Multidimensional geographic information science

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Multidimensional Geographic Information Science

Multidimensional Geographic Information Science Jonathan Raper

London and New York

First published 2000 by Taylor & Francis 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Taylor & Francis Inc 29 West 35th Street, New York, NY 10001 Taylor & Francis is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledges’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2000 Jonathan Raper All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Every effort has been made to ensure that the advice and information in this book is true and accurate at the time of going to press. However, neither the publisher nor the authors can accept any legal responsibility or liability for any errors or omissions that may be made. In case of drug administration, any medical procedure or the use of technical equipment mentioned within this book, you are strongly advised to consult the manufacturer’s guidelines. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Raper, Jonathan. Multidimensional geographic information science/Jonathan Raper. p. cm Includes bibliographical references (p. ). 1. Geographic information systems. 2. Spatial analysis (Statistics) I. Title. G70.212 .R367 2001 910'.285–dc21 00–062904 ISBN 0-203-30122-6 Master e-book ISBN

ISBN 0-203-35194-0 (Adobe eReader Format) ISBN 0-7484-0506-2 (Print Edition)—ISBN 0-7484-0507-0 (pbk.)

Publisher’s Note This book has been prepared from camera-ready copy provided by the author.

Contents

List of figures List of tables List of plates Acknowledgements Preface

PART I 1 2 3 4 5

The worldview of geographic information science Two-dimensional representations of space Multidimensional representations of space and time Multidimensional geo-representations for modelling Multidimensional geo-representations for exploration

PART II 6 7 8 9 10

vii ix x xii xvii 1 3 31 84 120 172 201

Hypermedia geo-representations for coastal management Geo-representation of dynamic coastal geo-phenomena Geo-representations of coastal change using virtual environments Three-dimensional modelling of coastal landforms Multidimensional geo-representation in coastal environments

205 212 218 224 232

References Index

250 293

List of figures 1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 5.1 5.2 5.3 5.4 II.1

Construction of a world view Naïve geography and scientific geography trajectories through life The four conceptual spaces of Couclelis (1992a) How the Puluwatan navigate using the ETAK system—the reference point is an island which is lined up with a series of stars Axial lines drawn through convex urban spaces for part of Lisbon How rural village land can be consolidated by rebuilding houses and merging plots through land reform How Eratosthenes calculated the earth’s circumference Conic sections Topographic features required by map users Platonic solids Improvements in timekeeping Tissot’s Indicatrix and graticule for the orthographic projection Light cones and world lines Conceptualising identity Spatial processes Definitions of topological terms Geometric objects in pointset topology Coordinatised Euclidean geometry Geo-representation using rasters Parametric solids A classification of 3D data structures Octree encoding Simplices Three-dimensional tetrahedronisations are not unique A taxonomy of three-dimensional spatial functions Space-time prism Georeferencing video imagery VRML coordinate space Scheme of links between information elements and abstractions in a Hypertext application Latencies in a monitoring system Location of Scolt Head Island and other sites in Part II

6 37 39 54 55 60 64 65 72 89 93 95 100 122 124 133 134 141 143 145 148 149 151 152 160 166 175 178 186 192 201

II.2 Map of Scolt Head Island 6.1 The time-space diagram in the SMP 6.2 The use of the SMPviewer for the extraction of geographic information from imagery 7.1 Wave orthogonal mapping at Far Point on Scolt Head Island 7.2 Space-time path for two days surveying the Far Points spits on Scolt Head Island in March 2000 8.1 Scolt Head Island Far Point spits in a gallery in the Virtual GIS Room with the currently selected model displayed on the viewing table 9.1 The sedimentary logs of the recovered core for the south Privet Hill site 10.1 Two spit cross sections at the same spatial location but one month apart

203 207 208 213 215 220 226 235

List of tables 1.1 Hempel’s four modes of scientific explanation 13 2.1 A model of spaces and scales 45 2.2 Some examples of user language for space with regard to land and mining 78 surveying practice 127 4.1 Space-time structures supporting geo-representations 4.2 Generic spatial query and analysis functions in three-dimensional modelling and 158 their effectiveness under different data structures 226 9.1 Sieve aperture sizes used in mm (upper row) and phi ( ) (lower row)

List of plates (Between pages 236 and 247) 6.1 The 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster in Arcview GIS, overlaid with the deaths; diffusion>agglomeration=the ‘contagion’ effect • births>deaths; agglomeration>diffusion=the ‘group development’ effect • deaths>births; diffusion>agglomeration=the ‘waste and disperse’ effect • deaths>births; agglomeration>diffusion=the ‘diminishing focus’ effect. This approach is most applicable to discrete individual-based models whose aggregate behaviour has a spatio-temporal expression. Space and time connection—integrated Spatio-temporal structures can also be constructed that integrate space and time (Raper and Livingstone 1995) in perdurantist fashion. One possible integrated approach would be the use of a Minkowski space-time manifold that is fully four-dimensional in nature. In this case, both space and time could be measured in commensurate units such as lightseconds although such standardisation is not a precondition for integration. Kelmelis (1998) shows how an event has causal influence through a spatio-temporal ‘extent’ whose size depends on its propagation through space and time. In the mesoscopic geographic world such causal propagation can regionalise space and time but there are complex forms of attenuation and amplification. Sound propagation provides many examples: wind can carry or inhibit sound and surfaces can reflect or amplify it (Shiffer 1995). System science can also provide a framework for the integration of space and time through its origins in thermodynamics (Von Bertalanffy 1950). Systems can be defined as sets of relationships between entities abstracted from the world (Thorn 1988). In a geographic context, these relationships are constituted by the spatio-temporal interaction of the processes that then change the state of the entities (Chorley and Kennedy 1971). Discretisation—continuous Space and time can be treated as physically continuous as they lack any intrinsic metrics (Grünbaum 1963). This continuity can be expressed in the algebraic symbology of a mathematical function. Behaviour in the spatio-temporal continuum can be represented through the use of functions in dynamic wave and flow models (Martinez and Harbaugh 1993). In such models space and time are fully integrated in sets of continuous differential equations, however, they must be approximated numerically (made discrete) to obtain predictions of conditions obtaining at any space-time point (Dalrymple and Ebersole 1979). Thill and Wheeler (1995) show how the logistic equation produces different forms of behaviour depending on whether it is implemented using continuous differential or discrete difference equations. This implies that the choice of discretisation may have consequences for the dynamics observed as continuous versions of the logistic equations never produce chaotic behaviour (Baker and Gollub 1990). Discretisation—discrete Physically continuous space and time can be discretised in a variety of ways that have been extensively documented in geographic information science (Herring 1991,

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Goodchild 1992a, Raper and Maguire 1992, Langran 1992, Worboys 1995, Molenaar 1998). Discretisation of space and time is focussed on the selections of metrics, geometries and orderings. Metrics of space and time have evolved from the practices of surveyors and astronomers respectively. The pre-eminent spatial unit is the metre, which was originally a 1/10,000,000th subdivision of the northern quadrant of the Paris meridian. Likewise, the pre-eminent temporal unit is the second, which is derived from a subdivision of a customary clock time originating with the ancient Babylonians. Geometries for the discretisation of space and time are derived from algebraic topology, which concerns the manipulation of geometric configurations of various types (Alexandroff 1932). Geometric configurations (see below) can be embedded in a space of dimension up to three or in a space-time of dimension four. Orderings of space and time are generally based on qualitative topological distinctions (see chapter two) originating with the work of Allen (1984). Cohn et al. (1998) showed how relations between spatiotemporally extended regions could be described topologically and hence ordered. Model—absolute In the ‘absolute’ model, entities are made within a universal reference frame of space and time and are identified by spatial and temporal boundaries marked by physical discontinuities in space and events in time (see chapter 3). This implies that representation of entities in space and time should proceed by identifying the spatial configurations corresponding to events. However, representation of absolute space and time must handle a spatial configuration for every event affecting any entity. Langran (1992) reviewed the spatial database designs that have been proposed as solutions to this problem. Model—relative In the relative space model, time is made of entities with a spatial and temporal extent. This implies that representation should proceed by identifying individuals by the role they play in the world and the relations they enter into. Multidimensional representation can be achieved by using methodologies to identify constitutive processes that produce individuals with distinctive attributes. However, representation of relative space and time requires a prior ontology and sophisticated methods of construction for individuals. Thorn (1975, 1983) suggested that the singularities associated with catastrophe theory could provide such an ontology and he argued specifically that a relative space-time could be built from these ontological foundations. He also notes that such a formulation requires that existence is determined by essence (‘the set of all the qualities of being’ Thorn 1983, p 91). This is the opposite of the absolute view that essence is determined by existence, which is ultimately provided by the space-time field. Combinations of space-time structures The three pairs of space-time structures can be combined to identify eight qualitative combinations of space-time properties and the associated geo-representations, which have

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been implemented for each type (see table 4.1). These space-time structure types are representational options for the geographic information scientist: commercial GIS have only generally implemented type 2. • Type 0: Integrated discrete absolute approach—corresponds to a four-dimensional GIS, which was suggested by Hazelton, Leahy and Williamson (1990) and implemented experimentally by Pigot and Hazelton (1992). • Type 1: Integrated discrete relative approach—suggested by Raper and Livingstone (1995) in their OOgeomorph design of a four-dimensional database of discrete points which could be conjecturally assembled into four-dimensional relational entities. • Type 2: Hybrid discrete absolute approach—typical of the design used by current GIS with temporal extensions, for example, the ESTDM model by Peuquet and Duan (1994). • Type 3: Hybrid discrete relative approach—corresponds to spatio-temporal autocorrelation between points in space and time (Griffith 1981). • Type 4: Integrated continuous absolute approach—the domain of field equations in physics. • Type 5: Integrated continuous relative approach—corresponds to a model of deterministic chaos with attractors in space-time (Orford and Carter 1995). • Type 6: Hybrid continuous absolute approach—equivalent to a four-dimensional process model implemented using differential equations (Ebersole andDalrymple 1979). • Type 7: Hybrid continuous relative approach—corresponds to the Catastrophe Theory of Thorn (1975) which can capture discontinuous change (e.g. jumps at cusps) through the operation of continuous change in variables controlling a system.

Table 4.1 Space-time structures supporting geo-representations

Space-time structure type Properties

Geo-representations

Type 0

Integrated discrete absolute

4D GIS

Type 1

Integrated discrete relative

e.g. OOgeomorph

Type 2

Hybrid discrete absolute

e.g ESTDM

Type 3

Hybrid discrete relative

Spatio-temporal autocorrelation

Type 4

Integrated continuous absolute Field equations of physics

Type 5

Integrated continuous relative

Chaos

Type 6

Hybrid continuous absolute

4D process model

Type 7

Hybrid continuous relative

Catastrophe theory

Several of these space-time structure types offer the possibility of richer georepresentations than those currently in use in GIS. Importantly, several of these space-


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time structure types offer a wider range of possible ways for space-time to constitute entities than the simple ‘timeless’ boundary-drawing approach. Models of time Theories of time offer a variety of ways of conceptualising events and change (Le Poidevin 1998). However, models of time are required to implement temporal conceptualisations. Frank (1998) argues that models of time can be classified by a consideration of types of temporal representation primitives (points or intervals), the distinction between linear and cyclic times, the contrast between ordinal and continuous times, and the viewpoint employed. Using Frank’s lattice-type classification of time models the primary distinctions are between: • ordinal time (time made of points marking events) and continuous time (time is dense); • linear time and cyclic time; • sequential ordered time and branching time; • valid time and transaction time. These distinctions allow the scope of a temporal model to be expressed. Most GIS can store ordinal, linear, sequential order and valid time concepts in object attributes, which defines the scope of the temporal model. As a consequence, GIS are unable to store or manipulate more sophisticated concepts such as continuous, cyclic, branching and transactional time, with knock-on consequences for representation. However, the physical sciences concerned with mesoscopic space and time have also developed models of time. Models of time have also been developed in geographical approaches to system science (Thorn 1988). System science introduced equilibrium models of time in which the output of a system could oscillate around an equilibrium value. Chorley and Kennedy (1971) identified various types of equilibrium found in systems including the metastable equilibrium (stability disturbed and re-established when the system crosses a threshold) and dynamic equilibrium (stable progression in line with a trend). The regulating mechanism for equilibrium maintenance is system feedback: positive feedback is the amplification of an input, negative feedback is the dampening of an input. Currently, GIS cannot represent equilibrium models of time and therefore they cannot be used to identify spatio-temporal phenomena associated with equilibrium and feedback behaviour, such as threshold conditions. In geomorphology, models of time have focussed on the temporal dependence or independence of processes describing a system such as a drainage basin at different time and space scales. In a classic paper Schumm and Lichty (1965) argued that the processes contributing to causal explanations of a geomorphic system such as a drainage basin were a function of the time (and space) scales of enquiry. For example, at short timescales (say days) Schumm and Lichty argued that geology, climate, relief, drainage network and hillslope morphology are independent variables, and only water/sediment discharge is a dependent variable in the explanation of landform morphology. Thus, Schumm and Lichty argued that the assessment of physical change is (time)frame-dependent in open physical systems, as a cascade of causal forces operates in a complex space-time fabric. However, Lane and Richards (1997) pointed out that the Schumm and Lichty analysis


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is focussed on immanent ahistorical processes (using the terminology of Simpson 1963) and does not take account of the contingent configurational circumstances. The ‘memory’ of a geomorphic form (such as the landform shape inherited from the last storm event) can be seen to condition process outcomes, which may then generate system feedback. In geomorphology this implies that immanent processes acting in space-time and the historically-contingent disposition of matter and energy are engaged in constant mutual feedback. This is the way that four-dimensionally extended phenomena are constructed through the operation of spatio-temporally constituted and contingent processes. Massey (1999) argued that this realisation should commit us to the treatment of time as historical rather than immanent and noted that the convergence of these viewpoints could bring together social studies of agency and physical studies of process. Raper and Livingstone (2000) supported this view and discussed the implications for representation. Wolman and Miller (1960) noted an empirical relationship between the magnitude of geomorphological events and their frequency of occurrence: high magnitude events occur infrequently and vice versa. This realisation has led to the search for the ‘return periods’ for events with a given magnitude, for example, the magnitude of the ‘50-year storm’. The return period can also be seen as an immanent conception if the causal elements underlying the geomorphological system are treated as ‘stationary’ through time. Orford and Carter (1995) analysed the records of storminess in tide gauge records in Atlantic Canada and found that there were 6 and 22 year forcing factors in the processes affecting landforms in the time series. This work can be interpreted as showing the need for the ‘historical’ approach to return period analysis. It also reveals another sense in which four dimensionally extended phenomena can be identified through the operation of spatiotemporally constituted and contingent processes. Scale and space Concepts of scale also play an important role in the process of spatial and temporal reasoning. In chapter two scale was characterised as a framing control that selects and makes salient entities and relationships at a level of information content that the perceiver can cognitively manipulate. It is clear that if both space and time are jointly constitutive of ontological schemes then scale is an important control over salience and, therefore, the identity of geo-phenomena and their inter-relationships. To phenomenologists this view is consistent with idealist arguments that entities are constructed and not discovered. However, it can be argued from a realist perspective that scale-dependency is an aspect of the world and that there really are structures in space-time corresponding to particular frames of reference. Thus, without an understanding of scale and its ontological role, realism will be an inadequate basis for spatial and temporal reasoning. Several approaches to the understanding of spatio-temporal scales have been developed in geomorphology. By adopting a systems approach, de Boer (1992) argued that scale could be identified with hierarchical levels of organisation in the physical system. A given level or ‘holon‘ in a hierarchy (Allen and Starr 1982) exchanges matter, energy and information with other levels, both above and below. The identity of a holon is determined by the entities with which it interacts: it is made up of entities with slower behaviour and smaller size, and it forms part of the environment for faster, larger entities.


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In this framework scale is defined by the identity and associations of the holon. Finding the context for a holon in geomorphology corresponds to discovering space-time structures with an appropriate functional identity. Church (1996) saw scale as a resolution at which information transfer, in the form of matter and energy movements, could be detected within the landscape. He argued that information transfer is constitutive of scale through its role in defining observables of behaviour and form (using the terminology of Casti 1989). Thus, every scale of consideration involves averaging and ‘censoring’ of entities and processes at larger and smaller scales in order to identify patches in space and persistence in time at the scale of consideration. This procedure produces functional geo-phenomena. Church (1996) suggests that different forms of explanation are available depending on the scale used: small spatial and short time scales are stochastic, mesoscopic scales are deterministic and chaotic, and large scales are contingent. That explanation at the largest spatial and longest temporal scales is contingent, is a function of the limited analogy that the present affords (Frodeman 1995). Scale is also coupled to explanation through the limits to the spatial dependency of processes. Phillips (1988) argued that the scale of spatial variability of a process can be studied by the use of geostatistics to discover the structure of spatial autocorrelation. Spatio-temporal process dependency is equivalent to ‘areal’ memory for a physical system; Trudgill (1976) termed geomorphic systems with short memory over large areas to be ‘labile’ and long memory over small areas to be ‘sluggish’. The spatio-temporal dependence of process may also lead to allometry, i.e. the tendency of landform types to change their shapes with size, through limits to process operation (Church and Mark 1980). Evans and McClean (1995) argued that allometry demonstrates that the land surface is not unifractal but multifractal, thereby showing the limits to self-similarity in the mesoscopic world. Evans (1998) argued that at least nine variables were necessary to characterise terrain, and that multifractal models of terrain need to be linked to fractal slopes and drainage networks.

THEORY AND PRACTICE OF GEO-REPRESENTATION The reflexivity between conceptualisations of phenomena and the new generation of multidimensional geo-representations is the key to the process of spatio-temporal reasoning in multidimensional geographic information science. The previous section has shown how space-time structures are constitutive of geo-phenomena identity. In this section the theoretical and practical preparations for the use of geometric tools that can be used for the representation of geo-phenomena states and processes are discussed. There are two methodological approaches to multidimensional geo-representation in three- and four-dimensions (Raper 1999). Firstly, the representation of forms, structures and properties of entities as three-dimensional states; this can be termed spatial data modelling. Secondly, the representation of processes as fluxes; this can be termed process modelling. Both approaches to geo-representation have had different histories, and hitherto they have mostly been developed by different research communities. However, with the proliferation of new computational tools, both kinds of geo-representation are


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now becoming more widely used both to implement spatio-temporal reasoning and to explore the identity of geo-phenomena in a wide range of disciplines. The following sections focus on the link between conceptualisation and geo-representation through spatial and spatio-temporal data modelling. Geo-representation of forms, structures and properties The representation of the forms, structures and properties of entities has mostly been the concern of geography and the geosciences. In its two-dimensional form georepresentation of forms, structures and properties has been used for mapping while in its three-dimensional form it has been used for the reconstruction of atmospheric, solid earth or oceanic domains. The representational tools used in such geo-representation for the most part have been drawn from database design and from geometry (Molenaar 1998). The rules and syntax of the design procedure for the construction of static georepresentations are often referred to as ‘data modelling’ although this term is understood differently in different disciplines (Raper and Maguire 1992). In database design, the data model is understood to be a mapping of a conceptual model about crisp ‘real world’ entities, relationships and processes onto a logical model of computable objects, associations and transformations (Tsichritzis and Lochovsky 1982). The ‘computable objects’ in this definition are usually understood to refer to elementary computer data types such as integers, real numbers, Boolean values, dates and monetary units. Frank (1992) extended the scope of this definition by defining a data model as ‘a set of objects with the appropriate operations and integrity rules defined formally’ (p410). Herring (1991) noted that no single approach to data modelling equivalent to that used in database design is available in geographic information science due to the diversity of the required modelling domains. Spatial data models must represent the spatial extension, structural character and qualitative spatial variation of entities, which forces spatial data modelling to use hybrid representational approaches employing geometry and databases. By definition, spatial data modelling must project the state of dynamic entities onto a static two-dimensional plane. Spatial data modelling must also provide approaches to the representation of the fuzzy as well as the crisp entity (Burrough 1996). Spatial data modelling has, therefore, developed methodologies that are coupled to conceptualisation and that use a variety of methods of spatial discretisation. Hitherto, the conceptualisation carried out by most geographical information scientists has been founded on an endurantist ontology and the discretisation has been based on a positivist epistemology employing a conjectural boundary drawing approach. This book argues the case for conceptualisation based on a spatio-temporally constituted perdurantist ontology and discretisation based on a neo-positivist epistemology. Entity identification involves ‘emergence’ from the spatio-temporal fabric. The ‘traditional’ conceptualisation has been based on reductionism about entities on a ‘timeless’ spatial plane. The alternative formulation suggested here recognises the inherence of spatio-temporal extension in entity identity. Spatial data modelling has been coupled to error modelling as a means of assessing the validity of the representational data and the operations carried out on them. Hence,


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Heuvelink (1998) defines error as ‘the difference between reality and our representation of reality’ (p9) to give a measure of the extent to which the geo-representation is out of step with the conceptualisation of the world in use. This is an absolute measure but one clouded by metaphysical and epistemological issues. By contrast accuracy can be defined as the ‘closeness of results, computations or estimates to true values…or values accepted to be true’ (Unwin 1995, p550). This definition permits the accuracy of a georepresentation to be de-coupled from the world entirely, allowing accuracy to be a property of the axiomatic system from which the geo-representation is drawn. This manoeuvre could lead geographic information science into ungrounded and internally justified statements when used uncritically. There is a choice in the use of systems for geo-representation between the kind with a fixed representational approach, requiring the user to adapt to the system, and the kind of system flexible enough to adapt (to some extent) to the user’s conceptualisation. This dichotomy has, ironically, marked out a distinction between systems imposing representation that are simple conceptually onto users, and systems allowing the incorporation of rich concepts that are complex to design and use! Two-dimensional data modelling The conceptualisation phase of spatial data modelling currently involves the identification of two-dimensional spatial expressions capable of geo-representation. The most common source and methodology is conventional cartography (see chapter 2) which employs a number of standard conventions to project from the world to a twodimensional map. This book has outlined a number of richer methodologies available for the constitution of geographical identity from social and environmental geo-phenomena. In particular, it is clear that there are space-time structures unused by GIS with the scope to reveal significant two-dimensional configurations or interactions as well as the scaledriven ‘framing’ of functional geo-phenomena. The challenge is now to develop these methodologies and to make them available in, or in association with, geo-representational tools. The representational phase of two-dimensional spatial data modelling is concerned with the range of geometric structures available to represent discretised configurations. Commercial GIS have each introduced a large number of ad hoc geometric formalisms and terminologies with which to construct geo-phenomena. Herring (1991) argued that these methodologies could all be made commensurable by the use of a universal template employing topological concepts. Topology can be defined as the study of those geometric properties that remain invariant under topological transformations such as a stretching or folding. Such properties, for example, connectivity, adjacency and containment can be termed topological properties. Distance, area and directional bearings are not topological properties as they are changed by any topological transformation. ‘Pointset’ topology based upon set theory is the study of topological properties. In pointset topology a theoretical ‘neighbourhood’ is conceptualised with an arbitrary shape or dimension that is made of an infinite number of points. If the points on the boundary are included in the neighbourhood it can be modelled as a closed set and termed the ‘closure’. If the points on the boundary are not included and the neighbourhood is only


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made up of its ‘interior’ then it can be modelled as an open set (figure 4.3). A counterpart to these concepts in the world of experience might be a garden (interior), its wall (boundary) and the legal property (closure) if the property included both the garden and the wall. Pointset neighbourhoods can be embedded in any dimension, although only a two-dimensional embedding is considered here. In a two-dimensional embedding such pointset neighbourhoods are the infinite set of points from which one-and twodimensional geometric forms can be instantiated. Pointset neighbourhoods can be transformed while retaining their topological properties if they are ‘connected’. Connected neighbourhoods have an unbroken path from any point to any other point within the neighbourhood. A connected neighbourhood with no holes is ‘simply connected’. Theoretical geometric objects can be made from pointset neighbourhoods. There are two main approaches according to Herring (1991): feature-based approaches in which the geometric primitives are entities, and positionbased approaches in which the primitives (usually squares in a grid) are locations for which attributes are available.

Figure 4.3 Definitions of topological terms

Worboys (1995) has suggested that in feature-based approaches all theoretical objects can be divided into either points and ‘extents’ (see figure 4.4). The ‘extents’ can be further subdivided into one-dimensional extents (boundaries with no interior) and twodimensional extents (the full closure of the object). Note that if the ‘boundary’ of a onedimensional neighbourhood is non-self crossing it can be termed ‘simple’. The names of these precisely defined topological forms have been made generic to avoid confusion with the wide range of terminologies used in commercial GIS. Such generic terms are of considerable use when designing data transfer standards for the exchange of data between different GIS. Algebraic topology is the study of how such theoretical topological objects can be


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assembled into complex objects using discrete geometric primitives (Alexandroff 1932, Massey 1967). The simplest approach to algebraic topology is to use ‘simplices’ as primitives, i.e. point (zero simplex), straight line segment (one simplex) and triangle (two simplex) forms. More sophisticated ‘cellular’ approaches of the kind used in many GIS allow multiple segment lines and closed two extents (‘cells’) formed from multiple segment lines. These approaches to algebraic topology require that the pointset neighbourhood be regularised so that ‘cells’ are forced to be closed, connected and nonoverlapping to avoid any ambiguity. In many GIS this step, known as ‘planar enforcement’, forces representational compromises since many geo-phenomena cannot be closed naturally (for example, a bay). Graph theory covers the manipulation of sets of nodes (junction points) and edges (lines) which may form objects or trees and which may be directed or undirected. There is no notion of interior in a graph, which is only concerned with connectivity.

Figure 4.4 Geometric objects in pointset topology (after Worboys 1995)


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Three-dimensional data modelling The conceptualisation phase of spatial data modelling in three-dimensions is quite different to that used in two-dimensional cases as there is no equivalent to conventional cartography as a source of information. This means that three-dimensional conceptualisation has to proceed from first principles in each case (Raper 1989b). Consequently different conceptualisation methodologies have developed in each application area and these are often incommensurable. Three-dimensional spatial data modelling is often also defined by professional codes of practice or standard workflows, especially in the hydrocarbon and mining industries. Three-dimensional spatial data modelling involves consideration of structure as well as configurational form and the spatial variation of qualitative properties. In fact, threedimensional conceptualisation can be driven by a variety of different imperatives, which differ depending on the domain of interest in the earth, ocean or atmosphere. Structure can be drawn from a geological ontology of strata and faulting in the earth (Houlding 1994), from a meteorological ontology of air masses, streams and weather fronts, or from an oceanographic ontology of tides, currents and basins (Li 1999). Three-dimensional spatial data models such as the model of Minneapolis on the cover of this book have also been made for urban environments. Three-dimensional models are, by definition, static and have to be made for a given time point or interval. This constraint is minimal for earth science and maximal for meteorology, given their respective typical rates of change. Turner (1989) identified the chief problems for three-dimensional spatial data modelling in the geosciences as: complexity of variation, fuzziness of geo-phenomena, poor sampling, uncertain information, and a lack of access to the domain of interest. The available information was divided by Kelk (1992) into samples of geo-phenomena (descriptions, test values, remote sensing) and indications about their character (heuristics from the geosciences). Kelk pointed out that consequently three-dimensional spatial data modelling is highly knowledge-driven. Frodeman (1995) argued that the process of piecing together a holistic picture from this kind of information requires the use of ‘narrative logic’ using global knowledge of sequence and succession to understand the local context. Achieving crisp definition in three-dimensional geoscientific ontologies involves conjecturing configurations with available samples or characterising spatial variation. In the former case, this means building on the dimensionality of sample points, lines or volumes collected by various devices or remote sensing methods to create georepresentations. In the latter case, it involves exploring the patterns of autocorrelation in the sampled variables using geostatistics (Houlding 1994). By plotting the difference in value between all possible spatially separated sample pairs against the distance they are apart, it is possible to characterise spatial variation using Kriging techniques. The average difference in value of all the sample pairs falling within given distance ranges can be plotted on a semivariogram to show how sample value varies with distance and direction. This information can be used to characterise a field model of spatial variation. The representational phase of three-dimensional spatial data modelling involves choosing geometric primitives that can mimic the discretised forms, structures and


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properties of entities. Three-dimensional solid modelling implies a geo-representation that encloses space or uses overfolded surfaces requiring three independent axes of description. This definition excludes non-overfolding surfaces since they can be treated as two-dimensional maps where the z value for each x, y location is treated as an attribute. Algebraic topology can be extended from two-to three dimensions to create three-dimensional simplex tetrahedron forms or cellular forms (Lattuada and Raper 1995). Such geometric forms can be embedded in a three-dimensional Cartesian frame. Similarly, a physical field can be discretised in three dimensions and represented using tesselations of regular solids such as cubes known as voxels. In three dimensions, since the process of conceptualisation is closely coupled to discretisation and representation, the commercial and research implementations of threedimensional GIS often proscribe both aspects of the spatial data modelling. The procedures employed by each system are described below in the section on threedimensional geo-representation: only the most generic aspects of geo-representation are discussed here. The first step in the geo-representation process is to obtain samples of the phenomena in the study domain in the form of property data for x, y, z locations at a time t which meet a specified set of criteria. Each of these data records x, y, z, t, property 1, property 2...property n can be called a tuple. The collection of these tuples of data is a sampling exercise. These tuples provide the starting point for solid geometric modelling techniques. Typical means of obtaining such samples are seismic profiling, aerial remote sensing, weather balloons, probes, systematic survey and borehole drilling. However, there are several drawbacks associated with point sampling of geo-phenomena using vertical sampling lines through a domain. Firstly, it can be very difficult to distinguish between the multiple occurrence of a similar feature down a line and the repeated occurrence of a single object through folding, re-entry or faulting. Secondly, the continuity between any two occurrences of any geo-phenomena taken from two neighbouring point samples cannot be assumed to be simple or predictable. The ‘device’ and ‘phenomenon’ exploration approaches are two alternatives for the gathering of tuples of data to describe geo-phenomena. In the case of the device exploration approach, the measurement technology defines the geometric arrangement of the observed tuples, and there is no search for an a priori geo-phenomenon (Houlding 1994). Thus, boreholes impose a linear structure on the measurements, characterising the sequence of points down the hole, and a photogrammetric survey of a terrain or section can generate a grid of measurements over the earth’s surface. However, a survey of the dispersal of tracer pebbles over a river bar will be contrained by hydraulic processes and recovery factors, and will generate a spatially non-regular set of observed tuples. In this approach the tuples recorded may only have the means of collection or selection in common. In the case of phenomenon exploration approaches, the search for an a priori geo-phenomenon will define the geometric arrangement of the observed tuples. The located tuples identified by the combination of ‘suggestive’ variables can form a spatial cluster with an arbitrary three-dimensional configuration. If geo-phenomena can be identified by a single key parameter and are known to exist in a discrete form from other knowledge of the domain (e.g. mine access, destructive examination) then the geo-phenomenon can be termed ‘sampling-limited’ (Raper 1989b).


