1. Introduction

Above-water radiometry generically refers to the application of field optical radiometers to the quantification of the spectral radiance emerging from the sea, i.e., the water-leaving radiance L_W. Such a process requires the removal of the radiance contributions reflected by the sea surface (i.e., sun- and sky-glint) from the total radiance measured by the sensor looking at the sea. Thus, determination of L_W requires accurate estimate of the sea surface reflectance factor, which is a wavelength dependent function of parameters defining the measurement conditions: observation geometry (viewing angles, sun zenith, relative azimuth between sun and instrument angles), sea state (wave height, slopes and direction, and also whitecap distribution), sky conditions (aerosol load and type).

During the last two decades above water radiometry methods gained increasing relevance in remote sensing applications related to the validation of satellite ocean color data products and in the study of optically significant materials suspended or dissolved in natural waters [1–4]. This increased relevance followed a demonstrated capability of above-water radiometry to determine L_W with accuracy comparable to that achievable with in-water methods, but also the perception that above-water deployment needs are less strict than those requested for in-water radiometry [5]. However, despite of the many incremental progresses, the determination of ρ is still a major challenge.

Values of ρ were comprehensively determined [6] at the wavelength λ of 550 nm using the Hydrolight radiative transfer numerical model [7], accounting for the dependence on the viewing and illumination geometries, and modelling the effects of sea state as a function of wind speed using Cox-Munk surfaces [8,9]. It is recalled that the sky radiance distribution was determined from an irradiance model [10] and experimental sky radiance patterns [11] by neglecting polarization effects, but implicitly including multiple scattering and aerosol effects. These ρ values have been extensively applied by the scientific community to determine L_W from above-water radiometry [12,13].

In the recent years an increasing attention has been given to polarization effects in above-water radiometry [14,15]. In agreement with a demonstrated relevance of polarization effects in retrieved L_W, new reflectance factors at 550 nm have been proposed accounting for the wave height and slope variance, in addition to reflection and transmission processes involving polarized radiance at the water surface [16]. Different from previous surface reflectance factors, the new ones have been determined for a clear purely molecular (i.e., Rayleigh) sky applying a single scattering analytic radiance model for the Stokes vectors. Consequently, this specific ideal case can be considered as representative of extreme polarization effects because of the absence of depolarization contributions from aerosols.

The new factors ρ exhibit marked differences with respect to the previous ones as a function of viewing and illumination geometries as well as wind speed. These differences intrinsically suggest an assessment of L_W data products derived from the application of the different factors ρ for actual measurement conditions. Within such a context, this study aims at evaluating the impact of these factors ρ on L_W derived from autonomous above-water radiometric measurements performed through the Ocean Color component of the Aerosol Robotic Network (AERONET-OC) [12]. Specifically, the analysis allows for investigations on the accuracy of factors ρ determined neglecting and conversely accounting for polarization effects, in combination with different assumptions applied for the modeling of sky radiance distribution and sea surfaces.

2. Data and methods

The impact on AERONET-OC data products due to differences of in factors ρ is assessed using matchups (i.e., data from the same site collected close in time under the same measurement conditions) of multispectral values of L_W(λ) determined from in-water and above-water radiometry. Specifically, the effects of the different reflectance factors are evaluated using determinations of above-water L_W(λ) made by applying sea surface reflectance factors ρ ^U and ρ ^P, proposed by neglecting [6] and alternatively accounting for [16] polarization effects. It is recognized, however, that the different modelling applied for sea surfaces and sky radiance distribution while computing ρ ^U and ρ ^P, may bound the capability of assessing the relevance of the sole polarization effects.

