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Abstract
Atmospheric correction (AC) of polarized radiances acquired by polarization satellite sensors, remains a challenge due to the complex radiative transfer processes of the coupled ocean–atmosphere system. In this study, we proposed an innovative polarized AC algorithm built on the near-infrared band (PACNIR) with an emphasis on the retrieval of the linear polarization components of the water-leaving radiance in clear open oceans. This algorithm was based on the black ocean assumption in the near-infrared band and fitted polarized radiance measurements along multiple observation directions with nonlinear optimized processing. Our retrieval algorithm notably inverted the linearly polarized components of the water-leaving radiance and aerosol parameters. Compared with that of the simulated linear polarization components of the water-leaving radiance via the vector radiative transfer model for the studied sea regions, the mean absolute error of the PACNIR-retrieved linearly polarized components (nQw and nUw) exhibited a magnitude of 10−4, while the magnitude of that of the simulated nQw and nUw data was 10−3. Moreover, the PACNIR-retrieved aerosol optical thicknesses at 865 nm exhibited a mean absolute percentage error of approximately 30% relative to in situ values obtained from Aerosol Robotic Network-Ocean Color (AERONET-OC) sites. The PACNIR algorithm could facilitate AC of the polarized data provided by the next generation of multiangle polarization satellite ocean color sensors.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarimetric ocean remote sensing is an increasingly important area in monitoring the optical characteristics of ocean–atmospheric systems [1,2] and studying vector radiance transfer in coupled ocean–atmospheric environments [3,4]. Several parameters of sea surface dynamic and oceanic components have been verified and retrieved through polarization observations, such as sea surface wind [5] and nonalgal particle concentration data [6,7]. Moreover, the polarization radiance is sensitive to the microscopic optical characteristics of atmospheric particles, such as the aerosol refractive index [8] and size distribution [8,9]. Consequently, combined with the vector radiance transfer simulation (VRTS) method for the coupled ocean–atmosphere system and signals measured by polarization sensors at the top of the atmosphere (TOA), both the polarized water-leaving radiances and aerosol properties can be jointly retrieved in theory through suitable optimization approaches [10–14].
To acquire water-leaving signals from TOA measurements, two general strategies have been developed for atmospheric correction (AC). Traditional AC methods obtain approximate atmospheric radiance signals through the black ocean concept in the near-infrared (NIR) band and then calculate the scalar water-leaving radiance in the visible band based on the band ratio relationship. These methods have been successfully used in open ocean environments, and similar attempts have been made to overcome the challenging problems of absorbing aerosols and nonnegligible water-leaving signals in the NIR band [15–19]. Another AC approach has been built based on joint inversions, which simultaneously inverts aerosol parameters and water-leaving signals and applies several flexible joint retrieval algorithms to obtain aerosol optical depth (AOD) and water quality parameters for changeable waters. Xu et al. [9] developed an optimization approach for the quantitative retrieval of atmospheric aerosol properties and normalized water-leaving radiance that included a multipixel smoothing constraint. Gao et al. [20] proposed an algorithm for atmosphere and ocean component retrieval focused on coastal waters that used a coupled ocean–atmospheric VRTS method to fit polarized signals of synthetic research scanning polarimeter (RSP) data. However, most of these algorithms focused on the inversion of atmospheric composition parameters rather than AC and lacked the capacity to directly calculate the polarization components of the water-leaving radiance from TOA polarization remote sensing signals.
Over the last few decades, several spaceborne polarization satellites have been launched, including ADEOS-I/POLDER-1 (1996.11−1997.6) [21], ADEOS-II/POLDER-2 (2003.4−2003.10) [22] and PARASOL (2004.12−2013.12) [23]. New satellites equipped with the next generation of multidirectional, multiangle polarization sensors have been scheduled for launch, such as the Plankton, Aerosol, Cloud, ocean Ecosystem mission (PACE) [24] and Multi-viewing, Multi-channel and Multi-polarisation Imager (3MI) sensors [25]. There are a large number of published studies [9,26,27] that describe the inversions of atmospheric aerosol properties and hydrosol parameters based on the above polarimeter datasets. However, no algorithms have been proposed to retrieve the polarization components of the water-leaving radiance to date.
In this study, we proposed a joint retrieval strategy to acquire linear-polarized components of the water-leaving radiance and aerosol parameters. Our algorithm was based on the black ocean theory in the NIR band for clear open oceans and combined the moderate brute algorithm (MBA) and Nelder–Mead simple algorithm (NMSA) for nonlinear optimized processing.
The content is organized into six sections. Section 2 introduces the synthetic measurement data and several indicators of model evaluation. Section 3 describes the details of the retrieval methodology. Section 4 examines the retrieval results. Section 5 explains several essential aspects of the retrieval algorithm. Section 6 provides the conclusions.
