PROSPECULAR: A model for simulating multi-angular spectral properties of leaves by coupling PROSPECT with a specular function

Understanding the optical properties of leaves is of great importance for characterizing the relationships between leaf traits and remote sensing signals. The relationship between biochemical parameters and leaf spectral reflection has been widely established through PROSPECT, while surface structural parameters can be linked to leaf multi-angular reflection through Bidirectional Reflectance Distribution Function (BRDF) models. However, it's still challenging to characterize how leaf spectra response changes with different illumination and viewing geometries, in connection to both biochemical and surface structural traits. To address this challenge, we propose the model PROSPECULAR, which combines PROSPECT with a specular function determined by illumination-viewing geometry parameters, wavelength-dependent refractive index, and roughness. This model simulates spectral and multi-angular BRF and retrieves both leaf biochemical and surface structural parameters. The PROSPECULAR accounts for the wavelength dependence of the leaf surface refractive index in the specular function and separates the specular reflection from PROSPECT in the diffuse component calculation. The accuracy of PROSPECULAR's spectral simulation was assessed using a multi-angular dataset measured in the hemispherical space (42 viewing zenith angles (VZAs) at 20–50° source zenith angles (SZAs)). Then, the inversion accuracy of PROSPECULAR was validated using a multi-angular dataset measured in the principal plane (13 VZAs and 20–50° SZAs). The results showed that PROSPECULAR was able to simulate multi-angular BRF (RRMSE = 16.27%) when SZA was <50° and retrieve a unified set of biochemical parameters for each leaf sample using multi-angular BRF (RMSE of chlorophyll, water, dry matter, protein, and carbon-based constituents were 11.31 μg/cm2, 0.0029 g/cm2, 0.0022 g/cm2, 0.00096 g/cm2, and 0.0028 g/cm2, respectively). The agreement between the calculations and measurements of multi-angular BRF for various plant species indicated that PROSPECULAR is an effective leaf optical model. In contrast, the existing radiative transfer models (PROSPECT, PROCWT, PROCOSINE, and PROSDM) showed varying levels of accuracy in inverting biochemical parameters, depending on the VZA. The advantage of PROSPECULAR is its potential for characterizing both spectral and directional properties of leaves at arbitrary given illumination-viewing geometry and inverting leaf parameters using BRF data from several VZAs in the hemispherical space.