Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere-Ocean System

Received 10 October 2014; revised 9 March 2015; accepted 25 March 2015)

Radiative transfer is one of the most important processes in the atmosphere-ocean system. It plays a critical role in the Earth's energy budget and material exchange by driving thermodynamic processes (Shi, 2007). Radiation is emitted, absorbed and scattered, including the inelastic scattering effect by components in the atmosphere-ocean system, such as molecular gases, aerosols, the sea surface, and ocean components (IOCCG, 2006). Absorption reduces the intensity of radiation, and reflection changes the direction; scattering changes the intensity and directionality, and also introduces or modifies the polarization state (Duan et al., 2010).

Radiative transfer in the atmosphere-ocean system is comprised of non-uniformly refracting layered media due to different refractive index values; therefore, refraction by the sea surface exerts very important roles in radiation processes. Assuming a flat ocean surface, the Fresnel-Snell law (Jin and Stamnes, 1994) can be used to calculate the reflectivity and transmissivity; however, in reality the ocean surface is wind-roughened and randomly oriented. This is relevant to wind velocity determining the variance of the density function of a wave slope obeying an isotropical Gaussian distribution. (Cox and Munk, 1954) estimated the statistical characteristics of the wave slope distribution through measurement of the sea surface; however, their calculations neglected the influence of surface roughness in the angular distribution of upwelling radiance and diffuse sunlight. Based on the results of (Cox and Munk, 1954), (Nakajima and Tanaka, 1983) further proposed a rough ocean surface model to calculate the reflectivity and transmissivity function, including the wave slope and shadowing effect.

Radiation processes in the ocean are influenced by four main components: pure seawater, phytoplankton, inorganic suspended material (sediment), and colored, dissolved organic matter (CDOM). In addition, temperature and salinity also have an effect on the absorption of water (R\"ottgers et al., 2010, 2014). In general, ocean waters are classified into Case 1 or Case 2 waters. The optical properties of Case 1 waters are dominated by phytoplankton, while Case 2 waters are influenced not just by phytoplankton but also by sediment and/or CDOM (IOCCG, 2000). Many studies have reported the impact of ocean components on radiation processes. (Tanaka and Nakajima, 1977) showed that ocean turbidity and the refractive index of hydrosols both affect the radiation processes in the atmosphere-ocean system. In Case 1 waters, observations and semi-analytic and OGCM model simulations have suggested that the upwelling radiance and variation of irradiance reflectance are influenced by the change of phytoplankton pigment concentration (Gordon et al., 1988; Morel and Maritorena, 2001; Lin et al., 2007). In the case of polarized radiation, previous research has shown that the polarization signal is important for satellite retrieval of aerosol properties over the ocean (Mishchenko and Travis, 1997; Goloub et al., 1999); the polarized reflectance in the 490 nm band at the TOA remains insensitive to chlorophyll, even in mesotrophic waters, according to analyses of Polarization and Anisotropy of Reflectance for Atmospheric Sciences coupled with Observation from a Lidar (PARASOL) and Research Scanning Polarimeter (RSP) data (Harmel and Chami, 2008; Chowdhary et al., 2012), and the use of parallel polarized radiance effectively reduces sun-glint interference and enhances the ocean color signal at the TOA (He et al., 2014). Moreover, some studies have also indicated that polarization information may be used in remote sensing (Takashima and Masuda, 1985; Chowdhary, 1999; Chowdhary et al., 2006; Chami, 2007; Zhai et al., 2010; Hollstein and Fischer, 2012a, 2012b).

However, research on the radiation impact of Case 2 waters, aerosols and the rough ocean surface, especially polarization effects, is still rare. In addition, a comprehensive understanding of radiation processes in the atmosphere-ocean system also plays an important role in the remote sensing of ocean color or aerosol monitoring. In this study, the impacts of ocean particles, a rough ocean surface, and aerosols, on upwelling radiance and polarization radiance for Case 2 waters were investigated using a vector radiative transfer model known as Pstar (Ota et al., 2010). The Pstar model uses the discrete ordinate and matrix operator method and has been developed based on the N-T model (Nakajima and Tanaka, 1983, 1986, 1988; Nakajima et al., 2000). The ocean part of the Pstar model has been recently improved from Case 1 waters to Case 2 waters.

