Spatial interpolation

<p><TT>The theory and practical application of techniques of statistical interpolation are studied in this thesis, and new developments in multivariate spatial interpolation and the design of sampling plans are discussed. Several applications to studies in soil science are presented.</TT><p><TT>Sampling strategies for collecting spatial data (both the number of observations and their location in the region to be studied) are discussed. It is shown that nested sampling is unsuitable if data are to be collected in an area in order to determine the spatial semivariogram, because semivariogram values for only a few distances are obtained. Furthermore, grid sampling is preferable to nested sampling if spatial interpolation is intended. Sequential sampling is advantegeous if the mean of a variable within an area is to be estimated and there is no spatial correlation. Sequential sampling requires only about 30% of the number of observations required by standard sampling schemes.</TT><p><TT>In this thesis universal kriging and cokriging (that is kriging and cokriging in the presence of a trend) are formulated in terms of regression procedures. Universal kriging is a special case of universal cokriging. Multivariate increments are extensions of univariate increments and of multivariate stationary variables. Conditions are formulated which permissible polynomial pseudo-covariance and pseudo- crosscovariance functions describing the spatial structure of the variables (or their increments) and their interaction, respectively, have to obey. The coefficients of these functions have been estimated by using the restricted maximum likelihood (REML) method. A practical application of universal cokriging is described.</TT><p><TT>The application of spatial interpolation in soil science is examined. One of the studies described investigates the problems of scale and the use of soil survey information on moisture deficits caused by groundwater extraction in the Mander area in the Netherlands. In another study the available water and the infiltration rates on terraces of the Allier river in the Limagne area in France are investigated. Cokriging becomes more precise as compared to kriging (and there is a concomitant reduction in costs) if the predictand is strongly correlated with the covariable. This is particularly true if the sampling of the covariable is denser than that of the predictand and the costs of sampling of the covariable are much less than those of sampling the predictand. Stratification of the survey area, e.g. by means of soil map delineations increases the precision of predictions when applying cokriging. An obvious gain in precision is achieved for homogeneous soil units, where the measured values are relatively small, and there is no spatial structure. Also, the use of cokriging permits fewer observations as compared to kriging, if a certain predescribed precision of predictions is defined. When simulation calculation models are used, e.g. to obtain values for moisture deficits, one should first calculate model results for every observation point, and then interpolate, rather than interpolate the input variables, and then calculate model results.</TT&gt