2. Data and methods
2.1. Satellite data
Multiangle polarimeter Level-1B data of the PARASOL sensor onboard the Myriade satellite within the A-train project [23] were collected from the ICARE data service center website (https://www.icare.univ-lille.fr). Three spectral bands (490 nm, 670 nm, 865 nm) of PARASOL are polarization observation, which can measure the first three components of the Stokes vector. The spatial resolution of PARASOL at the nadir is about 6 km, and the revisiting period is approximately 2 days. The observation setting of PARASOL is designed to capture ±55° range along track, with the field of view of 110° and up to 16 successive observations of a single pixel. To reduce the instrument error caused by the long-time span and the operation time, we employed the data for 2011 to verify the accuracy of the algorithm. We used the obtained multiangle polarimeter data as the vector radiances at the TOA and calculated the polarized water-leaving radiances at the bottom of the atmosphere (BOA).
The sea surface wind speed (W) was also considered as input in our algorithm. Wind speed data (10-meter wind speed, v7.0.1) of the WindSat Polarimetric Radiometer onboard the Coriolis satellite (2003.1–present) [28] were obtained from the Remote Sensing Systems website (https://www.remss.com/missions/windsat). The spatial resolution of the wind speed data is $25 \times 38$ km2 in no rain condition, and the nearest wind speed values relative to the PARASOL pixels are selected and input into the algorithm. Although a difference of the spatial resolution exists between wind speed data and PARASOL Stokes vector, this influence is expected to be limit as wind fields are usually homogeneous to a large scale in the open oceans.
We also collected satellite-derived, quality-assured, merged Level-3 chlorophyll a concentration (Chla; mg m-3) data and AOD at 865 nm (T865) data from the GlobColour website (https://hermes.acri.fr). Chla was considered input in each radiative transfer simulation. The T865 and Aerosol Robotic Network-Ocean Color (AERONET-OC) data were compared to the inversion results to evaluate the performance of the model. The selected satellite data regions are shown in Fig. 1 (orange rectangle).
Fig. 1. Selected polarization satellite data regions (orange rectangle), AERONET-OC sites (red stars), and BGC-Argo profiling floats (green dotted line) for statistical analysis of the accuracy of the inversion.
2.2. AERONET OC data
Considering the distribution of PARASOL satellite data, we collected cloud-masked and quality-guaranteed Level-2.0 in situ measured data from two AERONET-OC sites to assess the proposed inversion algorithm: the LISCO station in the Atlantic off the coast of the Western Long Island Sound and the WaveCIS site in the Gulf of Mexico. A ± 2−h time window during the satellite overpass was put into practice strictly to select the AERONET-OC data. The two sites provided enough observations during the PARASOL orbit to offer a unique opportunity for data validation and used the same instrument with the same calibration and postprocessing procedures. Moreover, these two sites were affected by aerosols mainly originating from weakly absorbing anthropogenic pollution and wildfires, according to the aerosol type global distribution in [29], which conforms to the limiting conditions of the aerosol model (AM) in our algorithm. Site-specific introductions of these two stations are provided in Table 1. The AERONET-OC data comprised measured AOD and normalized water-leaving radiance (${L_{WN - f/Q}}$) values from 412 to 1020 nm. The AOD was interpolated using a cubic spline strategy to the PARASOL polarization NIR spectral bands (865 nm) to ensure direct comparability with the algorithm calculation results. The spline interpolation technique was assumed adequate to correct the band difference between the in situ measurements and satellite retrieval results. Comparisons among different data sources might be affected by differences due to non-matching center wavelength of the data products. To minimize these uncertainties, ${L_{WN - f/Q}}$ was corrected based on regional bio-optical algorithms, and the ratio of the total backscattering and absorption coefficients and the extraterrestrial solar irradiance were used as inputs into the band shift function. Further details of this methods are provided in Zibordi et al. [30]. The spectral remote sensing reflectance (${R_{rs}}$) was consequently calculated from ${L_{WN - f/Q}}$ after band correction as follows:
where F0 is the extraterrestrial solar irradiance for each waveband [31]. Because of the unquantified uncertainties, measurements of ${L_{WN - f/Q}}$ at 870 and 1020 nm were not used [32].
Table 1. Detailed introductions of the 2 AERONET-OC sites: region, structure, location, distance from land, time period for validation, and number of level 2.0 measurements within the period
2.3. BGC-Argo data
Compared to the Level-3 Chla data of GlobColour, the Chla data measured by the biogeochemical Argo (BGC-Argo) float network exhibited a higher reliability. As the first ever near-real-time biogeochemical large-scale ocean observing system, the BGC-Argo float network can observe up to six critical biogeochemical and bio-optical variables: Chla, suspended particles, pH, oxygen, nitrate, and downwelling irradiance [33]. A total of 124 sea surface Chla profiles were obtained from BGC-Argo for the research areas, as shown in Fig. 1. Detailed information on the 4 selected BGC-Argo floats is provided in Table 2. Introductions of the detailed processing protocols can be found online (https://biogeochemical-argo.org). The frequency of profiling for each float was the daily level. In addition to matching the date, we selected the closest available pixel of PARASOL in a $3 \times 3$ pixel box near the BGC-Argo coordinates, which met the following criteria: (1) no cloud cover; (2) belonging to sea pixels; and (3) exhibiting more than 10 valid observation directions ($NViews\; \ge 10$) to ensure nonlinear least-squares optimization in the inversion.
