Assessing uncertainty in estimates with ordinary and indicator kriging

Abstract

The objective of this paper is to examine the applicability of three geostatistical approaches, ordinary kriging (OK), kriging with a trend model (KT), and indicator kriging (IK), to the assessment of uncertainty in estimates. This paper uses the OK and KT standard error and the conditional standard error of the conditional cumulative distribution function (ccdf) derived through IK to assess uncertainty in estimates of elevation. The mean OK and KT standard error and mean IK standard error, using data sampled from a remotely sensed digital terrain model (DTM), were used to ascertain the uncertainty in estimates. The estimates of elevation were assessed with reference to the complete DTM. Judgement on the success of the three approaches was made on the basis of the difference between the standard error of estimates and the mean kriging standard error. The mean OK and KT standard errors represent the standard error of estimation more accurately than the mean IK standard error, and OK (or KT) estimates of elevation values were more accurate than those for IK. Furthermore, IK may be significantly more costly to implement than OK (or KT) in terms of expenditure of time and effort. Also, the implementation of IK was demonstrated to be problematic in the presence of a low-frequency trend. A modified form of IK was also employed whereby the thresholds for estimation of the ccdfs were adapted locally in the basis of the available observations. This approach markedly reduced the problems encountered with IK employing fixed (global) thresholds. IK with locally adaptive indicator thresholds provided a more accurate guide to uncertainty on a local basis than OK or KT. It is suggested that IK recommended for the assessment of uncertainty in estimates locally where the estimation of accuracy of a specified will need to be implemented with a trend model to further improve results.

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