Abstract
The effective sea-surface skylight reflectance (ρ) is an important parameter for removing the contribution of surface-reflected radiance when measuring water-leaving radiance (Lw) using the above-water approach (AWA). Radiative simulations and field measurements show that ρ varies spectrally. To improve the determination of Lw (and then remote sensing reflectance, Rrs) from the AWA, we further developed a wavelength-dependent model for ρ to remove surface-reflected radiance, which is applied with a spectral optimization approach for the determination of Rrs. Excellent agreement was achieved between the AWA-derived and skylight-blocked approach (SBA)-obtained Rrs (coefficient of determination > 0.92, mean absolute percentage deviation < ∼ 11% for Rrs > 0.0005 sr-1), even during high wave conditions. We found that the optimization approach with the new ρ model worked very well for a wide range of water types and observation geometries. For developing remote sensing algorithms and evaluating satellite products, it would be beneficial to apply this approach to current and historical above-water in situ measurements of Rrs to improve the quality of these data. In addition, this approach could also increase the number of useable spectra where previously rendered unusable when processed with a traditional scheme.
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1. Introduction
Remote sensing reflectance (Rrs, sr-1) is a fundamental physical quantity from satellite ocean color measurements. It is defined as the ratio of the water-leaving radiance (Lw, W/m2/nm/sr) to the downwelling irradiance just above the sea surface (Es, W/m2/nm). Over the past four decades, several methods have been developed to measure Rrs in the field, which include in-water, on-water, and above-water methods [1–5]. Among these, the above-water approach (AWA) has become more popular, as measurement procedures and requirements for equipment by this scheme can be easily met. AWA data from platforms such as AERONET-OC are widely used for satellite ocean color validation [6].
The AWA platforms measure the total upwelling radiance (Lt, W/m2/nm/sr) instead of directly measuring Lw. The radiance Lt that enters the detector can be accurately determined by the following equation, which takes into account both the sky radiance (Ls, W/m2/nm/sr) incident onto the sea surface and the upwelling underwater radiance (Lu, W/m2/nm/sr) onto the sea surface from below [7]:
Over the past few decades, various revisions of Eq. (6) have been proposed to remove sky glint and/or sun glint [11–15]. The differences between these revisions are associated primarily with how sky glint (or sun glint) is removed from the surface signal. Among these approaches, the most widely used assumes that the near-infrared (NIR) water-leaving signal is zero, and thus Lt signal in the NIR is entirely due to glint [1]. For optically complex waters, this assumption is not valid as the NIR signal is often not zero, and many other methods have been proposed to correct for sky glint (or sun glint) in these waters [13,15,16]. Gould et al. [16], for example, used simultaneous in situ inherent optical properties to derive the glint component at 735 nm. In addition, several other correction schemes use a spectral optimization approach (SOA) [12,14,17]. For example, Lee et al. [14] proposed an SOA to determine the bias of Lw and then used it to eliminate surface-reflected light from the total remote sensing reflectance (Trs, the ratio of Lt to Es). All of these methods attempt to make surface measurements free from the effects of glint; however, most of them used a spectrally-constant ρ which has been questioned in recent studies [14,18,19].
The main objectives of this study are to assess the spectral dependence of ρ and develop a new model to represent its variation with wavelength. The proposed model is then incorporated into the SOA of Lee et al. [14] to process Rrs from AWA. Field measurements collected over a wide range of environmental conditions (including water types, sky conditions, wind speeds, sun glints and viewing geometries) are then used to evaluate the performance of the revised SOA (RSOA). Further evaluation of RSOA is conducted using measurements made by the skylight-blocked approach (SBA). Finally, a field experiment was conducted in order to understand the impact of viewing geometry on the determination of Rrs with RSOA.
