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  • View in gallery

    The P11 and −P12/P11 element of the phase matrix plotted against the scattering angle.

  • View in gallery

    Cartesian coordinates of the polarized reflectance at two wavelengths, (a) 0.865 and (b) 1.38 μm, for the ice crystal model compared with measurements of POLDER. For both cases the thin cirrus clouds optical thickness is 0.5, the aerosol optical thickness is 0.25, and the solar zenith angle is 43°.

  • View in gallery

    Contour diagrams of total reflectance and polarized reflectance at 0.865 μm vs the COT and AOT for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°; ϕs is the solar zenith angle and ϕυ is the view zenith angle. The underlying surface is black.

  • View in gallery

    Contour diagrams of total reflectance and polarized reflectance at 0.865 μm vs the COT and surface albedo for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The AOT is 0.5.

  • View in gallery

    As in Fig. 3, but at 1.38 μm.

  • View in gallery

    As in Fig. 4, but at 1.38 μm.

  • View in gallery

    The sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to COT as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

  • View in gallery

    As in Fig. 7, but the satellite zenith angle is 30°.

  • View in gallery

    The sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to AOT as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

  • View in gallery

    As in Fig. 9, but the satellite zenith angle is 30°.

  • View in gallery

    The sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to surface albedo as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

  • View in gallery

    As in Fig. 11, but the satellite zenith angle is 30°.

  • View in gallery

    The sensitivity indices of the TOA total reflectance and polarized reflectance at 1.38 μm to COT as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

  • View in gallery

    As in Fig. 13, but the satellite zenith angle is 30°.

  • View in gallery

    The sensitivity indices for aspect rations at 1.38 μm to aspect ratios as a function of scattering angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 43°.

  • View in gallery

    As in Fig. 15, but the solar zenith angle is 56°.

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Multiangular Polarized Characteristics of Optically Thin Cirrus in the Visible and Near-Infrared Spectral Region

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  • 1 State Key Laboratory of Remote Sensing Science,* Beijing, China
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Abstract

Optically thin cirrus play a key role in the earth’s radiation budget and global climate change. Their radiative effects depend critically on the thin cirrus optical and microphysical properties. In this paper, inhomogeneous hexagonal monocrystals (IHMs), which consist of a pure hexagon with spherical air bubble or aerosol inclusions, are applied to calculate the single-scattering properties of individual ice crystals. The multiangular polarized characteristics of optically thin cirrus for the 0.865- and 1.38-μm spectral bands are simulated on the basis of an adding–doubling radiative transfer program. The sensitivity of total and polarized reflectance at the top of the atmosphere (TOA) to different aerosol, cirrus, and surface parameters is studied. A new sensitivity index is introduced to further quantify the sensitivity study. The TOA polarized reflectance measured by the Polarization and Directionality of the Earth’s Reflectance (POLDER) instruments is compared to simulated TOA total and polarized reflectance. The test results are reasonable, although small deviations caused by the change of aerosol properties and thin cirrus optical thickness do exist. Finally, on the basis of the sensitivity study, a conceptual approach is suggested to simultaneously retrieve thin cirrus clouds’ optical thickness, ice particle shape, and the underlying aerosol optical thickness using the TOA total and polarized reflectance of the 0.865- and 1.38-μm spectral bands measured at multiple viewing angles.

Corresponding author address: Dr. Tianhai Cheng, Institute of Remote Sensing Applications of Chinese Academy of Sciences, Chaoyang District, P.O. Box 9718, Beijing 100101, China. Email: cthy122@126.com

