Block correlation and the spatial resolution of soil property maps made by kriging

The block correlation is the correlation between the block kriging prediction of a variable and the true spatial mean which it estimates, computed for a particular sampling configuration and block size over the stochastic model which underlies the kriging prediction. This correlation can be computed if the variogram and disposition of sample points are known. It is also possible to compute the concordance correlation, a modified correlation which measures the extent to which the block kriging prediction and true block spatial mean conform to the 1:1 line, and so is sensitive to the tendency of the kriging predictor to over-smooth. It is proposed that block concordance correlation has two particular advantages over kriging variance for communicating uncertainty in predicted values. First, as a measure on a bounded scale it is more intuitively understood by the non-specialist data user, particularly one who is interested in a synoptic overview of soil variation across a region. Second, because it accounts for the variability of the spatial means and their kriged estimates, as well as the uncertainty of the latter, it can be more readily compared between blocks of different sizes than can a kriging variance. Using the block correlation and concordance correlation it is shown that the uncertainty of block kriged predictions depends on block size, but this effect depends on the interaction of the autocorrelation of the random variable and the sampling intensity. In some circumstances (where the dominant component of variation is at a long range relative to sample spacing) the block correlation and concordance correlation are insensitive to block size, but if the grid spacing is closer to the range of correlation of a significant component then block size can have a substantial effect on block correlation. It is proposed that (i) block concordance correlation is used to communicate the uncertainty in kriged predictions to a range of audiences (ii) that it is used to explore sensitivity to block size when planning mapping and (iii) as a general operational rule a block size is selected to give a block concordance correlation of 0.8 or larger where this can be achieved without extra sampling.