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One of the long standing aims of science has been to impose a rational, internally consistent, framework upon 'nature'. The construction and implementation of that framework is intended to help us understand and predict the nature it describes. Whilst the development of such frameworks may be from a variety of perspectives, the importance of description should not be underestimated. Description may be directly of nature, or of the processes that result in observed phenomena, or of the scientific framework itself. This thesis is an attempt to construct such a scientific framework, one which can be used to describe and understand landscape.
The overall aim of this work is to develop a set of tools that may be used to describe any geomorphological landscape in a discriminating and succinct manner. Many attempts have, of course, been made to do this previously. The process of parameterisation of landscape is to identify and measure those properties of landscape that are seen as most fundamental in its description of form. The thesis presented here is that in order to successfully characterise a geomorphological surface, it is necessary not only to identify the parameters of that surface, but to identify, describe and visualise, the spatial association between parameters. 'Tools' are developed from several scientific sub-disciplines in order to achieve this.
Before embarking on a detailed description of the nature of this work, its scope is defined by addressing a number of underlying questions.
What should a characterisation of landscape attempt to achieve ?
The answer to this question touches on the nature of scientific method. Is it possible to identify an objective reality, that of the 'true' landscape ? If we assume the answer to thisquestion is yes, then characterisation becomes the process of identifying the optimal categorisation of that reality. However, the concept of 'landscape' embodies a host of ideas, not simply physically determined by geomorphological process, but culturally defined by its use and the preconceptions of the observer. As a consequence, a framework for objective testing of landscape characterisation is not possible without a stricter definition of terms.
It is more useful to consider an alternative assumption where our imposition of a scientific framework becomes a reality. The scheme we use to describe a landscape can be evaluated by its consistency with other scientific conventions, its discriminating power with respect to the applications it is orientated towards, and its own internal consistency. This is the approach that is taken during this study, both in the definition of landscape and in the evaluation of the tools developed to describe it.
How should landscape be modelled ?
In order to provide a somewhat objective scheme for development and evaluation of characterisation tools, a very specific definition of landscape will be used throughout this study. If we ignore our own 'filter of perception' in our appreciation of landscape, we can define any landscape in terms of its form (geomorphological), what lies upon it (landcover) and what it is used for (landuse). This study will be limited to a geomorphological treatment of landscape (see Figure 1.1).
In turn, a geomorphological landscape can be appreciated purely in terms of its measurable surface form (geomorphometric), the materials that make up the surface and sub-surface (material), and the processes that give rise to the geomorphometric and material characteristics (process). The former alone will be considered here. Of course, it should be recognised that a substantial part of geomorphological research has been devoted to relating these three elements together. The contribution offered by the current work is to provide a more effective mechanism for characterising form (geomorphometry).
The study of surface form, and more particularly, the taking of surface measurements from maps or models, has a long history dating back at least to the mid nineteenth century (Cayley, 1859; Maxwell, 1870). More recently, the accessibility of computing technology in the 1970's led to a renaissance in the approach, particularly with the work of Evans (1972, 1979) and Mark, (1975a, 1975b). The work reported in this volume represents what appears to be part of a second renaissance accompanied by the widespread availability of Geographical Information Systems.
Finally, within the context of GIS, surface geomorphometry is most commonly modelled either as a Digital Elevation Model (DEM), or as a Digital Terrain Model (DTM). Here, a DEM is defined as a regular two dimensional array of heights sampled above some datum that describes a surface. A DTM contains elevation information with the addition of some explicit coding of the surface characteristics such as breaks in slope, drainage divides etc. Since one of the aims of this study is to enable the production of such ancillary information, the work will be based upon DEMs only.
Figure 1.1 - The context of the Digital Elevation Model (DEM) as a representation of landscape.
How should tools for characterisation be built ?
Geomorphological characterisation tools can be derived using two broad approaches. The theoretical approach is orientated towards the construction of the tools themselves. Methodological development consists of evaluating existing tools, identifying weaknesses, and producing new or enhanced methodologies. Evaluation of tools produced using this approach is likely to be by assessment of internal and external inconsistencies, and discriminating power. Alternatively, an empirical approach may be adopted where landscapes with known characteristics are evaluated. Tools are developed that try to identify these characteristics. Evaluation is largely based on the effectiveness of characterisation in modelling known phenomena. There is a parallel here with the distinction between general and specific geomorphometry (see section 2.2).
The approach adopted here is of the former, theoretical one, inspired largely by the weaknesses in existing techniques for surface characterisation.
The intimacy of the link between interpolation, generalisation, and characterisation will become apparent throughout this work. In essence all three processes involve the same procedure. That is they all attempt to extract information from data. In the case of generalisation it is in order to represent information as efficiently as possible, with a minimum of data. For interpolation it is to extract the maximum amount of information necessary to inform the process of data creation. Characterisation can simply be regarded as the process of making information derived from data explicit. It is not surprising therefore, that much of the work considered in this study has origins in the fields of spatial interpolation and generalisation.
In summary, the aim of this study is to produce a set of techniques (or 'tools') that may be used to identify and discriminate between different surface forms. Throughout, gridded digital elevation models will be used as a surrogate for landscape, while recognising that they only model a very specific component - that of surface form.
More specifically, the study has the following (testable) objectives,
In meeting these objectives, a number of continuing themes become apparent; these are outlined below.
