Optimal updating of spatial sampling designs combining incomplete ground truth and auxiliary data from satellite images

The efficiency of area sample designs is influenced by the number of sampling stages, the size of sampling units (segments) and the selection procedure. Some authors have used estimates of spatial autocorrelation functions based on previous sample surveys for computing the optimum sample size and segment size in one stage sample designs (Carfagna 1998, Gallego et al. 1999) and, in two stage sample designs, the optimum size of primary and secondary sampling units and their sizes (Carfagna 2000). Then, some authors have proposed sequential selection methods based on the spatial autocorrelation (Arbia and Lafratta 2002). When previous ground surveys have not been performed or are not appropriate for planning an efficient sample design, satellite images can help. Carfagna (2000) has used the photo-interpretation of remote sensing data (CORINE) for computing correlograms in order to create an optimum two stage sample design for estimating the area of different kinds of forest in Europe. Photo-interpretation of remote sensing data cannot adopt a very detailed legend, the classes adopted are generally aggregations of the classes that are used for the ground survey and the sample design is optimized for the classes used for the photo-interpretation; thus this optimization is useful only if the two legends are similar. In the present work we consider optimal spatial sampling that take advantage of the notion of spatial correlogram. However this procedure cannot be applied straightforwardly because very few data are available at some distances. Thus, we explore the possibility to combine sample survey data and satellite images. In this paper, we suggest to combine the two sources of data using a method of moments.