The measurements related to this study were collected at the Acqua Alta Oceanographic Tower (AAOT) site located in the northern Adriatic Sea 8 nautical miles off the Venice Lagoon (45.314°N, 12.508°E). The site is representative of different water types: waters with optical properties solely explained by phytoplankton (i.e., Case-1 waters) for approximately 1/3 of the cases, and alternatively by optically complex waters (i.e., Case-2 waters) mostly characterized by moderate concentrations of sediments [17,18]. It is added that the aerosol at site is mostly continental with optical thickness characterized by mean value of the Ångström exponent α = 1.5 and standard deviation of 0.6 in the 488-870 nm spectral interval.

Since late 90s the AAOT site supports long-term ocean color validation activities through the Coastal Atmosphere and Sea Time-Series (CoASTS) measurement program [19], which ensures the collection of in water radiometry data and inherent optical properties for a few days several times a year. Since 2002 the CoASTS data have been complemented by autonomous above-water radiometry measurements performed within the context of AERONET-OC. Collocated CoASTS (in-water) and AERONET-OC (above-water) radiometric measurements, have permitted the construction of the L_W matchup data set applied in this study. It is emphasized that both above- and in-water radiometric measurements were collected from a fixed structure and consequently are not affected by perturbations due to motion of the deployment platform.

2.1 Above-water data and related uncertainties

AERONET-OC aims at delivering standardized in situ multi-spectral L_W(λ) data and derived products like the normalized water-leaving L_WN(λ) [12], in addition to the aerosol optical thickness τ_a(λ) [20,21] at a number of measurement sites mostly located in coastal regions. Peculiarity of AERONET-OC is the use of identical instruments at the various sites and the application of a sole measurement protocol. These basic elements are then complemented by the regular calibration of network radiometers through a single method in a dedicated facility, and additionally by the handling, processing and quality control of data through a sole code.

AERONET-OC spectrally asynchronous measurements [12] are performed at different center-wavelengths in the 412-1020 nm spectral region (nominally, 412, 443, 488, 531, 551, 667, 870 and 1020 nm). Like most above-water radiometry methods, AERONET-OC data relies on sky- and sea-radiance measurements, and estimates of the sea surface reflectance factor for the determination of L_W(λ). Specifically, L_W(λ) is quantified from measurements of the total radiance from the sea L_T(θ,ϕ,λ) and sky radiance L_i(θ′,ϕ,λ) derived from measurements performed with modified CE-318 (CIMEL-Electronique, Paris) sun-photometers. The viewing geometries are identified by angles θ, θ ′ and ϕ, where θ = 40 degrees and θ ′ = 180 - θ degrees are the directions relative to the zenith, and ϕ = ± 90 degrees is the relative azimuth with respect to the sun plane. It is once more remarked that an ideally better viewing geometry is that identified by ϕ = ± 135 degrees that further minimizes glint perturbations with respect to the use of ϕ = ± 90 degrees [6]. The selection of the apparently less favorable measurement geometry is however suggested by the need to minimize the impact of superstructure shadow on L_T(θ,ϕ,λ). In fact this perturbation is more relevant for ϕ = ± 135 degrees than for ϕ = ± 90 degrees, with effects increasing with the sun zenith angle (see the discussion on superstructure perturbations as a function of θ₀ for in-water measurements at the AAOT [22]).

In agreement with a consolidated protocol [12], AERONET-OC L_W (λ,θ,ϕ) is determined as:

where ρ(θ,ϕ,θ₀,W) [6] is the sea surface reflectance factor as a function of the measurement and illumination geometries defined by θ, ϕ, θ₀, and additionally depends on the sea state conveniently expressed as a function of wind speed W. It is further pointed out that factors ρ exhibit a spectral dependence [23]. Despite of this, they are commonly assumed independent from wavelength due to the lack of tabulated spectral values. The impact of such an assumption on the accuracy of L_W can be minimized by removing data perturbed by large glint and foam contributions: a filtering process that minimizes the spectral perturbations in L_T.