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An example would be a perched aquifer, a salt dome or a fault-limited block. By contrast if the geo-phenomenon is transient or continuous (e.g. a temperature field), or exists only as a spatially clustered set of observed tuples defined by a group of ‘suggestive’ parameters, then the geo-phenomenon can be described as ‘definition-limited’. An example of a definition-limited phenomenon would be a pollutant plume in the ocean defined by a threshold, or a sedimentary facies defined by limiting percentages of sand and clay (Orlic 1997). Hence, the ‘data model’ for a geo-phenomenon believed to exist in the earth, atmosphere or ocean may be defined by form, property and structural parameters in a specific combination. The three-dimensional spatial identity of the geo-phenomenon is then established by searching the population of selected characteristics for the boundaries of the defining conditions and recording the x, y, z coordinates. This means that by altering the contents of the data model, and iterating the search process, a new set of x, y, z coordinates defining the object can be created (Raper 1989b). The overall architecture of a domain can often be defined in different ways, depending on the contents of the data model for each element of the sequence defined. It is clear therefore, that establishing the spatial identity of definition limited geo-phenomena in the subsurface is highly sensitive to the contents of the data model. A key point is that the errors or bias inherent in the data model can be as great, if not greater than those introduced in the sampling of the parameters defining the geo-phenomena or in the process of its visualisation. Geo-representation of processes Representing processes has been the concern of a wide range of disciplines including physics, engineering, geosciences, geography, psychology, economics and planning. In these disciplines, geo-representation of process has generally been carried out either to predict (Haines-Young and Petch 1986), or to improve understanding of processes making up geo-phenomena (Richards et al. 1998). As in the representation of forms, structures and properties of entities, the geo-representation of processes in models depends critically on the discretisation of space and time. Models of processes making up geo-phenomena have been developed both for two dimensions of space plus one of time (2D+T), and for three dimensions of space plus one of time (3D+T). In these endurantist approaches, the time dimension tends not to be integrated with the spatial dimensions in the geo-representation of processes. In this section, it is argued that much current work is epistemologically dependent on endurantist forms of space and time discretisation. This has implications for the scope of process modelling and the scope of the spatio-temporal identity that can be constituted in such representations. The representation of processes in a dynamic computational environment necessitates spatio-temporal data modelling. As processes are fluxes of individuals (sensu lato) or the dynamic behaviour of geo-phenomena, spatio-temporal data modelling involves reasoning about identity and/or discretisation in both space and time. Methodologies for spatio-temporal data modelling are largely application-specific (Kemp 1993) and data driven (Smith et al. 1995) at present, meaning that the representation of processes often drives conceptualisation, rather than vice versa. Given the arguments above for the constitutive nature of space- time structures and the importance of knowledge for spatial


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data modelling, it is argued here that it is conceptualisation that should really drive the geo-representation of process. This approach involves selecting the representation that is appropriate to the conceptualisation during spatio-temporal data modelling, or extending existing modelling approaches (Raper et al. 1999). This is operationally challenging but it is argued here that such an approach is perhaps the only way to break new ground in the multidimensional modelling of processes. Approaches to process modelling A wide range of models has been produced to represent processes making up geophenomena. These models have been classified on their characteristics by a number of authors. Kemp (1993) reviews mathematical modelling applied to environmental domains and shows that implemented models can be distinguished using a dichotomous classification developed by Jorgensen (1990). According to Kemp mathematical models can be distinguished by their: • time-related behaviour (e.g. dependency of model variables on time and temporal parameterisation); • space-related behaviour (e.g. dependency of model variables on space and spatial parameterisation); • type of data, parameters and expressions (e.g. whether deterministic or probabilistic in nature); • model structure (e.g. holistic or reductionistic nature); and • mathematics. In a conceptually similar scheme, Burrough (1995) divided models into the following types: rule-based (based on logic), empirical (based on regression), physical (deterministic) and physical (stochastic). Burrough characterised each of these models in terms of their: • time/space discretisation (finite difference grids or finite element meshes); • mathematics (linear or feedback terms raised to powers); • formulation (global or local rules for behaviour); and • spatial variation (distributed or lumped parameterisation). Watney, Rankey and Harbaugh (1999) classified models from a geological perspective by purpose: models as learning tools; models as status calculations focussing on a specific question; or, models as simulations which are usable to address a wide variety of questions. From a geological perspective they divide models into the ‘inverse’ type (focussed on the reconstruction of past processes from extant geo-phenomena) and the ‘forward’ type (focussed on prediction of processes and the potential emergent geophenomena). Watney, Rankey and Harbaugh (1999) also classify models by their dimensionality (2D+T or 3D+T), since models with only two spatial dimensions do not allow the representation ‘out of plane’ (three-dimensional) physical processes. They look forward and characterise the future work needed on process models as relating to: • Input (lags, boundary conditions, scaling inputs, 3D+T datasets, non-linear conditions);


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• Model engines (scale-dependent algorithms, 3D nature of spatial processes, mixed stochastic/deterministic operation); and • Output (goodness of fit criteria, integration of inverse outputs into forward models, measures of uncertainty in output). Process models can also be classified by the way they implement theories of modelling. Ziegler (1976) defined modelling as an application of the theory of computation, which is grounded in general systems theory. Ziegler’s formalisation of modelling involves the definition of a ‘base model’ as an analogue for a ‘real system’ by the observation of inputs and outputs using the conditions specified by an experimental frame. Computed solutions are usually based on what Ziegler calls a ‘lumped model’, i.e. a simplification of the ‘base model’. By contrast Casti (1989) defined a model as ‘an encapsulation of some slice of the real world within the confines of the relationships constituting a formal mathematical system’ (p1), thereby acknowledging the dichotomy of concepts and mathematical symbols. Casti bases his modelling ontology on the concept of an ‘observable’, which is ‘a rule [for] associating a real number with each abstract state’ (p5). Since there are an infinity of ‘real’ states, the modeller must conceptualise and measure a meaningful subset of abstract states that can be represented by observables. By assembling a set of mathematical equations of state expressing the dependency relationships among observables, a modeller can implement a computable model. Finally, models can also be classified by their epistemological role. Haines-Young and Petch (1986) argued that models should be seen as part of a critical rationalist methodology, where models are ‘devices used to make predictions’ (p145). The model predictions can then be used to suggest possible falsifications for the theory, although the question of what constitutes a valid falsification has proved problematic for critical rationalism. By contrast, Richards et al. (1998) argue that models should be focussed on the improvement of understanding through a realist methodology. This can be achieved by the use of simulation modelling to assess system behaviour and to carry out sensitivity analyses. In a realist methodology, simulation modelling of causal processes implicitly lacks closure since the spatio-temporal setting is subject to uncertainty in boundary conditions and scale considerations. Thus, model results are only meaningful if contextualised in terms of contingent spatio-temporal configurations applying to the simulation model. For the most part the models that have been ordered and classified by the authors in this section have been based on an endurantist and critical rationalist epistemology. While they have brought new insights into processes making up geo-phenomena, they often lack true multidimensional scope. Spatio-temporal data modelling The aim of spatio-temporal data modelling is to represent functional and spatiotemporally extended entities whose behaviour can be modelled. The most common organising principle for this activity is the discretisation of space and time from the continuum of the conceptualised world. Kemp (1997) addressed the problem of dealing with continuity in modelling by reviewing the geometric solutions to the discretisation of


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space and time. She argued that there is a fundamental dichotomy between a ‘field view’ (geo-phenomena are continuous but can be discretised on a grid) and an ‘object’ view (geo-phenomena are discrete and can be discretised by mapping boundaries/structures). Couclelis (1992b) suggested that this dichotomy was analogous to the ancient Greek debate between the atomist and plenum ontologies of space (see chapter 2). Kemp (1997) argued in favour of the field view for the discretisation of a continuous space and time. She argued that fields can either be represented using finite difference numerical solutions solved for regular grids, or using finite element analytical solutions where the homogenous applicability of terms in the ruling equations allows the identification of elements delineated spatially. However, the finite element approach arguably belongs in the ‘object’ view. Note also that Kemp’s approach is definitively endurantist in nature as it accepts that it is necessary to discretise space and time separately. Since the field approach elaborated by Kemp (1993, 1997) is the dominant approach to spatio-temporal data modelling, then this has defined the typical scope for modelling the processes making up geo-phenomena (Goodchild et al. 1996, NCGIA 1996). In this approach, GIS have been seen as systems for sourcing the inputs to the lumped model (Ziegler 1976) or the observables (Casti 1989). This has led to debates about whether GIS and environmental models should be coupled (Nyerges 1992) or represented in a unified modelling language with spatio-temporal concepts (Smiths et al. 1995). However, these approaches to spatio-temporal data modelling leave much of the richness of spatio-temporal behaviour unrepresented. Certain concepts like multiple resolution processes, spatio-temporal latency, positive and negative feedback and chaotic behaviour are rarely accomodated by spatio-temporal data models developed by geographic information scientists. Tzetlaff and Harbaugh (1989) and Günther (1998) also drew attention to the difference between the Eulerian multiple grid-based models of many endurantist process models and the Lagrangian vector-based models for the movements of individuals. Cellular automata approaches to modelling have allowed the representation of more sophisticated inter-relationships between the cells in a field (Zijlstra 1999). However, these models have still involved sequential operation rather than the parallel processing seen in intelligent spatial agent models (Rodrigues 1999). Finally, spatio-temporal data modelling can be implemented in a 2D+T or 3D+T framework. The 2D+T framework aims to project from four dimensions to three without significant information loss. The 3D+T framework involves decisions about the constitution of spatio-temporal identity.

TWO-DIMENSIONAL GEO-REPRESENTATION Data models of conceptualised geo-phenomena as described above are represented in computational form using geometric tools. Two-dimensional computational tools are briefly described here since they provide foundations for three-and four-dimensional methods; comprehensive treatments can be found in Van Oosterom (1993), Worboys (1995) and Molenaar (1998). Theoretical topological objects defined in algebraic


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topology need to be realised in the world of human experience to be used in a GIS. By embedding objects from discrete ‘cellular’ algebraic topology in a two-dimensional plane with a fixed metric, geometric representations can be made using Euclidean geometry. Euclidean geometry defines points by the angle and distance they are from an origin (the straight line from the origin to the point is known as the ‘vector’). One and two extents can then be created from sets of point ‘vectors’. It is possible to carry out operations on the geometric objects using trigonometric procedures e.g. the angles of arbitrary shaped triangles can be calculated using the cosine rule and distances could be calculated by creating rightangled triangles and using Pythagoras’ theorem. Euclidean geometry can be embedded in a two-dimensional Cartesian frame and objects can be expressed in coordinate form in the feature-based approach. This has subsequently facilitated the implementation of coordinated Euclidean geometry in finite precision computers. In coordinate form a point can be represented as an x,y coordinate pair, a one extent by a straight line between such points (multiple line segment lines can be termed polylines) and a polygon by a polyline closed on itself (figure 4.4). The Cartesian coordinate framework is usually a ‘projection’ of the earth from three dimensions to two. The creation and management of topological relationships for georepresentation using the feature-based approach relies on the use of planar enforcement routines to ensure that all polygons are closed, connected and non-overlapping.

Figure 4.5 Coordinatised Euclidean geometry

In the alternative position-based approach, the formation of theoretical objects from


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pointset neighbourhoods begins by discretising locations with attributes from the underlying physical ‘field’. A physical field is a measurable quantity that can be defined anywhere at an infinite number of points. As in the case of algebraic topology (implementable using coordinated Euclidean geometry), the spatial variation of the field can be discretised using geometric tesselations (‘sets of connected discrete twodimensional units’). Whilst regular tesselations can be formed from triangles, hexagons and squares, only squares arranged in a grid are commonly used. A grid of squares (‘cells’ or ‘pixels’ [PICTure ELementS]) are easy to handle in computers as memory arrays are logically similar to the physical imaging technology of faxes, scanners, satellite sensors, cameras, videos and visual display units (figure 4.6). Such imaging systems capture/display the reflectance of a real world ‘scene’ for each pixel in the ‘raster’ within its range of sensitivity in the visible/non-visible part of the electromagnetic spectrum. The ‘scene’ can vary from the flat surface of a map to the surface of the earth viewed orthogonally or obliquely from an aerial or terrestrial platform which itself may be static or moving. Imaging devices capture ‘raster’ imagery in the optical band (e.g. map colours or reflected visible light from the earth) or in a combination of infra-red, optical and ultraviolet bands (earth surface spectral response), which can be recombined to form a composite image. The field approach is also suitable for storing sample values in nominal, ordinal, interval or ratio form obtained on a regular grid (Chrisman 1996). The most common form of data derived from sampling is terrain elevation (ratio data). However, any sample value can be assigned to a cell, for example, residential population counts (ratio data), risk factors (ordinal data) or origins/destinations of journeys (nominal). A key characteristic of raster data is the spatial relationship of each pixel to the geophenomena, as, by definition, the stored value in the raster must apply homogenously within the pixel. When the systems capture continuously varying geo-phenomena by taking all the values obtained by the sensor within the area of the pixel they must then apply ‘pixel averaging’ to get a mean value (e.g. satellite imaging and map scanning). By contrast, single measurements/samples at a point can be ‘assigned’ to the whole area of a pixel although in reality there may be (unsampled) internal variation within it (e.g. digital elevation models and risk factors). In both cases, the boundaries of the pixel will become sharp discontinuities (if the values stored in each pixel are different), even if in reality the variation is smooth and continuous. When the systems capture discretely varying data each pixel must be assigned a value corresponding to the spatially dominant observation within the pixel. Some GIS offer the possibility to store point measurements as regular grids of points called ‘lattices’ where the point values are not assigned to pixels by default but remain stored as points. This data structure offers the flexibility of dual display as either a surface with linear interpolation between the grid of points or as a ‘point assigned’ raster. The size of the pixel on the ground or the frequency of sampling of points defines the resolution of the data set in relation to the observed geo-phenomena. Such pixel resolutions may be pre-fixed as in the case of some earth observing imaging systems and some fixed resolution sampling. Frequently, however, pixel resolution can be arbitrary. In some cases the underlying field being discretised in a raster can be non-isotropic, i.e.


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there is a directional bias in the values. This is the case in travel time isochrones for calculating areas at equal travel time from some point. An early convention developed in spatial data modelling was that entities must be described separately in terms of their non-spatial and spatial attributes. This convention originated in the software architectures of the early GIS, where a geometry engine was integrated with an alphanumeric relational database management system (Shekhar et al. 1999). In later research ‘extended relational’ (Güting and Schneider 1993) and ‘objectoriented’ approaches (Egenhofer and Frank 1992) have been used in GIS so that spatial data models can now be constructed in most GIS without separating the geometry and the attributes. At their simplest geo-phenomena can be represented using two dimensions with one or more attributes, as in most current GIS (Burrough and McDonnell 1998). Such GIS are normally based on an x, y coordinate system projected from the earth with no third z coordinate. There are clear compromises in the use of such two-dimensional representations to represent geo-phenomena (Raper and Kelk 1991). Firstly, the surface elevation z coordinate must either be ignored or treated as a single valued attribute of x, y, which then restricts the representation to an infinitely thin surface which cannot overfold without giving multiple values of z. Secondly, temporal change must be ignored or treated as a series of two-dimensional ‘snapshots’ maps. While these compromises can be accommodated in GIS that are used for facility management or geodemographics, they usually cannot be tolerated for environmental and geoscientific applications.

Figure 4.6 Geo-representation using rasters

Single-valued surfaces can be mapped using GIS by storing the surface elevation as an attribute of x, y using either raster, vector or functional approaches. Raster approaches


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use digital elevation modelling (DEM) techniques (Hutchinson and Gallant 1999). Vector approaches involve either the storage of isolines that join points of equal attribute value or the use of triangulated irregular networks (TINs) to structure points (Weibel and Heller 1991). Interpolation may be necessary if the data source does not provide points prestructured in the form of a DEM or a TIN (Petrie 1989). Surfaces constructed with intrinsic linear constraints are needed for surfaces that are cut by faults, as in geological applications (Rüber 1989). The earth’s surface can also be classified and regionalised into slope elements by geomorphologically classified terrain shape (Dikau 1992, Wood 1996). If the peaks, pits and passes making up a terrain are identified from an interpolated surface model, then these surface-specific features can be connected to form a terrain network topology (Wood 1998). Functional approaches involve the use of continuous bivariate parametric equations for x, y and z coordinates to represent smooth and non-overfolding surfaces. The parametric equations used are usually based on bicubic polynomials for surfaces (Mortenson 1997). Hermite methods produce single patch surface solutions fitting approximately to a target set of points. B-spline methods produce multiple patch piecewise solutions that fit large point sets exactly. Auerbach and Schaeben (1992) used a triangulation as a source of the knots used to create and control quadratic B-splines to exactly represent a geological surface known from irregularly distributed data points. Single-valued surfaces can be mapped in two dimensions or visualised in three dimensions. Three-dimensional visualisations of single-valued surfaces use depth cueing to show the z attribute variation using perspective views and so they have become known as ‘two and a half dimensional’ (or 2.5D) models (McCullagh 1998). However, this kind of visualisation cannot cater for any situation where the phenomenon under investigation encloses space, e.g. in the atmosphere, solid earth or ocean, as is common in environmental applications. Approaches to this problem using two-dimensional representations typically involve the use of ‘stacked’ surfaces in an attempt to handle the occurrence of multiple z values (Siehl et al. 1992). This is usually not a very satisfactory solution since the solid geo-phenomena to be represented are often highly irregular with many occurrences of multiple z values and may even have internal holes. Accordingly, various new forms of three-dimensional geo-representation have been developed to represent this kind of phenomenon.

THREE-DIMENSIONAL GEO-REPRESENTATION Three-dimensional data models require geo-representations capable of capturing the form, structure and properties of the original geo-phenomena (Raper 1989a). In many cases, such geo-representations capture states of a dynamic system, which can be seen as a projection of the geo-phenomena onto three-dimensions. A wide range of computational geometric forms has been developed from algebraic topological forms to provide such tools, which are reviewed below. The issues discussed in this section are: generic solid geometric modelling techniques, the data structures developed for georepresentations, the design of associated databases and the functionality of the developed systems. This review aims to illustrate the scope and limitations of the three-dimensional


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geo-representations available to implement the spatial data modelling of states already discussed. Solid geometric modelling Three-dimensional geo-representation is a branch of solid geometric modelling. In solid geometric modelling all points have x, y and z coordinate values making it possible to model the distribution of form, structure and properties in three dimensions. Research in geographic information science and the geosciences has concentrated on the extension of generic techniques of solid geometric modelling (Mäntylä 1988). This research has been driven by the special challenges of three-dimensional geo-representation, i.e. large data volumes, complex data configurations, uncertain data, the need for interpretive control of the models, attribute linkage and the need for multiple resolution solutions (Houlding 1994). Requicha and Völcker (1983) and Requicha and Rossignac (1992) surveyed generic solid modelling techniques and divided them into three: constructive; boundary; and decomposition approaches. These approaches are explored in turn below and examined for their suitability for use in geo-representation.

Figure 4.7 Parametric solids

‘Constructive’ methods of solid geometric modelling are based on simple ‘primitive’ solids represented using continuous trivariate parametric equations for x, y and z coordinates using Hermite or B-spline methods. Primitive parametric solids (such as a cuboid) are bounded by six patches, which are two-dimensional functional representations (figure 4.7). The three-dimensional morphology of B-spline parametric


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models is controlled by weighting points (poles) and the piecewise solutions are joined by knot vectors at irregular (‘non-uniform’) intervals. B-spline methods use rational functional forms capable of the integrated representation of free form three-dimensional morphology as well as primitive parametric solids. These forms are known as nonuniform rational B-splines (NURBS). Primitive solids can be ‘instanced’ by applying transformation operations to scale their dimensions differentially, by applying constraints to their parameterisation, or they can be created by sweeping a curve or a surface through three-dimensional space. These parametric solids are usually topologically single-celled although multiple-celled solids with holes can be parameterised using ‘group technology’. Within the solid, for any point x, y, z, the ‘isoparametric’ surface is one for which one of the three parametric variables is constant (Mortenson 1997). Primitive ‘instances’ can be combined to make arbitrary shapes using ‘constructive solid geometry’ (CSG) methods, which are based on a series of union, intersection and difference Boolean operations on the original geometric object. Solid geometric models made with CSG methods can be represented as binary trees where the terminating roots are solid geometric models and the non-terminating roots are Boolean operations (Mäntylä 1988). Although CSG methods are fast to compute and always produce valid models, they cannot represent some of the complex morphologies found among geo-phenomena due to the inherent limitations of the underlying parametric approach. ‘Boundary’ approaches to solid geometric modelling are based on the decomposition of the phenomenon to be modelled into faces (two-dimensional planar facets or surfaces), meeting at edges (one-dimensional lines or curves), which join vertices (zerodimensional points) (figure 4.8). Unique faces can be identified by orienting their edges counterclockwise around the face with respect to the facet or surface normal. To be wellformed, ‘boundary representations’ (B-reps) must be closed, orientable, non-self intersecting, bounded and connected topologically. This requires a construction process capable of generating valid B-reps. Applying the constraint that the faces are planar and bounded by vertices joined by straight edges means that the B-rep will be a polyhedron. This is akin to the assumptions of two-dimensional vector geometry in GIS. Simple polyhedra obey Euler’s formula relating the vertices (V), edges (E) and faces (F):

(4.1) The Euler formula can be used to test the validity of the simple polyhedra including the regular polyhedra—the cube, tetrahedron, octagon, dodecahedron and icosahedron (figure 3.1). However, it requires modification for non-simple polyhedra with holes where the faces are topological discs and the edges are arcs. B-rep data structures are usually based on a hierarchical graph listing the vertices, edges and faces and their interrelationships (Boissonnat 1984). If there are internal holes several graphs have to be created and each is contained within a shell such that each shell is made up of closed and connected sets of faces. One of the most widely used approaches to B-rep construction is the three-dimensional triangulated irregular network method where the data points become the vertices of tetrahedra, which fill the convex hull (Fang and Piegl 1995).


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Boundary approaches are suitable for geo-representation since they are conservative, efficient and they adapt to variable data density. However, the models require validation since the data structure does not contain implicit checks as in CSG. The decomposition approach to solid geometric modelling involves breaking down the modelled object into either horizontal slices, prismatic columns, volume primitives such as alpha shapes (Edelsbrunner and Mucke 1994) or regular cubic cells such as voxels (Requicha and Rossignac 1992). Approaches based on voxels are known as spatial occupancy enumeration (SOE) methods as the model consists of attribute records for all the voxels making up a universe. SOE methods have huge data demands: even a 100 by 100 by 100 cubic universe has 1 million voxels. Three methods have been proposed to minimise this overhead: firstly, the reduction of the model to the voxels touching the boundary of the modelled object (3DDT approach); secondly, the indexing and compression of the voxels (octree approach); thirdly, run-length encoding of the voxels. The three-dimensional discrete topology (3DDT) approach was proposed by Kaufman, Cohen and Yagel (1993) as a way to ‘voxelise’ representations. 3DDT algorithms generate a ‘covering’ set of voxels from a parametric or B-rep source through intersection, and then reduce the number of voxels needed to a minimal set. Minimality is defined as a function of voxel adjacency: there are 6 neighbours to a voxel where only a face is shared, 18 neighbours where faces and edges are shared and 26 neighbours where faces, edges and vertices are shared. Hence, 3DDT voxel models can be classified as 6-, 18-or 26- ‘separating’ if they have 3D voxel configurations that satisfy adjacency conditions at one of these three ‘N’ levels of separation. Voxels intersected by the modelled object can be eliminated until a predetermined level of ‘N-separation’ is reached when an ‘N-minimal’ set of voxels is produced. Models made up of such ‘Nminimal’ sets of voxels can be manipulated and visualised effectively due to their relatively low voxel counts. The octree is the three-dimensional equivalent of the quadtree that recursively divides a universe into eight (Samet 1992) (figure 4.9). At each stage the algorithm tests whether any of the eight subdivisions is empty (i.e. outside the object) or full (i.e. inside the object) (Meagher 1982). If they are not either empty or full, i.e. the edge of the object passes through them, then the process of subdivision continues to a predetermined level of resolution. When encoded and compressed by octree methods the model is made up of voxels of different sizes and each voxel is internally homogenous. If the voxel dimensions of the universe are set before octree encloding and the number of voxels along the edges of the universe cannot be divided by eight then extra empty voxels are added as necessary. The subdivision can be recorded using a linear octree encoding where only the leaves of the tree that are part of the modelled object are stored as octal numbers, which allows efficient storage and querying (Gargantini 1982). Carlbom, Chakravarty and Vanderschel (1985) and Carlbom (1987) proposed a modified version of the octree called the polytree that identifies the geometric content of each voxel, i.e. whether full or empty, and whether a vertex, edge or surface cell modelled object. This hybrid voxel/B-rep scheme has the advantage of being a solid geometric representation amenable to rapid Boolean operations for three-dimensional spatial operations, whilst also identifying the geometric content of an individual voxel. Ayala et al. (1985), and Brunet and Navazo (1989) proposed the similar extended octree


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where leaves contained pointers to a unique set of planar half spaces. An attempt to develop a three-dimensional run-length encoding of a voxel universe was made by Bright and Lafflin (1986) but this approach offers less efficient spatial access to the voxels than an octree or polytree. Tamminen and Samet (1984) presented an algorithm for converting from a B-rep to an octree encoded voxel model using a ‘connected components’ labelling approach. Xiao et al (2000) discuss a vectorised octree implementation.

Figure 4.8 A classification of 3D data structures


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Three-dimensional data structures for geo-representation Researchers in GISc and the geosciences have extended and applied the methods of solid geometric modelling for the purposes of three-dimensional geo-representation. The choice of a data structure should be part of a holistic process of conceptualisation, data capture, sampling and data structuring which is recursively updated depending on the aims of the geo-representation (Raper 1989b). Jones (1989) surveyed the threedimensional data structures available for geo-representation at an early stage of their development and assessed their potential for geological applications. Fried and Leonard (1990), and Jones and Leonard (1990) reviewed three-dimensional modelling in the petroleum exploration industry, while Pflug and Bitzer (1990) and Pflug and Harbaugh (1991) collected together work by geoscientists on geo-representation in geological reconstruction and simulation.

Figure 4.9 Octree encoding (from Lattuada 1998)


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Turner (1992) presented an overview of the representational problems for a wide range of geo-phenomena, evaluated the data structures developed in CAD and image processing and gave examples of new geo-representation approaches. Vinken (1992) surveyed a wide range of approaches to the digitisation of the geological mapping process, including several early approaches to geo-representation. Moulding (1994) focussed on the process of geological characterisation and the role of geo-representation in these procedures. Ozmutlu (1997) collected together work on geological characterisation, georepresentation, simulation and the creation of virtual environments for geosciences. Schmidt and Götze (1998) summarised the requirements of geophysics for threedimensional solid modelling. In this section data structures specifically developed for geo-representation will be (re)surveyed (cf. Raper and Kelk 1991) to evaluate the performance of the implemented systems in parametric, B-rep, voxel and hybrid categories. Parametric approaches Much of the work on constructive parametric approaches to geo-representation has focussed on the use of NURBS since their piecewise nature allows the construction of surfaces with multiple values of the z coordinate (Tipper 1977). Kelk and Challen (1992) used the Intergraph Engineering Modelling System (EMS) to fit NURBS-based parametric surfaces to construction lines drawn in three dimensions in order to represent geological surfaces. Fisher and Wales (1992) used the same package to model oil reservoir morphology by joining the top and bottom surfaces to create quasi-solid geometric models. While transformations and analyses using NURBS are rapid and efficient, as a representation it enforces a continuity of curvature between modelled data points. This is an acceptable assumption for many, but not all, applications of georepresentation, as Mallet (1992) has noted. By contrast, Saksa (1995) developed the Rock-CAD system based on the Medusa 3D GIS, which uses quadratic polynomial parametric methods to define the facets of polyhedra constrained by the data points. These polyhedra can be combined using Boolean operations to form complex models. Flick (1996) developed a three-dimensional urban modelling system by integrating the ACIS parametric volume models with the Open GL visualisation environment and converting the parametric surfaces to polygonal facets. Kriegl and Seidl (1998) developed a method to search databases of surfaces and solids in point form by comparing parametric approximations of surfaces and ellipsoids to the point set records in the database. B-rep approaches By contrast, B-reps have been widely used and further developed for geo-representation. In algebraic topology a B-rep can be constructed from arbitrary geometry, i.e. any zero-, one-, two- or three-dimensional geometric component that is embedded in a threedimensional space (Burns 1988). Pigot (1992) outlined the theoretical background to three-dimensional geo-representation using cell complexes showing how geometric realisations are dependent for their validity and indexing on topological definitions of


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orientability, connectivity and identification. Pigot (1992) shows how the use of specific topological definitions will constrain the assumptions that need to be made about threedimensional geometric relationships when designing solid geometric data structures for geo-representation. Although cell complexes are more general and more flexible, they are also more difficult to create and maintain when developing data structures. Hence, most data structures for geo-representation based on B-reps have employed the simpler topological concept of the simplex rather than the cell. A 0-simplex is equivalent to a point, 1-simplex to a line segment, 2-simplex to a triangle and 3-simplex to a tetrahedron volume (Carlson and Frank 1987) (figure 4.10). From these primitives many higher order geometric constructs such as grids (constructed from equilateral triangle pairs) and polyhedra can be formed.

Figure 4.10 Zero-, one-, two- and three-dimensional simplices

A number of researchers have developed systems to implement three-dimensional data structures based on B-reps. Houlding and Stoakes (1990) and Houlding (1992, 1994) outlined a method of three-dimensional modelling using ‘volumetric components’ that has been used in the 3D GIS ‘Lynx’. Prismatic volumetric components are created by using the edges of a geometric object outlined on two-dimensional vertical cross sections. The outlined shape on each cross section is projected onto a central ‘mid plane’ where the (inevitably) different shapes are reconciled using a best-fit approach. The result is a polyhedron bounded by the cross sections, which can then be joined with other polyhedra. Lynx allows the creation of a voxel model from the three-dimensional components identified which is oriented at any angle appropriate to the structure of the geometric object (Orlic and Rösingh 1995). Ganter (1989) outlined a prototype system for triangulating serial cross sections across caves. Sides (1992) developed a Geological Discontinuity Modelling System (GDMS) for mining applications that allowed the creation of intersecting multi-valued triangulated surfaces with fault and fault-set handling. Kraak and Verbree (1992) show how terrain models can be ‘tetrahedronised’ from a base triangulation. Pilouk (1996) developed a tetrahedral network (TEN) data structure based on simplices that was implemented in the Integrated Simplicial Network Application Package (ISNAP). At the data structure level the mesh is the most generic form of geometric construct, as meshes can be subdivided into structured (finite difference grids) and unstructured (finite element triangulation) forms. Lattuada (1998) argues that the easy computational access


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to structured finite difference grid meshes is outweighed by the flexibility and expressiveness that can be achieved using unstructured finite element meshes. However, data structures for three-dimensional unstructured meshes based on simplices require the elimination of ambiguities and the storage of explicit topological information. Gable, Trease and Cherry (1996) described the ‘Geomesh’ modelling system that imports valid and connected three-dimensional parametric models, triangulations or grids and creates an unstructured tetrahedral mesh from it. Geomesh contains a variety of mesh editing, checking and refinement tools to pre-process three-dimensional data before its use in finite element modelling. Building on work by Tsai and Vonderohe (1991) on the triangulation of an Euclidean space to n dimensions, Lattuada (1998) used the Bowyer-Watson triangulation algorithm to create an unambiguous three-dimensional unstructured mesh based on tetrahedra. Lattuada prevents three-dimensional point degeneracies by including points in a tetrahedron that actually lie on the boundary of the circumsphere, or by shifting the point location very slightly to force the point into the mesh. These heuristics force the creation of valid three-dimensional tetrahedra (unlike the two-dimensional case where no unique set exists), although subdivision of the original tetrahedra may be desirable to remove any very long, thin forms (figure 4.11). Lattuada allows the addition of constraints to the tetrahedralisation and indexes the tetrahedra using an octree-like N-tree that is capable of dynamic update. Lattuada and Raper (1995) show how this approach can be used to model coastal landforms from borehole data while Lattuada and Raper (1998) focussed on the problems of salt dome modelling with seismic data.

