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Design of an Optimal Sampling Network for Estimating the Variogram¹

ABSTRACT

Kriging techniques for interpolating spatial phenomena have recently been applied by soil scientists to map soil properties in heterogeneous field. A fundamental component of these techniques is the variogram which has to be estimated experimentally. A method to design an optimal sampling network for estimation of the variogram is proposed. Using a constant number of pairs of points (N_p) per lag class, the criterion for selecting the location of the sampling points is the uniformity of the values of the lag vector, h, within a given lag class, for each of the lag classes which cover the field domain. For a given sample size, N, the method provides a set of scaling factors which in turn is used to calculate the new locations of the sampling points by an iterative procedure. Using the aforementioned criterion, the best set of the sampling points is selected. Analysis of the results showed that by using the proposed method, the variability of h within a given lag class, as well as the variability of h among the lag classes, was considerably reduced relative to the situation where the original locations were used. The method was found to be sensitive to both N and N_p as well as to the initial locations of the points. The effect of the method on the estimation of the variogram was tested using simulated realizations of a two-dimensional stationary and isotropic field. The results for fifty different realizations showed that the variograms which had been estimated from data generated on the coordinates of the sampling points provided by the method were smoother and fitted the theoretical variograms better than those which were estimated from data generated on the original coordinates of the sampling points. When only the smaller lag classes were considered, the differences between the two sets of the variograms become smaller.

¹ Contribution no. 747-E, 1983 series, from the Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel.

² Soil Scientist, Div. of Soil Physics, ARO, The Volcani Center, Bet Dagan, Israel.

Received for publication July 3, 1983. Accepted for publication February 29, 1984.