It should be additionally noted that the model implemented through Eq. (1) ideally relies on the sky-radiance from the direction identified by θ′ and ϕ, which is thus expected to represent the mean radiance around this direction reflected by wave facets into the field-of-view of the sensor. L_T(θ,ϕ,λ) and L_i(θ′,ϕ,λ) applied in Eq. (1) are assumed to be obtained with stable and clear sky illumination conditions and determined from the mean of n-independent measurements passing strict quality control criteria including tests to remove those data affected by superstructure, clouds and large sea surface perturbations [12].

The latter quality test applied to measurements of the total radiance from the sea deserves some discussion. In fact L_T(θ,ϕ,λ) is determined from the mean of relative minima of successive measurements of total radiance from the sea exhibiting standard deviations below given thresholds at each center-wavelength. As already anticipated, this specific quality control test aims at excluding from the determination of L_W(θ,ϕ,λ) those measurements which may be appreciably perturbed by foam and glint and consequently affect the amplitude and spectral dependence of actual ρ. The process is thus targeted to preserve L_W(θ,ϕ,λ) spectra affected by low uncertainties at the expense of the number of successful retrievals. A consequence of such a process [24] is an expected mismatch between wind speed and wave effects due the removal of individual measurements likely affected by most relevant glint contributions. Because of this, the actual wind speed applied for the determination of ρ among tabulated values, may not be that best representing the sea surface characterizing those measurements applied for the computation of L_W(θ,ϕ,λ): i.e., the factors ρ estimated through actual values of the wind speed are likely to represent sea surface perturbations more pronounced than those characterizing L_T(θ,ϕ,λ) after the filtering process. As previously suggested [12,24], this may lead to a systematic underestimation of L_W(θ,ϕ,λ) because of the application of factors ρ overestimated for the specific L_T(θ,ϕ,λ) applied in Eq. (1). This issue is accounted for in the uncertainty estimates and will be further addressed in the discussion section.

Final step in the computation of L_W(λ) at nadir view (i.e., θ = 0) from L_W(θ,ϕ,λ) determined with θ = 40 degrees, is the correction for the viewing angle dependence through:

where the ratio ℜ(0,W)/ℜ(θ,W) accounts for changes in surface reflectance and refraction, and the spectral ratio of Q-factors, Q(θ,ϕ,θ₀,λ,τ_a,Chla)/Q(0,0,θ₀,λ,τ_a,Chla), minimizes the effects of the anisotropic radiance distribution in the in–water light field as a function of observation and illumination geometries, atmospheric optical properties expressed through τ_a(λ), and water inherent optical properties solely conveyed as a function of chlorophyll-a concentration Chla. The latter assumption, which is only applicable to Case-1 waters, provides access to tabulated values of ℜ(θ,W) and derived values of Q(θ,ϕ,θ₀,λ,τ_a,Chla) [25]. The validity of this correction is uncertain at sites characterized by optically complex waters. In the specific case of the AAOT site, the uncertainty budget proposed for AERONET-OC data products includes an estimate of the uncertainties due to the assumption of chlorophyll-a dominated waters [12,26].

AERONET- OC data products are generated at three levels of quality control: i. Level-1.0 derived from any complete sequence of in situ measurements; ii. Level-1.5 obtained applying a series of quality tests designed to remove measurements affected by significant perturbations due to environmental effects (e.g., clouds, heavy sea state) or superstructure (e.g., shading, reflection); and finally iii. Level 2.0 generated after post-deployment calibration and assessment of each individual data record.

In agreement with previous investigations, a comprehensive evaluation of uncertainties for AERONET-OC Level 2 L_W(λ) data from the AAOT site are presented in Table 1. These values account for: i. uncertainties in absolute calibration [26] assumed equal and correlated for both L_T(θ,ϕ,λ) and L_i(θ′,ϕ,λ); ii. changes in instrument sensitivity during extensive field deployments [12]; iii. guessed uncertainties in corrections used for removing the viewing angle dependence, assumed 25% of the corrections applied to the data included in the current matchup data set (these relatively large percent values are expected to account for uncertainties due to the intrinsic assumption of Case-1 water at the AAOT); iv. uncertainty in the values of wind speed [12]; v. filtering of L_T(θ,ϕ,λ) applied to minimize the wave effects, estimated as the median of L_W(λ) percent differences between values computed with null and actual wind speeds; and finally vi. environmental perturbations due to wave effects and changes in water masses during measurement sequences, cumulatively quantified as the median of L_W(λ) percent differences between replicate measurements corrected for changes in illumination conditions.