Figure 4.11 Three-dimensional tetahedronisations are not unique (from Lattuada 1998)


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Mallet (1992) outlines an alternative form of three-dimensional geo-representation using B-reps as employed by the ‘GOCAD’ system. Starting from one or more surfaces in TIN form, GOCAD adds additional points to those in the original dataset in such a way as to minimise local roughness using the Discrete Surface Interpolation (DSI) algorithm. The triangulated surface created by DSI can then be densified, if necessary, to allow the path of a fault to be entered into the data structure. The surface can also be modified by manipulating the free nodes interactively or by the use of defined vectorial constraints. The volumes between the surfaces can be filled with tetrahedra by GOCAD to create a true solid geometric model (Mallet 1999). Conreaux, Lévy and Mallet (1998) show that topologically degenerate configurations can be handled computationally, without resorting to heuristics, by using the n-dimensional combinatorial maps of Lienhardt (1994) to decompose cells provably correctly. When three-dimensional B-rep solid models are constructed from simplices or polyhedra they must be indexed for effective use. Early work on three-dimensional data structures for geo-representation was based on the concepts used in two-dimensional vector GIS. Fritsch (1990) developed a hybrid 2.5D/3D data structure in which ‘terrain’ (x,y) and ‘situation’ (z) were indexed separately and then integrated. Molenaar (1990) developed a three-dimensional solid object-oriented data structure based on four classes of element, viz. point, line, surface and body, which are instantiated respectively by node, arc, edge and face geometry. Molenaar (1990) identified twelve conventions through which the integrity of geometry in a database could be guaranteed by eliminating degenerate configurations. These included the constraints that the geometric elements be topologically simple (non-intersecting with no islands), that they be planar and that the bodies created be disjoint. Pilouk (1996) extended the Molenaar (1990) model to include multi-theme solid models using ‘sub-bodies’. Trott and Greasley (1999) described a three-dimensional data structure for the Vector Product Format (VPF) which is fully integrated with topological vector GIS data structures. The ‘Arcview 3D Analyst’ GIS module supports three-dimensional geometric objects in a GIS database alongside singlevalued grids and TINs. Recent work (post 1995) on three-dimensional data structures for geo-representation has employed object-oriented concepts from virtual reality environments such as ‘World Toolkit/WorldUp’ from Sense 8. In these systems, and in the generic virtual reality modelling language (VRML) derived from the Open Inventor format from Silicon Graphics, data structures are based upon the scene graph (see chapter 5). The scene graph approach used in VRML has become a standard way to create a three-dimensional solid model using either B-rep or voxel geometry (Raper, McCarthy and Williams 1998). The surfaces and solids of a VRML model can be draped with appropriate imagery to create a highly realistic representation (Flick and Coors 1998). Three-dimensional models based on the scene graph include urban GIS (Köninger and Bartel 1998) and environmental planning (Verbree et al. 1999). Gong, Lin and Lin (2000) developed a system called Cave3D in which cave solid models were constructed from TINs of surface, ceiling and interior objects and then integrated in a VRML model. However, the creation of a virtual geo-representation made up of surfaces or solids draped with map data or imagery in VRML format requires a particularly large number of shaded triangular facets to represent them. Level of detail (LOD) algorithms have been


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developed so that only those objects near to the user’s current viewing position are displayed using enough triangular facets to give a high resolution effect (Muxaxo, Neves and Camara 1999). It is also possible to reduce the number of triangles used to form the surface or solid models by using filtering techniques. These techniques reduce the number of triangles making up the surface or solid by amalgamating them when the angles subtended vertically between adjacent triangles are small. The large data volumes in surface and solid models can also be handled more effectively by using multiresolution storage schemes. De Floriani (1989) described the Delauney Pyramid approach in which the elements of the TIN of each different resolution were stored hierarchically without duplication. Ware and Jones (1997) developed a multi-resolution data structure for models of intersecting surfaces in which the elements of the TIN representing each resolution were stored in relational tables and indexed using a quadtree. Voxel approaches Some of the earliest approaches to geo-representation were based on voxel representations. These early systems stored the voxels as three-dimensional layer-and row-ordered rasters, with each voxel and associated attribute values, stored explicitly. These models were primarily built for hydrocarbon exploration and reservoir management, for example by Shell (the MONARCH system, Bryant, Paarkedam and Davies 1991) and by Exxon (the GEOSET system, Jones 1988). Voxel models are useful in this application domain as three-dimensional data is collected in both seismic reflection time and borehole depth formats. These datasets are easy to reconcile in voxel format by resampling, especially where seismic reflectors require three-dimensional migration to remove reflections drawn from outside the nominal x, z plane of the seismic cross section (Brown 1991). However, despite the advances in computing power allowing the manipulation of higher numbers of voxels, it has proved necessary to employ octree encoding methods to compress and index voxels for the best performance in large models. Kavouras (1987, 1992) developed an octree encoding system for georepresentation called ‘Daedalus’, which constructed solid models from B-reps sources. Daedalus was implemented within the CARIS GIS, which acted as a source of surface and solid data and as a storage location for linear octree codes. Bak and Mill (1989) and Bak (1991) developed a Geoscientific Resource Management System (GRMS) which converted B-reps into using octree-encoded voxels. The GRMS was used in the reconstruction of mine infrastructure and ore bodies with seven level octrees. The GRMS offered three-dimensional querying capabilities by search window, by object surface intersection and by connectivity, all of which demonstrated much higher performance than comparable B-rep models. In most cases octree encoded voxel models have only represented the solid geometry of a single geo-phenomenon. Prissang et al. (1996) developed the linear octree based ‘Property Management System’ (PMS) to encode and index voxel models that were produced by converting B-rep component models from the Lynx system into a raster form (Bak 1991). However, PMS creates a geometry octree for the geometry of the threedimensional domain and further attribute octrees for each of the geometric objects with distinct attributes. Each of these octrees can be compared by traversing the tree through


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the same path in order to perform attribute queries on the geometry octree. The primary disadvantage of voxel modelling is the fixed cuboid shape of the voxels. The ‘Stratamodel’ system aims to model geological structures and their internal variation with voxels whose x, y shape remains grid-shaped but whose z thickness can be varied. The Stratamodel ‘geocellular’ approach builds models by creating geological units from top and bottom surfaces and then warping, truncating and cutting them to mimic the shape of the investigated geo-phenomenon while retaining the grid framework. The finished geocellular model is made up of multiple geological units fused together into a single voxel framework such that each grid cell on the model surface is the top of a column of variable thickness voxels. The Intergraph ‘Voxel Analyst’ can form models using hexahedral voxels. Hybrid approaches Some approaches to geo-representation employ hybrid generation techniques involving the conversion of one data structure to another. This approach can make it easier to produce a validated three-dimensional model. Two approaches are discussed, one that converts from a B-rep to a voxel reprepresentation (Lynx) and the other that converts from a grid to a B-rep (Earthvision). Houlding (1994) shows how the B-rep components created by the Lynx system can be converted to a voxel-based representation by intersection with a three-dimensional grid. Each voxel produced by the intersection is normally assigned the attribute of the geometric object at the voxel centre. If the voxel produced is heterogeneous in composition Lynx can produce a volume-weighted average. Where the aim is to produce a set of voxels with estimated values for a continuously varying geo-phenomenon, a three-dimensional interpolator can be used. The simplest approach to the estimation of voxel values is the use of a spherical search volume, with a linear distance weighting of the qualifying sample values. Houlding (1994) shows how a three-dimensional point kriging approach can be used by scaling the search volume to the range of the x, y and z semivariograms. Three-dimensional volume kriging takes account of the volume of the voxel where the voxels are variably sized or scaled, allowing the calculation of the average voxel value. Smith and Paradis (1989) outlined a minimun tension approach to creating georepresentations from points with numerical attributes that are scattered in threedimensional space. Earthvision begins by calculating values for a coarse three dimensional grid of voxels and then fits multivalued bicubic spline surfaces to the grid for user-specified attribute values of the attributes. The system then proceeds iteratively, comparing the values of the three-dimensional grid with scattered data values so that new surfaces can be computed with progressively lower differences between the grid values and the closest scattered data values. This ‘minimum tension with scattered data feedback’ approach outputs a three-dimensional grid and a set of parametric surfaces each corresponding to a particular attribute level. The resultant attribute ‘isosurfaces’ are converted to B-reps for display and clipped by structural constraints such as faults where necessary. Eddy and Looney (1993) evaluated the results of Earthvision interpolation procedures against input parameters such as voxel size and the variation in shape of the


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search zone used in the three-dimensional interpolation showing significant variations in output. Databases for geo-representations Despite the wide range of geo-representations developed, few database designs have been produced for three-dimensional solid modelling. There are two main reasons for this: many geo-representations are only made to reconstruct the three-dimensional form of a sampling-limited geo-phenomena, and, the challenges of developing integrated threedimensional data structures for geometric and non-geometric data are considerable. Yet, such database designs are important to the further development of geo-representations. A database approach to representation brings all the advantages of security and integrity of data as well as support for the management of model versions, multiresolution representation and query-based model decomposition. Approaches to database design for three-dimensional geo-representation are constrained by the semantics of the available data models for databases, i.e. relational or object-oriented. Meier (1986) first outlined the potential of relational databases for the storage of three-dimensional models in parametric and B-rep forms. Meier noted that although relational databases can store geometric data in normalised tables using geometric identifiers as keys to relations, a greater expressiveness can be obtained by adding ‘part-of and ‘is-a’ relationships to the relational model. Such relationships require spatial extensions to Structured Query Language (SQL) permitting the storage of nonatomic, non alphanumeric geometric data types and their retrieval through ‘part-of’ and ‘is-a’ associations (Bundock and Raper 1992). However, such extensions to the relational model are known to reduce the performance of querying operations as they cannot be optimised (Egenhofer 1992). By contrast, object-oriented techniques allow the database designer to define data types and associated operators together, making for great expressiveness but often introducing complex design and querying. These considerations mark out three design options for the databasing of threedimensional geo-representations: • Store geometric and non-geometric information in standard relational tables using relational joins and SQL queries to compose solid models; • Store geometric information in extended relational tables using spatial data types and non-geometric information in standard relational tables, and use extended SQL to compose solid models; • Store geometric and non-geometric information in an object-oriented database and use their associated operators to compose solid objects and to define interaction rules. While most of the database approaches have employed B-rep geo-representations, Kavouras (1987) showed how the Daedalus voxel model could be linked to associated attribute tables through a voxel indexing scheme. The first of these three approaches was implemented by Molenaar (1990) as part of a formal data structure for three-dimensional geo-representation. Rikkers, Molenaar and Stuiver (1994) show how node, arc, edge and face geometry and associated topological relationships can be stored in tables so that point, line, surface and body objects can be


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instantiated topologically. By using standard SQL queries, solids can be composed and topological queries can be answered. This approach is an implementation for threedimensions of the geo-relational model that is common in two-dimensions. Note that this approach requires the acceptance of planar enforcement as an organising principle, i.e. all surfaces and bodies are closed, connected and non-overlapping. Pilouk (1996) extended this approach in the Simplicial Network Integrated Database (SNIDB) where zero-, one-, two- and three-dimensional simplices were stored in relational tables. The second, extended-relational approach was implemented by Waterfeld and Schek (1992) for the DASDBS Geokernal. The Geokernal data model stored three-dimensional B-rep geometric elements as abstract data types in relational tables and supported the creation of complex solid models by composition. The Geokernal also implemented a cell index to the items of B-rep geometry in the database so that the geometric data could be clustered spatially on disk for query optimisation. The third object-oriented approach to three-dimensional geo-representation was implemented by Breunig, Bode and Cremers (1994) who developed the Object Management System (OMS). OMS consisted of an Object Manager and Type Manager to store and manage zero-, one-, two- and three-dimensional simplices as object types. To optimise geometric operations, OMS formed two- and three-dimensional complex objects (called as e3- and e2-complexes) from aggregations of simplices, whose coordinates were encapsulated with their bounding box. This design was elaborated with the development of ‘Geostore’ (Balovnev, Breunig and Cremers 1997) within the object-oriented DBMS Objectstore. Geostore was developed in order to reconstruct the evolution of large geological structures from cross sections with interpreted strata and fault surfaces (Alms et al. 1998). Since this problem involves four-dimensional reconstruction, Geostore allowed the user to browse the model by logical structure or through a three-dimensional viewer. Balovnev, Breunig and Cremers (1997) generalised the object-oriented architecture of Geostore by developing a class library for three- and four-dimensional solid modelling called ‘GeoToolKit’. The GeoToolKit class library supports simplices, complexes (curves, surfaces, solids), compound objects, and analytical objects (line, plane) and allows the user to specify their own types. These objects make up a ‘space’ which is indexed using an R-tree (for geometric data only) or LSD tree (for both geometric and attribute data). In GeoToolKit objects can change their representation without changing their object identifier, making it possible to support multiple representations. The indexes provide a multidimensional key into the data, facilitating the exploration of spatiotemporal behaviour. Köninger and Bartel (1998) used the object-oriented database Postgres95 to store the Open Inventor classes representing the three-dimensional urban form. The database is indexed using an R-tree and the geometry is organised into three ‘level of detail’ nodes. Balovnev et al. (1998) developed a CORBA-based data and systems integration environment for the GOCAD and IGMAS modelling systems. Three-dimensional spatial query and analysis As the three-dimensional modelling workflow extends beyond capture and visualisation


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into structured storage, so the scope for spatial query and analysis has increased. This is so since data structures can make some operations trivial (Raper 1989b). Ideally the conceptualisation of the geo-phenomenon should drive the choice of geo-representation in order to achieve the objectives of the exercise. Achieving this kind of closure between conceptualisation and representation should become more common as users become liberated from the constraints of data formats through standardisation efforts such as Open GIS. Selecting a representation based on the performance of spatial query and analysis presupposes some knowledge of typical outcomes. Raper (1990) proposed a nonmaximal generic set of spatial query and analysis functions for three-dimensional modelling for which typical outcomes could be predicted. The six categories of functions in Raper (1990) included visualisation manipulation, transformation, selection (by intersection), inter-relationship characterisation, geometric characterisation, and modelling functions. Their notional performance when structured using voxel and B-rep representations is set out in table 4.2 and is illustrated in figure 4.12.

Table 4.2 Generic spatial query and analysis functions in three-dimensional modelling and their effectiveness under different data structures

SPATIAL FUNCTION

VOXEL

B-REP

Translate

fast

fast

Rotate

fast

fast

Scale

slow

fast

fast

fast

slow

fast

AND

fast

slow

OR

fast

slow

XOR

fast

slow

NOT

fast

slow

Metric

fast

fast

Topological

fast

slow

Volume

fast

slow

Surface area

fast

fast

Visualisation

Reflect Transformation Shear Selection

Inter-relationships

Characterisation

Multidimensional geo-representations for modelling Centre of mass Orientation

159 fast

slow

slow

fast

fast

slow

Modelling Build

Some of these query and analysis functions have proved difficult to implement in any of the available data structures. One challenging task has been the development of threedimensional topological inter-relationships such as shortest path analysis. Kirkby, Pollitt and Eklund (1996) implemented a modified version of the Dijkstra (1959) shortest path algorithm in the ‘Vulcan’ 3D GIS, in which the gradient over a 2.5D surface was added into the computation. Scott (1994) implemented a shortest path algorithm for an unindexed three-dimensional voxel space using a cumulative distance cost approach. This approach produces a set of voxels that each contain an attribute with the cost of travelling to that voxel from a specified start point, if there is a uniform friction of movement throughout the representation. The three-dimensional pushbroom shortest-path algorithm moves through the ‘cost volume’ along the steepest cost slope from target to origin using a 3 by 3 by 3 search kernal. Kim, Lee and Lee (1998) implemented three-dimensional buffering and line of sight (or ‘lantern’) algorithms for solid geo-representations in VRML form. Three-dimensional buffering was carried out using a spherical extrusion function to surround the target object. The ‘lantern’ operation involves intersecting all geometric objects falling inside a cone with a specified azimuth, opening angle and length. The use of three-dimensional query and analysis functions creates a new feedback loop in the modelling workflow as the results of the queries/analyses may optionally be stored as new geometric objects within the database. This possibility raises the question of how appropriate metadata on the original and derived geometries should be stored. Livingstone and Raper (1999), and Duane, Livingstone and Kidd (2000) propose the use of the Hierarchical Data Format (HDF) as a means to store self-describing georepresentational datasets.

MULTIDIMENSIONAL GEO-REPRESENTATION Most of the geo-phenomena we seek to represent have spatio-temporal identities, and as such they demand multidimensional geo-representations capable of expressing behaviour through time. Since spatio-temporal identity involves temporal extension, appropriate multidimensional geo-representations require both spatial and temporal referencing. Multidimensional geo-representations with temporal referencing can be divided into the ‘spatio-temporal’ (two dimensions of space plus one of time) and the ‘four dimensional’ (three dimensions of space plus one of time). Spatio-temporal georepresentations can express temporal behaviour when projected from four dimensions to two spatial plus one temporal. A number of temporal GIS designs have been proposed and implemented, and are reviewed below. Four-dimensional geo-representations can


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express the full multidimensional character of the world: a few four-dimensional GIS and process modelling systems have been designed and implemented and are discussed below and in chapter 10. Some of these four-dimensional systems are capable of the implementation of the process modelling already discussed. The geo-representations available to implement multidimensional conceptualisations are discussed below. This section will review the foundations of spatio-temporal knowledge representation, the approaches to temporal GIS, object-oriented spatiotemporal GIS, the applications of time geography, the development of four dimensional GIS and multidimensional geo-representation. With the exception of temporal GIS, the relative lack of development in this field offers new scope for research into multidimensional geographical information science.

Figure 4.12 A taxonomy of three-dimensional spatial functions

SPATIO-TEMPORAL KNOWLEDGE REPRESENTATION A wide range of spatial knowledge representations based on two-dimensional ontologies have been developed from cognitive analyses and from a priori schemes (see chapter 2). However, these two-dimensional ontologies explicitly excluded time, seeing it as conceptually distinct from space and unnecessary in spatial knowledge representations. Langran (1988, 1992) was among the first to explore spatio-temporal knowledge representation, defining the concept of ‘dimensional dominance’ to describe how spatiotemporal information is usually dominated in display and query terms by either the space or time dimension. This situation is a function of the fact that uses of spatio-temporal


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information tend towards interest in space as an ordering (maps) or time as an ordering (case histories) rather than both. However, spatio-temporal knowledge representations need to express a unified spatial and temporal approach. There have been far fewer attempts to define spatio-temporal knowledge representations, as there are correspondingly fewer spatio-temporal ontologies available. Possible spatio-temporal ontologies divide into those based on absolute time and space and those based on relative time and space (Wachowicz 1999). Ontologies are defined by the spatial and temporal boundaries of events in the absolute approaches, and by the relationships between the geo-phenomena in the relative ones. These alternatives mark out different approaches to the definition of identity, and, therefore, different approaches to change. Peuquet (1994) proposed the TRIAD scheme where all geo-phenomena are defined by attribute, spatial and temporal references (‘what, where, when’) to form a ‘world history model’. This is an absolute time and space view that is equivalent to the ontological argument of attribute ‘bundles’. By contrast, Roshannejad and Kainz (1995) argued that while all multidimensional geo-phenomena need to be referenced by what, where, when information, object identity must be independent of referencing. This is a relative time and space view that is equivalent to the ontological argument of ‘essences’. In a formal approach to spatio-temporal knowledge representation, Claramunt and Thériault (1996) presented a typology of spatio-temporal processes from an absolute time and space perspective, based on the TRIAD scheme of Peuquet (1994). Claramunt and Thériault argue that there are three main types of spatio-temporal processes: the evolution of a single entity such as changes, transformations and movements; the functional relationships among multiple entities such as replacement and diffusion; and, the evolution of spatial structures involving several entities. On the basis of this typology they introduce an Event Pattern Language (EPL) which can describe the spatio-temporal evolution of a set of objects in terms of processes and operators. Although this is a useful and expressive formalism it cannot handle non-discrete geo-phenomena or gradual object identity change. The semantics of Claramunt and Thériault have recently been extended by Shu, Chen and Gold (2000). Hornsby and Egenhofer (2000) presented a formal scheme for spatio-temporal knowledge representation, based on possible changes to geo-phenomena, modelled as discrete objects at a high level of abstraction. In the Hornsby and Egenhofer (2000) Change Description Language (CDL), objects can be in the following states: existing; not existing with no history of a previous existence; or, not existing but with a history of previous existence. Changes from one state to another are defined as ‘transitions’, which in total allows nine combinations: continue existence without history; create; recall; destroy; continue existence; eliminate; forget; reincarnate; and continue non-existence with history. This scheme is an axiomatic system for the exploration of change semantics that produces a classification of the changes to an object identity defined in this way. The constitutive nature of ‘transitions’ (object inter-relationships) in the scheme implies that this approach is a relative time and space view. An alternative conceptualisation of change might be based on a psychological concept of ‘difference’ that is independent of referencing and representation. The set of all possible forms of change defined as difference, with the human construction placed on these scenarios is:


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• Same place, same geo-phenomena, different time (progression of geo-phenomena) • Different place, same geo-phenomena, different time (geo-phenomena that have moved) • Same place, different geo-phenomena, different time (monitoring place) • Different place, different geo-phenomena, different time (elsewhere) • Same place, same geo-phenomena, same time (real time feedback) • Different place, same geo-phenomena, same time (contemporaneous monitoring). This schema classifies difference, and, by implication the scope of multidimensional identity. Temporal GIS Temporal GIS are systems for representing the temporal behaviour of geo-phenomena when they have been projected from four dimensions to two spatial plus one temporal. Early approaches were based on the extension of commercial two-dimensional GIS to handle time with the attributes, which Langran (1992) classified into three types: sequent ‘snapshots’; ‘base state with amendments’; and, ‘space-time composites’. These designs mirrored the early approaches to developing temporal relational databases to handle change in the stored entities (Snodgrass 1992). Here, ‘snapshots’ are equivalent to the addition of new tables to the database; ‘base state with amendments’ is equivalent to the addition of tuples to a table; and ‘space-time composites’ are the equivalent of adding new items to an attribute. Snodgrass (1995) developed a temporal version of SQL TSQL2 to support temporal queries in relational databases, but this has not been widely adopted pending progress on the ISO standard SQL/MM. In both GIS and relational database, Langran (1992) showed that the creation of temporal ‘versions’ at relation, record or attribute level leads to unacceptable extra data volume and violations of integrity in the tables. Violating integrity rules, for example, by adding extra items to an attribute, meant that the standard query tools would not give valid results, requiring further potentially non-standard extensions to the system. Several alternative theoretical schemes for spatio-temporal data storage and access using GIS were evaluated by Langran (1992). These ranged from the insertion of objects into a versioned grid index (which expanded the number of objects unacceptably) to approaches using versioned map partitions based on R-tree indexing (which reduced the efficiency of searches due to the overlapping partitions). Xu, Han and Lu (1990) showed how to extend the R-tree to handle changing spatio-temporal data by adding nodes to the tree as change occurs to the spatial objects. Abraham and Roddick (1999) have surveyed and synthesised work in this area. Subsequent innovations in temporal GIS involved further extensions to geo-relational GIS designs. Raafat, Yang and Gauthier (1994) proposed a system in which temporal behaviour leading to changes is stored by the addition of tuples in the database. However, unlike the earlier users of this technique they propose a two-tier system in which only a master relation has the ‘essential property’ attribute conferring identity on an entity, while ‘slave’ relations contain all other data. This allows the temporal change to be stored as additional tuples at the level of entity identity, without expansion in all other tables— except where new geometric data is required to create the new spatial configuration. Although data volumes do increase, the system supports temporal queries on vector


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geometric entities using standard SQL and no extensions to the relational model are needed. Peuquet and Duan (1995) proposed an event-based approach to temporal change in raster geometric maps called the Event-based Spatio-Temporal Data Model (ESDTM). In ESDTM temporal behaviour is stored by recording changes to an initial raster map in an event list in the form of a sets of changed raster grid cells. In a more sophisticated design, Peuquet and Qian (1996) used the TRIAD scheme to define the TEMPEST temporal GIS in which all changes to the stored spatial entities are referenced to a set of unequal ordered temporal intervals. To capture the semantics of the change TEMPEST stored change to the extent and type of objects in a feature view, the times and locations that had changed in a time view, and the changes at-a-location in a location view. Mennis, Peuquet and Qian (2000) have developed the Pyramid scheme to add the semantics of object identity to TRIAD. These GIS-based or GIS-like approaches to storing temporal behaviour are really only suitable for a coarse temporal granularity of change which takes place in discrete ways, for example, changes in ownership or dimensions of an urban land parcel. In environmental applications highly dynamic phenomena change at a fine temporal resolution (minutes to weeks) in a continuous way, for example, in the seasonal migration patterns of animals or the hourly change of the tides in the coastal zone. Morris, Hill and Moore (1999) outline the Water Information System database design of the Spatio-Time Environmental Mapper (STEM), which uses a relational database to store what, where, when information in an optimised record-versioned data model. Recently, Yuan (1999) has argued that what temporal GIS have lacked is a means to handle spatio-temporal identity through semantic links between spatial and temporal information. She presents a three-domain model in which snapshot, space-time composite and spatio-temporal object approaches are fused by linking the storage of data in the semantic, temporal and spatial domains. The three-domain model allows efficient entitybased and location-based queries by storing the semantic associations and temporal transitions in a ‘space graph’ that indexes all the stored discrete spatio-temporal entities. In effect, the georelational implementation Yuan presents is a normalisation of the snapshot, space-time composite and spatio-temporal object models. Object-oriented spatio-temporal GIS In a search for more flexible and expressive forms of geo-representation to handle temporal change, a number of authors have developed object-oriented spatio-temporal GIS. The key design issue in object-oriented approaches to handling spatio-temporal behaviour is how to structure the object classes and attributes to handle temporal change, when projected from four dimensions to two spatial plus one temporal. This in turn depends on the temporal and spatial ontologies that are to be used, and in the case of time, whether the time used will be world time (valid time), database time (transaction time) or both together (Worboys 1998b). In the ‘absolute space and time’ approach objects are made within a space and time referencing system, and are bounded by events (ontologically, an ‘endurantist’ approach). ‘Events’ are defined as ‘instants in time’ when objects were extended in the third


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dimension in proportion to their temporal duration to create spatio-temporal (ST-) objects with individual identities. ST-objects can be decomposed into right prisms bounded by spatial boundaries and temporal events, called ST-atoms, each with its own identity. Worboys (1992) suggested ST-atoms could be implemented using zero-, one- and twodimensional simplices. Spatio-temporal queries could be evaluated by exploring the space-time intersections of ST-atoms. Yeh and de Cambray (1996) proposed a similar approach to spatio-temporal representation called the Behavioural Time Sequence (BTS) in which a three-dimensional B-rep scheme is used to represent temporal change of two-dimensional vector geometric objects. The BTS system can handle the gradual and discrete evolution of objects through time, as the change is defined using behavioural functions. Wachowicz and Healey (1994) suggested a design in which ‘events affecting objects’ created ‘versioned objects’ such that new and temporally different versions of an object would exist on either side of an event. This approach to spatio-temporal representation was implemented in the SpatioTemporal Data Model (STDM) approach of Wachowicz (1999), developed for the mapping of public boundaries. Ultimately spatio-temporal identity is a function of the boundary/event bounding. In the ‘relative space and time’ approach time is a property of the objects. Space-time is made of objects with a spatial and temporal extent, and where there are no spatiotemporal objects there is no space or time (ontologically, a ‘perdurantist’ approach). In most ‘relative space and time’ systems using object-oriented techniques, the objects are time stamped to create temporal versions of the original object. Kemp and Kowalczyk (1994) used the ‘Zenith’ object management system to develop a spatio-temporal data store capable of storing ‘has_version’ relationships for geometric objects. Events, therefore, do not force any change in the identity of the object or instance. Kemp and Kowalczyk point out that it is possible to divide attributes between levels in the object class hierarchy such that the time invariant attributes are stored at a higher level than the time variant attributes. The key question of implementation concerns the appropriate identity criterion to use, since all the attributes of an object may eventually change. Ramachandran, McLeod and Dowers (1994) proposed a design called TCObject in which objects with geometric and non-geometric attributes are given past, present and future states: the temporal reference is established using dates of birth and death for the object. In a similar approach, Hamre (1994) proposes a design based upon OMT (Rumbaugh et al. 1991) where a ‘four-dimensional dataset’ object is composed of a spatio-temporal component (including a ‘time of creation’ temporal reference) and a nonspatiotemporal component. Voigtmann, Becker and Hinrichs (1996) develop a timestamped attribute approach by extending their Object-Oriented Geodata Model (OOGDM) to form the T/OOGDM that can be queried using the T/OOGQL query language. El-Geresy and Jones (2000) have presented a typology of spatio-temporal representational architectures and the queries they can each support. They distinguish three state-oriented spatio-temporal models: the ‘where’ view of changes at a location (e.g. the Langran 1992 raster change model), the ‘what’ view of changes to objects (e.g. Raafat, Yang and Gauthier 1994), and the ‘snapshot’ view of change (e.g. Peuquet and Qian 1996). They recognise three change-oriented spatio-temporal models: the ‘when’


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view of temporal relations between events (e.g. Peuquet and Duan 1995), the integrated event view of changes in location, object and sequence, and the ‘space composite’ view in which relations between successive states are recorded in a single geometric layer. ElGeresy and Jones (2000) argue that these event and change models are limited by their descriptive capacities: new advanced models of change are now focussing on process (the ‘how’ view) and causality (the ‘why’ view). Chen and Molenaar (1998) have developed a model of spatio-temporal change motivated by coastal geomorphological applications, which is focussed on process. In their ‘star’ model they link views of attributes, location, sequence, object and process in a single integrated approach to representing change. The processes that they define viz. shift, appear, disappear, split, merge, expand and shrink can be compared to those put forward by Claramunt and Theriault (1996) and Hornsby and Egenhofer (2000), although they are less formally based. Allen, Edwards and Bédard (1995) presented a model of change driven by causal relations among objects, based on the Bunge (1966) model of causality. In the Allen, Edwards and Bédard model, causal chains originate with intentional or non-intentional agents, which precipitate a cascade of events that change the state of objects. This model facilitates the tracing of causes and effects in time and space, at least insofar as the causal chain is well founded. Research on spatio-temporal geo-representation is now focussed on the modelling of change rather than events. Hence, Tryfona and Jensen (1999) present a Spatio-Temporal Entity-Relationship (STER) model based on an ontology of entities in motion (e.g. a car) and discrete change in entities (e.g. land parcels). The STER model adds spatial, temporal and spatio-temporal modelling constructs to the Entity-relationship model of Chen (1976). Renolen (2000) reviews the alternative conceptual modelling frameworks for spatio-temporal information system design. These include the structural perspective of entity-relationship modelling, the functional perspective of data flow diagrams, the behavioural perspective of statecharts, rule-based approaches, object-oriented designs, action-workflow diagrams and agent models. Erwig et al. (1999) introduce ‘moving data types’ into a spatio-temporal database design using a many sorted algebra approach. Time geography Another context within which spatio-temporal geo-representation has been developed is ‘time geography’, which is the study of the spatio-temporal behaviour of individuals. The origins of time geography can be traced to Hägerstrand’s (1968) work on migration, but it was codified and developed by Pred (1977). Parkes and Thrift (1980) set time geography in the context of social studies of place and time. Time geography is concerned with the space-time paths marked out by individuals, and the problem of how such paths both create and constrain the fabric of human interactions. In this formulation, ‘place’ can be seen as a pause in movement, while the superset of all paths form ‘movement geographies’ such as a commuting pattern for a city. As such, this is a relative space and time view, since the patterns created form spatio-temporal identities (Wachowicz 1999). Adams (1995) used time geography concepts to explore the ‘ability of a person/group to overcome the friction of distance through transportation or communication’ (p267). Adams described individuals as simultaneously points at a location, which are grounded


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in space-time, and as ‘dendritic extensions’ engaging in social and natural phenomena at various distances, which are ungrounded [spatially] as they can take place at any distance. Kwan (2000) has noted significant gender differences in space-time constraints on personal time geographies.

Figure 4.13 Space-time prism

In order to realise time geographic concepts several distinctive spatio-temporal georepresentations have been.created. In a study of urban accessibility, Lenntorp (1976) calculated the area that was reachable by a traveller from a given location, within a specified time. The zone of accessibility can be represented as cone in a threedimensional space in which the z axis is time. The apex of the cone is at the current location and the slope of the sides is set by the attainable velocity. If the journey has to end up back at the same place by a certain time, then two identical cones of accessibility fit together to form a space-time ‘prism’ (Figure 4.13). Miller (1991) implemented the space-time prism concept in Arc/Info GIS as potential path areas (PPAs) by identifying which links in a road network were ‘reachable’ in the time interval available. Forer (1998) reviews time geographic concepts and applications and argues that it is


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time to re-evaluate the possibilities of this form of representation. He argues that the greatest potential lies in the implementation of space-time prisms in raster representations (Angel and Hyman 1976), rather than in vector representations as used by Jânelle (1968) and Miller (1991). Forer (1998) proposes a novel voxel-based spatio-temporal georepresentation called a ‘taxel’ referenced by two dimensions of space and one of time. Using the taxel representation Forer defined four kinds of spatio-temporal volumes: space-time prisms, space-time paths (lifelines), and both static and mobile facilities. Spatio-temporal queries can be implemented as masks excluding taxels that are either not reachable or denied access. The intersection of a space-time prism with the available facilities defines spatio-temporal opportunities. Forer suggested the use of octree encoding to compress the vast amounts of data that would be required to implement realistic spatio-temporal volumes. He calculated that the city of Christchurch, New Zealand (300,000 people and 180km2) would require 1100 million taxels to represent at 10 metre and 5 minute resolution. Four-dimensional GIS While spatio-temporal geo-representations can handle two dimensions of space and one of time, four-dimensional GIS are designed for three dimensions of space and one of time. A small number of fully four-dimensional systems have been designed to represent the forms, structures and properties of geo-phenomena and dynamic physical processes. Pigot and Hazelton (1992) showed that four-dimensional geo-representations for nonbranching time could be based on topological cellular complexes if snapshots of discrete configurations (for example in B-rep form) were available. Since algebraic topological theory can be extended to k-dimensions (Massey 1967), connected, homogenous and bounded k-manifolds can be defined with a k-cell geometric identity, when k=4. Pigot and Hazelton (1992) show that four-dimensional operations are equivalent to assembling and disassembling the k-cell complexes corresponding to the time between the snapshot representations. Hazelton, Leahy and Williamson (1990) developed a database design for a four-dimensional GIS based on simplices aggregated into temporally extended polytopes. Other approaches to four-dimensional representation have focussed on the indexing of hypercubes where data is referenced to three dimensions of space and one of time. Mason, O’Conaill and Bell (1994) developed a four-dimensional bintree to index a temporally extended three-dimensional ocean temperature grid. The bintree consisted of two 32 bit words, one for the four-dimensional location and one for the attribute field and object membership in terms of volume boundaries. The storage was not efficient compared to the raw data storage, however, the geo-representation offered rapid querying, interpolation and generalisation tools. A method based on Riemannian Helical Hyperspatial indexing called the HHCode was described by Varma (1999). The HHCode is a transformation of the geometric into the topological and can be used to break down an n-dimensional space into storage buckets of user-defined size with very high levels of compression. Since the HHCode implicitly stores the neighbourhood of the bucket and since it can be dynamically resized, it is a flexible representational tool and an efficiently queried index. The HHCode can be used


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to index temporally extended three-dimensional volumes that Varma terms ‘toxels’, which can then be ‘fused’ in an operation conceptually similar to a two-dimensional overlay. Raper and Livingstone (1995a) presented an object-oriented four-dimensional georepresentation called OOgeomorph, which assigned four-dimensional referencing to every attribute of every ‘observable’ stored. The set of ‘observable’ attributes is then assembled into a ‘phenomenon’ class based on application needs. This design makes it likely that the attributes of the ‘phenomenon’ class stored will be spatially and temporally heterogeneous, ranging from highly observation-dependent forms (‘over this space at this time’ attributes) to infinite steady forms (‘always, everywhere’ attributes). The approach forces the user to create phenomena with a functional identity as the phenomena will have multiple spatio-temporal identities needing rationalisation, i.e. an ontology is generated from phenomena rather than imposed onto it through a space and time framework. Since data storage is atomic at the scale of ‘observable’ data points, data storage is highly compressible and accessible through four-dimensional range queries (see chapter 10). Four-dimensional geo-representation can also be achieved by interpolation (Zhang and Hunter 2000). Hence, Mitasova et al. (1996) use a minimum tension approach to interpolate hypersurfaces of time series environmental data in the GRASS GIS environment. Shibasaki and Huang (1996) generate a set of voxels representing a spatiotemporal domain by optimising likelihood using a genetic algorithm to search the solution space. Miller (1997) developed a four-dimensional kriging approach (Deutsch and Journel 1992) based on a spatio-temporal semivariogram to estimate variable values at unknown spatio-temporal locations. Multidimensional process modelling While four-dimensional GIS aim to represent the forms, structures and properties of geophenomena, dynamic multidimensional process modelling aims to develop functional models of behaviour for systems with a spatio-temporal expression. Despite the fact that such processes surround us in society and the environment there are few multidimensional geo-representations of this kind. Watney, Rankey and Harbaugh (1999) note that this shortfall derives both from computational limitations and from the lack of knowledge of the dynamic systems concerned. A small number of multidimensional process models have been developed for geomorphological and geological environments. Tzetlaff and Harbaugh (1989) pioneered the SEDimentary SIMulation model (‘SEDSIM’) to represent the processes of erosion and deposition by numerically approximating the differential equations that model flow. They implemented a hybrid ‘marker in cell’ approach to unify the Lagrangian fluid element flow representation with the grid-based Eulerian representation within a 3D+T implementation. Martinez and Harbaugh (1993) extended SEDSIM with the WAVE model to represent incident waves, wave breaking, surf zone radiation stress, longshore currents, wave-current interaction and nearshore sediment transport over threedimensional deformable sea bed surfaces. Since computation limitations do not allow the modelling of realistic populations of fluid elements and sedimentary particles, SEDSIM


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calculates representative behaviour and scales the changes to user-defined intervals and spaces. Raper et al. (1999) modified SEDSIM/WAVE to grow coastal spit landforms through time given incident waves, an estuarine setting and a sediment supply. This study showed that a physically-based multidimensional process model could generate dynamic threedimensional forms that resemble those empirically observed (see chapter 10). Tuttle and Wendebourg (1999) also used SEDSIM to simulate a glacier ice-marginal deltaic environment in order to explore the spatio-temporal distribution of sedimentation and its likely influence on the hydraulic conductivity of the resultant deposits. Both these models used a procedure referred to as inverse modelling by Cowell, Roy and Jones (1991), who argued that the only way to develop an understanding of such environments is to ‘reverse engineer’ the processes responsible for the generation of forms by trial and error. The results of such modelling can then inform the ontologies and the behaviour of subsequent modelling efforts. In a distinctive approach, Penn and Harbaugh (1999) developed the ‘DYNASED’ model to explore the interdependencies among the coupled variables of land elevation, sea level and sediment transfer rate that DYNASED uses to model continental shelf deposition. Since DYNASED employs the logistic equation in its state equations, the results ranged from the cyclic through quasi-cyclic to chaotic depending upon input. Penn and Harbaugh point out that coupling is a fundamental feature of multidimensional processes and models, yet little is known about its sensitivity.

