UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The dynamics of urban expansion : a model for planning Mathieson, Ronald Arthur 1972

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata


831-UBC_1972_A6_7 M38_4.pdf [ 44.62MB ]
JSON: 831-1.0101682.json
JSON-LD: 831-1.0101682-ld.json
RDF/XML (Pretty): 831-1.0101682-rdf.xml
RDF/JSON: 831-1.0101682-rdf.json
Turtle: 831-1.0101682-turtle.txt
N-Triples: 831-1.0101682-rdf-ntriples.txt
Original Record: 831-1.0101682-source.json
Full Text

Full Text

THE DYNAMICS OF URBAN EXPANSION A MODEL FOR PLANNING by RONALD .ARTHUR MATHIESON B.A.(Hons.). LL.B., Australian National University, 1968, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE c i n the School of Community and Regional Planning We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June .1972 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the'Library shall make i t freely available -for reference and study. I further agree that- permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood'that copying or publication of this-thesis for sale or financial gain shall not be allowed without my written, permission. Department of Community and Regional Plajining The University of British Columbia Vancouver 8 , Canada Date S o j o ^ e _ n " X ABSTRACT The implications of urban expansion as a dynamic, evolutionary process: are far from self evident. Such problems as the ecologically sound allocation of land resources and the orderly provision of essential services•in urban fringe areas,• are not being solved. The importance of the rural-urban land conversion process, i n long range planning for met-ropolitan regions, requires that a method be found for describing the likelihood'of the rate, extent and location of urban expansion. Within this context the study is. concerned with f i r s t l y , the shortcomings of present methods for examining and forecasting urban expan-sion. I t i s pointed out that the regional planner needs to understand the dynamics of land assignment, i n the urban expansion process, i f he i s to know i n advance the probable consequences of his actions and be able to f u l f i l planning objectives. That this elementary point i s frequently ignored or misunderstood can be seen i n the attempts to prescribe how a process should behave, instead of f i r s t trying to discover how i t does behaveThis i s most noticeable where techniques. are used which entail Abstract i i i optimization or conditional prediction, based on generalized and unrealistic assumptions of human values and behaviour. As a result, the dynamics of change, including the'influence of chance events, are usually l e f t unac-counted for i n actions subsequently taken. Restrictive zoning i s an example, which more often than not seeks to force rather than f i t or guide urban, development. -Secondly, a simulation model of rural-urban land conversion i s developed for the Vancouver Regional Simulation Project, to demonstrate the advantages of experimental strategies and synthetic models i n regional plaxining.. The viewpoint is-taken that urban expansion can be represented as a spatial diffusion process. When formulated stochastically, spatial diffusion processes account for uncertainty i n land assignment practices. The model i s organized i n a regional systems framework, with structural properties ( i . e . , thresholds, boundaries, and lags), and feedback inter-actions, represented, to reflect the complex and dynamic nature of urban expansion.. I t i s emphasized that the-future cannot be forecast, on the basis of past and present conditions, with sufficient r e l i a b i l i t y for long range planning purposes. While i t i s . i m p l i c i t i n the model formulated.that emerging patterns of rural and urban land use bear some functional relation-ships to histori c a l patterns, they - are not constrained from evolving into new-and different-forms. ' Special attention i s paid to change and chance mechanisms to avoid indiscrjjminate extrapolation of present'trends. Abstract i v The experimental nature of the model i s considered i t s greatest strength. Because i t facilitates'experimental monitoring and regulation of process behaviour, we are made more aware of c r i t i c a l thresholds and capacity l i m i t s within metropolitan regional systems. Consequently, planning p o l i c i e s , compatible with the dynamic urban expansion process, can be devised with greater assurance of t h e i r success, and regional planning goals can be achieved more r e a d i l y . Thus the approach i s submit-ted as' a progressive step beyond the t r a d i t i o n a l reliance on s p e c i f i c predictions, as a primary basis f o r regional planning. TABLE OF CONTENTS Abstract i i List of Tables i x List of Figures x List of Plates xid Acknowledgments x i i i Chapter 1 THE PLANNING PERSPECTIVE AND STUDY OUTLINE 1 Background: And Cities, Just Like Topsy, Grew 1 Urban Spatial Growth and Planning Problems 4 Urban Growth Dynamics 8 The Study Context 12 Study Purpose and Structure 14 A Note on Terminology 17 Table of Contents v i PART T SELECTING A MODELLING APPROACH Chapter-2 MODELS- AS•STRATEGIES 19 The Nature and Role of Models in Applied Research 20 Types of Models 29 Causality and Chance: Accounting for Uncertainty 38 Chapter 3 MODELLING THE URBAN EXPANSION PROCESS 49 Spatial and Temporal Dimensions 50 Traditional Models of Urban Expansion 53 Diffusion Models = - 57 Urban Expansion as a Stochastic Process 66 Table of Contents v i i PART II; TOWARDS A MODEL OF URBAN EXPANSION THE VANCOUVER REGION Chapter 4 CHARACTERISTICS OF THE SPATIAL GROWTH OF VANCOUVER 75 JDitroduction 75 The Evolution of Urban Settlement 77 Characteristics of Urban Expansion 110 A Synthesis 120 Chapter-5 A. DIFFUSION MODEL OF URBAN EXPANSION FOR VANCOUVER 123 The Nature of Spatial Diffusion Processes 124 Formulation of the Model 125 Model Structure 136 Assumptions 140 Method for Application 141 Table of Contents v i i i PART I I I THE DYNAMICS OF URBAN EXPANSION: • SPATIAL ANALYSTS OR SYNTHESIS? Chapter 6 INTERPRETATIONS-. . 150 On Understanding Complex Systems 150 Modelling - Spatial Systems 153 ' -The Relationship of ; Model Strategy to HPS 155 Implications for Regional Planning 160 Literature Cited 165 APPENDIX -1; The- Vancouver Region - -A Series of Topographic Maps 176 APPENDIX II' The Vancouver Region - Population Density 1966 187 APPENDIX III' The Vancouver Region - Traffic Volumes and Travel Times, 1967-1968 188 APPENDIX IV Outline-for Operation-of the Model 189 LIST OF TABLES Table Page 1. Vancouver Region: Population and • Inter-Census Increments, 1921-1971 84 2. ' Land Consumption Rates 135 3.. Land Absorption Rates 135 4. Hypothetical Probability Matrix 145 5. Matrix of Random Numbers 146 6. Resistance Scales for Barrier Effects and Resilience- 146 7. Combined Resistance Scale for Barrier Effects and Resilience 148 LIST OF FIGURES Figure Page 1. ' DefJLning a Modelling Strategy 24 2. 'The Regional Planning Process 28 3; Urban Settlement in the Vancouver Region, 1898 79 4. Population: City of Vancouver 1886-1921 80 5. Vancouver Region: Extent of Urban Areas 1907 ' 81 6. Vancouver Region: Extent of Urban Areas 1934 81 7. Vancouver Region: Extent of Urban Areas 1946 86 8. Vancouver Region: Extent of Urban Areas 1956 86 9., Vancouver Region: Existing Development 1970 90 10. • Stages of Regional Systems 111 11. Topography of the Vancouver Region 113 12... Dominant Nodes and Their Urban Fields 1965 Circa 129 L i s t of Figures 13. Hypothetical Accessibility Function For Establishing the Limits of Urban Expansion •14. Hypothetical Relationships Between Propinquity Factor and the Probability of Land Conversion 15. Flow Diagram of General Rural-Urban Land Conversion 16. Hypothetical Relationships Between Accessibility and Propinquity Factors LIST OF PLATES Plate . Page 1. Vancouver:. A Country Town C1890-circa) 91 2. Vancouver: The Compact City (1910) 92 3. - Vancouver: The Dispersed City (1939) 93 4.. Rural-Urban Subdivision (1941) 94 5. Moodyville: A Resource Town.(1906) 95 6. The Emergence of North Vancouver (.1929) .96 7. Burrard Inlet: Two Shorelines (1938)- 97 8., New Westminster: The Dormant City (.1906) 98 9..- Hammond: A Rural Centre (.1928) 99 10. Cloverdale: A Fringe CcmiixLnity 0.953) 100 11. Richmond'; Filling in the Gaps (1955) 101 12. Burnaby: The Dilemma of Ex-Urbia (1957) 102 ACKNOWLEDGMENTS This thesis i s the cumulative product of two years spent at the University' of Briti s h Columbia.. • In particular, • i t reflects courses taken and other assistance received from Dr.. Craig'Davis, Dr. Michael Goldberg (thesis supervisors), Dr. Walter Hardwick, Dr.. Crawford Holling, Dr. Richard R a t c l i f f , and Dr. William Rees. Most of the concepts and issues described w i l l be familiar to those who followed developments i n geography and regional science during the 1960's, i n both Europe and North America. For my training i n these disciplines, I acknowledge a special debt to Professor Andrew Learmonth, formerly of the Australian National University and now at the Open University, England. Finally, the study i s often.concerned with philosophical and methodological aspects of regional planning.. Largely, this concern reflects my- reaction to the specialist-technique emphasis i n regional planning educa-tion. I' feel more planners should acknowledge Marshall McLuhan's warning that "the specialist i s the one-who never makes small mistakes while moving towards the grand fallacy." Chapter 1 THE PLANNING PERSPECTIVE AND STUDY OUTLINE Background: And,Cities, Just Like Topsy Grew The fact that most large North American cities have grown con-tinuously- over the last f i f t y years tends to obscure the cyclical nature of urban spatial growth. Recently, however, Malisz (.1963, 1969) drew attention to the vacillating conditions of congestion and urban expansion in metropolitan regions and described urban expansion as a process which involved the crossing of numerous successive thresholds. Malisz observed in his studies of cities in Poland that at various stages in the develop-ment of urban regions congestion mounted until the pressure created reached a level at which, the impediments to urban spatial growth were overcome, allowing a new phase of expansion to take place. The idea of cycles of urban spatial growth, is not new; both Geddes C1915) and Mumford (.1961) have considered i t . According to this view, urban spatial growth i s a function of two interrelated processes• On the one hand, increased demands Planning Perspective 2 for space are accommodated by concentrating activities and increasing popu-lation density through a process of drawing upon unused capacity in the urban system. However, the resilience of an urban system is finite, and after available capacity has been utilized, peripheral growth must take place to accommodate s t i l l more people and new activities. Thus the second process, urban expansion, can be recognized as the conversion of rural land to urban uses. The dual interdependent processes of changing intensity and extent, which, constitute, urban spatial growth, can only be distinguished with considerable difficulty in actual situations. While in unusual c i r -cumstances one process may account for a l l of the growth in a limited time period, i t is more likely that both processes w i l l operate simultaneously; though with varying degrees of prominence. An important and unexplained issue, is: whether each of these growth, processes is a function of different factors:. The pattern of urban spatial growth in the modern metropolis has: so far eluded meaningful generalization., Each urban region has its own unique landscape characteristics and these have provided the only disting-uishing- features at the macro-scale. Apart from landscape influences, urban regions- have, been described as "a continuous shapeless mass" of urban fabric, undifferentiated except for the occasional green patch or major communication corridor CMumford 1961 p.618). Both Patrick Geddes (.1915 p.26) and Lewis Mumford C1961 p.619) depict the^ patterns of urban spatial growth in a manner which suggests that urban regions grow randomly. In the words Planning Perspective 3 of Mumford (1961), . . .as one moves away from the centre, the urban growth becomes ever more aimless and discontinuous, more diffuse and unfocused, except where some sur-viving town has left the original imprint of a more orderly l i f e Clbid. p.619) and . . .the chief factor that keeps this dispersal from being of an entirely random nature are the expressways and connecting roads that have made i t possible Clbid. p.627). In addition to the processes of urban spatial growth and the patterns: which are. produced, there Is the matter of the spatial limits of urban regions., Surprisingly, this aspect of urbanization has received l i t t l e attention from scholars and "in most instances the topic i s ignored, or for convenience, the assumption is made of an infinite spatial environ-ment (.Korcelli 1970 p. 134). There is really no satisfactory explanation of the spatial limits, of urban regions and the indefinite nature of the urban boundary in the modern metropolis Ci.e., the. urban shadow or fringe), only adds to the difficulties. While i t may be possible to describe the ultimate limits of an urban region, as Mumford has (1961 p.624), by resolving the competing demands of adjacent cities for sustaining resources (e.g. water and land) and finding an equilibrium,point for the costs of transportation between these cities, this is not particularly helpful for establishing sequential boundaries through time. Approaching this same issue from a different viewpoint, Blumenfeld Planning Perspective 4 (.1967 p.67) notes that attempts to halt urban spatial growth by prescribing definite boundaries for cities have, since the times of Elizabethan England, been as futile as they were regular. But the growth of cities.has been only one of many problems. It seems that the variety of problems connected with urban spatial growth has multiplied as the size and population of urban regions have increased. .Urban Spatial Growth and Planning Problems Planners are very familiar with a multitude of problems connected with urban spatial growth;.in fact, a large proportion of the literature on the subject is directed at the disadvantages of urban sprawl. Given the complexity of urban systems,•and a strong tendency for specialized and deterministic forms of thought, i t is to be expected that the most easily recognized features of urbanization processes, that is the changes produced, should attract attention. Unfortunately, too few scholars have sought to analyze the nature of the underlying processes, particularly those, operating at the urban fringe. Instead, most have merely deplored the emerging patterns from any- number of different viewpoints CLeven 1968). Considering that community and regional planning is normally concerned with the monitoring and regulation of ongoing processes (.Wilson 1969 p.3) this amounts to misplaced emphasis. If public media are any indication, there is considerable con-fusion about the nature and value of urban growth. Metropolitan newspapers, Planning Perspective 5 radio, and television present numerous examples of conflicting viewpoints on the growth of cities.. For each pronouncement by an "expert" of another problem caused by continuing urban growth, there is an inducement to consumers in the city area to escape to the serenity of nearby "open space communities"'; and for every outcry for new: controls on growth there is a corresponding demand to encourage new development for the sake of addi-tional employment opportunities. But i t i s not only the layman'who is confused. Researchers in the. social sciences have, widely different evaluations and conflicting ideas on what should happen as a result of the spatial growth of the metropoli-tan area, depending- on their values and the particular discipline from which, they emerge. Geographers, sociologists, economists, architects, planners, regional scientists and ecologists have a l l made their contri-butions. The divergence of research, findings and opinions is largely the result of different evaluative approaches to the issue (Haworth 1970). Urban spatial growth, and associated settlement patterns are only rarely examined with reasoning free of social values.. Consider, for example, the respective viewpoints of Webber GL9.63) and Lean and Goodall (.1966). Lean and Goodall G.966 pp.187-189) emphasize economic criteria and criticize, the inefficient use of resources where discontinuous and sporadic settlement occurs.. Harvey and Clark. (.1965), who voice similar views-, imply that. misguided' public interference with the land market mechanism is largely responsible, for "sprawl." To confuse the issue, the Hellyer (1969) report on housing and urban development in Canada, which Planning Perspective 6 also criticized urban sprawl as uneconomic and inefficient, called for more public intervention in the land market. Webber, on the other hand, accepts urban spatial growth processes as the means, to a new diversity- and stability in communities, arguing that commonly- held precepts of city- form are outdated. These precepts are based, he claims, on rigid adherence to the separation of land uses, creating monotonous and sterile environments and tend to reflect social values which are no longer relevant. In yet another respect, the difficulties have arisen partly from consideration of urban spatial growth itse l f as a problem. Clearly, i t i s not, for that is to mistake' the processes for the changes produced. How-ever, as recent detailed studies, summarized by Lithwick C1970 p.61), tend to show, .. . .there can be ho doubt that the central hypothesis is valid: the major urban problems relate directly to the process of urban growth. So far these problems- have, not been spelled out. Sufficient attention has been given' to the. different problems associated with urban spatial growth in the literature, and i t would be repetitious to discuss them in depth here. Nevertheless, the main problems that have been docu-mented in connection with the. urban expansion process are set down in point form below: (1) The. costs of development, particularly for capital f a c i l i -ties, are. higher than seems, warranted for the standards of Planning Perspective 7 housing produced (Harvey- and Clark 1965, Pearson 1967, Clawson 1971]. C2) Land resources are often allocated to inappropriate uses and organized wastefully (Mumford 1961, Lower Mainland Regional Planning Board 1963, Harvey and Clark 1965, Clawson 1971). C3) With, respect to accepted planning ideals, the kinds of development which, occur lack social and aesthetic appeal (Mumford 1961, Lower Mainland Regional Planning Board 1963, Clawson 1971). !'"; C4) The land conversion process has failed to provide land for housing at a rate and cost considered desirable to meet the demands for housing Qfethieson 1970, Clawson 1971). C5) In many cases, prime agricultural land is removed per-manently from the rural sector, displacing skilled farmers and underpinning the agricultural economy of the region (Lower Main-land Regional Planning Board 1963, Parker 1966). C_6) The land conversion process operates in a fashion character-ized by high, levels of uncertainty thus inhibiting effective planning (Milgram 1967, Mathieson 1971). While a l l the points are significant, i t is probably the last which, has the greatest implications for community and regional planning and this study. Planning presupposes an understanding of the subject matter being planned for, and in the past the uncertainty inherent in urban spatial growth, was sought to be reduced by collecting copious amounts of data. As w i l l clearly emerge from later discussion, the availability of the data is Planning Perspective 8 a far less important problem than the lack of an understanding of the dynamics of urban spatial growth processes. Urban. Growth.: Dynamics Considering the large amount of research into urban issues, one could be forgiven for presuming that at least the basic processes of urban spatial growth, have been specified. This is not the case; in fact, the whole realm, of research into urban spatial growth and structure has been characterized by the haphazard formulation of theory (Haggett 1968 p.65). Moreover, Leven (196.8) shows there. Is s t i l l considerable disagree-ment about the appropriate conceptual approach to studies of urban spatial growth.. He strongly criticizes conventional approaches for "their inability to come to grips with, the urban, process it s e l f " as they proceed misguidedly, .. . .from various particular points of view not necessarily related to the urban process, but rather hoping to derive an understanding of that process by focussing on a process" 'within or a' particular character-i s t i c of the city (leven 1968 p.12). Obviously, without first, specifying, systematically, the relation-ships of essential factors in urban growth, there can be l i t t l e progress towards an appreciation of the mechanics of change. An understanding of the. s-1n7uctural dynamics of complex' systems is a prerequisite for tracing specific processes to their logical conclusion (Piaget 1970). Planning Perspective 9 The implications of urban growth as a function of dynamic pro-cesses are far from self-evident. For example, nowhere in the planning or related literature, to the writer's knowledge, is there a plausible explanation for the different patterns of urban growth which occur under similar social and cultural conditions, while comparable patterns have been found to occur in entirely different social-cultural environments, widely separated in time and space. To illustrate this point. Branch (1962) has.described the respective growth and land use patterns for Rome (Italy) and Richmond (Virginia), as a case study in topographic deterrcdnism. • Although separated'by 2,500 years and more than 4,000 miles, both. Rome and Richmond developed in a remarkably similar fashion. Given the i n i t i a l settlement location of both cities on a navigable river at a point where crossing was not di f f i c u l t , both spread fan-like, away from the river, while land suitable for urban uses, on the other side, remained relatively underdeveloped.. Although, the reasons for this similarity of urban, spatial growth, are not clear, at. their respective stages of mature development, both. Rome and Richmond had equivalent land use patterns for institutional, commercial and residential activities. Branch attributes these, startling•similarities to comparable landscape topographies and resources;. But one would need to be. a zealous environmental deteriTLinist to consider the similarities, predictable, particularly in view of the divergent technologies, economies and social conditions. It is more likely that a person confronted with, this knowledge would ascribe the similarities to chance. Planning Perspective 10 In geographical research, the "chance" element in settlement patterns: and processes has received specific attention by Curry (1964, 1966). By assuming- that uncertainty is an'inherent feature of social systems and a basic fact of l i f e for individuals and communities, he was able to derive an interpretation of the particular settlement pattern which is summed up in the statement: . . .where nature shows only a single result, i t is interpreted as the historical realization of a pro-cess which could just as easily have produced other results according to their attached probabilities CCurry 1966 p,40). Within the urban realm, this can be interpreted more specifically, as the uncertainty evident in land assignment practices. Land assignment, the process by which land resources are allocated and organized for use by individuals and society, is a function of institutional, social, techno-logical and economic factors CVance 1971). Viewed circumspectly, i t involves the resolution of a l l the decisions made with respect to land resources by individuals, communities and governments. In the North American context, the complexity- of this process has defied a l l but the most simplistic of explanations,. Furthermore, Vance C1971) has observed that currently, land assignment practices are in a state of transition. His study provides evidence that economic forces are weakening and social and institutional factors are. becoming more important * Beyond this observation he was only able to conclude that the process operates in an unclear fashion and that Planning Perspective 11 its results are generally unpredictable. Cturry C1964- p. 138) arrives impli-ci t l y at the same conclusion, although he is refering to a more general situation when he states that, ... .in any general location problem, particularly in a dynamic framework, one cannot begin to comprehend the infinite number of decisions, rarely coincident in time and separately motivated under differing circumstances and degrees of information. in an earlier study the author had occasion to examine the land assignment practices in British Columbia Ofethieson 1971). The general conclusion reached was that the results- of land assignment practices are not only unpredictable, but that the practices themselves are completely disorganized, even where, Cas within and between government departments), i t was reasonable to expect them to be coordinated.. The implications of this situation are more disturbing when i t is realized that government decisions with, respect to land resources in. many areas have a dominant influence, not only on the overall land assignment patterns, but also on economic welfare CSeastone 1970, 19.71). There is something ironic in the discovery- that the uncertainty confronting planners, many of whom work for the government, is in part due to shortsighted government practices. On the basis of the foregoing observations, i t seems reasonable to draw- the tentative conclusion that urban spatial growth, particularly that resulting from the conversion of rural land to urban uses, is charact-erized by uncoordinated growth and unforeseen change. In addition to emphasizing the dynamic nature of urban growth processes, both features Plarining Perspective 12 strongly indicate that planners lack, an appreciation of the mechanics of change and are s t i l l largely ignorant of general urban dynamics. Furthermore, planners' current views of dynamic urban systems do not paradoxically admit of the further evolution of cities into new -and radically different forms. There is a marked predilection among plan-ners to accept as the final state, the basic patterns of human settlement which have existed for more than f i f t y years and were recognized and described by- Patrick Geddes in his classic volume Cities in Evolution. This ignores, in the words of Bertram Gross (.1966 p. 137) . . .a central fact of this century; that the "United States Cand Canada*] is itself a tran-sitional society in the throes of a great transformation from the last stages of industri-, alism to the f i r s t stages of postindustrialism. While much larger urban regions may appear to be inevitable, history has shown few aspects of urban evolution to be that certain. Rather than persisting with the extrapolation of past trends, which appears to have no a priori justification, an approach to the study of urban spatial growth, processes emphasizing the conditions for structural changes in urban systems is desirable. The Study Context The most advanced scientific methodologies have been found wanting, Study Outline 13 time after time, in promoting an understanding of the modern metropolis. This perplexing state of affairs.has attracted the attention of many institutions, such as the Ford Foundation, and they have been funding innovative Cand usually expensive) projects designed to improve our research technologies and eventually, our understanding of complex social •systems. One such project, currently in progress at the University of British Columbia under the direction of Dr. CrawfordHolling and Dr. Michael Goldberg, provided the impetus for this study. The project, called the Inter-Institutional Policy Simulator (HPS) because of the cooperative nature of the venture, is s t i l l i n it s formulative stages, and is expected to take five years to complete (Goldberg 1970). Briefly, the Resource Science Centre at the University of Bri-tish Columbia, in conjunction with the Planning Director of the Greater Vancouver Regional District and Vancouver City Council, is developing a systems simulation model of man-environment interactions in the Vancouver Region, as a tool to assist in planning and policy formulation. Following the development of an elaborate mechanistic representation of the impor-tant community and environmental processes, i t is intended to experiment with, various policies'and observe the consequences. It is hoped that our understanding of community and environmental processes and their inter-dependencies w i l l be enhanced, and as a result, more effective policies can be. conceived. The success of this venture w i l l also greatly assist in determining the adequacy of the systems approach as an organizational framework: for the investigation of complex systems. Study Outline 14 The simulation model combines eight component sub-models cover-ing the following- areas: demography, land use, transportation, economics, human ecology, health services, capital service f a c i l i t i e s and pollution. The model developed i n this study represents the i n i t i a l contribution to the development of a rural-urban land conversion