The design of optimal sampling schemes for local estimation and mapping of regionalized variables—II: Program and examples☆

Abstract A FORTRAN IV program, OSSFIM, is presented for calculating estimation variances when interpolating by kriging from regular rectangular and triangular grids of data and previously-determined semi-variogram. The variances are computed for a range of grid spacings and block sizes, and the results graphed. The user chooses a block size, and can read from the appropriate graph the sample spacing corresponding to any prescribed maximum tolerable error. This is the optimal sampling scheme. Use of the program is illustrated with two examples showing different types of variation in soil. In one, the pH of topsoil is isotropic with a spherical semi-variogram and negligible nugget variance. An equilateral triangular grid is the best sampling scheme; it is approximately 10 per cent more efficient than a square grid. In the other example, variation is linear but anisotropic with a large nugget variance. In these circumstances, a triangular grid has no advantage over a rectangular one, which should be elongated in the ratio 1.88 to I in the direction of minimum variation.