Abstract

Optically thin cirrus play a key role in the earth’s radiation budget and global climate change. Their radiative effects depend critically on the thin cirrus optical and microphysical properties. In this paper, inhomogeneous hexagonal monocrystals (IHMs), which consist of a pure hexagon with spherical air bubble or aerosol inclusions, are applied to calculate the single-scattering properties of individual ice crystals. The multiangular polarized characteristics of optically thin cirrus for the 0.865- and 1.38-μm spectral bands are simulated on the basis of an adding–doubling radiative transfer program. The sensitivity of total and polarized reflectance at the top of the atmosphere (TOA) to different aerosol, cirrus, and surface parameters is studied. A new sensitivity index is introduced to further quantify the sensitivity study. The TOA polarized reflectance measured by the Polarization and Directionality of the Earth’s Reflectance (POLDER) instruments is compared to simulated TOA total and polarized reflectance. The test results are reasonable, although small deviations caused by the change of aerosol properties and thin cirrus optical thickness do exist. Finally, on the basis of the sensitivity study, a conceptual approach is suggested to simultaneously retrieve thin cirrus clouds’ optical thickness, ice particle shape, and the underlying aerosol optical thickness using the TOA total and polarized reflectance of the 0.865- and 1.38-μm spectral bands measured at multiple viewing angles.

Corresponding author address: Dr. Tianhai Cheng, Institute of Remote Sensing Applications of Chinese Academy of Sciences, Chaoyang District, P.O. Box 9718, Beijing 100101, China. Email: cthy122@126.com

1. Introduction

Optically thin cirrus are composed of nonspherical ice crystals, ranging from hexagons to highly irregular geometries with large variability in shape, size, and density depending on temperature and humidity (Korolev et al. 2000; Field and Heymsfield 2003; Francis 1995). They appear mostly in the upper troposphere and the lower stratosphere. Optically thin cirrus are difficult to detect in satellite images because of their transparent nature in the visible spectrum. Optically thin cirrus have been identified as one of the major unsolved elements in weather and climate research, largely because of their unique optical properties and altitude (McFarquhar et al. 2000). They affect the earth’s radiation budget because they reflect incoming solar radiation back to space and they absorb and re-emit terrestrial radiation (Liou 1986; Lynch 1996). The radiative effect of the optically thin cirrus is determined by the optical and microphysical properties. Thus, studies of the optical and microphysical properties of thin cirrus have become a popular issue.

Obtaining the optical and microphysical properties of thin cirrus is essential; to do so on a global scale, satellites must be used. Several approaches to the satellite remote sensing of optical and microphysical properties of cirrus using measurements of solar reflectance have been developed (e.g., King et al. 1992; Baum et al. 2000; Hong et al. 2007; Yang et al. 2007). The general approach is to compare measured radiances with radiances obtained by radiative transfer (RT) calculations. This method is based primarily on the measurements of spectral radiance, which is just one of the four Stokes parameters. The Stokes vectors are defined to completely specify the intensity and polarization state of the radiation field. However, the accuracy of the general approach suffers from the uncertainty of the surface albedo, the aerosol properties below the thin cirrus layer, and ice crystal shape (Rolland et al. 2000).

Many research efforts have focused on the polarization characteristics of atmosphere radiation. It was shown that the polarization characteristics in the visible and near-infrared spectral region contain a wealth of information that is useful for the retrieval of cloud and aerosol properties (Hansen 1971; Chepfer et al. 1998, 1999). Liou and Takano (2002) demonstrated that information of ice crystal shape and crystal orientation can be inferred from the reflected polarization patterns based on comprehensive theoretical interpretations. Chepfer et al. (2001) derived the ice crystal shapes in cirrus clouds derived from the Polarization and Directionality of the Earth’s Reflectance (POLDER-1)–Advanced Earth Observing Satellite 1 (ADEOS-1). Masuda et al. (2002) developed an algorithm for retrieving cirrus cloud optical thickness and ice crystal shape using spaceborne POLDER polarized reflectance data. Noel and Chepfer (2004) studied the ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements. However, these studies are restricted to studying the optical and microphysical properties of thick cirrus, not semitransparent cloud (i.e., thin cirrus). Significant uncertainties exist in the determination of optical and microphysical properties of thin cirrus because of the transparent nature of thin cirrus in the visible spectrum. The reflected sunlight signal is scattered by thin cirrus and aerosol simultaneously. To obtain accurate thin cirrus information, the underlying aerosol effect must be accurately accounted for. Thus, it would be beneficial to be able to retrieve both thin cirrus and aerosol properties.