component model of the larger land use sub-model. The object i s not to formulate a general theory of urban expansion, although theoretical aspects are considered at some length, but to design a subject specific model for the particular purposes of examining the process of urban expansion and forecasting rural-urban land conversion i n the Vancouver Region,. Study Purpose and Structure The purpose of the study i s twofold: CD to demonstrate the' inadequacies of present methods for examining urban spatial growth processes; and 02) to construct a model of rural-urban land conversion for long range planning, which increases our understanding of the dynamic nature of urban expansion. I t i s hoped that this contribution w i l l help resolve a number of dilemmas concerning the role of research i n the plan-ning process^ i n addition to throwing light on the evolution of urban regions, More specifically, i n relation to the f i r s t objective, the f o l -lowing proposition i s examined: Study Outline 15 the donuhant urban spatial growth processes are stochastic and are properly represented by probabilistic models, i The argument is advanced that because of inherent uncertainty in the evolution and-organization of the modem metropolis, the particular pattern existing at any time can be regarded as the historical realization of processes, which could have produced different patterns, in accordance with the probabilities attached to the-process components (Curry 1966). The advantage of this approach, which derives from the basic characteristic of probability theory, lies in the explicit recognition of considerable ignorance about causal relationships in the processes. In relation to the second objective, and on the basis of the experimental investigations reported in this thesis, i t is submitted that urban expansion can be described as a spatial diffusion process in which the conversion of rural land to urban uses is directionally random, other things being equal. The probability of rural-urban land conversion is a function of the demand for addi-tional space consequent upon population growth, the level of resilience in urban infrastructural systems, accessibility to urban nodes-, proximity to existing development and barrier' impediments inherent in the nature of land resources and settlement structure. Throughout the study, the approach emphasized for understanding complex systems is that of the experimental sciences. Preconceived notions Study Outline 16 of behavioural motivations are s t r i c t l y excluded and instead, i t i s sought to develop concepts and describe structural relationships by seeking order in empirical observations. As a result, the derived functions have a more objective basis than would otherwise be the case i f particular behavioural values were assumed. The experimental approach i s discussed more f u l l y i n the following chapters. For the most part, systems analysis i s used to provide the organizational framework. I t has already been noted that most of the planning literature on urban expansion i s evaluative of particular settlement patterns, and f a i l s to come to grips with the processes by which they come about. Con-sequently, this thesis i s concerned, more than usual, with the methodology of applied research as i t relates to planning -? CChapter 2). Because of the generally- haphazard development of urban growth theory and the poor specification of the various processes, the different conceptual approaches to urban growth are examined and compared (Chapter 3). However, i t should be clear that only one of the processes of urban growth, that i s urban expansion, i s of direct concern.. The ultimate objective i s to develop a model' of rural-urban land conversion for the Vancouver metropolitan region, which can be used to increase our understanding of the dynamic nature of the urban expansion process (Chapters 4 and 5.). Although the model i s not presented i n an operational form, because of time constraints and the lack of computer programming assistance, the approach can be supported generally, by empirical evidence on the nature of the' spatial growth of c i t i e s . A summary evaluation of the Study Outline 17 research methodology and comments on the model are presented in Chapter 6. A Note On Terminology It became apparent from comments on early drafts that some of the terms used have acquired various meariings and sometimes in different disciplines, conceptual connotations are at odds with the needs of the present study. In particular, "accessibility" caused a lot of confusion. Unfortunately, this term, along with some others used, often appears in the literature and is used imprecisely or ambiguously. For example, Gould (.1969 p.64) has observed that "accessibility. . .is a slippery notion. . . one of those common terms that everyone uses until faced with the problem of defining and measuring i t ! " To avoid misunderstandings, the practice has been adopted of defining terms likely to be misconstrued, where the concept to which they relate is- discussed. With proper deference to the'English language, the appropriate Shorter Oxford English Dictionary definition has been preferred over others whenever inconsistencies have arisen. mm! a The Law of the Instrument. . . Give a small boy a hammer, and he w i l l find that everything he encounters needs pounding. It comes as no particular surprise to discover that a [planner] formulates problems in a way which requires for their solution just those techniques in which he himself is especially skilled. Abraham Kaplan The Conduct of Inquiry Chapter 2 MODELS AS STRATEGIES Although, planners have used modelling approaches to problem solving as a matter of course for over a decade, i t is s t i l l necessary to look beyond the planning literature to discover the f u l l implications of the use of models. The occasional critique of planning methodology from authoritative sources outside planning CWartofsky 1968, Haworth 1970) as well as the extensive literature on the theory of modelling in other disciplines (e.g. Ackoff 1962, Kaplan 1964, Chorley and Haggett 1967, Bartos 1967), reinforce the opinion that planners s t i l l lack a sound philosophical appreciation of the role of models in applied research.. Without this appreciation, planners are. likely to choose inappropriate research and problem solving strategies for their purposes, for example, a deterministic rather than a probabilistic interpretation of social processes inherently uncertain, or a macro rather than a micro approach to investigating residential location where clearly the diversity of individual decisions is very important. Consequently, in the following, a modest attempt is made to point out theoretical aspects of Models as Strategies 20 modelling commonly ignored or misunderstood by planners, through a discussion of the task of defining a modelling approach. In this way i t w i l l be possible to arrive at a context in which a particular model is appropriate for the present study. The Nature and Role of Models in Applied Research Planning has been described as "essentially anticipatory decision making," in that i t is action oriented (Harris 1970, pp. 197-98). This statement is misleading, not for what is said, but for what is omitted. Like most definitions of complex constructs i t is imprecise and offers only a partial specification of meaning by trying to identify the thing by one or more of its prominent features. Contrary to the more obvious practices, planning is not just concerned with techniques, tools and tactics for achieving prescribed goals. When referring to communities of people, plan-ning entails a philosophy of social order and strategies for regulating i t , in much the same way that planning in business management presupposes as definite form of business organization and process of operation. Thus community and regional planning, insofar as i t is concerned with concepts of social order and cultural evolution, is also a behavioural science, and because i t is action oriented, problem investigation involves applied research (Ackoff 1962, p.8). Before proceeding with a discussion of the role of models in applied research, i t is necessary to digress and consider briefly, philo-sophical aspects of community and regional planning methods. This is neces-Models as Strategies 21 sary because of the confusion surrounding the nature of "planning theory," ("including the ju s t i f i c a t i o n of planrdng methods), which i s only too apparent from recent studies (Hightower 1969, Faludi 1970). F i r s t l y , unlike the natural and physical sciences, planning, to the extent that i t i s a behavioural science, involves two interpretive functions which need to be distinguished clearly: (i) i n i t i a l l y , the com-ponents and structure of a process need to be specified for the purpose of understanding i t s behaviour, and Cii) then, the process i s to be evaluated to arrive at a meaning of the behaviour (Kaplan 1964, p.32). Obviously, the order of the two interpretive functions i s crucial, for i t i s not pos-sible to evaluate behaviour which i s not understood. This i s because the value system inherent i n evaluative methods interacts with and becomes indistinguishable from actual process behaviour. That this elementary point has been misunderstood or ignored i n studies of urban expansion has already been noted. Secondly, the methods for understanding behavioural processes are governed by the same methodological norms which regulate the methods for understanding natural or physical processes (Kaplan 1964, p.33). In other words, there are not two kinds of understanding, but different things to understand." Thus, when i t i s stated that the methodology i n a planning study i s defined largely by the problem being investigated and the purpose of the study (Hamilton 1969, p.88), i t i s implicit that the approach i s also * For what i s meant by "understanding" i n this study, see Chapter 6. Models as Strategies 22 subject to the general constraints of logical scientific methods. However, this is not to imply that rigid adherence to accepted methodologies is a necessary or sufficient condition for scientific progress. Rather, as with the conditions for satisfactory (i.e. scientifically acceptable) measurement, methodological justification is desirable for objectivity and ease of comparative evaluation. It has been suggested that in model building, one of the main objec-tives i s to demonstrate characteristic properties of the particular system being studied (Haggett 1965, p.19). This helps to distinguish models from theories which are more general, conceptually. Barton (1970 p.25) reflects this view when he notes that theories, are purposely broad; they try to generalize over many specific cases. This is really an economy of communi-cation so that man does not need to pass hundreds and hun-dreds of detailed instances from one generation to the next. An object system is one of these detailed instances. To use theory, one must make the generalizations of the theory specific enough to guide the making of observations and the taking of actions. Models serve this purpose. Because models are really an attempt to conceptualize and extend our perception of specific 5 complex systems, they are neither true nor false in a l i t e r a l sense. Thus, the value of a model depends on both the contri-bution the model makes to our understanding of the system i t represents and its: usefulness for planning purposes (McMillan and Gonzalez 1965, p.7). From another perspective, models are strategies not only for analyzing Models as Strategies 23 processes or systems, but for investigating specific problem situations. When faced with a particular problem to be resolved systematically, there are several issues one should consider. First of a l l , i t is necessary to be clear as to the reasons for adopting a specific methodological approach. If i t is proposed to investigate the problem using a model this means i t is necessary to be aware of the characteristics of models to be taken advan-tage of. Secondly, for reasons associated with efficiency and relevancy of model strategy, the purposes of the investigation need to be explicitly defined. Finally, by combining the reasons for modelling and the study purposes with the problem characteristics, a general statement of model strategy- can be derived. In return, the strategy largely defines the type of model needed. It helps in understanding how this i s achieved i f the reasons and purposes which are set out in Figure 1 are described. Bartos (1967 pp.319§27) has described two main advantages to be gained from modelling which he refers to as "deductive" and "heuristic f e r t i l i t y . " Deductive f e r t i l i t y is a function of three characteristics: (i) the model's ability to reflect the nature of real world phenomena, ( i i ) the manner in which i t promotes understanding of process behaviour, and ( i i i ) i t s ability to allow predictions about future states of the process. Heuris-t i c f e r t i l i t y arises from the suggestive nature of models in that a successful model stimulates new observations, experiments and conceptualizations. Synthesizing the reasons for modelling, deductive f e r t i l i t y in a model is its successful abstraction of a specific process or system, while heuristic f e r t i l i t y refers to the extensions that can be made to more general situations. Models, as Strategies 24 F I G U R E 1 D E F I N I N G A M O D E L L I N G S T R A T E G Y DEDUCTIVE prediction explanation HEURISTIC suggestive • generality CHARACTERISTICS OF DESCRIPTIVE components structure behaviour EVALUATIVE conditional-prediction optimization tactics PURPOSES OF STUDY p objectives MODELLING STRATEGY ZT PROBLEM CHARACTERISTICS _ 4-relationships of problem components temporal dimension spatial dimension Models as Strategies 25 The kinds of objectives the model builder is likely to have in mind can be classified according to whether they entail evaluation or descrip-tion of process behaviour. Generally, evaluation involves the prescription of how a model process should behave on the basis of an assumed or inherent value, system, while the description of a model process is a representation of how i t dOes behave. Because evaluative models are normally concerned with alternative solutions, quantitative measurements of variables involved in the process are usually necessary. However, even i f valid, comparable measurements could be taken, unless the process components and their relation-ships have previously been specified satisfactorily, there is no guarantee the variables measured are relevant indicators of process behaviour. More-over, there are great difficulties in ascertaining relevant social indicators (Etzioni and Lehman 1967). While Britton Harris (.1968) seems to imply otherwise, not a l l models need to be evaluative to be useful in applied research and thus in the planning process. In fact, there is a growing tendency for descriptive models to be used, especially . . .as educational instruments which serve to bring to the consciousness of those who make decisions the complex interrelations among the variables, including those which can be manipulated for normative purposes. (Alonso 1968 p.253). With the recognition that too l i t t l e i s known about social processes and system behaviour, more attention is being given to the merits of purely Models as Strategies 26 descriptive models which stimulate greater specification of structural rela-tionships within systems. Hence, instead of spending large sums of money and considerable effort collecting detailed statistics of possibly inap-propriate entities and suspect variables, the main issue becomes one of describing component interaction within the system. Afterwards, the model can be tested to determine the sensitivity of components and a subsequent decision made on the need for more detailed data. Objectives requiring evaluative models give rise to another related issue concerning values and their role, not only in the planning process, but in model building. Because the planning process, especially as i t concerns decision making, involves altering ongoing social and economic processes in order to satisfy certain goals (Wilson 1969 p.3) i t is heavily value laden (Davidoff and Reiner 1962, Wartofsky 1968, Haworth 1970). It has been demonstrated, on the other hand, that models can be devoid of these same values and s t i l l be of considerable help to the planner. Thus i t is imperative the model builder state at the outset, the purpose and role of his model in the planning process, possibly by reference to the criteria shown in Figure 1. Inadequate attention to this issue can lead to ambiguity and frustration for a l l concerned with interpretation of the results, as the history of land resource evaluation models shows only too clearly (Mathieson et a l 1972). To return to our objective of selecting a modelling approach, i t can now be demonstrated, by linking the reasons for modelling, study pur-poses and problem characteristics, that the general type of model needed is Models as Strategies 27 prescribed by the model strategy. Once again models of urban expansion can -be used for illustration. Traditionally, this process has been approached . from one of two viewpoints. Either a micro-analytical market model has been used with urban expansion represented as a function of the aggregate pattern of individual decisions or a macro-analytical gravity analogue.has been used in which new urban development is shown to occur to minimize the frictional effects of distance. Neither approach has proven successful for the long term prediction of urban shape and size for reasons outlined by Lowry (1965) and Brindle (1970). Consequently, a model builder faced with the problem of forecasting the rate, extent and location of future urban growth and deterndning an optimal growth strategy does not have an adequate theoretical base on which to build a model. Because he cannot be certain of the nature of the component processes, neither can he be sure that an intuitively developed evaluation model w i l l produce results reflecting his objectives. Thus i t is necessary to begin with a descriptive model and omit, (for the time being at least), value laden assumptions such as rational behaviour of individuals, until a reasonable specification of system behaviour has been made. While this descriptive model could provide the rate, extent and location of urban expansion as a result of ongoing processes, i t is necessary, in order to find optimal growth strategies, for the model builder to intro-duce evaluative functions consistent with his goals, (e.g. least cost, greatest net benefit, or similar criteria). Here the information provided by the descriptive model becomes input for the evaluative model as shown in Figure 2. In Figure 2, the regional planning process is represented, using a Models as Strategies ~ ' 28 F I G U R E 2 T H E R E G I O N A L P L A N N I N G P R O C E S S DETERMINING STRATEGY PROCESS OF SOLUTION research analysis :: synthesis vK:W; INTERPRETATION implementation N a t u r e o f Pr o b l e m Obj e c t i v e s M e t h o d o l o g y R e p r e s e n t a t i o n o f P r o c e s s e s and Systems u b i i i i e a i i o n or A l t e r n a t i v e s R e s o l u t i o n o f A l t e r n a t i v e s D e c i s i o n I m p l e m e n t a t i o n M o n i t o r i n g R e s u l t s R,e - a s s e s s m e n t o f P r o b l e m Source Scottish Development Department (1968) Models as Strategies 29 flow diagram, as a relatively complex system with three main parts: (i) determining study strategy, ( i i ) process of solution, and ( i i i ) interpretation. In the f i r s t part, the nature of the problem, objectives and methodology are outlined, hopefully with reasons for selecting a particular approach. The second part consists of three stages; i n i t i a l l y , the subject process or system i s specified, then, alternatives are delineated by evaluative pro-cedures and finally, the alternatives are resolved according to whatever value system is chosen. Thus there is a logical solution process through synthesis of the various component processes specified, to evaluation and then recommendations. In the third part, the decision is implemented and results monitored and relayed back into the system. Hence i t can be seen that the regional planning process is a synthesis of a large number of inter-acting and very different sub-models. The particular model suited to any part of the planning process depends on its role and purpose in the process. Types of Models The number of possible modelling strategies, in practice, is virtually unlimited, a fact more apparent when different possible combinations of the dimensions of models are considered. Listed below are some of the different dimensions used to categorize models which can be found in the literature, Csee particularly Ackoff 1962, Lowry 1965, Charley and Haggett 1967, Bartos 1967, Harris 1968, and Walters 1971). The form of presentation used, a sequence of dimensional dichotomies and antimonies, is adapted from Britton Harris' (1968) review of quantitative models and their role in metro-Models as Strategies 30 politan decision making. Unfortunately, his review purposely omits discus-sion of descriptive models (Ibid p. 363) without acknowledging their role in the planning process. Consequently, the review represents only a part of the picture and as a result, often leads to misunderstandings about the nature, and merits of some modelling approaches. In an attempt to correct this situation, I have included several new dimensions and where necessary, made changes in existing dimensions and their terminology. 1. symbolic — iconic 2. descriptive — evaluative 3., synthetic — analytic 4.. macro micro 5. dynamic static 6. probabilistic — deterministic 7, holistic partial 8.. process -- compartmental 1. x'Symliblic'Tlcdnic Models A l l models are representations of phenomena but not a l l are abstrac-tions Here, lies the distinction between iconic and symbolic models. Iconic models represent the same properties at a different scale, they look like what they represent (Ackoff 1962 p. 109). The physical representation of the relevant properties in the architect's design of a building and the plan-ner ''s relief model of a landscape are iconic models. Symbolic models are representations by abstraction, by the use of symbols. When conventional mathematical symbols are used the model can be most easily manipulated (Ackoff 1962 p.10). This classification has been included for the sake of Models as Strategies 31 completeness and the remainder of this review is concerned only with symbo-l i c models. 2. Descriptive-Evaluative Models The difference between descriptive and evaluative models relates not to their form but to their function as perceived by the model builder CBartos 1967 p.299). Descriptive models are representations of what has or w i l l happen as a consequence of the operation of specific processes, in that they attempt to mimic real world phenomena. Evaluative models attempt to stipulate how change should occur on the basis of an assumed or inherent value system (i.e. they involve conditional prediction). Accordingly, they prescribe, how a model process should.behave, other things being equal, not necessarily how i t does behave. To illustrate this point, in the i n i t i a l formulation of the HPS project, there was a conflict of opinion whether the model should seek to optimize certain social goals and values (evaluative approach) or seek only to mirror ongoing processes in the Vancouver Region (descriptive approach). It was decided that the descriptive approach would be adopted (TIPS Serial No. 18, 1970). Sometimes the term "normative" is used instead of "evaluative," to refer to the class of models described. However, as Wartofsky (1968) points out, a l l models are normative (dependent on values) in that they are chosen for some purpose in mind, even i f that purpose is only to aid the understanding of a process or system.. Thus i t is desirable to avoid the use of "normative" in this respect. Models as Strategies 32 3. Synthetic-Analytic Models Whether a model is synthetic or analytic depends upon the metho-dological process required to arrive at a solution (Lowry 1965 p.162). For most modelling purposes the two terms are synonomous with inductive-deductive systems of problem resolution, respectively. Analytic models proceed by way of a process of logical deduction to arrive at a discrete solution, while synthetic models follow a step-by-step procedure to "construct" as i t were, the general solution (Forrester 1968 pp.3-5). It is for this reason that simulation models, which are one form of synthetic models, have been referred to as "experiments" (Barton 1970 p.29). When a process can be represented mathematically and solved analyti-cally', i t is usual to do so. However, often a mathematical statement of a situation cannot be resolved because i t is intractable, in which case synthetic models sometimes referred to as iterative models, are employed (Lowry 1965 p. 162, Hamilton 1969 p.95). It was the intractability of cer-tain mathematical problems concerning the atomic bomb that led to the develop-ment of Monte Carlo simulation during the 1940's (Barton 1970 p.138). By representing the mathematically unsolvable parts of the problems with sto-chastic processes, and by using probability theory, solutions were obtained indirectly through repeated experimentation. 4. Macro-Micro Models The level of aggregation of entities in a population determines whether a model is macro or micro (Lowry 1965 p.160). In macro models the properties of collectives or total populations are used to reflect process Models as Strategies 33 behaviour, for example, the growth force models* of urban growth based on gravity analogues, are macro scale models. On the other hand, micro models focus on the behaviour of individual entities in a population. Economic models based on the assumed rational behaviour of individuals within a market mechanism, which seek to optimize the allocation of resources, are examples. There is s t i l l considerable disagreement of the relative advantages of each, approach and Goldberg (.1970 p.3) has claimed that bridging the macro-micro gap remains one of the most important unresolved problems in modelling metropolitan development. Lowry (.1965 pp.160-61) who prefers the macro approach., and Harris (.1968 pp.373-75) who takes the opposite view, provide details of the respective positions. 5. • Dynamic-Static Models The feature element of this division is the treatment of process operation through time. Dynamic models concentrate on the changes brought about through the operation of processes, or variance in process components and functions, through time, while static models focuson equilibrium condi-tions of structural features in the past, present or future (Echenique 1968 p.13). Regional land use plans, based on a series of social, demographic and economic projections, and showing the proposed "optimal" allocation of resources at some future date, are essentially static models. Regional land development models, describing changes in land use over time, as a result of " In Growth Force Models "the dynamics of human behaviour and urban growth are based on assumptions about social forces rather than individual ddecisions" CKilbridge et a l 1970 p.15). Models as Strategies 34-population growth, increased economic activity and the like, are dynamic models. 6. F^obahilistic-Deterministic Models The outcome of a process can be viewed as (i) a function of chance events, which could have produced a quite different result, or ( i i ) as a function of specific cause and effect relationships between events which could produce only one result (.Curry 1966 p.40). Models reflecting the former view, and representing processes as stochastic, are probabilistic models, and successive runs of the model can produce varying results (Springer et al 1967 p.37). By comparison, deterministic models assume an understanding of causal relationships within a process, to arrive at predictions of single unique outcomes or changes as a result of process oper-ation . The variable results generated by probabilistic models do not mean the methods for handling stochastic processes are conceptually impre-cise; on the contrary, they allow forecasts of process behaviour with very specific probabilities attached (Bartos 1967 p.8). Whether the use of either type of model is suitable or necessary in a particular case is indicated by the nature of the process being modelled and the purpose for which i t i s needed (Harris 1968 p.378). 7. Holistic-Partial Models Each process or system can be represented by a number of com--ponents or subsystems and the manner in which this is done in a model deter-Models" as Strategies 35, mines whether i t i s holistic or partial (McMillan and Gonzalez 1965 p.9). A holistic model represents a l l components and subsystems and their inter-actions, to provide a general picture of the system's total behaviour. A partial model seeks to provide a detailed picture of specific parts of the system (Harris 1968 p.371). Thus the focus of the model builder, the number of variables determined outside the model and the purpose for which the model is needed, a l l indicate whether a model is partial or holistic. For example, i f the Vancouver metropolitan region were the sub-ject system and a model was required to generate the rate, extent and loca-tion of urban expansion, then one approach would be to focus on the rural-urban land conversion process and enter variables such as population growth and economic development, exogenously. This would be a partial model because essential structural components of the process were being determined independently of the model. However, i f a model of the metropolitan area were produced with a l l the pertinent processes generated endogenously, as is being attempted in HPS, then i t would be a holistic model. 