Table 1. Uncertainty budget (in percent) for L_W(λ) determined from AERONET-OC above-water measurements at relevant center-wavelengths

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In summary, the combined uncertainties for L_W(λ) from AERONET-OC above–water measurements are close to 4–5% in the blue-green spectral regions, but reach values of 7–8% at 670 nm due to the pronounced effects of wave perturbations on relatively small values of the water-leaving radiance. It is noted that the selection of an arbitrary threshold somehow different from 25% for the uncertainties related to the viewing angle correction would not significantly affect the overall uncertainty budget, that largely depends on the environmental variability and uncertainty of absolute calibration. It is also observed that for the considered measurement conditions the uncertainty budget estimated accounting for the contributions due to the filtering applied to L_T(θ,ϕ,λ) values, is higher for L_W(λ) determined with ρ ^P than for values computed with ρ ^U.

2.2 In-water data and related uncertainties

The in-water L_W(λ) data applied in the current study were determined from radiometric profiles performed with the Wire-Stabilized Profiling Environmental Radiometer (WiSPER) [19]. This winched system is deployed through a stabilizing structure preventing tilt of the profiling radiometers regardless of wave and current forcing. Satlantic (Halifax, Canada) OCR-200 and OCI-200 radiometers provide simultaneous measurements of upwelling radiance L_u(z,λ,t), upward irradiance E_u(z,λ,t), downward irradiance E_d(z,λ,t) and additionally of above-water downward irradiance E_d(z = 0⁺,λ,t), as a function of depth z and time t, at the nominal center-wavelengths 412, 443, 490, 510, 555, 665 and 683 nm.

WiSPER L_W(λ) data are determined from L_u(z,λ,t) following a consolidated protocol [19]. Specifically, values of L_u(z,λ,t) are normalized with respect to the time-corresponding above-water downward irradiance E_d(0⁺,λ,t) as if they were all taken at depths z at the same time t₀, according to:

where t₀ is generally chosen to coincide with the start of the profile. Omitting the variable t, the sub-surface $L_u(0^{-},\lambda )$ is then determined as the exponential of the intercept resulting from the least-squares linear regressions of $\ln L_u(z,\lambda ,t_0)$ versus z within an extrapolation interval z₀<z<z₁. In the case of WiSPER, z₀ is set to 0.3 m and z₁ is determined on a profile-by-profile basis within the range of 2-5 m to satisfy the requirement of linear decay with depth of the $\ln L_u(z,\lambda ,t_0)$data.

The water–leaving radiance L_W(λ) is then computed as:

where the factor 0.543, assumed independent of wavelength, accounts for the reflection and refraction effects at the air-sea interface.

Specific corrections are applied to $L_u(0^{-},\lambda )$ to minimize self-shading [27,28] and superstructure perturbations [22].

In agreement with previous investigations, uncertainty contributions included in Table 2 for L_W(λ) comprise: i. expected uncertainty of the absolute in–air radiance calibration of the L_u sensor [29]; ii. uncertainty in the theoretical determination of the immersion factor accounting for changes in instrument responsivity when operated in-water with respect to in-air [30]; iii. guessed uncertainty of the correction factors used to remove self-shading and tower-shading perturbations computed as 25% of the corrections applied to the data included in the matchup data set; vi. uncertainty in the extrapolation of sub-surface values due to perturbations induced by wave effects and changes in seawater optical properties during profiling, cumulatively estimated as the median of L_W(λ) percent differences from replicate measurements corrected for changes in illumination conditions.