The main motivation for this research stems from the need to develop optical and microphysical properties of thin cirrus retrieval algorithms based on multispectral and multiangle radiance and polarization observations. In this paper, the optical properties of thin cirrus at the wavelengths 0.865 and 1.38 μm (Gao et al. 2002) are studied. The top-of-atmosphere (TOA) total and polarized reflectance at 0.865 and 1.38 μm are evaluated, and the sensitivity of TOA total and polarized reflectance to thin cirrus optical parameters, aerosol properties, and surface albedo is investigated. A vector radiative transfer program is needed for the purpose of developing algorithms and performing such a sensitivity study. A number of vector radiative transfer models have been developed for multiple scattering, including the Monte Carlo method (Kattawar and Plass 1968), the adding–doubling method (Hansen and Travis 1974; De Haan et al. 1986), and VDISORT (Schulz et al. 1999). In this study, the vector radiative transfer model of Evans and Stephens (1991) is employed to simulate the full Stokes parameters reflected by thin cirrus.

This paper is organized as follows. Section 2 describes the ice crystal model and simulates the multiangular radiance and polarization characteristics of model cirrus particles based on the adding–doubling method. In section 3, the sensitivity study is presented. Results and discussion are given in section 4.

2. Modeling

a. Ice crystal model and single-scattering properties

To simulate the multiangular radiance and polarization characteristics of optically thin cirrus, an understanding of how electromagnetic radiation interacts with nonspherical ice crystals is required. It is essential to calculate the single-scattering properties including phase functions, extinction efficiency, single-scattering albedo, and the asymmetry factor for nonspherical ice crystals (Baum et al. 2005a,b, 2007). The scattering and absorption properties of ice crystal are determined by their shape and size, the ice crystal size distribution, the wavelength of incident electromagnetic radiation, and the complex refractive index of the ice crystal (Wyser and Yang 1998). Thus, it is necessary to define representative ice crystal size distributions and shapes for the calculations of phase functions and other relevant single-scattering properties.

In this study, the thin cirrus scattering models of inhomogeneous hexagonal monocrystals (IHMs), which were introduced by C.-Labonnote et al. (2000, 2001), are used to calculate the phase functions and other relevant single-scattering properties. This model is based on reanalysis of in situ data from a variety of midlatitude and tropical ice cloud field experiments (Knap et al. 2005). The full phase matrix and other relevant single-scattering properties, including the extinction efficiency and single-scattering albedo, are calculated. Randomly oriented nonspherical ice crystals have only six independent nonzero elements among the elements of the scattering matrix. The scattering phase function P11 and the degree of linear polarization −P12/P11 govern the total and polarized radiance, respectively, so P11 and −P12/P11 receive special attention.

Figure 1 shows calculations of P11 and –P12/P11 for the cirrus clouds scattering model of IHM with three aspect ratios L/2R (0.2, 2.5, 5.0) for a fixed key value of a mean free path length 〈l〉 = 15 μm, Rv = 40 μm, reff = 1.5 μm, and υeff = 0.05 at the wavelengths 0.865 and 1.38 μm, respectively. The other relevant single-scattering properties are not discussed. For the aspect ratio L/2R at two spectral bands, P11 displays two strong halo peaks caused by the refractions through specific angle in the solid columns and plates. Indeed, the 46° halo magnitude increases when L/2R decreases, whereas the 22° halo magnitude increases when L/2R increases. The strength and occurrence of halos in the −P12/P11 element depend on the aspect ratio of the crystal: for the columnar IHMs both halos are present, whereas for platelike IHMs only the secondary halo is present.