8.. - Process-Compartmental Models This dichotomy reflects an emerging consciousness on the part of model builders between structural and aggregative methods of model building, and the different ways they reflect wholeness, transformations and regulation within systems CPiaget 1970). Compartmental models, adopting the aggrega-tive approach, seek to represent systems as a composite of elements that are viewed, i n i t i a l l y at least, independently of the total system and described Models as Strategies 36 in terms of history, morphology and function. Process models, adopting the structural method, seek to represent systems by the interactions or relation-ships (i.e. processes) linking component elements (Walters 1971 pp.285-92; Holling 1972 pp.5-9). To illustrate the different methods, consider again the problem of inodelling urban expansion. One common compartmental approach, economic market models, requires urban land uses to be segregated into functional categories; residential, commercial, industrial, institutional and open space. Future land requirements for each activity can be generated according to individual "rent ceilings" and historical locational preferences. Aggregation of each sector's land requirements represents the pattern of urban expansion. Alternatively, a process model would focus on the interactions of key comp-onent elements in the rural-urban land conversion process. A model relating the dispersal of urban development to the interplay of' centrifugal and centri-petal forces governing location would be a process model. There is another dichotomy used frequently by planners in connection with models which relates to their predictive or explanatory nature (Lowry 1965 p.159; Alonso 1968 p.253; Kilbridge et al 1970 p.11). If I understand the import of this division correctly, then i t appears that there is either considerable misunderstanding among planners concerning the nature and purpose of models,, or that this particular use of terminology is ambiguous and to be avoided. "Explanatory" is generally used in these discussions in the sense of describing process behaviour in a similar way to that of descriptive models above (i.e. to represent operation and interaction of process components) Models as Strategies 37 while "predictive" is used to describe the ability of the model to arrive at conclusions .of what w i l l happen in the future. In fact, descriptive models are often used to provide forecasts of future states of the process or system and thus they are also predictive, in the sense that they are uncon- ditional predictors (i.e. not constrained by value inputs and goals). What is generally implied when predictive models are referred to is that the prediction is conditional upon (i) a particular event occurring, for example, the implementation of regulating policies, public development and the like, or ( i i ) a prescribed value system, for example, by optimizing resource allo-cation on the basis of assumptions of rational behaviour. Thus conditional predictive models are evaluative models. A final note on terminology is appropriate. There are frequent misunderstandings concerning the' meaning and proper use of the terms "pre-dict" and "forecast." Work (1968) in an excellent summary paper of the steps in decision making, chose to distinguish the terms in the following way-: . . .forecasting is the process of stating an e s t i -mate of what one expects to occur in the future. Hopefully, this statement also contains information pertaining to the uncertainty of the estimate. Prediction, on the other hand, connotes stating what w i l l occur in the future. Prediction is the province of the omniscient; forecasting is the province of (among others) the decision maker. (Ibid pp.16-17) While Work's distinction is supported generally by dictionary definitions of the. two terms, common usage tends to equate them. It seems that both are Models as Strategies 38 satisfactory, so long as i t is clear that neither term is without qualifi-cation as to the degree of error when used in connection with modelling. Causality and Chance: Accounting for Uncertainty When l i t t l e is known about the behaviour of a particular process, or when component elements of a process fluctuate inexplicably, the model builder is faced with the dilemma of how to account for uncertainty. At f i r s t , i t may not be known whether the uncertainty is a function of elements essentially random by nature or due to incomplete information about the process. The situation is further confused by the knowledge that the aggre-gate pattern of a multitude of chance events may be ordered behaviour with an apparent causal explanation, and alternatively, that the interaction of independent and individually deterndnate events may result in random patterns (Bunge 1963 p.194). There are some situations where observations of a particular process can be repeated under similar conditions but where, however rigorously uni-form conditions are maintained, irregularities occur in the operation of the process and the change produced is s t i l l variable. In this case i t is highly likely a component element is inherently random. Usually, however, i t is not possible to observe the same phase of process operation repeatedly under controlled conditions, in which case experiments with models may pro-' vide clues to the nature of the process. In applied research where the problems are more urgent, the issue is far more cr i t i c a l because action cannot be delayed indefinitely. But to Models as; Strategies 39 ignore the uncertainty may be to ignore the proper nature of fundamental causal relationships. Sometimes i t is felt that process behaviour has been adequately explained and structural relationships properly specified. In this situation, the treatment of uncertainty is relatively simple. A deterministic model can be used with the components provided with different values in each run of the model, (representing their probability range), to arrive at high and low outcomes, or optimistic and pessimistic future states of the process (Barton 1970 p.121). This is the technique of incorp-orating uncertainty in a deterministic framework. It entails the 'assumption of knowledge of causal relationships within the system being modelled. More often than not, planning involvement with urbanization pro-cesses and regional development requires the modelling of systems which are imperfectly understood. Ih these circumstances i t would be better to approach the problem acknowledging ignorance. This is the primary merit of probabilistic models, they do not require or assume the specification of causality within the model process CCurry 1966; C. Harris 1968; Barton 1970). The outcome is viewed as the realization of a stochastic process which could have just as easily produced a different result according to the probabili-ties attached to the component elements. This viewpoint is not difficult to grasp when i t is appreciated that the basic entity in social processes, at least to the planner, is the human individual, (although normally treated in the aggregate). It is a l l the decisions made by individuals and institu-tionalized groups of individuals that result in changes in social systems. Because the absolute number of decisions involved in a l l but the most Models as Strategies' 40 microscopic systems is enormous, and because of the incredibly diverse factors influencing these 'decisions, we are only just beginning to describe some basic decision forms (Isard 1969). We are s t i l l a long way from an under-standing of causal connections in social systems that account for elementary decision processes, possibly for the reasons given by Bunge (1963 pp.194-197) which were noted earlier. Therefore, i t seems eminently reasonable to suggest probabilistic modelling approaches to many of the problems confronting regional planners. However, what appeared to be a logical trend in this direction has been criticized as fadish and counter-productive (Harris 1968 p.318). As the c r i t i c , Britton Harris, is one of the more prominent and respected advocates of modelling in urban planning, i t is fitting that his criticisms be answered. Harris argues that while there w i l l always be chance elements in the patterns and processes of urban phenomena, the construction of models involving stochastic elements does not necessarily preclude the use of deterministic models. He allows of very few exceptions to his doctrine. For example, he claims that uncertainties arising out of human behaviour, particularly technological change and important decisions concerning the urban stmcture,' (.e.g. important communication links), should remain outside the model to be entered as inputs at the discretion of the investigator. Other uncertainties resulting from inconsistent behaviour, even those inher-ently random, should be included in the model as probabilistic statements of the error of measurements but within a deterministic framework. It is Models as Strategies 41 significant to note that this attitude corresponds to early views on the nature of indeterminism in science which are.notlonger generally supported (Neyman 1960). In his criticism of probabilistic models he seems to be saying that their outcomes are of l i t t l e or no practical interest as such because they represent chance distributions which are difficult i f not impossible to replicate. Consequently, they are difficult to relate to the planning-decision process. Further, they involve treating many phenomena as ran-domly motivated when in fact they may not be. On the other hand, the over-' riding advantage of deterrriinistic models, (note that Harris is only con-sidering evaluative models), is that they provide optimal solutions, on the basis of the information used, which can be demonstrated repeatedly. Harris has raised two issues; f i r s t l y , he considers that the objective of modelling is predominantly to generate results (conditional predictions) which are both reliable and repeatable as an experiment, and secondly-, he has questioned the treating of man's behaviour and activities as random. In relation to the f i r s t issue raised by Harris, i t is a short-sighted perspective of urban and regional problems which considers the r e l i a b i l i t y of a model's predictions in a unique case as the primary measure of i t s value, although at a particular stage of the planning process this aspect may appear to overwhelm a l l others in the eyes of planners. The ability to predict does not, by i t s e l f , provide solutions to urban problems. For example, even when i t is known that urban expansion w i l l occur, or is Models as Strategies 42 very- l i k e l y to, the responsible decision making body i s often unable to avert what may be perceived as the undesirable consequences, for a number of reasons. A satisfactory solution may not be known; constraints imposed by the cultAjral-institutional framework may effectively preclude implementa-tion of a policy at the appropriate spatial-temporal dimension believed to be a solution; or i t may be considered pointless to implement a policy known to be effective because i t has indirect consequences considered just as undesirable as the original problem. I t i s implicit i n the search for solutions to planning problems that the process i s understood and can be regulated. The control and regulation of dynamic processes and systems i s dependent, as McLoughlin (1969) has pointed out, upon knowledge of how they- operate and the way they react to different intervening policies. Moreover, this argument does not take into account the fact that planners are continually being frustrated i n their efforts to avert problems, such as those resulting from urban growth processes, because of the unexpected, chance elements i n the evolution of communities and their environments that no one could have foreseen on purely scient i f i c or rational grounds. Notwithstanding, Harris' viewpoint ignores an elementary but nonetheless crucial aspect of s c i e n t i f i c and planning philosophy which i s inherent i n the continuing drive for greater verification of general the-ories. Models i n this respect are merely mental props necessitated by the. number and complexity of variables being handled. Apart from the model's predictive a b i l i t y , the model building approach provides an excel-lent opportunity to gain insight into the processes at work, i n the system Models as Strategies 43 being studied, through experimentation. This quality has already been dis-cussed and was referred to as the model's heuristic f e r t i l i t y . As a result, decision makers and model.builders develop greater insight and become capable of asking better questions with their new found appreciation. More importantly, Harris is to be criticized for supporting deter-ministic modelling approaches in situations where i t is clear the process or system is imperfectly understood., Acknowledging limited understanding of relationships within a system on the one hand, and then assuming they have been correctly specified in the model, (inherent in the deterministic approach!, on the other, is contradictory and amounts to a logical inconsis-tency- in the methodological approach. Herbert Simon alludes to this point when he notes that: . . .the use of modelling in planning requires that the important features of system structure be already known^-that i s , that the basic research job has already been done. For this reason, the most serious limits on the use of modelling in planning today are limits on our understanding of system structure, not on limits on our data about the state of the system (Simon 1968 p.,367). The second issue can be clarified by reference to Gordon (1969 p.851 who points out that there are three cases where activity or behaviour can be legitimately treated as random for modelling purposes: (i) when the activity is random by nature', ( i i ) when the activity, although not random by nature, is poorly understood due to a lack of information about its beha-viour and ( i i i ) when the activity, again not intrinsically random, is Models as Strategies 44 causally- so complex that the aggregate activity pattern is considered ran-dom, within certain constraints, as a matter of necessity. An example of a study operating on the assumption of the second class is to be found in Curry's (1964) work where he argues cogently that men, motivated by various ideas, acting upon different degrees of infor-mation and operating in differing circumstances, act so that . . ..from the point of view of the locational structure as a whole, their actions appear as random (Ibid p.146). Examples of the third class are applications of sophisticated. Monte Carlo simulation to find solutions to problems otherwise intractable (Hammersley and Handscomb 1964). Finally, there is a practical problem arising from the use of deterministic models frequently ignored by both the model builder and the model user, which is explicitly accounted for in probabilistic models. Generally, the researcher-model builder cannot (or where he can is reluc-tant to do so), ascribe confidence limits to the predictive capacity of the model, deduced from the reliability of the data used. Subsequently, there is a dangerous tendency for predictions from deterministic models to be regarded with a respect not due to them. That each run of a deterministic model with the same inputs results in exact replication seems to reinforce this tendency, at least in the minds of some users. In conclusion, i t is proposed to advance, somewhat tentatively, guidelines for probabilistic modelling although i t is realized the evidence presented does not support them soundly. However, I am encouraged by a Models as Strategies 45 number of observations, not the least of which is the decline in recent years in the traditional bent for deterministic modes of logic (Neyman 1960) and the theoretical underririning of optimality concepts (Simon 1957). While these trends in the methodology of science cannot be logically equated with progress, fashion i t s e l f , as Kaplan has noted (1964 pp.292^93), does not necessarily preclude scientific achievement. In this age of "dynamic ^determinancy" (Neyman 1960), i t may be that social science can only aspire to probabilistic explanation in view of the nature of the phenomena dealt with (Nagel 1961). If, in the recent past, there were believed to be no a priori reasons for selecting a deterministic or probabilistic modelling approach, there appears to be emerging a convincing argument favouring the latter, where future states of social systems- (i.e. involving significant temporal dimensions), are being studied. In previous centuries when changes occurred at a slower pace, the causality principle made a lot more sense than i t does today. Because of the rapid assimilation of technology and i t s profound effect on the dynamic nature of social systems, statements of causality in social processes appear to ignore the temporal aspect of reality as we are beginning to appreciate i t . This means we must acknowledge the inadequacy of present specifications of cause-and-effect relationships in social pro-cesses, for the future. Thus the f i r s t guideline for probabilistic modelling can be. stated thus: Condition I: Probabilistic models should be used whenever the problem concerning the investigator, involves time Models as Strategies 46 dimensions in which significant and unpredictable changes can be expected to occur in the nature of component elements. The corollary is that deterministic models are best suited to static conditions.1 Obviously, the relevant time dimension changes with different social processes for the reason that some process components are more sus-ceptible to change. In the telecommunication field where revolutionary changes seem to be the order, almost annually, forecasts of the situation five years ahead may be excessive for deterministic models, while forecasts of population growth in most regions might be made with reasonable reliabi-l i t y by deterministic models ten years ahead. In cases where the use of deterministic models is not precluded by the time dimension limitation, i t may be s t i l l more appropriate to use a probabilistic model. When there is incomplete explanation of the process or system behaviour i t - i s necessary to use a probabilistic model i f a logi-cal inconsistency in the methodological approach is to be avoided. This point has already been discussed. Thus, the second conditions can be stated: Condition II: Probabilistic models should be used when-ever'cause-ahd-effect relationships between process com-ponents cannot be specified with reasonable assurance of their reliability. What is "reasonable assurance" in any situation depends on the purpose of the model and is largely defined by the level of confidence required of .model predictions. Finally, i f the process or system being modelled involves component elements which are inherently random, then a probabilistic model is appro-Models as Strategies 47 priate, though not absolutely necessary. It may be-that the uncertain behaviour of one or more components can be adequately accounted for in a deterministic model by changing their values for different runs. However, i f these random components are central to the whole process and tend, there-fore , to dominate process behaviour then a probabilistic model is definitely required. Condition III: Probabilistic models should be used when-ever the process being investigated contains component elements inherently random, however, this rule may be relaxed i f the components only play a subsidiary part in process behaviour, so long as they are represented in different runs of the model with opposing limit values. It should be recognized that the guideline statements are not in-dependent but contingehtcconditions for selecting a modelling approach.. For example, before a deterministic model is decided upon in accordance with the third condition, the previous two need to be satisfied. In conclusion, the representation of stochastic processes and the application of probabilistic models to practical issues concerning the re-gional planner is a field of research with recent origins and many unsolved problems.. Because stochastic processes have proven particularly useful for the representation of phenomena exhibiting uncertain and rapid change over time, probabilistic models are being used to an increasing extent by those who wish to understand the nature of evolution and transformations within processes and systems (Haggett 1965 pp.23-7, Bailey 1967 pp.1-4). Models as Strategies 48 Statisticians have sought to represent stochastic processes in rigorous theoretical formulations which now form the bulk of probability theory. These formulations are mathematically complex and the ability to derive original formulations suited to the more complex planning problems has proven beyond the skill s of even the mathematically gifted. However, there is a considerable body of applied mathematics, adopting a more heuris-t i c approach, which can be utilized to investigate the problems encountered in the regional planning process, with explicit recognition of uncertainty. Generally, these are the methods of probabilistic modelling. Chapter 3 MODELLING THE URBAN EXPANSION PROCESS In Chapter 2, the nature and role of models in the examination of planning- problems were considered in the context of selecting a model-ling approach. It is proposed in this chapter to describe particular characteristics of the urban expansion process which have a bearing on the selection of a. model.. Every model of the urban expansion process contains a theory of the spatial growth of cities tying the model to the real world. There can-not be a ''theory-less' model, for i t is either based on theory or abstracts and structures urban growth phenomena to a simpler form, thus creating theory- (Kilbridge. et al 1970 p.13). For example, models based on the gravity concept, whereby human behaviour and urbanization processes are considered in a growth force context, are theory based models. Lowry's C1964-) model for the allocation of residential, industrial and commercial activities in Pittsburg is of this, type. Market models, such as the model of the land conversion process by Drewett (1969), are also theory based, Modelling the Urban Expansion Process 50 relying on concepts of rational choice within the market and general equili-brium conditions. An example • of a model starting from observed phenomena and structuring the criteria inductively, thus creating theory, is the simula-tion model of urban expansion by Malm and Warneryd (1967). As a result of research into diffusion processes and the influence of barriers on urban growth by Hagerstrand (1965, 1967), Morrill (1965, 1968), Brown (1968), and Korcelli (1970), diffusion models of urban expansion could be developed which were theory based. However, most of the operational diffusion models are descriptive with inductive methodologies, and are thus more theory creative than theory based. It is interesting to note, however, that descriptive analogues of diffusion processes have been used to explain patterns of urban development for many years. The works of Burgess (1925) and McKenzie (1925), Blumenfeld (1954), Vance (1964) and Griffin (1965) are some examples. Spatial and Temporal Dimensions Each problem of land resource planning has its appropriate time and space dimension of study. Consequently, i t is important to regard, in proper perspective, the level of inquiry and the issues sought to be re-solved here. Firstly, the appropriate spatial dimension for exandning urban expansion processes does not correspond well with that involved in existing settlement theories. Settlement patterns and growth processes have been traditionally examined from one of two viewpoints. From one viewpoint, the objective has been to describe patterns of cities within a state or continental JMbdelling the Urban Expansion Process 51 framework., as exemplified by central place studies. From the other, the internal stoicture of urban areas has been the focus for analysis, shown by concentric ring and sector theory approaches. These approaches, refer-red to as the macro and micro-scale approaches respectively, were designed for purposes different from that in ndnd in this study. • Here we are con-cerned with forecasting where and when urban expansion w i l l occur as a result of growth processes far enough in advance to permit regulatory action to be taken, i f necessary. In this case the metropolitan region is the subject system; an intermediate order or scale which for the sake of con-sistent terminology-, can be called the meso-scale approach. While neither the macro or micro scale approaches is particularly suited for forecasting where and when urban expansion w i l l occur, at least in a way that reflects the mechanics of the expansion process, a meso-scale approach can be designed to specifically reflect these aspects. Secondly, we are dealing with a process which falls within the ambit of long range planning, with a time dimension of approximately 5-10 to 2.0-30 years ahead. Within this time scale, we are concerned with only those characteristics of the urban expansion process, which can be reasonably expected to persist. The greater the dependence of the variables included, on current levels of technology and patterns of social and economic behaviour, the greater the possibility of results diverging from what w i l l happen. Thus only the basic structural elements of the process, at the metropolitan regional scale, with long term implications, should be incorporated into the model. However, at the same time the results need to be sufficiently Modelling the Urban Expansion Process 52 precise to be of use in the long range planning process. It is unlikely that this dilemma can be resolved completely in any one model. The best that can be done is to justify as far as possible on the basis of existing knowledge, the structure of component processes in the model, and demonstrate that the likelihood of changes in their composition is slight for the time horizon under consideration. However, i t is possible to avoid gross assumptions about the dynamic nature of behaviour and technology, and thereby blunt the edge of arguments against forecasting. One purpose of having a series of interrelated land use models in HPS is to systematically increase the degree of resolution of land use and decrease the level of uncertainty with progressively shortening time horizons. Different assumptions about behavioural patterns and tehhnological change in. the separate models can be formulated to accomplish this. Thirdly, the model which accurately replicates past performance of urban expansion in the Vancouver Region is unlikely to be the appropriate model for simulating future growth. There is l i t t l e basis for expecting that the unique forces which molded city shape and size until now w i l l per-sist in the same form in the future, for with the assimilation of new tech-nology and the evolution of new social and economic, behavioural patterns, different factors w i l l undoubtedly play an important role (Wartofsky 1968). The uncertainty resulting from new innovations and social evolution which cannot be forecast and which inevitably alter the course of development (Drucker 1959), decreases the specificity of forecasts that can be made as the time horizon increases. Thus land w i l l not be allocated to particular Modelling the Urban Expansion Process 53 urban activities by the model of urban expansion, as this w i l l be handled by sub-models designed specifically for this purpose (Goldberg 1971) This point underlines the importance of connecting the patterns of behaviour of individual decision makers, represented by the micro-scale models, with the total behaviour of the system (Lowry 1965, Goldberg 1970). Ideally, i t should be possible to make judgements about the actions of individuals from the concepts inherent in the macro-scale models (Wilson 1970) but because this has generally proven impossible, the intermediary models should reconcile the inconsistency. Traditional Models of Urban Expansion The issues discussed above provide a suitable basis for evaluating traditional models of urban expansion. Two types of models in particular, market and gravity models, have been used frequently in the past and might normally be considered. Market models are the main kind of a group of behavioural models which are based on a concept of man as a rational decision maker attempting to optimize his- welfare according to prescribed criteria, such as locational advantages. The pattern resulting from the aggregated individual decisions represents- the product of land market planriing. Conceptually and practically, land market planning stands as the pole opposite to state planning through legislation. Where legislation for the allocation and organization- of land- resources, including the regulation and prohibition of activities, is extensive, the likelihood is low that Modelling the Urban Expansion