Change of support (block prediction)

Average values for square, rectangular or arbitrarily shaped blocks can be predicted in gstat for all kriging variants, for OLS or WLS prediction or for inverse distance weighted interpolation, or they can be simulated using multi-Gaussian simulation.

The mean value of a block, the size of a grid cell, is obtained by adding the command

blocks;

to the command file. Alternatively, block mean values for rectangular blocks with arbitrary size, centred at prediction locations are obtained when the block size is specified, in one dimension:

blocksize: dx = 1;

for a line element with length 1, in two dimensions

blocksize: dx = 1, dy = 2;

for a rectangular element with size 1 $\times$ 2 or in three dimensions

blocksize: dx = 1, dy = 2, dz = 3;

for a block with dimensions 1 $\times$ 2 $\times$ 3, see example 4 and example 8.

Block averages are approximated by discretizing (``representing'') the block with a limited number of points [13,1]. Blocks with arbitrary shapes may be defined by specifying the points discretizing the block (see appendix A.3).