2. Materials and measurements
2.1 Radiative transfer simulations of sky radiance
Based on the revised version of HydroLight (HL, version 5.1.2) in Lin et al. [20], a series of radiative transfer simulations were carried out to further refine and characterize the model for the parameter ρ. In order to account for the significant impact of sea surface waves on ρ, HL utilized Cox-Munk slope statistics to simulate the surface waves, which take into account both gravity and capillary wave slope effects [21,22]. Additionally, instead of the default Harrison and Coombes [8] in HL, we used SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) [23,24] to simulate the skylight. Previous studies showed that SBDART can model the radiance distribution of skylight or irradiance accurately [25,26]. In this HydroLight-SBDART (HL_S) coupled model, a standard atmospheric profile (mid-latitude summer) was used to model the atmospheric conditions. A total of three different aerosols (urban, oceanic, and tropospheric) were employed to generate simulations. The aerosol optical depth at 550 nm, τa(550), was set to three different values (0.05, 0.1, 0.15) along with three sun angles (θs = 0°, 30°, and 60°), and the model was parameterized for several wind speeds (ws = 0, 1, 5, 10, and 15 m/s). A range of viewing angles were included with four viewing zenith angles (θv = 0°, 30°, 45°, and 60°) and four viewing azimuth angles (φv = 45°, 90°, 135°, 180°). Further details of the settings used in the HL_S model can be found in Lin et al. [20].
2.2 AWA measurements
A spectroradiometer (Spectral Evolution SR-1901) was used to measure Es, Lt and Ls over a spectral range from ∼ 280 to 1900nm with a spectral resolution of ∼ 1.5 nm. Each measurement consisted of 5 scans, and then averaged to give one spectrum. The orientation of the Lt sensor was 40° from nadir and 135° from the solar plane. Ls was measured in the same plane as Lt, but at 40° from zenith.
Measurements were taken from four field campaigns (Fig. 1). The first was the VIIRS Ocean Color Calibration and Validation campaign on the NOAA ship Nancy Foster from 2nd to 13th December 2015 (VIIRS2015). Field measurements were collected at 18 stations along the Southeast US Coast and in offshore waters of the Western Atlantic. The measurements represent a range of environmental conditions in different water types (oceanic and turbid waters), sky conditions (clear and overcast sky), wind speeds and sun glint. Further details are given in Table 1. The second and third campaigns were performed in Massachusetts Bay (MassBay) over two days (17th & 18th September 2015) during clear sky conditions when 12 stations were occupied. To study the effects of viewing geometry on Rrs, further measurements were carried out in a field campaign on 12th May 2016 in the harbor of the University of Massachusetts at Boston (UMB) during blue sky conditions.
2.3 SBA measurements
An SBA was included in the radiometer measurement system to obtain “true” Lw during the field campaigns. This is a robust and accurate method for measuring Lw directly, with the surface-reflected light (sun and sky glint) blocked with a cone attached to the Lw sensor [2]. To avoid any shadowing or reflection effects on the measurements, the system was deployed well away from the research vessel [2]. For each station, the SBA and spectroradiometer were operated almost simultaneously. SBA measurements were recorded for more than 5 minutes, and an averaged Lw was obtained from all Lw spectra after data quality control to ensure that the package inclination was < 5°. More details of the measurement protocol can be found in Lee et al. [2].
3. Method development
3.1 Comparison of sky radiance from HL_S and default HL
Before assessing the spectral dependency of ρ, it is pertinent to compare the sky radiance simulated from HL_S and default HL. The radiative simulations from SBDART of normalized sky radiance (scaled by radiance at 410 nm) for selected solar zenith and viewing geometry angles are shown in Fig. 2(a), (c). The radiance spectra differ significantly at different solar zenith and viewing angles. By comparison, a set of sky radiance spectra using the same geometry angles was also simulated using the default Harrison and Coombes [8] skylight model in Hydrolight. The model was run with a scaling factor (π) derived from the total diffuse irradiance modeled from Gregg and Carder [27]. Figure 2(b), (d) shows the normalized spectrum of sky radiance from the model of Harrison and Coombes [8]. A uniform spectral shape of sky radiance is observed for different solar zenith angles and viewing geometry. This was not consistent with the output from SBDART and the observations of sky radiance [9,10]. Note that for the AWA correction approaches to determine Rrs [7,12,17], the radiative simulations of sky radiance were also based on the models of Gregg and Carder [27] and Harrison and Coombes [8], thus further improvement of these approaches to accurately derive Rrs is still required.