Table 2. Details of the 4 BGC-Argo floats: the World Meteorological Organization platform number, average latitude, average longitude, average Chla, time period for validation, and number of measurements.
2.4. Evaluating indicators
In this study, we used several metrics to assess the algorithm performance with measured data: the root mean square error (RMSE), mean absolute error (MAE), mean error (ME), mean absolute percentage error (MAPE), and coefficient of determination (R2). These metrics can be computed as follows:
3. Development of the polarized atmospheric correction algorithm
The traditional NIR-based AC strategy [34], herein referred to as GW94, was primarily developed for clear open oceans. Similar to the assumption of the black ocean in the NIR band of GW94, we developed the Polarized AC algorithm built on the NIR band (PACNIR). The aerosol parameters were then retrieved by fitting the calculated TOA radiance to that observed from space using nonlinear optimization.
The vector radiance field of the coupled ocean–atmospheric system can be expressed by the Stokes vector as follows:
The total radiation collected by a satellite ocean color sensor at the TOA can be exhibited as follows, per Gordon and Wang [34]:
The forward model was designed according to PARASOL and AERONET-OC characteristics. A structure of the PACNIR in this research is shown in Fig. 2. Details of the methodology are presented in the following sections.
Fig. 2. General structure of the PACNIR algorithm. The f* refers to the TOA observations. The ap parameter represents the vector of retrieved parameters in the forward model, including the aerosol model and aerosol optical depth. Full names of abbreviations are as follows: NIR refers to near-infrared band; MBA is the moderate brute algorithm; NMSA represents the Nelder–Mead simple algorithm; PLUT means the atmospheric diffuse transmittance lookup tables of the vector water-leaving radiance.
3.1. Numerical inversion of the aerosol parameters
The numerical inversion process of PACNIR for the multiangular polarimeter involved the use of the moderate brute algorithm (MBA) and Nelder−Mead simple algorithm (NMSA) to obtain the minimal value of the cost function. In the numerical inversion module, the MBA was designed to traverse the predetermined AM lookup table. A “moderate” denotation indicated that the algorithm traversed only the AM, rather than specific aerosol microphysical characteristics, such as the aerosol particle size distribution and complex refractive index. Since most of the target sea areas in this study were oceanic sites far from land, the AM lookup table contained tropospheric and maritime AM data according to [37], and the percentage of the relative air humidity (RH) varied between 50% and 98% (step size = 2%). In each operation of the MBA, the AM approached a definite variable, and the AOD was further confirmed based on the NMSA. The NMSA [38] was described for the minimization of the cost function of n variables (in our study, n = 1), and it depends on comparing the function values at the (n + 1) vertices of a normal simplex and then replacing the vertex with the highest value at another point. Therefore, the NMSA method does not need to calculate the gradient of the radiative transfer equation, which consumes a large amount of time in the radiative transfer simulation process, and thus, less calculation time is needed relative to other nonlinear optimization algorithms based on the gradient of the function. Eventually, two sets of aerosol parameters were obtained, which were optimal and suboptimal matching parameter combinations. The final apparent water-leaving reflectance at the TOA could be determined as the weighted inverse sum of the corresponding cost functions:
3.2. Cost function
We defined the following ${\chi ^2}$ function as the cost function for inversion optimization:
3.3. Forward model
Figure 3 shows the structure of the forward model in this study. The Ocean Successive Orders with Atmosphere Advanced (OSOAA) radiative transfer model was applied to simulate the vector apparent reflectance at the BOA and TOA. The OSOAA model uses the plane-parallel layer assumption and successive-orders-of-scattering method to process the ocean–atmosphere coupled vector radiative transfer [39]. Moreover, the Shettle and Fenn AMs were used as tropospheric and maritime AMs, respectively, for simulation purposes, which consider the sensitivity of the size distribution and refractive index based on the relative air humidity [37]. The two predefined models were based on a mixture of elementary components in the OSOAA model.
Fig. 3. Vector radiative transfer simulations process for the atmospheric radiance observed by a satellite.
