Open Access
Add to BibSonomy
Abstract
Water-leaving albedo (αw(λ)) is an important component of the ocean surface albedo and is conventionally estimated based on remotely sensed chlorophyll-a concentration (Chl) (termed Chl-αw). We show that estimated αw(λ) by Chl-αw could be significantly biased in global oceans, because there is no guarantee of closure between the modeled remote sensing reflectance (Rrs(λ)) from Chl-inferred inherent optical properties (IOPs) and the input Rrs(λ) that is used to derive Chl. We thus propose a simple and improved scheme, termed Chl-αw_new, and show that the step to infer IOPs from Chl is not necessary, where αw(λ) can be accurately estimated from satellite-measured Rrs(λ) and a Chl-based look-up-table (LUT) for the bidirectional relationships of angular Rrs(λ). Evaluations with both HydroLight simulations and satellite measurements show that Chl-αw_new is equivalent to the recently developed αw scheme based on IOPs (IOPs-αw, [Remote Sens. Environ. 269, 112807]), where both schemes could significantly improve the estimation of αw(λ) compared to Chl-αw. Comparisons among Chl-αw, Chl-αw_new, and IOPs-αw highlight that optical closure of Rrs(λ) is essential for accurate remote sensing of αw(λ), while the model for Rrs(λ) bidirectionality has rather minor impacts. The impact of improved αw(λ) estimations on the solar flux exchanges at the air-sea interface is preliminarily evaluated in this effort, where the use of Chl-αw_new could increase the estimation of reflected solar radiation by over 68.7% in turbid waters compared to that using Chl-αw, highlighting the necessity of incorporating accurate αw schemes into the coupled ocean-atmosphere models, especially for regional models in coastal oceans.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The broadband ocean surface albedo (α) is a key parameter in the coupled ocean-atmosphere models to quantify the amount of solar energy absorbed by the ocean and that reflected into the atmosphere [1]. α can be computed from the spectral ocean surface albedo α(λ) over the full shortwave domain, with α(λ) calculated as the ratio of spectral upward irradiance Eu(0+, λ) (in W m-2 nm−1) to spectral downward irradiance Ed(0+, λ) just above the sea surface [2]. In general, α(λ) is contributed by both surface-reflected and water-leaving radiation [3,4], where the surface-reflected albedo has been extensively investigated since the 1950s and is conventionally parameterized as a function of solar zenith angle and wind speed. The surface-reflected albedo is also slightly dependent on the atmospheric properties, such as aerosol optical thickness [5–8]. The water-leaving albedo, termed αw(λ) and defined as the ratio of water-leaving irradiance Ew(λ) to Ed(0+, λ), is commonly estimated using the concentration of chlorophyll-a (Chl, in mg/m3) [9–11].
The basis of the existing αw scheme, such as the one proposed in Feng et al. [10], is that Ew(λ), by definition, is the integral of water-leaving radiance (Lw(λ), in W m−2 nm−1 sr−1) in the upper hemisphere above the sea surface, weighted by the cosine of viewing zenith angle [12]. Thus, αw(λ) can be expressed as
The angular variation of Rrs(λ, Ω) in Feng et al. [10] is represented by the bidirectional reflectance distribution function (BRDF) developed by Morel and Gentili [13], which is expressed as
Here, $\mathrm{\Re }$ relates the transmittance of radiance crossing the water-air interface, f/Q is the in-water BRDF term, with f the model factor linking the irradiance reflectance just beneath the surface (R0) to inherent optical properties (IOPs) and Q the bidirectional function. a(λ) and bb(λ) are the water IOPs, representing the total absorption and backscattering coefficients, respectively. W and ${\theta _s}^{\prime}$ in Eq. (3) are the wind speed (in m/s) and the refracted solar zenith angle below the sea surface, respectively.
In the implementation of the scheme proposed by Feng et al. [10], αw(λ) can be estimated from Chl following Eqs. (2)–(3). Briefly, a(λ) and bb(λ) in Eq. (3) are inferred from Chl following the empirical relationships of Morel and Maritorena [14], with Chl from the standard product from satellite ocean color missions (e.g., the NASA OceanColor web, https://oceancolor.gsfc.nasa.gov). Note that this Chl standard product is derived from satellite-measured Rrs(λ) using the empirical Ocean Color Index (OCI) algorithm [15–17]. The values of $\mathrm{\Re }$ for specific viewing angles can be extracted from the look-up-table (LUT) provided in Gordon [18], with $\mathrm{\Re }$ later corrected for the solar zenith effects following Wang [19]. The values of f/Q can be retrieved from a separate LUT provided in Morel et al. [20] for different Chl values and viewing angles. Thus, the angular Rrs(λ) can be obtained from Eq. (3), which are then used to estimate αw(λ) via Eq. (2). This scheme is hereafter referred to as Chl-αw.
However, in this process of calculating Rrs(λ, Ω) in the upper hemisphere when employing Chl-αw, Chl is a “middle man”, there is no check of closure between the satellite-measured Rrs(λ) and the modeled Rrs(λ) from the Chl-inferred IOPs via Eq. (3). It is therefore of interest to investigate how this closure issue of Rrs(λ) may contribute to the uncertainties of estimated αw(λ) by Chl-αw. Other αw schemes, such as those proposed by Jin et al. [11] and adopted later by Séférian et al. [9], related αw(λ) to the irradiance reflectance just beneath the surface (R0(λ)), where R0(λ) is also modeled from Chl using the empirical Chl-IOPs relationship of Morel and Maritorena [14]. Thus, estimated αw(λ) by Jin et al. [11] may also be subject to uncertainties due to no closure of Rrs(λ). In this effort, we aim at demonstrating the lack of internal consistency of current Chl-based schemes and proposing an improved scheme that would avoid the closure issue of Rrs(λ).
