Digital Elevation Models (DEMs) are fundamental datasets for environmental modelling. They provide the basic data from which terrain indices that represent or influence environmental phenomena are derived, for example slope gradient and hydrological contributing area, and also the source from which specific morphometric features are quantified and characterised, for example mountains and drainage basins. This thesis focuses on the latter, with the aim being to develop an algorithm to characterise the landscape in terms of five morphometric features (peaks, passes, pits, ridges and valleys) and to assess its validity and effectiveness for characterising landform from DEMs. The research in this thesis is divided into two parts. First, an algorithm of morphometric characterisation of landform from OEMs is developed based on a locally fitted quadratic surface and its positional relationship with the analysis window. Five requirements are taken into account within the algorithm: (1) the ideal cases of different morphometric features are simply and clearly defined; (2) the output is spatially continuous to reflect the inherent fuzziness of landform features; (3) the output is easily combined into a multi-scale index across a range of operational scales; (4) the standard general morphometric parameters can be easily quantified due to the easy calculation of first and second order derivatives from the quadratic surface; and (5) the algorithm is applicable to the different data structures used to represent DEMs. An additional benefit of the quadratic surface is the derivation of the R?? goodness-of-fit statistic, which allows both an assessment of the reliability of the results and the complexity of the terrain. Of the five morphometric features identified using the algorithm, valleys are perhaps the most commonly used. Therefore the second part of this thesis is a more detailed comparison between the Multi-Scale Valleyness (MSV) and three existing algorithms (D8, D∞ and MrVBF). D8 and D∞ are global flow accumulation algorithms, and perform well when characterising valley centre lines. However, they do not identify the valley areas themselves, although this is to be expected given their formulation. MrVBF focuses on characterising valley bottoms and so performs well when characterising valleys in broad and topographically flat areas. It does not identify valleys in the steeper upland parts of a catchment, although this too is something to be expected given its formulation. MSV directly characterises valley areas from a geomorphometric point of view, and performs well for both upland and lowland catchments, irrespective of their width. Overall, the results show that the single- and multi-scale terrain indices developed in this research perform well when characterising the five morphometric features. The approach has considerable potential for use in environmental modelling and terrain analysis.