Scaling effect of area-averaged NDVI: Monotonicity along the spatial resolution

Abstract

Changes in the spatial distributions of vegetation across the globe are routinely monitored by satellite remote sensing, in which the reflectance spectra over land surface areas are measured with spatial and temporal resolutions that depend on the satellite instrumentation. The use of multiple synchronized satellite sensors permits long-term monitoring with high spatial and temporal resolutions. However, differences in the spatial resolution of images collected by different sensors can introduce systematic biases, called scaling effects, into the biophysical retrievals. This study investigates the mechanism by which the scaling effects distort normalized difference vegetation index (NDVI). This study focused on the monotonicity of the area-averaged NDVI as a function of the spatial resolution. A monotonic relationship was proved analytically by using the resolution transform model proposed in this study in combination with a two-endmember linear mixture model. The monotonicity allowed the inherent uncertainties introduced by the scaling effects (error bounds) to be explicitly determined by averaging the retrievals at the extrema of the resolutions. Error bounds could not be estimated, on the other hand, for non-monotonic relationships. Numerical simulations were conducted to demonstrate the monotonicity of the averaged NDVI along spatial resolution. This study provides a theoretical basis for the scaling effects and develops techniques for rectifying the scaling effects in biophysical retrievals to facilitate cross-sensor calibration for the long-term monitoring of vegetation dynamics. © 2012 by the authors.