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Abstract
The polarization characteristics of water-leaving radiation contain rich information on oceanic constituents. Determining the atmospheric diffuse transmittance is crucial for extracting the polarization information of water-leaving radiation from the radiation acquired by polarimetry satellites at the top of the atmosphere. However, there is still a lack of understanding of the atmospheric diffuse transmittance of the linear polarization component of water-leaving radiation. Here, we first evaluated the difference between the atmospheric diffuse transmittance of the linear polarization component (TQ, TU) and the intensity component (TI) of the water-leaving radiation based on the Ocean Successive Orders with Atmosphere Advanced radiative transfer model. As a consequence, there were apparent differences between TQ, TU and TI. In the case of a large solar zenith angle and a large viewing zenith angle, the difference between TQ, TU and TI will exceed 1. Meanwhile, compared with TI, the oceanic constituents had a prominent interference with TQ and TU, and the sediment concentration had little interference with TQ and TU in low- and medium-turbidity water with respect to the aerosol model, optical thickness, observation geometry, and phytoplankton. Moreover, TQ and TU lookup tables were generated for medium- and low-turbidity water, which laid the foundation for extracting the water-leaving radiation polarization information from the satellite observation polarization signal.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The polarization component of water-leaving radiation is abundant in the optical properties of the ocean and has a crucial value for quantitative remote sensing of ocean color [1–3]. The linear polarization components of water-leaving radiation are widely used to detect sea surface roughness, wind speed and other information about the sea state [4–6] and to suppress or strip sun glint based on the polarization difference of the sea surface at the Brewster angle [1,7]. Moreover, the particles scattered in water will change the polarization state of the incident light, so the polarization characteristics of water-leaving radiation can reflect the water substance composition properties [2,3,8–10]. Previous studies have shown that the polarization property of water-leaving radiation is helpful in inverting the concentration of the suspended particles [9,11] and the inherent optical quantities (absorption coefficient, scattering coefficient, and absorption attenuation ratio, etc.) [12,13] in turbid water, which can also be used to further distinguish inorganic and organic particles [14–16]. Consequently, the polarization component of water-leaving radiation is sensitive to the microscopic optical properties of the particles in water (such as size, refractive index, shape, etc.). In addition, combined with the simulation results of the vector radiative transfer model and the field measured data, the polarization signal of water-leaving radiation and those measured by satellite sensors at the top of atmosphere (TOA) can be compared [17,18] to retrieve the characteristic parameters of aerosols [19,20]. In general, the polarization component of water-leaving radiation provides a new direction for ocean color research, which is a valuable addition to the research on passive oceanic remote sensing based on the intensity-only method.
Due to the great application potential of polarization observations for oceanic quantitative remote sensing, several satellites with polarization sensors have been launched, such as ADEOS-I/POLDER-1 (1996.11 − 1997.6) [21], ADEOS-II/POLDER-2 (2003.4 − 2003.9) [22] and PARASOL (2004.12 − 2013.12) [23]. At the same time, satellites equipped with the new generation of multidirectional, multiangle polarization sensors, such as “Plankton, Aerosol, Cloud, ocean Ecosystem mission (PACE)” (National Aeronautics and Space Administration, NASA) [24] and “Multidirectional, Multipolarization and Multispectral (3MI)” (European Space Agency, ESA) [25], will be launched in the future. Atmospheric correction is essential for extracting the polarization signal of water-leaving radiation from the raw data received by satellite, and determining the atmospheric diffuse transmittance is an important step. Loisel et al. [17] showed that the polarized remote sensing reflectance could be measured from space over bright waters without aerosols and compared the linear polarization degree, DoLP, over two oceanic areas characterized by different nature of the bulk particulate assemblage and confirmed the sensitivity of the POLDER-2 DoLP values to the nature of the particulate assemblage. Chowdhary et al. [18] constructed the relationship between the reflectance and colored dissolved organic matter using airborne research scanning polarimeter data at different heights. Harmel and Chami [26] determined the sea wind speed based on PARASOL data after atmospheric correction and further compared it with the wind speed products of “The Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E)” (NASA) and found that the inversion accuracy was greatly improved. He et al. [27] proposed the concept of parallel polarization radiation (PPR), and the comparison results of vector radiative transfer simulation and POLDER-2 satellite data showed that compared with using the intensity-only method to invert the normalized water-leaving radiation, PPR could effectively suppress solar glint and improve the signal-to-noise ratio. However, despite a large number of previous studies on the use of the polarization property of the water-leaving radiation, most studies still used the assumption that the atmospheric diffuse transmittance corresponding to the linear polarization component of the water-leaving radiation was equal to that corresponding to the scalar component of the water-leaving radiation [17,18,26] or ignored the contribution of the water-leaving radiation to the polarization signal at the TOA [27]. At present, there are few studies on the atmospheric diffuse transmittance of the linear polarization component of water-leaving radiation under different ocean-atmospheric conditions.