Table 2. Uncertainty budget (in percent) for L_W(λ) determined from in-water profile data at center-wavelengths matching those of AERONET-OC data (see section 2.3)

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In summary, the combined uncertainties for CoASTS L_W(λ) data are approximately in the range 3–4% within the selected spectral region.

2.3 Comparison method

As already anticipated, the evaluation of changes in L_W(λ) due to the effect of differences between factors ρ ^U and ρ ^P is performed through comparison of above-water $L_W^{PRS}(\lambda )$ (i.e., Level-2 AERONET-OC data labelled as PRS) and in-water $L_W^{WIS}$(λ) data (i.e., CoASTS data labelled as WIS). The $L_W^{PRS}(\lambda )$ values utilized for match-up construction have been retained when: i. the difference between above- and in-water data sampling time was lower than 30 minutes to exclude data potentially affected by significant differences in measurement conditions; and ii. the sun zenith angle was lower than 70 degrees to avoid measurement conditions challenged by low sun elevation.

The application of the previous criteria led to the identification of 185 matchups from measurements performed between 2002 and 2013 with clear sky. An analysis of the measurement conditions characterizing the matchup data set are summarized in Fig. 1 through the distribution of values for quantities like: W, θ₀, diffuse attenuation coefficient K_d determined at 490 nm from in-water radiometric profiles, chlorophyll-a concentration Chla determined from water samples through High Precision Liquid Chromatography, and τ_a at 547 nm from AERONET retrievals.

 

Fig. 1 Frequency distribution of wind speed, sun zenith angle, diffuse attenuation coefficient at 490 nm (K_d), chlorophyll-a concentration and aerosol optical thickness at 547 nm (τ_a). N indicates the number of match-ups, m the median value and σ the standard deviation.

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In view of minimizing artifacts due to differences in center-wavelengths between $L_W^{WIS}(\lambda )$and $L_W^{PRS}(\lambda )$, spectral values from both data sources have been band-shifted [2] to match the ideal AERONET-OC center-wavelengths. Additionally, the effects of differences in illumination conditions due to diverse sun-zenith angles have been minimized by multiplying each $L_W^{WIS}(\lambda )$ value by cos${\theta }_0^{PRS}$/ cos${\theta }_0^{WIS}$, where ${\theta }_0^{PRS}$and ${\theta }_0^{WIS}$are the sun zenith angles for matching $L_W^{PRS}(\lambda )$and $L_W^{WIS}(\lambda )$spectra, respectively.

The statistical evaluation of the N matchups available is summarized through the mean of percent differences ψ indicating bias, and the mean of absolute percent differences |ψ | indicating dispersion.

The values of ψ are computed as:

where i is the match-up index, and ψ_i is:

where $L_W^{WIS}[i]$ are the reference values.

The absolute values |ψ_i | are used to compute |ψ | as:

In addition to the statistical indices ψ and |ψ |, the root mean square of differences rmsd and the determination coefficient r², are also provided as a further aid to the analysis.

2. Application of factors ρ^U and ρ^P s

$L_W^{WIS}(\lambda )$ and$L_W^{PRS}(\lambda )$spectra applied in the matchup analysis are displayed in Fig. 2. Results are summarized in Fig. 3 and Fig. 4 for values of $L_W^{PRS}(\lambda )$ determined using factors ρ ^U and ρ ^P, respectively.

 

Fig. 2 Spectra of$L_W^{WIS}(\lambda )$and $L_W^{PRS}(\lambda )$(computed using factors ρ ^U) applied for the construction of the N = 185 matchups. Gray lines indicate individual spectra, the continuous thick black line indicates the average of spectral values while the dashed lines indicate ± 1 standard deviation.

