A modified version of the kernel-driven model for correcting the diffuse light of ground multi-angular measurements

When using the kernel-driven bidirectional reflectance distribution function (BRDF) model to process multi-angular measurements, the input multi-angular measurements must be corrected for atmospheric effects. However, in current databases, a significant number of ground-based multi-angular measurements contain either no corrections or only approximate corrections for atmospheric effects. Thus, the blended diffuse light in the total incident irradiance will result in considerable smoothing of the reflectance anisotropy retrieved by the kernel-driven model unless an atmospheric correction process is conducted. In this study, we propose a diffuse-light correction (DLC) form of the kernel-driven model that improves its ability to process multi-angular measurements blended with hemispherical diffuse light. The DLC form of the kernel-driven model can be used to retrieve the intrinsic reflectance anisotropy of the observed target from atmospheric-uncorrected multi-angular measurements. This study used multi-angular data simulated by the PROSAIL and Radiosity Applicable to Porous IndiviDual objects (RAPID) BRDF model, atmospheric-corrected Polarization and Directionality of the Earth's Reflectances (POLDER), Cloud Absorption Radiometer (CAR) multi-angular measurements and their simulated data based on the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) tools to validate the effectiveness of the DLC form of the kernel-driven model. The results indicated that the reflectance factors directly retrieved by the kernel-driven model are considerably smoothed by the blended diffuse light, especially in hotspot regions. Even under clear and cloudless sky conditions, the retrieved hotspot reflectance in the red band is still underestimated by an average of 9.25%, 7.72%, 11.0% and 13.8% for the PROSAIL, RAPID, POLDER and CAR data, respectively. In contrast, the hotspot reflectance retrieved by the DLC form of the kernel-driven model is very close to the intrinsic reflectance anisotropy of the targets; the average relative error of the DLC form of the kernel-driven model is only 1.99%, 1.50%, 4.57% and 3.42%, respectively. Although the reflectance reconstructed by the DLC form of the kernel-driven model in the hotspot region represents a considerable improvement compared with the reflectance retrieved by the original kernel-driven model, its improvement on the root mean square error (RMSE) and the bias of the entire datasets is not very apparent. Using the DLC form of the kernel-driven model can significantly improve the ability of the kernel-driven model to process multi-angular measurements blended with hemispherical diffuse irradiance.