Relationships Between Errors Propagated in Fraction of Vegetation Cover by Algorithms Based on a Two-Endmember Linear Mixture Model

Remotely sensed reflectance spectra may be biased by several intervening factors, and the biases are propagated into estimations of the fraction of vegetation cover (FVC) by algorithms based on a linear mixture model (LMM). The errors propagated in FVCs depend on the retrieval algorithm used, due to differences in the assumptions of the model as well as constraints employed in the algorithm. These differences should be fully understood prior to algorithm selection for practical applications. Although numerous studies have investigated the relationships between errors propagated by different algorithms, these relationships have not been fully understood from a deterministic perspective. This study introduces a technique for deriving the analytical underpinnings of error propagation in FVC based on several LMM-based algorithms. The derivation assumes that measurement noise is band-correlated additive noise. The bias errors propagated in FVC depended on the endmember spectra assumed in the algorithm, the target spectrum, and the coefficients of the spectral vegetation index, which were employed as constraints, as well as magnitude of the input error. It was found that the relationships among the propagated errors assume asymmetric elliptical forms with coefficients that are determined by the input variables. These results suggest that the relationships depend heavily on the choice of endmember spectra as well as the spectrum of the target pixel and the vegetation index employed as a constraint. The present findings should assist in the selection of an optimum algorithm based on prior knowledge of the target field.