In this study, we simulated the variation in the atmospheric diffuse transmittance of the polarization component of water-leaving radiation with the following parameters: the water optical factor, observation geometry, and atmospheric optical thickness. First, the disparity between the atmospheric diffuse transmittance of the linear polarization component (TQ and TU) and the intensity component (TI) of the water-leaving radiation was compared and analyzed. Then, we analyzed the variation in TQ and TU under different ocean-atmospheric environment conditions and identified the main influencing factors. Moreover, according to the main influencing factors, the atmospheric diffuse transmittance lookup table of the Stokes linear polarization component of the water-leaving radiation was accurately constructed.
2. Theoretical background
2.1 Concept of atmospheric diffuse transmittance of the polarization component of water-leaving radiation
The vector radiation field of the coupled ocean-atmospheric system can be expressed by the Stokes vector, as follows:
The atmospheric diffuse transmittance of the polarization component of the water-leaving radiation is defined as the ratio of the polarization component of the water-leaving radiation at the bottom of atmosphere (BOA) to TOA under the interference of atmospheric diffusion [29]. For polarization remote sensing above the ocean, the water-leaving radiation and its Stokes components (Iw, Qw, Uw) at the BOA can be inverted according to the satellite remote sensing data at the TOA.
For the calculation of the TI, TQ and TU, we defined the nominal transmittance to make it convenient for the calculation of the Stokes components at the BOA:
When we get the contribution of water-leaving radiation at the TOA, we can obtain the linear polarization component of water-leaving radiation at the BOA through the nominal definition of transmittance using Eqs. (2–4). The denominator of Eqs. (2–4) corresponds to the water-leaving radiation at the BOA, and the numerator corresponds to the water-leaving radiation at the TOA, which can be expressed as follows:
where “bg” corresponds to the background radiation values caused by atmospheric scattering and absorption when the underlying ocean is total absorption.2.2 Radiative transfer simulations
In this study, the Ocean Successive Orders with Atmosphere Advanced (OSOAA) radiative transfer model was applied to simulate the atmospheric diffuse transmittance of the linear polarization part of the water-leaving radiation at the BOA and TOA. OSOAA uses the plane-parallel layer assumption and successive-orders-of-scattering method to process the ocean-atmosphere coupled vector radiative transfer [30], and it might be inaccurate at high solar zenith angle or high viewing zenith angle (e.g., larger than 60°) because of the assumption for the AOS. The atmospheric diffuse transmittance was calculated by two-step OSOAA simulation, including one for the background with the atmosphere and a “Black ocean” (i.e., the ocean was assumed to be total absorption), the other with the atmosphere, seawater with various optical properties. The partial input parameter settings of the two simulations are shown in Tab. 1 [31–33]. Aiming to simulate the “Black ocean” condition, sea depth value, Adet(440) and Ays(440) were set as 0.05 m, 100000 m-1 and 100000 m-1 in the “Black ocean” simulation to approach the total-absorption ocean. In the “Ocean-atmospheric conditions” simulation, five parameters in Table 1 were taken as different values in their range to explore :different ocean-atmospheric conditions.
Table 1. Partial input parameter settings of the radiative transfer simulation.
