Designing sampling grids from imprecise information on soil variability, an approach based on the fuzzy kriging variance

It is shown how, given a fuzzy formulation of the variogram of a soil property, a fuzzy set of grid spacings that will achieve a target kriging variance can be derived. This fuzzy set of grid spacings can then be defuzzified in a more or less conservative way to define a sampling scheme. The method is illustrated in three examples. The first uses a hypothetical fuzzy variogram. The second is a fuzzy variogram for topsoil organic carbon content in a field, based on the crisp variogram of a related ancillary variable and generalized information on topsoil variability at field scales. The third fuzzy variogram is for topsoil pH, assuming no local knowledge but representing in fuzzy form the range of variability in a collection of variograms for this property in the soil science literature.