Accurate estimation of polarized reflectance (R_p) of land surfaces is critical for remote sensing of aerosol optical properties. In the last two decades, many data-driven bidirectional polarization distribution function (BPDF) models have been proposed for accurate estimation of R_p, among which the generalized regression neural network (GRNN) based BPDF model has been reported to perform the best. GRNN is just a simple machine learning (ML) technique that can solve non-linear problems. Many ML techniques were reported to work well in solving non-linear problems and consequently may provide better performance in BPDF modeling. However, incorporating various ML techniques with BPDF modeling and comparing their performances have never been well documented. In this study, three widely used ML algorithms—i.e., support vector regression (SVR), K-nearest-neighbor (KNN), and random forest (RF)—were applied for BPDF modeling. Using measurements collected by the Polarization and Directionality of the Earth’s Reflectance onboard PARASOL satellite (POLDER/PARASOL), non-linear relationships between R_p and the input variables, i.e., Fresnel factor (F_p), scattering angle (SA), reflectance at 670 nm (R₆₇₀) and 865 nm (R₈₆₅), were built using these ML algorithms. Results showed that taking F_p, SA, R₆₇₀, and R₈₆₅ as input variables, the performance of the four ML-based BPDF models was quite similar. The KNN-based BPDF model provided slightly better results, and improved the accuracy of the semi-empirical BPDF models by 9.55% in terms of the overall root mean square error (RMSE). Experiments of different configuration of input variables suggested that using multi-band reflectance as input variables provided better results than using vegetation indices. The RF-based BPDF model using all reflectances at six bands as input variables produced the best results, improving the overall accuracy by 6.62% compared with the GRNN-based BPDF model. Among all the input variables, reflectance at absorbing spectral bands—e.g., 490 nm and 670 nm—played more significant roles in RF-based BPDF modeling due to the domination of polarized partition in total reflectance. Fresnel factor and scattering angle were also important for BPDF modeling. This study confirmed the feasibility of applying ML techniques to more accurate BPDF modeling, and the RF-based BPDF model proposed in this study can be used to increase the accuracy of remote sensing of the complete aerosol properties.

中文翻译：

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利用机器学习技术对地表双向极化分布函数建模

准确估计陆地表面的偏振反射率（R _p）对于遥感气溶胶光学特性至关重要。在过去的二十年中，已经提出了许多数据驱动的双向极化分布函数（BPDF）模型来精确估计R _p，其中据报道，基于广义回归神经网络（GRNN）的BPDF模型表现最佳。GRNN只是一种简单的机器学习（ML）技术，可以解决非线性问题。据报道，许多机器学习技术可以很好地解决非线性问题，因此可以在BPDF建模中提供更好的性能。但是，将各种ML技术与BPDF建模相结合并比较它们的性能从未得到很好的证明。在这项研究中，将三种广泛使用的ML算法-支持向量回归（SVR），K近邻（KNN）和随机森林（RF）-用于BPDF建模。使用由PARASOL卫星（POLDER / PARASOL）上的地球反射的偏振和方向性收集的测量值，R之间的非线性关系_p和输入变量，即菲涅耳因数（F _p），散射角（SA），在670 nm（R ₆₇₀）和865 nm（R ₈₆₅）处的反射率，都是使用这些ML算法建立的。结果表明，取F _p，SA，R ₆₇₀和R ₈₆₅作为输入变量，四个基于ML的BPDF模型的性能非常相似。基于KNN的BPDF模型提供了更好的结果，并且以总均方根误差（RMSE）而言，半经验BPDF模型的准确性提高了9.55％。输入变量不同配置的实验表明，使用多波段反射率作为输入变量比使用植被指数提供了更好的结果。基于RF的BPDF模型使用六个波段的所有反射率作为输入变量，产生了最佳结果，与基于GRNN的BPDF模型相比，将整体准确性提高了6.62％。在所有输入变量中，由于偏振分区在总反射率中占主导地位，因此在吸收光谱带（例如490 nm和670 nm）处的反射率在基于RF的BPDF建模中起着更为重要的作用。菲涅耳因子和散射角对于BPDF建模也很重要。这项研究证实了将ML技术应用于更精确的BPDF建模的可行性，并且本研究中提出的基于RF的BPDF模型可用于提高完整气溶胶特性的遥感准确性。