THE POTENTIAL FOR MULTIDIMENSIONAL GEOREPRESENTATION This chapter has explored three-and four-dimensional conceptual modelling and georepresentation in depth in order to evaluate their potential to realise the opportunities of multidimensional geographic information science. The evidence suggests that when conceptual modelling is coupled with geo-representation in a multidimensional framework, then powerful new insights can be obtained and fed back into concepts. The benefits of such a view are manifesting themselves in many different fields ranging from hydrocarbon exploration to urban planning and from water management to the mapping of time geographies. Insisting that multidimensional geo-representation always moves from concepts to tools and never the other way around means that the concepts of identity, change and spatio-temporality have become more important. Before the design of the current generation of multidimensional tools, representation was frequently driven by implementation, which often led to the destruction of spatio-temporal identity as it was divided up into the formats the system supported. With the emergence of systems that deal with change by updating identity in a four-dimensional framework, we see new possibilities for realist representations in explanation. While this chapter dealt with the representations that can be built from geometric foundations, the next chapter explores the potential of spatial multimedia and virtual reality systems to represent in a more direct fashion. Rather than representing through


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geometry, chapter 5 examines the direct spatio-temporal exploration of spatial multimedia and virtual reality geo-representations.

CHAPTER 5 Multidimensional geo-representations for exploration INTRODUCTION While three- and four-dimensional GIS have been developed to represent multidimensional geo-phenomena using geometry, the development of spatial multimedia and virtual reality systems has opened up new possibilities for multidimensional representation of a more direct nature (Câmara and Raper 1999). Spatial multimedia and virtual reality systems use dynamic imagery, sound, perspective viewing and real time feedback from the geo-representation to recreate multidimensional geo-phenomena. These spatial multimedia and virtual reality systems give much more responsibility to the ‘reader’ of their representations than to their ‘writer’ (unlike GIS), since the imagery, configurations and feedback invite exploration and interpretation. Gilbert (1995) argued that this kind of system is a more postmodern mode of expression, and goes further towards the phenomenological account of representation than a GIS approach. This approach marks out a distinction between the conjectural reconstruction purpose that characterises three-and four-dimensional GIS, and the insight/exploration purpose that characterises spatial multimedia and virtual reality systems. This chapter focusses firstly on multimedia and virtual reality architectures through which spatio-temporal behaviour can be represented and examined. Then, the management, retrieval and analysis of multimedia and virtual geo-representations are reviewed from the perspective of the new GIS applications supporting these concepts. Finally, the multidimensional exploration of these resources is discussed through applications of multimedia and virtual reality systems.

SPATIAL MULTIMEDIA AND VIRTUAL REALITY ARCHITECTURES Definitions ‘Spatial’ multimedia and virtual reality are distinguished from the generic technologies by their focus on the capture of geo-phenomena and the georeferencing of the data storage. Câmara and Raper (1999) feature urban planning, tourism, transportation engineering, coastal zone mapping, environmental monitoring and GIS education among the applications of spatial multimedia and virtual reality discussed. The georepresentations employed by these applications are dominated by the use of video, but dynamic imagery, sound and virtual worlds are also used.

Multidimensional geo-representations for exploration

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The generic technologies of multimedia and virtual reality have been defined in a variety of different ways. Multimedia has been defined by Laurini and Thompson (1992) as ‘a variety of analogue and digital forms of data that come together via common channels of communication’, thereby emphasising the information integration aspects. By contrast Steinmetz, Rückert and Recke (1990) argued that multimedia systems deal primarily with ‘processing, storage, presentation, communication, creation and manipulation of independent information from multiple time-dependent and timeindependent media’, thereby emphasising its time-based nature. In the context of GIS applications, Raper (1997) defined spatial multimedia as ‘the use of hypertext systems to create webs of multimedia resources organised by theme or location’, thereby emphasising the information structuring offered by hypertext. However, the term ‘multimedia GIS’ has often been used in the GIS literature in a much wider sense than this. Bill, Dransch and Voigt (1999), extending Raper (1997), identify three uses: ‘GIS in multimedia’, where spatial functionality is incorporated into multimedia applications; ‘multimedia in GIS’ where multimedia data types are incorporated into GIS software; and, ‘web pages with spatial multimedia or virtual reality content’. Bringing these definitions together, when multimedia resources are structured and geo-referenced they can be referred to as multimedia geo-representations. Virtual reality has also been defined in a variety of ways. Kalawsky (1993) suggested that the science of virtual reality encompasses the ‘creation, storage, manipulation of models and images of virtual objects’ (p9). Carr and England (1995) contrast definitions based on the experience of virtuality with definitions based on the nature of computergenerated environments. In the former case of virtuality, Ellis (1995) defined a ‘virtualisation’ as ‘the process by which a viewer interprets patterned sensory impressions to represent objects in an environment other than that from which the impressions physically originate’ (p15). Ellis argued that there are three levels of ‘virtualisation’: a virtual space in which layouts and pictorial cues are perceived; a virtual image where objects are perceived in depth; and, a virtual environment where a field of view is perceived through motion parallax. In the latter of Carr and England’s (1995) definitions relating to computer-generated environments, virtual reality systems can be said to create an environment in which the user can experience simulated visual, auditory and force sensations. Virtual reality systems can be further sub-divided into two sub-groups: firstly, ‘immersive’ virtual reality which uses a helmet-mounted video/audio system to give the user the experience of interactive immersion within the virtual environment; and, secondly, desktop or ‘through the window’ virtual reality, which displays the virtual environment on a traditional two-dimensional monitor screen. Virtual reality systems can be said to create the experience of a virtual environment for the user both in the sense of virtuality and of computer simulation. Virtual environments are made up of content (actors and objects), geometry (metrics and topology) and topology (a set of interaction rules) (Ellis 1995). Jacobson (1991) was one of the first to see that geographic virtual environments would have considerable representational power. Raper, McCarthy and Williams (1998) defined geographic virtual environments as ‘multidimensional representations of geo-phenomena in natural and built environments permitting the realistic monitoring, analysis and evaluation of the component


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phenomena’ (p1). Examples of the data types that can be used to create geographic virtual environments include satellite imagery and aerial photography, surface modelling, three-dimensional modelling, real-time positioning and dynamic process modelling. When four-dimensional virtual environments with interaction and feedback properties are georeferenced they can be referred to as ‘virtual geo-representations’. In summary, multimedia and virtual reality technologies have the power to create rich new forms of multidimensional geo-representation. The key challenges have been to give multimedia and virtual environments geographic qualities and to show that the use of such representations has had ontological significance and epistemological validity. Multimedia data types as geo-representations Multimedia systems have considerable scope for geo-representation in the form of video and sound resources. Video is a system for the recording, storage and playback of television pictures, although the term has become synonymous with the imagery itself (Trundle 1994). It is a cognitively rich representation that can encode and store dynamic visual imagery that has sufficient quality to be comparable to that experienced by a user directly through their own vision. The near universal familiarity of television pictures has led to the widespread comprehension of video imagery. Laurillard (1997) has argued that the widespread comprehension of multimedia can be used as a powerful means to present formal models in a familiar form. This comprehension is also important because it can be argued that video filters the world rather than (re)constructs it, as many forms of georepresentation do using geometry. Note that video imagery is ultimately a limited facsimile of visual imagery as it has a finite frame rate and it extends into the infra-red band of the electromagnetic spectrum. In a general sense all video is representational since its captures imagery of the world. However, video imagery is also specifically geo-representational in certain respects: firstly, through the location of the camera when recording; secondly, through camera field of view movement, i.e. whether panning, tracking or zooming; and thirdly, by vantage point context (figure 5.1). Geo-representation can also be achieved through time lapse analysis of video imagery in order to map nearshore wave breaking behaviour (Lippmann and Holman 1989). Video imagery can also be photogrammetrically processed to recover elevation information if ground control with world coordinates is visible in the imagery, as Eleveldt, Blok and Bakx (2000) have shown for a coastal environment. Video is also implicitly temporal by virtue of the regular sequential sampling offered by video imagery. A video image sample can be played back at any desired speed enabling the ‘slow motion replay’ or speeding up of specific sequences, creating a distinction between ‘world time’ and ‘playback time’. However, the temporal structure of the world is not fully incorporated into such a video sequence. Firstly, the frame per second rate of video sampling implies limits to the temporal representation by limiting the shortest event that can be captured. Secondly, a fixed frame rate provides the same granularity of sampling for all circumstances, thereby restricting the ability of video to capture accelerations and decelerations (Foote and Horn 1999). Hopgood (1993) argued that the twin ‘world’ and ‘playback’ time models required for video meant that only


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relative time referencing could structure the temporal relationships in the imagery. This is because the world time in the video imagery and the playback time of the recorder cannot be related to each other or to a universal absolute timeline in any simple fashion. In video presentations perhaps time is best represented by imagery sequences with appropriate orderings in world time and in playback time.

Figure 5.1 Georeferencing video imagery

Since video is a spatio-temporal projection of the world in imagery, it can be considered capable of fully multidimensional geo-representation. It can be used for mapping from moving platforms (Livingstone, Raper and McCarthy 1999), for target positioning (McCarthy 1999), for the measurement of geo-phenomena such as air pollution (Ferreira 1999), and as a process monitoring system (Holland and Holman 1997). Video imaging has also become a recognised and valuable new technique of remote sensing in the 1990s (Mausel et al. 1992, King 1995). Analogue video imagery is recorded by the camera as brightness/colour levels, line by line at 30 or 25 frames per second, and is then modulated onto a waveform to be transmitted to a remote receiver or recorded on to tape. Digital video imagery is recorded by the camera as brightness/colour levels, pixel by pixel at 30 or 25 frames per second, and is stored in memory to be compressed in ‘key frame plus changes’ format. Georeferenced videography can be defined as the linkage of positional information such as Global Positioning System (GPS) coordinates to individual video frames (Cooper, McCarthy and Raper 1995). The GPS positional information can be stored with a frame once per second either using the audio track (Paragee 1997) or by using the inter-frame Vertical Line Interval (VLI) (Raper and McCarthy 1994a). Sound is also intrinsically representational as it is time-varying and spatially distributed. Sound can be recorded using georeferenced directional microphones and played back in such a way that the hearer can recover movement across the field of


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sound. Sound recordings in audio data form can convey changing volume levels at different locations through time. Shiffer (1995a) has demonstrated the sound of aircraft taking off as heard from different locations for a planning enquiry, while Cassettari and Parsons (1993) discussed the representation of sound in a GIS for airport noise monitoring. D’Souza (1994) studied road traffic noise in a neighbourhood in London noting that since noise levels varied from continuously high levels near major roads to only periodically high levels in residential areas, noise is very difficult to map in twodimensions. The transient nature of noise means that it must be sampled spatio-temporally before it can be represented. The very wide acoustic range of noise in the urban environment also means that it must also be measured in the logarithmic decibel scale. Sound is also reflected and blocked by obstacles, making sound propagation very complex. Taken together, these factors make sound representation complex. However, since sound can be described using a wide range of variables it is suitable for use as a symbolisation as well as a direct representation. Krygier (1994) showed how sound characteristics could be used as cartographic variables including: location, loudness, pitch, register, timbre, duration, rate of change, order and attack/decay. Fisher (1994) discussed the use of audio playback as a measure of reliability when browsing classified remotely sensed imagery. Compression of video and sound is of crucial importance to their effective storage and delivery. Compression techniques can be divided into lossless methods (the images compressed are recovered exactly) and lossy methods (the images compressed are recovered approximately). Lossless methods are appropriate for the compression of data which must be preserved exactly such as many geo-representations and can generally achieve an average of a 3:1 reduction in data volume. However, lossy techniques can be used to compress images-to-be-viewed/sounds-to-be-heard such as photographs or speech recordings since human perception of the high frequency variations in imagery/sound is poor. Most systems now use the Joint Photographic Experts Group (JPEG) standard for still image compression which in lossy mode can achieve an average 25:1 compression while retaining excellent reconstruction characteristics. Similarly, audio can be compressed at up to 10:1 ratio using the MPEG2 Layer 3 Audio (usually known as MP3). For video, a further data reduction can be obtained over and above that of individual image frames by using the Motion Picture Experts Group (MPEG) video standards. The MPEG standards designate some frames of the video as ‘reference frames’ and other frames are then encoded in terms of their differences from the nearest reference frames. The MPEG1 standard was limited to video captured at 288 by 352 pixels in 24 bit colour at 24/30 fps and is now largely superseded. MPEG2 is the new standard as it allows for full screen video playback on digital television and on computers. The commercial Quicktime and RealVideo systems have been designed for streaming video presentations over the Internet. While video imagery can be seen as a cognitively rich representation, many factors influence exactly what video imagery is recorded (Foster and Meech 1995). Access to the video technology and the skill to use it are primary constraints; secondary constraints include the place and time in which the ‘videographer’ is able to operate; finally, the ‘interest’ of those who capture video must be considered. Which events or dialogues were recorded, and which were left out? Despite these constraints video is now routinely


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captured for security surveillance, environmental monitoring, traffic monitoring and by individuals, and can now be considered to be a mass form of representation both at the level of capture and consumption. Virtual environments as geo-representations Virtual environments function directly as geo-representations through their reconstruction of environmental content, geometry and topology (Ellis 1995). Mesoscopic virtual environments that are larger than an individual room and smaller than the earth have been widely constructed for virtual exploration (Raper, McCarthy and Williams 1998), the visualisation of geo-phenomena (Neves et al. 1999) and for planning and urban management (Verbree et al. 1999). While virtual environments are much less cognitively rich than video and sound, they are qualitatively different from three- and fourdimensional modelling since there is interaction with, and feedback between, user and model. Batty et al. argue that it is this ‘connection’ between the user and the model that is the distinctive measure of the virtual environment. Dykes, Moore and Wood (1999) suggest that interaction with virtual environments can provide a ‘sense of place’ (or ‘spatiality’) through the ability of the user to situate themselves within the model. Bodum (1999) proposed a spectrum of abstraction from reality through enhanced reality, enhanced virtuality to full virtuality for interaction with virtual environments. Neves and Câmara (1999) survey the use of virtual environments with GIS. Virtual geo-representations reproduce the characteristics of geo-phenomena in the virtual environment, specifically the physics and dynamics used, the spatial and temporal referencing system, the geometric form, the view characteristics, the interaction rules and the scale dependency of the display. Although a number of virtual reality systems have been developed e.g. World Toolkit/WorldUp from Sense 8, most virtual georepresentations are now made using the Virtual Reality Modelling Language (VRML), which, in the form of VRML 1.0, was developed from the Silicon Graphics Open Inventor format. The design of the more sophisticated VRML 2.0 format led to the specification of VRML97 as an ISO standard language (ISO 14772) for describing threeand four-dimensional virtual environments (or ‘worlds’), which is now maintained by the Web 3D Consortium. The majority of virtual environments are now based on desktop virtual reality using VRML 97 files in browsers, which are accessed using a mouse and on-screen navigation tools. The experience of immersive virtual reality now extends beyond head-mounted displays to include virtual reality theatres and ‘caves’, where the virtual environment is projected onto the four walls, floor and ceiling of a room (Batty et al. 1998). Kraak, Smets, and Sidjanin (1999) outlined the design of an immersive virtual environment designed to allow the geographic exploration of the Delft Technical University campus. VRML 97 is based upon the ‘scene graph’ data structure, which is a hierarchical arrangement of ‘nodes’ representing geometric objects and their properties, sensors, behaviour and relationships. A VRML97 world file is displayed in a browser after it has been validated by a parser and the scene graph recovered. The scene graph is composed of a transformation hierarchy (containing nodes) and a route graph (connected to the sensors), which collectively represent the virtual environment. The transformation


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hierarchy represents objects in the virtual environment using a shape node, which includes primitive geometric objects (Box, Cone, Cylinder, Sphere), surface grids (ElevationGrid), B-reps (IndexedFaceSet), and other geometry (IndexedLineSet, PointSet, Extrusion). Shape nodes can have further sub-nodes that specify their geometric properties and their appearance (e.g. texture mapping), and they can be grouped by behaviour. Other nodes in the transformation hierarchy describe light sources, sensors, interpolators and time dependent nodes such as audio or video clips. The route graph describes how nodes receive events and how they act upon them. Each VRML97 world has a viewpoint from which the virtual environment is (initially) being viewed, and offers navigation ‘paradigms’ such as walking, flying and examining, by which the user moves through the model. The script node allows developers to add functionality using programming languages like Java or link other applications (Brutzman 1998). Physics and dynamics are properties of virtual geo-representations rather than part of a ‘given’ external framework. Hence, many virtual reality systems make gravitation and collision detection optional, and different settings can be assigned to the various objects within the scene graph. Spatial referencing systems are typically three-dimensional Cartesian coordinate systems with limited precision, which normally have their origins at the geometric centre of the world. This is the case in VRML97, which uses a ‘righthanded’ coordinate system in which the horizontal plane is defined by x and z axes, and where the y axis defines the vertical (figure 5.2). These conventions on origins and the directions of the axes are different to many two-and three-dimensional geo-representation systems, leading to specific data transfer difficulties between them (Williams 1999).

Figure 5.2 VRML coordinate space (after Williams 1999)

The limitations of fixed precision right handed world-centred coordinate systems in VRML97 has led to the development of new nodes for geographic data within the GeoVRML framework (Rhyne 1999). The GeoVRML version 1.0 Recommended Practice adds facilities to VRML97 to support non-Cartesian coordinate systems, origin


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shifts, geographic metadata, navigation and animation, without changing the underlying referencing of the standard. Coordinate system support for projected and geographic coordinates has been built on top of the Synthetic Environment Data Representation and Interchange Specification (SEDRIS) Geographic Reference Model (Rhyne 1999), and is accessed through a new geoCoordinate node. Origin shifts and axis rotations are accessed through the geoOrigin node. The GeoVRML version 1.0 Recommended Practice also provides facilities for georeferencing VRML97 worlds (geoLocation node), locating mouse clicks on a shape node (geoTouchSensor node), positioning a viewpoint in geographical space (geoViewpoint node) and animating objects in that space (geoPositionlnterpolator). In each case the GeoVRML approach transforms the standard VRML97 model using geographic functions. Time is represented in VRML97 by timestamping events using double-precision floating-point numbers counting seconds since 1st January 1970; time can be speeded up or slowed down if the application calls for it. Events are either generated by time sensors when activated by user interaction with a scene graph node (e.g. direct manipulation or proximity), or they are generated when continuous changes (e.g. movements) are temporally intersected by discrete events. This concept of time does not accommodate the need to replay user interactions with the world or to animate change in a time other than the system time (Lutterman and Grauer 1999). Accordingly, Lutterman and Grauer propose the addition of a history node to VRML97 that allows the grouping of nodes in a temporal scene graph by their time varying behaviour. Lutterman and Grauer used the Java interface to the script node to display time dependent geometries and textures read from a three-dimensional GIS of ground water levels. The geometric form of objects in a virtual geo-representation using VRML97 are usually based on ElevationGrid and IndexedFaceSet node types. These are equivalent to rasters and TINs in GIS respectively: the former render quickly as they are compact but are fixed resolution, while the latter offer more a data dependent and adaptable display (Brown 1999). Two-and three-dimensional GIS can be used to convert the syntax of georepresentations into that of VRML97 using import/export tools, although this can only generate shape nodes which do not have any associated behaviour (Raper and McCarthy 1994b). The GeoVRML version 1.0 Recommended Practice adds a geoElevationGrid node to VRML97 so that the elevation grids can be manipulated using projected and geographic coordinates. Virtual geo-representations also present specific challenges to the characterisation of viewing. Since virtual environments use planar coordinate systems, in theory any object can be seen at any distance, as long as there is enough light and no fog (in practice, a fixed minimum pixel resolution limits what is displayed). The same is not true of views in the world, as there are limits to visibility due to the curvature of the earth and atmospheric attentuation. Williams (1999) shows how some virtual reality systems can specify artificial horizons beyond which the model will not be rendered. These ‘yon clipping’ distances need to be viewing height-dependent, otherwise when the viewpoint is high above the ground then the artificial horizon may cut off a large part of the model which the user expects to see. Virtual environments have also been defined for spherical spaces where the virtual geo-representation is made from imagery that has been integrated seamlessly using a photo-stitching tool and accessed using ‘enhanced reality’


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systems such as Quicktime VR (Bodum 1999). Dykes (2000) shows how stitched imagery can be explored using the Panoramap application, which links the panoramic view to an associated map by displaying the angle and direction of the current view. Panoramap allows the rapid exploration of the virtual environment by allowing the user to ‘see what the view is like’ from points with panoramas. Interaction with virtual geo-representations requires new skills to use them effectively. Neves et al. (1997) argue that users of virtual geo-representations need to synthesise the direct manipulation skills used for the haptic space of sensorimotor experiences, and the camera manipulation skills needed for the pictorial space of visual experiences. The synthesis of haptic and pictorial spaces over time results in the creation of a new ‘transperceptuaP space that requires way finding skills to move through the sensed virtual environment, i.e. remembering how a given virtual location was reached. Neves et al. (1999) developed the immersive Virtual GIS Room with wall poster maps, a table on which selected maps become surface models, and pen manipulation tool in order to explore the use of these different spaces (see chapter 8). The use of photographic imagery by Dykes (2000) confers an important advantage in virtual environment navigation as the transperceptual space is based on cognitively richer representations. Note that different skills are required for desktop and immersive virtual reality experiences. In desktop virtual reality the user must adapt to being situated within the transperceptual space and must develop skills in the interface tools that control movement (Brown 1999). In immersive virtual reality systems the user must become used to the experience of head-mounted displays, and, typically, a slight latency of system response to head movements and gestures (Kraak, Smets and Sidjanin 1999). Multi-user virtual environments have also been developed for groupware and chat services, where individuals are represented as ‘avatars’ within spaces designated for specific purposes. Lin and Smith (1997) developed an architecture for collaborative virtual environments where distributed users could work together on three-dimensional models. The creation of virtual geo-representations made up of surface models draped with map data or remotely sensed imagery usually requires a particularly large number of shaded B-reps (usually simplices) to represent the virtual environment. This processing overhead is minimised by reducing the data volumes before import and by employing real-time generalisation algorithms during viewing. Reducing the size of the surface model involves the use of filtering techniques that cut the number of triangles making up the terrain by amalgamating them when the angles subtended vertically between adjacent triangles are small. This procedure is usually empirical and applied uniformly across the surface, although there would be benefits in developing density or elevation specific surface generalisation. Wright, Watson and Middleton (1997) discussed the use of preprocessing polygon decimation techniques to improve the speed of display of surface models. Virtual reality generalisation algorithms have been developed so that only those objects either near to the user’s current viewing position or orthogonal to their viewing direction are displayed with adequate enough triangles to give a high resolution view (Neves and Câmara 1999). Those triangles further away or viewed obliquely are displayed at a simplified level by real time generalisation or by recalling an appropriate set of nodes from a level of detail (LOD) quadtree data structure. Level of detail (LOD) nodes group


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together shape nodes so that progressively more detail can be displayed as the levels of the quadtree are traversed, i.e. when the user looks in a given direction or moves close to a given area. Muchaxo, Neves and Câmara (1999) describe a wavelet compressed quadtree LOD technique which is based on a terrain adaptive TIN. The GeoVRML version 1.0 Recommended Practice adds a geoLOD node to allow access to LOD indexes in projected or geographic coordinates. There are contrasting views on the value of virtual environments to understanding. Dykes (1999) characterised a virtual environment as a model understood by a geographic metaphor. Bishop (1994) raises the question of the appropriate level of (photo)realism in virtual geo-representation: highly abstract representation may be incomprehensible, while highly realistic representation may be dominated by aesthetic considerations as the expense of comprehension. Dykes, Moore and Fairbairn (1999) defined a representational spectrum from the (photo) realism of Imhof’ s terrain drawings to the abstraction of Chern off’s symbolic faces, and suggest that VRML offers new possibilities all along the spectrum. Boyd Davis and Athoussaki (1997) argue that the construction of virtual environments is a design process in which (photo) realism is neither achievable or desirable. They point out that ‘viewing’ is an active process in which the user is engaged through authorial devices such as those used in film or theatre to change focus or perspective (Laurel 1991). Foster and Meech (1995) explored the social dimensions of virtual reality through Baudrillard’s (1983) view of simulation in which reality can be reflected, perverted, denied or invented in an all-encompassing paradigm of representation. This is the view that virtual environments do not and cannot mimic the world: in this sense, at best, virtual environments are ‘consensual hallucination’ (Gibson 1986). Likewise, Pimentel and Teixeira (1993) divided approaches to virtual environments into those based on ‘here’ (the current reality), ‘there’ (a reflection) and ‘elsewhere’ (a simulacrum or invention). In these terms, virtual geo-representations are mostly simulacra (so far). Database storage of multimedia and virtual geo-representations Since multimedia and virtual geo-representations cannot be handled by standard relational database systems, they must be stored either in extended relational databases, object databases or in application-specific data stores (Nwosu, Thuraisingham and Berra 1997). While some database solutions have been defined for these geo-representations, many application-specific solutions have been developed. Subramanian (1998) has identified three main requirements for a multimedia database management system: storage and query of heterogeneous data types, the management of very large amounts of data and the presentation of a query result in an appropriate viewer. In contrast, virtual reality systems require support for the hierarchical data storage of the scene graph. For example, Köninger and Bartel (1998) used the database Postgre95 to store virtual georepresentation data. One of the most advanced virtual reality database systems is the object-oriented dVS operating system from Division, which is designed to distribute activities between different processors in a multiprocessor system. In dVS ‘actors’ are responsible for sensing the attitude of the user, the user’s position in the virtual environment, display and


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control of the virtual environment and other activities such as collision detection. The virtual environment is composed of ‘elements’ such as boundaries, constraints, visuals, audios and lights which are grouped together in hierarchies (e.g. a wall is a hierarchy made of a visual and boundary). The ‘actors’ communicate by placing instances of ‘elements’ in a shared data space (the VL database) monitored by all actors. Division’s dVISE virtual world simulation system runs on top of dVS. Given the need for heterogeneous data storage, multimedia database design is focussed on efficient organisation of this content and support for queries on it. Subramanian (1998) has suggested that designs can be based either on autonomous storage of each data type, uniform indexing of all data types on a semantic basis, or on hybrid schemes. The autonomous approach is efficient in storage terms but requires the computation of joins across data types during queries; object-oriented databases are the preferred method of implementation. The uniform approach requires the creation of metadata for each data type so that queries can be made efficiently on the metadata. The extended relational database is the preferred method of implementation. Many extended relational databases are now introducing support in tables for multimedia data types such as video and sound, in a move towards the implementation of the ‘universal server’ capable of managing all types of data. In these extended relational designs tables are able to support both alphanumeric and multimedia data types, although the latter are not used as a key. The querying of such hybrid tables involves the use of vendor-specific extensions to SQL, since SQL does not support non-alphanumeric data types in versions 1 and 2. This restriction in the data types supported, and, in consequence, the types of queries permitted, is being addressed by the release of SQL version 3 or ‘SQL/multimedia’. Object-oriented databases offer more flexible methods of integrated alphanumeric and multimedia data storage, since they permit the unified treatment of both kinds of data. This means, for example, that keys can be defined over heterogeneous sets of attributes made up of both alphanumeric and multimedia data. Hence a ‘multimedia object’ can be defined by its key, and the similarity between it and any other ‘multimedia object’ can be ascertained by comparing their keys. Grosky (1994) suggested that the similarity of content-based multimedia keys could be based on a ‘multidimensional distance function’ (p18) defined over the attributes. The result will not usually be an exact match but a fuzzy similarity measure. This procedure is limited to those attributes originally extracted from the multimedia data using content-based methods, which of course is specific to the system creator. Multimedia data contains information that can be recognised and extracted in different ways by different users. This means that users of multimedia databases can derive their own attributes in order to form new keys defining ‘multimedia objects’ of interest. Users can therefore interactively define multimedia objects of interest and then query the database for other objects that are ‘similar’, i.e. multidimensionally close in attribute space. Little et al. (1993) developed such an approach for a digital video system although the multimedia objects could not overlap along the movie timeline. These approaches could have a wide range of applications for multimedia geo-representations, such as the content-based extraction of dynamic process signatures like sea wave direction and speed (Raper and McCarthy 1994a) (see chapter 7).


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Multimedia development and standards Multimedia application development involves the synthesising of alphanumeric and multimedia data into a multimedia presentation. While multimedia data can be played back in its native form, storing it in a structure which is aggregated with other data allows it to be explored and queried using a multimedia authoring tool. Such tools can be classified by the informational structures and metaphors they use to give access to the multimedia resources. The simplest informational structures for multimedia are based on slide shows (such as Microsoft Powerpoint), scenario-building and evaluation based on user interaction (such as Authorware) or movie making (such as Director or Premiere), although the sophistication of some of the latter systems has been extended using scripting languages. More complex informational structures allow the linking of multimedia data types grouped into abstractions in semantic nets (Subramanian 1998). Researchers have created more complex applications offering richer forms of structuring and retrieval. Weiss, Duda and Gifford (1995) developed the ‘video algebra’ system using C++ in which video ‘expressions’ (which may overlap each other on a master timeline) are created from a video stream by a ‘creation’ operation and interactively assigned content-based attributes. Using a ‘composition’ operation, a hierarchically organised ‘presentation’ is created in which the ‘expressions’ are ordered temporally and by position on the display device. The web browser interface to the system invoked Tool Command Language (TCL) scripts to dynamically create Hypertext Markup Language (HTML) documents in response to user requests. Video algebra queries search the content-based attributes hierarchically for a match, which can then be played or displayed with reference to the master timeline. By contrast, Hirzalla, Falchuck and Karmouch (1995) developed an advanced temporal model for interactive multimedia, which can manage alternate timelines based on user choices. The actual timeline followed by the user is called a timepath and can be visualised as a path through a tree of possible timelines. This system aims to ensure that each possible timepath preserves the integrity of the basic multimedia elements in the system, i.e. not playing one piece of video before another piece that sets the first piece in context. With the proliferation of software tools in the multimedia field, the need has been recognised for data exchange standards capable of translating one proprietary system into another. There are several standards in development. HyTime is an international standard ISO 10744 (1997) for the representation of information structures for multimedia resources (Newcomb, Kipp and Newcomb 1991) through the specification of document type definitions, and is based upon Standardised Generalised Mark-up Language (SGML) (ISO 8879). The Multimedia and Hypermedia information encoding Experts Group (MHEG) is a standard (ISO 13522) for representing hypermedia in a system independent form (Meyer-Boudnik and Effelsberg 1995). It is optimised for run time use where applications are distributed across different physical devices or on networks. The PResentation Environment for Multimedia Objects (PREMO) is a standard (ISO 14478, 1998) which defines how different applications present and exchange multimedia data. It defines interfaces between applications so that different applications can each simultaneously input and output graphical data. Each of these standards has developed a different concept of space and time. The


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PREMO and MHEG standards support a single three-dimensional space plus onedimensional time to provide a comprehensive frame of reference for all events in a multimedia presentation. HyTime allows multiple space and time reference systems, for example, permitting both ‘video frame rate time’ (30 frames per second) and ‘user playback time’, the latter describing how the multimedia resources are actually played by a user who is responsible for pauses and fastforward events. The resolution of these debates and the concepts of space and time that are implemented have important implications for the spatio-temporal analysis of multimedia geo-representations, e.g. security camera records. Hypermedia development environments The hypertext or hypermedia model is a semantically rich method of structuring multimedia data (Nielsen 1995) which is suitable for structuring geo-representations. The origins of the ‘hypermedia’ concept go back 50 years to the mid 1940s when Bush put forward his ‘Memex’ idea—a kind of multidimensional diary with links between all ‘connected’ things (Bush 1945). This early suggestion remained an unimplemented idea until Nelson explored its implications in terms of the associative linking of facts and ideas in the 1960s and created some early prototypes (Nelson 1965). Early Hypermedia designs such as Nelson’s Xanadu envisaged text-based and single-media applications. The technology and theoretical structures required to fully implement these ideas were not developed until the 1980s when the ability to handle non-alphanumeric multimedia data and new high-level computer languages became available. Later systems such as Notecards (1985) and Guide (1986) added static graphics to the data types supported, while Hypercard (1987) supported a comprehensive range of multimedia data, and offered a scripting language called Hypertalk. These tools inspired the development of the World Wide Web in the mid 1990s when hyperlinked multimedia data in HyperText Mark-up Language (HTML) form became accessible through browsers (Berners-Lee et al. 1994). Browsers are now the definitive hypermedia applications. In the abstract, the hypermedia model can be described as a set of nodes connected together by links, where the nodes are abstractions consisting of multimedia information elements (McAleese 1989). According to Campbell and Goodman (1988) the architecture of a hypermedia system can be divided into three levels (from bottom to top), i.e. the multimedia database, hypertext abstract machine (HAM) and presentation levels. At the bottom is the database where all the raw multimedia data is stored, above which is the HAM that houses the logical model of the hypermedia system. The HAM also describes the possible link forms: explicit links which are anchored in screen buttons; implicit links that are made when the user makes a request; and, computed links which are determined on the basis of some context-specific heuristic. Links are not always bi-directional and can also take a one-to-many form, although this is not supported on the web. The superset of node information, content and links, as found in an HTML-formatted web page or a Hypercard stack, is often referred to as a hyperdocument. In the case of Hypercard the nodes are called cards, which can contain as many information elements such as text fields, graphics, video, sound and links as the developer wishes to place there. Deciding on the content and organisation of the nodes (and constituent information


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elements) is often a problem of knowledge elicitation and abstraction from the information available. Design decisions in this process involve the transformation of knowledge into the nodes—which itself requires a definition of their semantic proximity and distinctness. Note that this process is unconstrained by the need to define a complete set of attributes for any node, as there are no explicit integrity constraints as there are in relational databases. Since hypermedia models aim to provide maximum flexibility in the connectedness of knowledge, a key problem has been how to define an organisational framework without dictating a rigid user model. This has been achieved by treating the nodes in a hypermedia application as part of a semantic network (Jonassen 1989) where links are made based on knowledge of the information domain. Hence, the web structures information using low-level link constructs, leaving the user to impose their own high level structure through interaction patterns. Sutcliffe (1997) set out a scheme of taskrelated information analysis that preferred hypertext methods for information delivery when non-sequential pathways are needed. Above the HAM is the presentation level, which controls the appearance of the HAM to the user. Typically an organising metaphor such as a page or a gallery is employed to guide user interaction. The organising metaphor provides concepts such as a network or hierarchy to depict the arrangement of the nodes, e.g. as stops on a tour, or sections of a book. The greatest dangers in hypermedia design are avoiding the ‘lost in hyperspace’ problem and not overloading the user with too much information. The latter problem can be greatly reduced by customisation of the presentation level according to the user’s knowledge and employing all the modalities of perception in the metaphor including depth cueing and colour. Note that many of the most common of such metaphors are spatial, such as the tour and map metaphors, providing a variety of visualisations for the arrangement or content of the nodes. This is one particular characteristic which makes the hypermedia model an appropriate way to store and organise spatial data as these metaphors can also be used to structure the nodes (Raper 1991). The implementation of the hypermedia model has also become intrinsically linked to object-oriented programming (OOP). The concept of classes and sub-classes in OOP matches the hypermedia notion of nodes and information elements grouped according to a scheme of abstractions. In most hypermedia systems information elements and nodes, as well as links can be typed and named providing a basic form of organisation which application programs can exploit (see figure 5.3). OOP has made it possible to create robust hypermedia applications where arbitrary associative links can be established and complexly nested in any configuration. The hypermedia form of information structuring also infers new forms of access to multimedia data. McAleese (1989) identified a ‘navigation’ mode of use, where the user followed a pre-defined path through a hierarchy or network of nodes. Nielsen (1995) described some of the aids to navigation in hypermedia such as backtracking, history lists, bookmarks and overview diagrams (which can be generalised or nested if they become too large). The overview diagram often takes an explicitly spatial form such as a map (Raper 1991) or uses a spatial transformation. By contrast, McAleese (1989) distinguished a ‘browsing’ mode where the user accessed the nodes by associative links between abstractions based on knowledge of the information domain. In the browsing mode there need be no pre-existing links since the user can make them in real time.


