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 theresolutions. 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.
Highlights
Satellite remote sensing provides a historical record of the biophysical parameters that may be used to model the global vegetation dynamics [1,2], and the data provides input variables for climate and surface process models [3,4,5]
Jiang et al [25] suggested that the area-averaged normalized difference vegetation index (NDVI) should shift monotonically in moving from coarser to finer resolution because the land surface heterogeneity within any given pixel should decrease as the spatial resolution increases
These results indicate that the error bounds on the average NDVI associated with a given spatial resolution are determined by the two extreme resolution cases
Summary
Satellite remote sensing provides a historical record of the biophysical parameters that may be used to model the global vegetation dynamics [1,2], and the data provides input variables for climate and surface process models [3,4,5]. The scaling effects arise from the uncertainty caused by surface heterogeneity and nonlinearity in algorithms for retrieving pixel scale reflectance data [34,35,36,37]. Hu et al investigated the scaling effects in the NDVI using a Taylor series expansion They concluded that the scaling effects depended on the nonlinearity of the algorithm and the variances of the reflectance spectra within a target pixel [24]. Biases in the area-averaged NDVI as a function of the spatial resolution were never investigated These biases should be studied to determine how the error bounds are affected by changes in the spatial resolution. We elucidated the error bounds of the scaling effects of the NDVI by proving the monotonicity of the area-averaged VIs as a function of the spatial resolution under certain conditions. The point spread function is assumed to be uniform over the x- and y-axes, in other words, the sensor response is assumed to be perfect for the purposes of an analytic discussion
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