Combined Eqs. (2–7), the atmospheric diffuse transmittance of Stokes vectors can be calculated as follows:
where L1 and L2 represent the Stokes vectors obtained from the “Black ocean” and “Ocean-atmospheric conditions” simulations, respectively, and “TOA, BOA” correspond to the Stokes vectors at the TOA and BOA, respectively.The key impact factors of TL are determined by calculating the relative error of TL with different ocean-atmospheric parameters. The parameters considered include the aerosol model (Shettle and Fenn Model, SFM) [35], aerosol optical thickness (τa), solar zenith angle (SZA or θs), viewing zenith angle (VZA or θv), relative azimuth angle (φ), chlorophyll concentration (Chla), sediment concentration (Csed), the absorption coefficient of yellow substance at 440 nm (Ays(440)) and absorption coefficient of detritus at 440 nm (Adet(440)). At the same time, the influence mechanism of marine optical properties (clean water, productive water, and turbid water) on atmospheric polarization diffuse transmittance is discussed.
2.3 Evaluating indicators
The evaluation indicators applied in this study include the relative error (RE), root mean squared error (RMSE), and coefficient of determination (R2), as shown in the following equations:
3. Results
3.1 Differences among TI, TQ, and TU
The atmospheric diffuse transmittance of the I component (TI) is mainly determined by atmospheric molecules and aerosols. By affecting the bidirectional distribution of I below the ocean surface, the optical properties of the ocean also interfere with TI [36]. Previous studies have rarely included a systematic analysis of the impacts of ocean optical properties on TQ and TU. Figures 1 and 2 show the distributions of TI, TQ, TU corresponding to clean water (CW), productive water (PW), and turbid water (TW) under M99 and M50 aerosol models, respectively. The aerosol model here is expressed in the form of “aerosol type + percentage of air relative humidity (RH)”. For example, M99, T50, C60, and U99 mean the maritime aerosol type with RH being 99%, tropospheric aerosol type with RH being 50%, coastal aerosol type with RH being 60% and urban aerosol type with RH being 99%, respectively. The key parameters of CW, PW and TW in this study are shown in Table 2. To make it clearer of the impact of the scattering term on TQ and TU, the values of Chla (mg m-3), Adet (m-1) and Ays (m-1) are set as zero in TW. In the follow-up simulations, θv is directly output by OSOAA (0–90°, and the step size is approximately 2°). θv is zero for the sensor looking vertically downward. The relative azimuth angle (φ), ranging from 0° to 180°, corresponds to the azimuth difference between the solar and the observation plane. As an example, an azimuth difference of 180° corresponds to that the half solar plane containing the sun and sensor are similar, then an azimuth difference of 0° corresponds to the specular plane where the sun and the sensor are located in two opposite planes. The step size of φ is 3° in Figs. 1 and 2, and 20° for other figures.
Fig. 1. The spatial geometric distributions of TI, TQ and TU under M99. The simulated wavelength was 0.565 µm. θs was 15°. The range of θv was 0–90°. The range of φ was 0–180°. τa was [0.01, 0.10, 0.30, 0.50]. The polar coordinate axis label and scale reference the subgraph of (CW, TI, τa = 0.01).
Table 2. Partial input parameter settings of the radiative transfer simulation.
Compared with Figs. 1 and 2, when the SFM and water type were unchanged, TQ and TU had a decreasing trend with increasing τa, especially in the part of θv close to 90°, and there was an apparent decreasing trend of polarization diffuse transmittance. In the case of TW, the decrease in transmittance even approached 1.0 (e.g., subgraph (TW, TQ, τa = 0.5)). Moreover, when SFM and τa remained unchanged, only the water type varied, and TI remained almost the same, but TQ and TU changed distinctly with the change in water type at some angles. TQ and TU remained basically unchanged when θv was close to 0° and the water type was CW or PW. However, the decreasing trend of TQ and TU was obvious in the case of TW. Meanwhile, when θv was approximately 15°, that is, at the position where the sun glint occurred, TQ and TU in TW also had obvious high or low value anomalies. On the other hand, when the water type remained unchanged and the aerosol model switched from M99 to M50, TQ and TU also demonstrated clear changes; especially in the part of θv close to 90°, TQ demonstrated a trend changing from positive to negative. It is worth noting that, when comparing M99 with M50, the diffusion transmittance of the linear polarization components of the water-leaving radiation had similar spatial geometric distributions. In general, TI ≠ TQ ≠ TU, and each of them was affected by the water type, aerosol model and optical thickness. Compared with TI, water type interferes more prominently with TQ and TU.