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McAleese described distinct browsing, scanning, searching, exploring and wandering strategies, which he saw as different approaches to traversing the nodes. Blades (1994) analysed hypermedia navigation in terms of the wayfinding theories of Siegel and White (1975), suggesting that designers need to present information as landmarks which can be connected together to form routes. Passini (1999) argued that such routes are best thought of as decision plans, implying that sign posting is an essential design element.

Figure 5.3 Scheme of links between information elements and abstractions in a Hypertext application

These hypermedia approaches contrast with conventional database designs which require the use of querying facilities to extract a specific subset of information which can be displayed or input into an analysis procedure. In this sense the hypermedia model is particularly useful for heterogeneous collections of data where many abstractions have unique properties and cannot be typed or named in advance, or where arbitrary aggregations are meaningful. It is also possible to define abstractions with widely differing granularity, such that the user of the system appears to move between nodes at different levels of information aggregation, or between different ranks of any pre-existing hierarchy. Such moves between nodes may also reflect decision-making, permitting the recording of a decision history. While small scale hypermedia systems have been implemented widely, and the web has enabled global information access, many users would find it useful to be able to turn their whole computing environment of file handling, word processing, spreadsheets and programming into a hypermedia system in itself. This is the goal of open hypermedia systems (OHS). Engelbart (1990) classified OHS into those designed to intemperate within an individual’s workspace and those designed to allow interoperability within and between groups. Hall (1994) argued that explicit links have come to dominate the presentation level of hypermedia systems such as browsers on the web, making them rigid and unresponsive to user concepts. In such hypermedia systems, the links must also be stored with the node data making it difficult to update and change nodes without disturbing the links. Hall, Davis and Hutchings (1996) argue that the links should be


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dynamically created by the user or by a query operation that finds the most ‘similar’ match using information retrieval techniques employing relevance criteria. The ‘Microcosm’ database maintains a set of links associated with each node in an application that is ‘fully or partly aware’ of Microcosm and allows the user to edit the links and customise the interface. Open hypermedia systems like Microcosm have been proposed in order to reduce the dependence on package-specific file structures and to provide operating system level support for associative linking of multimedia resources. Hypermedia systems in the form of browsers reading web pages have now become the dominant information access mode for most computer users. There is now scope for microbrowsers on other information devices such as mobile phones and hand-held computers to extend hypermedia systems into new settings (Dobrowolski, Nicholas and Raper 2000). The arrival of such a widely used new information infrastructure demands new approaches to information systems and visual communication (Horn 1999), which Jacobson (1999) has called information design.

SPATIAL MULTIMEDIAAND VIRTUAL REALITY SYSTEMS The software architectures of multimedia and virtual reality systems have made it possible to develop multidimensional geo-representations with new expressive power. These geo-representations offer richer concepts than two-dimensional GIS as they extend the dimensionality, the data types, the analytical powers and the information management capabilities of existing systems. In addition to these architectural extensions, the new systems have developed new interfaces and new forms of interaction which engage the user, and allow a greater reflexiveness in the use of geo-representations. These new georepresentations are discussed under the headings multimedia/hypermedia GIS, web GIS, virtual reality GIS, real-time GIS and geolibraries. Multimedia/hypermedia GIS Attempts to design and develop multimedia/hypermedia GIS have focussed on the questions of how to combine the semantics of hypermedia with georeferencing and how to construct multimedia geo-representations (Buttenfield and Weber 1993, Cartwright, Peterson and Gartner 1999). An early multimedia/hypermedia GIS system was developed by Polyorides (1993) who developed the Great Cities of Europe using Toolbook extended with C++, georeferencing the multimedia data through the city maps. Shiffer developed the Collaborative Planning System (CPS) based on Supercard and Quicktime to evaluate planning scenarios for Washington, DC. The CPS allowed the user access to a wide range of multimedia data by selecting resources from a geo-referenced image map base. The geographic footprint and orientation of multimedia data such as simulations or videos were shown on the image map base to orient the user. More recently Chen, Wang and Zu (2000) developed a multimedia atlas for the Yuxi tourist information system in China. Raper and Livingstone (1995b) developed a multimedia/hypermedia system called Scolt Multimedia Project (SMP) (see chapter 6) to store and explore multimedia georepresentations using the object-oriented Hypercard hypermedia system. Using the


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terminology of the HAM and figure 5.3, SMP stored the georeferenced multimedia data as information elements and grouped them into hyperdocument node abstractions based on location. Certain links were generated by the system designer, some were ‘computed’ by searching and some were added by the user when they edited the hyperdocuments. The presentation layer employed a ‘time-space’ diagram (figure 6.1) to plot the period and the place that the hyperdocument related to. As SMP permitted the annotation of hyperdocuments through the addition of comments and vector geometry (figure 7.1), integrity was guaranteed by the encapsulation of methods and data with the information elements. Jones et al. (1996) developed the Semantic Hypermedia Architecture (SHA) to structure semantic, spatial and temporal relationships among stored knowledge in the form of multimedia data. The semantic relationships ‘is_a’, ‘has_a’, ‘part_of’ and ‘kind_of’ were used to define spatial and temporal relationships using containment/adjacency and interval concepts respectively. The multimedia data was linked to these structural relationships using the semantic relations. Spatial, temporal and spatio-temporal queries creating links were implemented through the concept of semantic closeness between multimedia data. Although this approach allows the construction of rich multimedia geo-representations organically, it does not necessarily ensure semantic consistency within the stored and computed knowledge. When a multimedia geo-representation uses a map as the primary index to the multimedia data, then the links and abstractions are explicitly geographic, and the application can be termed a hypermap (Raper 1991). A hypermap is usually presented as a visualisation of a metric or topologic space that is accessed by browsing. Laurini and Milleret-Raffort (1990) and Laurini and Thompson (1992) presented data structures for a hypermap containing points, lines and areas forming geographic features on a map, and proposed the use of R-trees to store their spatial inter-relationships. They suggested that spatial to non-spatial relationships might also be structured using R-trees, although this requires the transformation of the documents into rectangles in 2D coordinate space. Since the hypermap does not impose integrity constraints or planar enforcement of geometry in its design, there is a flexibility in the implementation that is attractive when the overall size of the multimedia database is not too great. Kraak and Van Driel classified hypermap functionality into access by spatial, temporal or thematic criteria using the TRIAD model of Peuquet (1994). Early work on bringing multimedia data types into GIS led to the development of a number of conceptual models based on GIS designs such as Wallin (1990) and Yeorgaroudakis (1991). Kemp (1995) evaluated the alternative implementations of this approach concluding that the geo-relational model falls short of aspirations, since the multimedia data and processing are not really integrated into the GIS. Instead, Kemp suggests that multimedia/hypermedia GIS should be implemented as applications using object-oriented languages constructed over object oriented database systems. Examples of this approach include Kemp and Oxborrow (1992), who developed a system to handle ambulance journey-related multimedia data in the object-oriented database Zenith. Groom and Kemp (1995) developed an endangered species database using the multimedia data type support of Postgres. Boursier, Kvedararauskas and Spyratos (1996) developed the Magic Tour system by linking a multimedia authoring system to databases


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and GIS through inter-application communication protocols. Hall, Davis and Hutchings (1996) linked the open hypermedia system Microcosm to the SPANSmap GIS (Simmons, Hall and Clark 1992) in order to link spatial and non-spatial data referring to a development site. Recently, Christel, Olligschlaeger and Huang (2000) have showed how geographic information can be extracted from videos of news bulletins containing maps. Web GIS Widespread access to the Internet, the ubiquity of browsers and the explosion of commodified geographic information has made it possible to develop new forms of multimedia geo-representations on the web. These include hypermaps, image browsers and cartographic visualisers. The simplest form of web GIS is a clickable raster hypermap with an associated ‘imagemap’ consisting of vector outlines identifying specific features. In this approach the vector data is restricted to unstructured polygons and the coordinates are local and not geographic. Kraak and Van Driel (1997) developed a prototype hypermap on the web called the Delft hypermap, which offered query capabilities, information filtering and allowed users to update the hypermap by adding features. Sarkola (1997) described how Finland’s base maps have been made available via hypermaps on the web. Fernandes et al. (1997) outlined the design of the Portugal Interactive project that offered web access to a national database of orthophotos in a service called GeoCid. Cartwright (1999) outlined the design of the GeoExploratorium, a web-based interface to multimedia georepresentations with multiple access modes. Huang and Lin (2000) describe the webbased 3D Visualisation and Analysis Server, which uses extensions of Arcview. Browser functionality can also be extended through the addition of ‘plug-in’ code to their component architecture. Plug-ins allow the browser to display and manipulate additional data types referenced by the HTML including multimedia, animation, VRML, raster and vector data. Plug-ins have allowed the inclusion of geo-representations on web pages to: play geo-referenced video (McCarthy 1999); animate mapping (Cartwright 1999); present high resolution aerial photography compressed using wavelets; and, display vector data in standard forms such as computer graphics metafile (CGM). Browsers can also be extended through the use of network-portable languages such as java. Java ‘applets’ are embedded in a web page and compiled locally on the users’ computer by a ‘virtual machine’ that cooperates with the operating system. As java is machine-independent, applets should run in the same way on all operating systems and in all browsers, although this rarely true in reality. Java applications can also operate in standalone mode. A wide range of java applets and applications have been developed for geo-representation, ranging from the digital terrain modelling application Landserf (Moore, Dykes and Wood 1999) to the cartographic visualisation applet Descartes (Andrienko and Andrienko 1999). Browser software using plug-ins or java can now be used as a platform for the delivery of geographic information and the software functionality necessary to explore it. Brinkhoff (2000) explores the server and client support required for efficient map serving on the web including multiple sorting and look-ahead fetching, while Wang and Jusoh (1999) discuss the data integration aspects. The next-generation markup language called


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Extensible Markup Language (XML) can be extended so that developers can add support for new data types such as those required to support both multimedia and virtual georepresentations. XML will also facilitate the adaptation of the web page content to the kind of device that is displaying the content. Support for geo-representations will also be found in the Scaleable Vector Graphics (SVG) format for web pages, and in the geoVRML extensions of VRML97 (Rhyne 1999). Virtual reality GIS Virtual reality GIS have been developed to allow the creation, manipulation and exploration of geo-referenced virtual environments. Fairbairn and Parsley (1997) described an early virtual geo-representation using VRML modelling of the University of Newcastle campus in north east England. Most of the virtual reality GIS have been developed for desktop platforms, although the Virtual GIS Room used immersive techniques (Neves et al. 1999), and the Internet GIS for London used a virtual reality theatre (Batty et al. 1998). Raper, McCarthy and Williams (1998) used the Sense 8 WorldUp platform to develop a four-dimensional virtual environment using geo-referenced terrain data and moving vehicles. The virtual geo-representation was created by the export of a TIN surface model from GIS and its conversion into an indexedFaceSet format terrain using geographic coordinates. The VRGIS system consists of a model window for interactive access to the virtual environment and a map window for the display of a moving map. The map window displays an arrow symbol to display the location and orientation of the user in the virtual environment. Vehicle models can be introduced into the virtual environment with geographic behaviour that defines their location and movement as plotted on the map. McCarthy (1999) showed how the VRGIS system could display in real time each triangular fece directly below an aircraft moving over the surface of the terrain in the virtual environment. Moore, Dykes and Wood (1999) outlined the architecture of the traVelleR and Urban modeller systems implemented as Java applets communicating with VRML97 models through the script node interface (Brutzman 1998). TraVelleR is designed to support the interactive exploration of a virtual geo-representation draped with imagery by providing an adjacent map interface with orientation and query tools. The traVelleR virtual environment is scriptable so that pre-defined tours around the virtual environment can be offered to users. Verbree et al. (1999) outlined the KARMA VI system that is implemented in Sense 8’s WorldToolKit and closely integrated with the Spatial Database Engine of the GIS Arc/Info. This architecture allows users of Karma VI to manipulate objects within the virtual environment and to commit the changes to the spatial database. Brown (1999) proposed the use of a virtual environment as an interface to geographic information. The Virtual Reality User Interface (VRUI) is presented on a web page with one frame containing a VRML97 model displayed with the CosmoPlayer plug-in and another frame describing the content of the model. A Java applet controls the imagery draped over the VRML model and allows the user to query the geo-representation. As the user moves around the VRML model the different types of geographic information available for each location are reported to the user.


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Some work has also been carried out on collaborative work within virtual environments. Batty et al. (1998) describe the use of the Alphaworld virtual world server for experiments in urban planning where ‘visiting’ avatars can give their opinions on the constructions they ‘see’ there. This methodology has been adapted for the purpose of collaborative planning in the Wired Whitehall project (Doyle, Dodge and Smith 1998). Gong and Lin (2000) discuss the different senses of space employed in a virtual world server including Internet, data, graphics, cognitive and social spaces and describe the VirtualPark prototype. Real-time GIS With the availability of real-time positioning systems and cost-effective mobile telecommunications, it has become possible to develop real-time GIS that monitor, transmit, record and analyse the movement of mobile agents such as vehicles, people or animals. Laurini (2000) presented a typology of ‘telegeomonitoring’ architectures, dividing them into centralised (mobile agents communicate through a single control centre), co-operative (mobile elements communicate with each other directly) and federated (mobile agents are communicating with multiple control centres) types. However, real-time GIS can also include location-based services, where a moving agent receives information depending on its location, and real-time ranging systems. Real-time GIS have been developed for transportation, monitoring, geographic messaging services, tourism, and ecological applications. In transportation many organisations need to monitor the position of their vehicles for scheduling or safety reasons. Each mobile agent transmits positioning information to appropriate control centre(s), where it is entered into a database of timestamped positions. The database can be summarised by static geometric primitives or cleared at specified intervals. Some applications can monitor the proximity of the mobile agents to specified locations or advise on alternative routes based on traffic reports (Laurini 2000). Real-time GIS have also been used in monitoring applications where positioning, video and ranging systems must all be integrated on a common timebase (Raper, McCarthy and Williams 1998, McCarthy 1999). Such integration requires the standardisation of event timing by calculating the intrinsic time delay (latency) between the world time of measurement and database time of storage. Once the latencies of the different sources are determined, the real-time data can be re-based on a common timeline. Figure 5.4 shows an error analysis of a real-time multimedia GIS from McCarthy (1999) in which latency errors are shown to overwhelm sensor and data processing errors. Real-time GIS are also being used for geographic messaging services (GMS), where information is sent to agents on the basis of their location. Imielinski and Navas (1999) outlined architectures for the implementation of GMS, including geographic routing where a message is forwarded to geographically appropriate wireless transmitter nodes, and mobile clients pick it up when they enter the service area of the node. In tourism applications, a number of real-time GIS have been developed to provide a location sensitive information service, where details of attractions are given to users as they approach, for example in the GUIDE project Jose and Davies 1999). The GUIDE project defined a hierarchy of locational ‘contexts’, each with a geographic footprint, such that


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location based servers provide information only to appropriate contexts. Mountain and Raper (2000) developed the Location Trends Extractor (LTE) for the user to automatically define their own dynamic ‘contexts’ such as daily envelopes, by data mining their spatio-temporal behaviour. Real-time GIS architectures have also been developed for ecological simulations. Westervelt and Hopkins (1999) outline a method of high level coupling between the GIS GRASS and a modelling system (IMPORT/DOME) that permits the simulation of agent movement over terrains and their consequent social behaviour. This individual-based modelling architecture allows the use of both static and dynamic terrains as a backdrop to the simulation of animal movement. Bian (2000) developed an object-oriented system for representing mobile objects in an aquatic environment. Rodrigues (1999) outlines the architecture of a real-time GIS for the simulation of vehicle decision-making and behaviour in car parks using an intelligent agent-based approach.

Figure 5.4 Latencies in a monitoring system

Geolibraries The commodification of geographic information envisaged by Openshaw and Goddard (1987) has now generated a massive global collection of data covering: • base mapping of topography; • imagery, photography, videography; • elevation and terrain data; • environmental information; • census, electoral and government information;


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• property and utility facilities. However, these collections of data are highly heterogeneous in organisational and storage terms, making it difficult for a potential user to access and integrate the data with which to create new geo-representations (Larsgaard 1998). Kacmar et al. (1994) outlined the design of a digital library architecture for spatial datasets. Goodchild (1998) has argued that these data collections should be structured for access in a distributed network of ‘geolibraries’. The key practical barrier to the creation of the geolibrary is a working definition of the fundamental unit of resource. Goodchild (1998) made a case for distinguishing georeferenced information (any phenomenon that can be located geographically), from geographic information (descriptions of geographic configurations). The former category is much easier to implement in a geolibrary as simple geometric data types can be used for georeferencing; this approach implies the extension of traditional library indexing models such as US MARC (z39.2). The latter category is more difficult to implement as it requires the storage of a wide range of geo-representations. Such geo-representations cannot be handled in library indexing models and require interoperable geographic data architectures. Library indexing models depend on metadata, i.e. data about data, which has not traditionally included much support for geographic referencing (Holmes 1990). The simplest approach to georeferencing has been the use of gazeteers or geographic thesauri, which link place names to geographic coordinates (Brandt, Hill and Goodchild 1999). Woodruff and Plaunt (1994) described a scheme for the automatic extraction of place names from text documents to allow their indexing by gazeteers. Storage of geometric data to describe geo-representations implies the extension of library indexing schemas, for example by storing bounding coordinates or representative geometric data for a geophenomenon. The US standard for information retrieval (z39.50) has been extended by the GEO profile to handle spatial and temporal referencing and queries on topological and metric criteria. Nebert (1998) discussed forms and hypermap approaches to defining a search and the results of the query as a download or metadata about the dataset. Dublin Core has also been considered as a standard metadata form. Duane, Livingstone and Kidd (2000) have shown how environmental modelling output can be described and queried by using the National Center for Supercomputing Applications Hierarchical Data Format (HDF). A wide range of geographic metadata libraries have been developed; Larson (1997) reviews and summarises a number of systems. Walker et al. (1992) described the Midlands Regional Research Laboratory spatial metadatabase and the free text methods of querying it using spatial and temporal constraints. The MEGRIN project is a consortium of European national mapping organisations who have worked together to create a catalogue of geographic data available on the web. The European Spatial Metadata Infrastructure (ESMI) project is developing a distributed spatial metadata catalogue. In the USA the Federal Geographic Data Committee (FDGC) have developed a Content Standard for Digital Geospatial Metadata (CSDGM) to provide the framework for information retrieval from the Federal Geospatial Data Clearinghouse. In Portugal, the National Centre for Geographic Information co-ordination agency (CNIG) has developed a metadata library called the National Geographic Information System (SNIG) that


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structures geographic metadata produced by government agencies. In the UK the National Geospatial Data Framework (NGDF) has developed a metadata query service (‘ask Giraffe’) capable of searching federated government geographic databases. Bishr and Radwan (2000) outline the software architecture options for the development of geospatial data infrastructures (GDI). Yuxia, Zhengyi and Jianbang (2000) discuss solutions to the problems of poor semantic interoperability in geographic metadata libraries using metadata mediation. By contrast to the creation of metadata libraries, the storage of the full range of georepresentations has implied the implementation of geolibraries in distributed databases on the digital library model (Bawden and Rowlands 1999). The first major attempt to establish a geolibrary was the ‘Alexandria Project’ which was established by a consortium of US libraries, research groups and industrial corporations (Smith and Frew 1995). Users of Alexandria could access, browse and retrieve specific items from the data collections of the library by means of web-based interfaces that integrated visually-based and text-based query languages. The Alexandria Project initially included access to maps, orthophotos, AVHRR, SPOT and LANDSAT images and geodemographic data for California. The Microsoft Terraserver project also showed how geo-representations (largely imagery) could be served through a hypermap interface. NASA has also developed the Data Information and Access Link (DIAL) server to support metadata searching of the heterogeneous spatial databases and downloading of spatial data through the Earth Observing System (EOS) Data Gateway (EDG). DIAL supports the HDF metadata format and interfaces to Open Database Connectivity (ODBC) and Java Database Connectivity (JDBC) compliant data sources, which support the EOS VO interoperability protocol for catalogues. Goodchild (1998) suggested that the geolibrary should consist of browser, basemap, gazeteer and collection components. While the collections in a digital library can be considered to consist of ‘information bearing objects’ (IBO), in a geolibrary the atomic information entities corresponding to geo-representations have been termed ‘geographic information bearing objects’ (GIBO) by Goodchild (1997). Raper (1999) argued that information ontologies defined by processes of recording, ordering, signification and control in society are emerging that will determine the precise semantics of the GIBO. Goodchild (2000) noted that geolibraries must also take account of the changes that take place in GIBOs as they pass through the collection, structuring, transformation and dissemination processes of the data lifecycle. Geographic metadata must reflect ‘truth in labelling’ so that metadata records function as a form of communication between the producer and the user about lineage and error. Such considerations will become more complex when geolibraries are seen not just as production environments but as sharing architectures such as the Hubserver developed by Dykes, Moore and Wood (1999). Larson (1997) outlined a proposal for the design of a geographic information retrieval architecture supporting point-in-polygon, region, distance/buffer zone, path and multimedia queries. Larson developed a geographic browser toolkit based on the Sequoia 2000 Tioga architecture for information browsing, supporting known item searching and probabilistic retrieval based on document contents.


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MULTIDIMENSIONAL EXPLORATION OF GEOREPRESENTATIONS Given the availability of multimedia and virtual geo-representations, architectures for their structuring and their integration with information infrastructures, many new systems for their multidimensional exploration have emerged over the last decade. These systems extend the nature of geo-representation and offer new scope for the exploration of spatial multimedia and virtual environments. A selection of applications allowing multidimensional exploration in hypermedia spatial databases and visualisation/animation is surveyed in the following sections. Hypermedia spatial databases When multimedia/hypermedia GIS are used as the front-end to a heterogeneous database of geo-representations, the combination can be termed a ‘hypermedia spatial database’. Before the arrival of multimedia data support in web pages (c.1996), the creation of such databases usually relied upon hypermedia authoring tools such as Hypercard/Supercard, Toolbook or Microcosm. Recent web-based hypermedia spatial databases have tended to use javascript embedded in HTML for development. Hypermedia spatial databases typically contain multimedia geo-representations that need to be accessed by geographic criteria. This requires the ‘typing’ and naming of geographic abstractions made from sets of information elements, which may be aggregated into collections of higher level abstractions in the sense of the HAM model (Campbell and Goodman 1988). An example of this approach would be a database of tourist information in which museums, historic buildings and parks (with their component information elements) are typed as ‘attractions’ and aggregated into tours (Buttenfield and Weber 1993). Such abstractions can be transitory, such as the one-off route of a special road race like a marathon. Using this approach hypermedia spatial databases have been created and explored for a variety of educational, planning, tourism, environmental and facilities management purposes. Perhaps the earliest hypermedia spatial database to be developed was the Domesday System based on BBC microcomputers and the analogue Phillips LaserVision discs (Rhind et al. 1988). The Domesday system was accessed by map gazeteers or tours and contained a huge number of multimedia geo-representations relating to population, employment and environment. Lewis and Rhind (1991) demonstrated how hypermedia interfaces could be constructed to provide new forms of access to the data on the Domesday LaserVision discs after the BBC microcomputer became obsolete. Multimedia encyclopedias such as Encarta from Microsoft and the New Grolier Multimedia Encyclopedia (NGME) have also incorporated multimedia geo-representations since the early 1990s. DiBiase (1999) showed how the multimedia geo-representations of the NGME were planned with respect to the required interactive exploration functions for the instructional objectives. Another educational application of the hypermedia spatial database is the digital atlas (Hocking and Keller 1992). Al-Faraj (1998) suggested that four generations of digital atlas could be identified. Firstly, there were systems replicating the static format of the


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paper analogue, such as the Electronic Atlas of Arkansas, released in 1986. Secondly, there were systems with interactive control over map display and gazetteer look up facilities. These included the electronic atlas of the North American French-speaking communities (Raveneau et al. 1991) and the National Atlas Information System of the Netherlands (Koop and Ormeling 1990), both developed using Hypercard. Thirdly, systems offering interactive cartography were developed, such as the cdv tool for census data access developed by Dykes (1996), and the system developed by Fonseca and Câmara (1997) to explore planning-related multimedia geo-representations. Fourthly, web based atlases delivered on the web to user’s specifications have been developed, such as the National Atlas of Switzerland (Spiess and Richard 1997) and the Descartes system (Andrienko and Andrienko 1999). Using this classification scheme exploration can be seen to have evolved from the simple following of authored hyperlinks to the interactive specification of the user’s own computed hyperlinks which generate customised geo-representations. Another common motivation for the development of a hypermedia spatial database has been the need to visualise the environment for planning purposes, as in the following cases. Camara et al. (1991) described Hypersnige, which was developed in Hypercard for the exploration of regional planning information by the Centro Nacional Informação Geografica (CNIG), Portugal. Parsons (1992) described the London Covent Garden explorer in Hypercard, which used an aerial photo hypermap index annotated with points of interest which are then illustrated by animation or video if activated. Ertl, Gleixner and Ranziger (1992) described the Move-X system, which was designed to merge video footage of vacant sites with architectural models and GIS data. Grüber and Wilmersdorf (1997) developed the three-dimensional CyberCity hypermedia spatial database of the built urban form in Vienna. Shiffer (1999) described a Level of Service Representation developed using multimedia geo-representations of traffic movements and volumes through intersections accessed through a web browser. One of the most ambitious hypermedia spatial databases was the ‘Great Cities of Europe’ (GCE) system developed as part of the European Union COMETT programme (Polyorides 1993). The GCE contained georeferenced planning information on a number of European cities organised by city, theme and image collection. The thematic information was accessed by a thesaurus while the city information was accessed from a map base. The GCE was based on the multimedia GIS architecture developed by the University of Patras and Exodus Multimedia, which uses Toolbook extended with C++ and integrated with the Windows multimedia extensions. It was delivered with data for 29 European cities on CD-ROM. These planning applications of hypermedia spatial databases have attempted to familiarise users with proposed developments through exploration of the geo-representations. However, typically the technical barriers to use have prevented their widespread use: Shiffer (1995a) found that a technically competent ‘facilitator’ was needed to ensure productive use in public enquiry situations. Tourism applications have also made wide use of hypermedia spatial databases. Mogorovitch et al. (1992) described an approach based on the integration of Arc/Info with videodisc images and video for tourist planning applications. The user could interactively access points of interest on the map and see images and video for that feature, search for all occurrences of a particular type of tourist sight, or they could plan


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tourist routes. Blat et al. (1995) described the creation of the PARCBIT CD-ROM, which contains a large quantity of tourism-related data for the island of Mallorca. The user is presented with various methods of structured browsing which tests conducted on users showed had considerable time advantages over traditional approaches. Al-Faraj (1998) developed a hypermedia spatial database for Kuwait using javascript to customise web pages, which had distinct use modes of use for students, citizens, business users and tourists. Hypermedia spatial databases have also been used in facility management applications. Green and Kemp (1993) described the development of a pipeline management system developed in Toolbook on the PC which integrated a map base showing the pipeline at various different scales with detailed photographs (aerial and terrestrial) of the pipeline route. State (1993) developed a railway track information system based on video footage of the line and trackside equipment. By integrating inertial navigation systems with the video footage the distances were exported to Arc/Info and stored with details of the trackside equipment. Craglia (1994) summarises work by Aurigi to develop a hypermedia spatial database for the public transport system of Florence, which is implemented by integration between Hypercard and the GIS MapGrafix. Giertsen, Sandvik and Torkildsen (1997) developed an oil pipeline database linked to terrain data for Western Norway. Given the wide variety of multimedia geo-representations created for environmental management, many applications of hypermedia spatial databases have been developed for multidimensional exploration. Fonseca et al. (1995) and Fonseca and Câmara (1997) developed a system in Supercard which integrated a hypermap with a hypermedia spatial database for environmental impact assessment at the former Expo’ 98 construction site in Lisbon. The user could browse and overlay images, maps and video of the site and morph one site design into another to visualise the differences between alternatives. Raper and Livingstone (1995b) described the design and implementation of a spatial data explorer called SMPviewer which allows the user to extract interpretations of images and maps digitised on a hypermap using the mouse. Simmons, Hall and Clark (1992), Simmons (1993) described a hypermedia spatial database developed using Microcosm linked to the SPANSmap GIS for an environmental management system. Romão et al. (1999) presented the CoastMAP application for visualising coastal change using a hypermap linked to other databases, which is overlaid with symbols representing change. The CoastMAP interface allowed movement along the coast through a seamless aerial photography mosaic at one of several levels of image resolution, while additional contextual information was displayed alongside the imagery. Visualisation, data mining and animation of geo-representations The traditional way to visualise representations of the world over geographic spaces is the map. Cartographic processes have been developed over centuries to conceptualise, select, classify and symbolise geo-phenomena on the map (Robinson et al. 1995). However, the new opportunities offered by computer visualisation and geographical information systems have led to profound changes in cartography. Fisher, Dykes and Wood (1993) suggested that there have been three main consequences of these


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technologically driven changes: firstly, the availability of new visual variables, secondly, new computational possibilities for representation and transformation, and thirdly, increased levels of interaction between the user and the map. The implications of these changes have been far-reaching as the map production of traditional cartography has been transformed by the pattern exploration of geographical visualisation (GVIS). Thus, Harley (1989, 1990) deconstructed the map by asking who made maps and why, a point taken up by Dorling and Fairbairn (1997). DiBiase (1990) reconceptualised mapping as part of the scientific process, distinguishing between the visual thinking of the private realm and the visual communication of the public realm. MacEachren (1995) argued that GVIS should be concerned with techniques to allow gestalt understanding of multidimensional patterns in real time. These techniques included recognition and noticing in maps and relationship identification in dynamic models. However, Kraak (1995) pointed out that while the new technologies of presentation have undoubtedly assisted visualisation, there have been few developments which codify the exploration and analysis of new multimedia data types in the context of the theories of semiology and the ‘grammar’ of cartography. Work on the multidimensional exploration of geo-representations has focussed on developing Exploratory (spatial) Data Analysis (ESDA) ools (Hearnshaw and Unwin 1994, McEachren and Taylor 1994). Such tools enable users to focus on re-basing the information by time, scale or unit of reporting and to attempt exploratory analysis of the relationship between spatially and temporally distributed variables. Exploratory (spatial) Data Analysis has been realised for spatial data through systems such as REGARD (Haslett, Willis and Unwin 1990) and Exploremap (Egbert and Slocum 1992). Unwin (1996) identified the problems of exploring spatio-temporal data series such as the large number of cases and variables, the difficulty of identifying time lags in associations and the complexity of flows in complex systems. Pictorial simulation models for spatial datasets such as those defined by Câmara et al. (1991) over a simple raster offer powerful alternative tools for spatial analysis using multimedia primitives. Gluck (2000) used sonification methods to facilitate ESDA based on augmented seriation. Multidimensional exploration of geo-representations has recently been reconceptualised in terms of data mining and knowledge discovery in databases (KDD). Such approaches call for the selection of appropriate datasets from a data warehouse, their data mining for knowledge discovery and the analysis of the extracted patterns. Spatio-temporal data mining involves the development of multidimensional knowledge discovery strategies for characterisation, classification, association and clustering operations. Han, Koperski and Stefanovic (1997) described the Geominer system, which uses KDD techniques to query patterns in a multidimensional data cube, although Lee and Kemp (2000) warn that such on-line analytical processing (OLAP) must take account of the modifiable areal unit problem. Andrienko, Jankowski and Andrienko (2000) developed a spatial data mining tool using a Classification Tree algorithm for the Descartes dynamic mapping system and integrated it into the Kepler data mining architecture. Gaheganetal. (2000) developed the Java-based GeoVISTA studio as a visual approach to abduction, by producing hypotheses that generate classifications). MacEachren et al. (1999) attempted to bridge the cognitive approach of GVIS with the analytical approach of KDD by facilitating the application of GVIS ‘interaction


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forms’ (e.g. colourmap manipulation) with KDD representations (scatterplots, threedimensional views and parallel plots). These techniques can be seen as part of a wider set of information searching models (Wilson 1999), in which the user’s cognitive space plays an important part (Ingwersen 1996). In developing an automated query processing system for tropic cyclone monitoring, Yuan (1998) showed that all these operations are critically dependent on the form and richness of spatio-temporal representation employed. Gahegan (1999) argued that further GVIS progress requires faster rendering, understanding the visual stimuli behind operations like ‘noticing’, reducing the complexity in the assignment of data attributes to visual properties, and improving the effectiveness of virtual environments as exploratory settings. The exploration of multidimensional representations can also be carried out using dynamic map displays, especially those organised by time (Dorling 1992). Shepherd (1995) classified the sources of time variation in visualisations by the temporal nature of data input, the dynamism of symbology, the change of observer viewpoint, the behaviour of visual elements and simulation characteristics. Shepherd argues that the extension of the graphical sign system of Bertin (1983) involves the use of four-dimensional displays incorporating visibility variations, locational change of symbols, and the growth and decay of displays. Giertsen, Sandvik and Torkildsen (1997) proposed an open architecture for dynamic visualisation based on Open Inventor and produced animation sequences by generating dynamic scene components viewed by (moving) virtual cameras. A wide range of different approaches to dynamic visualisation have been employed. Openshaw, Waugh and Cross (1994) suggested that animation of a temporal map series could be used to speed up time or to re-order the data within specified time periods for applications ranging from cancer cluster analysis to crime incidence. Weber and Buttenfield (1993) described a cartographic animation of average temperatures for the USA over the last 100 years that could be run in either direction in time. Schwarz von Raumer and Kickner (1994) show how Toolbook and Arc/Info can be linked together to show visualisation of pollution levels in real time. The Centennia interactive historical atlas of European history from Clock Software presents spatial animations of changing political boundaries allowing movement forward and backwards through time and generalisation of the hierarchical level of the political units shown. Koussoulakou (1994) presented an animation of air pollution change in which arrows representing wind magnitude and direction changed dynamically through time. Jomier, Peerbocus and Huntzinger, (2000) offer a classification of the ways to visualise spatio-temporal change.