This paper first discusses the radiative transfer model and describes the modified ocean components in detail. Then, the effects of ocean particles on radiation processes, as well as polarization, are analyzed and discussed. Finally, the influence of the rough ocean surface and aerosol on the bidirectional reflectance and polarization degree at the TOA are discussed, and a nonlinear optimal method is also used to investigate the inversion of aerosol and wind velocity simultaneously.

The Stokes parameters, I,Q,U, and V, respectively characterize the intensity, the degree of polarization, the plane of polarization and the ellipticity of a light wave, and satisfy I²≥ Q²+U²+V². The traditional scalar radiation intensity I is thus replaced by the vector I=(I,Q,U,V) in the vector radiative transfer equation (RTE). The polarized radiance I _p and the degree of polarization are defined as \(I_\rm p=\sqrtQ^2+U^2+V^2\) and P=I _p/I. In the atmosphere-ocean system, the value of V is very small and can generally be ignored (Kattawar et al., 1976; Plass et al., 1976).

Due to the reflectance of the ocean surface, the source function in the RTE for the diffuse component of the Stokes vector is invoked by the direct solar beam reflected by the sea surface. Thus, the RTE is as follows:

\begin{eqnarray} \mu\!\dfrac{d\bm{I}(\tau;\mu,\phi)}{d\tau}&\!=\!&-\bm{I}(\tau;\mu,\phi)+\nonumber\\ &&\omega\int_{-1}^1\!\!\int_0^{2\pi}\!\bm{Z}(\mu,\phi;\mu',\phi')\bm{I}(\tau;\mu',\phi')d\phi'd\mu'\!+\nonumber\\ &&\bm{S}+(1-\omega)\bm{B}(\tau) , (1)\end{eqnarray}

where τ is the optical depth measured from the TOA, μ and μ' are the cosine of the viewing zenith angle and incident zenith angle measured from the negative z-axis respectively, and φ is the azimuth angle. The scalar ω denotes the single scattering albedo, defined as the ratio of the scattering coefficient to the extinction coefficient. S is the source function of single scattering and B(τ) is the thermal emissions vector. Z(μ,φ;μ',φ') is the phase matrix and is defined as

\begin{equation} \bm{Z}(\mu,\phi;\mu',\phi')=\bm{R}(\pi-x_2)\bm{P}(\Theta)\bm{R}(-x_1) , (2)\end{equation}

where P(Θ) is the scattering matrix, Θ is the scattering angle, and R is the rotation matrix. The incident meridian plane can be rotated into the scattering meridian plane according to the two rotation angles, x₁ and x₂, which denote the angle between the corresponding meridian plane and scattering plane. The expression of S in the atmosphere and ocean system is different (Ota et al., 2010). In the atmosphere, it is defined as

\begin{eqnarray} \bm{S}&=&\omega\bm{Z}(\mu,\phi;\mu_0,\phi_0)\bm{F}_{0}e^{-\tau/\mu_0}+\nonumber\\ &&\omega \bm{Z}(\mu,\phi;-\mu_0,\phi_0)\bm{R}_{\rm s}(-\mu_0,\phi_0;\mu_0,\phi_0) \bm{F}_{0}e^{-\frac{2\tau_{\rm a}-\tau}{\mu_0}} ,\quad (3)\end{eqnarray}

where F₀ is the solar flux vector, R _s(-μ₀,φ₀;μ₀,φ₀) denotes the specular reflection matrix of the ocean surface, and τ _a is the optical thickness of the whole atmosphere. The ocean is assumed to be sufficiently deep that no light is reflected from the bottom, allowing S to be written as

\begin{equation} \bm{S}=\omega\dfrac{\mu_0}{\tilde{\mu}_0}\bm{Z}(\mu,\phi;\tilde{\mu}_0,\phi_0)\bm{T}_{\rm s}(\tilde{\mu}_0,\phi_0;\mu_0,\phi_0)s\bm{F}_{0} e^{-\frac{\tau_a}{\mu_0}}e^{-\frac{\tau-\tau_a}{\tilde{\mu}_0}} , \end{equation} where \(\bmT_\rm s(\tilde\mu_0,\phi_0;\mu_0,\phi_0)\) represents the transmission matrix of the ocean surface, 0 means solar direct incident/reflection, and \(\tilde\mu_0\) is the cosine of the solar zenith angle in the ocean. Both R _s and T _s can be calculated by the Fresnel-Snell law (Jin and Stamnes, 1994), assuming a flat ocean surface, or by the N-T model (Nakajima and Tanaka, 1983), to account for the wave slope and shadowing effect of the rough ocean surface.