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Fig. 3 Scatter plot of above-water $L_W^{PRS}(\lambda )$ versus in-water $L_W^{WIS}(\lambda )$ spectral data at different center-wavelengths (i.e., 412, 443, 488, 547, and 667 nm) and for spectrally averaged values (right panel in the lower row), determined by applying the surface reflectance factors ρ ^U. Root mean square of differences, mean of absolute percent differences, mean of percent differences and determination coefficients, are indicated as rmsd, |ψ |, ψ, and r². N is the number of matchups while M is the total number of points (i.e., N × 5) applied for the statistical analysis of spectral averages.

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Fig. 4 As in Fig. 3, but for$L_W^{PRS}(\lambda )$ determined by applying the surface reflectance factors ρ ^P.

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Inter-comparison results related to the application of factors ρ ^U exhibit values of ψ increasing from 0 at 412 nm to + 3% at 547 and 667 nm, with spectrally averaged values of + 2% (see Fig. 3). Results obtained from the application of factors ρ ^P show values of ψ varying between + 2 and + 4% in the 412-547 nm spectral interval, increasing to + 11% at 667 nm, with spectrally averaged values of + 5% (see Fig. 4). It should be also noted that results from ρ ^P generally exhibit higher values of rmsd and |ψ | and also lower values for r², with respect to those obtained from the application of ρ ^U. Comparison results illustrated in Fig. 3 and Fig. 4, both show high consistency with estimates of the absolute combined uncertainties presented in Table 3 for $L_W^{WIS}(\lambda )$ and $L_W^{PRS}(\lambda )$. In fact these absolute uncertainties computed multiplying the mean of $L_W^{WIS}(\lambda )$ and $L_W^{PRS}(\lambda )$values by the combined relative uncertainties derived from the quadrature sums given in Tables 1 and 2, exhibit close agreement with the rmsd values shown in both Fig. 3 and Fig. 4. Nevertheless, after recalling that the comparison is restricted to the single AERONET-OC measurement geometry and to relatively low wind speeds, a generic better performance is observed when applying factors ρ ^U.

Table 3. Combined relative (in percent) and combined absolute (in units of mW cm⁻² µm⁻¹ sr⁻¹) uncertainties estimated for $L_W^{WIS}(\lambda )$ and for $L_W^{PRS}(\lambda )$ matchup data, with$L_W^{PRS}(\lambda )$determined using factors ρ^U and alternatively ρ^P (the latter are given in brackets).

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4. Discussion

The reflectance factors ρ ^U and ρ ^P relevant to the AERONET-OC viewing geometry (i.e., θ = 40 degrees and ϕ = ± 90 degrees) are illustrated in Fig. 5 as a function of the sun zenith angle for different wind speeds.

 

Fig. 5 Reflectance factors ρ ^U (a) and ρ ^P (b) as a function of sun zenith angle for different wind speeds (i.e., 0, 4, 8 and 12, m s⁻¹ in blue, green, yellow and red, respectively) for the AERONET-OC measurement geometries defined by θ = 40 degrees and ϕ ± 90 degrees.

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Notable are the differences between the two sets of reflectance factors. In particular ρ ^P exhibits values almost linearly decreasing with increasing sun zenith and slope increasing with wind speed. Differently, ρ ^U does not show any significant dependence with sun zenith at low wind speeds (tentatively below 4 m s⁻¹). Conversely, the dependence with sun zenith becomes pronounced for values lower than approximately 40 degrees and wind speed higher than approximately 4 m s⁻¹. This suggests that the largest differences in comparisons are expected at sun zenith angles lower than 40 degrees with wind speeds higher than approximately 4 ms⁻¹. The limited range of wind speeds characterizing the matchups (see Fig. 1), which exhibit values in the range of 0–7.5 m s⁻¹ with median of 2.2 m s⁻¹ and standard deviation of 1.1, nevertheless restricts the comparisons to most favorable measurement conditions. Still, the previous distribution of wind speeds is close to that characterizing the entire AAOT Level 2 $L_W^{PRS}$ data set showing median of 2.6 m s⁻¹ with standard deviation of 1.9. It is however recognized that different AERONET-OC sites might show wider distributions of wind speed values.

