Exploring the relation between spatial structure and wavelength: implications for sampling reflectance in the field
Recently, the variogram has been used to represent the spatial dependence in remotely sensed data obtained from ground-based, airborne and satellite-borne sensors. The variogram may be used in a variety of techniques such as kriging, cokriging, and conditional simulation and, in particular, optimal sampling design. However, little is known about the relation between spatial variation (summarized by the variogram) and spectral wavelength. Therefore, an investigation was undertaken to determine the relation between spatial dependence and wavelength for two field sites in England: one at Middlebere Heath on the Isle of Purbeck, Dorset, and the other at the Isle of Grain, Kent. At both sites, visible and near-infrared reflectance spectra comprising 252 wavebands were obtained using a Spectron SE-590TM spectroradiometer for 100 observations spaced 1m apart along 100m transects. Variograms were computed for 235 wavebands and these plotted as a three-dimensional surface. The resulting surfaces revealed changes with wavelength not only in the amount, but also in the scales of spatial variation. The spatial variation in all 235 wavelengths was approximately two-dimensional for both case studies. The implication for the design of optimal strategies with which to sample reflectance in the field is that two (and only two) sample spacings are necessary to sample all 235 wavebands.