Abstract
Retrieval of complete aerosol properties over land through remote sensing requires accurate information about the polarization characteristics of natural land surfaces. In this paper, a new bidirectional polarization distribution function (BPDF) is proposed, using the generalized regression neural network (GRNN). This GRNN-based BPDF model builds a quite accurate nonlinear relationship between polarized reflectance and four input parameters, i.e., Fresnel factor, scattering angle, red, and near-infrared reflectances. It learns fast because only a smoothing parameter needs to be adjusted. The GRNN-based model is compared to six widely used BPDF models (i.e., Nadal–Bréon, Maignan, Waquet, Litivinov, Diner, and Xie–Cheng models), using the Polarization and Directionality of the Earth’s Reflectance (POLDER) measurements. Experiments suggest that the GRNN-based BPDF model is more accurate than these models. Compared with the best current models, the averaged root-mean-square error (RMSE) from the GRNN-based BPDF model can be reduced by 13.4% by using data collected during the whole year and is lower for 97.4% cases with data collected during every month. Moreover, compared to the widely used BPDF models, the GRNN-based BPDF model provides better performance when the scattering angle is small, and it is the first model that is able to reproduce negative polarized reflectance. The GRNN-based BPDF model is thus useful for the remote sensing of complete aerosol properties over land.
Highlights
Solar radiation scattered by natural land surfaces is partly polarized [1,2,3,4]
In order to simplify the modeling process, we did not directly use refractive index, sun-sensor geometry, and vegetation coverage as input parameters because; on one hand, the generalized regression neural network (GRNN)-based bidirectional polarization distribution function (BPDF) model requires too many input parameters, on the other hand, the vegetation coverage is neither provided by the Polarization and Directionality of the Earth’s Reflectance (POLDER) bidirectional reflectance distribution function (BRDF)–BPDF dataset nor easy to be retrieved from the dataset
Six BPDF models have been proposed, i.e., Nadal–Bréon, Maignan, Waquet, Litivinov, Diner and Xie–Cheng models. All of these widely used models indicate that the polarized reflectance of natural land surfaces is a nonlinear function of variables related to refractive index, sun-sensor geometry, and/or vegetation coverage
Summary
Solar radiation scattered by natural land surfaces is partly polarized [1,2,3,4]. The polarized radiation reflected by natural land surfaces is anisotropic and varies with the sun-sensor geometry [7,8]. The angular distribution of the polarization of light reflected by natural land surfaces can be quantified by the bidirectional polarization distribution function (BPDF). The popular BRDF models found in the literature, such as the RPV [13] and kernel-driven models [14], among others, cannot be used directly for describing BPDF, and a separate model is needed for modeling polarization of light reflected by natural land surfaces Compared to the bidirectional reflectance distribution function (BRDF), the BPDF is quite different as, on one hand, it is insensitive to wavelengths in the visible to near–infrared (NIR) region of the electromagnetic spectrum [9], and on the other hand, the maximum polarized reflectance always appears in the forward scattering directions, but not the backward scattering directions [10,11,12].
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