelling irradiance and upwelling radiance, K_d(λ) and K_Lu(λ) were calculated [see Fig. 1(b) for K_d(490) histogram] from a linear regression between the depth z and logarithm transformed E_d(z, λ) and L_u(z, λ) over a depth interval of 3~10 m, which varied with the wavelength. L_u(z, λ), was extrapolated with K_Lu(λ) to estimate L_u(0^-, λ) and further across the sea surface to determine the spectral water-leaving radiance.

L_{w} (λ) = 0.543 L_{u} (0^{-}, λ) .

R_rs(λ) at 9 nominal SPMR bands of 412, 443, 490, 510, 520, 555, 565, 670, and 780 nm were estimated with L_w(λ) and measured E_d(0⁺, λ), and multiple measurements were averaged [referred to as R_rs^SPMR(λ)].

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 [5], the overall inter-comparison uncertainty between the two sensors (FieldSpec and SPMR) was estimated to be about 5%.

4. Results

4.1 ρ(λ)

The optimization-retrieved ρ^Opt(λ) are subdivided into two subsets [Figs. 2(a) and 2(b)] according to the S_rs(750) value of each station and approximate threshold of 0.15 sr⁻¹.

Fig. 2 ρ(λ) retrievals at major ocean color bands under different cloud coverage and thus skylight distribution. (a) Clear or partly cloudy subset (S_rs(750)<0.15 sr⁻¹); (b) Overcast and mostly cloudy subset (S_rs(750)>0.15 sr⁻¹). The dashed lines correspond to the stations. The thick solid lines are the average, and the error bars are the standard deviations. The red horizontal lines correspond to a spectrally constant ρ of 0.028.

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Under the clear or partly cloudy sky with smaller S_rs(750) values (with an average of 0.03 ± 0.03 sr⁻¹, N = 39), the spectra variability of each ρ^Opt(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, ρ^Opt(λ) increases towards longer wavelengths, and the absolute percentage increment Q [defined in Eq. (18)] from 400 to 700 nm reaches 35 ± 27%.

Q = \frac{| ρ^{Opt} (700) - ρ^{Opt} (400) |}{ρ^{Opt} (400)} \times 100 % .

Under mostly cloudy or overcast sky (cloud coverage over 90%), corresponding to the higher S_rs(750) values (with an average of 0.33 ± 0.08 sr⁻¹, N = 39), spectra of ρ^Opt(λ) are almost flat [Fig. 2(b)]. The CV of each ρ^Opt(λ) curve is less than ~2%.

The ρ^Opt(λ) spectral variability may be attributed to the difference in the spectral components of skylight contained in T_rs(λ) and S_rs(λ). Under clear or partly cloudy sky with the non-uniform skylight distribution, S_rs(λ) is usually rich blue as a result of the dominated contribution from Rayleigh scattering; whereas, T_rs(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 [1]. Under overcast sky, the skylight distribution tends to be uniform, and the difference in the spectral components of skylight in T_rs(λ) and S_rs(λ) will diminish to vanish, thus leading to the low spectral variation of ρ^Opt(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 [4].

A model that relates CV of ρ(λ) and S_rs(750) is proposed to characterize the effect of the skylight distribution on the spectral variability of sea surface skylight reflectance [Fig. 3(a)]

C V = - 0.1308 \times {log}_{10} [S_{r s} (750)] - 0.0574, (R^{2} = 0.76, N = 78) .

which is applicable to a rough range of S_rs(750) from 0 to 0.36 sr⁻¹. A similar relationship exists between S_rs(750) and Q [Fig. 3(b)].

Fig. 3 Relationships between S_rs(750) and the spectral variability of ρ(λ) in terms of CV (a) or Q (b), defined in Eqs. (19)-(20). The solid lines are the regression results. The open circles are data from the clear or partly cloudy subset, and the grey dots are from the overcast and mostly cloudy sky subsets.

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Q = - 0.3246 \times {log}_{10} [S_{r s} (750)] - 0.1459, (R^{2} = 0.66, N = 78) .

To independently validate the optimization-retrieved ρ^Opt(λ) and its spectral variability, ρ(λ) is computed directly (referred to as ρ^Mea(λ)) by Eq. (16) with R_rs^SPMR(λ) from the in-water measurement, and T_rs(λ) and S_rs(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 R_rs(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 ρ^Opt(λ) and ρ^Mea(λ) are <20% from 412 to 555 nm. If we confine the comparison to the relatively clear waters (K_d(490) < 0.2 m⁻¹) observed with local SZA between 30 and 60 deg under which conditions the more robust and reliable profiling R_rs(λ) estimates may generally be expected and achieved, a closer match (<15%) can be found (the numbers in parentheses of Table 2).

