The influence of variogram parameters on optimal sampling schemes for mapping by kriging

Abstract

Using spatial simulated annealing (SSA), spatial sampling schemes can be optimised for minimal kriging variance. Two optimisation criteria are presented in this paper. The first criterion minimises the average kriging variance, the second the maximum kriging variance. In a simple case with 23 observations, performances of a sampling scheme obtained with SSA were compared with performances of a triangular grid. SSA reduced the average kriging variance from 40.64 to 39.99 [unit] 2. The maximum kriging variance was reduced from 86.83 to 53.36 [unit] 2. Starting with a preliminary, irregularly data set of 100 observations, an additional sampling scheme of 10 observations was optimised. This reduced the average kriging variance from 21.62 to 15.83 [unit] 2. The maximum kriging variance was reduced from 70.22 to 34.60 [unit] 2. As the kriging variance is considerably influenced by variogram parameters, their influence on the optimised sampling schemes was investigated. A Gaussian variogram produced a different sampling scheme than an exponential variogram with the same nugget, sill and (effective) range. Exponential, spherical and linear variograms without nugget resulted in irregular similar sampling schemes. A very short range resulted in irregular sampling schemes, with observations separated by distances larger than twice the range. For a spherical variogram, the magnitude of the relative nugget effect did not affect the sampling schemes, except for very high values (0.75).