2. Improved Chl-based scheme for αw
The closure issue of Rrs(λ) can be simply illustrated by comparing satellite-measured Rrs(λ) with that modeled from Chl. As a demonstration, the monthly composite Rrs(λ) product of Visible Infrared Imaging Radiometer Suite (VIIRS) of March 2019 was employed here with descriptions of VIIRS imagery provided in Section 3.2. First, Chl was estimated from VIIRS Rrs(λ) using the OCI algorithm, from which Rrs(λ) can be modeled by Chl-inferred IOPs following Eq. (3). Given that VIIRS Rrs(λ) product is corrected to the nadir-viewed Rrs(λ) with the Sun at the zenith [18,19], i.e., equivalent to Rrs(λ,0,0,0), the modeled Rrs(λ) from Chl is thus computed via Eq. (3) with the values of $\mathrm{\Re }$ and f/Q extracted from their respective LUT for θs = 0 and θv = 0. Then, we calculate the difference between VIIRS-measured Rrs(λ,0,0,0) and the modeled Rrs(λ,0,0,0) from Chl. The differences between the two Rrs(λ), quantified by the relative percentage difference (RPD), in the global ocean are shown in Fig. 1 for the five VIIRS bands in the visible domain (i.e., 410, 443, 486, 551, and 671 nm). RPD is defined as
where x and y are the modeled Rrs(λ,0,0,0) and VIIRS-measured Rrs(λ,0,0,0), respectively.
Fig. 1. The relative percentage difference (RPD) of the VIIRS Rrs(λ) in March 2019, referring to the modeled Rrs(λ) from Chl-inferred IOPs using Eq. (3).
Results in Fig. 1 suggest that the modeled Rrs(λ) via the Chl-αw system significantly deviate from the input, satellite-measured, Rrs(λ). For example, for 45.6% of the global ocean, the absolute RPD is greater than 25% for Rrs(443) (see Fig. 1(b)), while 54.1% of the global ocean is observed with an absolute RPD greater than 25% for Rrs(551) (see Fig. 1(d)). These deviations are attributed to the uncertainties in Chl-inferred IOPs, as the validity of the Chl-IOPs relationship of Morel and Maritorena [14] relies heavily on the Chl-specific absorption and Chl-specific backscattering coefficients, which varies greatly in the global ocean [21–25]. In other words, using fixed Chl-IOPs relationships would result in large errors in the derived IOPs in global oceans, and the errors will be propagated to the modeled Rrs(λ), and thus the estimated αw(λ).
As indicated by Eq. (2), the key information required for the estimation of αw(λ) is the angular distribution of Rrs(λ), whereas satellite ocean color remote sensing provides Rrs(λ) for one set of Ω, referred to as Rrs(λ, Ω0) hereafter. Based on Eq. (3), Rrs(λ, Ω) is related to Rrs(λ, Ω0) through
3. Data and methods
3.1 Simulated datasets by HydroLight
Since field measurement of αw(λ) is not yet possible due to difficulties in separating the surface-reflected irradiance from the total upwelling irradiance [26], numerical simulations of radiative transfer by HydroLight code [27] are used in this study for the evaluation of Chl-αw_new. HydroLight was selected because it can provide the angular distribution of Lw(λ) and thus the computation of ‘true’ αw(λ). Detailed descriptions of the configurations of HydroLight simulation can be found in Section 2.2 of Yu et al. [28]. Briefly, three simulated datasets were generated by HydroLight to evaluate the sensitivity of Chl-αw_new to particle scattering phase function, Raman scattering, and chlorophyll fluorescence. The water was assumed homogenous and optically deep, whereas the default atmospheric models in HydroLight to characterize the sky radiances and irradiances distribution were employed with the assumption of zero cloud coverage (clear sky).
The first dataset, termed SynData, was generated with 500 sets of IOPs representing clear to turbid waters, three sets of wind speeds (5, 10, and 15 m/s), eight options of θs (0°, 15°, 30°, 45°, 60°, 75°, 80°, and 88°), and the Petzold average particle scattering phase function with an effective particulate backscattering-to-scattering ratio (bbpr) of 1.83% [29]. The simulated Rrs(λ) and αw(λ) cover a spectral domain of 400–750 nm with an interval of 10 nm. Note that inelastic scattering, including Raman scattering and chlorophyll fluorescence, were not considered in SynData. The second dataset, termed SynData-FF, was generated following the same configuration as that in SynData, except that the particle scattering phase function was modeled by the Fournier-Forand model with an effective bbpr of 1% [30]. The third dataset, termed SynData-RF, was simulated with Petzold average particle scattering phase function but with considerations of both Raman scattering and chlorophyll fluorescence, where the fluorescent quantum efficiency was set to 0.020.
