Optimum isarithm interpolation in digital modelling: an examination of the performances of some computer contouring and interpolation methods and techniques applicable within digital terrain modelling

Abstract

Surface interpolation and, more particularly isarlthm interpolation are common procedures in the Earth Sciences and increasingly common ones in most other disciplines. Data for such Interpolation are increasingly being stored in a computer-accessible form as a prerequisite to a computer-derived solution. This has resulted in the development of a large assortment of computer software to perform the interpolation. The scientist is thus faced with a predicament of which is the optimum method of isarlthm interpolation for his data- This thesis describes an empirical evaluation of the performances of a comprehensive selection of software in relation to data characteristics. Much of the software is available in the academic environment or was developed by the author. The evaluation utilises detailed, photogrammetrically derived digital terrain data which are related to some currently used data classification systems. Additionally, several techniques, mostly derived from geomorphometry, are used to examine the data in more depth, in an attempt to establish reliable descriptors of their data characteristics. These descriptors are designed to be used in a multi-disciplinary environment. The interpolation process is essentially classified into three stages for evaluation. Random-to-grid algorithms are evaluated by considering the interpolated grid in relation to an observed grid. Grid-to-isarithm and random-to-isarithm interpolation are evaluated by considering the interpolated Isarithms with observed isarithms. In both cases, geometric errors and the morphological trueness of the interpolation product are considered using graphical and numerical parameters. These statements of accuracy are correlated with the data characteristics to establish the main factors influencing isarithm interpolation.