Quantifying spatial heterogeneity at the landscape scale using variogram models

The monitoring of earth surface dynamic processes at a global scale requires high temporal frequency remote sensing observations which are provided up to now by moderate spatial resolution sensors. However, the spatial heterogeneity within the moderate spatial resolution pixel biases non-linear estimation processes of land surface variables from remote sensing data. To limit its influence on the description of land surface processes, corrections based on the quantification of the intra-pixel heterogeneity may be applied to non-linear estimation processes. A complementary strategy is to define the proper pixel size to capture the spatial variability of the data and minimize the intra-pixel variability. This work provides a methodology to characterize and quantify the spatial heterogeneity of landscape vegetation cover from the modeling of the variogram of high spatial resolution NDVI data. NDVI variograms for 18 landscapes extracted from the VALERI database show that the land use is the main factor of spatial variability as quantified by the variogram sill. Crop sites are more heterogeneous than natural vegetation and forest sites at the landscape level. The integral range summarizes all structural parameters of the variogram into a single characteristic area. Its square root quantifies the mean length scale (i.e. spatial scale) of the data, which varies between 216 and 1060 m over the 18 landscapes considered. The integral range is also used as a yardstick to judge if the size of an image is large enough to measure properly the length scales of the data with the variogram. We propose that it must be smaller than 5% of the image surface. The theoretical dispersion variance, computed from the variogram model, quantifies the spatial heterogeneity within a moderate resolution pixel. It increases rapidly with pixel size until this size is larger than the mean length scale of the data. Finally based on the analysis of 18 landscapes, the sufficient pixel size to capture the major part of the spatial variability of the vegetation cover at the landscape scale is estimated to be less than 100 m. Since for all the heterogeneous landscapes the loss of NDVI spatial variability was small at this spatial resolution, the bias generated by the intra-pixel spatial heterogeneity on non-linear estimation processes will be reduced. © 2006 Elsevier Inc. All rights reserved.