3.2 Satellite imagery
The level-3 monthly composite global Rrs(λ) product of VIIRS, at a spatial resolution of 9 km, was acquired from NOAA CoastWatch (https://coastwatch.noaa.gov) and was used in this study to evaluate the performance of different αw schemes. Here VIIRS monthly composite Rrs(λ) of March 2019 was downloaded for demonstration. Note that using a different VIIRS imagery will not change the results and conclusion of this effort.
3.3 Broadband albedo
In addition to the estimated spectral αw(λ) from multiple schemes, evaluation results of the broadband αw in the visible domain (αw_VIS) are also provided. For hyperspectral αw(λ), αw_VIS is calculated as the integral of αw(λ), weighted by Ed(0+, λ), between 400 and 700 nm [31], which can be expressed as
For multi-bands αw(λ) derived from ocean color measurements, αw_VIS can be calculated following
Table 1. The MRPD of estimated αw(λ) and αw_VIS by Chl-αw_new and IOPs-αw for evaluation results using SynData, SynData-FF, and SynData-RF, respectively.
3.4 IOPs-based scheme for αw
For proper comparison, a recently-developed αw scheme based on remotely sensed IOPs is also employed in this study for scheme inter-comparison [28]. The scheme based on IOPs, hereafter termed IOPs-αw, ensures the closure of Rrs(λ) but employs a different model to describe the bidirectional variation of angular Rrs(λ) [32], which is expressed as
Note that Wei et al. [34] also employed Eq. (8) to model the angular Rrs(λ, Ω) but with bbp(λ) and a(λ) inferred from Chl using the Chl-IOPs relationship of Morel and Maritorena [14]. Thus, the scheme proposed by Wei et al. [34] cannot guarantee the closure of Rrs(λ) and can be considered a variant of the Chl-based scheme.
4. Results and discussions
4.1 Evaluation of Chl-αw_new with numerical simulations
The performance of Chl-αw, Chl-αw_new, and IOPs-αw are first evaluated with SynData, with validation results of αw(λ) and αw_VIS estimated by the three schemes presented in Fig. 2. The median RPD (MRPD) of estimated αw(λ) and αw_VIS are also provided in Fig. 2 as a quantitative measure. Here RPD is first calculated using Eq. (4) with x as the estimated αw(λ) and y as the known αw(λ) from HydroLight simulations. MRPD is subsequently calculated as the median value of computed RPD of all simulations. Note that both the estimated αw_VIS and known αw_VIS are computed from the hyperspectral αw(λ) using Eq. (6). As shown in Fig. 2, for the simulated dataset SynData, Chl-αw_new outperforms Chl-αw with much smaller errors in the estimated αw(λ) at all wavelengths. The absolute values of MRPD of estimated αw(λ) by Chl-αw_new are generally less than 3.4% in comparison to over 32% for that by Chl-αw. The systematic underestimations of αw(λ) by Chl-αw are due to the modeled Rrs(λ) from Chl-inferred IOPs are overall smaller than the input Rrs(λ) (see Fig. 1), resulting in negative MRPD at all spectral bands. Since both Chl-αw_new and IOPs-αw are exempt from the errors associated with the closure issue of Rrs(λ), the uncertainties in estimated αw(λ) by these two schemes are mainly attributed to the respective model for the bidirectional variation of angular Rrs(λ), which are acceptable given the small values in MRPD. Figure 2 shows that Chl-αw_new has quite comparable performance with IOPs-αw at all spectral bands, with all their retrievals closely distributed along the 1:1 line. In particular, the MRPD of estimated αw_VIS by Chl-αw_new and IOPs-αw are 1.7% and 1.5%, respectively. The difference in MRPD is only 0.2%, which is not statistically significant. Thus, Chl-αw_new can be considered an alternative to IOPs-αw to accurately estimate αw(λ) from remote sensing, but much easier in calculations as it does not require the step to obtain IOPs.
Fig. 2. Validation of estimated αw(λ) at five VIIRS bands and estimated αw_VIS by Chl-αw (circles), Chl-αw-new (triangles), and IOPs-αw (squares) using SynData.
Chl-αw_new was further employed to estimate αw(λ) using SynData-FF and SynData-RF to evaluate the sensitivity of Chl-αw_new to the particle scattering phase function, Raman scattering, and chlorophyll fluorescence, with the statistical measure tabulated in Table 1. Note that results from IOPs-αw are also included in Table 1 for comparisons, while results from Chl-αw are not shown here given its poor performance. It can be found in Table 1 that the absolute MRPD values are generally less than 3% for estimated αw(λ) and αw_VIS by Chl-αw_new for SynData-FF and SynData-RF, which are quite comparable with that obtained in SynData. Thus, we can conclude that Chl-αw_new is insensitive to the particle scattering phase function, Raman scattering, and chlorophyll fluorescence, and could be applicable for the estimation of αw(λ) in a wide range of water types. Note that the evaluation results regarding the sensitivity of Chl-αw_new to wind speed are not shown here as wind speed has negligible impacts on the estimated αw(λ) by Chl-αw_new. Different wind speeds may alter the value of $\mathrm{\Re }$ (Ω), but such an impact is largely canceled out when the ratio of $\mathrm{\Re }$ (Ω) to $\mathrm{\Re }$ (Ω0) is used to model the angular Rrs(λ) (see Eq. (5)).