3.2 Modelling of spectral ρ
With the above radiative simulations using HL_S, ρ is calculated using Eq. (5). For the sky radiance data shown in Fig. 2, the resulting ρ spectra for various sun zenith and viewing angles are shown in Fig. 3. The distribution of ρ from SBDART increases at longer wavelengths (Fig. 3(a), (c)), which is consistent with the previous findings on the wavelength dependency of ρ [14,19]. By comparison, ρ spectra derived from the model of Harrison and Coombes [8] are mostly flat (Fig. 3(b), (d)).
We also investigated the distribution of ρ spectra from SBDART over a range of wind speeds from 0 to 15 m/s (Fig. 4). The magnitude of ρ over the entire spectrum increases significantly with increasing wind speed, as higher wind speeds could result in more sun glint being observed. In addition to wind speed, the aerosol also has an impact on the spectral feature of ρ. To illustrate this impact, Fig. 5 displays the distribution of ρ spectra obtained from SBDART simulations for different values of τa(550) and aerosol types (urban, oceanic, and tropospheric). The ρ spectra exhibit variations with respect to both the aerosol optical depths (Fig. 5(a), (c)) and types (Fig. 5(b), (d)). Despite the differences in the values, the shape of the ρ spectra remains relatively consistent.
The spectra of ρ presented in the figures above exhibit similar shapes, and our analysis revealed that these spectra can be effectively described by a power-law function:
where h0 and h1 are model parameters that vary for different ρ spectra. This formula contrasts with previous skylight correction algorithms [12,17], which assume ρ to be spectrally constant. Fig. 6 shows a comparison of HL_S simulated ρ and those modeled using Eq. (7). The power-law function can model ρ accurately with a small mean absolute percentage deviation (MAPD) (∼1.5%) compared to ρ derived using Eq. (7), where MAPD is defined as:3.3 RSOA to remove surface-reflected light
The original SOA by Lee et al. [14] used a spectrally constant ρ to eliminate the surface contribution of skylight in producing Rrs. In this study, we extend the SOA by incorporating the spectral model of ρ (Eq. (7)). The revised SOA has a similar parameter setup to the original one, but a genetic algorithm (GA) is used instead [28]. More details of the RSOA can be found in the Appendix.
4. Results and discussions
4.1 Comparison of different correction approaches with field measurements
To highlight the new algorithm’s performance, we compared four approaches for calculating Rrs from AWA measurements. These included the conventional method of Mobley [7] (M99), the 3C method [12,17], the original SOA of Lee et al. [14] (SOA2010), and the RSOA in this study. In M99, Rrs was derived following:
4.1.1 VIIRS2015 dataset
Firstly, the correction approaches were evaluated using the VIIRS2015 dataset. The field measurements were collected at 18 stations covering various water types (blue open ocean, brown and green coastal water) with Rrs(490) varying from ∼ 0.0002 to 0.007 sr-1 and under different environmental conditions (e.g., clear sky, haze or scattered clouds, varying waves at the sea surface). A list of these measurements can be found in Table 1. To highlight the optimal performance of the RSOA in this study, the clear sky measurements were firstly selected (9 stations with cloud coverage ≤ 30%).
Figure 7 compares the SBA-measured Rrs (RrsSBA) with those derived from AWA approaches. Different performance was observed for the four approaches in correcting the above-water measurements. Generally, M99 overestimated Rrs, especially at short wavelengths (< 550 nm, Fig. 7 blue lines). The SOA2010 and 3C methods improved the estimation of Rrs over the whole spectrum. The RSOA method exhibited the most accurate glint correction using a wavelength dependent ρ. More details also can be found in Table 2.