The atmosphere contains a mixture of molecules and aerosols. In the simulation, the gas absorption and scattering were taken into consideration. The 1976 United States standard atmosphere, with 30 layers, was used for the atmosphere profile, and a more realistic multi-component scattering approach was adopted in the aerosol model. In this approach, instead of using an average refractive index of a single component to represent the mixture of different kinds of aerosols, the refractive index of each type of aerosol particle was calculated by taking hygroscopic growth into account (Shettle and Fenn, 1979; Yan et al., 2002). In the simulation, an external mixture aerosol model, comprising sea spray and tropospheric aerosols, was used (Shettle and Fenn, 1979).

In the ocean body, we considered four optical property-altering components: pure seawater, phytoplankton, sediment, and CDOM, or yellow substance with a homogeneous vertical distribution. The absorption and scattering coefficient of pure seawater were taken from (Pope and Fry, 1997) and (Hale and Querry, 1973), respectively. Moreover, the absorption coefficient is influenced by the temperature and salinity according to R\"ottgers et al. [2010, Eq. (4)]. The calculation of the phase function of seawater was treated using Rayleigh scattering theory with a depolarization factor of δ=0.039 (R\"ottgers et al., 2010), due to their similar volume scattering function (Morel, 1974).

Living phytoplankton strongly absorb visible light, and this is the principle component of Case 1 waters. The absorption coefficient of phytoplankton was computed using the empirical formula of (Bricaud et al., 1995):

\begin{equation} a_{\rm ph}(\lambda)=A(\lambda)[{\rm Chl}]^{1-B(\lambda)}. (5)\end{equation}

Here, [Chl] is the chlorophyll concentration (mg m^-3), and A(Λ) and B(Λ) are positive, principal wavelength-dependent parameters. The scattering coefficient of phytoplankton b _ph(Λ) was calculated using (Huot et al., 2008), based on (Morel and Maritorena, 2001):

\begin{eqnarray} b_{\rm ph}(\lambda)&=&0.347[{\rm Chl}][\lambda/660]^{v([{\rm Chl}])} ,\nonumber\\[1mm] v([{\rm Chl}])&=&0.5(\lg[{\rm Chl}]-0.3) ,\quad 0.02<[{\rm Chl}]<2 ,\quad \\[1mm] v([{\rm Chl}])&=&0 ,\quad [{\rm Chl}]>2 .\nonumber (6)\end{eqnarray}

The scattering phase matrix of phytoplankton cells was calculated using Mie theory. The refractive index relative to seawater was 1.05 and the volume spectrum distribution was assumed to follow a Junge-4 distribution with a radius range of 0.1-50 μm (Chami et al., 2001).

The absorption and scattering coefficient of sediment were calculated based on the bio-optical model adopted from Bowers et al. (1988). The scattering phase matrix was also calculated using Mie theory, and determined to have a refractive index of 1.2-0.001i. The size distribution also followed a Junge distribution (He et al., 2014). The yellow substance was treated as a pure absorber: it strongly absorbs blue light, and its absorption coefficient decreases rapidly with increasing wavelength. The wavelength-dependent absorption coefficient of yellow substance a _ys(Λ) can be parameterized by an exponential empirical relation based on the absorption coefficient at 440 nm, a _ys(440), as proposed by (Bricaud et al., 1998):

\begin{equation} a_{\rm ys}(\lambda)=a_{\rm ys}(440)\exp[-0.014(\lambda-440)] . (7)\end{equation}

Given these assumptions, we calculated the bidirectional reflectance ρ(Λ) and the polarization bidirectional reflectance ρ _p(Λ), which have units of sr^-1, by:

\begin{equation} \begin{array}{rcl} \rho(\lambda)&=&\pi I_{\rm u}(\theta,\phi)/E_{\rm d}\\[2mm] \rho_{\rm p}(\lambda)&=&\pi I_{\rm up}(\theta,\phi)/E_{\rm d} \end{array} , (8)\end{equation}

where I _u and I _up are the upwelling radiance and upwelling polarized radiance, E _d is the downwelling irradiance, and θ and φ are the viewing zenith and azimuth angles, respectively. This calculation was performed at three "altitudes": just above the ocean surface, just below the ocean surface, and at the TOA.