Oceanic regions far away from land were the target areas considered in this study, and their bio-optical properties are determined by phytoplankton [15]. The absorption and scattering coefficients of phytoplankton were estimated from the chlorophyll concentration (Chl) (in mg m-3) as follows [40,41]:
The scattering matrix of ocean water in our study can be written as:
Both the scaler and polarized radiances attributed to the water-leaving components were close to zero relative to the atmospheric portion in the NIR band [48]. Therefore, in this study, the ocean was assumed completely absorbing (${L_w},\; {L_{wc}} = 0,\; 0\; W \cdot {m^{ - 2}} \cdot n{m^{ - 1}} \cdot s{r^{ - 1}}$) in the NIR band, hence the black ocean term. Moreover, sun glint sea areas were masked from data analysis (${L_g} = 0\; W \cdot {m^{ - 2}} \cdot n{m^{ - 1}} \cdot s{r^{ - 1}}$). In addition, the radiance due to molecular scattering (${L_r}$) could be easily obtained through precalculated Rayleigh scattering lookup Tables [49]. Based on the prior calculation above, the vector radiance at the TOA (${L_t}$) is uniquely determined by the aerosol parameters in the NIR band, and aerosol parameters were then retrieved by matching the calculated TOA vector radiance to that measured from space using the inversion method of PACNIR.
3.4. Atmospheric diffuse transmittance of the vector water-leaving radiation
For polarization remote sensing over the ocean, the water-leaving radiance and its Stokes components (Iw, Qw, and Uw) at the BOA could be inverted according to the corrected water-leaving radiance at the TOA using the corresponding atmospheric diffuse transmittance (TI, TQ and TU). TI, TQ and TU can be nominally calculated as follows:
In our previous research [50], atmospheric diffuse transmittance lookup tables (PLUTs) of the vector water-leaving radiance for medium- to low-turbidity waters were constructed. Based on PLUTs, the vector water-leaving apparent reflectance ($n{L_{w,\; BOA}}$) at the BOA could be determined using the corresponding $n{L_{w,\; TOA}}$ value at the TOA.
3.5. Remote sensing reflectance
In the study of ocean color systems, the water-leaving signal is usually described by the spectral remote sensing reflectance defined as ${R_{rs}} = {I_{w,\; BOA}}/{E_{d,\; BOA}}$, where ${E_{d,\; BOA}}$ is the downward irradiance and ${I_{w,\; BOA}}$ is the upward water-leaving radiance at the BOA [51]. ${R_{rs}}$ can be inferred using the water-leaving apparent reflectance at the TOA ($n{I_{w,\; TOA}}$) as follows:
where $n{I_{w,TOA}}$ is the water-leaving apparent reflectance at the TOA defined in (9). The transmittance of downward irradiance ${t_{E,\; BOA}}$ indicates the solar irradiance from the TOA to the BOA: where ${E_d}$ is the solar irradiance at the BOA and ${\theta _0}$ is the solar zenith angle.To eliminate the dependence of ${R_{rs}}$ on the observation geometry, the BRDF, ${C_{BRDF}}$, was used to correct ${R_{rs}}$ so that it conformed to the observation results defined by [52] with a solar zenith and nadir direction as follows:
To extract ${R_{rs}}$ from multiangle PARASOL satellite data and compare it to the ${R_{rs}}$ calculation results of AERONET-OC, we only considered the apparent reflectance at the minimal ${\theta _v}$ value for each band and utilized PACNIR and BRDF correction as introduced above. For $\theta _v^\mathrm{^{\prime}}\; < 15^\circ \; ({{\theta_v} < 20^\circ } )$, ${{\Re }_0}/{\Re }$ approximated a constant value of 1, especially under low wind speeds, but when the value of ${\theta _v}$ was larger, the ratio increased with increasing W and ${\theta _v}$ [52,53]. In this study, we ignored ${{\Re }_0}/{\Re }$ in Eq. (20) because of the utilization of small W and ${\theta _v}$ values, but this might have caused underestimation of ${R_{rs}}$ relative to the ${R_{rs}}$ results of AERONET-OC, partly due to the black ocean assumption.
4. Results
4.1. Retrieval results on PARASOL measurements
To quantify the performance of PACNIR, we conducted retrievals using PARASOL data from 22 June 2011, the selected regions of which are far from land. Figure 4 shows indispensable parameter information of the PARASOL image selected to retrieve aerosol parameters, among which the Chla (mg m-3) and W (m s-1) data were obtained from the Level-3 products of GlobColour and WindSat, respectively. To improve the quality of the input data and reduce cloud decision errors, the selected points should satisfy the conditions whereby all parameters were associated with valid data and that each point occurred in the center of a $9 \times 9$ pixel window with no cloud cover. The mean view zenith angle (VZA) and mean solar zenith angle (SZA) of the pixels in Figs. 4(b) and 4(c) were basically under 70°, which indicated that the OSOAA model could achieve accurate simulations. Moreover, the variation in Chla and W in Figs. 4(e)–4(f) helped discriminate between the water-leaving radiance components in different regions, which made the final inversion results comparable among the different sea areas. Due to the lack of in situ data, we used the satellite-retrieved Chla from daily merged GlobColour Medium Resolution Imaging Spectrometer (MERIS)/Moderate Resolution Imaging Spectroradiometer (MODIS) products, which might contain uncertainty. Nevertheless, based on the validation results of the satellite-derived Chla product [54–56], the Chla data for the selected sea areas in Fig. 4 were expected to be suitable as input (the relative uncertainty in Chla product for the selected regions was ∼40%).
