PhD Thesis

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The Geomorphological Characterisation of Digital Elevation Models

PDF versions: Chapters 1-3 (2,545 kb) Chapter 4 (500 kb) Chapters 5-7 (4,360 kb)

Citation: Wood, J.D. (1996) The geomorphological characterisation of digital elevation models PhD Thesis, University of Leicester, UK,


Techniques and issues are considered surrounding the characterisation of surface form represented by Digital Elevation Models (DEMs). A set of software tools suitable for use in a raster based Geographical Information System (GIS) is developed. Characterisation has three specific objectives, namely to identify spatial pattern, to identify scale dependency in form and to allow visualisation of results.

An assessment is made of the characteristics of error in DEMs by identifying suitable quantitative measures and visualisation processes that may be enabled within a GIS. These are evaluated by contour threading a fractal surface and comparing four different spatial interpolations of the contours. The most effective error characterisations are found to be those that identify high frequency spatial pattern. Visualisation of spatiall arrangement of DEM error is used to develop a deterministic error model based on local surface slope and aspect.

DEMs are parameterised using first and second derivatives of quadratic surfaces fitted over a range of scales. This offers advantages over traditional methods based on a 3 by 3 local window, as geomorphometric form can be characterised at any scale. Morphometric parameters are combined to give a feature classification that may also be applied over a range of scales. Multi-scale measurements are combined to give a feature membership function that describes how properties change with scale. These functions are visualised using modal and entropy measures of variability. An additional method of visualising scale dependency is suggested that graphically represents statistical measures of spatial pattern over a variety of spatial lags. This is found to be most appropriate for detecting structural anisotropy in a surface. Characterisation tools are evaluated by applying them to uncorrelated surfaces, fractal surfaces and Ordnance Survey DEMs of the Lake District, Peak District and Dartmoor.

Chapter One: Introduction

Surface characterisation - from gridded DEMs only, research objectives; Scientific visualisation - common methodology to most work covered in this thesis; Image processing - similar aims and issues to geomorphometry; Uncertainty in surface models - cannot be separated from the process of characterisation; Thesis outline.

Chapter Two: Research Context

The Digital Elevation Model - development and context; Geomorphometry - development and problems; Hydrological characterisation - problems and solutions; Image processing and pattern recognition - similarity with geomorphometic approaches; Fractals as models of scale dependency - techniques and problems.

Chapter Three: DEM Uncertainty

Qunatifying uncertainty - momental descriptors, spatial measures, hypsometric analyis; Visualising DEM uncertainty - four contour interpolation methods, GIS visualisation techniques, detecting algorithm error; Modelling DEM uncertainty - photogrammetric groundtruth, planimetric offset error.

Chapter Four: The Parameterisation of Geomorphological Surfaces

Aims of parameterisation; Morphometric parameterisation - slope, aspect, surface curvature; Limitations of quadratic modelling; Importance of scale - multi-scale quadratic approximation, constrained approximation, weighted least squares; Spatial extensions - spatial autocorrelation lag diagrams, co-occurrence matrix lag diagrams.

Animation 1 - Quadratic approximation of Lake District DEM.

Animation 2 - Quadratic approximation of a poorly autocorrelated surface.

Animation 3 - Change in cross-sectional convexity with scale.

Chapter Five: Morphometric Characterisation

Feature identification - quadratic approximation; Slope and curvature tolerances; Multi-scale feature classification; Hydrological modelling - drainage basin identification.

Animation 4 - Change in feature classification with scale.

Figure - Feature membership visualisation.

Figure- Cross-sectional curvature function.

Chapter Six: Results

Control surfaces - uncorrelated Gaussian surfaces, object surfaces, fractal surfaces; Terrain models - Lake District, Dartmoor, Peak District; Assessment of quadratic approximation tools - non-spatial analysis of residuals, spatial analysis of residuals, quadratic approximation for surface generalisation; Calibration of spatial dependence measures - spectral synthesis of fractal surfaces; Terrain characterisation.

Chapter Seven: Conclusions and Further Work

Re-evaluation of research aims and objectives; Further work - application, textural analysis and lag diagrams, data structure development.


References used in the thesis.


GRASS source code - data creation modules, file conversion modules, DEM analysis modules, output statistics modules.