From BRDF to BPDF: a premilinary study on evolution of the basic remote sensing quantitative inversion model

The essence of light is shear wave electromagnetic wave vector. The scalar remote sensing system based on the bidirectional reflectance distribution function (BRDF) model only uses the overall intensity information of reflected light from vegetation. The structural information of leaf surface, leaf, and canopy contained in reflected radiation cannot be distinguished. On the basis of scalar remote sensing, considering the two-dimensional polarization vector characteristics (intensity and direction) perpendicular to the propagation direction of electromagnetic waves, it can be deepened into a vector remote sensing system, which is expected to accurately describe a variety of information contained in the reflected light and improve the inversion accuracy of vegetation parameters. The bidirectional polarization distribution function (BPDF), which describes the spatial distribution of polarization reflection, has the problems of low accuracy and poor generalization at present. Therefore, it is urgent to further explore the basic theory of vector remote sensing and construct the basic model of vegetation vector remote sensing with strong universality. In this paper, we aim to use the interaction between photons and vegetation elements to construct a more general physical model of vegetation BPDF. Firstly, based on the spectral invariant model of photon-vegetation elements interaction, the basic form of vegetation BPDF physical model based on directional escape probability is proposed, and the analytical expression of the model is derived based on the radiation transfer theory of vegetation single reflection. Then, by considering the variation of leaf scattering with dry matter content, the spectral invariant model was optimized and the general expression of the model was derived. Finally, the 3D vector radiative transfer model and multi-scale measured data were used to realize the direct and indirect verification of the model. The results show that the root mean square error of the forward polarization reflectance of the analytical expression and the general expression of the BPDF physical model constructed in this work is within 0.001 under different vegetation scenes, which is consistent with the forward results of the vector radiation transfer model in the hemisphere space. The stability of the model relationship is also briefly verified by the multi-scale measured data. The model R2 is generally higher than 0.9. Compared with the existing vegetation polarization reflection model, the model constructed in this paper has a physical mechanism, simple form, acceptable parameterization scheme, high accuracy, and strong generalization ability, and is universal for dense vegetation. It provides a theoretical basis and an exploratory scheme for the transformation process of further considering the two-dimensional polarization characteristics of BPDF to form a vector remote sensing system based on BRDF one-dimensional scalar remote sensing.