Error Bounds of Area-averaged Ndvi Induced by Differences in Spatial Resolution under a Multiple-endmember Linear Mixture Model

Scaling effect of area-averaged NDVI is known as a source of error induced by differences in spatial resolution of two independent measurements over a fixed area. It deteriorates accuracy in parameter retrieval via NDVI, thus its mechanism needs to be fully understood for a better rectification of NDVI. The objective of this study is to investigate error bounds of averaged NDVI within a fixed area as a function of spatial resolution under assumptions of multiple-endmember linear mixture model (LMM). The NDVI behavior was first analyzed to identify the conditions regarding the choice of endmember spectra at which the averaged NDVI becomes the maximum and minimum. A series of numerical simulations were conducted by assuming a four-endmember LMM to demonstrate the finding such that the values of NDVI which show non-monotonic behavior fall into the ranges estimated from the two-endmember cases at all the resolutions by choosing appropriate pairs of endmember spectra predicted from the analysis. It was concluded that the error in the averaged NDVI over a fixed size of area composed of multiple endmembers can be bounded from the simpler two-endmember cases which would be a key to predicting the maximum and minimum errors caused by the scaling effect.