Furthermore, comparisons between Chl-αw_new and IOPs-αw in Table 1 show that Chl-αw_new has slightly degraded performance compared to IOPs-αw in SynData-FF, but their difference is overall comparable. However, for SynData-RF, Chl-αw_new has shown improved performance than IOPs-αw with a much smaller MRPD of estimated αw_VIS. Thus, Chl-αw_new would be highly recommended for applications in eutrophic waters where chlorophyll fluorescence could be significant.
4.2 Evaluation of Chl-αw_new with satellite imagery
VIIRS imagery is further employed to evaluate the performance of Chl-αw_new in the global ocean, especially for its comparison with Chl-αw and IOPs-αw. Here, VIIRS monthly composite Rrs(λ) of March 2019 are employed to estimate αw(λ) for the subsequent demonstration and analysis. Other inputs required for Chl-αw and Chl-αw_new are the solar zenith angle and wind speed, with θs set as 0 given the fact that VIIRS Rrs(λ) product is equivalent to Rrs(λ,0,0,0). Note that wind speed has rather minor impact on αw(λ) [28], thus a constant 6.64 m/s is used for all pixels, which is the global average wind speed at 10 m above the ocean [35]. The extra input required for the implementation of IOPs-αw is θs, which is also set as 0.
The differences between estimated αw(λ) by Chl-αw and its improved version Chl-αw_new in global oceans are first evaluated for all the five VIIRS visible bands with results presented in Fig. 3. RPD is calculated following Eq. (4) with estimated αw(λ) by Chl-αw as the reference (i.e., the denominator in Eq. (4)). Comparisons of spectral αw(λ) estimated by Chl-αw_new and IOPs-αw for global oceans are not shown here as they are very comparable. As shown in Fig. 3, for most oceanic waters, Chl-αw systematically underestimates αw(λ) at the five VIIRS bands, except for waters in the North Atlantic Ocean and the North Pacific Ocean. In most coastal regions, Chl-αw tends to overestimate αw(λ) except for those with high turbidity or shallow depths.
Fig. 3. Same as Fig. 1, but for RPD of the estimated αw(λ) by Chl-αw_new, referring to that by Chl-αw. The black, white, and red boxes in panel (d) highlight the locations of three regions of interest in the North Atlantic Ocean (NAO), South Pacific Gyre (SPG), and Yangtze estuary, respectively.
Further, we select three regions of interest (ROIs, highlighted in Fig. 3(d)) to highlight the different αw(λ) obtained by Chl-αw, Chl-αw_new, and IOPs-αw in different types of waters. These three ROIs are the North Atlantic Ocean (NAO, 55°W – 45°W, 43°N – 47°N), the South Pacific Gyre (SPG, 124°W – 104°W, 32°S – 22°S), and the Yangtze estuary (YE, 120.7°E – 123.0°E, 29.5°N – 32.5°N), which are selected because NAO represents oceanic waters where Chl-αw_new yields significantly smaller αw(λ) than Chl-αw, while SPG is for oceanic waters with larger αw(λ) estimations by Chl-αw_new. YE is selected due to it is characteristics of extremely turbid waters [36]. The bio-optical properties (Chl and IOPs) are also derived from Rrs(λ) to highlight the contrasting water characteristics in these three ROIs. Specifically, Chl is estimated by the OCI algorithm [15–17], while a and bb are derived using the quasi-analytical algorithm (QAA) [33]. Note that the latest version of QAA (QAA_v6, available at http://www.ioccg.org/groups/Software_OCA/QAA_v6_2014209.pdf) was used in this study. In Fig. 4, we present the median spectra of derived αw(λ) by the three schemes in the three ROIs, as well as the spectra of VIIRS-measured Rrs(λ) and the modeled Rrs(λ) from Chl-inferred IOPs.
Fig. 4. Comparisons of the estimated spectral αw(λ) (aligned to the left y-axis) by Chl-αw_new, Chl-αw, and IOPs-αw, and comparisons of the spectral Rrs(λ) (aligned to the right y-axis) from VIIRS measurements and that modeled from Chl-inferred IOPs, for NAO, SPG, and YE, respectively. The median values (med) of αw(λ) and Rrs(λ) are plotted here, with the error bar indicating the standard deviation (std). Remotely sensed Chl, a(443), and bb(443) (med ± std) are also presented to highlight the distinguishing characteristics of water properties in the three ROIs.
It can be observed in Fig. 4 that, for all three ROIs, the estimated αw(λ) by Chl-αw is significantly deviated from that by Chl-αw_new and IOPs-αw. As a quantitative measure, Table 2 tabulates the median RPD of the estimated αw(λ) by Chl-αw_new, referring to the estimation by Chl-αw, for the three ROIs, as well as the median RPD of VIIRS Rrs(λ), referring to the modeled Rrs(λ). It can be found that Chl-αw_new, on average, predicts much smaller αw(λ) in NAO than that by Chl-αw, with MRPD generally less than −20% in the blue-green domain. For SPG and YE, estimated αw(λ) by Chl-αw_new are significantly greater than that by Chl-αw, especially for the YE where MRPD could be over 2000%. As shown in Table 2, the MRPD values calculated for VIIRS Rrs(λ), referring to the modeled Rrs(λ) by Chl-αw, are very comparable with the MRPD for estimated spectral αw(λ) (see also the comparison of Fig. 1 and Fig. 3), suggesting that the large discrepancies of estimated αw(λ) between Chl-αw_new and Chl-αw could be mainly attributed to the uncertainties introduced by the modeling of angular Rrs(λ) from Chl-inferred IOPs. Thus, it is safe to conclude that Chl-αw_new provides a more reasonable estimation of αw(λ) than Chl-αw in global oceans, given that it avoids the uncertainties associated with the closure issue of Rrs(λ).
