Deriving Polarization Properties of Desert-Reflected Solar Spectra 1 with PARASOL Data

. One of the major objectives of the Climate Absolute Radiance and Refractivity Observatory (CLARREO) is to conduct highly accurate spectral observations to provide an on- orbit inter-calibration standard for relevant Earth- observing sensors with various channels. To 3 calibrate an Earth- observing sensor’s measurements with the highly accurate data from the CLARREO, errors in the measurements caused by the sensor’s sensitivity to the polarization 5 state of light must be corrected. For correction of the measurement errors due to the light’s 6 polarization, both the instrument’s dependence to on the incidentce’s polarization stateus and the 7 on-orbit knowledge of the polarization state of light as a function of observed scene type, 8 viewing geometry, and solar wavelength, are required. In this study, an algorithm for deriving 9 the spectral polarization state of solar light from desert is reported. The desert/bare land surface 10 is assumed to be composed of two types of areas: Fine sand grains with diffuse reflection 11 (Lambertian non-polarizer) and quartz-rich sand particles with facets of various orientations 12 (specular-reflection polarizer). The adding-doubling radiative transfer model (ADRTM) is 13 applied to integrate the atmospheric absorption and scattering in the system. Empirical models 14 are adopted in obtaining the diffuse spectral reflectance of sands and the optical depth of the dust 15 aerosols over the desert. The ratio of non-polarizer area to polarizer area and the angular 16 distribution of the facet orientations are determined by fitting the modeled polarization states of 17 light to the measurements at 3 polarized channels (490, 670, and 865 nm) by the Polarization and 18 Anisotropy of Reflectances for Atmospheric Science instrument coupled with Observations from 19 a Lidar (PARASOL). Based on this physical model of the surface, the desert-reflected solar 20 light’s polarization state at any wavelength in the whole solar spectra can be calculated with the 21 ADRTM.