The Pstar model has been shown to simulate radiation processes well, including polarization in the atmosphere (Kokhanovsky et al., 2010). With regard to oceanic radiation processes, the performance of the Pstar model was determined by comparing the radiative processes in the ocean with the standard radiative transfer problems defined by (Mobley et al., 1993). Table 1 shows the results of the Pstar model and its comparison with the standard values for problem 5 (Mobley et al., 1993), a check of performance of the ocean radiative transfer model considering chlorophyll, sea water and the rough ocean surface. It assumes that the water body is horizontally homogeneous and infinitely deep, with a single scattering albedo of 0.9, and a Petzold phase function (Petzold, 1972), truncated by the delta-M method (Wiscombe, 1977). Before the radiative transfer calculation, the real part of the refractive index of water was 1.340. The ocean surface was assumed to be rough, with a wave slope standard deviation of 0.2, corresponding to a wind velocity of 7.23 m s^-1, based on the (Cox and Munk, 1954) capillary-wave spectrum at a solar zenith angle of 80^°. The irradiance perpendicular to the Sun's rays just above the ocean surface was 1 W m^-2 nm^-1, and the influence of the atmosphere was ignored. Good agreement between the Pstar and Mobley-derived average values was demonstrated. The average difference of radiance (1.6%) and irradiance (1%) were very small, indicating that the Pstar model simulated radiative processes in the ocean body well.

A series of sensitivity experiments were performed to study the influence of ocean particles in the upwelling radiance, as well as polarization effects over the ruffled ocean surface. The simulation was performed at ten wavelengths (380, 400, 412, 443, 490, 510, 550, 670, 750 and 865 nm), i.e. the central wavelengths of the detecting bands of ocean color satellites; a constant salinity of 35 practical salinity units and a temperature of 12^°C was assumed. The solar zenith angle was fixed at 30^°. All results were specified in the principal plane. Atmospheric conditions were taken into account with three aerosol optical thicknesses (AOTs) of τ=0.01,0.2 and 0.5, and three wind velocities at 10 m height over the ocean surface (2, 5 and 8 m s^-1).

The numerical results for Case 1 waters, where the non-water component is dominated by phytoplankton, were investigated first. The concentrations of chlorophyll used in the simulations were 0.03, 0.1, 1.0, 5.0, 10.0 and 20.0 mg m^-3. Table 2 summarizes the absorption coefficients of chlorophyll at different concentrations for two different wavelengths. As expected, a _ph(Λ) increased with concentration and displayed a wavelength dependence: the absorption coefficient at 412 nm was almost twice as high as that at 670 nm.

Research on bidirectional reflectance just below the ocean surface is valuable due to its close relationship with remote sensing. Figures 1a and b show the angular distribution of ρ(Λ) for different chlorophyll concentrations at 412 nm and 670 nm, respectively. The results indicate that ρ(412) decreased as the concentration increased due to the strong absorption of blue light by chlorophyll; more chlorophyll added more of an absorption effect. At 490 nm, a pivot point appeared in which ρ(Λ) was barely dependent on chlorophyll concentration (not shown). The bidirectional reflectance increased as the chlorophyll concentrations increased at 670 nm, owing to the weak absorption effect and significant scattering (Fig. 1b). The distinct relationship between chlorophyll and upwelling radiance on both sides of the pivot point form a theoretical basis for the ratio method of chlorophyll remote sensing (Gordon and Morel, 1983). It is noted that ρ(Λ) showed a slight dependence on the geometry of observation just below the ocean surface and its variation with viewing zenith angle curved more uniformly for high chlorophyll concentrations.

Figure 1.  Angular distribution of the bidirectional reflectance for different chlorophyll concentrations at (a) 412 nm and (b) 670 nm, just below the ocean surface. In these simulations, the wind velocity was set to 5 m s^-1 , the aerosol optical thickness at 500 nm was 0.2, and the solar zenith angle was set to 30^°. Note that the positive half of the plane is the specular plane and the negative half is the solar plane.

Figure 2.  As in Fig.1, but for simulations of polarized bidirectional reflectance at (a) 412 nm and (b) 670 nm.

Figure 3.  Angular variation of (a) bidirectional reflectance and (b) polarized bidirectional reflectance, just above the ocean surface, for different chlorophyll concentrations at 412 nm.

Figure 4.  Angular variation of bidirectional reflectance and the degree of polarization at the TOA as a function of chlorophyll concentration at 412 nm.