Process 5 4 market planning forces are creating the settlement form and structure of the area. Because the conversion of r u r a l land to urban uses has been characterized by a plethora of c o n f l i c t i n g interests (with equally sincere groups of farmers, developers, speculators, and conservationalists at odds as to what should be done i n the best interest of the community) the ten-dency f o r ad hoc responses by.government bodies to the demands of various pressure groups has not been uncommon. As a r e s u l t , the conversion process has become a confused medley of resolutions by uncoordinated government planning and market mechanisms (Clawson 1971). Therefore, i t would be extremely d i f f i c u l t at present, i f not impossible, to determine causal relationships between urban form and growth processes. Even within the scope of a large scale project such as HPS, i t would be a costly and probably impossible task to evaluate the influence of s p e c i f i c governmental and private decisions r e s u l t i n g i n the present ubban form, and even then extrapolation into the future could hardly be j u s t i f i e d . We cannot be even reasonably sure that the severely constrained land market operates at a l l as theory or i n t u i t i o n dictates CDrewett 1969). While the foregoing reason i s no doubt s u f f i c i e n t , there are a number of other grounds f o r r e j e c t i n g market models of the land conversion process. F i r s t l y , they show a strong dependence on c r i t e r i a such as land prices (a surrogate f o r a host of 1 landscape and socio-economic features), which fluctuate widely over time (Hoyt 1960), and depend to a large extent on v o l a t i l e s o c i a l and economic conditions. Secondly, the basic assumption of r a t i o n a l individuals and groups optimizing t h e i r welfare, when they have Modelling the Urban Expansion Process 55 only-imperfect information, and d i f f e r e n t constraints, i s questionable (Simon 19571.. Thirdly, the i n t e g r i t y of the approach suffers when diverse interest groups,,for example, r e s i d e n t i a l commercial i n d u s t r i a l , public authority and the l i k e , are aggregated.. The micro-analytic market. approach i s better suited to situations where high degrees of resolution are required f o r short periods ahead and when diverse i n t e r e s t groups or a c t i v i t i e s need to be separated. I t was f o r these reasons that a d i f f e r e n t t h e o r e t i c a l approach than a market-behavioural approach was sought. Gravity models are the simplest and most popular of. a group of macro-analytic models based on a greffafth force concept derived from Newtonian physics. In t h e i r simplest form they assume r a t i o n a l i t y and r e g u l a r i t y i n describing mass behaviour CKilbridge et a l 1971 p.15) according to the p r i n c i p l e that the a t t r a c t i v e force of a centre (e.g. the CBD), varies directly- with the mass of the centre (e.g. commercial f l o o r space) and inversely with the distance from the centre. When several centres are involved each exerting an a t t r a c t i o n a l force, the concept of intervening opportunities i s used to allocate proportional a t t r a c t i o n . This r e s u l t s i n p r a c t i c a l d i f f i c u l t i e s , however, f o r the actual e f f e c t of the intervening opportunity i s d i f f i c u l t to guage, as i t depends heavily on unique s o c i a l and c u l t u r a l patterns of behaviour CBrindle 1970). The gravity models have not been followed f o r reasons less pragmatic and more th e o r e t i c a l i n nature. As Isard (1960) and Harris (1966) have capably demonstrated, the gravity analogue dependency on smoothed Modelling the Urban Expansion Process 56 and aggregative data (i.e. distance and population), conceals important differences in the effect of accessibility for disparate activities and components of population. The practice of weighting various population groups and transposing straight line or cross country distance into sur-rogate indices such as trip-time, while necessary to better mirror reality, seems to be falling into the trap of patching up inadequate theory (Harris 1966 p.264). More importantly, however, is the deficiency of gravity models in reconciling the macro and micro-analytical theories of urban development and metropolitan expansion. Gravity models have very poor specification of the actual processes of expansion and i t is not possible to deduce expli-cit information about the behaviour of the individual decision makers. To summarize: . . ..the basic criticism of models of this type is not that they do not work--so far they have been used with greater success than microscopic models—but that there are theoretical and practical objections to the lack of explanation of causes. Critics point out that i f pro-jections are to be based on the assumption that present aggregated characteristics w i l l apply in the future, then we should know the reasons for these characteristics i f we want to modify them to f i t possible changes in behaviour CBrindle 1970 p.2.25). There are a number of other types of growth force models which have, been used for modelling urban expansion. One in particular, the Modelling the Urban Expansion Process 57 probabilistic model of residential land development by Donnelly, Chapin and Weiss (1964), has been influential in recent research. In this model, a growth index, based largely upon the "attractiveness" of differ-ent sites, allocates land to residential use. The criteria for determining site attractiveness were derived from a previous study of the factors influ-encing development, in which regression analysis was used extensively (Chapin and Weiss 1962). Some of the features incorporated in the growth index were land values, availability of sewerage, and accessibility to employ-ment nodes, major communication corridors and elementary schools. The reliance of this model on. factors, such as land values, which fluctuate con-siderably over time for reasons not necessarily associated with the urban condition, i s a major deficiency for long term forecasts. Further, while the approach is- essentially behaviouralistic in that residential preferences play- a central role, the model falls short of promoting a reasonable explan-ation of the urban expansion process at the scale desired. For example, the overall directions.of growth are taken as given and entered as inputs in the model.. This limitation is recognized by the authors who emphasize that testing the particular methodology for application was their primary purpose in this- particular model. Diffusion Models The spatial patterns associated with the growth of settlements have been frequently characterized by diffusion processes. Generally, diffusion can be considered the outward movement of a process or activity Modelling the Urban Expansion Process 58 as a result of centrifugal forces. At the macro-rscale, Turner's frontier hypothesis of the westward spread of•settlement in the United States (Turner, 1920), Perry's analysis of the spread of settlement in New South Wales (Perry 1963) and the 'Berkeley School' of settlement geography, led by Carl Sauer, have their common bases in diffusion analogues. Nearer to the micro-scale, spatial diffusion, to describe the outward spread of city-type settlement, has been used in several recent studies to develop models for predicting the timing and location of urban expansion. Morrill (.1965) for example, hypothesized that the expansion of the. urban fringe is a spatial diffusion process in which new development, essentially random in direction (.land being equal), follows a direct pro-bability distribution with respect to variations in land and neighbourhood quality and follows an inverse probability distribution with respect to distance from existing development. Morrill, being dissatisfied with the deterministic models of urban spatial structure and growth, adopted a stochastic approach whereby a probabilistic function is used to describe the relationships between the variables. His choice of variables and conceptualization of the development process reflects considerable dependence on the work of Chapin and Weiss (1962). He details for each of ten elements (constituting propinquity to existing development, accessibility and site quality characteristics), probability statements based on empirical data obtained from a study of actual land use changes in the north Seattle area. This information when incorporated into the model, permitted Morrill to simulate expansion in the study area. The patterns established by the Modelling the Urban Expansion Process 59 simulation runs were at odds with the real world in some places, but con-sidering; the project was s t i l l in i t s preliminary stages and the somewhat intuitive formulation of the model, not sufficiently far off to wholly discredit the effect. Differences found seemed to reflect underestimation of institutional effects, such as land ownership patterns, degree of land fragmentation, and variation in land quality. Malm and Warneryd (1967), in a more simplistic approach, attempted to simulate urban growth as a diffusion process incorporating barrier effects. Again, the influence of Chapin and Weiss' (1962) work is noticeable, but more'importantly, the authors have sought to build their model on a stronger theoretical base. To this end they relied on Yuill's interpretation of the influence of barriers in spatial diffusion processes (Yuill, 1965). The simulation model was based on the hypothesis that the degree of sprawl evidenced by a metropolitan community depends upon variations in total construction costs resulting from terrain characteristics, communication and u t i l i t y networks. Costs are related to hypothetical housing units. The range of the set of random numbers reflected the magnitude of development costs. A grid was placed on a map of the study area, part of the district of Hisihgen, in Gothenburg, Sweden, and a set of random numbers assigned to each square. According to the rules of their 'game', squares where the terrain provided good foundation conditions were classified by number 1 and i f 'hit' were accepted for development immediately. Number 2, hard bedrock areas, had to be hit twice and number 3, clay areas, had to be hit Modelling the Urban Expansion Process 60 three times before acceptance. After each acceptance, costs for services and u t i l i t i e s were readjusted according to the new conditions, construction costs recalculated and transformed once again to random numbers and the game repeated.. This sequence was repeated at regular intervals for the period 1920-40. The simulated pattern did not compare accurately with ' the actual built up areas. This is attributed, by the authors, to insuf-ficient differentiation of the study area, due to the large square sizes used, and also as a result of underestimation of the importance of proximity to previously built up areas. Considering this simulation study was conducted without computer f a c i l i t i e s , which were not available, (therefore i t was only feasible to use a small number of cells and fewer variables)', the approximate comparison obtained by the theoretical model of the real situation' is a creditable performance. Yuill (1970) synthesizes many of the elements, providing a focus for the two studies discussed above, into a general simulation model of urban spatial growth. The success he achieves demonstrates that the diffusion approach, reconstructed in i t s entirety since the early descrip-tive analogues, has considerable potential. His model for operational convenience is deterministic, and limited to a description of relationships between a large number of factors resulting in the shape, size and intensity of urban development.. Thus i t represents the product of both urban spatial growth processes. He uses the growth and distribution of population, in terms of varying density surfaces, as a universal metric in the model. Following a diagnosis of the principal factors influencing urban spatial growth, in which he relies heavily on the works of Borchert (1961,1962) Modelling the Urban Expansion Process 61 and his own earlier study (Yuill 1965) for the influence of the physical landscape, and of Chapin and Weiss (1962) for factors related to the cul- tural landscape, he formulates three input parameters: (i) the capacity  of the urban site is a synthesis of factors determining the maximum capacity of residential population for any site and includes land suitability, com-peting uses of land, the nature of housing and social and political restric-tions ; ( i i ) site permeability and rate of growth is a function of character-is t i c s , classified as having an accelerating or retardating effect on growth rates, such as varying topography, waterside locations, and proximity to polluting industries; Ciii) connectivity and differential growth is a synthesis of accessibility factors and they can either impede or facilitate urban development. Allowance is made for their influence in terms of effective rather than direct distance measurements. The values of input parameters remain constant throughout the simulation and no allowance is made for technological changes and the possible influence they may have. Nevertheless the simulated growth pat-terns for eleven cities selected in the U.S.A. are good, (better generally for the smaller cities than the larger ones) particularly as no account is made of important unique events (e.g. major bridge), in the simulation of the individual city. The model i s primarily concerned with the general factors of spatial growth and not the particular factors. While Yui l l substantially f u l f i l l e d his objectives, the study has a number of weaknesses in relation to the purposes of the present study. Firstly, no attempt is made to distinguish, (or explain the codification of) Modelling the Urban Expansion Process 62 the spatial expansion process from the spatial intensification process, which i s more serious than may be immediately apparent. Brown (1968 pp.34—35) records that recent research on spatial diffusion processes tends to indicate that different phases of diffusion (e.g. expansion-intensification) are controlled by different processes. Secondly, there is no supporting explanation of actual process operation or social beha-viour (cf.. Korcelli 1970). The model seems too purposeless in its des-criptive structure. Finally, the factors influencing spatial growth in-corporated in the model, relate specifically to residential activities. It i s a pity Y u i l l could not overcome this specialization and in fact pro-duce a general model for urban growth. Korcelli's (1970) work emphasizes the mechanics of diffusion processes more strongly than do the studies of Morrill, and Malm, and Warneryd. As a point for departure, Korcelli has taken the concept of interaction between centrifugal and centripetal processes of population dispersal (Blumenfeld 1964) which., when combined with the fact of spatial growth on the urban periphery, implies a wave-like pattern of metropolitan expansion. By such a description, he means to imply both frontal and axial growth. The i n i t i a l , theoretical basis for Korcelli's model lies in the accessibility approach; that i s locations! decisions are considered to be taken so as to minimize the frictional effects of distance. In successive refinements, however, he departs frcm the gravity concept and includes geo-graphic, social, and economic characteristics and relationships. The f o l -Modelling the Urban Expansion Process 63 lowing is a summary of his procedures. 1. The i n i t i a l model, because i t assumes a Von Thunen type isolated and homogenous landscape, is constructed solely on accessibility criteria. The . resulting pattern is symmetrical.. 2. In the second step, the sociological concept of human succession (pene-tration, invasion, consolidation, and saturation), i s incorporated, dis-torting the symmetrical shape. 3. At the regional scale, fluctuations in growth rates are caused by external forces such as economic, political and technological change. These factors are included by oscillating rates of increase of metropolitan territorial'expansion. 4. In the fourth step, the differential attraction of regional sub-areas is accounted for. The factors affecting urban expansion are tabulated into •an Index of Local Resistance which includes positive, factors (site quality, transport, service, and settlement networks),.and negative factors • (physiological barriers and institutional restrictions). 5. He then hypothesizes the presence or emergence of a secondary growth point within the urban region whose growth is synchronized within the pat-tern of waves emanating from the region's main centre. Higher displacements result from the combined influence of the waves generated. 6. Finally, he superimposes part of another growth cycle, (possibly brought about by a major revision of the transportation system or reflecting the influence of another nearby metropolitan centre) and.makes allowances for changes in wave amplitude consequent upon the passing of important thresholds in the system, such as city size thresholds. Modelling the Urban Expansion Process 64 At the time of publication, Korcelling model was. not operational and the-model's ability to-simulate the real world is supported only by limited diagramatic evidence. The Scottish Development Department (1968), in conjunction with the Planning Research Unit at Edinburgh University, under the direction of.Professor Percy Johnson-Marshall, has produced a detailed planning report for urban expansion in the Grangemouth-Falkirk Region based on population dispersal and barrier effects. The technique employed, referred to as threshold analysis., after a theory-formulated by Mali sz in-Poland (Malisz 1963, 1969), is derived from empirical research showing that while the growth of population in most'regions is represented by a smooth curve in arithmetic graphical representations, the spatial expansion of urban develop-ment is irregular and non-continuous. Minor increases or decreases (fluctu-ations) in population densities, resulting from changing standards of accommodation and proportions of excess capacity in infrastructural systems, are caused by barrier impediments to urban development (Malisz, 1969). While the economic significance of barrier effects may be less - significant where operation of the market is not constrained, in communities where growth is controlled and directed,.and frequently contained within specific areas for long periods, barrier effects assume increased economic importance as a resulting of bunching effects (Lean 1970; Famelis 1970). The application of threshold analysis by the Planning Research Unit attempts to acknowledge these effects and was-carried out in two parts. Firstly, urban, growth'.'potential was determined .by ascertaining areas suitable Modelling the Urban Expansion Process 65 for urban expansion throughout the Grangemouth-Falkirk region on physio-graphic and ecological criteria, e.g.. land suitability.. The areas were ranked according to priority criteria to provide a basis for sequential development and overall growth potential was calculated by applying average urban density standards. Three basic barrier effects were then investigated; topography, utility networks, and existing urban stmcture. For each, overlay maps were prepared showing per capita costs involved in developing particular areas: for example^ .-.slope and soil conditions, drainage, sewerage, roads, existing development, and degree of land required for conversion to urban use. Secondly, cost indices of per capita costs required for each new ijTimigrant within the potentially developable areas were determined from estimates of total expenditure needed to >plan and develop the land for urban purposes within each expansion sector. Decisions for sequential expansions of the urban area were based on a graphic solution to directions of least resistance (cost minimization). The Planning. Research Unit claimed that the application of threshold analysis in the study resulted in less subjective decisions for succeeding stages of the planning process by providing a quantitative basis for selecting areas for development and by permitting the programming of public invest-ment to be related comprehensively to the existing regional stiructure. The diffusion approach to the spread of urban settlement based on population or activity dispersal as modified by the physical-cultural environment, is s t i l l being formulated. The above five studies are the only Modelling the Urban Expansion Process 66 ones known to the writer presenting actual models based on diffusion pro-cesses which are in sufficient detail to warrant serious consideration. In the following, the study methodology is described and in Part III a model is developed, incorporating many of the ideas contained in these studies. Urban Expansion as a Stochastic Process Traditional approaches to the search for•order in the urban region have mainly been concerned with describing urban structure and spatial growth patterns. This method, which can be compared with that used in compartmental modelling, relies on the identification of morphological features, sometimes by- reference to the history of urban development and specialized activity functions. While this approach has enjoyed considerable popularity, especi-ally among urban geographers, the degree of order found has been far less than the degree of order left unexplained. One of the main reasons appears to be that these attempts at discerning patterns have been based, implicitly, on a static concept of the urban region, which Blumenfield (1967) correctly considers anachronistic. The modern city, he says, .. . .is constantly changing and growing, and, as i t grows, i t burst i t s girdle and overflows into the countryside. The result is universally viewed with alarm as "urban sprawl" as being "neither city nor country." In this fluctuating mass, the old static patterns dissolve. If any pattern can be discerned, i t can only be the pattern of flux. This apparent chaos can no longer be grasped as formation but only as transformation, Modelling the Urban Expansion Process 67 as historical process. (Blumenfield 1967 p.50) Moreover, as a result of this search for patterns in the urban region, the situation now exists, claims Simmons (1965 p.170), where geographers are in a state of cognitive dissonance; accepting simultaneously three concepts of urban structure, (concentric zone theory, sector theory, and multiple nuclei theory), which are in apparent conflict. The point of this criticism is not to deny the usefulness of the search for order by describing patterns. Rather, the criticism is that the traditional geographic attempts to describe patterns, and hence to arrive at "morphological laws" (Bunge 1969, Gale 1970), appear to be biased by pre-conceived notions of the type of order to be found. In particular, there has been a marked emphasis on determining spatially discrete patterns in the organization of urban activities, classified according to different functions. The three conflicting theories referred to above, f a l l into this category.. They seem to be seeking the type of order which existed in pre-industrial cities, where a definite pattern of spatial organization was engendered by a relatively stable social structure (Mumford 1961, Vance 1971). However, there is' general agreement amonggthe outstanding scholars of the modern metropolis that such order no longer exists. Contemporary patterns of urban spatial growth and structure are characterized by "a vast irregular growth" (Geddes 1968 p.26); "sprawling giantism. . . ever more aimless and discontinuous, more diffuse and unfocused" (Mumford 1961 p.619); and "constantly changing and growing" (Blumenfeld 1967 p.50). The obvious implication from these statements is that urban spatial growth and Modelling the Urban Expansion Process 68 structure, and therefore urban expansion, should be viewed in terms of dynamic processes with explicit recognition of uncertainty. While recent explorations into the nature of urban spatial growth and structure have resulted in a number of theories emphasizing dynamic aspects CChapin 1964), there have been relatively few attempts to specifically account for uncertainty in the evolution of cities or particular development processes operating at the urban level. Notable exceptions have been the studies by Malm and Warneryd (1965), Morrill (1965), Olsson C1966), Curtis Harris (1968) and Drewett (1969). However, these studies contain incomplete justifications for adopting the stochastic approach. Only Ctirry (1964, 1966) and Rogers (1967) have pursued the issue of behavioural indeterminism to a significant depth. In substance, they have presented similar arguments in favour of probabilistic interpretations of human behaviour as they relate to urban spatial growth. They consider that the overwhelming complexity of human behaviour and social organization renders futile attempts to deterministically equate behaviour and urban spatial patterns. There i s , they claim, a random element in people's behaviour that should be acknowledged in theories and models of urban spatial growth. Accordingly, both Curry and Rogers recommend the use of stochastic approaches. The advantage of regarding urban expansion in this way becomes apparent when the nature of stochastic processes is examined. Processes refer to phenomena which exhibit or produce change in the course of time. Modelling the Urban Expansion Process 69 Their essence is the change produced. Stochastic' processes generate vari-able results in an ordered sequence from probability functions, meaning each event in a sequence of events, depends on some chance element. Sto-chastic processes as represented in probabilistic models, are especially appropriate when we are concerned not only with the outcome but also with actual process behaviour• (Springer'et al 1968 p.39). They are to be contrasted with deterministic processes which generate a single unique result for each, run where the input remains, unchanged. Two basic criticisms which have been levelled against modelling urban phenomena can be resolved by probabilistic models when used in the' appropriate organizational framework. It has been argued that attempts to find order in the modern metropolis, (i.e. the level of abstraction necessary to satisfy the needs of modelling), are a fundamental denial of the disorderly and complex nature of urban phenomena (Kilbridge 1970 p.l). In response to this criticism i t is acknowledged that many processes are inherently so complex they cannot be abstracted realistically by conventional mechanistic models. But the stochastic approach has the particular advantage of allowing a process to be investigated with recognition of considerable ignorance of i t s nature (Curry 1966). A stochastic process model requires the specification of process components and their interactions at a mono-tonic level, which allows their transformation and regulation to be observed, at a much higher level of complexity, when employed within- the framework of systems analysis (Holling 1972). The degree of complexity which can be handled, therefore, is considerably greater than that which might otherwise Modelling the Urban Expansion Process 70 be achieved through intuitive or conventional analytical approaches (For-rester 1969 pp.107-114) and as a result, our understanding of process behaviour is greatly enhanced.. This is not to claim that the approach is entirely adequate for the investigation of complex phenomena. On the contrary, there are shortcomings but as yet their precise nature is not clear, for this type of study, due to the early stage of their development. However, the approach shows promise of being a considerable improvement over alternative methods available (Harvey 1967 pp.570-588). The second criticism has been that the form of abstraction usual in model building is a regression to "nineteenth century scientism," par-ticularly in view of contemporary realizations of the dynamic and indeterminate nature of many phenomena.. It is argued that social evolution, changing technology, and their effects on patterns of human behaviour make nonsense of predictions QCilbridge 1970 p.l). The grounds for response to this criticism have been considered at length in a previous section (Supra pp.38-48) and only the main points w i l l be repeated here. Where a process has been shown to be dynamic and characterized by uncertainty, the stochastic approach is eminently suitable because i t does not require the specification of causation among component elements. It focuses on changes produced and explicitly allows for uncertainty arising out of chance events and inadequate representation of process behaviour, thereby compensating for the dynamic nature of processes and our limited ability to conceptualize (Curtis Harris 1968 p.29). When this approach is chosen i t is usual to begin with: Modelling the Urban Expansion Process 71 . .. .unconstrained independent random variables and, by introducing dependencies and constraints, achieve results of various likelihoods. Where nature shows only a single result, i t is interpreted as the histo-r i c a l realization of a process which could just as easily have produced other results according to their attached probabilities (.Curry 1966 p.40). If the complexity and uncertainty arising directly and indirectly from the development and assimilation of technology are manifested in the nature of urban structure and spatial growth processes, the advantage of approaching urban expansion in this manner is considerable. One question remains to be answered. Can the pattern of urban land development on the urban periphery be considered random, legitimately, for the purposes of modelling? Theoretical justification is not denied by- the fact that individual decisions concerning land development may be considered the outcome of a planned course of action. Even i f the assump-tion is made that individual decisions are determinate, i t does not neces-sarily follow that their sequence of collective pattern is not random. In fact, Bunge (1963 p..194) maintains that: . . .the interplay of numerous nearly independent and individually determinate entities results always in chaotic situations...orderly individual behaviour may f i t a random collective pattern. Recent studies by Vance (1971) and Clawson (1971) provide con-siderable evidence that actual patterns of urban expansion in North American Modelling the Urban Expansion Process 72 cities can be interpreted in accordance with this principle. For example, Vance in his study of the dynamics of urban spatial growth and structure, through an examination of land assignment practices, in precapitalist, capitalist and postcapitalist cities, finds i t necessary to conclude with respect to the modern metropolis that . . .the traditional practices have everywhere been questioned and in some places abandoned, but as yet land assignment within the postcapitalist city operates in an unclear fashion (Vance 1971 p.120). Further, Clawson in his extensive study of the conversion of rural land to urban uses in the United States of America makes the following observations: . = . . .the decisionnnaking process in urban expansion is highly complex and diverse. It is incredibly fragmented and diffused among-a wide variety and large number of private individuals and organizations and among many public agencies at each of the major levels of govern-ment (Clawson 1971 p.58). It would be miraculous i f such a diffused process came out with the same results as one where a single person or group was charged with the whole responsibility and given the means to exercise i t . Under the diffused system, actions are often nullified, in part or in whole, by other actions (Clawson 1971 p.75). It w i l l be remembered that in a previous section (Supra pp.11-12) the allocation and organization of land in the Vancouver Region was described Modelling the Urban Expansion. Process. 