CONCLUSIONS This chapter has classified the representational nature of the new multimedia and virtual geo-representations and examined how they can be explored. Ontologically, these georepresentations are richer than three-and four-dimensional geometry as they share the conceptualisation process between developer and user through interaction. Virtuality engages users in exploration and allows them to define their own geo-phenomena in


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multidimensional spaces. Hypermedia structuring then allows the association of geophenomena into semantic networks using both exploration and design approaches without the constraints of formal data modelling. Such applications may imply a greater focus on information representation techniques in future (Raskin 1999). However, epistemologically these new geo-representations pose further questions. MacEachren (1995) argues that ‘GVIS represents a substantial change in emphasis from maps as a presentation tool to maps as part of a thinking-knowledge construction process’ (p460). Implemented in this sense GVIS is a highly effective source of hypotheses generation about specific relationships. However, as Petch (1994) noted, such hypotheses are heavily context dependent, and the patterns noted may be partial or local. If, as many social theorists believe, there are no regularities of behaviour to be found in the world, then perhaps context-dependent outcomes are useful ends in themselves if they are documented and published.

Part II INTRODUCTION

Figure II.1 Location of Scolt Head Island and other sites in part II

In part I of this book a methodological platform has been built for the geographical information scientist. The central argument was that there is a coherent and valid rationale to the use of spatial and temporal representation, despite the various critiques. The representational apparatus of geographical information science was outlined and it


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was shown how recent theoretical and technological advances have made it possible to improve the richness and extend the modality of this apparatus. In this section these arguments are illustrated and exemplified. In the following chapters short case studies are presented to show how the new forms of spatial representation outlined in part I can be used. For practical and theoretical reasons these case studies all use the same location, that of Scolt Head Island on the North Norfolk coast of eastern England. The practical reason is that 10 years of research into coastal geomorphology, coastal sedimentology, coastal simulation modelling, airborne remote sensing and environmental management during the 1990s has led to the accumulation of a huge and diverse archive of georeferenced data for this location. The theoretical reason is that coastal environments present profound challenges to the ‘standard model’ of twodimensional spatial representation as they lack a comprehensive ‘built structure’ to provide identity criteria, they are chaotic and highly dynamic, and they pose complex interdisciplinary management problems. The use of a common location for all the case studies also permits the creation of a kind of representational scrapbook in which a wide range of views of the environment and society of the area can be placed. Such a wide range of views also offers its own argument for representation, as the very diversity on show demonstrates the scope of current methodologies. The potential use of these representations offers further evidence of the role that multidimensional representation can now play when they include: public enquiries, environmental impact assessments, field trip planning, nature conservation education, coastal engineering decision support and tourist management. Hopefully, in a small way this section of the book can also help write a turn-of-the-Millennium geography of a part of England’s rural coastline, highlighting some the issues that face geographers, biologists, engineers and residents of this area. The geography of the North Norfolk Coast Scolt Head is a barrier island consisting of a line of sand dunes backed by salt marshes which forms part of the low-lying N.Norfolk coast (figure II.1). It experiences a westerly longshore drift of sediment into a spit (sandy bar) at the western end reflecting the tidal circulation and the dominant north east wave energy in this area of the southern North Sea. Research into the origin and development of this coast in general and the island in particular has been continuous since the beginning of the century—a monograph by Steers (1960) gives a comprehensive introduction. The model of evolution for Scolt Head developed by Allison (1985) suggests that the island developed from a beach ridge during the Holocene marine transgression, and that since its inception has extended 7km to the west as a result of longshore drift. This development has taken place as a repeated cycle of extension, stabilisation and incorporation of recurved spits at the westerly end of the island. There are now 20–30 recurved spits of this kind extending southwards from the main ridge (figure II.2). Each of these spits encloses a salt marsh of westerly decreasing elevation, reflecting the progressively more recent initiation of marsh mud deposition when protected from wave attack by the spit. The initiation and development of these spit bars is, therefore, a crucial determinant of the development of the salt marshes which in turn provide coastal protection and calmer waters to residents and water users.

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The dynamic form of these spits reflects a balance between wave and tide energy in the short term and relative sea level change in the medium and long term. Since the tidal channels at either end of the island are barriers to longshore sediment movement the spits act as reservoirs for coastal sediments. Hence, spits and bars marginal to tidal channels may be both sensitive indicators of aggregate coastal change and reservoirs of sediment whose budgets may be of considerable importance to the management of the adjacent coastline on an annual and decadal scale.

Figure II.2 Map of Scolt Head Island in 1990, showing gravel spits in black, sandy dunes in stipple and marshes in white within the outline

A coastline such as this one poses many management issues for fanners, engineers and conservationists. If relative sea level rise continues then the question of how the coast will respond is of considerable importance, especially since some of the coast to the west of the island has been stabilised by engineers and some marshes south of the island has been reclaimed by land owners. So although the ‘natural’ response will be for washover and dune migration inland during storm surges in some places on the coast away from Scolt Head this process is being resisted. The aim of the research being carried out at Scolt Head is to provide the holistic understanding of the natural processes that will allow good management decisions to be taken. Potential visitors should note that Scolt Head is an isolated National Nature Reserve separated from the mainland by dangerous tidal channels. Local advice from English Nature wardens or the harbourmaster should be sought before attempting a visit.

CHAPTER 6 Hypermedia geo-representations for coastal management CONTEXT Coastal environments are amongst the most dynamic in geomorphology and the most troublesome for coastal managers (Carter 1988). This is because their landform and process regimes are characterised by rapid change over the short term (days and weeks), making them difficult to predict and manage over the medium term (periods of months and years). This dynamic behaviour is determined by the inherent variability of the forces driving coastal processes, meaning that the whole shape of the coastline can be rapidly changed, especially under storm conditions. This is especially true on low depositional coasts and in estuaries that are characterised by beach barriers, dunes and salt marshes, as in both cases the unconsolidated sand and gravel that makes them up is particularly mobile. Around the low depositional coasts of the southern North Sea in eastern England and the north-west of the Netherlands, large tidal ranges and frequent storms mean coastlines exhibit complex spatial and temporal behaviour. In addition, world-wide sealevel rise and the various forms of human intervention such as sea wall construction, land reclamation, and dredging each pose complex environmental problems in themselves. The dynamic nature of the coastal processes and landforms is paralleled by the diverse interests of the agencies and stakeholders who make the coast a social, political and economic battleground. Even a stable coast sees a conflict between economy, conservation and leisure interests over access to the shoreline, use of the sea’s resources, protection from flooding, and preservation of biodiversity and amenity. A changing coastline sees stakeholders and agencies of local and central government battle over the impacts of change on existing interests or potential new ones. With the acceleration of change driven by sea level rise has come the realisation that ad hoc decisions by individual agencies are not effective and a holistic approach is needed. Accordingly, using regular monitoring data, scientific studies, and evidence from interested parties, Shoreline Management Plans have been drawn up by the UK government to provide a framework for coastal management and planning (Cooper et al. 2000). Information and education must be at the heart of coastal planning as the dynamic nature of the coast means that a coastal engineering solution designed for the short-term can fail quickly if it is not designed well. The information needed to address holistic coastal management objectives such as whether to allow the coast to retreat takes a variety of forms, ranging from documents and tabular data to profiles, maps, imagery, surfaces and models (Raper et al. 2000). Storage of this heterogeneous collection of geo-representations poses challenges for most data models and database structures available and so data types are typically stored


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separately and brought together for individual studies. This set of geo-representations can be complex to understand and voluminous in nature, yet their holistic understanding is essential to policy, decision-making and learning. One approach to this problem is to use the hypermedia model to structure the data holdings and to provide an access model (see chapter 5). This chapter discusses some experiments in coastal data management using a hypermedia approach.

EXPERIMENTS IN HYPERMEDIA GEO-REPRESENTATION Hypermedia geo-representation offers new ways to access data, the means to annotate datasets, multimedia data storage and multidimensional exploration of datasets. These experiments have all been built using the North Norfolk coast datasets described at the beginning of Part II. Scolt Multimedia Project The Scolt Multimedia Project (SMP) aimed to provide a storage architecture and exploration metaphor for multidimensional geo-representations (Raper and Livingstone 1995b). The SMP took the form of a very large hyperdocument covering the socioeconomic and environmental evolution of the nature reserve. Implemented as a Hypercard stack, the hyperdocument consisted of heterogeneous nodes with socioeconomic and environmental resource data with spatial and temporal referencing. The system was capable of storing a wide range of data including statistical data, text, graphics, terrestrial photography, video, maps, air photos and other imagery. Primary access to the nodes was by selecting a resource type in an appropriate cell in a time-space diagram (a ‘zone’), that acted as an exploration metaphor. Figure 6.1 shows the interface and some specimen resources. This diagram defined a matrix of time/space zones that were chosen to reflect a progressive sequence of four time periods. These were: today, the turn of the century—100 years ago, the last millennium—1000 years ago and the end of the Ice Age—10,000 years ago); and, three different spatial scales defining different extents of the North Norfolk coast. Selection of the resource type for a time-space zone took the user to an index node where a comprehensive listing of qualifying resources was found for that timespace/resource combination. This index was implemented as a hypermap showing the appropriate outline map for the zone. Footprints, denoting available information, were located on this map according to their position and covering the area over which they actually extend. The footprint also acted as a hyperlink to the lowest level ‘basic’ nodes in the hierarchy and their resources. At this level the user could also create and position their own footprints on the time-space zonal hypermap and link them to any other resource to which they could navigate in the SMP. These connections formed a web of links corresponding to an ‘annotation structure’ which a user can re-access each time they use the system by navigation (McAleese 1989). Given the lack of entity integrity in a hyperdocument, nodes could be placed in one or more time-space zones as required, making for multiple links between basic nodes and zones.

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Clicking on a node footprint on a particular time-space zone hypermap linked to the basic nodes. If the basic node contained a map, image or orthophoto then the georepresentation was also treated as a hypermap. In the SMP hypermap geo-representations were opened through a separate module called the SMPviewer which provided some GIS functionality. Unlike the time-space zone hypermap in the SMP database, which is designed only to facilitate access to information, the hypermaps accessed by the SMPviewer are designed to support a full range of spatial functions including annotation, measurement, analysis and output.

Figure 6.1 The time-space diagram in the SMP

When accessing a geo-representation stored on a basic node in the SMP using the SMPviewer, the control and tool palettes are opened (figure 6.2) and any spatio-temporal metadata on the resource is read. These palettes permit the annotation, extraction and output of any user-defined features in vector form. This is achieved by on screen digitising using the mouse. The geometry defined is stored as a hypertext object with spatial and temporal attributes, rather than in a database table. Such user-created georepresentations were referred to as hypergeometry objects and were stored in the industry-standard Arc/Info ‘ungenerate’ data format. An experimental java application called GIS-scape was developed to provide SMPviewer functions on a generic software platform (Raper and Livingstone 1996). While this implementation was application-driven and based on a ‘closed’ hypermedia platform (Hypercard), the implementation is capable of wider application. The SMP offered overlapping and flexible access methods based on time-space metaphors, browsing and searches, it allowed users to save their paths through the semantic net of


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hyperlinks, and it offered users the chance to extract their own interpretations from the information resources. Six years after SMP was developed it is now possible to envisage a web-based interface linked to a (meta)database using a web portal servlet architecture to deliver the basic nodes to a client, and a java-based version of SMPviewer such as GIS-scape.

Figure 6.2 The use of the SMPviewer for the extraction of geographic information from imagery

The SMP design offers coastal management a way to index the vast amount of monitoring information in such a way that data from similar time-space scales can be readily browsed and annotated. Hypermedia interfaces are also easier to use than conventional applications making the SMP design suitable as a foundation for a public access information application. Multidimensional organisation of coastal georepresentations would promote a more historically aware view of the process of coastal planning and highlight the long-term cycles in coastal processes. Annotation of historical maps and images could also allow the local community to contribute its knowledge to the collection of geo-representations that will be considered during policy-making. Hypermedia functions in GIS Desktop GIS now support limited forms of hypermedia functionality, such as the hyperlinking of vector geometry to external and multimedia data types. This allows the implementation of a hypermap model in GIS, although it is not usually possible to


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semantically structure the external and multimedia data. The hypermap model is a suitable basis for coastal data management where the data types are highly heterogeneous but can be indexed spatially within a coastal corridor. Romão et al. (1999) developed CoastMap using this approach. In effect the GIS is used as a geolibrary index to the available geo-representations and georeferenced information. Multimedia geo-representations such as photographic images and videos can be linked to geometric data stored in a GIS using pointers containing the path to the storage location. Selecting a piece of hyperlinked geometry causes the geo-representation to be displayed using operating system specific applications. Plate 6.1 shows a 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster in Arcview GIS. The points plotted on the map represent the location of the photographic images: one was taken at the western end of Scolt Head Island, while the other shows the village hall. Other desktop GIS such as GeoMedia and Maplnfo have similar capabilities. GIS can also link to external database tables containing geometry. Plate 6.2 shows an SQL connect operation using ODBC in Arcview GIS, which links to a table in a Microsoft Access database containing geometric and attribute data for coastal landforms. The data in the Access database can be plotted on an outline map in Arcview GIS with a predetermined symbology, so that coastal management priorities can be visualised alongside process classifications. In the application shown in plate 6.2, a coastal metadatabase has been constructed in Microsoft Access, in which coastal spit and ness landform locations are linked to their source, dataset type and classification. By using Arcview GIS as a front end to this data, connections between features and a wide range of documents and images can be managed and queried. By using map views of different scales both overview and site-specific coastal management data can be accessed and hyperlinked. Web GIS architectures are also now emerging as potential hypermedia interfaces to geo-representations such as coastal management data. By using a plug-in GIS such as MapGuide, or a downloadable java applet, the GIS front end can be embedded in a web page and viewed with a browser. Choices made using the client interface can be sent within an HTTP universal resource locator (URL) to a server process such as a java servlet, which then can process the user queries. The resulting geo-representation or document can then be returned to the browser for viewing. This architecture makes it possible to develop a multidimensional hypermedia semantic network based on hyperlinks, where individual nodes can be documents or geo-representations that are customised in real time by calls to the server from the client. This kind of hybrid hypermedia and GIS architecture is a suitable platform for delivery of information within organisations via an intranet, or to the public via the Internet. Panoramap hypermedia environment Panoramap, developed for the Virtual Field Course (VFC) project in the cross-platform TCL/TK development environment, can be described as a georeferenced browser of multimedia geo-representations (Dykes 2000). Panoramap allows the user to place geometric features on a georeferenced base (e.g. map or imagery) which are linked to multimedia geo-representations stored locally or in a remote database accessed via the


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‘hubserver’ metadatabase (Dykes, Moore and Wood 1999). Each link to a georepresentation on the mapbase has a (user)-defined application for viewing it e.g. text, HTML or video. Panoramap itself displays panoramic imagery, vector polygons and GPS track data and provides interaction tools for each of these data types. In the case of panoramic imagery, the view direction and the field of view are drawn on the map base and updated as the panorama is scrolled either to the left or right. As multiple panoramas can be opened it is possible to choose panoramas that can be turned towards each other. The Panoramap georeferenced map base has a hypermap function allowing users to click on footprints placed on the map base, which link to new larger scale map bases. In plate 6.3 the 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster (as shown in plate 6.1) has been loaded into Panoramap and overlaid with aerial photograph footprints. The points are linked to panoramic photographic images, two of which are displayed along with their field of view. The vertical arrowheads within the images represent the positions of other panoramic images; their lengths are proportional to their distance from the current panorama location. By clicking on the arrows in the panorama, it is possible to highlight the corresponding symbol on the mapbase. When double-clicking on a selected arrowhead the target panorama opens making it possible to move step-by-step across the area of the base map. This allows the user to build up an allocentric virtual environment from multiple egocentric panoramic views (see chapter 2). Panoramap is a novel and rich form of hypermedia interface to geo-representations that has many potential applications in coastal data management and exploration. The open nature of its architecture and the cartographic design of its user interface makes it a powerful geo-representation browser. The ability to control the symbolisation of points and to shade polygons by values in attribute data files makes Panoramap a useful data integration tool. Its integration with the VFC ‘hubserver’ metadatabase also makes it a potential ‘geolibrary front end’ to stored multidimensional geo-representations.

POTENTIAL These three experiments in hypermedia using coastal management data illustrate the potential of hypermedia techniques in the structuring and exploration of georepresentations. While these applications are suited to browsing through semantic networks, there can be a poor cognitive fit between the functionality available for the exploration of hypermedia geo-representations, and therefore the user’s efficient and effective completion of any associated information tasks (Gluck and Fraser 1997). Effective task-oriented information seeking requires an understanding of the cognitive setting of the user (Dervin 1983) and appropriate information system design based on task-related information analysis (Sutcliffe 1997). These elements have been brought together in information design (Jacobson 1999). There have been few attempts to develop cognitive settings, information analyses or designs for the exploration of multidimensional geo-representations. Progress on these objectives will ensure that MacEachren’s (1995) GVIS ‘thinking-knowledge construction process’ is contextualised and underpinned by new methodologies. The most critical


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elements of this new methodology are new ontologies for multidimensional geophenomena.

CHAPTER 7 Geo-representation of dynamic coastal geophenomena CONTEXT The high rates of change in geo-phenomena at the coastline demand the use of dynamic geo-representations for their exploration using multimedia techniques. Multimedia data types offer new approaches to dynamic geo-representation through video, sound, animation and real-time monitoring systems. These systems can be termed ‘dynamic’ due to their high rates of sampling relative to the increments of change. Such high rates of sampling ensure that there is a very low probability of an unmeasured event between any two samples. Examples of dynamic geo-phenomena at the coastline are windblown dust particles or smoke, water flows and waves, vegetation growth and shifting landforms in declining order of rates of change. Human movement patterns also exhibit spatiotemporal behaviour, and can be regarded as a special case of dynamic change. The goal of dynamic geo-representation is to model continuous multidimensional identity using discrete dynamic systems so that the available concepts of change can be enriched. Dynamic geo-representation must though operate under certain representational constraints. Change must be made discrete by sampling at a specified spatial and temporal resolution. Dynamic geo-representations require a correspondence to be established between the world time of their origin and the playback time defined by the user. When dynamic geo-representation ‘filters’ the world using multimedia techniques (see chapter 5), then there can be no implicit index to the content, and queries will depend on knowledge-driven content-based indexing. When dynamic geo-representation animates geometric reconstructions using maps or models, then queries depend on the indexing of represented objects, their inter-relationships, the viewpoint and the qualitative aspects of display. The nature of change captured by ‘filtering’ and ‘reconstruction’ is subtly different in these two representational contexts.

EXPERIMENTS IN GEO-REPRESENTATION OF DYNAMIC COASTAL PHENOMENA These experiments exemplify some of the forms of dynamic geo-representation discussed above and in chapter 5. These case studies refer to Scolt Head Island or other sites in eastern England, where attempts have been made to explore the dynamic nature of coastal change using new representational forms, over a variety of timescales.

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Videometric measurement of processes Raper, McCarthy and Williams (1998) defined the term ‘videometry’ in the context of geo-representation as ‘procedures used to extract robust georeferenced measurements of the position of phenomena visible in video imagery using orientation parameters recorded at the time of acquisition’. The simplest form of this general case is orthogonal or pseudo-orthogonal viewing of a scene by a video camera. Raper and McCarthy (1994a) outlined techniques for the vertical case from aerial platforms while Foote and Horn (1999) discuss the requirements of the horizontal case for beach and flume studies of swash wave run-up behaviour. The more complex cases involve oblique viewing such as those used for coastal monitoring by Holland and Holman (1997) and Eleveld, Blok and Bakx (2000), and for target positioning (McCarthy 1999).

Figure 7.1 Wave orthogonal mapping at Far Point on Scolt Head Island

Wave processes are the most important dynamic processes in the coastal environment as they have an important influence on landform evolution. Figure 7.1 shows a digital camera image taken on November 1997 for Far Point of Scolt Head Island, showing waves breaking on the very end of the spit landform. The image was imported into the SMPviewer application (Raper and Livingstone 1995b) (see chapter 6) and annotations were made on the image to indicate the outline of the spit and to mark wave crest orthogonals close to the bar. The wave crest orthogonals clearly show the wave refraction around the end of the spit. However, this is a static analysis: using video georepresentations it is possible to record the movement of the waves as they break. Plate 7.1 shows four sequential video frames of breaking waves filmed from the air. Between frames timed at 09:06:51 and 09:06:54 the large bow shaped breaking wave in the centre moves across the frames to the right as the aircraft moves. However, the wave also


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advances on the shoreline and changes shape sufficiently to see that it is a spilling wave and not a plunging one. Such insights can only be gained from the analysis of dynamic imagery if there are no observers on the shoreline. Video imagery of dynamic environments can also be made into a strip map by playing the video through a frame matching system. Frame matching finds the overlap between successive frames, orients them together, and then adds the frames into the strip map. Plate 7.2 shows a strip map made from aerial video imagery for the mouth of the Ore River at Shingle Street in Suffolk. The way that the waves are blocked by the small intertidal swash bars is clearly seen in the static image. However, in the live video sequence the flow of the Ore River in two distinct channels can be distinguished by the interference patterns between river and waves, and approximate speeds of movement calculated. Such methods can be used to update marine charts in places where the landforms change very rapidly. Animating multidimensional landform behaviour The rapid change that occurs in coastal landforms can be captured by high rates of mapping or imaging. If the individual map/images are comparable samples of the geophenomena through time, then the geo-representations can be animated to reproduce the change. Such animations of geo-representational scenes allow the user to replay the events either forwards or backwards and at any chosen speed. In a sequence of scenes shown rapidly there is a tendency to interpolate between them. Surveys over 8 years of the rapidly changing spits on Scolt Head Island have produced over 20 separate maps of the terrain at Far Point (Raper et al. 1999). Terrain elevation and surface sedimentary composition data for the currently active Far Point spits was captured at six-monthly intervals between April 1992 and September 1995, then at monthly intervals during the winters of 1995–6 and 1996–7 and then again at six-monthly intervals subsequently. These surveys were conducted using a total station surveying instrument with sampling points at approximately 10m horizontal resolution, and were based on a set of ground control monuments used to define a local coordinate system (Raper et al. 1999). The surveys of elevation since 1993 (plate 7.3) show that the spit develops through a process of longshore transport. Sediment eroded from the shoreface close to the end of the barrier beach becomes deposited at the very end of the spit. Washover appears not to be important on the spits at Far Point except in high-magnitude storm events. After a period of several years, a new spit is formed (as in 1994), which initially extends from the beach of the main barrier. The new spit then follows a similar path to the old spit further to the west, becoming elongated and progressively recurved (as in late 1995). The extension of a new spit appears to coincide with the gradual degradation of the older spit. This is interpreted to indicate that the new spit is capturing sediment that might otherwise have been supplied to the older spit. The processes that lead to the degradation of the older spit are largely attributed to tidal currents that trim the end of the spit and create breakthroughs. This is the most common cycle of spit development and degradation in (almost) a decade of observations. The net result is a gradual accretion process, where the net deposition volume is much less than the sum of each of the recurved spits.

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Two alternative animations have been made to study the change that takes place in these landforms. Firstly, an animation of the coloured contour maps in plate 7.3 was produced using animated GIF file techniques, using frame rates that echo the intervals at which the surveys were carried out. The resulting animation conveys several forms of behaviour that cannot be elicited from the static maps: firstly, there appear to be ‘pulses’ of sediment which move along the spits from the barrier island; secondly the whole landform complex rotates while moving; and thirdly, as the spits grow out to the west, the whole complex moves to the east, as a whole. Hence, the spit elongation that appear to occur as the spit grows is not actually making any forward progress, except at certain points when the angle of the spit to the barrier island increases to the point that a new spit can develop. An alternative animation was made using VRML models of the spits at Far Point for the same set of surveys. Each model was turned to the same viewing perspective, captured as a screen shot and animated in the same way as the maps. However, the visual impression is not as striking as in the case of the animated maps since many more aspects of change can now be seen, making it difficult to grasp them all simultaneously. Smith, Spencer, and Möller (2000) animated three late summer CASI aerial remote sensing images of the Far Point spits for the period 1994–96. The animation shows a single growth phase of the main spit in which it enlarges while earlier spit shrinks as its sediment supply is cut off. Human spatio-temporal behaviour The availability of hand-held Global Positioning System (GPS) receivers has made it possible to map personal movement paths more easily than ever before. Such paths through space-time can be stored in real-time GIS (see chapter 5), although they pose new problems for structured spatio-temporal database storage. Such space-time paths are a novel form of dynamic geo-representation, capturing instantaneous position, speed and heading. Figure 7.2 shows the space-time path for the two days used to survey one of the maps shown in plate 7.3, showing: the activity at the field site; the use of a store in the survey area (centre of the western path cluster); return journeys to the field centre accommodation (origin of journeys to the east); and the arrival/departure from the field site. Various derivative geo-representations can be envisaged such as daily envelopes of movement and self-contained periods of activity in certain locations. With the move to include this geolocation technology in mobile phones over the next few years such dynamic geo-representations may become widely available (Mountain and Raper 2000).

Figure 7.2 Space-time path for two days surveying the Far Points spits on Scolt Head Island in March 2000


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POTENTIAL A range of different dynamic geo-representations have been surveyed from high frequency process monitoring and low frequency landform change, to human movement mapping. Since multimedia and geolocation technologies permitting the collection of dynamic geo-representation data have rapidly grown during the last few years, this kind of multidimensional application is likely to become much more common. Currently, the databases and analyses needed for multidimensional datasets of this kind are still poorly developed and there is considerable scope for further development.

CHAPTER 8 Geo-representations of coastal change using virtual environments CONTEXT The inaccessibility of the coastal environment and the limited number of people who experience the extraordinarily dynamic change that takes place there, are two important reasons to develop virtual geo-representations of the (Norfolk) coast. Limited time and the arduous nature of the walk to the Scolt Head island National Nature Reserve means that many tourists, visitors and field trip students do not ever experience first hand one of the few natural and unmanaged parts of England’s lowland coastline. While a virtual environment is a poor substitute for that personal experience it is arguably better than no substitute at all, and, when combined with interpretive material it can be valuable, as Dykes, Moore and Wood (1999) have argued. While the author has seen over 20 years of change at the Far Point spits on Scolt Head Island, few others can have witnessed this dynamic behaviour. A virtual geo-representation allows a wider audience to explore the geomorphological change from user-defined perspectives within the model. These two scenarios correspond to the ‘here’ (the current landscape) and the ‘elsewhere’ (a simulacrum of landform change) respectively, of the Pimentel and Teixeira (1993) virtual environment representational scheme (see chapter 5). Most of the work done so far on virtual geo-representation has focussed on realism and reconstruction. Yet this representational form also allows other perspectives to be explored, ones that cannot and will not ever be seen directly, but ones that could be constitutive of multidimensional change. Hence, this chapter will also explore new analytical and exploratory virtual geo-representations in an attempt to ‘see’ change in geo-phenomena multidimensionally. A new 3.5D visualisation approach was developed using analytical drapes over virtual geo-representations. These representations are much more complex that those used traditionally. Note that Shneiderman (1997) has argued that the human cognitive system can cope with more information than usually presented in current user interfaces, if they are well designed.

VIRTUAL GEO-REPRESENTATION OF COASTAL CHANGE These experiments explore the possibilities of virtual geo-representation in both realistic and analytical environments. These perspectives are used to situate the user in an environment (the realistic model) and then to allow the exploration of multidimensional representations of coastal change.

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Interfaces to virtual geo-representations Modern virtual environments offer a powerful visual experience: on coming face-to-face with the real place, one of the author’s own students, having earlier explored a model of that location, commented immortally ‘it looks just like the virtual world’! Plates 8.1 and 8.2 (similar to the ones the student saw) show the hilltop view over the coastal plain and the equivalent ‘virtual view’ of the virtual geo-representation, which is a terrain model draped with a satellite image. Although the virtual view lacks buildings, colour and people it is recognisably the same place, especially wihen viewed dynamically. More sophisticated virtual reality systems can produce much more realistic geo-representations. The virtual geo-representation shown in plate 8.2 can be explored by the user through the standard PC interface, using the mouse and its buttons to move around. However, without pre-existing knowledge of the location it is difficult for users to orient themselves in the virtual geo-representation. This led to the development of the VRGIS system (Raper, McCarthy and Williams 1998) which added a map interface alongside the virtual geo-representation. The VRGIS 1.0 system illustrated in plate 8.3 is made up of two main windows: virtual reality (right) and GIS (left). In the application illustrated in plate 8.3 there is a dynamic element in the virtual world viz. an aerial survey plane that moves around. The terrain model grid cell in the VR window vertically below the survey plane is highlighted as it moves over the terrain. The yellow rectangle in the GIS window displays the current aircraft position on the map, and the black stars show the previous positions of the aircraft since it began to move. As the plane flies around in the virtual world, the map scrolls to keep up with the plane. In VRGIS 2.0 constructed as part of the Virtual Field Course (Dykes, Moore and Wood 1999), the ability to change the map and the VR surface drape were added to the interface (plate 8.4). Users were given greater control over the movement in the virtual world with options to specify a height of movement or to enter terrain-following mode. By clicking on the map users could also query features on the map and receive a report of all the attributes attached to the vector or raster data at that point. The ability to read source data from the Virtual Field Course hubserver was added so that the system could read metadata and import data from remote sources. Analysing coastal change using virtual worlds The challenge of showing change in a three-dimensional geo-representation, such as the evolution of a landform, are considerable. On Scolt Head Island the spits at Far Point grow, move and change shape, all at the same time, making it difficult to track their evolution. Since the spit landforms are only represented in a 2.5D surface model, visualising their dynamic behaviour can be termed a ‘3.5D problem’. One attempt to present this information was to use the Virtual GIS room developed by Neves et al. (1999) to view the terrain models in an exhibition. Each model in turn could be selected from the ‘wall’ display and placed on the ‘table’ in the Virtual GIS Room and examined by the user from any angle or resolution (figure 8.1). While this approach was useful, it did not meet the need to visualise and analyse the full dynamic behaviour of the landform morphologies as it was not possible to see the changes that occurred between models.