Table 2. The MRPD of estimated αw(λ) by Chl-αw_new, referring to that estimated by Chl-αw, and the MRPD of VIIRS Rrs(λ), referring to that modeled from Chl, for the three regions of interest in NAO, SPG, and YE, respectively.
Consistent with the results presented in Table 1 for the evaluation results with SynData, Chl-αw_new and IOPs-αw have quite comparable performance when implemented to VIIRS data, where the spectral αw(λ) estimated by both schemes are almost congruent in the three ROIs, especially in NAO and SPG (see Fig. 4(a) and Fig. 4(b)). Discrepancies in the estimated αw(λ) are observed in the YE but are statistically insignificant (see Fig. 4(c)). Table 3 tabulates the MRPD between estimated αw(λ) by Chl-αw_new and IOPs-αw, with estimations by IOPs-αw as the reference, where MRPD are found within ± 5% for most spectral bands for all three ROIs, suggesting a good agreement between Chl-αw_new and IOPs-αw. More importantly, the differences between the estimated αw_VIS by the two schemes in the three ROIs are even smaller, with MRPD of 0.2%, −3.6%, and 2.9% for NAO, SPG, and YE, respectively. Thus, evaluation results with satellite imagery also suggest that Chl-αw_new is a good alternative to IOPs-αw. Here αw_VIS is converted from the narrowband αw(λ) following Eq. (7). As shown in Table 3, although there are small discrepancies in the spectral αw(λ) estimated by Chl-αw_new and IOPs-αw, estimated αw_VIS by the two schemes are quite consistent with the absolute MRPD less than 4% at all the three ROIs.
Table 3. The Median RPD (MRPD) of estimated αw(λ) and αw_VIS by Chl-αw_new, referring to that estimated by IOPs-αw, for the three regions of interest in NAO, SPG, and YE, respectively.
In Fig. 5(a), we show the global distribution of αw_VIS estimated by Chl-αw_new using the VIIRS monthly composite data of March 2019. The differences between estimated αw_VIS by Chl-αw_new and IOPs-αw in global oceans are demonstrated in Fig. 5(c), with the comparison of Chl-αw and IOPs-αw shown in Fig. 5(b). Results in Fig. 5(c) confirm that Chl-αw_new could be equivalent to IOPs-αw for the estimation of αw_VIS, as the differences in estimated αw_VIS by the two schemes in the global ocean are generally less than 5%. In contrast, the median RPD values for the three ROIs calculated from Fig. 5(b) are 39.9%, −33.0%, and −86.5%, respectively, suggesting that both Chl-αw_new and IOPs-αw can significantly improve the estimation of αw_VIS compared to Chl-αw, especially for turbid waters.
Fig. 5. Global distribution of αw_VIS in March 2019 estimated by Chl-αw_new using VIIRS monthly composite data (a). Panels (b) and (c) show the RPD of estimated αw_VIS by Chl-αw and Chl-αw_new, referring to αw_VIS estimated by IOPs-αw, respectively (note the difference in the scale of the colorbar in panels (b) and (c)).
4.3 Uncertainties in different αw schemes
Since Chl-αw and Chl-αw_new employ the same model to describe the bidirectional variation of Rrs(λ), comparisons between these two schemes conclude that optical closure of Rrs(λ) is the main error source for estimated αw(λ) by Chl-αw. The underestimation or overestimation of αw(λ) by Chl-αw in the global ocean is driven largely by the extent of underestimation or overestimation in modeled Rrs(λ) from Chl, which is determined by the uncertainties in the Chl-inferred IOPs, particularly the ratio of bb(λ) to a(λ). Since the Chl-IOPs relationship used in Chl-αw was proposed for “Case-1” waters [14], it is not surprising that larger uncertainties of estimated αw(λ) by Chl-αw are found in most coastal waters, which are typically more optically complex and IOPs are not solely determined by Chl [37]. However, for oceanic waters, Chl-αw is still underperformed and its performance is region-dependent (see Fig. 3), which can be explained by the uncertainties in Chl-inferred IOPs in different regions.
For instance, the overestimation of αw(λ) by Chl-αw in NAO could be mainly due to underestimated absorption coefficient of colored dissolved organic matter (CDOM), termed ag(λ) hereafter. Comparing with Fig. 1(b) of Morel et al. [38], we can observe that the purple to black pixels in Fig. 3 are highly coincident with waters of high CDOM-to-Chl proportion. Chl-αw uses an empirical relationship to estimate ag(λ) from Chl [14] could result in large uncertainties in estimated ag(λ) when applying the relationship to global oceans, especially for waters where the CDOM-to-Chl proportion differs largely from these statistical averages. For those waters with a high CDOM-to-Chl proportion, the empirical Chl-ag(λ) relationship used by Chl-αw would underestimate a(λ), which results in larger modeled Rrs(λ), and hence an overestimation of αw(λ) (see Fig. 4(a)).