Table 2. Comparison between ρ^Opt(λ) and ρ^Mea(λ). The numbers in parenthesis correspond to the validation in relatively clear waters under favorable observation conditions (see text for details). MAPD standards for the median of absolute percentage difference defined in Eq. (21), the advantages of which are providing equal weighting to underestimation and overestimation, and avoiding the effect of extreme outliers on the statistics. To be compared with existing literatures, the values of the average absolute unbiased percent difference [5] Ψ are also given. RMS stands for root-mean-square-error. N is the number of samples.

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Fig. 4 Scatter plot of ρ_rs(λ) by optimization retrieval and concurrent above- and in-water observations.

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M A P D = \exp [m e d i a n | \ln (\frac{y_{i}}{x_{i}}) |] - 1, i = 1, 2 \dots N .

Furthermore, the spectral variability found from ρ^Opt(λ) is also confirmed by the CV values of ρ^Mea(λ); for the clear (or partly cloudy) and overcast (or mostly cloudy) sky subsets, CV values of ρ^Mea(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 ρ^Mea(λ) at the seven discrete SPMR bands, and thus are not directly comparable in magnitude with that based on hyperspectral ρ^Opt(λ) from 350 to 780 nm).

4.2 R_rs(λ)

Optimization-derived R_rs^Opt(λ) is shown in Fig. 5, which indicates a broad range of turbidity in the study area.

Fig. 5 R_rs(λ) at all sampling sites retrieved by the optimization method.

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For the coastal waters with K_d(490) up to 1 m⁻¹, the agreement (<20%) in the blue and green bands is achieved between R_rs^Opt (λ) and the concurrent R_rs^SPMR(λ) (Fig. 6 and Table 3), which is better than that between R_rs^SPMR(λ) and R_rs^Const(λ), as estimated from spectrally invariable ρ values according to wind speed and SZA [4]. The comparisons at sites (N = 10) from relatively clear waters (K_d(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).

Fig. 6 Scatter plot of R_rs(λ) by above-water and concurrent profiling observations. The comparison is based on data (N = 58) from waters with K_d(490) < 1.0 m⁻¹. The circles represent results from ρ^Opt(λ); the crosses ( + ) correspond to those from Eq. (2) and a spectrally constant ρ [4].

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Table 3. Comparison between above-water R_rs(λ) estimates with synchronous in-water ones (R_rs^SPMR). The numbers in parenthesis correspond to the assessment in relatively clear waters (K_d(490)<0.2 m⁻¹) under favorable observation conditions (30°<SZA<60°) and stable light field. The above-water R_rs(λ) were derived from optimization method (R_rs^Opt) or Eq. (2) with the spectrally constant ρ (R_rs^Const) [4]. The bidirectional effect is corrected by the look-up table method [24].

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Figure 7 illustrates the effect of ρ values on R_rs(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 R_rs(λ) is mainly on the R_rs(λ) curve magnitude; whereas under clear sky [Fig. 7(b)], the difference in the spectral shape of above-water R_rs(λ) is noticeable, especially in the blue (<500 nm) and red bands (>600 nm).

Fig. 7 Comparison between the estimated R_rs(λ) by above-water measurements (solid curves) and in-water ones (red circles linked by dashed lines) under overcast (a) and clear (b) sky. The various R_rs (λ) by above-water observation are estimated by the use of optimized ρ(λ) (green), or a spectrally invariant constant according to the look-up Table [4] (purple).

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Table 4 shows the effect of ρ value variation on above-water R_rs(λ) band ratios, commonly used by empirical ocean color algorithms [25–29], which indicates that band ratios based on R_rs(670) or R_rs(412) may have MAPD of about 10%.

Table 4. Effect of the ρ value and its spectral variability on R_rs(λ) band ratios. These ratios are calculated and compared based on R_rs^Const(λ) and R_rs^Opt(λ), respectively (N = 58).

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5. Discussion

Sea surface skylight reflectance ρ(λ) is the widely regarded as the most important source of the uncertainties in above-water R_rs(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 R_rs(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 R_rs(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 (K_d(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 R_rs(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 R_rs(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 S_rs(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 [32]. 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 R_rs(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 [33], 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.

5. Conclusions

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 S_rs(750)≡L_sky(750)/E_d(750). Under overcast or mostly cloudy sky with a uniform skylight distribution (S_rs(750)>~0.15sr⁻¹), ρ(λ) shows little spectral variability; under clear or partly cloudy sky with a non-uniform skylight distribution (S_rs(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 R_rs(λ) and concurrent profiling ones is improved. Under non-uniform skylight, ignoring ρ’s spectral dependence may introduce significant uncertainty into R_rs(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 R_rs(412) or R_rs(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.