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Figure 8.1 Scolt Head Island Far Point spits in a gallery in the Virtual GIS Room with the currently selected model displayed on the viewing table

A 3.5D geo-representation requires comparable surface models, an analysis of the change that has occurred and a visualisation of the dynamic behaviour as it occurs. In this experiment the surface models were produced using TIN methods as there were a large number of surface elevation point samples in each time period, and from field experience, these were known to capture terrain shape well. For analysis of the evolution of the spit geo-phenomena two potential methodologies can be identified: ‘window of comparison’ methods; and ‘regions on surface’ methods. Each of these methodologies can be implemented for both TIN and grid raster surface modelling approaches. The ‘window of comparison’ methods are based on the assumption that successive surface models constructed from point sampled data can be compared within the same georeferenced frame. Various possible frames of comparison can be defined depending on overlap and the type of surfaces to be evaluated. Firstly, all surfaces can be compared


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using a mimimal fixed frame such as the unique area of overlap between all the surfaces in a set. This approach has the advantage of strict comparability as it compares the character of the surface at the same location, but has the disadvantage of ignoring the information from the surfaces lying outside the minimal fixed frame. Secondly, all surfaces can be compared using a maximal fixed frame where the surfaces are compared against an area containing all the data points from all the surfaces. This approach has the advantage of having no redundancy as all the data points are used in comparisons. However, many of the surfaces will be compared against ‘no data’ areas for other surfaces. Sometimes the area of actual overlap may be quite small (or even non-existent) for surfaces created from samples that are far away from each other in time and where the geo-phenomena moves rapidly (e.g. a cyclone) Other ‘window of comparison’ methods may be defined which use the overlap of each pair of surfaces. A logical AND comparison between two surfaces will give results for the unique area of overlap and will ignore areas where only one surface has data. The disadvantage of this approach is that the surfaces are compared against a ‘local’ overlap zone, specific to the two surfaces, and are not compared against any ‘global’ comparison frame that is of significance to the whole set of surfaces. Comparisons can also be made by using externally defined zones in two dimensions to define ‘windows of comparison’: examples would include low tide or mean atmospheric pressure lines. Comparisons between surfaces can also be made by ‘regions on surface’ methods which identify parts of both surfaces to be compared. Firstly, the surface can be regionalised by a partition of the z attribute (e.g. elevation) and the area of the zones enclosed by these regions can then be compared for overlap and area. These methods have the advantage of using a ‘global’ criterion for comparison that can be used for any pairs of surfaces, but the disadvantage that the ‘region’ frame of comparison is fixed through time. Secondly, the surface can be regionalised by overlaying a secondary map with zones of significance for the comparison e.g. sediment type in geomorphology or areas of rainfall in meteorology. In this case, the surfaces are compared in terms of the correspondences of the z attribute within the ‘significance’ zones defined. This method has the advantage of using a physically based zone of comparison but the disadvantage of using a comparison method employing secondary rather than primary attributes of the surface. The pairwise surface to surface comparisons produced by ‘window of comparison’ or ‘regions on the surface’ methods can be used to generate a third surface showing the change. These change surfaces have both positive and negative values reflecting the surface differences and are amenable to further analysis. Change surfaces can be calculated for raster grids by simple subtraction. For TIN’s the value of the change is determined by interpolating the value of the point in the second surface at the x, y location of the point in the first surface. Positive values indicate accumulation or increase in the z attribute while negative values indicate removal or decrease in the z attribute. The positive and negative zones can be delineated by a zero change line, which can be mapped through time. The identified changes can be ‘balanced’ by a comparison of volumes between positive and negative areas, if it is clear that no net gain/loss over the external boundaries of the models takes place. Note, however, that these changes could either be indicative of change in situ through time, or of the movement of a phenomenon


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through space over time: the change identified must be physically explored and justified in itself. In this experiment the data availability and the dynamic behaviour was such that a ‘maximal fixed’ frame approach produced the most useful surface to surface comparisons. Areas in one model compared to ‘no data’ areas in the other were unchanging and have been ignored. Since each ‘change surface’ spans two time periods, each survey surface also belongs to two change periods, i.e. ‘change up to this point’ (past); and, ‘change from this point on’ (future). Plate 8.5 shows two surface models (with different data coverage) of the Far Point spits for September 1993 and March 1994 shaded by elevation. To visualise the change of elevation between these two surfaces the differences between them were calculated by TIN techniques and visualised using a dichromatic legend palette from red (deposition) to blue (erosion). This change surface was then draped over the earlier survey surface i.e. September 1993 (plate 8.6). The model in plate 8.6 shows where the deposition that will take place in the next six months will occur in a ‘change from this point on’ type representation. Positive redorange-yellow changes are located in the prominent east-west trending intertidal bar north of the spits and at the end of the ‘current’ spit. Negative blue-purple changes are located along the northerly edge of the spit and at the southern end of the ‘inner spit’. As it is difficult to find any one position within the virtual world where all the change can be seen at once, the model has been built using VRML so that the user can move around within the change-draped-surface model. This geo-representation gives an analytical view of the change allowing the exploration of the differences between the survey maps. As the VRML model allows the surface draped over the model to be changed quickly, the ‘change up to this point’ surface can also be displayed to explore the change prior to the current time period. These geo-representations are good examples of ‘simulacra’ type defined in the Pimentel and Teixeira (1993) classification of virtual environments. Time-dependent display of virtual worlds Virtual environments can also be used to display time-dependent behaviour. In the coastal environment the diurnal tidal cycle changes the processes operating on the spits and strongly influences accessibility to the island. Visualising this behaviour involves calculating the height of a given tide in metres and ‘flooding’ the model to that depth by inserting a tide water object. Plate 8.7 shows a surface model of the sea wall and marsh south of Scolt Head Island captured using laser surface-profiling LIDAR techniques and shaded for elevation. Since LIDAR has a footprint of 2m and is accurate to a few centimetres, every building, tree, yacht mast and telegraph pole is shown. The model has a ‘spiky’ appearance due to the vertical exaggeration of these features. Both high and low tide states of the tidal model as calculated in the Arcview GIS are displayed using 3D Analyst. An automatically updating display could be calculated if the tide water object was given temporal attributes.


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POTENTIAL The use of virtual environments has huge potential to represent the inaccessible reality and ‘unseeable’ phenomena of geo-phenomena. These experiments show some examples of multidimensional geo-representations showing how they can extend the scope of current representation. In particular, virtual environments make it possible to develop 3.5D representations to allow the analytical exploration of multidimensional change.

CHAPTER 9 Three-dimensional modelling of coastal landforms CONTEXT Understanding the genesis and evolution of sedimentary landforms requires knowledge of their internal structure and sedimentary facies composition so that the depositional environment of formation can be reconstructed. Such knowledge can come from natural field exposure, destructive sampling such as boreholes or non-destructive sensing such as geophysical surveys. In the absence of natural exposures, representational techniques are needed to reconstruct the structure and composition of landforms. The simplest georepresentation that can be created is a cross section, which can be produced by linking together boreholes or interpreting the plot produced by a geophysical survey. These cross sections can be used directly or, by picking sedimentary strata of interest from all available cross sections and interpolating their elevation values, it is possible to form single-valued surface models. Surfaces can be stacked together and intersected where necessary to form pseudo three-dimensional geo-representations, which divide but don’t enclose space (see chapter 4). While sedimentologists have developed many significant sedimentary facies models based on such information (Miall 1983, Anderton 1988), it is accepted by many that where depositional environments are complex it is difficult to resolve some problems of interpretation (Kelk 1992). Accordingly, sedimentologists have looked to new threedimensional representational tools to make models of complex sedimentary environments (e.g. Orlic and Rösingh 1995). Solid three-dimensional geo-representations allow the reconstruction of sedimentary architectures and permit the interpolation of volumetric property variation. The insights gained from such new geo-representations have advanced the science and practice of sedimentology in the last few years and offer further new opportunities for research when suitable datasets are collected. In coastal sedimentology and geomorphology, barrier island and tidal inlet landforms and processes pose considerable scientific and management problems due their highly dynamic behaviour (Biegel and Hoekstra 1995). One element of the landform assemblage in this environment is the spit landform: ‘a detached beach that is tied to the coast at one end and free at the other, with a free end that often terminates in a hook or recurve’ (Raper et al. 1999). Spits are usually produced by longshore movement of sand and gravel across inlets where wave and tidal processes interrupt the shore parallel movement of sediment and recurve the landform into the inlet. Since spits are highly mobile they often require active management (Bradbury and Kidd 1998), which depends on their monitoring (Zuhar et al. 1997) and analysis of their mobility (Riddell and Fuller 1995). Spits can also be regarded as barometers of contemporary sea level change and

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they serve as useful analogues for the coastal environments reflected in the many sedimentary basins of economic importance. On Scolt Head Island Steers (1960) suggested that the main east-west trending barrier and the spits recurving to the south were composed of ‘shingle’ (gravel and cobbles), which formed a platform extending under the salt marsh muds. The widespread existence of shingle was confirmed in a comprehensive study by Allison (1985), who augered 42 boreholes in locations across the island, encountering shingle at depth in 21 holes. However, the work by Allison concentrated on the stratigraphy and did not make any detailed investigation of the relationship between the spits, the salt marsh muds and any underlying ‘platform’. The question of the formation of the spits has remained unexplored. A project to drill boreholes into a small segment of a spit on Scolt Head Island was undertaken to develop a three-dimensional geo-representation of its composition and sedimentary architecture. Such reconstructions allow the linkage of form and process to composition and structure. Two alternative three-dimensional modelling approaches were used to create the geo-representation of the spit segment: firstly the Earthvision minimum tension approach, and secondly the tetrahedron modelling approach developed by Lattuada (1998). The geo-representations produced by these two systems are compared to assess their relative merits for sedimentological explanation.

EXPERIMENTS IN THREE-DIMENSIONAL MODELLING OF COASTAL LANDFORMS The set of borehole data used in these experiments into the three-dimensional georepresentation of spit sedimentary architecture came from the south Privet Hill field site on Scolt Head Island (figure II.2). The Privet Hill relict spit runs 500m NNW to SSE from Privet Hill (a relict sand dune) to Norton Creek, separating two marshes. The crest of the Privet Hill spit lies 3.8–3.9m above Ordnance Datum (OD), while the marshes are now only 1m lower at 2.8m on the younger, west side, and 3.0m on older, east side. The tidal range in this area extends from around 1.3m OD to 4.0m and closely mirrors the height of the spit. In cross section the bar is asymmetrical, being steeper on the eastern (formerly inner, sheltered) side. At the south Privet Hill field site 26 holes were bored in a 52m by 32m rectangle placed across the bar, and are distributed within the site at approximately 10m spacing (figure 9.1). The positions of these holes were surveyed onto a local grid oriented to magnetic north, and tied to a benchmark on the crest of the bar. The holes were bored to a maximum of 5m depth using percussion coring techniques. A full sedimentological log was compiled from the core at the time of recovery, and samples were taken every 25cm. These samples were analysed to determine their particle size distribution (PSD), that is the percentage of the sample falling in a range of particle size classes ranging from gravel to clay. To determine the PSD the samples recovered from the 20 holes were: • sieved using the aperture sizes shown in table 9.1, with samples having substantial fine fractions below 4 (63 microns) being further analysed analytically in a sedigraph machine (128 samples, 12 holes); and


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• processed in a laser granulometer device (119 samples, 8 holes)

Figure 9.1 The sedimentary logs of the recovered core for the south Privet Hill site

Table 9.1 Sieve aperture sizes used in mm (upper row) and phi ( ) (lower row) 16

8

4

2

1

0.71

.5

.355

.25

.18

.125

.09

.063

.045

.038

−4

−3

−2

−1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

4.75

The statistical parameters that were chosen to describe the samples’ grain-size distributions were the mean, standard deviation (sorting), skewness and kurtosis. The method of calculation was based upon the experiments by Swan et al. (1979) who indicated that the errors due to grouping the grain sizes within an interval of one central measure were small as long as the interval was also small: ie 1 or smaller. Swan et al. (1979) also concluded that lumping the unanalysed sediments (finer than the smallest sieve aperture) into one lower fraction gave statistically valid results if the unanalysed percentage was less than about 12%, but above 12% the mean becomes less accurate. For most sediments, Swan et al. suggested a bounding measurement value of 10 or 14 , however, 5 is sufficient for sands and gravels. Since samples with more than 30%


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unanalysed sediment may have a mean that does not fall within 0.5 of the real value these values were treated with caution, although in most cases these samples have a clay size mean which the missing data would not change. In this study only the mean particle size in phi units ( ) were modelled. In three dimensions this is equivalent to a set of 247 mean particle sizes arranged in 20 vertical sequences at 25cm vertical intervals. The objective of the modeling process was to develop a three dimensional georepresentation of the sedimentary architecture using sample data, which was consistent with the sedimentary log of the recovered core (figure 9.1). This model could then be compared with the hypothesis that these relict spit bars are composed of ‘shingle’ (gravel and cobbles) connected directly to an underlying platform composed of the same sediments. It may also provide an insight into the processes of spit formation and development. Minimum tension isosurface modelling The Earthvision system was used to interpolate from scattered data to a 3D grid using minimum tension isosurface modelling, and, to create isosurfaces from the 3D grid. However, the selection of interpolation options strongly influences the characteristics of the model. This is primarily because a deterministic three-dimensional interpolator is highly dependent on the input options. It is necessary to control inputs and evaluate outputs carefully to avoid the generation of models with artifacts. In most cases this involves the creation of several generations of models with quality assessments of each. The most important inputs to the Earthvision modelling of sedimentary architecture are appropriate structural constraints. In this case examination of the sedimentary logs showed that 21 out of 26 holes contained a single or double layer of mud (similar in consistency and grading to marsh mud) which appears to pass right through the spit below the level of the modern marsh surface. Since this is an important structural feature of the sedimentary architecture it was decided to divide the data points into three zones using the upper and lower surfaces of this ‘mud’ zone as boundaries. These surfaces were created separately in Earthvision by using the 18 data points with ‘mud’ depths in an area 5% larger than the bounding box containing the 20 boreholes with the completed sample analysis. A mean grain size property model was made for each of the ‘lower’, ‘mud’ and ‘upper’ structural zones. The top of the model was clipped using ground elevation data, while the deepest point reached in boring was used as a clip for the base. In forming the model the following Earthvision interpolation settings were selected: • Conformality: all three grids were interpolated such that each was both top-and bottomconformal. This option was selected since it was considered likely that sedimentation had been influenced by the palaeo-topography of the mud unit and by the surface topography of the bar itself. • Zone expansion: a zero ‘zone expansion value’ was used to prohibit interpolation using values outside, but adjacent to, each zone grid, since inspection of the sedimentary logs indicated that the mud layer represented a sharp hiatus in sedimentation. • Property value range: after experimentation it was decided to restrict grid values to the exact range of data values in the scattered data within each bounded zone. Without this


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constraint it was found that some improbably high and low values were generated by the interpolation process, probably due to the rapid changes in mean grain size over short vertical distances. • Z-influence factor: the default value of the ‘Z-influence’ factor was used because experimentation showed little difference in the resultant grids, even if a factor of 0.5 was used to introduce greater horizontal influence in interpolation. The final model shaded by mean grain size in units is shown in plate 9.1. Model quality was assessed by checking the model against the sedimentary logs, and by evaluating the residuals between the input data points and values calculated from the grid at those locations (‘back interpolation’). The upper and mud zones have a wide distribution of residuals indicating that in some locations the grid has generated some spurious values. However, the lower zone has a very narrow range of residuals suggesting that the grid approximates the mean values of the samples well. In order to produce the best possible grids for three dimensional geo-representation, the grid of residual values was added to the first grid to create a ‘corrected’ grid in which all mean grain size values from the samples match the values in the grid. Two main theoretical problems arise which cannot be precisely resolved. The first problem concerns the use of the mean as a one-dimensional summary of the grain size distribution. Swan et al. (1979) pointed out the conditions in which a mean was an acceptable estimate of the population given standard calculation procedures and assumptions. Ultimately, the mean best summarizes uni-modal, well-sorted sediments. This was a condition that seemed to be acceptably met in the present case. A second theoretical problem concerns the widely differing sampling interval between x-y (10– 20m) and z direction (mostly 25cm). This clearly poses problems for an interpolation algorithm, although the problem is partly alleviated by using a different number of grid cells in the horizontal and vertical axes. In this study the horizontal grid cells were 1m square, but 0.1m thick in the vertical direction: a ratio of 10:1. Despite the qualifications noted above, much can be learned about the sedimentary architecture of the spits. The three zones are now examined in turn and compared with the generally accepted hypothesis of bar formation. The crest of the bar viewed in plate 9.1 can clearly be seen crossing the model diagonally runs SENE: the base of the ‘upper’ zone is delineated by the thin blue coloured ‘mud’ zone. At the surface of the ‘upper’ zone the west (left) side of the bar is made up of muds from the modern salt marsh while on the east (right) side the model is composed of coarse, largely gravel sized sediments. Viewing the model from the SE it can be seen that there is an extremely sharp gradient between the west side muds and the east side gravels, and little sign of a ‘core’ is evident. Sedimentary logs suggest that there are ‘accretionary’ layers of medium sands and fine gravel in the core of the bar that are characteristic of a beach. However, little structure can be determined for the core of the bar in the model due to the high variability of the sediments relative to the frequency of vertical sampling. The ‘lee side’ gravels on the east side (which can clearly be seen in the sedimentary logs) are inferred to be a wedge of washover sediments associated with the active development of the bar, probably indicating that storm tides overtopped the bar from left to right as viewed. The mud zone can be seen to pass right under the bar and under the modern salt marshes. From the sedimentary logs it is known that this actually occurs, but it is not clear


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whether the two zone merge or whether the more recent marsh muds always overlie the mud zone in the spit. At present it is suggested that the mud zone is the remnant of a marsh which was developing in the lee of the developing bar, and that the whole bar has migrated over the mud by a process of overwashing. This has preserved what was originally a lee side salt marsh under the spit itself. It is also likely that on the side of the bar exposed to wave attack, the mud was progressively removed as the bar migrated east. The composition of the lower zone can be seen as a fining up sequence, perhaps indicating a reduction in energy as the spit developed here. Tetrahedron-based modelling The tetrahedron-based approach of Lattuada (1998) was used to produce a different georepresentation of the spit sedimentary architecture using the same boreholes and samples (see chapter 4). Tetrahedra-based modelling algorithms structure the data points directly by triangulating them in three dimensions to form solids; there are few parameters to influence the outcome. In this case the data points are close to each other in the z dimension and more widely spaced in x, y meaning that the tetrahedra formed are very thin. In order to improve the performance of display and analysis, the tetrahedra were subdivided using data points added inside the tetrahedra produced from the original data (Lattuada and Raper 1995). The completed model is shown in plate 9.2, viewed from the east, and showing the NNW to SSE trending ridge (shaded orange). In tetrahedra models a method is needed to assign attributes from data points to tetrahedra. Starting with the base triangulation the ‘added data points’ are assigned attributes based upon the influence vertices in the surrounding Voronoi region. Where constraints have been added to the tetrahedra then limits are placed on interpolation in certain directions. If the attributes are assigned discretely to tetrahedra then points on the boundary may have different attribute values depending on the direction from which they are approached, i.e. the tetrahedron through which they are approached. Once all the original and ‘added’ data points have attributes, then normals are computed for triangles to determine tetrahedron membership of triangles. Attributes can be calculated for each tetrahedron depending on the attribute values calculated for its four triangular faces. The resulting attribute shaded tetrahedra in plate 9.2 are a function of data point weighting. The model is shaded by particle size such that the coarser sand and gravel of the spit picks out the line of the ridge, while the muds of the marsh extend out to the west. The sands of the underlying sedimentary platform are visible at the base of the model. The geo-representation can be broken down into attribute zones or individual tetrahedra by simple boolean operations.

POTENTIAL Both of these geo-representations suggest that the spit is not made of gravel nor is it connected to a coarse underlying deposit as Steers (1960) and Allison (1985) suggested. The models offer support for the view that the spit was being forced back to the east as it recurved to the south since the mud layer cannot have formed in situ, and must have once


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formed a lee-side mudflat/salt marsh. These insights can be gleaned from figure 9.1 but visualisations of sedimentary logs such as this are hard to place in any elevational framework. The two models have distinct advantages and disadvantages as geo-representations. The Earthvision model is easier to view and explore as it is made up of smoother geometric elements than the tetrahedra approach of Lattuada (1998). However, the tetrahedra are a more conservative form of geo-representation since they only display tetrahedra bounded by data points or subdivisions of them unlike Earthvision, which has transformed the original data points into a grid. The grid base of Earthvision also promotes interoperability and error quantification through ‘back interpolation’ methods. The experience of making geo-representations using these two systems reinforces the need to carefully specify three-dimensional data modelling so that appropriate selections can be made during the modelling process.

CHAPTER 10 Multidimensional geo-representation in coastal environments CONTEXT One of the greatest challenges for geo-representation is the multidimensional process modelling of geo-phenomena. This is a definitively four-dimensional problem, where process and forms must be fused in a structural and functional representation. The goal of multidimensional process modelling is the simulation of geo-phenomena using boundary conditions and mechanisms derived from empirical investigation. It is accepted that the outcome will not be and can not be ‘realistic’ in the metaphysical sense. The aim is rather to make a projection from a known starting point and then to compare the model outcome with independent observed outcomes. The comparison should pose further epistemological questions and generate new ontological concepts to motivate the rethinking of multidimensional identity and evolution. Developing multidimensional process modelling for the coastal environment is challenging because the processes change forms and the forms change processes in a reflexive cycle that operates at high frequency. In the case of coastal spits there is evidence from the elevation surveys (chapter 7) and from the theory of May and Tanner (1976), that the movement of sediment along the shoreline by waves is controlled by shoreline cells formed out of the incoming incident wave field by infragravity waves (oscillations at right angles to incident waves). Waves focus within shoreline cells, i.e. wave crests become slightly concave shoreward when viewed from above, so that waves are larger at the centre of the cell (which can be 100–300m across). This means that sediment transport along the shoreline is highest where the waves are highest (cell centre), and lowest at the cell margins, with transport being driven overall in the direction of the wave approach. Sediment movement speeds up and slows down as it is ‘handed on’ from cell to cell, which is consistent with some features of the animation discussed in chapter 7. Wave refraction and diffraction recurve the cell shape to produce the typical spit morphology. When trying to develop multidimensional process models for coastal spits a number of representational problems emerge. Firstly, it is clear that much of the sediment transport goes on in the narrow swash zone as it moves up and down with the tide, yet almost all computational designs use the same spatial resolution close to the shore as elsewhere. Secondly, it is difficult to develop shoreline cell implementations with the ability to self modify under variable wave direction inputs. Thirdly, most models do not simulate ‘storm reconfiguration’ which may push the spit out of position and enable an intertidal shore-parallel bar to extend into the newly vacated space. Despite these limitations a multidimensional process model based on the SEDSIM system has produced results that

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raise further questions about coastal behaviour. Multidimensional exploration of geo-phenomena can also be envisaged when large amounts of spatially and temporally referenced data have been recorded. The ability to carry out four-dimensional range queries on multidimensional datasets poses new representational and analytical challenges. This research aims to identify ‘emergent’ behaviour by exploring the space-time structure of the geo-phenomena.

MULTIDIMENSIONAL COASTAL GEO-REPRESENTATION EXPERIMENTS Simulation of spit morphodynamic behaviour The SEDSIM model was developed by Tzetlaff and Harbaugh (1989) to simulate the erosion, transport and deposition of sediments in three dimensions over geologic timescales. SEDSIM was originally developed to simulate unidirectional unsteady flow in rivers, but has since been modified by the addition of the WAVE module (Martinez and Harbaugh 1993), which allows the simulation of coastal and nearshore environments affected by wave-induced erosion, transport and deposition. SEDSIM/WAVE is a hybrid four-dimensional finite-difference/finite element model that simulates wave-induced nearshore currents and is linked to algorithms that redistribute sediments in response to these currents. The model simulates incident waves, wave breaking, surf zone radiation stress, longshore currents, wave-current interaction and nearshore sediment transport over three dimensional deformable sea bed surfaces. Modifications to the operation of the model have been made by Livingstone and Raper (1999) and Raper et al. (1999) to optimise SEDSIM for spit evolution modelling over engineering spatial and temporal scales. Thus, the model was run for periods of months and years over a grid of (variously) 500m to 1500m in dimension. The three-dimensional modelling in SEDSIM/WAVE uses simplified assumptions for calculating longshore transport within the surf zone but a complex morphological representation of that transport, which feeds back into morphological change into the model at each time step. The three-dimensional model provides incident wave control, wave breaking over input sea bed topographies, variable sediment transport across the breaker zone, differential movement of four grain sizes, onshore-offshore sorting of sediment and a mobile bed of sediment. SEDSIM/WAVE determines which cells are in the breaker zone by comparing their current elevation with the input wave base. The empirically determined sediment transport rate is distributed over this breaker zone area according to the approximation of cross-shore and longshore transport. Since most radiation stress is dissipated within the surf zone as longshore and onshore-offshore currents the momentum from the wave field is dissipated among the cells in the breaker zone. This is achieved using a non-linear cross-shore function for each shore-normal column of grid cells, which is at a maximum just shorewards of the breakers, falling off to a minimum offshore and at the shoreface. This approach simulates cross-shore variation in bed shear stress on a time and depthaveraged basis as real onshore-offshore processes oscillate with each passing wave.


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SEDSIM/WAVE models sediment transport for four different user-specified grain sizes by using a transportation efficiency factor derived from the threshold shear stress required for entrainment. To approximate the net change in the elevation of the bed in the surf zone, SEDSIM/WAVE must model erosion and deposition of sediments under the specified sediment transport rate in the calculated breaker zone. SEDSIM/WAVE uses a series of ‘accounting procedures’ to manage the transportation of the sediment. SEDSIM/WAVE calculates the entrainment of sediments and the amount of each grain size that is removed. It then moves this sediment to the adjacent cell under continuity constraints and deposits it, leaving the remaining sediment in its existing grid cell. Grid cells are filled and emptied by deposition and erosion during a user-prescribed number of time steps, before the sequence of sediment types in the cell is ‘closed’ and recorded (it can still be eroded later). Finally, cross-shore sorting of grains are simulated by redistributing the proportions of different grain sizes without changing the elevation. The ‘topography generation’ program ‘Sedmodel’ was developed in Arcview GIS using the Avenue programming language so that controlled experiments can be created and converted to a format suitable for SEDSIM/WAVE. Sedmodel allows ‘basement’ topographies to be built from imported polygonal shapes to represent coastline configurations like headlands and bays. Sedmodel also allows the creation of ‘deposit’ layers of deformable sediment in conformance with the ‘basement’ topography. Wave inputs were specified as a transport rate in the surf zone, which were based upon the empirical expression developed by Komar and Inman (1970). These topographic and process inputs were scaled to the conditions on the North Norfolk coast based on field experience there. Since the fundamental objective was to ‘reverse engineer’ spit evolution a systematic trial and error approach was taken to the experimentation. Once the calibration had indicated the stable ranges for the input parameters both separately and in combination, a set of experiments was designed to promote spit growth. A number of experiments were run over a simulated three month period with a constant wave climate to study the influence of wave direction on spit development. An initial topography was selected that had proven stable in conjunction with a range of input parameters. The topography consisted of a 4m thick deposit of sediment draped over a predefined basement designed to simulate a simple headland with an acute angle with a constantly sloping beach at an angle of 1:15. Each experiment used the wave rate form to specify wave climate. The experiments can be visualised as surface models in plate 10.1. In the centre map of plate 10.1 waves were coming directly onto the beach from the south while other models showed waves coming increasingly from the east or west. The experiments clearly show the sensitivity of the model to changing wave direction. The growth of landforms with a spit-like morphology is more pronounced as waves swing round from south towards the south-west. The direction of wave approach that produced features with the most spit-like morphology was approximately in the range 20 to 40 degrees west of model south. Inspection of wave data for the North Norfolk coast indicates that the most frequent waves have a similar direction of approach. While the models are sensitive to input change and show moderate similarity with Scolt Head spit features, the real value of these models lies in their potential for investigating critical controls on spit-formation, such as angle of wave approach.


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The experiments have shown that the SEDSIM/WAVE model can simulate the longshore movement of sediment to form features like spits that develop in a similar way to those observed in morphodynamic monitoring. Using the inverse modelling approach of Cowell, Roy and Jones (1995) this work has shown how to stabilise the model parameters for engineering time and spatial scales and with appropriate wave energy and sediment transport values. The modelling reported here shows how spits evolve under steady state conditions in swell wave environments and bear a similarity to recorded change at Scolt Head Island. Three-dimensional models like SEDSIM/WAVE are potentially valuable tools for investigating the effect of nearshore topographies and wave approach angles on spit evolution and can show how sea bed elevation can feed back onto spit evolution. Currently the model is limited in its ability to handle variable wave approach, variable sediment transport rates, tides and wave tide interactions and nondepth-averaged radiation stress in the surf zone. In the future it is hoped to introduce real wave climates based upon wave measurements as well as tidal flows. Multidimensional exploration of coastal change A further challenge for multidimensional geo-representation is the ability to explore fourdimensional datasets for patterns or conjunctions that are constitutive of geo-phenomenon identity. The superset of all data points collected for elevation surveys at Scolt Head approaches 17,500 over eight years (plate 10.2). This dataset, where each point describes surface elevation at-a-time, can be explored multidimensionally to seek evidence for some of the behaviour conjectured for the evolution of spits. For example, this data can be searched for spit slope facets that are close in space-time to other spit slope facets where the angle has changed considerably. Such discoveries may shed light on the idea that sediment moves along spits in pulses, whose movement is often correlated with slope angle change.

Figure 10.1 Two spit cross sections at the same spatial location but one month apart

Plate 6.1 Reproduced by kind permission of Ordnance Survey © Crown Copyright NC/00/1136. The 1:50,000 scale topographic map of the North Norfolk coast around Brancaster in Arcview GIS overlaid with points representing aerial photograph locations.

Plate 6.2 An SQL connect operation using the Open Database Connectivity (ODBC) protocol in Arcview GIS, which links to a table in a Microsoft Access database containing geometric and attribute data for coastal landforms.

Plate 6.3 Reproduced by kind permission of Ordnance Survey © Crown Copyright NC/00/1136. The 1:50,000 scale topographic map of the North Norfolk coast around Brancaster in Panoramap, overlaid with orange points representing the location of photographic images, two of which are shown with their respective fields of view. Courtesy of Virtual Field Course (J.Dykes).

Plate 7.1 Four sequential video frames of breaking waves filmed from the air. Courtesy of Airborne Videography Ltd.

Plate 7.2 A strip map made from aerial video imagery for the mouth of the Ore River at Shingle Street in Suffolk. Courtesy of Airborne Videography Ltd.

Plate 7.3 Surveys of elevation at Scolt Head since 1993 (label gives month and year of survey). Spit landforms denoted by dark brown colour.

Plate 8.1 A hilltop view over the coastal plain showing Brancaster Staithe and Scolt Head Island (land on right hand side of the channel extending away from the viewer).

Plate 8.2 The equivalent virtual geo-representation of the view shown in plate 8.1 made by draping a terrain model with a satellite image in Sense8 WorldUp.

Plate 8.3 VRGIS 1.0. The virtual world is displayed on the right with a moving aircraft and the terrain grid cell vertically below it being highlighted as it moves. The map on the left shows the track of the aircraft and its current position inside the yellow rectangle.

Plate 8.4 VRGIS 2.0 with controls for viewing and querying the virtual world and the map. Courtesy of the Virtual Field Course (T.McCarthy).

Plate 8.5 Two surface models (with different geographical data coverage) of the Far Point spits on Scolt Head Island for September 1993 and March 1994, shaded by elevation. The orange colour corresponds to the dark brown colour of plate 7.3.

Plate 8.6 The change of elevation between September 1993 and March 1994 for the Far Point elevation surfaces calculated using TIN techniques and visualised using a dichromatic legend palette from red (deposition) to blue (erosion). The arrow shows a bright orange/yellow location in the VRML model where high deposition took place in this time interval.

Plate 8.7 Surface model of the sea wall and salt marsh south of Scolt Head Island, captured using laser surface-profiling LIDAR techniques and shaded for elevation. Data is copyright Environment Agency.

Plate 9.1 Three-dimensional minimum tension isosurface model of the spit section at the Privet Hill south site shaded by mean grain size phi ( ) units.

Plate 9.2 Three-dimensional tetrahedra model of the spit section at the Privet Hill south site shaded by attribute ranges. Courtesy of R.Lattuada.

Plate 10.1 Surface models showing coastal sedimentary landforms generated by SEDSIM experiments. Courtesy of D.Livingstone.


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Plate 10.2 The 17,500 superset of all data points collected for elevation surveys at Scolt Head over eight years between 1992 and 2000.

In the research at Scolt Head Island this kind of four dimensional query has been implemented experimentally. The experiment called for the creation of firstly, a database of morphology, composition and process information which was standardised in terms of coordinate system and spatial/temporal datum, and secondly, a multidimensional access tool allowing the user to specify spatio-temporal queries on this data. Data collected across space and time was stored in the Arc View GIS as a series of geometric layers. Arcview was used to measure distances and height differences between points at a similar position in absolute space for the two different times. In figure 10.1 the two cross sections show the profiles of the spit shoreface for two pairs of points that are very close to each other in space but one month away in time. Surveyed points represented ‘breaks of slope’ where slope angle changed sharply, suggesting that these observed differences reflect real changes in slope configuration. This multidimensional access tool allows the user to compare spatial locations at different times (for example, by the construction of time-difference maps) or to track the movement of spatial configurations through time. An improvement in efficiency can be expected if this access tool were to be implemented in a true four-dimensional GIS.


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POTENTIAL Multidimensional simulation and exploration are two new elements in an emerging multidimensional geographic information science. When space and time are fused into new representations new problems and opportunities for the reconstruction of multidimensional identity emerge. It seems likely that these new methodologies will open up new questions not previously attempted.

