Modeling Bidirectional Polarization Distribution Function of Land Surfaces Using Machine Learning Techniques

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.