73 as a complex function of both market and state planning mechanisms, with the latter uncoordinated with respect to the former as well as internally. Consequently, i t i s submitted that there i s adequate theoretical and empirical jus t i f i c a t i o n for the basic assumption required for a probabilistic model of urban expansion, that land development on the urban fringe can be treated as a stochastic process. MM! m The Regional Planner can never reckon with "types" of landscape; he has no other recourse but to make an empirical study of the landscape in which he wishes to operate. Artur-.- Glikson Regional Planning arid Development Chapter 4 CHARACTERISTICS OF THE SPATIAL GROWTH OF VANCOUVER Introduction In this chapter ? the aim i s to identify the factors influencing the rate and direction of urban spatial growth i n the Vancouver metropolitan region. The observations made are selective and are guided by (i) the spatial-temporal dimensions of the urban expansion process and ( i i ) the need to interpret the process of urban settlement, to arrive at concepts and structural relationships of phenomena with a bearing on urban expansion. Thus, the following account does not purport to explain the evolution of the Vancouver urban region to i t s present form or t e r r i t o r i a l extent. How-ever, depending on the success of the model described i n Chapter 6, i t might be possible to advance a theory to this effect. In a l i t e r a l sense, the investigation i s an exploratory experiment into the dynamics of urban expansion i n which i t i s sought to identify the following specific characteristics: Characteristics of the Spatial Growth of Vancouver 76 1. associations between population growth, the spread of settle-ment, and the physical-cultural landscape which can lead to the formulation of concepts describing time lags and discon-tinuities i n the process of urban expansion; 2. changes i n the nature of urban expansion, i n time and space, through an examination of the histor i c a l development of the urban region, which reflect the kinds of boundary conditions operating to contain urban spatial growth; and 3. relationships between factors observed to influence the spread of urban settlement which throw light on the nature of structural thresholds and resilience i n the process of urban expansion. Subsequently, an attempt i s made to find order i n these character--i s t i c s through, classification and descriptive inter-relation. This i s a necessary prerequisite to developing general concepts and specifying struc-tural relationships of component elements i n the urban expansion process. It i s emphasized that the approach avoids, as far as possible with the limited data available, the specification of process behaviour directly from observed spatial patterns. Because the relationships between spatial form and process may be assymetrical (Olsson 1968) there are inherent dangers i n specifying a process on the basis of trends i n the aggregate patterns of urban growth. Moreover, when the process i s required for predicting future conditions, the technique may become a circuitous device for perpetuating the past, indiscrimi-Characteristics of the Spatial Growth of Vancouver 77 nately. For these reasons,•Borchert's (1962) time series analysis of the evolution of land, use patterns i n the Minneapolis - St. Paul region i s not satisfactory'for the present study. Ideally, quadrat analysis, a refined c e l l counting technique directed more towards characteristics of processes as they are manifested i n spatial patterns (Rogers 1969) might have been used.. Unfortunately, a lack of suitable and reliable data, precluded this possibility. The conclusions reached i n this chapter rely on a large and d i -verse collection of graphic materials, including a collection of photographic plates with a commentary on each. Some of these graphics have been included i n the Appendixes for convenience. The virtue of these graphic materials l i e s i n their a b i l i t y to i l l u s t r a t e many facets of the spatial growth of Vancouver without the need for a lengthy text. They are also particularly helpful i n providing the reader with an indication of the interpretative process used i n formulating some of the concepts which otherwise might be obscure., The Evolution of Urban Settlement Settlement i n the lower Eraser River - Burrard Inlet region was entering i t s third decade when a recognizable embryo of the present urban system formed. With the trans-continental Canadian Pacific Railway commenc-ing operations i n 1887, and three bridges crossing False Creek, to complete a basic network for communication, by 1889, a permanent superstructure was provided for the urban development to follow (Gunn 1968). By 1890, a com-Characteristics of the Spatial Growth of Vancouver 78 mercial core had established in Gastown, industrial activities surrounded False Creek, and the East End and the Fairview area had consolidated into the f i r s t residential districts (Robinson 1971). Of the other early settlement nuclei, at New Westminster, Moody-vi l l e (North Vancouver), Hastings townsite (now Hastings Park), and Marpole-Eburne at the entrance to the North Arm of the Eraser River (Figure 3), only Moodyville, connected by ferry to the foot of Granville Street, continued to grow in the f i r s t phase of urban expansion which took place from 1890-1910. New Westminster, the original administrative, commercial and military centre, had been eclipsed by Vancouver in the late 188O's and ceased to expand significantly, until after World War I. In Vancouver, development of the railway and related port and industrial activities, provided the catalyst for rapid urban growth and accession to regional dominance which has per-sisted to the present (Robinson and Hardwick 1968). Urban development in the Eraser River - Burrard.Inlet region occur-red in alternating stages.of expansion and stagnation which can be identi-fied largely by the oscillating rates of population growth (Figure 4). Ih the sfir sis--phase of urban expansion from 1890-1910, development was rapid and continuous with the peripheral spread of settlement notable for i t s relative compactness (Figure 5). At the same time, there was progressive consolidation of existing urban areas (Plate 2). On the north shore of Burrard Inlet, urban expansion,consisting mostly of single detached housing, spread fan-like from the ferry terminal and a growing number of commercial and industrial activities located at the foot of Lonsdale Street (Plate 5). Characteristics of the Spatial Growth of Vancouver 79 Characteristics of the Spatial Growth of Vancouver 80 FIGURE 4. POPULATION: CITY OF VANCOUVER , 1886-1921. 1890 1900 1910 1920 In Vancouver, westward expansion was restricted by Stanley Park, then a military reserve where development was prohibited. However, residences quickly covered the limited land available (Robinson 1971). To the east, development extended by the end of the period to the old Hastings townsite. Hastings Street became a ribbon of commercial development and on either side residential development f i l l e d the available land, eventually joining in the south with the growing Fairview residential district. Elsewhere to the south, industrial development took place around False Creek, and with the impetus provided by street car lines extending into south Vancouver, resi -dential development reached Twelfth Avenue and as far west as Jericho Beach. 81 E x p l a n a t o r y Note : The l i g h t brown shading r e p r e s e n t s the urban areas at the s t a r t of the p e r i o d ; dark brown r e p r e s e n t s urban expansion d u r i n g the p e r i o d . Data Source: Department of Mines and T e c h n i c a l Surveys , A t l a s of Canada, 1957. Characteristics of the Spatial Growth of Vancouver 82 By the end of the f i r s t phase of expansion in 1910, a basic communications network had been established for the future Vancouver metro-politan region. All-weather roads joined the smaller centres south of Burrard Inlet directly to Vancouver or New Westminster. Bridges had been completed across the Eraser Paver, at New Westminster in 1904 and Mitchell Island in 1905 (Meyer 1966). Elsewhere, key crossing points were served by ferries. Railway construction had been particularly prolific. By 1910, Vancouver was linked directly to Port Moody and the upper Eraser Valley in the east; in the south to Marpole-Steveston; and through New Westniinster to Delta-White Rock, Cloverdale-Langley-Aldergrove and Fort Langley-Mt. Lehman (Roy 1966). Following the f i r s t wave of urban expansion, a period of economic stagnation and declining population, lasted from 1911 to about 1916. Jones (1966 p.146) attributes this collapse in the development impetus to the economic recession preceding World War I. However, there is probably some truth, in the observation by Robinson and Hardwick (1968 p.447) that in the f i r s t phase of expansion, Vancouver had also over-extended i t s economic potential for there was a substantial exodus of people from Vancouver during the. five years that followed (Figure 4). The second phase of urban spatial growth, from 1917-1930, came with, improvement in the economic situation and in addition, was stimulated, by two fundamental changes which had been occurring gradually but which were hastened along by World War I. The automation of industry and trans-portation was given a boost, with the result that intra-urban mobility was Characteristics of the Spatial Growth of Vancouver 83 greatly increased, and economic activity became increasingly concentrated in the main urban centres (Jones 1966 p.152). The declining urban popu-lation was quickly reversed and in the period 1916-1921 the population of Vancouver rose 70 per cent from 96,000 to 163,000 (Figure 4). By 1930, the population was fast approaching the quarter million mark. While some other areas also recorded proportionately large increases, notably Burnaby and Richmond, the City of Vancouver absorbed three-quarters of the popula-tion increment in the region during 1921-1931 (Table 1). The network of roads and railway lines built in the f i r s t phase of expansion became the major channels for growth in the second phase (Meyer 1966). Because the network was s t i l l incomplete in that i t did not service a l l areas uniformly, expansion tended to occur only in those locations with close proximity to communications corridors. Several large pockets of land were left undeveloped and this broke the regular pattern of expansion which characterized the earlier expansion phase. For the f i r s t time, urban expan-sion ceased to be a continuous peripheral spread from the original settlement nuclei and became a series of movements often producing new nuclei separated from established urban areas CFigure 6, Plate 3). In Vancouver, development extended south in parallel tongues along Dunbar, Granville and Eraser Streets to the North Arm of the Fraser River (Plate 4) ? and south, east along Kihgsvjay towards New Westminster. Hastings Street continued to provide a focus for development to the east which pushed well into Burnaby. The pattern of development in Burnaby, particularly along Kingsway, was sporadic and a number of villages located at the major stops Table 1. VANCOUVER REGION POPULATION 1921—1971 MUNICIPALITY OR AREA CENSUS OF CANADA 1921 1931 1941 1951 1956 1961 1966 1971 BURRARD PENINSULA Endowment Lands - 575 636 2 120 2 ,999 3 272 2 979 3 ,510 Vancouver 163,220 246 593 275 353 344 833 365 ,844 384 522 410 375 422 ,278 Burnaby 12,883 25 ,564 30 328 58 376 83 ,745 100 157 112 036 124 036 New Westminster 14,495 17 524 22 959 30 ,108 33 ,093 35 104 38 013 42 083 Fraser Mills 600 616 552 369 216 165 164 157 Coquitlam 2,374 4 ,871 7 949 15 697 20 ,800 29 053 40 916 52 ,123 Port Coquitlam 1,178 1 ,312 1 539 3 ,232 4 ,632 8 111 11 121 19 ,570 Port Moody 1,030 1 ,260 1 512 2 ,246 2 ,713 4 789 7 ,021 10 ,780 Buntzen _ 540 468 482 528 570 669 Indian Reserves - 148 199 239 284 325 TOTAL BUR. PENINSULA 195,780 298 ,855 341 444 457 ,662 514 ,809 566 ,027 623 619 674 ,537 NORTH SHORE West Vancouver 2 434 4,786 8,362 13 ,990 19 ,197 25 ,454 31 987 36 ,273 North Vancouver City 7 652 8,510 8,914 15 ,687 19 ,951 23 ,656 26 851 31 ,863 North Vancouver Dist. 2 950 4,788 5,931 14 ,469 26 ,252 38 ,971 48 124 57 ,123 Indian Reserves - - 384 519 621 738 845 Lions Bay • - - 51 153 396 TOTAL NORTH SHORE 13 036 18,084 23,591 44 ,665 66 ,021 88 ,819 107 807 125 ,655 SOUTH SHORE Richmond 4,825 8 ,182 10 ,370 19 ,186 25 978 43,323 50 460 61 ,376 Delta 2,839 3 ,709 4 ,287 6 ,701 8 752. 14,597 20 664 45 175 Surrey 5,614 7 ,888 13 ,240 29 ,729 43 927 70,838 81 826 96 ,651 White Rock 200 500 1 ,600 3 ,941 5 439 6,453 7 787 10 ,244 Barnston Island - - 88 93 94 98 Indian Reserves 56 76 91 108 123 TOTAL SOUTH SHORE 13,478 20 ,279 29 ,553 59 ,721 .84 ,280 135,413 160 958 213 ,446 TOTAL . .222,294 337,218 394,588 .562,048 665,110.790,259 892,384 1013,638 .OTTER-CENSUS INCREMENTS - 1921^71 MUNICIPALITY OR AREA 1921-31 1931-41 1941-51. . 1951-56 . 1956-61 1961-66 1966-71 (2) "METRO" AREA BURRARD PENINSULA Endowment Lands 575 61 1,484 879 273 -293 531 Vancouver 83,373 28 ,760 69,480 21,011 18,678 25,853 11 ,903 Burnaby 12,681 4 ,764 28,048 25,369 16,412 11,879 12 000 New Westminster 3,029 5 ,435 7,149 2,985 2,011 2,909 4 ,070 Fraser Mills (1) 16 -64 -183 -153 -51 -1 -7 Coquitlam 2,497 3 ,078 7,748 5,103 8,253 11,863 11 ,207 Port Coquitlam 134 227 1,693 1,400 3,479 3,010 8 449 Port Moody 230 252 734 467 2,076 2,232 3 759 Buntzen 540 V72 14 46 42 99 Indian Reserves 148 51 40 45 41 -TOTAL BUR. PENINSULA 103,075 42 589 116,218 57,147 51,218 57,592 51 912 NORTH SHORE West Vancouver 2,352 3 576 5,628 5,207 6,257 6,533 4 286 North Vancouver City 858 404 6,773. 4,264 3,705 3,195 5 012 North Vancouver Dist. 1,838 1 143 8,538 11,783 12,719 9,153 8 999 Indian Reserves - 384 135 102 117 107 Bowen Island _ - „ Lions Bay - - - - - 243 TOTAL NORTH SHORE 5,048 5 507 21,074 21,356 22,798 18,988 18 540 SOUTH SHORE Richmond 3,357 2 188 8,816- 6,792 17,345 7,137 10 916 Delta 870 578 2,414 2,051 5,845 6,067 24 511 Surrey 2,274 5 352 16,489 14,198 26,911 10,988 14 825 White Rock 300 1 100 2,341 1,498 1,014 1,334 2 457 Barnston Island - 88 5 1 4 _ Indian Reserves 56 20 • 15 ' 17 15 -TOTAL SOUTH SHORE 6,801 9 274 30,168 24,559 51,133 25,545 52 709 TOTAL "METRO" AREA 114,924 57,370 167,460 103,062 125,149 102,125 123,161 Notes: (1) Fraser Mills was incorporated into the Municipality of Coquitlam on Nov. 1, 1971. (2) Figures for 1971 preliminary estimates only; D.B.ST. Characteristics of the Spatial Growth of Vancouver 85 on the. road and railway lines to New Westminster coalesced into a large island of urban settlement midway between Vancouver and New Westminster (Robinson 1971). The bridges built across the Eraser River allowed access to Rich-mond and Surrey and several small urban centres established (Plate 10). Ccquitlam and Port Moody exhibited a similar pattern of sporadic develop- . ment. Only on the North Shore in North.Vancouver, and later in West Van-couver, was urban development relatively compact (Plate 6). The 1930 economic depression precipitated the second period of stagnation.. Population growth was halted in the Vancouver region but unlike the previous recession, there was not a large exodus of people to rural areas. However, with the exception of West Vancouver which benefited from the opening of the Lions Gate Bridge in 1938, urban expansion was negligible for the following decade and land in many premature subdivisions reverted to the municipalities in lieu of payment of taxes (Parker 1966 p.,167). As before, the onset of war proved a stimulus and by 1940-41, moderate growth was being experienced. The following decade from 1941-1950 was more a period of gradual recovery than a new wave of expansion. Although the population of the Vancouver region increased by 160,000 in the ten years, development was piecemeal and for the most part represented i n f i l l i n g and consolidation of vacant areas remaining from the second phase of expansion (Figure 7). In the City of Vancouver this was the last period of significant urban spatial growth. The undeveloped enclaves of land considered unsuit-able for development previously or not warranting the capital investment Explanatory Note: The l i g h t brown shading represents the urban areas at the s ta r t of the pe r iod ; dark brown represents urban expansion during the pe r i od . Data Source: Department of Mines and Technica l Surveys,At las of Canada,1957. Characteristics of the Spatial Growth of Vancouver 87 required for their development were taken up for urban uses. Subsequently, Burnaby became the most important urban expansion area and there was even a small overflow of development into Coquitlam. In Richmond some of the smaller scattered centres were consolidated by new development. Surrey was the only municipality to double its population in the decade but there was s t i l l not a sizable urban area, with numerous dispersed settlements remaining the rule. On the North Shore, urban expansion occurred uniformly in North and West Vancouver, once again as small rings of peripheral growth. The third phase of urban expansion from 1951-1970, began slowly in the early 1950 ,:s following a large increase in population growth and quickly gathered momentum when the rate of population increase was maintained. In two decades, the Vancouver regional population almost doubled (Table 1). Four areas registered a three-fold population increase: Port Coquitlam, Port Moody, North Vancouver District and Delta. Another four areas more than doubled their population: Coquitlam, West Vancouver, Richmond and Surrey. By the early 1960's, the rate of urban expansion was being viewed with alarm, especially as less than one half of the land being converted from rural to urban uses was actually being developed (Lower Mainland Regional Planning Board 1963; See Appendices I and II).. It can be observed from Figure 8 that consolidation and i n f i l l i n g were s t i l l general traits of urban spatial growth until 1956. Richmond and Burnaby are notable in this respect (Plates 11 and 12). On the North Shore, West Vancouver and North Vancouver District were expanding peripherally in an orderly fashion. However, in the Coquitlam area to the east, and Characteristics of the Spatial Growth of Vancouver 88 Surrey- and Richmond areas to the south, there were signs of the extensive urban development to follow. During the 1960's, large areas of scattered urban settlement in Richmond, north-east Surrey and Coquitlam, consolidated to become fully urbanized. At the same time, Port Coquitlam, south and east Surrey, Delta and White Rock, began large scale, piecemeal transfor-mation from rural to urban areas (Figure 9). Freeway construction was instrumental in the development of new urban areas during the most recent phase of expansion (Meyer 1966). The Deas Island Throughway and Massey Tunnel under the Fraser River increased substantially the ease of communication to established urban areas from Delta, White Rock and south Surrey (Plate 10). The Port Mann Bridge and the Trans-rCanada Highway greatly stimulated urban development in East Surrey and Port Coquitlam. This is reflected in the traffic volumes and traffic times from outlying areas in 1967-1968 (See Appendix III). The foregoing description of the spread of settlement in the Fraser River Burrard Inlet region shows that urban expansion was neither symmetri-cal nor continuous. • Rather, the urbanization of the region proceeded from a number of isolated centres in three distinct phases.. From 1890 to 1910 growth occurred mainly around Burrard Peninsula, particularly along the foreshores of English Bay and Burrard Inlet. In the second phase of urban expansion from 1917 to 1930, development extended south to the North Arm of the Fraser River, along.the major transportation'route to New Westminster and east into Burnaby. A period of moderate growth followed from 1941 to 1950, character-ized mainly by consolidation and i n f i l l i n g but with seme small areas of Characteristics of the Spatial Growth of Vancouver 89 peripheral expansion on the North Shore, and sporadic expansion in Rich-mond, Coquitlam and Surrey municipalities. The third phase of urban expan-sion from 1951 to 1970 resulted in the large scale conversion of rural land in Richmond, Delta, Surrey and Port Coquitlam. 90 EXISTING DEVELOPMENT, 1970. F I G U R E 9 CIVIC AND INSTITUTIONAL PARKS AND RECREATIONAL AGRICULTURAL GREATER VANCOUVER REGIONAL DISTRICT PLANNING DEPARTMENT JANUARY, I970 GREATER VANCOUVER REGIONAL DISTRICT BRITISH C O L U M B I A C A N A D A . V a n c o u v e r : A C o u n t r y Town ( 1 8 9 0 c i r c a ) V a n c o u v e r : fhe D i s p e r s e d C i t y (19393 nip; Hammond R u r a l C e n t r e ( 1 9 2 0 ) Characteristics of the Spatial Growth of Vancouver 103 PLATE 1. VANCOUVER: A COUNTRY TOWN (1890 circa.) Two o{ the. eanJLXest settlement wxcleX. Xn the. fnasen RXven^ Bunnand Inlet negXon wene, UoodyvXlle., a tXmben nesounce. town on the. nonth shoKe. 0^ Bunnand Inlet:, and Vancoixven, a quXckly gn.owX.nq commencXal ce.ntne. Both one. &hown Xn thXs photograph, taken {n.om the. Canadian ?acl{Xc Railway Hotel, about 1890. Vanc.ou.veA had by thXs time, become, a t>lgnl{Xcant de.ep sea pout, and the. tenmXnal {on a tnans ^ Canada naXlway line. The. popular tlon was oven 10,000. The, i>catlenzd &eltlement hhown hene. Xi kXmXlan In many nespe.cls to the, patteJtn o{ de.veJLopme.nt Xn Hammond Xn 1918 {Vlate, 9) and Clovendale. Xn 19.53 [Vlate, 10\. PLATE 2. VANCOUVER: THE COMPACT CITY (.1910) The, longest settlme.nt Xn Bnltlsh ColumbXa by 1910 was Vancouver with a population o{ 100,000. The, onlglnal townsXte, had be,en completely developzd and the, {Xnst wave, o{ unban expansion had itejxched Xts pe,ak. Two o{ the, thne,e, bnldges • cnossXng False, Cne.e.k at this tone. pnovXdlng accents to KXtsXlano, Volnt Gne,y and as {an, south as the fiat,en, RXven, one. i>hown Xn this photognaph taken {nom West 11th Kvemxe, and Oak'Stmel. In the. {one.gnou.nd, the, Talnvtm n.esXdzntXal dlstnlcl Xs &hown as the, houthenn IXmXts o{ unban development, while. Xn centne.-night, the, {XUXng o{ Valse. Cne,ek Is alneady unden way to pnovXde. level land {on. Xndustny. Characteristics of the Spatial Growth of Vancouver 104 PLATE 3. VANCOUVER: THE DISPERSED CITY (1939) Until the First World War, Vancouver was a compact: city and Spatial growth was- outwards In a {an-llke motion {rom the ce.ntx.iL. However, danlng the, 1920's, radial expansion along the. major transportation lines became the. rule., resulting In a more dispersed settlement pattern, large. Islands o{ undeveloped land could be. found near to the. central city area even after the. Second World War.. In this panoramic view of downtown Van.cou.ven. and the, North Shore,, taken from Queen Elizabeth fork, [the. focus of one. Island of vacant land), the. edge, of urban development Is clearly evident.. At the. foot of the, mountains, on the. north shore, of Burrard Inlet, the, well established settlement In North Vancouver [centre-right) and the, comparatively recent settlement In West Vancouver [centre.-le.lt) are. visible,. PLATE. 4. RURAL-URBAN SUBDIVISION (1941) During the, second wave of urban expansion In the, 1920's, develop-ment extended south, from Vancouver In several parallel tongues to the North Arm of the Fraser River. After the depression years, and with the advent of the. Second World War, there was a gradual economic revival and urban expansion proceeded. In Kerrlsdale, at the foot of Elm Street, the land-Scape, was still predominantly rural, however, this photograph records the beginnings of a transformation In 1941 to a suburban residential landscape. This scene Is typical of development In Richmond, Delta and Surrey during the 1960's.. Characteristics of the Spatial Growth of Vancouver 105 PLATE 5. MOODYVILLE: A RESOURCE TOWN (.1906) UoodyviZle developed {rom a sawmill-^-company town prior to 1890, to an important resource town and nucleus {oft settlement on the. north shore o{ Burrard Inlet. By 1900, MoodyviZle Wad its own commercial and industrial. Base although it still reLLed heavily on Vancouver Ion. many services. Thii 1906 photograph shows Lonsdale. Street which was the. axis {on. unban develop-ment in Month- Vancouver and the. {erry which pn.ovid.zd regular services to Vancouver.. PLATE 6. THE EMERGENCE OF NORTH VANCOUVER (1929) The. opening o{ the. Second Marrows Bridge {on. road and railway tra{{ic In 1925 proved a considerable stimulus {on. seJM.eme.nt in the Month Shore municipalities. Both the City and Municipality o{ Month Vancouver, were, ass.un.ed o{ relatively easy access to Vancouver, across Burrard Inlet. However, the location o{ the. bridge was {ar less convenient {or West Vancouver wlilch grew slowly until, the first Marrows Bridge [Lions Gate.) Was completed in 1938. In thli> 1929 photograph, taken {rom the Georgia Hotel In downtown Vancouver, residential, development is shown extending well up the slopes and industry ts beginning to locate along the {oreshores o{ Burrard Inlet. Characteristics of the Spatial Growth of Vancouver 106 PLATE 7. BURRARD'INLET: TWO SHORELINES (1938) In comparison to the Vancouver, watcn.fn.ont across Burrard Inlet, the shoreline of North Vancouver wot, relatively undeveloped as late as 1938 when tills photograph was taken. In that year, the Lions Gate Bridge was opened and during the 1940's and 1950 's all the waterfront land In North. Vancouver, except for the Indian Reserves, was taken up by Industry. In West Vancouver, on the other hand, shoreline development was predominantly residential. PLATE 8. NEW WESTMINSTER: THE DORMANT CITY (1906) Good access from an area suitable for development to a major centre, such, as New Westminster Is not necessarily a sufficient condition to encourage settlement. New Westminster had been the traditional centre for an extensive, productive rural region, Including Delta, Surrey, Langley and Mats qui: municipalities, since the earliest settlement In the region and when the first combined road-roll bridge across the Fraser River was built at New Westminster It was thought that urban development would spread across Into Surrey. In fact, Vancouver attracted nearly all the new development, and North Surrey did not become urbanized until World War II. Meanwhile, New Westminster looked across the Fraser River at the rural landscape shown here. Characteristics of the Spatial Growth of Vancouver 107 PLATE 9., HAMMOND: A RURAL CENTRE (1928) Throughout the Vraser Valley, small towns' sprung up In the early decades o{ this century to serve the surrounding rural communities. Some o{ these have already become part o{ the urban region [e.g. Brighouse, VZchmondl; others have become {ociZ {or urban development in the most recent wave o{ urban expansion (e.g. CloverdaZe, Surrey; Plate 10); and stilt others are showing signs o{ taking on this {unction in the immediate {uture. Ham-mond f between the Vraser River and Lougheed Highway and near to Haney, {alls into the latter category. This particular photograph, although somewhat datedf shows the characteristic pattern o{ development in these centres prior to the. in{luence o{ widespread urbanization {orces. PLATE 10. CLOVERDALE: A FRINGE COMMUNITY C1953) CloverdaZe is representative o{ old rural centres on the threshold o{ rapZd urban growth. At one time i t was one o{ two dominant centres [the other was Abbots{ord\f in the extensive rural region between the Lower Vraser River and the United States border.. It stagnated until the 7950''4, although served 6tf two major arterial roads and a railway. Since then {reeway- develop-ment, ZmmediateZy* to the east and west, has brought i t within commuting distance o{ commercial, industrial and cultural nodes Zn the urban regZon. Consequently, during the 1960'-s there was a revival'and by 7 970 i t was obvious to the residents o{ CloverdaZe that i t was only a matter o{ time be{ore their town became part o{ the Vancouver urban region. Characteristics of the Spatial Growth of. Vancouver 108 PLATE. 