Fig. 4. Distributions of the given parameters involved in inversion. The sea area occurred in the region of 10 °N−20 °N and 140 °W−160 °W, in 22 June 2011. (a) Distribution of the cloud-free area, i.e., cloud indicator = 0; (b) distribution of the mean view zenith angle (VZA) of all directions (°); (c) distribution of the mean solar zenith angle (SZA) of all directions (°); (d) distribution of the mean relative azimuth angle (RAA) of all directions (°); (e) distribution of Chla (mg m-3); (f) distribution of W (m s-1).
The cloud-free regions in Fig. 4(a) denote the selected sea area used to validate the nIw, nQw, and nUw products retrieved from the PARASOL image by the proposed algorithm. Since PACNIR was applicable to tropospheric and maritime aerosol types, the sea areas used for result validation were mainly those far away from land and dominated by non-absorbing aerosols. References [57,58] confirmed that the selected regions are qualified. Figures 5 and 6 show the validation results processed by the PACNIR and VRTS algorithms, respectively, using the given parameters vs. the target regions in Fig. 4, and N is the number of verification points available for all valid directions for the 490 nm band. The linear regression slopes of the nIw, nQw, and nUw were 0.74, 0.83, 1.14, respectively, which were close to 1. The RMSEs and MAEs of them were on the order of 10−4 and were significantly lower than their mean values. It was clear that PACNIR performed well for the retrieval of nIw, nQw, and nUw.
Fig. 5. PACNIR results of (a) nIw, (b) nQw, and (c) nUw retrieved from PARASOL images vs. those calculated from GlobColour Chla data. The calculated results of nIw, nQw, and nUw were based on the 490 nm band, which contained abundant information on the water color components. The red line indicates the linear regression corresponding to the first equation in the upper left corner of each subgraph.
Fig. 6. Comparisons of nIw, nQw, and nUw retrieved based on Chla (top panels), PACNIR (middle panels), and corresponding mean errors (MEs) between the data (bottom panels) at 490 nm. (a), (d) and (g): retrieved nIw based on Chla, PACNIR, and ME; (b), (e) and (h): retrieved nQw based on Chla, PACNIR, and ME; (c), (f) and (i): retrieved nUw based on Chla, PACNIR, and ME.
One obvious advantage of PACNIR was that it inverted aerosol parameters based on the polarization information of NIR images, which confirmed the black ocean assumption, especially in waters dominated by phytoplankton (PDW) [48]. Site-specific validation results are shown in Figs. S1−S9 (see Supplemental Material). Compared to the VRTS-derived nIw values based on Chla, the PACNIR-derived nIw values were lower when the overall nIw value was small, which resulted from the black ocean assumption in the NIR band. Nevertheless, this problem was improved due to the addition of polarization information while the water color component signal increased, which made the inversion results more credible.
Due to the higher proportion of the water color signal in the TOA signal at 490 nm relative to that at 865 nm, we employed nIw, nQw, and nUw at 490 nm to obtain the distribution of the results, as shown in Fig. 6, and comparisons of the aerosol parameters from GlobColour and PACNIR at 865 nm are shown in Figs. 7 and 8. Figure 6 shows that PACNIR could suitably determine the spatial distribution characteristics of nIw, nQw, and nUw; notably, nIw, nQw and nUw decreased from north to south, from east to west, and from west to east, respectively. Moreover, the magnitude of ME was approximately 10−3 and was roughly evenly distributed throughout the inversion region, which reflected the prominent spatial applicability of PACNIR.
Fig. 7. Comparisons of the T865 from GlobColour and optimal and suboptimal T865 retrieved from PACNIR. (a) and (b) T865 and its error estimation from GlobColour; (c) and (d) the optimal and suboptimal T865 from PACNIR. (e) and (f) scatterplots of optimal and suboptimal T865 results.
Fig. 8. Aerosol model results of optimal and suboptimal inversion of PACNIR. (a) and (b) aerosol type. (c) and (d) RH results. T and M in (a) and (b) indicate tropospheric and maritime aerosol types, respectively.
Because of the lack of in situ aerosol measurements, we used the GlobColour T865 product to validate the accuracy of the PACNIR T865 results. Owing to the different transit times among the satellites, the cloud mask might be different; thus, the valid T865 points of GlobColour were not as dense as those of PACNIR retrieved from the PARASOL data in Fig. 7. Despite this limitation, considering the magnitude of error estimation of the GlobColour T865 product in Fig. 7(b) (∼67%), scatterplots between T865 of PACNIR and GlobColour presented the results of 0.05 (RMSE), 0.04 (MAE), 32% (MAPE). Moreover, from the perspective of the RH distribution, the RH in the cloud-intensive sea areas was high (∼90%), corresponding to the dark red regions in Figs. 8(c) and 8(d), while the RH in the clear sea areas was approximately 70%, corresponding to the yellow regions in Figs. 8(c) and 8(d). This occurred because cloud cover is positively correlated with the RH and large-scale vertical velocity [59,60]. Moreover, several areas were found to yield an approximately 50% RH, which corresponded to the areas with higher χ2 values in Figs. 9(a) and 9(b), respectively. This was likely caused by the dense cloud cover in these areas, which led to inaccurate masking and thus inaccurate inversion of the aerosol parameters. Figures 8(a) and 8(b) show that the study regions were primarily dominated by maritime aerosol types, while the tropospheric aerosol type generally emerged at the edge of cloud cover. Furthermore, these results indicated that accurate assessment of the cloud cover boundary is important for the inversion of aerosol parameters. This was one of the major reasons why we adopted the center point of $9 \times 9$ unclouded pixels to verify the accuracy of PACNIR so that many pixels subject to incorrect cloud determination could be excluded.