The performance of RSOA was not affected by water type. For coastal waters (e.g., Fig. 7(c) and Fig. 7(g), (h)), Rrs estimated from RSOA were in good agreement with RrsSBA and this consistency was also observed for turbid brown water (Fig. 7(h)), where both the spectral shape and magnitude were very similar. For blue waters, although some Lt measurements (Fig. 7(a), (b)) were affected by sun glint, RSOA still performed very well in removing sun glint from Lt. These results illustrate that RSOA can be applied with confidence and accuracy in a wide range of water types.
Fig. 8 shows scatter plots of the different approaches against the RrsSBA. M99-estimated Rrs generally agrees well with the SBA measurements (R2 = 0.81, and MAPD = 58.2%), but it generally overestimates Rrs over the entire spectrum. The 3C approach shows large deviations from the SBA measurements due to overcorrection of the spectra (MAPD = 41.5%), which could be attributed to the incorrect ρ in the 3C approach, and leads to an overcorrection of surface-reflected radiance from Lt. High scatter at 380 and 442 nm was observed in both M99 and 3C approaches due to the influence of sun glint. The SOA2010 approach improved on both M99 and 3C (R2 = 0.94, MAPD = 36.9%). The RSOA approach exhibited the highest accuracy with R2 = 0.97 and MAPD = 22.3% (Fig. 8(d)), which decreased to ∼ 11% for Rrs > 0.0005 sr-1. These results emphasize the superior performance of RSOA in correcting sun glint in above water measurements.
Sky conditions can have a significant impact on estimates of Rrs using AWA measurements [6,30]. To assess the performance of correction approaches under partially cloudy or cloudy conditions, we analyzed their performance in these conditions, as shown in Fig. S1 (see Supplement 1). The 3C approach proved to be better than M99, though in some specific cases, 3C resulted in incorrect values (e.g., negative Rrs values at station 1). Using SOA2010, most of the derived Rrs were more accurate than M99 and 3C spectra. RSOA derived Rrs showed the best agreement with RrsSBA (Fig. S2).
4.1.2 Massachusetts Bay dataset
The MassBay measurements were primarily taken in green and brown waters with Secchi depths ranging from ∼3−12 m. The measurements were collected mainly under clear blue skies. In these types of waters, the Rrs at NIR are generally larger than 0, thus setting Rrs to zero at this wavelength could be questionable.
To evaluate the performance of different correction approaches, Fig. 9 shows a comparison of RrsSBA with those corrected by four different approaches. The RSOA approach proved to be more reliable and accurate than the other three methods in estimating Rrs. Even under conditions where the other models showed high sun glint contamination, the RSOA approach still obtained very reasonable Rrs values, as demonstrated by stations 3, 4, and 12 in Fig. 9.
The scatter plots further supported the superior performance of the RSOA approach (R2 = 0.92, and MAPD = 19.5%) compared to the other approaches, as shown in Fig. 10. Full details of the statistical metrics for each approach and station are provided in Table 3. These results provide strong evidence of the effectiveness and robustness of the RSOA approach, even under challenging conditions, and highlight its potential to improve the accuracy and reliability of remote sensing reflectance measurements in green and brown waters.
4. 2 Dependency on viewing geometry
Removing surface-reflected light for above-water measurements is highly challenging because of the ambiguous and unpredictable glints due to surface waves [6,7,30–32]. Mobley [7] recommended an optimal measurement geometry to minimize the effect of glint. Generally, a viewing geometry of 40° from the nadir (θv) and 135° from the sun (φv) was suggested for the measurement of Lt, and a θv of 40° from zenith and φv of 135° from azimuth is required for the measurement of Ls [7]. In the field, achieving this is highly dependent on the salient sea conditions and especially on the wave conditions, where the viewing geometry of radiometers relative to the position of the sun is not stable. In particular, for a continuous underway system [30], φv often varies over a wide range (e.g., ∼50°−160°), which could differ significantly from the recommended optimal φv (135°).
