Large amounts of information generally arise from remotely sensed images and from other kinds of sensors. This can lead to two difficulties: the first is that there is so much information that it is difficult to identify and interpret any spatial structures they might contain, and the other is the huge amount of data that needs to be stored. Both of these can be addressed by different geostatistical methods. They are illustrated using part of a SPOT image near to Atlanta, Georgia, and one variable -- normalized difference vegetation index (NDVI).
The variogram of NDVI for this area is nested, it suggests that there are two distinct spatial scales of variation present, one of about 15 pixels (300~m) and the other of 165 pixels (3.3 ~km). Since the variation is nested factorial kriging can be used to krige (predict) the short- and long-range variation separately. This geostatistical method filters the variation, and the aim was to try to gain insight into the spatial variation of NDVI. The variogram has no nugget variance, i.e. no observed `noise', therefore there are just two components to extract. The filtered long- and short-range estimates were then mapped using UNIMAP to display the variation. The map of the short-range variation shows a complex local pattern that appears to be related to the dissection in the landscape and the variation this induces in the ground cover. The long-range component seems to be associated with the main landform units and the major changes in vegetation type. Both of the scales of variation are evident in the map of ordinary kriged estimates.
To explore the second problem the image data were sampled in stages by taking one pixel in four, one in nine, and so on, ending with one in 49. For each reduced sample the aim was to assess the accuracy with which the values that had been excluded could be restored using the variogram model and both ordinary kriging and geostatistical simulation. The results were mapped using UNIMAP and compared visually. In addition the restored values were compared with the original values that had been removed, and the mean squared difference were computed. Kriging always produced estimates closer to the original values on average than did simulation. Visually, however, the results of simulation appear to be closer to those of the original image. This is because the simulation retains the original variance in the image, but does not produce optimal predictions, whereas the kriged estimates are optimal.
The results from both kriging analysis and data compression will be discussed.