Fig. 9. Distributions of the cost function values (χ2) of the (a) optimal, and (b) suboptimal aerosol parameters
4.2. Validation of the retrieval results by AERONET-OC measurements
The red stars in Fig. 1 show the locations of the AERONET-OC stations applied to examine the ${R_{rs}}$ products calculated from PARASOL (2011 year) data. Due to the limitation of the PARASOL observation time and the limiting conditions of the AMs considered in our algorithm, we found that only the WaveCIS and LISCO sites provided enough valid data to verify the accuracy of the inversion algorithm among all the valid AERONET-OC sites. Figures 10−12 show the validation results processed by PACNIR, and N is the number of verification data available for the selected sites. The linear fitting results in the upper left corner of each subgraph indicated that the PACNIR-derived ${R_{rs}}$ values were smaller than the AERONET-OC ${R_{rs}}$ values when the ${R_{rs}}$ value was low. Nevertheless, the underestimation of ${R_{rs}}$ values was improved with increasing ${R_{rs}}$ value. We believed that this was due to the black ocean assumption in the NIR band, similar to the results of Fig. 5. Since we assumed that the total vector radiance at the TOA in the NIR band did not contain water color signals, which might not be valid when for turbid water (which often occurs near the shore), PACNIR would underestimate the water color signals and cause lower PACNIR-derived ${R_{rs}}$ values than AERONET-OC ${R_{rs}}\; $ values. However, due to the addition of polarization signals, the estimation of atmospheric signals in the NIR band was more accurate than that considering only scalar signals [61,62], which ameliorated the problem of water color signal underestimation, especially as the water color signals were enhanced.
Fig. 10. PACNIR results of ${R_{rs}}$ (Sr-1) calculated from PARASOL data vs. those calculated from AERONET-OC ${L_{WN - f/Q}}$ data at the (a), (c) WaveCIS site and (b), (d) LISCO site. The points shown in the red boxes were removed from (c) and (d) relative to (a) and (b), respectively.
The comparisons in Fig. 10 show that several PACNIR ${R_{rs}}$ values were higher than the corresponding AERONET-OC values. We suspected that this was due to the impacts of the AERONET-OC stations (i.e., shadow of the physical structure of station and its higher reflectivity), and the accuracy of inversion was greatly affected by these outliers. The MAPEs of the WaveCIS and LISCO sites could decrease by 9.94% and 5.64%, respectively, if the points in Figs. 10(a) and 10(b), respectively, were removed.
The T865 results in Fig. 11 supported our previous explanation of ${R_{rs}}$ underestimation by PACNIR, as shown in Fig. 11. Overestimation of aerosol scattering reduced the proportion of the water-leaving radiance at the TOA. Although the inversion values of T865 were overestimated at both stations, the MAPEs of the optimal inversion values of T865 at both stations were approximately 30%. Histograms of ${\chi ^2}$ for all the pixels calculated in each setting are shown in Fig. 12. The most likely ${\chi ^2}$ value of all the scenes was 0.03.
4.3. Validation of the retrieval results by BGC-ARGO measurements
Compared with the Level 3 Chla data of GlobColour, the Chla measured by the BGC-Argo float network is more reliable. High-precision input data are the foundation for assessing the model accuracy. Therefore, we simulated the corresponding nIw, nQw, and nUw values based on the surface layer Chla data of the 4 BGC-Argo floats and compared them with the PACNIR results. Moreover, PACNIR was applied to the AC process for the vector radiance data received by PARASOL at the TOA, and the PLUT was further consulted to continue the transmittance correction process for nIw, nQw, and nUw. The green dotted line in Fig. 1 shows the drift trajectories of the four selected BGC-Argo floats. The comparison results of all the observation directions are shown in Fig. 13, and the results for each direction are shown in Figs. S10−S12 (see Supplemental Material). Due to the limitation of the VRTS method used, which employs the plane-parallel layer assumption and successive orders of scattering method to process the ocean–atmosphere coupled vector radiative transfer, we eliminated the points with relatively large errors by excluding those with view zenith angles greater than 75°. In theory, with the plane-parallel layer assumption, due to the Earth’s curvature, a large viewing zenith angle could introduce a significant error [49], as shown in Figs. S10-S12 in the Supplemental Material.