Abstract. One of the major objectives of the Climate Absolute Radiance and Refractivity 1 Observatory (CLARREO) is to conduct highly accurate spectral observations to provide an on-2 orbit inter-calibration standard for relevant Earth-observing sensors with various channels. To 3 calibrate an Earth-observing sensor's measurements with the highly accurate data from the 4 CLARREO, errors in the measurements caused by the sensor's sensitivity to the polarization 5 state of light must be corrected. For correction of the measurement errors due to the light's 6 polarization, both the instrument's dependence to on the incidentce's polarization stateus and the 7 on-orbit knowledge of the polarization state of light as a function of observed scene type, 8 viewing geometry, and solar wavelength, are required. In this study, an algorithm for deriving 9 the spectral polarization state of solar light from desert is reported. The desert/bare land surface 10 is assumed to be composed of two types of areas: Fine sand grains with diffuse reflection 11 (Lambertian non-polarizer) and quartz-rich sand particles with facets of various orientations One of the major objectives of the Climate Absolute Radiance and Refractivity Observatory 5 (CLARREO) (Wielicki et al., 2013) is to conduct highly accurate spectral observations to 6 provide an on-orbit inter-calibration standard for relevant Earth-observing sensors with various 7 channels. To calibrate an Earth-observing sensor's measurements with the highly accurate data 8 from the CLARREO, errors in the measurements caused by the sensor's sensitivity to the 9 polarization state of light must be corrected (Lukashin et al., 2013;Sun and Lukashin, 2013;Sun 10 et al., 2015). For correction of the measurement errors due to light's polarization, both the 11 instrument's dependence on the incidentce's polarization stateus and the on-orbit knowledge of 12 the polarization state of light as a function of observed scene type, viewing geometry, and solar 13 wavelength, are required. Empirical polarization distribution models (PDMs) (Nadal and Breon, 14 1999;Maignan et al., 2009) (Deschamps et al., 1994) may be used to correct radiometric bias (Lukashin et al., 2013). But 17 these can only be done at 3 or 4 solar wavelengths (i.e. 490, 670, and 865 nm) at which the 18 PARASOL has reliable polarization measurements. Since the CLARREO is designed to measure 19 solar spectra from 320 to 2300 nm with a spectral sampling of 4 nm (Wielicki et al., 2013), 20 which has potential to inter-calibrate space-borne sensors at nearly all of the solar wavelengths 21 (Sun and Lukashin, 2013), the PDMs for the inter-calibration applications should be made as 22 functions of every sampling wavelength of the CLARREO. Due to strong dependence of solar 23 light's polarization on wavelength (Sun and Lukashin, 2013), the applicability of empirical 1 PDMs based on only 3 or 4 channels of PARASOL polarization measurements will be very 2 limited. In our previous studies (Sun and Lukashin, 2013;Sun et al., 2015), polarized solar 3 radiation from the ocean-atmosphere system is accurately modeled. Because the refractive index 4 of water at solar spectra is well known (Thormählen et al., 1985), Sun and Lukashin (2013) 5 actually can produce the PDMs for ocean-atmosphere system at any solar wavelength. However, 6 it is still a difficult problem to obtain spectral PDMs for other scene types. For scene types other 7 than water bodies, although many studies have been conducted (Coulson et al., 1964;Egan, 8 1968;Egan 1969;Wolff, 1975;Egan, 1970;Vanderbilt and Grant, 1985;Tamalge and Curran, 9 1986;Grant, 1987), no reliable surface reflection matrix such as that based on the Cox and Munk 10 (1954; 1956) wave slope distribution models for oceans is available. For scene types dominated 11 by diffuse reflection, like fresh snow, grass lands or needle-leaf trees/bushes, this may not be a 12 serious problem. But for scene types like desert, snow crust/ice surfaces, or even broad-leaf trees, 13 specular reflection is still significant (like what happens at the ocean surface), polarization of the 14 reflected light can be very strong, thus needs to be accurately accounted for. For example, the 15 PARASOL data show that the degree of polarization (DOP) of reflected light from clear-sky 16 desert can be ~30%. The broad-leaf trees also can reflect solar light with a DOP of ~70%. For a 17 sensor with a sensitivity-to-polarization factor of only ~1%, its measurement for light with a 18 DOP of ~30% and ~70% will have relative errors of ~0.3% and ~0.7%, respectively, solely due   In this study, an algorithm for obtaining the spectral polarization state of solar light from desert 6 with the PARASOL data is developed. The method of deriving the polarization state of solar 7 light from desert-atmosphere system at any wavelength with the PARASOL-measured polarized 8 radiances at 490, 670, and 865 nm is reported in Section 2. Numerical results and discussions are 9 presented in Section 3. Summary and conclusions are given in Section 4. The polarization of reflected light is related to the surface roughness (Wolff, 1975) and to the 12 size of reflecting elements (Egan, 1970). In this study, the desert/bare land surface is assumed to   Assuming desert is a stationary sand "ocean" with quartz-rich sand-particle facets as specular-4 reflection "waves" and Lambertian reflection sand grains as "foams", we can adopt the formula 5 given in Cox and Munk (1956) for where  denotes the roughness parameter of the desert surface, and where n is the real refractive index of the silica and λ denotes the solar wavelength in μm. In this 2 study, to account for the impurity absorption in the quartz-rich sands, we assume the imaginary 3 part of the sand refractive index to be 0.02. This assumption of sand's imaginary refractive index 4 could have a small effect on the modeled total reflectance from the desert, but has little effect on 5 the DOP and AOLP calculations.
6 However, f,  , and RL must be obtained from observations for desert. In this study, the spectral is the reflectance of the Lambertian desert area, which 18 as the first element of the RL, is linearly extrapolated to the CLARREO solar wavelength limit of 19 320 nm. The empirical spectral reflectance of desert from this process is displayed in Fig. 1 is applied for calculation of the Stokes parameters of the reflected light from the desert-  , 2006; 2009; 2013). Two-mode lognormal size distributions (Davies, 1974;Whitby, 1978;16 Reist, 1984;Ott, 1990;Porter and Clarke, 1997)

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where λ is the solar wavelength in μm. Dust AOD decreases with the increase of wavelength.

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In this study, the ratio of the non-polarizer area to polarizer area of the desert and the angular  However, it is's worth noting here that the errors in the AOLP from the ADRTM due to our 21 assumptions for dust refractive index will only have a minor effect on the polarization correction 22 accuracy. This is due to the fact that the DOPs at these observation angles are very small, and 23 also that the AOLP errors in these observation angles actually will not result in any significant 1 difference in polarization correction, i.e. AOLP = ~0 o and AOLP = ~180 o means the same to the 2 satellite sensor. However, at 670 nm, the PARASOL data for desert show stronger reflectance in 3 the backward-reflecting directions than in the forward-reflecting directions. This is significantly 4 different from the ocean cases. Desert's reflection ofto solar radiation is a complicated 5 phenomenonissue thatwhich is neither Lambertian nor specular-reflection. Thus, our simple 6 approach here shows some difference in reflectance from the data. However, our objective for 7 this study is to accurately model the desert DOP accurately, and to accurately model the desert 8 AOLP accurately when the DOP is not trivial. Such modeling errors in the total reflectance are to 9 be expected and not the concern of this study. Errors in modeling the reflectance is ignorable for 10 this purpose.

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For an even longer wavelength of 865 nm, Figures 14 to 19 show that, similar to the cases for the