For waters in SPG and other oceanic waters where Chl-αw underestimates αw(λ), the underestimations of the modeled Rrs(λ) are mostly attributed to the underestimated bb(λ) from Chl. For example, Chl-inferred a(λ) in SPG are overall comparable with the derived a(λ) from VIIRS Rrs(λ) using QAA_v6, but Chl-inferred bb(λ) are underestimated by more than 30% at the five bands (results not shown here). Consequently, the underestimations of bb(λ) result in smaller modeled Rrs(λ) in SPG, which explains the biased lower αw(λ) estimation by Chl-αw (see Table 2). For YE, Chl-inferred a(λ) and bb(λ) are both of large uncertainties, but underestimation of bb(λ) prevails over the underestimation of a(λ) given that the waters in YE are extremely turbid and are characteristics of strong backscattering. Thus, modeled Rrs(λ) from Chl in YE are significantly underestimated, hence the estimated αw(λ) (see Fig. 4(c)).
On the other hand, both Chl-αw_new and IOPs-αw avoid the uncertainties associated with the closure issue of Rrs(λ), while their differences lie in the models for bidirectional variation of Rrs(λ). Comparisons of Chl-αw_new and IOPs-αw for their performance in both HydroLight simulations and VIIRS data show that the model for Rrs(λ) bidirectionality has rather minor impacts on the uncertainties in the estimated αw(λ). It is worthy to point out that the uncertainties of derived Chl from OCI could be considerably large in optically complex waters [39–41], which will introduce errors to modeled angular Rrs(λ) as the values of Ψ in Eq. (3) is Chl-dependent. However, it is found that the ratios of Ψ(Ω) to Ψ(Ω0) are in a much smaller range than the range of the Ψ values [20]. Thus, Chl-αw_new could be less sensitive to the uncertainties in the Ψ values associated with the use of empirically estimated Chl, which can explain the consistent performance of Chl-αw_new in the extremely turbid waters in YE as presented in Fig. 4(c). It is also noted that the LUT to describe Rrs(λ) bidirectionality in IOPs-αw, i.e., the G values in Eq. (8), is weighted for all wavelengths and could result in uncertainties in modeled angular Rrs(λ) for a specific wavelength, especially for the red domain [28]. In contrast, the LUT for Ψ is wavelength-dependent, which might explain the result that Chl-αw_new outperforms IOPs-αw for the estimated αw(670) as shown in Table 1. This suggests that IOPs-αw might be further improved if the LUT for G values is wavelength-dependent.
4.4 Implications for coupled ocean-atmosphere models
Since both Chl-αw_new and IOPs-αw could significantly improve the estimation of αw(λ) compared to the conventional Chl-αw, the remaining question would be how much the improvement could affect the interpretation of solar radiation transfer at the air-sea boundary layer in coupled ocean-atmosphere models and climate models. Many previous studies considered only the reflected albedo in their parametrizations of the ocean surface albedo (α(λ)) or simply use a constant broadband α value for global oceans [42]. The broadband α, termed αbroad, is calculated as the integral of spectral α(λ) over the full shortwave domain and weighted by Ed(0+, λ) [31]. Some recent efforts included the contribution of αw(λ) to α(λ) but the contribution of αw(λ) might be largely underrepresented as they employed Chl-αw [9–11]. Given that the reflected albedo is generally less than 0.03 for solar zenith angles less than 30° (see Fig. 15 in Feng et al. [10]), we can preliminarily assess the contribution of αw(λ) to αbroad as the broadband αw (termed αw_broad) is about 42.3% of αw_VIS if neglecting the contribution of αw(λ) from ultraviolet and near-infrared bands [28]. The selection of the value of 42.3% is simply because Ed(0+, λ) in the visible domain accounts for roughly 42.3% of Ed(0+, λ) in the full shortwave domain [43]. Such an assumption is valid for most of the global oceans except for extremely turbid waters, where αw_broad could be much larger than 42.3% of αw_VIS due to contributions from αw(λ) of near-infrared bands.
Take the SPG for example, the median αw_VIS estimated by Chl-αw_new and Chl-αw are 0.017 and 0.011, respectively, resulting in the median αw_broad of 0.0072 and 0.0046 when multiplying αw_VIS by 42.3%. Taking the reflected albedo as a constant of 0.03, αbroad would increase from 0.0346 to 0.0372 if Chl-αw_new is employed. Such a change in αbroad would have minimal impacts (∼ −0.4%) on the calculation of solar radiation absorbed by the ocean, which is a function of 1 – αbroad (i.e., 0.965 vs 0.963). However, the amount of reflected flux towards the atmosphere would be increased by 7.5% in this case, which could be important for the energy budget given gyre waters account for over 30% of surface areas of the global oceans. Furthermore, if applying the same calculation scheme to YE, the median αbroad estimated by Chl-αw and Chl-αw_new would be 0.0335 to 0.0565, respectively, which means the solar radiation absorbed by the ocean would decrease by 2.4% if Chl-αw_new is employed, while the reflected solar energy towards the atmosphere will surge by 68.7%. Note that if the contribution of αw(λ) from near-infrared bands is taken into consideration, a larger αbroad in YE would be expected, which means more solar radiation will be reflected into the atmosphere at the air-sea interface.