The above-water measurements taken in the UMB harbor were used to further understand the impact of viewing geometry on the determination of Rrs(λ). The measurements were collected under blue skies with a solar zenith angle of ∼ 30°. Several viewing geometries were used to measure Ls and Lt (φv = 45°, 90°, 135°, and 180°, and θv = 30°, 45°, and 60°). For each viewing geometry (φv, θv), a total of 5 attempts were performed to obtain concurrent measurements of Es, Ls, and Lt. A total of 60 Rrs spectra were estimated for each correction approach.
Fig. 11 shows the RrsSBA compared with those derived from the other four approaches. The value of ρ in M99 was taken from the look-up table in Mobley [29] as a function of the viewing geometry. M99 significantly overestimated Rrs compared with the SBA measurements (Fig. 11(a)). For both 3C and SOA2010, the derived Rrs spectra showed similar magnitudes and shapes with RrsSBA, but some deviations were still observed (< ∼ 450 nm in Fig. 11(b) and Fig. 11(c)). For the RSOA, the estimated Rrs spectra were more consistent with the RrsSBA (Fig. 11(d)). Fig. 12 shows the standard deviation (STD) of the different approaches to estimating Rrs. Rrs estimated with RSOA had the lowest STD among all the approaches tested, illustrating a superior performance of this model and approach. When the methods were compared as scatter plots, they clearly indicated that the sensitivity of RSOA to the viewing geometry is at a minimum at each wavelength. Overall there is a better agreement between RSOA estimates and measurements from SBA (Fig. 13).
5. Summary
Through both radiative simulations and field measurements, we observe that ρ is spectrally dependent and this spectral dependence can be empirically modeled as a power-law function of wavelength. With this wavelength-dependent ρ model, the previous SOA2010 processing scheme was further extended using the RSOA approach. This new scheme was evaluated against three other methods (M99, 3C, and SOA2010) using independent field measurements collected during four campaigns covering different environmental conditions. Our results showed that the RSOA approach obtained more reliable and accurate Rrs compared to the other three schemes, and was effective in removing sun glint contamination, which has been a major challenge for AWA measurements. Furthermore, this approach also exhibited a relatively low dependency on measurement viewing geometry. The RSOA approach holds great potential for improving ocean-color data required for developing remote sensing algorithms and validating satellite products.
Appendix
With the new ρ(λ) model (Eq. (7)), total remote-sensing reflectance (Trs, ratio of LT to Es) is expressed in the following equation:
In Eq. A2 there are six unknowns that can be retrieved using the genetic algorithm (GA in MATLAB optimization toolbox [28]) following initial parameterization [38]:
To highlight the spectral difference between Rrs(λ) and Srs(λ), the shortest wavelength is extended to 350 nm. Finally, the cost function is defined as:
Funding
European Commission Horizon 2020 project Copernicus Evolution – Research for harmonised and Transitional-water Observation (CERTO, 870349); European Space Agency AMT4OceanSatFlux (4000125730/18/NL/FF/gp), AMT4CO2Flux (4000136286/21/NL/FF/ab); Natural Environment Research Council (NERC) National Capability funding to Plymouth Marine Laboratory for the Atlantic Meridional Transect (CLASSAMT).
Acknowledgments
The authors would like to thank the captain and crew of the NOAA ship Nancy Foster. This work was supported by the Joint Polar Satellite System (JPSS) funding for the NOAA ocean color calibration and validation (Cal/Val) project. Some of the in-situ data used in this study were collected from the NOAA dedicated VIIRS ocean color calibration and validation (Cal/Val) cruises supported by the Joint Polar Satellite System (JPSS) program and the NOAA Office of Marine and Aviation Operations.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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