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Designing optimal sampling configurations with ordinary and indicator kriging

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The objective of this paper is to examine the applicability of two geostatistical approaches, ordinary kriging (OK) and ordinary indicator kriging (IK), to the design of optimal sampling strategies. This paper uses the OK variance and the conditional variance of the conditional cumulative distribution function (ccdf) derived through IK to assess local uncertainty in estimates. The mean OK variance and IK variance for a given grid spacing, using data sampled from a remotely sensed DTM, were used to ascertain the sample spacing required to achieve a particular accuracy. The estimates of optimal sample spacing were assessed with reference to the complete DTM. Judgement on the success of the two approaches was made on the basis of the correlation between the OK variance and the errors of OK estimation and between the IK variance and the errors of IK estimation, and the form of the relationships were discussed. The IK variance was found to represent the estimation errors more accurately than the OK variance, although OK estimates of elevation values were more accurate than those for IK. The IK is significantly more costly to implement than OK in terms of expenditure of time and effort and the implementation of the technique was demonstrated to be problematic in the presence of a low frequency trend. Despite these limitations IK was recommended for the design of optimal sampling strategies where the estimation of accuracy of a specified degree is particularly important and where the analysis relates to an area over which the spatial variability may be considered similar. Comparison and integration with a segmentation approach was suggested for future work, and the results of a related approach presented, to improve the implementation of IK in the context of digital elevation data.