Figure 6 displays the ρ ^U and ρ ^P values applied for the determination of $L_W^{PRS}(\lambda )$given in Fig. 3 and Fig. 4. In agreement with the reflectance factors displayed in Fig. 5 for the relevant wind speeds, the values in Fig. 6 show very different ranges even though coincidently exhibiting identical median values.

 

Fig. 6 Distributions of the surface reflectance factors ρ ^U and ρ ^P for the considered matchups. N, m and σ indicate the number of matchups, the median value and the standard deviation, respectively.

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Comparison results are hereafter discussed by partitioning the match-up data set as a function of sun zenith and wind speed values.

4.1 Dependence on sun-zenith and wind speed

The analysis addressing the dependence of $L_W^{PRS}(\lambda )$on the sun zenith angle benefits of matchups covering a wide range of values varying from approximately 20 to 70 degrees with median of 35 degrees and standard deviation of 14. The analysis has been performed by partitioning the data set into three different intervals: θ₀<30°, 30°≤θ₀<50° and 50°≤θ₀<70°. Values of ψ shown in Tables 4 and 5 indicate a larger dependence on θ₀ for $L_W^{PRS}(\lambda )$ determined with ρ ^P rather than with ρ ^U. This result, particularly marked at 412 and 667 nm, indicates that for the considered measurement conditions the factors ρ ^U better account for the sun zenith dependence. Additionally, the opposite trends observed for ψ values suggest that actual reflectance factors would exhibit dependences on sun zenith falling within those characterizing ρ ^U and ρ ^P.

Table 4. Statistical results from the comparison of $L_W^{PRS}(\lambda )$ with $L_W^{WIS}(\lambda )$ at the center-wavelengths 412, 547 and 667 nm (assumed representative for the considered spectral interval) and the spectrally averaged values resulting from data at all center-wavelengths (i.e., 412, 443, 488, 547, 667 nm). The row “ρ^U (all)” displays values of rmsd, |ψ |, ψ, and r² determined for $L_W^{PRS}(\lambda )$ computed with factors ρ^U. The additional rows refer to statistical values obtained partitioning the data set into different ranges of sun zenith (in units of degrees) and wind speed (in units of ms⁻¹).

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Table 5. As in Table 4, but for statistical values determined with the reflectance factors ρ^P.

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Different from the case of sun zenith, the analysis on wind speed dependence is limited by the relatively small range of values generally characterizing AERONET-OC data products. It is recalled that this is largely due to the application of filters restricting quality assured measurements to cases ideally not affected by foam or high glint.

Equivalent to the sun zenith case, the data set has been partitioned into three intervals: W<2 m s⁻¹; 2≤W<4 m s⁻¹; and W≥4 m s⁻¹. Results summarized in Tables 4 and 5 indicate a general negative trend in the values of ψ for $L_W^{PRS}(\lambda )$determined with W≥4 m s⁻¹ for both ρ ^U and ρ ^P, even though slightly more pronounced for the first. This finding, albeit supported by a very small number of data, confirms a possible underestimate of $L_W^{PRS}(\lambda )$ with an increase of wind speed in agreement with the application of the filtering scheme used to reduce glint perturbations (see additional discussion in section 4.2).

Further results from inter-comparisons performed partitioning the values of aerosol optical thickness τ _a(547) using a threshold of 0.2 (not presented here), indicate only a slightly better performance with τ _a(547) < 0.2 for factors ρ ^P in agreement with the basic assumption of clear and purely molecular sky applied for the computation of the surface factors.

4.2 Alternative determination of L_T

As already mentioned, AERONET-OC L_T(θ,ϕ,λ) is computed from the mean of relative minima of successive values of the radiance from the sea collected during a measurement sequence (i.e., typically using 2 measurements out of 11). This solution differs from the scheme relying on the mean of all values of radiance from the sea commonly considered in protocols [31].