3.2 Main influencing factors of TQ and TU
The previous section showed that TI ≠ TQ ≠ TU, and TQ and TU would change significantly with the water composition. To explore and confirm the key impact factors affecting the spatial geometric distributions of TQ and TU, we used the evaluation index of Eq. (9) to analyze the effects of different ocean-atmospheric parameters on the atmospheric diffuse transmittance of water-leaving radiation. The parameters include the aerosol model (SFM), aerosol optical thickness (τa), solar zenith angle (θs), viewing zenith angle (θv), relative azimuth angle (φ), chlorophyll concentration at the sea surface (Chla), concentration of sediment at the sea surface (Csed), absorption coefficient of yellow substance at 440 nm (Ays(440)) and absorption coefficient of detritus at 440 nm (Adet(440)).
3.2.1 Aerosol model and aerosol optical thickness
Figure 3 shows the relative changes in TQ and TU with respect to TI to analyze and compare the influence of SFM (SFM = M99/50) and τa (τa = 0.01, 0.10, 0.30, 0.50) on TQ and TU. The calculation formulas were as follows:
Fig. 3. The spatial geometric distributions of REQ|I and REU|I varied with water type and τa under (a) M99 and (b) M50. The simulated wavelength was 0.565 µm. θs was 15°. The range of θv was 0–90°. The range of φ was 0–180°. The polar coordinate axis label and scale reference the subgraph of (CW, REQ|I, τa = 0.01).
As shown in Fig. 3, while the SFM remained the same, the variation in τa significantly impacted TQ and TU, and the amplitude change of TQ was visibly greater than that of TU. Especially in the part of θv ≥ 60°, the closer to 90°, the more highlighted the change of TQ and TU appeared relative to TI. When τa remained constant and only the SFM changed, the changes in TQ and TU were more obvious in the part of θv ≥ 60°, such as TQ and TU corresponding to (PW, τa = 0.50) at different SFM values. In reality, this also verified that the distributions of TQ and TU were closely related to the aerosol optical properties [29], and SFM and τa were the main impact factors of TQ and TU. More results about SFM = U99/50, T99/50, C99/50, can be found in Figs. S1-S3 in Supplement 1.
3.2.2 Solar-satellite observation geometry
SFM (SFM = M99/50) and τa (τa = 0.15) were set, and Fig. 4 shows the variation in REQ|I and REU|I with different spatial geometric distributions of θs. Results of SFM = U99/50, T99/50, C99/50 can be found in Figs. S4-S6 in Supplement 1. The diagrams showed that the variation in REQ|I with varying θs values was more prominent than that of REU|I, especially at the angle of sun glint. Simultaneously, as the water optical properties remained in a fixed state, the absolute value of the overall distribution of REQ|I seemed to increase with increasing θs. When θv ≥ 60°, REQ|I changed from positive to negative as θv continued to increase. In contrast, compared with REQ|I, in the range of θv ≤ 60°, the variation in the spatial geometric distribution of REU|I was not obvious and was close to 0, that is, TU ≈ TI, so the spatial geometric distributions of TU and TI were similar and had apparent two-dimensional distribution characteristics. In short, the above results distinctly showed that the solar-satellite observation geometry was the key factor influencing TQ and TU.
Fig. 4. The spatial geometric distributions of REQ|I and REU|I varied with θs under (a) M99 and (b) M50. The simulated wavelength was 0.565 µm. The aerosol optical thickness was 0.15. The solar zenith angle was [5°, 15°, 30°, 50°]. The polar coordinate axis label and scale reference the subgraph of (CW, REQ|I, SZA = 5°).