Fig. 13. PACNIR results of (a) nIw, (b) nQw, and (c) nUw calculated from PARASOL images vs. those calculated from BGC-Argo Chla data.
The slope value (0.75) of linear regression shown in Figs. 14(a) and 14(b) showed the overestimation of the atmospheric aerosol optical thickness during inversion, which resulted in several negative values after AC, as shown in Fig. 13(a). Figure 14(c) shows that the most likely error estimate of the GlobColour's T865 products corresponding to the locations of BGC-Argo floats was over 60%, while the MAPE values of both Figs. 14(a) and 14(b) were approximately 52%. Considering the error estimates for the GlobColour T865 products, the retrieved aerosol optical thickness results of PACNIR were mostly within the error range. Figure 14(d) shows the AM inversion results of PACNIR, the RH of which was roughly consistent with the mean relative humidity distributions in the target regions, as determined in a previous study [63]. In addition, the most likely ${\chi ^2}$ values of the optimal and suboptimal inversion results were approximately 0.009, as shown in Fig. 15, which are in the appropriate range relative to the magnitudes of nIw, nQw, and nUw.
Fig. 14. T865 results of (a) optimal and (b) suboptimal inversion of PACNIR vs. the GlobColour T865 product; (c) error estimation results of GlobColour's T865 (%); (d) aerosol model results of optimal (x-axis) and suboptimal (y-axis) inversion of PACNIR. The origin coordinate corresponded to $RH = 50\%$, and the closed circles denote the Gaussian kernel density estimation of each float’s aerosol model.
5. Discussion
5.1. Computation efficacy of the algorithm
The strategy of retrieving AMs rather than individual aerosol parameters greatly reduced the inversion time. With approximately 14 valid observation directions for each pixel, the mean calculating speed for one point with PACNIR was approximately 5 minutes with a single CPU core (AMD Ryzen 7 5800 H). Compared to the retrieval speed of more than 30 minutes per pixel when considering the aerosol complex refractive index and particle size distribution separately, the computational acceleration was 6 times greater with a single CPU core. Moreover, the inversion speed of aerosol parameters could be improved with increasing observation directions of the pixels. This was apparently due to the addition of more constraints in the model inversion process so that the nonlinear optimization process could converge faster.
In the inversion process of the aerosol parameters, the iterative calculations of the VRTS model required the most time. In this study, we reduced the number of calculations of the VRTS model as much as possible by combining the MBA and NMSA. Moreover, in addition to optimizing the number of calculations, the inversion algorithm for aerosol parameters could be accelerated by reducing the calculation time of the single VRTS model. There are several methods to lower the computational cost of VRTS during AC, including simplifying the VRTS method [9,64] and using machine learning models to encapsulate the VRTS method [20], which could be used for further optimizing the PACNIR computational speed in the next step.
5.2. Explanations regarding the assumptions in the inversion
As shown in Fig. 3, the vector radiance attributed to water component signals was assumed to be zero in the NIR band, while VRTS processing was verified to remain stable under the conditions of phytoplankton dominated waters (PDW). According to Zhai et al. [48], in the PDW, the fraction $\eta = 100 \cdot \rho _w^{\prime}/{\rho _t}$ was approximately 2% or less at wavelengths smaller than 354 nm or larger than 760 nm, and the contributions of the corresponding polarized water-leaving radiances to the TOA polarized radiances were generally less than 1%. Through this assumption, the aerosol parameters could be conveniently deduced from the satellite vector radiances at the TOA. However, we still found that the algorithm overestimated the atmospheric radiance when the magnitude of the water-leaving radiance was small at 490 nm. This was probably due to the presence of nonalgal particles in the real water environment, which imposed a strong backscattering effect, thus challenging the assumption. When the magnitude of the 490 nm water-leaving radiance was increased, the inversion accuracy of the water-leaving radiance was improved because of the further enhancement in equation constraints, which resulted from the improved inversion of the atmospheric components due to the addition of polarized radiances. Moreover, since the hyperangular HARP−2 sensor in the PACE provides more measurements of different observation directions in the NIR band, this could greatly help the inversion of the polarized water-leaving radiances.