Although the term Scientific Visualisation has only received popular attention in the last decade, the geographical tradition of illustrating spatial (and non-spatial) information graphically, has predated the discipline by many centuries. Visualisation is used in this study in two contexts. Firstly, the figures presented in this volume should provide an effective means of communication of embodied ideas. Secondly, and more importantly, the visualisation process has been instrumental in the development of many of the ideas presented. It is one of the primary arguments of this thesis that the visualisation process provides an important methodological approach that is necessary for the effective use of the tools presented. That process involves a dynamic interaction between user and computer, a process that cannot befully conveyed in a written dissertation.
More specifically it is possible to enlarge on DiBiase's (1990) notions of visualisation in the public and private realms. Many of the techniques described in this volume have arisen from exploratory ideation (McKim, 1972) firmly in the private realm of visual thinking. Yet if the methodologies described are to have use elsewhere, their visualisation must be capable of being used in the public realm of visual communication. Thus graphical representation is used in a variety of contexts within this work. It ranges from the visual communication of DEM uncertainty (see Chapter 3) to the private realm of visual thinking implied by the use of textural lag diagrams (see Chapter 4). Visualisation should take a more important and central role than conventional statistical measures of surface characterisation.
The original impetus for this work was a recognition that many of the tasks confronted by the image processing community have similarities with those facing geomorphometry. Much of the image processing literature is given to issues of information extraction from 2-dimensional raster representations of (reflectance) surfaces. This relationship is illustrated in more detail in Figure 1.2.
Figure 1.2 - The relationship between the characterisation of Digital Elevation Models and digital images.
Some of the ideas discussed here, particularly those of 'texture analysis' and 'edge detection' are fundamental to the disciplines. Techniques such as co-occurrence matrix analysis (see Chapter 4) are borrowed directly from the image processing literature. Others such as feature classification (see Chapter 5) have a geomorphological origin, yet could be equally appropriate for the segmentation of a grey-scale image. One of the problems of the somewhat parallel evolution of both disciplines is the different use of terminology adopted by each. Throughout this work, a geomorphometric nomenclature is chosen where possible, although it is readily acknowledged that many of the ideas used have arisen from both disciplines.
It was the original intention of this work to consider only those techniques suitable for geomorphometric analysis. Yet within a few months of study it became apparent that in many cases it was difficult to separate the attributes of surface form that were due to geomorphological process from those due to model uncertainty. Consequently, it has become one of the objectives of this work to distinguish the two sets of influences. An entire chapter is given over to considering the techniques suitable for identifying uncertain or inaccurate elements of surface models (see Chapter 3). This is a necessary consideration and one that cannot be ignored if effective surface characterisation is to be achieved
It has only been possible to begin to separate the effect of uncertainty from geomorphological form because of its relatively unique spatial and scale based characteristics. The notions of scale and spatial distribution do themselves recur throughout this volume, and are perhaps central to the uniqueness of the approach adopted within.
Chapter 2 presents the research context from which this study has arisen. In making reference to literature several issues are considered. Firstly the research problem is more fully defined by considering attempts to characterise surfaces effectively, and more particularly their limitations. Secondly, the themes that run through this research are considered in more detail. It is hoped that by considering the research context, a research 'niche' is made apparent, one which is investigated in the following four chapters.
Chapter 3 is devoted to considering DEM uncertainty in greater depth. The first part considers how the effects of data uncertainty may be quantified and visualised. The emphasis is placed on the use of the interactive visualisation process and a consideration of spatial and scale dependent characterisation. The second part of the chapter considers an example of uncertainty modelling as a mechanism for separating data error from geomorphometric form. Again the use of visualisation as part of the research process is emphasised.
Chapter 4 covers in some technical detail the process of surface parameterisation using quadratic patches to model local surface form. The emphasis is placed on a computational implementation of the process. The second part of the chapter considers how parameterisation should be applied over a range of scales in order to provide effective surface characterisation. The third part of the chapter is a description of alternative tools for scale-based description. In particular, the notion of the 'lag-diagram' - a two-dimensional map of spatial association -is considered an important part of the visualisation of spatial behaviour.
Chapter 5 goes on to consider how some of the surface parameters discussed in the previous chapter can be used in a geomorphological context. In particular, the derivatives of quadratic surface patches are used to provide a classification of surface feature type. The second part of the chapter is a consideration of how some of the hydrological descriptions of a surface can be used to characterise surface form.
Chapter 6 consists of an evaluation of the tools developed in the previous three chapters. Many of the visualisations are new and do not allow intuitive interpretation. So one of the objectives of this chapter is to 'calibrate' the tools by applying them to surfaces with known properties. These range from simple geometric objects, uncorrelated Gaussian surfaces, through simple polynomial functions, to fractal surfaces. The tools are also evaluated by applying them to contrasting Ordnance Survey DEMs of the English Lake District, the Peak District and Dartmoor. The objective of this chapter is not to characterise the landscapes per se, but to assess the effectiveness of the tools developed.
The final chapter draws conclusions from the development and assessment of characterisation tools by re-evaluating the aims and objectives stated in the introduction. The continuing research themes that have arisen out of this work are identified and provisionally assessed.
Over 20,000 lines of C code have been produced as part of this research. It has been in the production of workable software, that by far the greatest effort has been expended. The emphasis in coding has been on clarity, as it is the description of algorithms that, in many cases, is as useful as a working system. It is for this reason that all C code has been included as an appendix to this volume. Frequent reference is made to these appendices, but where an algorithm is considered to be of more general use, it is also represented as a figure within the main body of text.
