Non-stationary models for optimal sampling and mapping of terrain in Great Britain

The primary aims and objectives of this thesis are to use non-stationary geostatics to (i) characterise effectively spatial variation in terrain (as represented by digital terrain data); (ii) to estimate optimally and (iii) design optimal sampling strategies for updating existing data sets and sampling new data sets. This thesis involved the analysis of contour data and remotely sensed digital terrain data.Several approaches have been developed and applied to the characterisation of terrain as represented by digital terrain data. The fractal dimension was estimated for a moving window and the fractal dimension was divided into sub-sets with similar spatial variation through the use of a region-growing segmentation algorithm. Variograms for each of the segments were used to inform kriging and the design of sample strategies. Marked increases in accuracy were noted over the global model. Another approach utilised was to estimate the variogram for a moving window, automatically fit a model to the variogram and estimate, using kriging, on a point by point basis. The approach was shown to be beneficial where sample spacing is relatively large.A by-product of kriging is the kriging variance, a measure of confidence in estimates. The kriging variance is a function of the form of the variogram (or other measure) and the sampling configuration. By relating the maximum kriging variance to different sample spacings it was possible to ascertain the sample spacing necessary to achieve a particular accuracy. This thesis shows that the mean kriging standard error provides an accurate guide to the standard error where segmentation is used. Another approach, indicator kriging (IK), which unlike ordinary kriging (OK) does not depend on assumptions of normality, was used in this thesis. IK was shown to be potentially very useful in the design of optimal sampling strategies as the conditional variance of IK is dependent on the data values and it provides an accurate guide to uncertainty in estimates.