The influence of chlorophyll on the upwelling polarization bidirectional reflectance ρ _p(Λ) just below the ocean surface was also investigated (Fig. 2). The overall variation pattern of ρ _p(Λ) was similar to that of ρ(Λ), except that ρ _p(Λ) showed obvious dependence on the viewing zenith angle, especially in the large viewing zenith angles of the specular plane. The polarization bidirectional reflectance decreased with an increase in chlorophyll concentration at 412 nm due to the strong absorption of chlorophyll and depolarization of multiple scattering (Fig. 2a). At 670 nm, ρ _p(Λ) increased with an increase in oceanic turbidity due to the weaker absorption effect of chlorophyll and the stronger backward scattering of multiple scattering after the competition with its depolarization effects (Fig. 2b).

Next, the dependence of ρ(Λ) and ρ _p(Λ) just above the ocean surface on the chlorophyll concentration were investigated (Fig. 3). The bidirectional reflectance was clearly sensitive to chlorophyll concentration, with similar rangeability among viewing zenith angles at 412 nm. It decreased with [Chl] increase, but a significant difference was that the change of ρ _p(Λ) for different chlorophyll concentrations was only obvious in the highest viewing angles of the specular plane, with a maximum relative difference over 44%. Meanwhile, the polarization reflectance was fairly insensitive to [Chl] in the backscattering region, owing to less reflected skylight and a low degree of polarization. In general, the varying amplitude of ρ(Λ) and ρ _p(Λ) just above the ocean surface, dependent on the chlorophyll concentrations, was smaller than that just below the ocean surface.

Figure 5.  Angular variation of (a) bidirectional reflectance and (b) the degree of polarization, just below the ocean surface, for different sediment concentrations at 550 nm.

Figure 4 shows the angular variation of bidirectional reflectance and the degree of polarization at the TOA as a function of chlorophyll concentration. The radiance was slightly sensitive to the chlorophyll concentration, and decreased as the concentrations increased at 412 nm. There was a relative difference of 11.8% when [Chl] changed from 0.03 to 20 mg m-3 at nadir zenith angle (Fig. 4a), while the degree of polarization barely varied in the principal plane, except at the complementary angle relative to solar zenith (Fig. 4b). Note that greater insensitivity was apparent at longer wavelengths due to more significant absorption of sea water (not shown). This demonstrated that total radiance and polarized radiance at the TOA were predominantly from the atmospheric layer; in particular, the Rayleigh scattering strongly polarized the diffuse radiance.

In the coastal ocean or estuarine region, ocean particles are dominated by inorganic suspended material with higher refractive index than phytoplankton. In the sensitivity simulations, the concentrations of sediment were defined as 1.0, 5.0, 10.0 and 20.0 mg l^-1. The concentrations of yellow substance were represented by the a _ys(440) in Eq. (7), and was set to 0.01, 0.1 and 1.0 m^-1.

Figure 5 shows the angular variation of ρ(Λ) and the degree of polarization just below the ocean surface for different sediment concentrations at 550 nm. ρ(Λ) increased with increasing concentration, and the increasing amplification decreased from 1 mg l^-1 to 20 mg l^-1. The degree of polarization, which is typically characterized by a "bell shape" with a neutral point in the total backscattering region, decreased with increasing sediment concentration owing to the depolarization of multiple scattering. It was also noted that the amplitude of variation was more obvious in the longer wavelengths (figure not shown).

Figure 6.  Spectral variation of the (a) bidirectional reflectance and (b) polarization bidirectional reflectance, just below the ocean surface, in different concentrations of CDOM, for the nadir zenith angle. In these simulations, the wind velocity was set to 5 m s^-1 and the aerosol optical thickness at 500 nm was 0.2.

The dependence of the radiance reflectance and polarization degree just above the ocean surface on the concentrations of sediment was similar to that just below the ocean surface. However, the response of the degree of polarization just above the ocean surface at 670 nm to the change of chlorophyll and sediment was obviously different (Fig. 6). Similar observations were also made in the specular plane. A significant amount of sediment can induce strong depolarization, while the degree of polarization for chlorophyll changes slightly with the increase of concentration. Such a situation is also similar at the TOA, it has been demonstrated that the degree of polarization in the specular plane at 670 nm can potentially be used to retrieve the sediment due to its more significant sensitivity to sediment than chlorophyll (Chami and McKee, 2007; Ibrahim et al., 2012).

