Scaling Effect in the Area-Averaged Fraction of Vegetation Cover Derived by Linear Mixture Model with Two-Band Spectral Vegetation Index Constraint

Multi-sensor analysis for monitoring terrestrial vegetation suffers from systematic errors due to the differences in spatial resolution, called scaling effect. This study investigates mechanisms underlying the scaling effect on fraction of vegetation cover (FVC) estimation, derived using a two-band spectral vegetation index (VI)-isoline based linear mixture model (VI-isoline based LMM). The two-band spectral VI includes a normalized difference vegetation index (NDVI), a soil-adjusted vegetation index (SAVI), and a two-band enhanced vegetation index (EVI2). A focus of this study is the monotonicity in an area-averaged FVC estimation along with spatial resolution. The proof of monotonicity provides intrinsic uncertainties (error bounds) of the area-averaged FVC attributed to scaling effect. A resolution transformation model was employed to investigate the monotonicity and derived results showed that a factor ξ, a function of ’true’ and ’estimated’ endmember spectra of vegetated and non-vegetated surfaces, is responsible for distinguishing the monotonicity and the non-monotonicity as well as increasing/decreasing trend of the area-averaged FVC along with spatial resolution. When the averaged FVC was monotonic, the increasing/decreasing trend was identical across FVCs derived using different two-band VIs. The derived results also described the condition by which scaling effect in the FVC is eliminated. Such findings were adverse to the scaling theory of two-band VI. Numerical experiments with a simulated spectral image verified the relationship between the monotonicity and the spectral conditions. The practicality of the scaling theory and the possibility of developing a scale-invariant FVC algorithm using two-band VI were evaluated in numerical experiments with Landsat7-ETM+ data.