3.2.3 Ocean-color components
According to the above results, the spatial geometric distributions of REQ|I and REU|I in CW and PW were extremely similar. Figure 5 shows the RE distributions of PW and TW relative to CW under the conditions of SFM = M99/50:
where TQ1 and TU1 represent the atmospheric diffuse transmittance of the Q and U components corresponding to CW, respectively. Meanwhile, RE distributions of PW and TW relative to CW under conditions of SFM = U99/50, T99/50, C99/50 could be found in Figs. S7-S9 in Supplement 1.Fig. 5. The spatial geometric distributions of ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$ varied with τa under (a) M99 and (b) M50. The simulated wavelength was 0.565 µm. θs was 15°. The polar coordinate axis label and scale reference the subgraph of (PW-CW, ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$, τa = 0.01).
Based on Fig. 5, the comparative analysis showed a visible approximate equal relationship between TQ and TU of PW and CW, especially regarding TU. However, this equal relationship clearly weakened among the TQ and TU of TW and the other two water types, especially when θv approached 90°, and there was a relatively large RE value between TW and the other two water types. According to the parameter values of the key components of CW, PW, and TW (Table 2), when three water types with different optical properties were used to carry out the simulation, the differences in the water color components were basically due to Chla, Csed, Ays(440) and Adet(440). Since REQ|I ≈ REU|I ≈ 0 between CW and PW, the results indicated that the different parameters of CW and PW were not the key factors affecting the TQ and TU values and their distributions. Logically, it was further speculated that the key factor affecting TQ and TU was Csed.
To confirm our hypothesis, we summarized the two obvious distribution features in Fig. 5 and judged the key impact factors of TQ and TU by whether the two characteristics also evidently appear in the simulation process. On the one hand, when ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$ were close to 90°, due to the extension of the atmospheric transmission path, there was a visibly high value of RE, especially in TW-CW. In addition, near the observation geometry in which sun glint was produced, such as (θv = 15°, φ = 0°), local extremely high or low RE values appear in ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$.
By changing the optical input parameters of the bio-optical part in OSOAA, TQ and TU were simulated to judge the main control factor of its spatial geometric change. The input parameters of the bio-optical model in the radiative transfer model corresponding to the following four cases are shown in Table 3:
- (a) Case I: To judge the impact of Chla on TQ and TU. TQ1 and TU1 correspond to the TQ and TU at Chla = 0.10 mg m-3, respectively. In the simulation of TQ1 and TU1, Chla could take any of the four values, which had little effect on the distribution of the results of Eqs. (14) and (15). The same applies below.
- (b) Case II: To judge the impact of Csed on TQ and TU. TQ1 and TU1 correspond to the TQ and TU at Csed = 10 mg L-1, respectively.
- (c) Case III: To judge the impact of Ays(440) on TQ and TU. TQ1 and TU1 correspond to the TQ and TU at Ays = 0.10 m-1, respectively.
- (d) Case IV: To judge the impact of Adet(440) on TQ and TU. TQ1 and TU1 correspond to the TQ and TU at Adet = 0.10 m-1, respectively.
Table 3. Parameter settings of the water component inputs of the four cases.
Figure 6 shows the spatial geometric distribution of ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$ with different Chla under the SFM of M99/50. Distributions of SFM = U99/50, T99/50 and C99/50 can be found in Figs. S10-S12 in the Supplement 1. Apparently, changing the Chla could produce an extreme value near the sun glint geometry, which is similar to the findings of Fig. 5. However, when θv approached 90°, there was no visibly extreme value in RE. This indicated that Chla was not the key parameter controlling TQ and TU.
Fig. 6. The spatial geometric distributions of ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$ varied with Chla under M99 and M50. The simulated wavelength was 0.565 µm. The solar zenith angle was 15°. The aerosol optical thickness was 0.15. The polar coordinate axis label and scale reference the subgraph of (M50, ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$, Chla = 0.01 mg m-3).
Figure 7 displays the spatial geometric distribution of ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$ with various values of Csed. Other results of SFMs same with that of Chla are shown in Figs. S13-S15 in the Supplement 1. The diagrams showed that ${\rm{R}}{{\rm{E}}_{Q|{Q_1}}}$ and ${\rm{R}}{{\rm{E}}_{U|{U_1}}}$ had extreme values while θv approached 15° and 90°, corresponding to the features in Fig. 5. This further confirmed that Csed was indeed one of the key impact factors of TQ and TU. In Figs. 8 and 9, extremums were not generated by changing Ays(440) and Adet(440), which could also be found in Figs. S16-S21 in Supplement 1, indicating that these two parameters were not the main parameters controlling the distributions of TQ and TU.