The strong forward peaks shown exhibited here result from the relatively large size of ice crystals compared to the wavelength. There is no way to run the current vector radiative transfer model (Evans and Stephens 1991) at high enough angular resolution because of the presence of considerable angular structure in the scattering phase function (Fig. 1). The vector radiative transfer model (Evans and Stephens 1991) had to compute too many Legendre polynomial expansion terms in the azimuthal decomposition of the radiance. To use the current vector radiative transfer model to accurately simulate the total reflectance and polarized reflectance, the phase functions of ice cloud are expanded in terms of Legendre polynomials using the δ-fit method, since the reflected radiances resulting from use of the δ-fit phase function are the same as the true values resulting from use of the true phase function [the details of the delta fit are available in Wiscombe (1977) and Hu et al. (2000)].

b. Modeling multiangular radiance and polarization characteristics of thin cirrus

To account for thin cirrus multiple scattering effects, as well as the effect of Rayleigh scattering, aerosol scattering, and surface albedo, the ice crystal optical properties are used in the vector radiative transfer model to compute the Stokes parameters of the emergent light at the TOA. The inhomogeneous atmosphere is simulated by three homogenous layers for 0.865 μm (Cheng et al. 2008): the thin cirrus layer, the molecule layer above the thin cirrus layer, and the molecule and aerosol layer below the thin cirrus layer. For 1.38 μm, the inhomogeneous atmosphere is simulated by three homogenous layers (Hutchison and Choe 1996): the top layer is composed of the water vapor above thin cirrus clouds, the middle layer contains the thin cirrus clouds, and the bottom layer consists of aerosols and water vapor (which accounts for about 90%–99% of the total atmospheric water vapor) (Gao et al. 2002). The surface albedo is taken into account as a limiting condition at the ground.

Given the Stokes parameters of the emergent light at TOA, one can calculate the total reflectance and polarized reflectance at a given wavelength as follows:
i1520-0469-67-3-749-e1
i1520-0469-67-3-749-e2
where I, Q, and U are the Stokes parameters; μ0 is the cosine of solar zenith angle; F0 denotes the incident solar flux density at the given wavelength, and the π factor converts the dimension from flux density to radiance. The sun-view geometry is defined by the view zenith angle θ, the solar zenith angle θ0, and relative azimuth angle (φφ0).

In this study, the total reflectance and polarized reflectance at the wavelengths 0.865 and 1.38 μm are calculated respectively based on vector radiative transfer model. The complete distribution of reflectance and polarized reflectance for fixed μ0 are known as the bidirectional reflectance distribution function (BRDF) and the bidirectional polarized reflectance distribution function (BPDF). For 0.865 and 1.38 μm, F0 = 986.23 and 364.64 W m−2 μm−1, respectively (Thuillier et al. 2003).

To test the simulated TOA total reflectance and polarized reflectance using the vector radiative transfer model, comparisons between measurements and simulations are present. In this paper, POLDER measurements (Deschamps et al. 1994; Goloub et al. 1994; Bréon and Colzy 1999) are obtained for 12 September 2003 over China. The TOA total reflectance for an atmosphere containing thin cirrus is affected by reflections from the surface, which vary with the viewing geometry, on the vegetation cycle and on ground humidity. Therefore, it would be difficult to test the simulated TOA total reflectance because of the uncertainty in the prescription of surface albedo. For cirrus overlying a surface illuminated by direct sun, the contribution of polarized right reflected by the surface is negligible (Nadal and Bréon 1999; Goloub et al. 1994). So we use the TOA polarized reflectance of POLDER to test the simulated polarized reflectance.

Figure 2 shows the Cartesian coordinates of the polarized reflectance at two wavelengths for the ice crystal model. The x axis shows the scattering angle (from 60° to 180°) and the y axis represents the polarized reflectance. The correlation of polarized reflectance at 0.865 μm of POLDER is also displayed in Fig. 2a. Since POLDER does not have a 1.38-μm polarization channel, the simulated data of 1.38 μm are not tested (Fig. 2b). Figure 2a demonstrates that the simulated polarized reflectance using the vector radiative transfer model compares reasonably well with the measurements of POLDER, although small deviations due to the change of aerosol properties and thin cirrus optical thickness do exist.