11, RICHMOND: FILLING IN THE GAPS C1955) The sporadic growth o{ unban. settlement, characteristic o{ Rich-mond since WonZd Wan. II, has resulted in a substantial, crop o{ planning problems. Apart {rom large discrepancies in land development costs between dispersed and consolidated development [Rawson and Morville 7963), there are great di{{iculties in rationalizing subsequent development, i.e. {Ming in the under-utilized land. This aerial photograph taken in 7955 indicates the magnitude o{ the problem. The scene shown is an excellent example o{ settlement patterns resulting {rom the urban expansion process on the {lot terrain in the south o{ the Vancouver Region. It is also possible to discern the abrupt change in the patterns o{ settlement on either side o{ the fraser River which {lows right, to le{t, slightly above the centre o{ the photograph.. PLATE 12. BURNABY: THE DILEMMA OF EX-URBIA (1957) i Some urban residents like to live in a rural environment and typically, when they move to their new home they like to think that they will be the last newcomers. Apparently, so do the people who move in later.. These semi-rural communities seldom last {or very long and even i{, through exclusionary zoning or the like, they are passed over {or the time being, they-soon become vulnerable to mounting development pressures. 0{ten the. very- {acility that allowed the early residents access to these rural areas [i.e. orientals and {reewaysl, stimulates the {orces which cause their Characteristics of the Spatial Growth of Vancouver 109 complete urbanization.. Here the Lougheed Highway provides easy access to Vancouver [iop-centrel. The area shown In the photograph was almost completely developed by Industry , commerce and housing at 1970. Characteristics of the Spatial Growth of Vancouver 110 Characteristics of Urban Expansion One of the difficulties faced when interpreting a dynamic pro-cess, such as urban expansion, is the need to break the process down into components. The more dynamic a process, the less justification to be found for dismembering i t , for there is an increasing danger of obscuring funda-mental interdependencies. Thus in examining the urban expansion process, through the identification of characteristics, we need to be constantly aware of the inter-relationships of components in the total process. This is facilitated in the following by taking the view that urban regions are open systems, defined by movements, networks, nodes, hierarchies and surfaces (Haggett 1965); i.e. a progression from energy flows to easily recognized landforms and settlement patterns (Figure 10). The interpreta-tions of characteristics of urban expansion in the Vancouver region discus-sed in this section are derived in part from this abstraction of urban systems. Five characteristics of urban spatial growth with a bearing on the dynamic nature of urban expansion have been identified from the descrip-tion of urban settlement in the Vancouver region: 1. the bio-physical landscape, 2. the sequential development of the communications network, 3. the evolution of dominant nodes in the Vancouver region, 4. the diversity of urban settlement patterns in areas experie-ncing rural-urban land conversion, 5. time lags and discontinuities in the urban spatial growth processes Characteristics of the Spatial Growth of Vancouver 111 F I G U R E 10. STAGES OF REGIONAL SYSTEMS movements networks nodes hierarchies surfaces Source: P. Haggett (1965 p.18] Each of these characteristics w i l l be considered in detail. The bio-physical landscape is composed of the natural landforms. the vegetation and wildlife, and water bodies. In the Vancouver region, the spread of settlement reflects in many ways., the substantial molding influence of topography, and to a lesser degree, the distribution of par-ticular flora and fauna. It is difficult to portray the Vancouver regional landscape on Characteristics of the Spatial Growth of Vancouver 112 a two dimensional surface in a way that adequately represents the dominant characteristics. However, a creditable attempt by cartographer-geographer Tom Peucker, in the form of a computer produced, block diagram, is shown in Figure 11. The mountainous north shore appears in strong contrast to the floodplains of Pdchmond to the south, while the Burrard Peninsula is shown as a moderately undulating core extending from east to west. In addition, each landform type is separated by a water body; Burrard Inlet separates Vancouver proper from the North Shore, and the Fraser River separates Richmond from Vancouver. This unique arrangement of diverse landforms and water bodies is reflected in both the aereal extent and density of urban development (Figure 9, Appendix II). Changing slopes and terrain ruggedness, the suitability of dif-ferent landforms for various types of urban activities (e.g.. soil foundation conditions), and the likelihood of periodic innundation as a result of the Fraser River flooding are just some of the factors which determine the feasibility of urban expansion into different areas, as well as influence the location of development through variances in construction and land preparation CHurd 1924, Yu i l l 1970). A problem being faced in Port Moody-Coquitlam illustrates yet another aspect of the influence of topography. Even with good access, suitable land and considerable pressure for development, settlement has been curtailed east of loco because of an inability to reticulate water above the 300 foot contour without a major upgrading of the water supply system (Mann-Urban Program Planners—personnel communication). F I G U R E II. T O P O G R A P H Y OF T H E V A N C O U V E R REGION Characteristics of the Spatial Growth, of Vancouver 114 The influence of the bio-physical landscape on the spread of urban settlement can be interpreted in terms of barrier impediments to the flow of movements (Malisz 1963, 1969; Yui l l 1964). According to this view, different landscape characteristics operate to varyihggdegrees to impede or facilitate urban expansion. The sequential development of the communications network in the Vancouver Region was of paramount importance to the direction and spread of urban settlement for numerous inter-related reasons. These reasons have been detailed by Roy (1966) in a paper examining the development of railways in the Lower Fraser Valley, by Meyer (.1966) in a comparable study of road development, and by Jones (1966) and Siemens (.1966 pp.30,46) in more general studies of the evolution of settlement in the Fraser River - Burrard Inlet region. For present purposes i t is sufficient to consider only the ones that relate directly to the main characteristics of urban expansion. Firstly, the Vancouver urban region evolved almost completely within the period of automated road and r a i l transportation. As a result, the historic need for compact urban development, to facilitate intra-urban communication, ceased to be important early in the history of settlement. The potential urban region covered increasingly larger geographical areas as the distances which could be travelled, without involving prohibitive effort or time, multiplied. Secondly, Vancouver's importance as a port, from early in i t s history, for the export of natural resources and some manufactured goods, promoted the development of major communication links to a l l parts of i t s hinterland which were potentially productive. Consequently, the Characteristics of the Spatial Growth of Vancouver 115 number of transportation links and the capacity of the communications net-work, were generally far greater than the urban population would normally warrant. Finally, the limitations imposed in several directions by the topography were often overcome, not through pressure exerted by the urban population, but because of the progressive development of the communication network built to serve the hinterland. Transportation links often preceded urban settlement, particularly where major bridges were constructed, and as a result, had the effect of channelling future growth along these communi-cation lines. In many cases, where these new communication lines met a road established earlier, to serve local rural needs, the development of a new village or town was encouraged, creating a new settlement nuclei in the urban region. These characteristics have a number of significant implications. By providing a measure of the ease of communication among disparate local-i t i e s , the communications network can be interpreted as either promoting or impeding urban spatial growth, directionally. Thus to a large extent, the communication network, existing at any point in time, helps to define the potential urban field. As a result, i t is possible to derive, in con-junction with other factors, mathematical statements pinpointing the urban boundary with varying probabilities. The evolution of dominant nodes in the urban region might be con-sidered a fait accompli at this stage in the development of the Vancouver urban region. It was observed that urban expansion has combined to spread-into peripheral rural areas from Vancouver and New Westminster from before the Characteristics of the Spatial Growth of Vancouver 116 turn of the century. However? the fact that Vancouver and New Westminster have prevailed as the dominant nodes for eighty years does not preclude the possibility of the emergence of new f o c i i for future urban development. Centres presently remote, such as Langley or Haney, (or even a completely new nuclei), could conceivably emerge as dominant nodes. Dominant nodes can be identified as the locations of greatest commercial activity, or alternatively, as the areas with the highest population densities (Appendix II). This characteristic is inherent in a l l theories of urban spatial growth, although the rature of peripheral settlement often varies. The particular interpretation of this character-is t i c in the present study, requires l i t t l e explanation, being a straight-forward descriptive relationship based on empirical observation. Urban expansion is considered a process involving the diffusion of urban acti-vities from the dominant nodes into the surrounding rural areas. Darwent (1969) and Kbrcelli (1970) discuss various theoretical interpretations of this characteristic. The diversity of urban fringe settlement patterns in the Vancouver region challenges most traditional concepts of urban development which emphasize separation of urban activities on the basis of economic criteria and the formation of relatively static land use patterns indicating inher-ent locational advantages. However, while i t was observed that in some areas, notably on the north shore of Burrard Inlet, relatively compact urban settlement occurred fitting traditional descriptions, in the Richmond-Del ta-rSurrey area to the south fragmented urban settlement was the rule, Characteristics of the Spatial Growth of Vancouver 117 (often associated with numerous small commercial nuclei). The evolution of settlement in Burnaby and the Coquitlam area indicated that both types of urban settlement can be found in the same area. An explanation of these differences would require, inter a l i a , intensive studies of the decision process of fringe area residents. However, a number of studies, including one by the Lower Mainland Regional Planning Board (1963) suggest interpretations consistent with these characteristics. Firstly, there seem to be a large group of people, mostly with young families, who choose to live considerable distances from the city proper, so long as they can commute to the city within an hour (Hardwick 1970 p.116). They have many reasons for their decision and the reduced cost of land and housing is obviously.very important (Harvey and Clark 1965, Lower Mainland Regional Planning Board 1963). Other reasons suggested include family and social ties in the area, a lust for the outdoors, space for the children, or just an affection for l i f e in small communities (Lower Mainland Regional Planning Board 1963, Hodge 1970). The advancing boundary of the urban region is due in part to these people who are willing to travel further and further back to the city area to their jobs as acces-si b i l i t y is increased into the hinterland (Plate 12). But, i f i t does not seem to matter to them how far away from the city area they live, they s t i l l show a strong tendency to seek out estab-lished or newly establishing communities. The lack of services and the general inconvenience of the most isolated localities is undoubtedly very Characteristics of the Spatial Growth of Vancouver 118 important in this respect CChapin and Weiss 1962). However, this character-i s t i c could also be a manifestation of general social tendencies and i f a study of planned residential communities in California is any indication, an important factor influencing their decision is the l i f e style image of the community in the preferred location (Werthman, Mandel and Dienstfrey 1965). Secondly, the dispersed settlement pattern can also be attributed in part to the operation of the land market. Sinclair (1967) has argued that contrary to the graded land use patterns described in the Von Thunen model, vacant and under-utilized land is a common feature on the periphery of contemporary urban regions as a result of the premature conversion of rural land. In successive periods some land is subdivided and sold while comparable adjacent land is held over by a diligent farmer or a more optimistic speculator. As a result, while there is a general trend for land holdings to become increasingly fragmented, only small parcels of land become available for actual development at the same time and therefore dispersed urban settlement patterns occur. Time lags and discontinuities in urban spatial growth processes are characteristics frequently obscured by the spatial and temporal dimensions considered in most studies of urban areas. However, these characteristics emerge clearly from the foregoing description of urban evolution, in the Vancouver region. While large scale changes in the rates of population growth are reflected, more or less, in the main phases of urban- expansion, the con-Characteristics of the Spatial Growth of Vancouver 119 tinuous smaller oscillations are not rrdrrored directly in spatial growth patterns-. Robinson and Hardwick C1968 p.4-47) have noted in referring to the period immediately preceding 1910, that the development of the Vancouver region's economic base lagged behind commercial and residential expansion and Vancouver grew too fast. According to the Lower Mainland Regional Planning Board (1963) a similar situation prevailed in the late 1950's, and early 1960's. At other times, urban spatial growth seems to have lagged behind rapid increases in the economic base and large population increments-, notably during the early years of both the First and Second World Wars. Periods of consolidation and i n f i l l i n g were observed to precede a new wave of expansion suggesting that as the available capacity was taken up, conditions became ripe for a new wave of urban settlement. • As the Lower Mainland Regional Planning Board (1963) has clearly shown, rapid urban expansion removes large areas of agricultural land from the rural sector, much of which remains undeveloped for considerable periods of time. By- this process the development potential in the urban area is replenished. A similar situation has been observed in the Sydney region by Rutherford, Burdekin and MacGregor (1971). The concept of development potential or unused capacity is well known to the investor-developer groups operating in urban areas. They may not refer to i t by these names but the different terms employed have simi-lar connotations. For example, the investor-developer group concentrating on the apartment market, pay keen attention to trends in apartment vacancies Characteristics of the Spatial Growth of Vancouver 120 and the number of apartments under construction CWendt and Cerf 1969). Both are used as indicators of future market potential. Investors and developers involved in the provision of office space, multiple purpose industrial premises, and retail space employ similar indicators for their purposes (Ratcliff 1961 pp.255-271). Planners, engineers, and real estate specu-lators are also concerned with monitoring the unused capacity in existing facilities and resources and the continuing provision of new capacity. A l l of these measures'are, in effect, assessments of resilience in various parts of the urban system. Both the time lags between significant changes in population growth, and the resulting pattern of urban development, and the discontinuous nature of urban expansion, are important characteristics when the urban region is approached from a systems viewpoint. In particular, they reflect a domain of stability in the operation of urban systems in which minor oscillations in the number of urban activities and population can be absorbed without any dramatic change, to the urban area. This stability is a consequence of resilience in urban infrastxnactural systems. A Synthesis It has been shown how, on the flat and gently undulating lands of Richmond, Delta, and Surrey, urban expansion was hindered for a long time by poor access to the primary centres in the Vancouver urban region. With the construction of bridges across the Fraser River, development of freeways, and the increased use of the automobile, early access was facilitated Characteristics, of the Spatial Growth of Vancouver 121 to the nodes of commercial, industrial and cultural activities. There being negligible other barriers to urban growth, settlement proceeded;- rapidly along the roadways. The resulting pattern has been characterized as sprawl and as Figure 9 and Plate 11 show, development in these areas was extremely dispersed, grid—like in appearance, and with the centres of the superblocks empty Csee also Appendix I). In contrast, settlement on the North Shore developed in a distinctly different pattern. Ini t i a l l y , access across Burrard Inlet was a limiting factor but with construction of the Lions Gate Bridge, this problem was overcome, temporarily. However, the ensuing development remained compact because, of strong containing forces imposed by the physical terrain and the difficulties involved in extending u t i l i t y networks into more remote areas. On the basis of what has been discussed, i t is proposed to advance a preliminary synthesis of the characteristics of urban expansion in the Vancouver Region and adopt i t as the basis for formulation of the model in the next chapter. Generally, urban expansion in the Vancouver metropolitan area can be considered the result of the spread of urban activities consequent upon population growth. The extent and location of urban settlement can be viewed as molded by two sets of interacting forces. Firstly, with the development of corrmunication links facilitating accessibility into peripheral areas, the centrifugal forces stimulated by population growth are released, with subsequent dispersal of urban activities. Opposing this outward thrust is a containing force generally favouring propinquity of urban settlement. Characteristics of the Spatial Growth of Vancouver 122 This tendency for settlement to cluster around existing development, even in a period of rapid expansion, helps explain islands of urban development around existing rural centres before being brought completely within the compact urban field. Secondly, barriers to urban expansion, inherent in the physical nature of the landscape and in urban stjructures (e.g.. limits to the expansion of u t i l i t y network systems and political boundaries), operate to contain urban settlement. Acting in opposition is a force which increases in strength as the resilience in urban infrastrnactural systems (e.g. vacant land, residential, commercial and industrial space) is exhausted. When the forces exerted by demands for new space and facilities and stimulated by increased accessibility, exceed the counteracting forces, or rather containing influences, of barrier effects and the tendency for settlement propinquity, the threshold for urban spatial growth is crossed and urban expansion continues. Each of these forces operates with varying intensity, depending upon the particular attributes of the locality, the rates of population growth, the level of technology and most importantly, as a result of reinforcement by the institutional system in programs for public u t i l i t y development, land use controls, regulation of urban activities and generally the permissable practices for allocation and organi-zation of land resources. Chapter 5 A DIFFUSION MODEL OF URBAN EXPANSION FOR VANCOUVER In considering the spatial growth of Vancouver, the viewpoint has been taken that urban expansion can be represented as a spatial dif-fusion process whereby changes are produced in the distributional pattern of rural and urban land use over time. It is implicit in this viewpoint that emerging patterns bear a functional relationship to historical patterns, but they are not constrained from evolving into new and differ-ent forms (Brown 1968 p.87). When organized and investigated in an urban systems framework, diffusion processes are also characterized by structural properties Ce.g. thresholds, boundaries and lags) and the typical systems quality of feedback interactions between process components (Holling and Orians 1971). The purpose of the proposed model is to describe these spatial, historical, structural and feedback properties. ' A Diffusion Model of Urban Expansion for Vancouver 124 The Nature of Spatial Diffusion Processes Spatial diffusion has been defined by Brown (1968 p.2) as the spreading or dispersal of phenomenon over time, either through relocation or expansion within a given area. Because we are concerned only with a division between urban and rural land use functions, (i.e. dispersing urban land development in the aggregate), the problem of relocation of urban activities does not arise for a l l activities coopting land from the rural sector are considered members of the existing population of urban activities. Brown (1968) in seeking to provide a framework for systematically exananing spatial diffusion processes describes six different elements common to diffusion problems.. They are: (!) the subject area or environment where the diffusion occurs, defined by its spatial, physiological and cultural attributes; C2) the time element, including the time intervals between diffusion generations and time lags before adoption by receptors; . (3) the item being diffused, which is expected to be functionally connected to the qualities incorporated in the diffusion process; (4) the origin node, characterized by the frequency of emissions of diffused items and the time during which the node continues to operate as an emitter; (5) the receptor or destination node which is character-A Diffusion Model of Urban Expansion for Vancouver 125 ized by locational criteria and the ability to receive the item diffused; and C6) the relationship between the origin and destination nodes i n time and space; including the paths of move-ment, distance, the history of movement between the nodes, intervening opportunities and the like. Diffusion processes are sometimes thought of in terms of waves, but more often the process is represented by items (e.g. members of a popu-lation) being diffused through hierarchies of receptors with diffusion occurihg^in step-like penetration. Whatever the analogy used, the emphasis in diffusion processes is strongly oriented to structural relationships of phenomena in time and space as they appear in the particular process . being studied.. Fused in the idea of dynamic processes i s the concept of interacting forces which indicates that diffusion models are in one respect another type of growth force models. However, the approach is essentially behavioural in that i t focusses on the likelihood of people making decisions with respect to land development and personal migration (Yuill 1970 p.17). Therefore, i t is an important conceptual step towards bridging the tradi-tional discrepancies between macro and micro scale approaches. Formulation of the Model On the basis of the investigations reported in the foregoing chapters, i t is submitted that urban expansion can be described as a spatial A Diffusion Model of Urban Expansion for Vancouver 126 diffusion process in which the conversion of rural land to urban uses is directionally random, other things being equal. Furthermore, i t is hypo-thesized that; the probability of rural-urban land conversion is a function of the demand for additional space consequent upon population growth and the level of resilience in urban infrastructural systems; and the probability of rural-urban land conversion in a  particular location is dependent, in addition, on two sets of interacting forces; Ci) the centrifugal force resulting from continually increasing accessibility into the urban hinterland which e^xpands the potential boundary limits of the urban region, and the centripetal force requiring propinquity of new urban activities to existing urban development thereby promoting compact forms of urban settlement; (113 the centrifugal force generated by dimimshing levels of unused capacity, i.e. decreasing resilience in urban infrastmctural systems, and the barriers to urban expansion inherent in the nature of land resour-ces and settlement structure. Basically, this means urban expansion occurs to accommodate new activities generated by increased population. However, for any area the A Diffusion Model of Urban Expansion for Vancouver 127 relationship is not constant but depends on the particular set of a t t r i -butes characterizing the locality. The relationship is modified by the boundary conditions imposed by limits of accessibility to the dominant urban nodes Cthe CBD and maybe New Westminster in the Vancouver urban region) and proximity to existing development in the locality. The closer . the area to existing urban development, and to the major nodes of the urban region, the greater is the likelihood•that conversion of rural land w i l l occur. The relationship is also modified by fluctuations in the unused capacity of urban infrastructural systems reflecting the resilience of the urban system; as resilience increases, the probability of urban expansion declines because new activities can be absorbed without exceeding the domain of stability (Holling and Orians 1971). However, physiographic features, u t i l i t y networks and existing rural development operate to various degrees, as barriers to outward expansion. As the aggregate barrier effect increases, the likelihood of urban expansion decreases. The nomenclature adopted to describe variables and the concepts which they involve need to be explained in more detail and given an oper-ational form. Urban land is defined, for the purposes of this study, as the area developed to urban uses 'and the area withdrawn from rural uses which is available for urban development. Thus i t incorporates a l l land used for residential, commercial, industrial, recreational, civic and institutional functions which serve the urban population, and land used for transportation and communication u t i l i t i e s required for the preceding urban functions A Diffusion Model of Urban Expansion for Vancouver 128 CGad 1970 p.3). In addition, vacant land earmarked for urban development, and on which rural pursuits have ceased, such as undeveloped subdivisions, is also considered urban land (Ibid., p.4). Dominant Urban Nodes are the communications f o c i i of the urban region. Their relative importance, Cwhere there is more than one), can be measured by reference to the flow of people, goods, and services to and from them, or by the more usual surrogate, total commercial floor space. A particular node is considered dominant when its influence over nearby rural land is greater than any other node in the urban region. Thus on the basis of a study by Hardwick (1970),• Vancouver could be considered a bi-nodal' region as there is some, evidence that New Westjriinster- has a greater influence than the CBD over rural areas in the municipality of Surrey. However, as a result of construction and associated freeways which focus on the CBD, New Westminster may be eclipsed by Vancouver once again. A diagramatic representation of the hypothesized spheres of influence of dominant nodes in the Vancouver urban region is shown in Figure 12. It needs to be -emphasized that the relationship between the dominant node and its rural hinterland is based on observation and is a purely descriptive relationship. However, recent studies on the concept of growth centres initiating and transmitting social and economic development into their hinterlands may provide a theoretical foundation for the relationship. • Darwent (1969) provides an excellent review of the literature on growth centre theory. A Diffusion Model of Urban Expansion for Vancouver 129 Figure 12. Doirdnant Nodes and Their Urban Fields 1965 Circa Vancouver New Westminster Accessibility has been treated in many different ways in the literature, sometimes as a measure of proximity between two points and other times as a measure of the inherent advantage of a locality with res-pect to overcoming the frictional effects of distance (Ingram 1971). In this study accessibility is used to connote the ease of communication bet-ween a particular locality and the dominant nodes in the urban region. More specifically, i t is proposed to define an accessibility function which establishes probability limits for potential urban growth, (i.e. boundary conditions), in the form of a probability statement of land conversion, as shown in Figure 13. A Diffusion Model of Urban Expansion for Vancouver 130 Figure 13. Function for Establishing the 1 BJIIUI Limits of Urban Expansion Probability of ^^^^^^H Rural Land p!ii§lllli§!s Conversion 30 60 90 Travel Time in Minutes from Dominant Node Sources: Wolforth 1965, Appendix III. Often, models of urban expansion make no provision for boundary conditions and assume an unlimited environment (Korcelli 1970 p.134). The approach adopted here is an attempt to overcome this problem by defiiiing boundary limits stochastically, in a way which reflects the comparative advantages of sites near to carimunication corridors focussed on the urban node rather than those further away from them (Yuill 1970 pp.122-127). Accessibility is not constant over time, for with the assimilation of advances in communication and transportation technology, the potential boundary of the urban region is extended further into the hinterland. It w i l l be necessary to either make assumptions with respect to adjustments in the time-distance relationships for the future to account for this or make provision for input frcm the HPS transportation model. A Diffusion Model of Urban Expansion for Vancouver 131 While increases in accessibility extend the potential boundary of the urban region considerably and increase the probability of rural land conversion further afield, there is a counteractive force promoting spatial proximity of urban functions. This agglomeration force is refer-red to here as the tendency for propinquity of urban activities, indicat-ing nearness in space. The concept behind this force i s derived from Tornqvist (1968 p.101), who states-that: The need for contacts and exchange of information between increasingly- specialized functions in the community.,- . .is an essential motive force in the process of urbanization. The concept has also been applied successfully by Morrill (1965b) in his study of the diffusion by. expansion of a ghetto in Seattle. In his study-, he suggests there are psychological forces encouraging residen-t i a l settlement propinquity..