The preliminary assessment discussed above highlights the fact that αw(λ) contribution to αbroad should not be neglected in the coupled ocean-atmosphere models, especially for the models requiring the reflected solar flux at the air-sea interface and models for solar radiation transfer in optically complex waters, such as the Regional Ocean Modeling System. It is highly recommended to implement either Chl-αw_new or IOPs-αw to the coupled ocean-atmosphere models and climate models for an accurate estimation of αw(λ). It can be expected that with more accurate inputs of αw(λ), the interpretation of solar radiation transfer at the air-sea boundary layer in these models and the feedback of ocean surface albedo to the climate change could be altered [44], particularly for the potential impacts on the air dynamics in the middle-to-low latitude oceans where the average solar zenith angles are relatively low and αw(λ) has high contributions to αbroad.
5. Conclusions
In this effort, we show that the conventional Chl-based αw scheme could result in large uncertainties in the estimation of αw(λ) for global oceans, which is mainly because of no closure between the modeled Rrs(λ) from Chl-inferred IOPs and the input Rrs(λ) for the retrieval of Chl. With a simple but analytical modification, we proposed a new scheme termed Chl-αw_new, which skips the step to estimate IOPs from Chl, thus reducing the uncertainties in the estimated αw(λ) greatly in global oceans. Comparisons between Chl-αw_new and the IOPs-based scheme demonstrate that the closure of Rrs(λ) is the main error source for the estimation of αw(λ) by Chl-based schemes, while the model for Rrs(λ) bidirectionality have rather minor impacts. Note that the field measurement system for αw(λ) has already been proposed [26], further evaluations of the three αw(λ) schemes could be carried out when field-measured αw(λ) become available. Finally, this study highlights the necessity of incorporating accurate αw(λ) in the coupled ocean-atmosphere models, especially for the estimation of reflected and scattered solar radiation towards the atmosphere at the air-sea interface.
Funding
National Natural Science Foundation of China (42006162, 41941008, 41890803); China Postdoctoral Science Foundation (2019M662234).
Acknowledgments
X. Yu is funded by the Outstanding Postdoctoral Scholarship of the State Key Laboratory of Marine Environmental Science at Xiamen University. The authors would like to thank Dr. Menghua Wang and Dr. Lide Jiang for providing the VIIRS data.
Disclosures
The authors declare no conflicts of interest.
Data availability
MATLAB scripts for both Chl-αw and Chl-αw_new, as well as data underlying the results presented in this paper are available in Ref. [45].
References
1. J. P. Abraham, M. Baringer, N. Bindoff, T. Boyer, L. Cheng, J. Church, J. Conroy, C. Domingues, J. Fasullo, and J. Gilson, “A review of global ocean temperature observations: Implications for ocean heat content estimates and climate change,” Rev. Geophys. 51(3), 450–483 (2013). [CrossRef]
2. R. E. Payne, “Albedo of the sea surface,” J. Atmos. Sci. 29(5), 959–970 (1972). [CrossRef]
3. M. Fogarty, M. Fewings, A. Paget, and H. Dierssen, “The influence of a sandy substrate, seagrass, or highly turbid water on albedo and surface heat flux,” J. Geophys. Res. Oceans 123(1), 53–73 (2018). [CrossRef]
4. Z. Jin, T. P. Charlock, W. L. Smith Jr, and K. Rutledge, “A parameterization of ocean surface albedo,” Geophys. Res. Lett. 31(22), L22301 (2004). [CrossRef]
5. B. P. Briegleb, P. Minnis, V. Ramanathan, and E. Harrison, “Comparison of regional clear-sky albedos inferred from satellite observations and model computations,” J. Climate Appl. Meteor. 25(2), 214–226 (1986). [CrossRef]
6. J. Taylor, J. Edwards, M. Glew, P. Hignett, and A. Slingo, “Studies with a flexible new radiation code. II: Comparisons with aircraft short-wave observations,” Q. J. R. Meteorol. Soc. 122(532), 839–861 (1996). [CrossRef]
7. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44(11), 838–850 (1954). [CrossRef]
8. Z. Jin, T. P. Charlock, and K. Rutledge, “Analysis of broadband solar radiation and albedo over the ocean surface at COVE,” J. Atmos. Oceanic Technol. 19(10), 1585–1601 (2002). [CrossRef]
9. R. Séférian, S. Baek, O. Boucher, J.-L. Dufresne, B. Decharme, D. Saint-Martin, and R. Roehrig, “An interactive ocean surface albedo scheme (OSAv1. 0): formulation and evaluation in ARPEGE-Climat (V6. 1) and LMDZ (V5A),” Geosci. Model Dev. 11(1), 321–338 (2018). [CrossRef]
10. Y. Feng, Q. Liu, Y. Qu, and S. Liang, “Estimation of the ocean water albedo from remote sensing and meteorological reanalysis data,” IEEE Trans. Geosci. Remote Sens. 54(2), 850–868 (2016). [CrossRef]
11. Z. Jin, Y. Qiao, Y. Wang, Y. Fang, and W. Yi, “A new parameterization of spectral and broadband ocean surface albedo,” Opt. Express 19(27), 26429–26443 (2011). [CrossRef]