3. Sensitivity studies

To identify the thin cirrus and aerosol information content in TOA total reflectance and polarized reflectance at 0.865 and 1.38 μm, sensitivity studies are presented. The TOA total and polarized reflectance have been calculated using the vector radiative transfer model to compare the sensitivity of TOA total reflectance and polarized reflectance to different aerosol, thin cirrus parameters, and surface parameters. A standard midlatitude atmosphere was assumed in the model with appropriate humidity and trace gas profiles. The aerosol model following Deuzé et al. (2000) was used. Thin cirrus are composed with the IHM model, which was inserted between 10 and 11 km. The calculation has then been repeated using all possible combinations of nine solar zenith angles (20°–60°), 20 satellite zenith angles (3.4°–88°), and 16 relative azimuthal angles (0°–180°), along with six surface albedo values (0–1), five aerosol optical thickness (0–1), seven thin cirrus optical thicknesses (0–1.5), and three shapes of ice crystal model (L/2R = 0.2, 2.5, 5.0). The resulting TOA total reflectance and polarized reflectance have been compared to each other.

TOA total and polarized reflectance at 0.865 μm is the sum of contributions from different sources: scattering from molecules, aerosol, thin cirrus, and reflections from the surface. The contribution of scattering by molecules is low at 0.865 μm and is well understood, so their contribution to the TOA total reflectance can be calculated easily from the time of the observation and the viewing geometry.

Figures 3 and 4 show how the TOA total and polarized reflectance at 0.865 μm are affected by the changes in aerosol optical thickness, optically thin cirrus optical thickness, and surface albedo. These results were simulated using solar zenith angles of 45° and satellite zenith angles of 3.4° for three cases of azimuth angles.

From Fig. 3, we can see that TOA total and polarized reflectance at 0.865 μm increases with increasing optical thickness of thin cirrus cloud and aerosol. The TOA total and polarized reflectance at 0.865 μm has information about the aerosol and thin cirrus optical thickness. Figure 3 shows that to obtain accurate thin cirrus optical thickness using the TOA total and polarized reflectance at 0.865 μm, the aerosol effect must be accurately accounted for. Unfortunately, that is difficult to accomplish only using TOA total reflectance and polarized reflectance at 0.865 μm.

From Fig. 4, we can see that TOA total and polarized reflectance at 0.865 μm increases with increasing optical thickness of thin cirrus. TOA total reflectance at 0.865 μm increases with increasing surface albedo, whereas TOA polarized reflectance at 0.865 μm is nearly insensitive to surface changes (this conclusion is the same as in previous studies; see Hansen 1971; Chepfer et al. 1998, 1999). Figure 4 shows that to obtain accurate thin cirrus information using the TOA, total reflectance must be separate the thin cirrus signal from the surface signal, which is known to change and depend on various parameters, not all of which are known. The TOA polarized reflectance at 0.865 μm can distinguish the combined signal of optically thin cirrus from the surface signal.

Figures 5 and 6 show how TOA total and polarized reflectance at 1.38 μm are affected by the changes in aerosol optical thickness, thin cirrus optical thickness, and surface albedo. These results were produced using solar zenith angles of 45° and satellite zenith angles of 3.4° for three cases of azimuth angles.

From Figs. 5 and 6, we can see that the TOA total and polarized reflectance at 1.38 μm are nearly insensitive to aerosol optical thickness and ground albedo changes because most of the energy is absorbed by water vapor before it can be reflected back to space. TOA total and polarized reflectance at 1.38 μm is solely influenced by optically thin cirrus, which increases with increasing optically thin cirrus optical thickness. The TOA total and polarized reflectance at 1.38 μm can distinguish the thin cirrus signal from the aerosol signal and the surface signal, so we can use the TOA total reflectance and polarized reflectance at 1.38 μm to retrieve the thin cirrus properties.