- Webber (1963), on the other hand, claims that this type of social-physchological force is weakening for residential location and being superseded by ones reflecting specialization of occupa-tions and interests. Notwithstanding, Tornqvist's view is not weakened for the reason that . ., .the individual in today's society finds that the more advanced his education is and the greater the degree to which specialization has been carried, the narrower i s his choice of possible places of residence (Tornqvist 1968 p.104). Figure 14- suggests a series of possible relationships between A Diffusion Model of Urban Expansion for Vancouver 132 decreasing propinquity (real or perceived?) to the probability of land conversion. Obviously, there is a need for basic data to determine the nature of this relationship in the Vancouver region. Figure 14. Hypothetical Relationships Between Propinquity and the Probability of Land Conversion 1 Decreasing Propinquity > Resilience in dynamic systems refers to the ability to absorb shocks or perturbations. Used in reference to urban systems i t can be defined to mean the ability of urban infrastructural systems to absorb increases in population and urban activities. Inherent in the concept of resilience is the identification of bounded entities (i.e. domain of stability) beyond which changes take place in the system, either to restore stability through evolution of a new system structure or resulting in a collapse of the system (Holling 1971). A Diffusion Model of Urban Expansion for Vancouver 133 Bounded entities can be recognized-in urban systems, particularly as they relate to the urban expansion process. For one, land i s f i n i t e and new demands for space have to be met by urban expansion i f they cannot be satisfied by vertical development. Moreover, there are limits to the ser-vices and u t i l i t i e s that can be provided i n limited areas, i f community expectations are to be' satisfied and excessive congestion avoided. The primary'need here i s to identify suitable indicators of resilience-in urban- systems as they relate functionally, to the urban expan-sion process. Because residential development i s the major user, at least i n i t i a l l y , of land converted from the rural sector, this seems one promising area i n which to search. For example, a suitable indicator might be dwelling vacancy rates as a function-of total occupancy rates (i.e. vacancies per thousand dwellings occupied). However, there i s a problem involved i n the use of housing occupancy rates, as the-basis of an indicator, because dwelling occupancy- fluctuates over time and space for reasons not directly related to housing shortages. Changing social preferences for types of dwellings (e.g. the large increase'in non-family dwellings i n the last two decades i n central city areas) and c y c l i c a l economic conditions, (par-t i c u l a r l y unemployment), cause significant deviations i n numbers of people per dwelling. Another potentially suitable indicator might be derived by compar-ing the rates of land conversion per. capita increase, with the total amount of urban land consumed per capita i n the urban region. The fact that data are available for a number of North American c i t i e s makes this indicator A Diffusion Model of Urban Expansion for Vancouver 134 particularly-attractive (Gad 1970). However, there are problems concern-ing changing space requirements per capita over time, as well as with increasing city size. Tables 2 and 3 give an indication of the nature of these problems and an idea of the differences between consumption and absorption rates. Notwithstanding, analysis of the situation in the Vancouver urban region might show that the problems are not as severe as they f i r s t appear.. It would seem desirable to avoid using a combination of factors for the likelihood of even larger errors occuririg is increased (Alonso 1968). It is proposed that i n i t i a l l y , a land absorption-consumption indicator should be tested for i t has the desirable characteristic of adding a heur-is t i c quality- with respect to nature of land requirements. Barriers to the growth of urban areas refer to the restraining influence of (i) physical barriers such as rivers, marshes, steep slopes, and rugged and dissected terrain, ( i i ) structural limitations which result from the need to displace existing activites and overcome severe fragmenta-tion of property rights in land, for new development to take place, ( i i i ) technological limitations imposed by the difficulties and great costs involved in. extending public u t i l i t y networks such as electricity and water reticulation, sewerage and stormwater drainage and communication f a c i l i t i e s , into some new areas, and (iv) institutional impediments in the form of zoning restrictions and building controls (Malisz 1969, Y u i l l 1970 pp.105-114). To simplify the quantification of barrier effects in the model, i t is proposed to classify land for each of these four groups according to A Diffusion Model of Urban Expansion for Vancouver 135 Table 2. Summary of 'Land 'ConsumptionRates Cacres per 1,000 population) Source and Date of Survey City Size Bartholomew Niedercorn Hind-Smith Hind-Smith DMA Metro Planning Cpop.) 1940*s 1960 1951 1961 1950- Board 1960's 1960's 10,000 191 175 115 20,000 100 106 120 105 50,000 92 106 93 100,000 80 102(77) 97(94) 85 200,000 80 85 78 500,000 50 67 69 1,000,000 63 62 Table 3.. Summary of Land Absorption Rates (acres per. 1,000 population increase) Source and Date of Survey City Size (pop.) Niedercorn Krueger, Sinclair Krueger, Sinclair .1940-^ 1960 1934-1954 1954-1958 Hind-Smith Metro Planning 1951-1961 Board 1960's 10,000 102 20,000 206 50,000 143 76 164 100,000 95 75 72(136) 500,000 1,000,000 45 Average: 91 Source: Gad (1970) A Diffusion Model of Urban Expansion for Vancouver 136 the following categories CScottish Development Department 1968). a. land unsuitable for urban development b. . land needing improvements, or institutional changes before becoming suitable for urban development; i.e., requiring moderate expenditure for land preparation or hindered by fragmentation of land holdings c. land immediately suitable for urban development; i.e., where new urban activities can locate without requiring significant changes in the institutional system or expenditures on land preparation and property consolidation. Model Structure The hypothesized interaction between the various parts of the model is demonstrated in Figure 15. With a change in the demographic condition, evidenced for example by population growth, demands are created for new acti-vities , Chousing, industry, etc.), and networks, (roads, communications, ser-vices , etc.). Some of this demand w i l l be absorbed in unused irifrastrnactural capacity, but eventually, i f the population increase is large enough, new activities and networks w i l l be needed and w i l l emerge to meet the demand. Additional space requirements may result in conversion of rural land to urban uses as well as consolidation and i n f i l l i n g in some existing urban areas. The result w i l l be a new urban content, shape, and size which may or may not satisfy the demographic condition. In the event that the new urban condition does satisfy the demands created by the additional population, the probability of further land conversion w i l l tend towards zero, at least i f there is no residual demand 137 FIGURE 15 FLOW DIAGRAM OF GENERAL RURAL-URBAN LAND CONVERSION AWAIT NO YES ACCESSIBILITY SUB-MODEL POfENTI A URBAN FIELD / RURAL LAND CONVERS ION PROB-\ABILITY MATRIX y RESISTANCE TO DISPERSED SETTLEMENT . NEW DEMOGRAPHIC CONDITION NEW DERIVED DEMAND FOR LAND UNSATISFIED DEMAND LEVEL OF RESILIENCE TOTAL LAND REQUIRED EXISTING UNUSED RAPACITY ABSORBEI RESILIENCE SUB-MODEL INCREASED CAPACITY DISPERSAL POTENTIAL RURAL - URBAN LAND CONVERSION URBAN EXPANSION THRESHOLD DISPERSAL RESISTANCE ' NEW URBAN > vSHAPE & STRUCTURE/ PROPINQUITY SUB-MODEL BARRIERS SUB-MODEL I A Diffusion Model of Urban Expansion for Vancouver 138 for land from the previous time period.. • On the other hand, a continuing deficiency w i l l promote.further activity and increase the probability of further land conversion. When resilience in the urban system is high, for example, where there is considerable opportunity for absorbing and increased housing needs, i t can.be anticipated that the time-lag before'activity and network response would be greater'than i f resilience were low. The- likelihood of rural-urban- land conversion in any particular locality- is modified by additional interactive forces. On the left hand side of the flow chart, the interaction of accessibility and propinquity forces results in the probability of land conversion resulting from the operation of-these forces. • To demonstrate the variable nature of the interaction of these two forces,- Figure 16 shows two hypothesized functions relating accessibility to proximity for different localities in the Vancouver urban region.. In the f i r s t case, representing a hypothetical locality-immediately contiguous to the main urban area, (e.g. in south Richmond), the relationship is linear with decreasing accessibility matched by decreasing proximity-., • In the second example, representing a hypothetical locality near an 'island'' of development in the outer metropolitan region,. (e.g. White Rock or Cloverdale), i t is possible to have a relatively high level of accessibility corresponding to a low level of proximity, in the rural area between the 'island'' and the main urban area, followed by an increase in. proximity closer to the--'island' before both accessibility and-proximity decline on the metropolitan boundary side of the 'island'. There is a feedback to the propinquity sub-model after each sequence A Diffusion Model of Urban Expansion for Vancouver 139 r of ruralTurban land conversion, • requiring readjustment of propinquity rat-ings.- Variations in accessibility ratings are determined, exogenously, pos-sibly in.the transportation model. Figure 16. Hypothetical Relationships Between Accessibility and Propinquity Characteristics Decreasing Accessibility Decreasing Propinquity Decreasing Propinquity On the right hand side of the flow chart, the interaction of barrier effects and resilience forces results in a series of threshold levels denoted by a step-like decrease in the probability of land conversion with increasing resistance to urban expansion. • Because of the- number of components constituting the barrier sub-model, the forms of relationships between the two counteractive forces can be expected to be diverse and numerous. The feedback effects resulting from land conversion require that new barrier and resilience ratings be calculated within the-model after each diffusion sequence., A Diffusion Model of Urban Expansion for Vancouver 140 Generally, i t would be difficult i f not impossible to guess the likely outcome of each diffusion sequence, Ceven when a favourable situ-ation was seen, to exist in any area) because of the highly- interactive nature of the model. This characteristic reflects the dynamic.nature' and the uncertainty inherent in-the real world land conversion process. The above flow chart and description represents the static condi-tion and does not fully account for the likelihood.of a particular site being converted from-rural to urban uses in a discrete time period. This requires the inclusion of three additional elements; Ci) a fixed time sub-script, which, could be one,, two or more years, ( i i ) time"lags in the response of some process components,-for example, the resilience function, and ( i i i ) the translation of population increases, in each time period, to demand for land by varying the number of diffusion emissions, in proportion to the population increase. So far, insufficient information is available on these elements to warrant specific recommendations at this stage. However, this is not considered of great importance for they can only be resolved during the testing of the model. Assumptions Two important assumptions have been made which conceivably limit the modelrs suitability for use in other urban regions but which detract l i t t l e from the model's general validity with respect to the Vancouver Region. Firstly, settlement is assumed to spread out'from existing nodes. This is fundamental to diffusion processes and probably is not unrealistic A Diffusion Model of Urban Expansion for Vancouver 141 in the. Vancouver metropolitan region, where the pioneering centres of New Westminster and later Downtown Vancouver have acted as spring-boards for settlement of the hinterland-(Rose 1966). Secondly, while assuming a completely unlimited spatial environ-ment, as Korcelli (1970) was obliged to, has been avoided, the model does not provide for modifying and limiting influences resulting from the growth of other urban, centres such as Bellingham or Seattle. To the south i t is possible to view the international border as an absolute boundary for the purposes of the model, although pragmatically, this is unreal, for Canada and the United States have a meagre but significant history of coordination in the provision of urban services and fa c i l i t i e s . The implications of assuming the absence of negative feedback forces from other urban regions is not a major weakness at this point in time, but negative feedback could become very important within one or two decades. For example, undesirable consequences as a result of industrial development on the southern shores of Boundary Bay, and in the Puget Sound area in general, may make i t neces-sary to incorporate an additional element in the barriers sub-model.account-ing for the localized effects of pollution. This could be'handled without any difficulty. Method for Application: Monte Carlo Simulation Expansion of the urban area has been likened to a spatial diffusion process, with sequential urban development radiating out from the nodes of the metropolitan region.. If the- Vancouver Region is to be considered a A Diffusion Model of Urban Expansion for Vancouver 142 bi-nodal :. region, which w i l l be necessary i n the f i n a l version of the model, the rate of diffusion emission can be taken to be proportional to the size of the nodes, measured for example by total commercial floor space. In the i n i t i a l formulation,-however,.it i s proposed that the Vancouver region be considered as having only one'origin node for emissions,• represented by the CBD, • The rural-urban land conversion process described can-be simulated, appropriately, as a diffusion process using a probabilistic model. While Markov chain techniques have been adapted to probabilistic representations of urban expansion (Bourne 1969, Curtis Harris 1968, Drewett 1969) they are considered unsuitable here. In ferkov chain techniques the probabilities of land conversion, represented-by transition probability matrices for land use i n each sub-area, remain constant over time. While this i s not a serious weakness i n short term forecasts, i t i s an unsatisfactory assumption,. for obvious reasons, where medium and long range forecasting i s involved. Although, transition-probabilities can be made to vary with time i n 'Markov process techniques, this involves greatly increased mathematical complexity and a decrease i n ease of operation (Harvey 1967). I t i s suspected that the stochastic processes contained i n the present model are sufficiently complex,, as a result of the number of variables and their interactive nature, that they could not be handled analytically by Markov analysis without an undesirable number of simplifying assumptions being made to avoid mathematical i n t r a c t i b i l i t y CBailey 1964).' On the other hand, the Monte Carlo approach which involves proceeding A Diffusion Model of Urban Expansion for Vancouver 143 from probability distributions describing the relevant variables, to the desired event or outcome, using a sampling procedure which reflects the structure of the process under examination (Bharucha-Reid 1960) seems suitable. Appli-cation of the Monte Carlo method to probabilistic problems sometimes referred to as direct simulation CHammersley and Handscomb 1964), involves four basic operations: (a) identifying the probability values or random variables in the stochastic process; Cb) obtaining a set of random numbers; (c) using the random numbers to sample from the probability distributions to convert them to random variates according to some specified method; and (d) repeating the operation many times to reduce variance and obtain an approximate solution to the model process (Harvey 19.67-p.582). Because diffusion processes are concerned with random flow in a generally deterministic medium they are appropriately studied by direct simulation, and i t is recommended that Monte Carlo methods be used for application of the model.. Specifically, direct simulation of the land conversion process could take the form described below.. The general approach is adapted from the technique described in the simulation study of barrier effects on urban growth by Malm and Wameryd (1967). The methodology recommended for use in this model can be described in three parts, representing the three direct A Diffusion Model of Urban Expansion for Vancouver 144 inputs to the land conversion process, shown in the flow diagram in- Figure 15. 1. • Directionally, the emission of the. diffused particles (i.e. urban, activities) in the. diffusion process is assumed to be random. The-aggregate number of 'particles'' emitted, varies as a function of total popu-lation increase, translated into a demand for land, in each time period. Land conversion is assumed to take place when the required number of 'hits' have been registered in cells of a grid placed over the metropolitan region. On the basis of Malm and Warneryd'-'s C1967) study,1 500 metre squares (i.e. approximately 63 acres) would seem to be a satisfactory size for models of metropolitan, regions.- When land already developed for urban uses has been excluded, the simulation, model w i l l be required to handle a maximum of 2,Q00 - 3,000 cells in any one iteration, involving a potentially develop-able area of approximately- 200-300 square miles. 2. The combined effects of accessibility and propinquity factors in any locality, are registered, i n i t i a l l y , as probabilities in the cells of a regional grid. This spatial probability matrix specifies for each cell area the probability of - being hit in any time period. A hypothetical example of a field presented in this way, taken from Malm, Olsson and Warneryd (1966), is shown in Table 4. The probabilities i n this figure can be interpreted, for present purposes, as the probability of land in any cell being converted to urban uses vis a vis land in any other c e l l . The differences in probabilities can be assumed, for purposes of illustration, to represent the effect of A Diffusion Model of Urban Expansion for Vancouver 145 local area attributes on accessibility and propinquity. Table 4 Hypothetical probability matrix a b c d e A .022 .028 .032 .028 .022 B .028 .045 .063 .045 .028 C .032 .063 .127 .063 .032 D .028 .045 .063 .045- .029 E .022 .028 .032 .028 .022 Source: Malm, Olsson and Warneryd, 1966. These probabilities are then transformed into a matrix of random numbers to f a c i l i t a t e the use of Monte Carlo methods as shown i n Table 5. In the random number matrix from 000 - 999, 'each random number represents a probability of .001. Hence, the probability for Be (.063) i s represented by the numbers 205-267, Ce (.032) by 627-658, Da (.028) by 659-686 and' so on..,- The diffusion of particles i s simulated by the consecutive selection of random numbers i n the 000 - 999 range, thus, the drawing of numbers 352 and 425 would be recorded as hits i n cell s Ca and Cb, respectively. Whether i n fact land conversion would be assumed i n the cells h i t depends on the restrictions imposed by the input from the resilience-barrier threshold shown i n the flow diagram (Figure 15). A Diffusion Model of Urban Expansion for Vancouver 146 Table 5 Matrix of Random Numbers . a b c d e A 000-021 022-049 050-081 082-109 110-131 B 132-159 160-204 205-267 268-312 313-340 C 341-372 373-435 436-563 564-626 627-658 ' D 659-686 687-731 732-794 795-839 840-867 E 868-889 890-917 918-949' 950-977 978-999 Source: Malm, 01sson and Warneryd (1966) 3. The input from the resilience-barrier threshold level takes the form of step—like levels of resistance to land conversion, from 1 to 5, (i.e. the number of separate hits required by each cell in each time period before acceptance of land conversion). To illustrate the technique consider the following example. Resilience and barrier effects can each be placed into three classes and resistance values assigned to each class, as shown in Table 6. Table 6 Aggregate Barrier Effects Number of Hits•Required Aggregate Resilience Number of Hits Required No significant Low barrier effects 1" Resilience 1 Moderate Barrier• Moderate Effects 3 Resilience 3 Strong Barrier High Effects . 5 Resilience- 5 A Diffusion Model of Urban Expansion for Vancouver 147 Obviously, the resistance values should bear a.resemblance to the resistance of these factors in the real world. In i t i a l l y , for operational convenience, this can be done by the reverse approach of classifying barriers and resilience factors according to the predetermined probability classes. By aggregating the resistance values assigned to resilience and barrier effects in, each, ce l l area, a single resistance factor can be entered into the land conversion process, from each ce l l area. To avoid difficulties with 'half-rhitsthe resistance values 1, 3 and 5 were chosen and the aggregate values divided by two. Consequently, there are five different levels of resistance depending on the particular combination of c l a s s i f i -cation categories, as shown in Table 7. To.summarize, the probabilities of land conversion, when acces-s i b i l i t y and propinquity factors are considered, are contained in the random number matrix in Table 5. .In each period of diffusion emissions, a number of ce l l areas w i l l be 'hit' and considered for conversion. Whether they are accepted depends on the level of resistance ascribed to each c e l l , as a result of resilience and barrier effects,. to"the form of the number of 'hits' required, Table 7. Because of feedback effects on some factors, caused by changes in the shape and structure of the urban region after land conversion, the probabilities for each ce l l w i l l need to be revised after each diffusion generation. For operational convenience, this w i l l need to be handled within the model. The original intention in this study was to present the model in an operational form at this stage. Unfortunately, due to a shortage of A Diffusion Model of Urban Expansion for Vancouver 148 computer programing assistance, this was not possible. Nevertheless, the notation and procedures, for the model were tentatively resolved in'discus-sions with a computer programming advisor at the University of British Columbia Computer Science Centre. They are presented in a generalized form, in Appendix IV. Table 7 Total Number of Hits Required Before Acceptance Corresponding Conditions 1 Insignificant barrier effects-low resilience 2 Insignificant barrier effects -moderate resilience Moderate barrier effects -low•resilience 3 Insignificant barrier effects -high resilience Moderate barrier effects -moderate resilience Strong barrier effects -low resilience 4 Moderate barrier effects -high, resilience Strong barrier effects -moderate resilience 5 Strong barrier effects -high resilience HEM? nnn The paradox of mechanization is that although i t i s . i t s e l f the cause of maximal growth and change, the principle of mechanization excludes the possibility of growth or the understanding of change. For mechanization is achieved by fragmentation of any process and by putting the fragmented parts in a series. Yet, as David Hume showed in the eighteenth century, there is no principle of causality in a mere sequence. Marshall McLuhan The Medium is the Message' Chapter 6 INTERPRETATIONS On Understanding Complex. Systems Throughout this dissertation, i t has been maintained that the central purpose' of modelling in applied science is to provide an understand-ingVof behavioural processes. Unfortunately, what is mean by "understanding" behaviour is far from clear in this context. . The point was made previously that planning, to the extent that i t is a behavioural science, involves dual interpretative functions. The f i r s t involves the description of process structure and the second'involves evaluation of process behaviour to arrive at an explanation for i t . The confusion surrounding the concept of "under-standing" can be. traced,'it.is submitted, to the failure of behavioural scientists to appreciate the differences between these two functions. Cornmonly, understanding is equated to explanation, denoting that reasons have been provided for the behaviour of a process.. "However, in complex systems evolving through time, the nature of cause-and-effect Interpretations 151 relationships is a function of the state of the system at a fixed point in time (Hardin 1963). As a result, causal relationships in complex and evolu-tionary systems can vary over time. Consequently, "explanatory" understand-ing is- concerned with an instantaneous state of knowledge, i t requires the system-or process to be "frozen"' in time to facilitate analysis. This is basically the analytical method. It is a "static" concept of understanding and the analytical approach to urrierstanding evolutionary systems might be thought of as the historical method, in that the system structure at the moment of "freezing" is already- in the past, Instantaneous or static understanding is a poor conceptual basis for the investigation of dynamic conditions for as McLuhan (1965 p.16) has remarked, understanding stops action. - However, the-weakness of static understanding can. be largely overcome by accepting a different concept of understanding, one less demanding and focussing on the rate and scale of change in human affairs over time. Scheffler (1957) proposes that the type of understanding which acknowledges dynamic and evolutionary phenomena, is necessarily a function of the specification of comprehensive relationships among events.