Monotonicity of Area Averaged NDVI as a Function of Spatial Resolution based on a Variable Endmember Linear Mixture Model

Choice of area averaging strategy to produce data of normalized difference vegetation index (NDVI) is one of the sources of uncertainty, which is eventually propagated into the simulation results of global climate changes. The purpose of this paper is to investigate this scaling effects of NDVI, especially, on its monotonicity as a function of spatial resolution defined as a number of sampling points within a target area. A simple two-endmember linear mixture model (LMM) is used to analyze the differences among the results of area averaged NDVI with different resolutions. It is proofed analytically that the area averaged NDVI changes monotonically as the spatial resolution becomes higher (more number of sampling points within a fixed area) under the two-endmember LMM, only if a certain condition is satisfied. On the other hand, when the condition is not satisfied, the monotonic behavior of the averaged NDVI value is no longer guaranteed even within an assumption of two-endmember LMM.