To further quantify the sensitivity of the TOA total reflectance and polarized reflectance to different aerosol, thin cirrus, and surface parameters, sensitivity indices are introduced to compare the various sensitivities:
i1520-0469-67-3-749-e3
where ΔR(χ) is the variation of TOA total reflectance or polarized reflectance, Δχ is the variation of parameter, and max(R) − min(R) is the difference between the maximum of TOA total reflectance or polarized reflectance and the minimum of TOA total reflectance or polarized reflectance. The value max(R) − min(R) was introduced to normalize the sensitivity indices so the sensitivity indices of TOA total reflectance and TOA polarized reflectance can be compared.

Figures 7 and 8 show the sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to the thin cirrus optical thickness, both for several values of aerosol optical thickness (0.0, 0.5, 1.0). Thin cirrus optical thickness changes from 0.5 to 1.0. These results were simulated using surface albedo of 0.0 and aspect ratios of 2.5 for three cases of azimuth angles.

Figures 7 and 8 also show the variation of the sensitivity indices with satellite zenith angles and solar zenith angles, respectively. In Figs. 7 and 8 we see that the sensitivity indices of TOA total reflectance to the thin cirrus optical thickness increase throughout the satellite zenith angles and solar zenith angles, respectively. They are slightly reduced when the aerosol optical thickness is high, and this reduction is much stronger at high satellite zenith angles and solar zenith angles. The sensitivity indices of TOA polarized reflectance are also reduced when the aerosol optical thickness is high, and this reduction is much stronger than the reduction of TOA total reflectance sensitivity indices. The sensitivity indices of the TOA total reflectance are larger than that of TOA polarized reflectance, which means that the TOA total reflectance is more sensitive to the thin cirrus optical thickness than the TOA polarized reflectance is.

Figures 9 and 10 show the sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to the aerosol optical thickness, both for several values of thin cirrus optical thickness (0.25, 0.75, 1.25). Aerosol optical thickness changes from 0.25 to 0.75. These results were simulated using surface albedo of 0.0 and aspect ratios of 2.5 for three cases of azimuth angles.

Figures 9 and 10 show the variation of the sensitivity indices with satellite zenith angles and solar zenith angles, respectively. Figures 9 and 10 show that the aerosol thickness influences the both TOA total reflectance and polarized reflectance. This means that the aerosol properties below the thin cirrus have to be considered in the retrieval of thin cirrus properties using TOA total reflectance and polarized reflectance at 0.865 μm. The sensitivity indices for AOT are similar to those for COT, even larger than for COT in some cases, which means that aerosols can be easily sensed below thin cirrus clouds. Aerosol properties are retrieved assuming the thin cirrus properties using the TOA total reflectance and polarized reflectance at 0.865 μm. The sensitivity indices are reduced when the thin cirrus optical thickness is high, and this reduction is much stronger at high satellite zenith angles and solar zenith angles.

Figures 11 and 12 show the sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to the surface albedo, both for several values of thin cirrus optical thickness (0.25, 0.75, 1.25). Surface albedo changes from 0.2 to 0.6. These results were simulated using AOT of 0.25 and aspect ratios of 2.5 for three cases of azimuth angles.

Figures 11 and 12 show the variation of the sensitivity indices with satellite zenith angles and solar zenith angles, respectively. We see that the surface albedo has the largest influence on the TOA total reflectance. The sensitivity indices decrease throughout the satellite zenith angles and solar zenith angles, respectively. It is slightly reduced when the COT is high, and this reduction is much stronger at high satellite zenith angles and solar zenith angles because of the increased optical path through the thin cirrus clouds layer and aerosol layer. The TOA polarized reflectance is nearly insensitive to surface albedo changes because that aerosol and thin cirrus clouds scattering has a stronger polarized effect than surface reflection.