Acknowledgments

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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	Mean ± SD	Min~Max
Wind speed / m s⁻¹	4.9 ± 1.7	0.3 ~8.8
Wave height / m	1.5 ± 0.7	0 ~3.5
Wave period / s	4.3 ± 1.8	0 ~9
Secchi depth / m	6.0 ± 4.9	0.7 ~21.0
Water color	9 ± 4	5 ~19
Water depth / m	31.0 ± 16.6	10 ~74
Aerosol optical / depth τ_a(550)	0.49 ± 0.51	0.08~2.20
SPM / g m⁻³	4.46 ± 6.20	0.50~23.90
Chl-a / mg m⁻³	2.27 ± 4.37	0.21~35.91
a_g(400) / m⁻¹	0.21 ± 0.11	0.08~0.67
a_t(440) / m⁻¹	0.36 ± 0.33	0.09~1.59
b_bp(440) / m⁻¹	0.0731 ± 0.1632	0.0038~0.8633
K_d(490) / m⁻¹	0.44 ± 0.48	0.07~1.95
b_b/(a + b_b)	0.0954 ± 0.0844	0.01782~0.3533

Wavelength / nm	MAPD	Ψ	RMS / sr⁻¹	N
412	14%(12%)	17%	0.0105(0.0051)	66(10)
443	14%(6%)	18%	0.0130(0.0036)	64(10)
490	14%(11%)	24%	0.0204(0.0066)	63(10)
555	18%(6%)	27%	0.0363(0.0116)	60(10)

Wavelength /nm		MAPD	Ψ	RMS / sr⁻¹	R²	N
412	R_rs^Opt vs. R_rs^SPMR	19%(20%)	25%(17%)	9.5010⁻⁴(5.7010⁻⁴)	0.84(0.39)	58(10)
412	R_rs^Const vs. R_rs^SPMR	24%(16%)	34%(32%)	1.4110⁻³(1.0910⁻³)	0.68(0.00)	58(10)
443	R_rs^Opt vs. R_rs^SPMR	14%(6%)	18%(7%)	9.1010⁻⁴(2.1810⁻⁴)	0.92(0.74)	58(10)
443	R_rs^Const vs. R_rs^SPMR	23%(18%)	29%(14%)	1.5110⁻³(8.2910⁻⁴)	0.82(0.00)	58(10)
490	R_rs^Opt vs. R_rs^SPMR	14%(7%)	18%(10%)	1.4310⁻³(3.4710⁻⁴)	0.93(0.52)	58(10)
490	R_rs^Const vs. R_rs^SPMR	17%(12%)	26%(13%)	1.8910⁻³(9.2310⁻⁴)	0.87(0.02)	58(10)
555	R_rs^Opt vs. R_rs^SPMR	16%(12%)	16%(13%)	1.7310⁻³(3.3010⁻⁴)	0.93(0.54)	58(10)
555	R_rs^Const vs. R_rs^SPMR	19%(20%)	24%(13%)	2.1310⁻³(7.1010⁻⁴)	0.90(0.11)	58(10)

	MAPD	Ψ
R_rs(670)/ R_rs(490)	15%	19%
R_rs(670)/ R_rs(555)	13%	18%
R_rs(412)/ R_rs(510)	9%	12%
R_rs(412)/ R_rs(490)	8%	10%
R_rs(670) + R_rs(555)	7%	18%
R_rs(443)/[R_rs(555) + R_rs(670)]	7%	11%
R_rs(443)/ R_rs(555)	5%	9%
R_rs(555)-0.5[R_rs(443) + R_rs(670)]	2%	3%
R_rs(490)/ R_rs(555)	2%	3%

	Mean ± SD	Min~Max
Wind speed / m s⁻¹	4.9 ± 1.7	0.3 ~8.8
Wave height / m	1.5 ± 0.7	0 ~3.5
Wave period / s	4.3 ± 1.8	0 ~9
Secchi depth / m	6.0 ± 4.9	0.7 ~21.0
Water color	9 ± 4	5 ~19
Water depth / m	31.0 ± 16.6	10 ~74
Aerosol optical / depth τ_a(550)	0.49 ± 0.51	0.08~2.20
SPM / g m⁻³	4.46 ± 6.20	0.50~23.90
Chl-a / mg m⁻³	2.27 ± 4.37	0.21~35.91
a_g(400) / m⁻¹	0.21 ± 0.11	0.08~0.67
a_t(440) / m⁻¹	0.36 ± 0.33	0.09~1.59
b_bp(440) / m⁻¹	0.0731 ± 0.1632	0.0038~0.8633
K_d(490) / m⁻¹	0.44 ± 0.48	0.07~1.95
b_b/(a + b_b)	0.0954 ± 0.0844	0.01782~0.3533

Spectral variability of sea surface skylight reflectance and its effect on ocean color

Abstract

1. Introduction

2. Model