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Index

A A-series time, 104 abduction, 12, 200 absolute space, 34, 57, 66, 92, 101, 122, 126, 162 Access database, 212 Achilles, 86 ACIS volume model, 151 action-at-a-distance, 12 Adelard of Bath, 88 agents, 50, 193 agglomeration, 124 air photo interpretation, 79 Alberti, 53, 66 Alexandria Project, 195 algebraic topology, 125, 133 Al-Idrisi, 59, 64, 68 Al-Khwarizmi, 64, 68 allocentric, 38, 40, 42, 48, 82, 213 allometry, 130 Al-Mamun, 87 alpha shapes, 146 Alphaworld, 193 Analogue video, 176 animated GIF, 217 animation, 180, 191, 197, 198, 199, 201, 215, 217, 235 annotation structure, 208 anthropic, 8, 15 Anthropological, 4, 54, 56, 59, 109 antirealism, 14, 15, 16, 115 Apollonius, 90, 95 Arc/Info, 192, 198, 209 archaeology, 4 Archimedes, 95 architecture, 49, 54, 59 Archytas, 63 Arcview 3D Analyst, 155, 225 Arcview GIS, 212, 225 Aristotle, 6, 7, 32, 40, 63, 68, 86 arithmetic, 85 arrow of time, 108

Index artificial intelligence, 24, 36, 47, 49 astronomers, 125 attractors, 106, 127 attribute bundles, 163 audio, 177 autocorrelation, 127, 130 automata theory, 24 autopoesis, 24 avatars, 182, 193 axiomatisation, 105 Ayer, 11 B B-series time, 104 Babylon, 85, 126 back interpolation, 230, 232 Bacon, 11, 98 Baghdad, 88 Bartolomeu Dias, 69 basic-level categories, 51 Battle of the scales, 70 beach, 216 Beatus, 68 Bedolina petrograph, 67 Behavioural geography, 44, 47, 60 behavioural space, 73 Behavioural Time Sequence, 165 behaviourism, 16, 17, 18, 21, 23, 107, 110, 112 Berkeley, 7, 98 bifurcation, 106 big bang hypothesis, 100 binary trees, 146 binocular vision, 84 bintree, 170 Bohr, 101 Bolyai, 67, 97 bona fide boundaries, 41, 46 Boole, 106 boreholes, 227 Boundary Representation, 107, 145 Brancaster, 213 breaks of slope, 253 Brentano, 17 Broadbent’s rule, 111 Brunelleschi, 66, 90 B-spline, 144 Buache 70

294

Index C cancer cluster analysis, 201 Cantor, 24, 41, 95, 104, 105 CARIS GIS, 155 Carnap, 11, 15, 24, 102 cartesian scheme, 32 cartographic communication, 73, 75, 79 cartographic disinformation, 76 cartographic visualisation, 75 cartography, 4, 71 CASI, 218 Catastrophe Theory, 105, 126, 127 Cauchy, 96 causal chain, 166 causal relations, 38 causality, 12, 16, 28 Cave 3D, 155 caves, 179 cdv, 198 cell decomposition, 107 cells, 133 Cellular automata, 140 Centennia, 201 Central Place Theory, 110 centuriation, 68 Change Description Language, 163 change, 32 chaos, 86, 106, 119, 127 chaotic, 125 chat, 182 Chernoff, 182 Chinese and time, 85, 90 chora, 32 chorology, 34, 60 Christianity, 87 chronobiology, 108 chronos, 86 Chu Ssu Pen, 68 circadian clocks, 108 Clarke correspondence, 92 classification of spaces, 39 Classification Tree algorithm, 200 closed time, 103 closure, 132 coastal data management, 208 Coastal environments, 208 CoastMAP, 199, 212 cognitive collage, 44

295

Index

296

cognitive environment, 20 cognitive maps, 37, 40, 44, 48, 57, 58, 107 cognitive perception, 21 cognitive science, 5, 21, 23, 37, 76, 121 Collaborative Planning System, 189 collision detection, 180, 183 Columbus, 92 commodification, 27 common-sense psychology, 17, 23, 31 communicative action, 21 complementarity, 101 computational geometry, 49 computer science, 4 Comte, 8, 11, 16 conceptual schemes, 8, 10, 13, 18, 21 conditioned responses, 107 conditioning, 107 configurational knowledge, 47 Conformality, 230 conic sections, 66 conies, 90, 91 connectionist, 24 connotation, 27 connotative, 21 consciousness, 8, 12, 38 conservation laws, 98 consilience, 28 constant conjunction, 12 constructive modelling, 144 Constructive Solid Geometry, 107, 145 contagion, 32 Content Standard for Digital Geospatial Metadata, 195 content-based indexing, 215 contextualism, 33 contingency, 33, 81 contingent, 7, 9, 35, 121, 122, 123, 128 continuum hypothesis, 105 conventionalism, 102 convex hull, 146 convex spaces, 55 Cook, 93 coordinates, 65, 137, 140, 144, Copernicus, 6, 66, 69, 91 CORBA, 159 cosine rule, 141 cosmogenesis, 32 cosmogony, 32 cosmology, 84, 91, 95, 98, 101, 102, 116

Index CosmoPlayer, 192 Covering Law model, 12 critical rationalism, 11, 15, 110, 139 critical realist, 12, 15, 35, 113 critique of GIS, 80 cross section, 227 Cubists, 53 cultural milieu, 35 cultural universals, 51, 54, 57 CyberCity, 198 cycloids, 66 cyclone, 201, 224 D Daedalus, 156 daily envelopes of movement, 217 Data Information and Access Link, 196 data mining, 193, 199, 200 data warehouse, 200 database time, 165 decibel, 178 deconstruction, 76, 81, 113 deductivist, 12 deep structure, 121 deep syntax, 19 definition-limited, 136 Delauney Pyramid, 155 Democritus, 63 denotative, 21 depictive structure, 23 deposition, 236 depositional coasts, 208 depth cueing, 144 Descartes, 7, 11, 18, 40, 66, 91, 97, 98 Descartes system, 197, 200 desktop virtual reality, 174 determinism, 13, 16, 28, 59 deterministic, 8, 13, 23, 130, 138 developmental psychology, 47 Diderot, 33 différance, 34 differential equations, 125, 127 diffusion, 124 digital atlas, 197 digital camera, 216 digital elevation modelling, 142 digital library, 195 digital transition, 81

297

Index

298

digital video, 176 dimensional dominance, 162 Dionysius Exiguus, 87 direction of time, 101, 103 directionals in language, 52 discourse, 9 Discrete Surface Interpolation, 154 distanciation, 113 dogmatists, 11 Domesday System, 197 dualism, 7, 11, 18 Dublin Core, 195 dunes, 208 Dura Europa shield map, 68 durée, 33 dVISE virtual world, 183 dVS operating system, 183 DYNASED, 171 E Earth Observing System, 196 Earthvision, 157, 228, 230 Easter, 87 eclipse, 87 ecliptic, 93 ecology, 34 economic spaces, 60 economics, 137 edge detection, 49 edges, 146 egocentric, 38, 42, 48, 49, 82, 213 Egyptians, 85 Einstein, 14, 33, 67, 92, 95, 98, 99, 101, 102, 103, 105 electromagnetic fields, 95 electromagnetic spectrum, 176 ElevationGrid, 180 elliptic spaces, 67, 97 emancipatory, 17, 81 emergence, 22, 25, 36, 121, 131, 235 empiricism, 11, 14, 16, 26, 58 empty space, 32, 91, 101 Encarta, 197 encounter field, 56 Endurantism, 102, 123, 130, 136, 138, 165 engineering, 137 enough light and no fog, 180 enskifte, 61 entification, 34

Index

299

entrainment, 237 Enuma Elish, 32 environmental determinism, 60 environmental impact assessments, 204 environmental problems, 208 Epicurus, 63 epistemes, 111 epistemology, 5, 9, 10, 11, 16, 19, 28, 31, 58, 59, 60, 76, 98, 105, 115, 131 equations of state, 139 equifinality, 106, 123 equinox, 90 Eratosthenes, 64, 68 ergodic, 28, 47 erosion, 236 error, 131, 137 essence, 10, 126, 163 essential property attribute, 164, 320, 322 essentialism, 76, 121 ESTDM, 127 estuaries, 208 ETAK, 54 ether, 95, 99 ethics, 4, 5, 20, 80 Euclid, 11, 32, 39, 54, 63, 64, 67, 88, 91, 95, 96, 97 Euclidean geometry, 49, 71, 91, 97, 105, 106 Euler, 92, 94, 95, 96, 107, 146 Eulerian representation, 140, 170 European Spatial Metadata Infrastructure, 195 event horizons, 115 Event Pattern Language, 162 Event-based Spatio-Temporal Data Model, 164 experientialism, 10, 20 explanation, 3, 9, 12, 13, 16, 31, 32, 49, 60, 68, 75, 124, 130 exploration, 90, 92, 93, 119 Exploratory Data Analysis, 75, 200 Expo ‘98, 199 extended octree, 147 extended relational databases, 143, 183 Extensible Markup Language, 191 extension, 91 extrasignification, 74 F faces, 146 falsification, 110 fault, 135, 154 Federal Geographic Data Committee, 195 feedback, 195

Index

300

Fermat, 66, 91 fiat boundaries, 41, 46 Fibonacci, 65 field equations, 99, 100, 127 field trips, 140, 205 finite difference, 138, 140, 153 finite element, 137, 140, 153 flume, 216 formism, 33 four-dimensional GIS, 126, 253 fractal, 46, 49, 130 frame matching, 217 frames of reference, 129 Frege, 24, 106 Freud, 108 Fuzzy entities, 43 Fuzzy concepts, 103, 131 G gaia, 86 Galileo, 7, 91 Gauss, 11, 70, 97 gazeteers, 195, 197 geist, 8 gender, 167 General Geography, 59 General Systems Theory, 24, 139 General Theory of Relativity, 99 generalisation, 45 generative grammar, 19 geocellular, 156 geocentric reference systems, 51 GeoCid, 191 geocognostics, 50 geocomputation, 3 geodesic, 99 GeoExploratorium, 191 geographic individuals, 33, 46 geographic information bearing objects, 27, 196 geographic information retrieval, 196 geographic information science (GISc), 3, 10, 16, 19, 21, 23, 27, 28, 76, 84, 120, 125 geographic information systems (GIS), 3, 4, 76 geographic kinds, 40 geographic messaging services, 193 geographic metadata, 180, 195 geographic virtual environments, 174 geographic visualisation (GVIS), 75, 199 geographical entities, 41

Index geographical matrix, 111 geographical ontology, 40, 41, 44 geographical realism, 33 geography, 3, 4, 24 geolibraries, 194, 213 geolocation, 218 geology, 59 GeoMedia, 212 Geomesh, 153 Geominer, 200 geomorphological kinds, 121 geomorphology, 123, 128, 144 geo-phenomena, 81, 129 geophysical surveys, 227 geopolitical entities, 41 geo-representation, 4, 9, 81 geoscientific ontologies, 135 geostatistics, 130, 135 Geostore, 159 GeoToolKit, 159 GeoVRML, 180 Gestalt, 11, 19, 23, 107, 200 Giotto, 66, 90 Giraffe, 196 GIS-scape, 210 glacier, 171 Gläser, 69 Global Positioning System, 77, 217 God, 6, 7, 8, 11, 87, 91 Godel, 24 granularity, 37 Graph theory, 134 GRASS, 170, 194 gravitation, 91, 92, 99 Great Cities of Europe system, 189, 198 Greeks, 85 Gregorian calendar, 85 Ground Truth, 80 grounding, 5, 8, 29, 31, 82 Guide, 186, 193 GVIS, 213 Gyogi-Bosatu, 68 H Halley, 70, 73 hallucination, 183 handlebody, 107 haptic, 182

301

Index Harrison, 70, 93 Harun al-Rashid, 87 Heidegger, 10, 18, 33, 54 Heisenberg, 101 Helical Hyperspatial indexing, 170 heliocentrism, 91 Helmholtz, 97 Henry the Navigator, 68 Heraclitus, 33, 86 hermeneutic, 21, 112 Hermite, 144 Herschel, 95 Hesiod, 86 heterotopia, 33 hexagons, 142 hexahedral, 157 Hierarchical Data Format, 195, 196 Hilbert, 97, 102, 105, 106 Hipparcos, 68, 86, 90 hippocampus, 49 historicism, 26 Holocaust, 76 holon, 129 Homer, 84 Hopi, 57, 109 Hubble, 100 Hubserver, 196, 213, 222 human cartography, 81 human interests, 112 Humboldt, 33, 59 Hume, 12, 98 Husserl, 18, 33 Hutton, 95 Huygens, 93 hydrocarbon exploration, 156 hyperbolic spaces, 67, 97 Hypercard, 186, 189, 197, 198, 199 hypercubes, 170 hyperdocument, 186, 209 hypergeometry, 210 hypermap, 190, 195, 196, 198, 199, 209 hypermedia model, 186 Hypermedia spatial database for Kuwait, 198 hypermedia, 81, 186 Hypersnige, 198 hypertext abstract machine, 186 Hypertext Markup Language, 185, 320 hypertext nodes, 186

302

Index

303

hysteresis, 106 HyTime, 185 I idealism, 7, 8, 9, 11, 13, 14, 17, 28, 31, 112, 128 identity, 34, 39, 53, 100, 115, 117, 121, 129, 131, 137, 161, 163, 215, 235, 238 ideology, 16, 32 image schemas, 20, 21, 52, 72, 116 immanent, 123, 128 immersive virtual reality, 174 implicatures, 20 IMPORT/DOME, 194 incident wave, 235 indeterminism, 8, 9, 14, 31, 59, 62 IndexedFaceSet, 180, 192 indicatrix, 95 indiscernibility of individuals, 92 individual-based modelling, 193 induction, 12, 15, 20, 98 inertia, 91 inertial frame, 66, 91, 102 infinitesimals, 86 infinity, 86, 95, 100, 103, 105 informatics, 5, 28 information bearing object, 27, 196 information design, 21, 26, 188, 213 information flow, 4 information ontologies, 196 information representation, 201 information transfer, 129 information, 24 informational society, 26 informational structures, 185 informavores, 26 infragravity waves, 235 infra-red, 142, 175 Inquisition, 6, 91 intellectual property, 27 intentionality, 9, 17, 18 interior, 132 International Meridian Conference, 94 International Time Zone system, 69, 86, 94 Internet GIS for London, 191 interoperability, 233 Interpolation, 142 intrasignification, 74 intrinsic difference, 122 Intrinsic reference systems, 51

Index introspection, 107 inverse modelling, 170, 238 isoparametric, 146 isosurfaces, 157 J Java Database Connectivity (JDBC), 196 java, 180, 191, 192, 211 javascript, 197, 199 Judaism, 87 Julian calendar, 85, 90 Julius Caesar, 87 K Kant, 7, 11, 19, 22, 33, 49, 59, 67, 95 KARMA VI, 192 k-cell complexes, 169 Kepler, 6, 91, 100 kinaesthesia, 54 kinematics, 34 Klein, 67, 97, 98, 106 k-manifolds, 169 knowledge, 3, 15, 16, 17, 21, 24, 25, 26, 28, 36, 117 knowledge discovery in databases, 200 knowledge representation, 40, 47, 49 Kriging, 135, 157, 170 Kuhn, 5, 15 kurtosis, 229 L labile, 130 Lagrange, 92, 95, Lagrangian representation, 140, 170 Lambert, 70, 95 landforms, 121, 227 landmark knowledge, 47 lantern, 161 laser granulometer, 229 latency, 140, 182, 193 lattices, 142 laws of conservation, 95 leap years, 87 legal time, 93 Leibniz, 33, 58, 92, 99 Leonardo da Vinci, 33 level of detail, 159, 182 Lhuilier, 96 libraries, 26

304

Index Library indexing models, 195 LIDAR, 225 light-seconds, 125 linear octree encoding, 147 linguistic categories, 19 linguistics, 5, 17, 19, 21, 23 Lobachevski, 67, 97 local knowledge, 81 local time, 93, 114 locale, 113 Location Trends Extractor, 193 location-based services, 193 locative, 51 Locke, 33, 36, 98, 103 locomotion, 45 logical model, 130 Logical positivist, 110 logistic equation, 125, 171 Longitude Act, 93 longitude, 87, 92 longshore sediment transport, 235 Lorenz transformation, 99 lossless compression methods, 178 lossy compression methods, 178 LSD tree, 159 Lucretius, 33 lunar cycle, 85 lunar distance method, 92 Lynx, 153, 156 M Mach, 8, 11 macrosigns, 74 Magellan, 69, 92 Magic Tour, 190 magnitude/frequency, 129 Maimonides, 88 MapGrafix, 199 MapGuide, 212 MapInfo, 212 mapping, 31 57, 60, 63, 65, 68, 69, 80, 81, 117 MARC, 195 Marco Polo, 69 marine charts, 79, 217 markedness, 53 materialism, 7 mathematical function, 125 mathematics, 4, 24

305

Index

306

Matthew Paris, 68 May and Tanner theory, 235 Maya, 85 Mayer, 93 maze, 107 mean day, 91 mean tidal level, 77 mean times, 114 meaning, 19, 26, 74 Mecca, 88 mechanicism, 33 medial axis transforms, 49 Medusa 3D GIS, 152 MEGRIN, 195 Memex, 186 memory, 74, 108 mental maps, 43, 112 mentalese, 21, 23, 110 Mercator, 69 Mereological actualism, 41, 121 mereology, 9, 34, 41, 58 mereotopological, 41, 117 meridian, 92, 94 mesh, 153 mesoscopic, 41 metadata, 195 metadatabase, 212 metaphysical realists, 9, 31, 40, 121 metaphysics, 5, 10, 19, 22, 31, 34, 36, 40, 102, 110, 121, 131, 235 methodological individualism, 34 methodological realism, 123 metre, 125 Michelson-Morley experiment, 96, 99 microbrowsers, 189 Microcosm, 189 Middle Ages, 6, 87, 90 Middle Egyptian, 85 Mill, 7 Minkowski, 125 mobile phones, 218 Möbius, 96 modifiable areal unit problem (MAUP), 47 monster polyhedra, 96 morphological laws of space, 54 morphology, 34 movables, 43 Move-X, 198 MP3, 177

Index

307

MPEG, 178 multidimensional distance function, 184 multidimensional geo-representations, 114, 117, 121, 174, 235 multidimensional Hilbert spaces, 102 multidimensional phase spaces, 105 multidimensional representation, 31, 90 multidimensional scaling, 61 Multimedia and Hypermedia information encoding Experts Group, 185 multimedia geo-representations, 174, 205 Multimedia, 174 multiple representations, 44 Mursi, 109 N naïve geography, 35 naïve physics, 35, 36, 39, 102, 116 Napoleonic wars, 70 narrative logic, 135 National Geospatial Data Framework, 195 natural kinds, 9, 19, 121 natural numbers, 95 naturalism, 16, 19, 28 nature conservation, 205 Navaho, 110 navigation, 31, 38, 47, 54, 63, 77 neighbourhood, 45 nested in information, 25, 26, 28 Neurath, 11 New Grolier Multimedia Encyclopedia, 197 Newton, 33, 66, 91, 92, 95, 101, 102 Newtonian physics, 13, 57 Nile, 85 9-intersection model, 50 noise, 178 nominalists, 9 nomological, 9, 13, 26 non-Euclidean geometries, 39, 67, 97, 99, 102 non-orientable surfaces, 97 North Norfolk coast, 208 Notecards, 186 N-separation, 147 N-tree, 154 NURBS, 145, 152 O objectivism, 9, 16, 21, 115 Object-Oriented Geodata Model, 166 object-oriented programming, 143, 187

Index

308

observable, 26, 104, 130, 139 octal numbers, 147 octree, 147 Open Database Connectivity (ODBC), 196, 212 Odyssey, 85 OLAP, 200 Omar Khayyam, 90 OMT, 166 onshore-offshore processes, 236 ontogenesis, 58 ontological dependence, 41 ontology, 4, 5, 9, 18, 19, 22, 24, 28, 40, 58, 121, 122, 126, 135, 162 Oogeomorph, 127, 170 Open GIS, 159 OpenGL, 151 open hypermedia systems, 188 Open Inventor, 155, 159, 179 open time, 103 optic flow, 22 orbis terrarum, 68 Ordnance Survey, 212 organicism, 33 orientation, 44 Origin of the Species, 95 Ortelius, 69 ostension, 20 P Palegrave, 66 Panoramap, 212 paradigm, 3, 15, 29, 117 parallel plots, 201 parallel postulate, 97, 105 parametric equations, 144 PARCBIT, 199 Parmenides, 63 particle size distribution, 228 particulars, 9, 18 parts, 33, 41 Pascal, 91 Pavlov, 107 Peano, 106 perception, 12, 19, 22, 23, 57, 97, 108, 110 Perdurantism, 102, 123, 125, 130, 165 personal movement paths, 217 Phei Hsiu, 68 phenomenalism, 7, 8, 9, 11, 22 phenomenology, 8, 10, 18, 28, 32, 53, 60, 102, 108, 112, 115, 117, 121, 128, 174

Index

309

phi units, 229 philology, 90 photogrammetry of video, 175 photorealism, 182 physical field, 135 physicalist, 18, 19, 24 physics, 137 physiology, 34 place cells, 48 place, 32, 34, 43, 91, 112, 113 planar enforcement, 134, 141, 158 Planck, 101 planning, 137 Plato, 7, 9, 11, 32, 63, 86, 87, 88, 96 Platonic solids, 88 playback time, 175 Playfair, 97 Plotinius, 87 Poincaré, 99, 102, 106 Poinsot, 96 pointset topology, 50, 132 political economy of informatics, 81 Polybius, 87 polygon decimation, 182 polyhedra, 88, 96, 97, 106, 146 polynomials, 91, 105, 144 polytopes, 170 polytree, 147 Pope, 87, 90 Popper, 12, 15, 26, 111 portolan charts, 69 Portugal Interactive, 191 Portuguese National Geographic Information System, 195 positivism, 4, 11, 14, 16, 22, 58, 110, 130 possibilism, 60 Postgres, 159, 183, 190 Postmodernism, 8, 61, 113, 174 post-positivism, 58, 81 Poststructuralist, 35 potential path areas, 167 pragmatism, 14, 15, 26 present at hand, 18, 121 PResentation Environment for Multimedia Objects, 185 primal sketch, 23, 108 primal spatial experiences, 53 primary theory, 56 Prime meridian, 70 primitive instancing, 107, 145

Index principle of cohesion, 48 principle of contact, 48 principle of continuity, 48 principle of selection, 46 Privet Hill spit, 228 privileged frame, 58 probabilist, 12 probability, 13 process modelling, 127, 130, 235 production of space, 35 professional language for space, 77 propaganda, 74, 76 Property Management System, 155 propositional attitudes, 17, 19, 116, 121 propositional structure, 23 propositions, 8, 10, 115 protophysics, 102 Psychologists, 38 psychology, 4, 12, 97, 137 Ptolomy, 32, 59, 65, 68, 87, 90 public enquiries, 205 Public Land Survey System, 59 public participation, 81 Puluwatan, 54, 57 Pygmies, 109 Pyramid, 165 Pythagoras, 63, 86 Pythagoras’ theorem, 141 Q quadtree, 182 qualia, 18 qualitative spatial reasoning, 50 qualitative, 126 Quantitative Revolution, 60 quantum mechanics, 16 quantum physics, 8, 13, 62, 101, 103, 105, 115 Qusta ibn Luqu, 88 R raster, 142 rationalism, 11, 26, 28, 58, 103, 107 rationality, 14, 15, 16, 28, 80 Raymond of Marseilles, 69 real numbers, 95 realism, 8, 9, 14, 16, 20, 28, 129, 138 reasoning, 120, 129 Recorde, 66

310

Index reductionism, 18, 36, 131 reference frame, 126 REGARD, 200 Region Connection Calculus, 50 regions on surface methods, 224 relational database management system, 142 relational, 101, 122 relationalism, 92 relationism, 100 relationist, 58 relative space, 34, 57, 92, 99, 101, 126, 162 relative time, 176 relativism, 15, 21 relativity, 14, 16, 92, 98, 99, 102, 105, 115 relevance, 28 Renaissance, 11, 53, 65, 69, 90, 91 representation, 4, 31 Representational art, 52 representational process, 82 representational theory of mind, 17 res cognitans, 7 res extensa, 7 reservoir management, 156 residuals, 231 resolution, 129 return period, 129 Riemann, 67, 97, 104 right-handed coordinate system, 179 Ritter, 59 Rock-CAD, 151 Roemer, 91 Roman Empire, 87 rough sets, 43 routes, 48 RTM, 17, 18, 19, 21, 22, 23, 28 R-tree, 159, 164, 190 rule-based models, 137 S Sacrobosco, 66 salience, 36, 57, 82, 116, 121, 129 salt dome, 154 salt marsh, 205, 208 sampling-limited, 135 Sargasso Sea, 42 satellite imagery, 77 Saultaux, 109 Savoy Cadastre, 70

311

Index scale, 44, 128 Scaleable Vector Graphics, 191 scene graph, 179, 180, 183 scepticism, 11, 15 Schlick, 11 science, 3, 8, 13, 21, 22, 26, 28 scientism, 59 Scolt Head Island, 204, 215, 221, 228 Scolt Multimedia Project, 189, 209 sea level change, 227 sea level rise, 205, 208 Second Law of Thermodynamics, 101 sedigraph machine, 228 sedimentary architecture, 228, 229, 231 sedimentary facies, 227 sedimentological log, 228 SEDSIM, 171, 235 semantic bleaching, 53 Semantic Hypermedia Architecture, 189 semantic nets, 184, 213 semantic proximity, 186 Semantics, 19, 24, 26 semiology, 73, 200 semiotics, 20 semivariogram, 135, 157, 170 sense perception, 22 sense-making, 49 sensorimotor skills, 35, 39, 84 Sequoia 2000, 196 servlet architecture, 211 sexagismal system of numbers, 85 shadow, 86 shape grammars, 49 shape, 49 shoreline cells, 235 Shoreline Management Plans, 208 shortest path algorithm, 160 simplices, 133 Simplicius, 63, 90 simply connected, 133 simulacrum, 183, 221 skewness, 229 slope facets, 238 SMPviewer, 199, 210, 216 social constructivism, 16 social theory, 4, 34 Socrates, 11 sonification, 200

312

Index Sophists, 33 Sothic calendar, 85 Sound, 125, 177, 215 space as difference, 34 space as territory, 59 space curves, 91 space graph, 164 Space Syntax, 54 space-time composites, 163 space-time prism, 167 space-time structures, 126 space-time, 33, 99, 122, 125 SPANSmap, 191, 199 spatial agent, 140 spatial behaviour, 82 spatial data modelling, 130 spatial elasticity, 113 spatial inference rules, 48 spatial occupancy enumeration, 147 spatial reasoning, 49 spatial representation, 4 Spatial Semantic Hierarchy, 49 spatial thinking, 38 spatiality, 35, 80, 113, 179 Spatio-Temporal Data Model, 165 spatio-temporal data modelling, 136 Spatio-Temporal Entity-Relationship, 166 spatio-temporal projection, 115 Spatio-Time Environmental Mapper, 164 Special Geography, 59 Special Theory of Relativity, 98 speed of light, 91, 96, 99 spheroid, 70 spit, 72, 205, 216, 227 SQL/multimedia, 164, 183 St Augustine, 86, 87 St Sever, 68 St Thomas Aquinas, 64, 87 standard deviation, 229 star constellations, 85 states of affairs, 9, 21, 27, 31, 115 Statutes (Definition of Time) Act, 93 stereometry, 88 ST-objects, 165 stochastic models, 137 storm surges, 206 Strabo, 59 Stratamodel, 156

313

Index

314

structuralism, 16, 60, 112 structuration, 113, 114 Structured Query Language, 158 Su Sung, 90 substantivalist, 57, 92, 100 sundials, 85 Supercard, 199 Superstring, 102, 105 surf zone radiation stress, 235 surface models, 135, 222, 227 surveillance, 178 survey knowledge, 47 surveying, 4, 77, 125 swash, 216 sweep models, 145 sweeping, 107 Synthetic Environment Data Representation and Interchange Specification, 180 system theory, 111 T taxel, 168 taxonomy, 34 TCL/TK, 212 TCObject, 166 telegeomonitoring, 193 teleological beliefs, 87 Temne, 54, 57 TEMPEST, 164 Temporal GIS, 163 temporal ontologies, 103 Terraserver, 196 tesselations, 136, 141 tetrahedral network, 153 tetrahedron modelling, 228 tetrahedron, 136, 232 Thales, 63 theatre, 183 Theogony, 86 theories of modelling, 138 Theory of communication, 19, 25, 73 Theory of computation, 23 Theory of the Earth, 95 thermodynamics, 125 thesauri, 195 thing-moment, 102 3.5D visualisation, 221 3-manifolds, 106 three-dimensional discrete topology, 147

Index three-dimensional interpolation, 230 threshold, 230 thrownness, 18 tides, 85, 87, 204, 225 time geography, 167 time lapse analysis, 175 time models, 175 time/space zones, 209 timekeeping, 90, 94 timepath, 185 TIN, 222 Tioga, 196 Tissot, 95 T-O maps, 68 Toolbook, 189, 197, 198, 201 topogenesis, 32 topographic maps, 73 topological, 37, 47, 50, 126, 132 tortoise paradox, 86 total station, 217 TOUR model, 49 toxels, 170 transcendental realism, 113 transformations, 131 transperceptual space, 181 traVelleR, 192 Treaty of Tordesillas, 92 TRIAD, 124, 163, 190 triangulated irregular networks, 143 triangulation, 69 trivariate parametric equations, 144 truth in labelling, 196 truth, 9, 10, 14, 15, 16 TSQL2, 164 tuple, 136 Turing, 24 U Uccello, 90 Ukiyoe, 53 ultra-violet, 142 uncertainty principle, 14 underdetermined theories, 15 underdetermined, 123 universal server, 184 Universal Time, 95 universalism, 33 universals, 7, 9

315

Index

316

universe, 8, 9, 13, 14, 27, 100, 102 Urban modeller, 192 utility companies, 77 V V0 interoperability protocol, 196 vacuum, 91 Varenius project, 4 Varenius, 33, 59 Vasco da Gama, 68 Vector Product Format, 154 vector, 140 vectorised octree, 147 Venerable Bede, 87, 90 verb tenses, 85 verge-and-foliot clocks, 90 verification, 110 Vertical Line Interval, 177 Vidal de la Blache, 60 video, 142, 175, 215 Video algebra, 184 video strip map, 217 videometry, 216 Vienna Circle, 8, 11 virtual environments, 179 Virtual Field Course, 221 virtual geo-representations, 175 Virtual GIS Room, 181, 191, 221 Virtual Reality Modelling Language (VRML), 154, 179, 225 virtual reality systems, 221 Virtual Reality User Interface, 192 virtualisation, 175 virtuality, 175, 179 VirtualPark, 193 VL database, 183 Voltaire, 33 volumetric components, 153 Von Thunen’s theory, 110 Voronoi region, 232 Voxel Analyst, 156 voxels, 136 VRGIS, 192, 222 Vulcan, 161 W Waghenaer, 69 Warburton, 70 warranted assertion, 14

Index washover, 231 water clocks, 90 Wave refraction, 235 WAVE, 235 wave-current interaction, 235 wavelet, 183 wayfinding, 36, 48, 58, 181, 188 web GIS, 190, 212 Web3D Consortium, 179 Wellington, 70 Werner, 92 West Indies, 92, 93 Wheatstone’s Electric telegraph, 94 wholes, 33, 41 Whorf s hypotheses, 21, 57, 116 window of comparison method, 222 Wired Whitehall, 193 wireframes, 107 Wittgenstein, 11 world history model, 124 world line, 114 world time, 165, 175, 215 World Toolkit/WorldUp, 155, 179, 192 World Wide Web, 185 worldview, 5, 10, 31, 33 Wundt, 97 X Xanadu, 186 XML, 192 Y yon clipping, 181 Z z39.2, 194 z39.50, 195 Zenith, 166 Zeno, 86, 104 Z-influence factor, 230 Zodiac, 85

317

Multidimensional geographic information science

Foundations of Geographic Information Science

A Research Agenda for Geographic Information Science

Geographic Information Science and Public Participation (Advances in Geographic Information Science)

Collaborative Geographic Information Systems

Geographic Information Systems Demystified

Geographic Information Analysis

Geographic Information Analysis

Geographic Information Systems Demystified

Geographic Information Analysis

Frontiers of Geographic Information Technology

Geographic Information Research : Transatlantic Perspectives

Geographic Information Systems in Business

Geographic Information Systems in Business

Geographic Information Systems: Socioeconomic Applications

Frontiers of Geographic Information Technology

Principles of Geographic Information Systems

Statistical Image Processing and Multidimensional Modeling (Information Science and Statistics)

Self-Organising Maps: Applications in Geographic Information Science

Geographic Information Systems and Science (2005)(22nd ed.)(en)(536s)

Beyond Mapping: Meeting National Needs Through Enhanced Geographic Information Science

Self-Organising Maps: Applications in Geographic Information Science

OLAP Solutions: Building Multidimensional Information Systems

OLAP Solutions: Building Multidimensional Information Systems

Geographic Information Systems in Transportation Research

Landscape Ecology and Geographic Information Systems

Information Science

Developing Geographic Information Infrastructures: The Role of Information Policies

Geographic Information Systems in Water Resources Engineering

Geographic Information: Value, Pricing, Production, and Consumption

Multidimensional geographic information science

Foundations of Geographic Information Science

A Research Agenda for Geographic Information Science

Geographic Information Science and Public Participation (Advances in Geographic Information Science)

Collaborative Geographic Information Systems

Geographic Information Systems Demystified

Geographic Information Analysis

Geographic Information Analysis

Geographic Information Systems Demystified

Geographic Information Analysis

Frontiers of Geographic Information Technology

Geographic Information Research : Transatlantic Perspectives

Geographic Information Systems in Business

Geographic Information Systems in Business

Geographic Information Systems: Socioeconomic Applications

Frontiers of Geographic Information Technology

Principles of Geographic Information Systems

Statistical Image Processing and Multidimensional Modeling (Information Science and Statistics)

Self-Organising Maps: Applications in Geographic Information Science

Geographic Information Systems and Science (2005)(22nd ed.)(en)(536s)

Beyond Mapping: Meeting National Needs Through Enhanced Geographic Information Science

Self-Organising Maps: Applications in Geographic Information Science

OLAP Solutions: Building Multidimensional Information Systems

OLAP Solutions: Building Multidimensional Information Systems

Geographic Information Systems in Transportation Research

Landscape Ecology and Geographic Information Systems

Information Science

Developing Geographic Information Infrastructures: The Role of Information Policies

Geographic Information Systems in Water Resources Engineering

Geographic Information: Value, Pricing, Production, and Consumption

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