Figures 5 and 6 indicate that the TOA total reflectance and polarized reflectance at 1.38 μm are nearly insensitive to aerosol optical thickness and surface albedo changes, being solely influenced by optically thin cirrus, so the sensitivity indices for the aerosol optical thickness and surface albedo were not calculated. In this paper, we only studied the sensitivity of the TOA total reflectance and polarized reflectance at 1.38 μm to the optical and microphysical properties of thin cirrus.

Figures 13 and 14 show the sensitivity indices of the TOA total reflectance and polarized reflectance at 1.38 μm to the thin cirrus optical thickness, both for several values of aerosol optical thickness (0.0, 0.5, 1.0). Thin cirrus optical thickness changes from 0.5 to 1.0. These results were simulated using surface albedo of 0.0 and aspect ratios of 2.5 for three cases of azimuth angles.

Figures 13 and 14 show the variation of the sensitivity indices with satellite zenith angles and solar zenith angles, respectively. In Figs. 13 and 14 we see that the sensitivity indices of TOA total reflectance increase throughout the satellite zenith angles and solar zenith angles, respectively. The sensitivity indices of the TOA total reflectance are larger than those of TOA polarized reflectance, which means that the TOA total reflectance is more sensitive to the thin cirrus optical thickness than TOA polarized reflectance. Both TOA total reflectance and polarized reflectance at 1.38 μm appear to be sensitive to COT; therefore, the COT can be retrieved from the TOA total reflectance and polarized reflectance at 1.38 μm.

Figures 15 and 16 show the sensitivity indices for aspect rations at 1.38 μm as the function of scattering angles, both for several values of thin cirrus optical thickness (0.25, 0.75, 1.25). These results were simulated for two cases of solar zenith angles. The sensitivity indices of the TOA polarized reflectance is larger than that of TOA total reflectance, which means that TOA polarized reflectance is much more sensitive to different aspect rations of IHM models than TOA total reflectance is. It is slightly reduced when the COT is high. The sensitivity indices of TOA total reflectance are small, which means that the effect of shape of ice model to TOA total reflectance is negligible. The thin cirrus optical thickness can be retrieved using TOA total reflectance at 1.38 μm. Then the aspect ratios of IHM models can be retrieved using TOA polarized reflectance at 1.38 μm, taking the cirrus optical thickness into account.

Now the conceptual approach for the remote sensing of all three parameters (thin cirrus optical thickness, aspect ratios of ice models, and aerosol optical thickness below thin cirrus clouds) using the TOA total reflectance and TOA polarized reflectance for the 0.865- and 1.38-μm spectral bands measured at multiple viewing angles is presented. First, we use the TOA total reflectance at 1.38 μm to retrieve thin cirrus clouds’ optical thickness, and then we use the TOA polarized reflectance at 1.38 μm to retrieve the aspect ratios of ice models, taking the retrieved thin cirrus optical thickness into account. Last, we use the TOA polarized reflectance at 0.865 μm to retrieve the aerosol optical thickness information, taking the retrieved thin cirrus clouds properties into account.

4. Summary and conclusions

Optically thin cirrus has been shown to exist globally and to affect the remote sensing of the lower troposphere and surface. To accurately quantify the optically thin cirrus optical properties and thus their radiative effects, the multiangular polarized characteristics of thin cirrus clouds for the 0.865- and 1.38-μm spectral bands are studied, and the sensitivity of TOA total and polarized reflectance to different aerosols, optically thin cirrus, and surface parameters is also studied. A conceptual algorithm has been suggested to simultaneously retrieve both thin cirrus properties and the underlying aerosol properties using the TOA total and polarized reflectance for the 0.865- and 1.38-μm spectral bands measured at multiple viewing angles.

