Extension of the Hapke model to the spectral domain to characterize soil physical properties

Abstract

The Hapke bidirectional reflectance model has mainly been used in planetary remote sensing and has given rise to some studies in Earth science. However, it has not yet been comprehensively evaluated using data from different sources, and its ability to model reflectance spectra needs to be further explored. Therefore, the objective of this study was to develop a tangible parametric model of soil hyperspectral bidirectional reflectance via the evaluation and extension of the Hapke model (hereafter named the Hapke-HSR model). Comprehensive directional and spectral soil reflectance datasets, including satellite, field data, two spectral libraries, and simulated reflectance spectra, were used. First, the two widely used versions of the Hapke model, namely, the SOILSPECT and original Hapke models, were compared. Thereafter, the simplified SOILSPECT model was extended to characterize soil hyperspectral reflectance by deriving an approximate relationship between the single-scattering albedo and wavelength. We obtained the following results. (1) Both versions of the Hapke model agreed well in fitting soil bidirectional reflectance data. However, the SOILSPECT model (R2 = 0.983–0.997, RMSE = 0.007–0.014) performed better than the original Hapke model (R2 = 0.800–0.988, RMSE = 0.014–0.057) when both satellite and field data were used. (2) The Hapke-HSR model could effectively capture the characteristics of the soil hyperspectral reflectance (R2 = 0.963–0.983 and RMSE = 0.018–0.028) based on both spectral libraries. The simulated reflectance spectra showed that the Hapke-HSR model can capture the soil moisture content variations (R2 = 0.987, RMSE = 0.011). In addition, the residual prediction deviation (RPD) values of the Hapke-HSR model were greater than 3, indicating a high prediction accuracy. These findings demonstrate that the Hapke-HSR model performs well with respect to the characterization of soil hyperspectral directional reflectance.