By recognizing that the efficacy of the filtering scheme is only supported by experimental evidence, Table 6 presents comparison results between $L_W^{PRS}(\lambda )$ and $L_W^{WIS}(\lambda )$with L_T(θ,ϕ,λ) computed from the mean of all values of the total radiance from the sea collected during each measurement sequence (i.e., 11). It is anticipated that this additional analysis relies on 181 out of the 185 matchups previously considered. This is due to the action of basic AERONET-OC quality assurance tests removing a few additional data from the Level-2 data generated using mean values of the total radiance from the sea. Results from this analysis, when compared to those presented in Tables 4 and 5, indicate a significant positive bias at all wavelengths for both ρ ^U and ρ ^P cases, but a dependence (not shown) on measurement conditions (e.g., on θ₀ and W) similar to those observed for$L_W^{PRS}(\lambda )$ determined applying the filtering scheme. This finding further confirms that filtering of L_T measurements appears an effective solution to remove unwanted glint and foam perturbations. Additionally, it suggests that the underestimate of $L_W^{PRS}(\lambda )$ shown by data in Tables 4 and 5 for W≥4 m s⁻¹ does not appear (only) due to the filtering applied to L_T measurements.

Table 6. Statistical results from the comparison of $L_W^{PRS}(\lambda )$ (determined using mean values of available L_T measurements) versus $L_W^{WIS}(\lambda )$ at the center-wavelengths 412, 547 and 667 nm and the spectrally averaged values resulting from data at all center-wavelengths. The row “ρ^U (all)” and “ρ^P (all)” display the values of rmsd, |ψ |, ψ, and r² obtained from $L_W^{PRS}(\lambda )$ computed with factors ρ^U and ρ^P, respectively.

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5. Conclusions

The study focused on the evaluation of the impact on L_w derived from above-water radiometry of differences between: i. theroretical sea surface reflectance factors ρ ^U [6] determined assuming a sky radiance distribution accounting for aerosols and multiple scattering, but neglecting polarization, and quantifying sea surface effects through Cox-Munk wave slope statistics; and ii. alternative factors ρ ^P [16] determined accounting for polarization, but assuming Rayleigh sky radiance distribution, and quantifying wave effects through wave elevation and slope variance spectra.

The analysis has been carried out by comparing AERONET-OC L_W(λ) data computed applying factors ρ ^U and ρ ^P, with collocated reference L_W(λ) values determined from in-water radiometry. Results from the inter-comparison, restricted to i. a single measurement geometry (i.e., 40 degrees viewing angle and 90 degrees azimuth offset with respect to the sun plane) and ii. a limited range of measurement conditions (e.g., low wind speeds, which are an intrinsic feature of AERONET-OC data products),

Considering that factors ρ ^U and ρ ^P were determined by differently modelling sea surface and sky radiance distribution and polarization, results from this study cannot unequivocally indicate the reason for the slightly better performance of factors ρ ^U with respect to ρ ^P. It is however acknowledged that factors ρ ^P refer to an extreme ideal case that ignores multiple scattering and aerosols with their depolarization effects.

From the applicative point of view, the study suggests that AERONET-OC L_W(λ) data determined from measurements performed with wind speeds tentatively higher than 4 m s⁻¹ may exhibit uncertainties larger than those presently estimated, with an expected tendency to underestimate. This may recommend to restrict the use of AERONET-OC L_W(λ) data to values determined with wind speed lower than 4 m s⁻¹ when high accuracy is a stringent requirement.

The overall analysis, without minimizing the relevance of the newly proposed factors ρ ^P, i. re-confirms the suitability of factors ρ ^U for AERONET-OC above-water radiometry with wind speeds typically lower than 4 m s⁻¹, and ii. further reinforces the need for additional theoretical investigations on polarization effects in above-water radiometry with the objective to produce spectral reflectance factors through a radiative transfer code fully accounting for polarization, multiple scattering, height- and and slope resolved sea surface, and embracing a number atmospheric cases characterized by different aerosol types and loads.