For the purpose of simulating the TOA total and polarized reflectance and performing a sensitivity study in case of a cloudless atmosphere as well as in an atmosphere containing optically thin cirrus, the single-scattering parameters were computed for inhomogeneous hexagonal monocrystal (IHM) models. To test the simulated TOA total and polarized reflectance, the TOA polarized eflectance of POLDER instruments was used. The results demonstrated that the simulated polarized reflectances for the 0.865-μm spectral band using the vector radiative transfer model compare reasonably well with the measurements of POLDER, although small deviations due to the change of aerosol properties and thin cirrus optical thickness do exist.

A new sensitivity index was introduced to quantify the sensitivity of the TOA total reflectance and polarized reflectance to different aerosol, thin cirrus, and surface parameters. With this sensitivity parameter we studied the sensitivity of the TOA total and polarized reflectance at 0.865 and 1.38 μm to the thin cirrus optical thickness, aerosol optical thickness, surface albedo, and aspect ratios L/2R of ice crystals for different viewing geometries. It was demonstrated that the thin cirrus clouds properties can be retrieved using the TOA total reflectance and polarized reflectance for 1.38 μm, once the thin cirrus properties were accounted for, and the aerosol properties were retrieved using the TOA polarized reflectance for 0.865 μm.

In future work, we will update the crystal habit models to study the multiangular polarized characteristics of thin cirrus clouds and the sensitivity to different aerosol, thin cirrus parameters, and surface parameters.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant 40701109) and the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering (Grant KZCX2-YW-303). We thank C.-Labonnote (Laboratoire d’Optique Atmospherique) for providing us with the single-scattering properties of the ice crystal model (IHM).

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Fig. 1.
Fig. 1.

The P11 and −P12/P11 element of the phase matrix plotted against the scattering angle.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 2.
Fig. 2.

Cartesian coordinates of the polarized reflectance at two wavelengths, (a) 0.865 and (b) 1.38 μm, for the ice crystal model compared with measurements of POLDER. For both cases the thin cirrus clouds optical thickness is 0.5, the aerosol optical thickness is 0.25, and the solar zenith angle is 43°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 3.
Fig. 3.

Contour diagrams of total reflectance and polarized reflectance at 0.865 μm vs the COT and AOT for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°; ϕs is the solar zenith angle and ϕυ is the view zenith angle. The underlying surface is black.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 4.
Fig. 4.

Contour diagrams of total reflectance and polarized reflectance at 0.865 μm vs the COT and surface albedo for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The AOT is 0.5.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 5.
Fig. 5.

As in Fig. 3, but at 1.38 μm.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 6.
Fig. 6.

As in Fig. 4, but at 1.38 μm.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 7.
Fig. 7.

The sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to COT as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 8.
Fig. 8.

As in Fig. 7, but the satellite zenith angle is 30°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 9.
Fig. 9.

The sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to AOT as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 10.
Fig. 10.

As in Fig. 9, but the satellite zenith angle is 30°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 11.
Fig. 11.

The sensitivity indices of the TOA total reflectance and polarized reflectance at 0.865 μm to surface albedo as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 12.
Fig. 12.

As in Fig. 11, but the satellite zenith angle is 30°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 13.
Fig. 13.

The sensitivity indices of the TOA total reflectance and polarized reflectance at 1.38 μm to COT as a function of the satellite zenith angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 45°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 14.
Fig. 14.

As in Fig. 13, but the satellite zenith angle is 30°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 15.
Fig. 15.

The sensitivity indices for aspect rations at 1.38 μm to aspect ratios as a function of scattering angles for various viewing directions: (a) ϕsϕυ = 0°, (b) ϕsϕυ = 84°, (c) ϕsϕυ = 180°. The solar zenith angle is 43°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

Fig. 16.
Fig. 16.

As in Fig. 15, but the solar zenith angle is 56°.

Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS2996.1

* The State Key Laboratory of Remote Sensing Science is cosponsored by the Institute of Remote Sensing Applications of the Chinese Academy of Sciences and Beijing Normal University.

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