Inter-Algorithm Relationships for the Estimation of the Fraction of Vegetation Cover Based on a Two Endmember Linear Mixture Model with the VI Constraint

Measurements of the fraction of vegetation cover (FVC), retrieved from remotely sensed reflectance spectra, serves as a useful measure of land cover changes on the regional and global scales. A linear mixture model (LMM) is frequently employed to analytically estimate the FVC using the spectral vegetation index (VI) as a constraint. Variations in the application of this algorithm arise due to differences in the choice of endmember spectra and VI model assumptions. As a result, the retrieved FVCs from a single spectrum depend on those choices. Therefore, the mechanism underlying this dependency must be understood fully to improve the interpretation of the results. The objective of this study is to clarify the relationships among algorithms based on the LMM. The relationships were derived analytically by limiting both the number of endmembers and the spectral wavelength band to two each. Numerical experiments were conducted to demonstrate and validate the derived relationships. It was found that the relationships between two algorithms of this kind could be characterized by a single parameter that was determined by the endmember spectra and the coefficients of a VI model equation used in the algorithms.