Based on Figs. 6–9, we concluded that the main factor affecting TQ and TU among the four water optical parameters was Csed. For medium-low turbidity water, i.e., Csed was relatively low, the inherent optical properties were mainly determined by Chla [37–39]; since Chla was not the main parameter impacting TQ and TU, TQ and TU were not greatly affected by the water optical parameters.
3.3 Construction of TQ and TU lookup tables
The analysis of the variation patterns of TQ and TU with various optical parameters in the coupled ocean-atmospheric system was the basis for the operational calculation of the Stokes vectors of the water-leaving radiation above the water surface based on oceanic polarization remote sensing data. Therefore, high-precision TQ and TU lookup tables were essential. The above results showed that the key water optical factor affecting TQ and TU was Csed, while the atmospheric diffuse transmittance of the linear polarization component of the water-leaving radiation corresponding to the medium-low turbidity water was not greatly affected by the water optical parameters, which provided a possibility for constructing lookup tables of TQ and TU of the water-leaving radiation suitable for the vector atmospheric correction algorithm of the medium-low turbidity water.
The bands used to construct the TQ and TU lookup tables corresponded to the 0.441 µm and 0.549 µm bands of the HARP2 sensor on the PACE satellite [40]. The aerosol model adopted the Maritime and Tropospheric model summarized by Shettle and Fenn [30,35], and RH values were 50%, 70%, 80%, 90%, and 98%. The aerosol optical thickness range was 0–0.40, with an interval of 0.02. The range of θs of incident light was 0–80°, and the interval was 2°. The range of φ was 0–180°, and the interval was 5°. The output of OSOAA was adopted for θv.
According to Section 3.2, considering that the simulation wavelength (λ) would affect SFM and τa, six parameters were summarized as the input parameters of the TQ and TU lookup tables for medium-low turbidity water (Table 4). The final lookup table of TQ and TU for medium-low turbidity water could be expressed as ${T_Q}({2 \times 10 \times 21 \times 41 \times 37 \times 51} )$ and ${T_U}({2 \times 10 \times 21 \times 41 \times 37 \times 51} )$, where $2 \times 10 \times 21 \times 41 \times 37 \times 51$ represented $\lambda \times SFM \times {\tau _a} \times {\theta _s} \times \varphi \times {\theta _v}$.
Table 4. Input parameters of the TQ and TU lookup table for medium-low turbidity water.
4. Discussion
In this study, comparisons of TQ and TU under various ocean-atmospheric conditions showed that in the chlorophyll-dominated water body (e.g., CW and PW), the change in Chla interfered little with the distributions of TQ and TU. In other words, TQ and TU were not sensitive to Chla. In summary, there were two primary reasons for this outcome. On the one hand, compared with the polarization operation caused by the effect of refraction and reflection at the ocean-atmospheric interface and the scattering of atmospheric particles (especially atmospheric molecules and aerosol particles), the change in the linear polarization state resulting from the influence of the scattering of phytoplankton particles was relatively weak [15,23]. Therefore, the Qw and Uw at the TOA corresponding to the contribution of phytoplankton particles were further diminished [9,17]. On the other hand, the linear polarization component of water-leaving radiation would be significantly depolarized after atmospheric transmission [29], resulting in further weakening of the impact of changes in Chla; thus, the variation in Chla had little impact on TQ and TU (Fig. 6). Therefore, while setting the polarization channels in the oceanic satellite sensor, the aerosol model could be better estimated by combining the polarization with scalar water-leaving radiation, and the current operational atmospheric correction algorithm could be further optimized [15,41,42].