Figure 7.  Variation of the degree of polarization just above the ocean surface at 670 nm for different concentrations of chlorophyll and sediment. The viewing zenith angle is 60^°.

Figure 8.  Variation of (a) bidirectional reflectance and (b) the degree of polarization, with the viewing zenith angle at 670 nm, at the TOA, for different AOT and wind velocities. The wind velocity (symbolized by `W') was set to 2, 5 and 8 m s^-1, and AOT (symbolized by "T") at 500 nm was set to 0.05, 0.2 and 0.5. The solar zenith angle was set to 30^° and the concentrations of ocean particles were 0.03 mg m^-3, 0.1 mg l^-1 and 0.01 m^-1 for phytoplankton, sediment and CDOM, respectively.

The yellow substance only absorbed; therefore, increasing its concentration increased the absorption of radiation in the ocean body. The radiance and polarization reflectance just below the ocean surface decreased by a similar ratio (Fig. 7), and the dependence of ρ(Λ) and ρ _p(Λ) on concentration was more significant in the shorter wavelength region due to the stronger absorption coefficient.

Radiance just above the ocean surface was also more sensitive to the change of the concentrations of yellow substance when compared with the polarized radiance below 670 nm (figure not shown). For example, the variation of ρ(Λ) was 54.8%, while it was about 22.6% for ρ _p(Λ) at 412 nm when the absorption coefficient of CDOM changed from 0.01 m^-1 to 0.1 m^-1.

At the TOA, the radiance and polarization reflectance were insensitive to the variation in yellow substance concentration, since the main radiance and polarization effects came from the contribution of the atmospheric layer and ocean surface.

At longer wavelengths, radiation sensitivity to varying concentrations of oceanic components was smaller, due to the significant absorption effects of seawater, which allowed the derivation of aerosol concentration and wind velocity. A primary objective of atmospheric correction of satellite images is to extract the effects of aerosol on the upwelling radiance at the TOA.

In the following sensitivity experiments, the solar zenith angle was fixed at 30^° and the concentrations of ocean particles were set to 0.03 mg m^-3, 0.1 mg l^-1 and 0.01 m^-1 for phytoplankton, sediment and CDOM, respectively. The variations of ρ(Λ) and degree of polarization at the TOA are shown in Fig. 8.

The results of the specular plane direction simulation demonstrate that the bidirectional reflectance ρ(Λ) increased with AOT when the viewing zenith angle was large. The opposite was true when the viewing zenith angle was small, especially in the sun-glint region (Fig. 8a). This may be because, at larger viewing zenith angles, diffused sky radiation is reflected more by the atmospheric layer than direct solar radiation in the turbid atmosphere with high AOT, which increases as AOT increases. At smaller viewing zenith angles, the upwelling radiance mainly comes from the reflection of direct solar radiation, so the direct transmittance decreases when the atmosphere is more turbid with heavy aerosol. As for the degree of polarization, it mainly decreases with increasing AOT, due to the depolarization effect by increased scattering order, and this phenomenon is more significant in the larger viewing zenith angles.

In view of the wind velocity dependence of the radiance reflectance and degree of polarization on the viewing zenith angles (Fig. 8), it is worth noting that ρ(Λ) was the most sensitive to the wind velocity in the sun-glint region, suggesting that a robust signal might be used to retrieve the wind velocity. ρ(Λ) decreased with increasing wind velocity in the sun-glint region, while the degree of polarization showed different variation patterns in that region. Relatively less dependence of the degree of polarization on the sun-glint region was found, indicating that the degree of polarization could effectively reduce sun-glint contamination (Fougnie et al., 1999; Zhou et al., 2013; He et al., 2014). Moreover, the pattern of "W-8-T-0.2" (i.e. a wind velocity of 8 m s^-1 and an AOT of 0.2), shown in Fig. 8a, indicates that the curve of the upwelling radiance was less sharp and its variation with viewing zenith angle curves more uniform for stronger wind velocity. Consequently, the ocean surface tended to be a Lambert reflector as wind velocity increased.

Nevertheless, in the solar plane, the radiance and degree of polarization were almost unchanged with wind velocity, and their dependence on wind velocity was significantly smaller than AOT (Fig. 8). Taking the viewing zenith angle of -30^° as an example, the results show that the ρ(Λ) for AOT = 0.5 (0.0876 sr^-1) increased by ∼194.0% relative to that for AOT = 0.05 (0.0298 sr^-1), while the ρ(Λ) only increased by ∼0.8% (from 0.0503 sr^-1 to 0.0507 sr^-1) when the wind velocity increased from 2 to 8 m s^-1. Therefore, the radiance in the back-scattered direction can be useful to retrieve aerosol information.

