A semi-empirical BPDF model for improving characterization of polarimetric reflection of land surfaces: Validation using laboratory and POLDER polarization data

Bidirectional Polarization Distribution Function (BPDF) models, widely used to characterize the polarimetric properties of light reflected from targets, are crucial for linking polarization with land surface structural parameters and understanding surface contributions to polarization in radiative transfer. However, existing BPDF models face challenges in accurately representing variations in both the magnitude and distribution of polarimetric reflection across surfaces with varying structural characteristics. In this study, a three-parameter BPDF model (GMF model), which can effectively characterize polarimetric reflection of surfaces ranging from smooth to rough, was developed by combining the GGX distribution function with the Fresnel equation and a shadowing function. Multi-angular polarimetric data from laboratory measurements over three plant samples and from Polarization and Directionality of the Earth's Reflectances (POLDER) satellite observations over various land surfaces, each exhibiting distinct polarimetric reflection properties, were used to validate the proposed model. Compared with five existing models, the new model achieved the highest accuracy in simulating polarimetric reflection, reducing the overall RMSE by 33%–68% for laboratory samples and by 8%–30% for POLDER observations. This improvement is attributed to the incorporation of the GGX distribution function, which enables the new polarization model to accurately characterize the polarimetric properties of surfaces with varying structures, including sharp specular peaks over smooth surfaces and broad angular distributions over rough surfaces. Furthermore, the analysis of the model's response to parameter variations demonstrated that the GGX distribution function enhanced the ability of the GMF model to modulate the magnitude and distribution of polarimetric reflection induced by surface structure variations. The proposed polarization model is expected to advance polarized remote sensing applications in land surface monitoring.