5.3. Limitation of radiative transfer simulation validation
In this study, we applied a vector radiative transfer model, namely, OSOAA, for a coupled atmosphere–ocean system to process the nonlinear optimization in the PACNIR algorithm. Currently, due to the lack of in situ polarized water-leaving radiance data and unavailability of on-orbit polarization satellites, the performance of the proposed polarization AC algorithm was examined by using the simulated polarized water-leaving radiance with the input of in situ Chla and W. This has limitations in terms of rigorous validation, as such a method belongs to indirect validation. Nevertheless, under the current conditions with no available on-orbit polarization satellite, validation by comparing the polarized water-leaving radiance data retrieved from the historical PARASOL satellite and the radiative transfer simulations with the input of in situ parameters is indeed a practical method. In fact, a large number of studies have supported the consistency between the polarized water-leaving radiance simulated by the vector radiative transfer model and field-measured values. For example, Liu et al. [65] designed an above-water instrument to directly measure the polarized water-leaving radiance and found that the Stokes components of the measured water-leaving radiance were consistent with those of the radiative transfer simulation results of the PCOART model, with a determination coefficient and mean relative error of 0.67 and 18.86%, respectively. Ottaviani et al. [66] successfully reproduced the polarization properties measured by two polarimeters (the shipborne HyperSAS-POL and airborne RSP sensors) by vector radiative transfer simulations at the selected sites during the Ship-Aircraft Bio-optical Research (SABOR) cruise. Moreover, the verification of the retrieval algorithm using radiative transfer simulations is a common method in the absence of in situ data. For example, Gao et al. [20] developed an algorithm for aerosol and ocean color retrieval, which was validated against synthetic data generated by a vector radiative transfer model. In this study, we validated the model-retrieved polarized water-leaving radiance with vector radiative transfer simulations, and to compensate for the lack of verification of the polarization water-leaving radiance, we also used in situ data of AERONET-OC to verify the retrieved scalar water-leaving radiance and aerosol optical thickness.
OSOAA is not suitable for pixels with large satellite viewing zenith angles because of the plane-parallel layer assumption. Thus, cases in which the sensor's viewing zenith angles were greater than 75° were mostly eliminated in this study. After all, the VRTS accuracy was the basis of the prominent performance of the PACNIR inversion process. Moreover, Figs. 4(b) and 9 show that the pixels with large ${\chi ^2}$ values mostly corresponded to the regions with relatively large satellite viewing zenith angles. This made the inversion results of the algorithm slightly unstable in pixels with relatively large VZAs; notably, the uncertainty in the AC inversion results would increase, which was probably due to ignoring the effects of the Earth’s curvature. Considering the Earth’s curvature effects, we recommend the PCOART-SA model [49] as the VRTS model in the next version of the PACNIR.
6. Summary
In this study, we designed a novel algorithm, namely, PACNIR, based on the black ocean assumption in the NIR band to retrieve polarized water-leaving radiances. PACNIR first utilized the MBA to traverse the predetermined AM lookup table. Then, in each operation of the MBA, the AOD was further confirmed based on the NMSA. Moreover, an essential assumption in our optimization algorithm was the black ocean assumption in the NIR band, which is consistent with the traditional scalar water-leaving radiance AC algorithm, but we further extended it to the field of polarized water-leaving radiances. In addition to creatively adding a moderate brute step to the optimization algorithm, we focused on the AM rather than the individual aerosol parameters, both of which made the AC process acceptably time-consuming.
The vector water-leaving apparent reflectance retrieved by PACNIR from PARASOL data was validated using the VRTS results based on the Chla products of GlobColour and in situ Chla measurements of BGC-Argo floats. Moreover, the PACNIR-derived remote sensing reflectance (Rrs) results were compared with the Rrs values derived from the field measurements of AERONET-OC stations. The vector water-leaving apparent reflectance ($n{I_w}$, $n{Q_w}$, and $n{U_w}$) derived by PACNIR exhibited a highly consistent spatial distribution with that of the simulated VRTS results based on input Chla data. Compared with the $n{I_w}$, $n{Q_w}$, and $n{U_w}$ values simulated from the Chla measurements of the BGC-Argo floats, the vector water-leaving apparent reflectance was reliably retrieved with an R2 value over 0.57 and an RMSE of approximately 0.001 for $n{I_w}$, $n{Q_w}$, and $n{U_w}$. In addition, the Rrs results retrieved by PACNIR were consistent with the in situ values of AERONET-OC sites RMSE of approximately 0.002 after removing abnormal values. The retrieved T865 also exhibited good accuracy with RMSE less than 0.015 and MAPE less than 31%. Overall, these preliminary validation results showed that PACNIR was encouraging for the atmospheric correction of polarization satellite data. More comprehensive studies for reducing the consumption of PACNIR and testing algorithm are planned in the future.
Funding
National Natural Science Foundation of China (41825014, 42176177, U22B2012); Natural Science Foundation of Zhejiang Province (LDT23D06021D06); "Pioneer" Research and Development Program of Zhejiang (2023C03011).
Acknowledgments
AERONET-OC PIs Sam Ahmed, Alex Gilerson, and Sherwin Ladner are duly acknowledged for their continuous effort in maintaining the network and running the sites. The BGC-ARGO data are collected and provided free of charge by the International Argo Program and the national programs involved in the project (http://www.argo.ucsd.edu, http://argo.jcommops.org). The BGC-Argo Program is part of the Global Ocean Observing System. We also thank the staff of the satellite ground station, satellite data processing and sharing center, and marine satellite data online analysis platform of the State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources (SOED/SIO/MNR), for their help in data collection and processing.
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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