Based on the above analysis, a full physical inversion method for aerosol and wind velocity according to optimal estimation theory (Rodgers, 2000) was tested for Case 1 waters by using multiple wavelengths and sun glint combined with out-of-sun-glint radiance. The state vector x is determined by minimizing the cost function according to the following iterative equation:

\begin{eqnarray} \label{eq1} \bm{x}_{i+1}&=&\bm{x}_i+(\bm{S}_a^{-1}+\bm{K}_i^T\bm{S}_\varepsilon^{-1}\bm{K}_i)^{-1}[\bm{K}_i^T\bm{S}_\varepsilon^{-1}(\bm{y}-\quad\nonumber\\[1mm] &&\bm{F}(\bm{x}_i))-\bm{S}_a^{-1}(\bm{x}_i-\bm{x}_a)] , (9)\end{eqnarray}

where x_i is the solution at the i-th iteration step, including the optical thickness of fine and sea salt (coarse) particles, the soot fraction in fine particles, wind velocity, and the concentration of chlorophyll; F(x_i) represents an observation model using x_i at six wavelengths (380, 490, 550, 670, 765 and 865 nm); K_i is the Jacobian matrix; S_a and S_ε are the a priori covariance matrix and measurement error covariance matrix, respectively; and the accuracy of the satellite radiance in the measurement is set to 2%.

Figure 9.  Simultaneous retrieval of aerosol optical thickness for fine and sea salt particles at 550 nm, and wind velocity compared with input values. The blue lines denote the values 10% smaller or higher than input values.

Figure 9 shows the results of the numerical simulation carried out to investigate the performance of the optimal method for retrieving aerosol and wind velocity. For all the retrievals, synthetic measurements (input values) for a given atmospheric state were generated using the radiative transfer model. Simulated retrievals (output values) were then performed based on optimal estimation theory. The statistics of the total degrees of freedom for signals (the trace of the averaging kernel matrix) were over 4.2, which was comparable to the number of state parameters and reveals that the retrieval was stable and not seriously affected by measurement noise. It was demonstrated that the relative errors in simultaneously determining the optical thickness of fine and sea salt particles were less than approximately 10%. The relative error for the inversion of wind velocity was less than 1.4%, due to an observation in the sun-glint direction. Therefore, a multi-angle satellite observation covering in-and out-of-sun-glint conditions is probably useful for the simultaneous retrieval of aerosol and wind velocity, which reflects the results reported by (Harmel and Chami, 2012) using polarized information.

This study used a radiative transfer model of the atmosphere-ocean system to investigate the influence of ocean components on upwelling radiance and polarized radiance. Simulations were performed at three distinct "altitudes": just above and below the ocean surface, and at the TOA. The impact of the ruffled ocean surface, represented by the wind velocity 10 m above the ocean surface, was considered, as was that of aerosol. The polarization radiance showed an obvious dependence on the observation geometry for different chlorophyll concentrations, while radiance curved more uniformly in the higher chlorophyll concentration region, just below the ocean surface. The polarized radiance at the TOA was less sensitive to the influence of ocean particles than just below the ocean surface, due to depolarization by multiple scattering in the atmosphere. The upwelling radiance changed slightly for high sediment concentrations just below the ocean surface. At 670 nm, sediment showed a more significant variation pattern than chlorophyll for the degree of polarization. At longer wavelengths, the dependence of radiance or polarized radiance on the changing concentrations of ocean particles was smaller, due to the highly significant absorption effects of seawater. In the back-scattered direction, the change of radiation with wind velocity was hardly variable, which is useful for the retrieval of aerosol. Meanwhile, in the sun-glint direction, radiance generated robust information by wind velocity, which could be used for the inversion of wind velocity, while the degree of polarization seemed to reduce the sun-glint contamination. Based on the sensitivity experiments, an inversion algorithm was constructed to simultaneously retrieve the aerosol and wind velocity from multi-wavelength, multi-directional radiance. Since we used a relatively simple aerosol model in the inversion, it would be important to use polarized information for the retrieval of aerosol, wind velocity and water-leaving radiance in future work.