Compared with CW and PW, the TU and TQ of TW dominated by inorganic particles were highly impacted by Csed (Figs. 5 and 7). The field experiments [11,43] and the theoretical derivation of radiation transmission [9,44,45] also showed that the linear polarization component of the water-leaving radiation was sensitive to the change in Csed. This was basically because inorganic particles had strong backscattering and prominent scattering depolarization effects [9,17]. Simultaneously, the polarized light field under water was affected by the single scattering of particles in water and its own directionality. When Csed increases, the amount of scattering of natural light in water increases synchronously, which weakens the underwater radiation directionality and, thus, depolarizes the light exiting water [43]. Moreover, the radiative transfer simulation results in our research showed that the scattering of sediment in TW was stronger than that in CW and PW, and the change in the linear polarization component of water-leaving radiation caused by sediment was further reflected in the polarization signal received at the TOA although diffuse attenuation of atmospheric particles existed. It also explained that the spatial geometric distributions of TU and TQ would vary greatly with Csed in the above simulation results. Furthermore, due to the large influence of Csed on the linear polarization component of water-leaving radiation, it could be used to invert the Csed and other inherent optical parameters in nearshore and turbid water [12,15].
Moreover, for turbid water, besides the same six parameters considered in medium-low turbidity waters, Csed will become one of the essential factors while constructing lookup tables of TQ and TU. However, due to the large changeable range of Csed (0-2000 mg L-1), a small iteration step for all cases would not be an acceptable method to carry out. Therefore, we would like to use unequal step lengths to build lookup tables for Csed, for instance a small step (5 mg L-1) of Csed for the rapidly changing regions of TQ and TU, and a rough step (100 mg L-1) for the almost unchanged regions of TQ and TU.
5. Conclusion
In this study, we explored the major control factors and the spatial geometric distribution pattern of the atmospheric diffuse transmittance of the linear polarization component of water-leaving radiation and constructed TU and TQ lookup tables for medium-low turbidity water. First, we simulated the vector radiative transfer under several aerosol models and water types and found that the atmospheric transmittances corresponding to I, Q and U were not equal. Then, the effects of nine parameters, including SFM, τa, θs, θv, φ, Chla, Csed, Ays(440) and Adet(440), on TQ and TU were calculated and compared. The analytical results showed that the key factors affecting the spatial geometric distributions of TQ and TU were the solar-satellite observation geometry, aerosol model, aerosol optical thickness and sediment concentration, while Chla was not one of the key factors. Furthermore, because the optical properties of medium-low turbidity water were mainly determined by Chla, TQ and TU were not prominently affected by the water optical parameters of medium-low turbidity water.
Considering the key factors interfering with TQ and TU, we built TQ and TU lookup tables suitable for medium-low turbidity water. The corresponding input parameters were λ, SFM, τa, θs, φ and θv. Since a new generation of oceanic satellites, i.e., PACE, was about to launch, the bands of the TQ and TU lookup tables were 0.441 and 0.549 µm, respectively, corresponding to the blue-green bands of the multiangle polarization sensor (HARP2) mounted on PACE.
Overall, this study found that there were apparent differences between TQ, TU and TI. Compared with TI, the oceanic constituents had a prominent impact on TQ and TU in low- and medium-turbidity water with respect to the aerosol model, optical thickness, observation geometry, and phytoplankton. Moreover, TQ and TU lookup tables suitable for medium- and low-turbidity water were generated, which laid the foundation for extracting the water-leaving radiation polarization information from the satellite observation polarization signal. Limited by the computational power of the computer, we only consider the situation of medium-low turbidity water, although the main water optical parameter affecting TQ and TU was determined to be Csed. Certainly, the situation of high turbidity water should be considered in the development of tables in follow-up studies. In addition, only nominal transmittance was calculated in this study, and the coupling impacts of different components of the Stokes vector of the water-leaving radiation should be further considered in the future. In the next study, we will focus more on the atmospheric correction of the linear polarization component of the water-leaving radiation based on TQ and TU lookup table.
Funding
Key Special Project for Introduced Talents Team of the Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (GML2019ZD0602); National Natural Science Foundation of China (41825014, 42141002, 42176182); Natural Science Foundation of Zhejiang Province (2017R52001); Second Institute of Oceanography, State Ocean Administration (QNH3126); Startup Foundation for Hundred-Talent Program of Zhejiang University (LR18D060001).
Acknowledgments
We thank the staffs of the satellite ground station, satellite data processing & 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 with the simulation and data processing. We thank four anonymous reviewers for their constructive comments to improve the manuscript quality.
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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