12. C. D. Mobley, Light and water: radiative transfer in natural waters (Academic, 1994).
13. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. II. Bidirectional aspects,” Appl. Opt. 32(33), 6864–6879 (1993). [CrossRef]
14. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res. 106(C4), 7163–7180 (2001). [CrossRef]
15. J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998). [CrossRef]
16. C. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: A novel approach based on three-band reflectance difference,” J. Geophys. Res. 117(C1), C01011 (2012). [CrossRef]
17. M. Wang and S. Son, “VIIRS-derived chlorophyll-a using the ocean color index method,” Remote Sens. Environ. 182, 141–149 (2016). [CrossRef]
18. H. R. Gordon, “Normalized water-leaving radiance: revisiting the influence of surface roughness,” Appl. Opt. 44(2), 241–248 (2005). [CrossRef]
19. M. Wang, “Effects of ocean surface reflectance variation with solar elevation on normalized water-leaving radiance,” Appl. Opt. 45(17), 4122–4128 (2006). [CrossRef]
20. A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002). [CrossRef]
21. A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995). [CrossRef]
22. H. Loisel and A. Morel, “Light scattering and chlorophyll concentration in case 1 waters: A reexamination,” Limnol. Oceanogr. 43(5), 847–858 (1998). [CrossRef]
23. Y. Huot, A. Morel, M. Twardowski, D. Stramski, and R. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5(2), 495–507 (2008). [CrossRef]
24. R. A. Reynolds, D. Stramski, and B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res. 106(C4), 7125–7138 (2001). [CrossRef]
25. M. Stramska, D. Stramski, R. Hapter, S. Kaczmarek, and J. Stoń, “Bio-optical relationships and ocean color algorithms for the north polar region of the Atlantic,” J. Geophys. Res. Oceans, 108 (2003).
26. Z. Shang, X. Yu, and Z. Lee, “Direct measurement system of water-leaving albedo in the field by the skylight-blocked approach: Monte Carlo simulations,” Opt. Express 30(13), 23852–23867 (2022). [CrossRef]
27. C. D. Mobley and L. K. Sundman, “Hydrolight 5.3 Ecolight 5.3 Users’ Guide,” Sequoia Scientific Inc. (2016).
28. X. Yu, Z. Lee, S. Shang, M. Wang, and L. Jiang, “Estimating the water-leaving albedo from ocean color,” Remote Sens. Environ. 269, 112807 (2022). [CrossRef]
29. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (DTIC Document, 1972).
30. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, (International Society for Optics and Photonics, 1994), 194–201.
31. J. C. Ohlmann, D. A. Siegel, and C. D. Mobley, “Ocean radiant heating. Part I: Optical influences,” J. Phys. Oceanogr. 30(8), 1833–1848 (2000). [CrossRef]
32. Z. P. Lee, K. Du, K. J. Voss, G. Zibordi, B. Lubac, R. Arnone, and A. Weidemann, “An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance,” Appl. Opt. 50(19), 3155–3167 (2011). [CrossRef]
33. Z. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41(27), 5755–5772 (2002). [CrossRef]
34. J. Wei, T. Ren, P. Yang, S. F. DiMarco, and E. Mlawer, “An improved ocean surface albedo computational scheme: Structure and Performance,” J. Geophys. Res. Oceans, e2020JC016958 (2021).
35. C. L. Archer and M. Z. Jacobson, “Evaluation of global wind power,” J. Geophys. Res. Atmos. 110(2005).
36. X. Yu, Z. Lee, F. Shen, M. Wang, J. Wei, L. Jiang, and Z. Shang, “An empirical algorithm to seamlessly retrieve the concentration of suspended particulate matter from water color across ocean to turbid river mouths,” Remote Sens. Environ. 235, 111491 (2019). [CrossRef]
37. IOCCG, “Remote Sensing of Ocean Colour in Coastal, and Other Optically-Complex, Waters,” Sathyendranath, S. (ed.), Reports of the International Ocean-Colour Coordinating Group No.3, IOCCG, Dartmouth, Canada (2000).
38. A. Morel, H. Claustre, and B. Gentili, “The most oligotrophic subtropical zones of the global ocean: similarities and differences in terms of chlorophyll and yellow substance,” Biogeosciences 7(10), 3139–3151 (2010). [CrossRef]
39. G. F. Cota, H. Wang, and J. C. Comiso, “Transformation of global satellite chlorophyll retrievals with a regionally tuned algorithm,” Remote Sens. Environ. 90(3), 373–377 (2004). [CrossRef]
40. S. Shang, Z. Lee, G. Lin, Y. Li, and X. Li, “Progressive scheme for blending empirical ocean color retrievals of absorption coefficient and chlorophyll concentration from open oceans to highly turbid waters,” Appl. Opt. 58(13), 3359–3369 (2019). [CrossRef]
41. C. Le, C. Hu, J. Cannizzaro, D. English, F. Muller-Karger, and Z. Lee, “Evaluation of chlorophyll-a remote sensing algorithms for an optically complex estuary,” Remote Sens. Environ. 129, 75–89 (2013). [CrossRef]
42. J. Li, J. Scinocca, M. Lazare, N. McFarlane, K. Von Salzen, and L. Solheim, “Ocean surface albedo and its impact on radiation balance in climate models,” J. Clim. 19(24), 6314–6333 (2006). [CrossRef]
43. J. Gibson, “UVB radiation: definition and characteristics,” USDA/CSU Available online: https://uvb.nrel.colostate.edu/UVB/publications/uvb_primer.pdf. (2003).
44. A. Hall, “The role of surface albedo feedback in climate,” J. Clim. 17(7), 1550–1568 (2004). [CrossRef]
45. X. Yu, “MATLAB scripts for the new retrieval algorithm of water-leaving albedo based on Chlorophyll-a concentration”, retrieved 9/3/2022, https://github.com/oceanopticsxmu/Chl_osaw. (Github, 2022).
