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

Abstract

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.

Remote Sensing of Fractional Green Vegetation Cover Using Spatially-Interpolated Endmembers

“…Non-linear unmixing approaches also exist (e.g., [13][14][15]), but the linear approach is used most often due to its simplicity, rationality, and feasibility in practical applications [16]. The number of spectral bands in an image limits the number of endmembers that can be used for unmixing [17], so for images with relatively few spectral bands, a common approach is to assume that FVC can be estimated by the linear combination of two endmembers: bare soil and 100% green vegetation cover [3,6,7,12,18]. In this two endmember model, it is also typically assumed that dead vegetation is spectrally-similar to bare soil [3], although [19] found that surface albedo can be used to separate soil and dead vegetation in areas with low-albedo soils.…”

Comparison of the Noise Robustness of FVC Retrieval Algorithms Based on Linear Mixture Models

“…The choice of endmember variable (endmember model) and constraints on the algorithms are summarized in Table 1. Below, we briefly introduce the three algorithms for the two-band case, as assumed in previous studies [28,29]. Table 1.…”

“…In these studies, a two-endmember LMM assuming two multispectral bands was used throughout to facilitate analytical derivations. Previous studies have investigated the relationship among the three types of LMM-based FVC algorithms under a two-endmember assumption [28]. Here, the relationship between FVC values derived from different algorithms is expressed analytically.…”

“…This study focuses on an LMM-based algorithm that shows some variation in the retrieved FVCs owing to differences in the model assumptions and constraints on the retrieval algorithms [27,28]. This study is performed as a series of investigations [28,29] about the three LMM-based FVC algorithms, which are widely used in practical applications.…”

“…This study is performed as a series of investigations [28,29] about the three LMM-based FVC algorithms, which are widely used in practical applications. In these studies, a two-endmember LMM assuming two multispectral bands was used throughout to facilitate analytical derivations.…”