MSc thesis subject: Including variogram estimation error in spatial sampling design optimisation

Spatial data collection, such as used in hydrology, soil science and ecology is a costly affair, both time-wise and money-wise. Sampling design optimisation aims to achieve what is needed at lowest cost. For instance, in geostatistics we can use sampling design optimisation to minimise the number of required sampling points while ensuring that the spatial average kriging variance stays below a pre-defined threshold. The aim of this MSc research is to extend current spatial sampling design optimisation techniques as developed for regression kriging, such that the optimisation also account for variogram estimation errors.

You will first study the geostatistical literature on spatial sampling design optimisation. In particular, you will learn how a technique known as simulated annealing can be used to minimise the spatially averaged regression kriging variance. You will apply and adapt existing software (R scripts) to optimise a design for estimation of soil chemical elements (e.g. Cu, Ni, Cd) for (parts of) Europe, using the GEMAS database and WorlGrids covariates to calibrate the model. The optimal design will strike a balance between optimisation in geographic and feature space: a uniform spreading over the study area is advantageous while also the covariate space must be covered well. However, a well known problem is that these designs provide poor estimates of the variogram, in particular the nugget variance, since uniform spreading over the geographic space fails to acquire the short-distance spatial variation. This problem has been tackled for the ordinary kriging case by including variogram estimation error in the optimisation, but a solution for the regression kriging case has not yet been published. You will develop the methodology and provide a software implementation of that solution, and you will evaluate the performance of your method using cross-validation on a synthetic and the GEMAS dataset. This MSc research supports the PhD-research of Alexandre Wadoux.


  • Understand the geostatistical literature on spatial sampling design optimisation
  • Understand and be able to modify existing R scripts that optimise spatial sampling designs using simulated annealing and similar techniques
  • Extend existing spatial sampling design optimisation approaches to a case where variogram uncertainty is included in a regression kriging context
  • Apply and evaluate the developed method on a synthetic case and using the GEMAS soil chemistry database



  • Solid background in geostatistical modelling, such as obtained through the Spatial Modelling and Statistics course
  • Experience with programming in R

Theme(s): Modelling & visualisation