• In a nutshell, this is the doctrine of a movement in the behavioural sciences called structuralism (Piaget 1970). In separate disciplines, structuralism is complemented-by the more specific methodologies of systems theory, communication theory and cybernetics. Structuralist's concepts underline much of the work used as a starting point for this study, particularly - Forrester's (1968, 1969) work on the nature of systems and urban dynamics, and Holling's (1969, 1972) work Interpretations 152 on stability in spatial systems and process oriented modelling strategies. These studies are basically descriptive and involve specifying: (i) system components and their relationships to reflect feedback properties, ( i i ) functional relationships between components in time and space, and ( i i i ) time lags, thresholds and boundaries•(Forrester 1969 ppi112-114, Holling 1969). The model or rural-urban land conversion described in earlier sections of this.dissertation, represents a process which is an integral part of the much more complex system, the Vancouver region. The process is dependent on other component processes in the system and at the same time constrains in a number of ways the operation of these other processes. Through this-interrelation- of - processes, the complexity and evolutionary nature of the Vancouver regional system can be approximated. Subsequently, our understanding of system behaviour can be enhanced by attending to several characteristics common to complex systems. Firstly, complex systems are non-linear, and as a result, the behaviour of the total system-is influenced to varying degrees by changes in component processes. The nature and degree of system response depends on the state of the system at the time when the change is registered (Hardin 1963). -A Secondly, and arising out of the f i r s t property, cause.'arid effect relationships are often widely divergent in time and space. Frequently, apparent causal connections are only the close correlation of coincident symptoms (Forrester 1969 p.110). Interpretations 153 Finally, with most complex systems there are usually a few points in i t s structure which are f o c i i of influence and small changes registered at these points can cause reverberations through the whole system. However, as a result of the two properties described above, these points are usually not self-evident and must be discovered through investigation of the structural dynamics of the system. Modelling Spatial Systems The emergence of regional spatial systems as a separate area of research, emphasizing evolutionary processes subject to change, has focussed attention on the indeterririjiistic nature of spatial dynamics (Curry 1966). The argument that there is a strong random element in aggregate patterns of human behaviour is beginning to find support among social scientists as the number of probabilistic models of urban spatial growth clearly shows (supra Chapter 3). Moreover, the investigation and representation of complex social and economic systems, subject to change and chance mechanisms, (a major practical and theoretical difficulty in the use of deterministic models), is facilitated-using stochastic methods. The traditional probabilistic methods which are the- basis of sta-t i s t i c a l theory, have been found ill-suited to the' investigation of chance phenomena developing in time and space. Since World War II alternative procedures have been devised which concentrate on the frequency of various possible outcomes generated-from processes defined stochastically. This is: the approach, characterized by Neyman (1960) as dynamic indeterminism, in Interpretations 154 comparison to statistical indeterminism- which is essentially static. The basis of the new approach is the design of experiments using hypothetical chance mechanisms which simulate the process being investigated. Spatial diffusion models have been among the most promising applications of the theory of stochastic processes to understanding complex human behaviour. Because spatial diffusion models are designed to handle social, economic or environmental-processes in both time and space concur-rently, they are especially suited to' the investigation of spatial dynamics (fiould 1969). The essence of spatial diffusion models is that emerging patterns of behaviour relate functionally to historical patterns. Thus they display two major characteristics of complex systems, spatial and historical properties. Further, by adapting easily to a systems framework, they can readily reflect feedback, interactions and structural properties which chara-cterize.-complex processes and systems.• However, i t is emphasized that future patterns of rural and urban land use are not constrained from evolving into new and different forms.- Rather, i t is acknowledged that the future cannot be forecast, on the'basis of past and present conditions, with suf-ficient re l i a b i l i t y for long range planning purposes. In fact, Drucker (19.59 p.8) argues forcefully that "long range planning is necessary, precisely because, we cannot forecast." For these reasons, special attention has been paid in this- study to change and chance mechanisms to avoid indiscriminate extrapolation of present trends. While the concept of interacting forces is fused in spatial diffusion Interpretations 155 models., i t does: not necessarily mean that these models are simple growth force models like gravity'analogues. Indeed the approach Is fundamentally behavioural in that i t focusses on.the likelihood of people making decisions' with respect to their personal migration, or of the distribution of pheno-mena (Yuill 197Q). One of the more, contentious features of the new trend is the theo-retical justification for stochastic representations of human behaviour and their incorporation in probabilistic models of spatial'growth. The effect has been, to generate discussion on scientific methods of applied research. While theoretical justification for probabilistic modelling has been found in contemporary theories of dynamic indeterminism in science, an interesting side effect of the general debate has been the disclosure of theoretical deficiencies i n some fields using applied research methods. Planning in particular has come under heavy criticism (Gross, 1967, Rogers 1967, War-tofsky 1968, Forrester 1969, Haworth 1970) and much of the discussion in Part IT is aimed at resolving some of these criticisms. • , The Relationship of the Model Strategy to TIPS In formulating the model of rural-urban land conversion in the Vancouver region, a definite strategy was used. This strategy was described in general terms i n Chapter 2, but i t remains to interpret the manner in which i t relates to the development of the model for use in the HPS proj ect. Seven interrelated requirements of the model were identified and they have been resolved in the following way.• Interpretations 156 1. The model needs to be generated within the present TIPS framework, and meet the demands of the HPS project. The process of urban expansion represents only a small part of the complex system being modelled in the HPS project. However, the fact that urban expansion has been' considered separately in this study should not be interpreted as implying that urban expansion is independent of other regional processes or the other models in HPS. On the contrary, various components in the rural-urban, land conversion model are constrained by con-ditions generated in other submodels. For example, transportation develop-ments to serve the Port of Vancouver may not be a response to the needs of the metropolitan population, yet they would be significant to urban evolu-tion. That transportation corridors influence the spread of settlement has already been established, and thus i t is easy to see that the transporta-tion sub-model w i l l provide important parameters to the land conversion model. Similarly, changes in the shape and size of the urban region arising out of urban expansion w i l l establish input parameters for the operation of other sub-models, notably the land use allocation models. The model capitalizes on the advantages of the systems approach, adopted as the framework for the HPS project, by utilizing direct simulation for its application. As a result, there was greater freedom in the specifi-cation of the urban expansion process, non-linear functions were able to be. used, and structural properties could be represented which emphasize the dynamics' of urban expansion. Interpretations 157 2. The model .should mimic the urban expansion process and generate the problems which characterize settle-ment on the. urban fringe. Throughout formulation of the model, the point was repeatedly made that the model is designed to reflect what is likely to happen, not what is thought desirable. In this respect the model is value free and inherently descriptive. Most "problems"'associated with urban fringe settlement take on this character because of the particular values 'of the individual perceiving them. Consequently, instead of trying to recreate ."problems," the model was designed to mirror structural dynamics of the actual process. Thus the user is required to interpret or evaluate the process to determine the reasons for the pro-blems he perceives. 3. The model should provide forecasts of rural-urban land conversion and at the same time pro-mote an understanding of the urban expansion process. The model is designed to provide forecasts of the rate, extent and location of rural-urban land conversion in each time generation. A dominant emphasis in the model's construction was on the struc-tural relationships of components in the urban expansion process, on the basis.that only by.seeking to identify the interactions of "the primary forces Interpretations 158 which provide the impetus for urban spatial growth can we increase under-standing of the process. 4... The model should account for uncertainty in the urban expansion process.. This is reflected strongly in the model by treating rural-urban land conversion as-' a stochastic process and by the explicit assumption, in the diffusion analogue used, that directionally, urban expansion is random. The implication of these two characteristics is that the particular pattern existing at any time can be interpreted as the historical realization of a process which might just as easily produce a different settlement pattern, according to the probabilities attached to the forces simulated. 5. • The model should only incorporate those elements, and relationships which can reasonably be expected to persist in the future and should omit factors overly susceptible to change. In structuring elements and developing concepts.for the model, a concerted attempt was made to work, with those least dependent on existing social, economic and technological standards. Of course the dependence cannot be completely removed, but the resilience-barrier approach to urban expansion helps minimize the dependency. Further, calibration of the model w i l l need to be guided' by emerging conditions and not those recognized in the past. Interpretations ' 159 How effectively this is done w i l l have a great bearing on the model's suc-cess., 6. The model should reconcile the overall behaviour of the system (macro-scale characteristics) with the processes of the individual decision makers (micro-scale characteristics). This aspect has not been resolved in the present model-, to the degree originally hoped. Tt was discovered that really tackling this issue required introducing factors very susceptible to change over short time periods, thereby falling foul of point 5 above. In the final outcome,. how-ever, there are a number of innovations helping to bridge the macro-micro gap, normally not found in models of urban spatial growth. The propinquity element can be interpreted as recognizing the social tendency of people for close proximity to others in their place of residence as well as the need for the easy exchange of information between specialized community functions. The resilience element can be interpreted, depending on the level of resilience, as one of the motivating forces encouraging individuals and urban, activities to' move into suburbia and beyond in their search for space. Further, i t could generally be observed' that the types of barrier impedi-ments considered i n the model influence the individual decision maker in much the-same way as they influence aggregate patterns of spatial growth. Finally, and most importantly, the diffusion approach links the dynamic growth forces Interpretations 160 at the macro level to individual behaviour in that i t focusses on the like-lihood of people making decisions with respect to land use. 7. The model should'have a basic heuristic f e r t i l i t y in that i t should not only enhance our understanding of the processes at work, but suggest" new observations, experiments and conceptualizations. The effects of barriers on urban spatial growth and the concept of stability in urban systems has attracted the attention of scholars in recent years, particularly since Malisz's conceptualization of threshold theory for long range planning (Malisz 1963, 1969, Scottish Development Department 1968), . The pervasive influence of Malisz's theory on planning practices throughout Europe indicates- that the approach has considerable heuristic f e r t i l i t y . Whether the present model has inherited the necessary "gene" depends on the response to the model of urban expansion described in this- dissertation. Implications, :for Regional Planning In order to f u l f i l plaroiihg objectives, the regional planner must f i r s t understand behavioural processes i f he is to know in advance the probable impact of intervening measures. From this apparently simple pro-position., i t is implicit that the regional planner exercises three functions. Firstly ? to articulate objectives consistent with the planning environment, Interpretations ]61 he is required to be a social philosopher. Secondly, in order to under-stand behavioural processes he needs to be a behavioural scientist. Thirdly, to evaluate in advance the consequences of his recommendations he needs to be proficient in applied research. This dissertation is primarily concerned with the two latter"functions. However, the function of planners as social philosophers places a caveat on the other two roles which requires a brief discussion. When referring to communities of people and their relationships to the environment, planning entails a philosophy of social order and strategies for regulating the operation of behavioural process (Glikson 1955). Thus i t i s necessary to make explicit the limitations of logic and scientific methods:. There are a number of issues which cannot be treated satisfactorily by existing scientific methodologies. Paramount among these, and of extreme importance to planning, is the matter of ethics. While logical methods of problem investigation may increase the likelihood of arriving at a better understanding of behavioural processes or suggest one or more possible solutions, there is no guarantee-or justification to be derived from this logic that the solutions are morally or ethically "right." This issue is beyond science and remains a matter for independent formulation (Haworth 1970). It is anticipated that as a result of the continuing debate on the nature of planning methodology, (including the use of modelling techniques), the philosophy of planning strategies could become a new focus of study in planning education. At a time when strategic procedures and philosophical Interpretations 162 issues- are receiving considerably less attention than specialized tactics and. the development of analytical techniques, the prospect is to be welcomed. As behavioural scientists, i t appears from earlier discussions, that regional planners have lagged behind in the assimilation of methodologies designed to promote an understanding of complex behavioural processes. In particular, this study has shown that there has been a tendency to adhere to fragmented conceptualizations of the nature of urban spatial growth. The proliferation of many deterministic and static theories of urban spatial growth processes, considering widely divergent spatial-temporal dimensions and sometimes at odds with each other, is symptomatic of this situation. To the detriment of planning, however, the aggregation of diverse and • specialized techniques]does not engender holistic appreciation. Moreover, . the tendency to confuse the two interpretative levels of behavioural science is- further evidence that regional planners as behavioural scientists, are not benefiting from available methodologies to the f u l l extent possible. The use of probabilistic and synthetic models, emphasizing the structural dynamics of complex .processes, similar to the one developed in this study, is submitted to be a marked improvement. Not only do they account specifically for uncertainty in process behaviour, they are inherently dynamic and permit the evolution of different component elements to be monitored. Thus they provide a fuller understanding of the nature of change and chance elements in behavioural processes, in time and space. It i s in the field of applied research, that regional planning is Interpretations 163 especially deficient.- While by definition, planning is concerned with the futurity of present decisions CDrucker 1959 pp.8-9), there has been l i t t l e real progress in the development of methods whereby various policies can be tested before they are implemented. The present study helps pinpoint this deficiency. Theoretically and practically, the most c r i t i c a l implication of urban expansion as a dynamic and evolutionary process is that the future w i l l bring changes in the rate, scale, or patterns of urban expansion. Con-sequently, i t is highly desirable that the regional planner, through experi-mental " methods, be able to represent ongoing processes in a way that permits tests to be carried out. For example, i t is clear that automated transporta-tion, particularly the extensive use of the-private automobile, produced a substantial shock to the urban system in the early decades of this century and had the effect of thrusting the system into a new condition with a con-siderable increase in development potential. This crossing of a c r i t i c a l threshold or "break boundary" resulted in the city evolving into continuous urban highways, where for the f i r s t time, the countryside became the domain of leisure and the city the centre of work (McLuhan 1965 p.38). The impli-cations of this evolutionary characteristic are obviously of crucial importance to the planner. Changes in the nature of component elements in a process, their relationships within the process, or a change in the relation of the process to other processes operating within the complex regional system may generate new potential in the system or result in its collapse. Whether or not a change in process behaviour, whether by chance Interpretations 164 or design, w i l l be c r i t i c a l i n the sense of. precipitating a rapid evolution (or devolution) to a new condition depends on three qualities: the nature of the change generated, where its impact is felt in the system and the state of the system at the time the change is felt (Hardin 1963). Consequently, the purpose of applied research in regional planning is not primarily a mat-ter of predicting specific quantities at some'future date but the experi-mental monitoring and regulation of behavioural processes so that we are more aware of c r i t i c a l thresholds and system boundaries. It is in this respect that the implications of the present study for regional planning are strong-est. By design the rural-urban land conversion model was formulated as an interactive field-laboratory experiment, eminently suited to the examina-tion of the urban expansion process and the testing of various planning policies. V LJTTT^ATURE CITED Ackoff, R,L, 1962 Scientific Method; Optijiiizing Applied Research DecisionsT John Wiley and Sons, New York. Alonso, W; 1968 "Predicting Best With Imperfect Data", Journal of the.American Institute of Planners, July 1968: 248-255. Bailey, .N.T.J. • 1964 .The Elements of Stochastic'Processes With  Applications to .the Natural Sciences. John Wiley and Sons, New. York. Barton,.R.F. 1970 A Primer on Simulation and Gaming. Prentice-Hall, Englewood C l i f f s , N.J.. Bartos, D.J. • 1967 'Simple Models of Group Behaviour. Columbia University Press, New'York. Bharucha-Reid, A.T. 1960 Elements of the Theory of Markov Processes  and'Their Application.. McGraw-Hill, New York,-Blumenfeld, H. 1954 "The Tidal Wave of Metropolitan Expansion", Journal of the American Institute of Planners, Winter 1954: 3-14, Blumenfeld, H, 1967 The Modern Metropolis; i t s ; Origins,.Growth, Characteristics, and Planning, Edited by P.D. Spreiregen, Harvest House,' Montreal, Borchert, J,R, 1961 "The Twin-Cities Urbanized Area; Past, Present and Future",.Geographical Review 51: 47-70. Literature Cited 166 Borchert, J.R. 1962 "Time Series Maps for the Projection of Land Use Patterns", Highway-Research Board Bulletin Number 311, pp.13-26; National Research Council, Washington,.D,C. Branch, M.C. 1962 "Rome and Richmond - A Case Study in Topographic Determinism'1 j•Journal of the American Institute of Planners 28: 1-9,' Brindle, R.G, 1970' "Calibration of an Opportunities Model for Resi-dential Development", in Analysis of Urban Development (N. Clark, ed.) Transport Section, Department of C i v i l Engineering, Uni-versity of Melbourne, Melbourne.• Brown, L.A. • 1968 Diffusion Processes and Location. Bibliography T Series -Number 4, Regional Science Research Institute, Philadelphia. Bunge,.M. 1963 The Myth of Simplicity - Problems of Scientific Philosophy. Prentice-Hall, Englewood Cl i f f s , N.J. • Bunge, W, 1969 "Simplicity",. Geographical Analysis 1: 388-391. Burgess, E.W. • 1925 "The Growth of the City", in The City (R.E. Park and E.W. Burgess, eds:3. University of Chicago Press, Chicago. 1967 pp.47-62.• Chapin, F.S, • 1964 "Selected Theories of Urban Growth and Structure", Journal of the American Institute of Planners 30: 51-58. Chapin-F.S,, and S,F, Weiss, 1962 Factors Influencing Land Development. Urban Studies Research Monograph, Institute for Research and Social Science,. University of North. Carolina, Chapel H i l l . Chorley, R,J., and P. Haggett, 1967 Models in Geography. Methuen, London. Clawson,.M. 1971 Suburban Land Conversion in the United States: An Economic and Governmental Process. Resources for the Future Inc., by John Hopkins Press, Baltimore. Curry,.L. • 1964 "The Random Spatial Economy: An Exploration in Settlement Theory", Annals of the Association of American Geographers 54: 138-146, Curry, L, 1966 "Chance and Landscape", Tn Northern Geographical Essays  in Honour'of G.H.J. Davsh. CJ.W, House, ed.). Department"of Geography, University of Newcastle-Upon-Tyne, Oriel Press Ltd. Literature Cited- 167 Darwent, D.F. 1969 ''Growth Poles and Growth Centers in Regional Plan-ning -A Review"', Environment and Planning .1: 5-32, Davidoff, P, and T.A. Reiner, 1962 "A Choice Theory of Planning", Journal of the American Institute of Planners May 1962: 103-115. Department'of Mines and Technical Surveys, 1957 Atlas of Canada. Department of Mines and Technical Surveys, Ottawa. Donnelly, T,G., F.S, Chapin and S.F. Weiss, 1964 A Probabilistic Model  for Residential Growth. Centre for Urban and Regional Studies, University of North Carolina, Chapel H i l l , Drewett, J.R. • 1969 "A Stochastic Model of the Land Conversion Process", Regional Studies 3: 269-280. Drucker,. P. F. 1959 "Long-Range Planning Means Risk Taking", in Long- Range Planning.for Management (D.W. Ewing, ed.). ' Harper and Row, New York. 1964 pp.7-20. Echenique, M, 1968 Models: A Discussion. Working Paper 6, Centre for Land Use and Built Form Studies, University of Cambridge. Etzioni, A, and.E.W. Lehman, 1967 "Some'Dangers in 'Valid' Social Measure-ment", Annals of the American Academy of Political-rahd Social Scientists Vol. 373, Sept, 1967.' Faludi, A. 1970 "The Planning Environment and the Meaning of Planning", Regional Studies 4: 1-9. Famelis, N. 1970 "On the Validity of Urban Threshold Theory: Further Comment", Journal of the Town Planning Institute 56: 21-22. Forrester, J,W. 1968 Principles of Systems. Wright-Allen Press, Cambridge, Mass. Forrester, J.W, 1969 Urban Dynamics. The M.I.T. Press, Cambridge, Mass.. Gad,"G, 1970 "A Review of Methodological Problems in Estimating Urban Expansion"Research Paper.Number 25, Centre for Urban and Community Studies, University of Toronto, Toronto. Gale, S, 1970 "Simplicity Isn't That Simple", Geographical Analysis 2: 400-402. Ij.tera.ture Cited 168 Geddes, P. 1915' Cities in Evolution. Howard Fertig, New York. 1968 Edition. Glikson, A, 1955 Regional Planning and Development.• Netherlands Universi-ties Foundation for International Cooperation,•The Hague. Goldberg,-M.A. 1970 "Quantitative Approaches to Land Management",-Roneod paper, .A.A,A,.S, Chicago Meeting. • December 1970.' Goldberg, MiA. 1971 . "HPS Land Use Models: Present and Future", Roneod paper, Resource Science Centre, University of British Columbia, Vancouver, Gordon, G. 1969 System Simulation. Prentice-Hall, Englewood-Cliffs, N.J. Gould, P.R. 1969 Spatial Diffusion. Resource Paper Number 4, Associa-tion of-.American Geographers, Commission on College Geography, Washington. D.C. Griffin, T.L.C. • 1965 "The Evolution and Duplication of a Pattern of Urban Growth", Economic Geography 41: 133-156. Gross, B.M.. 1966 ."The.City of Man: A'Social Systems Reckoning", in Environment for Man (W.R. -Ewald, ed,). Indiana University Press, Bloomington.. 1967 • pp.136-156. Gunn, A.M.. 196,8 Vancouver: ' Profile of Canada's Pacific Metropolis. Angus M. Gunn,"University of.British Columbia, Vancouver. Hagerstrand., T. 1965 ."A Monte Carlo Approach to Diffusion", in Spatial  Analysis (B.J.L, Berry and D.F. -Marble, ed.). Prentice-Hall, Englewood.Cliffs, N.J. 1968 pp.368-384. Hagerstrand,.T, 1965- "Aspects of the Spatial Structure of Social Com-munication and the Diffusion of Information'', Regional Science Association, Cracow Congress Papers 16: 27-42. Hagerstrand, T. 1967' Innovation Diffusion as a Spatial Process. Edited by A. Pred, University of Chicago Press, Chicago. Haggett, P, 1965 Locational Analysis in Human Geography. Edward Arnold, London. Haggett, P. 1968 ' The Spatial Siructure of City Regions. Working Paper 6, Centre for Environmental Studies, Regent's.Park, London. Literature Cited 169 Hamilton,'K.R., G,E, Goldstone, J,,W, Milliman, A.L. Pugh, E.B. Roberts and A. Zellner, 1969 Systems'Simulation for Regional Analysis - • An Application-to' River-Basin Planning. The M.I.T. Press, Cambridge, • Mass, Hammersley, J M. - and D. C. Handscomh, 1964• - Monte • Carlo Methods. Methuen, New York. " Hardin, G. 1963 "The Cybernetics-of Competition:- A Biologist's View of Society", in The Subversive Science CP. Shepherd and D. McKinley, eds.:). .Houghton Mifflin, Boston.. 1969 pp.275-296. Hardwick, W.G. 1970 "Vancouver: The Emergence of a "Core-Ring" Urban Pattern", iri'Geographical'Approaches•to Canadian Problems (R.L. •Gentlicore, ed.)". rtrentice-Hall, Scarborough, Ont. 1970 pp.112-118. Harris, B. 1966 "The Uses-of Theory in the Simulation of Urban Phenomena", Journal of the American Institute of Planners 32: 258-273. Harris, B. 1968 "Quantitative Models of Urban Development: . Their Role in Metropolitan. Policy Making", iri Issues in Urban Economics (H.S, Perloff and L. Wingo, eds.). 'Resources for the Future, Inc. by the John Hopkins Press, Baltimore. 1968 • pp.363-410. Harris, B., 1970- "New Tools for Research and Analysis in Urban Planning", in Urban Planning in Transition (E. Erber, ed.). Grossman Publishers,•New York. 1970- pp.192-202. Harris, C.C; 1968 "A Stochastic Process Model of Residential Develop-ment", Journal of Regional Science 8(1): 29-39. Harvey, D. 1967' "Models of the Evolution of Spatial Patterns in Human Geography", in Models in Geography (R.J. Chorley and P. Haggett, eds.). Methuen, London. 1967 pp,549-608. Harvey, R,0., and W.A.V. Clark, 1965 "The Nature and Economics of Urban Sprawl", Land Economics 41: 1-9. Haworth, L. 1970 "Planners, Philosophers and the Good City", Plan Canada 1QC3); 72-83, Hellyer, P.T. 1969 Report of the Task Force on Housing and Urban Develop- ment , The Queen's Printer,.Ottawa.-Hightower, H..C. 1969 "Planning Theory in Contemporary Professional Education", Journal of the American Institute of Planners 35: 326-329. literature Cited 170 Hodge,..G, 1970 A Probe of Living Areas in the Periphery of the Toronto  Urban Field. Research Paper Number 30, Centre for Urban and Commuriity Studies, University of Toronto, Toronto. Holling, C.S. 1969 "Stability in Ecological and Social Systems", Brookhaven Symposia in Biology 22: 128-141. Holling, C.S'. 1971 The Concept of Resilience in Regional Systems.-Roneod paper, Resource Science Centre, HPS Serial Number 2/19, University of British Columbia, Vancouver. Holling, C.S. 1972- Ecological Models: A Status Report. Roneod paper. Institute of Animal Resource Ecology, University of-British Columbia, Vancouver. Holling, C.S., and G. Orians, 1971 "Toward an Urban Ecology", Ecological Society of America, 1971 Bulletin 52(2): 2-6. Hoyt, E. 1960 Dynamic Factors in Land Values. Technical Bulletin Number 37, Urban Land Institute', Washington^ D.C. • Hurd, R.M. 1924 Principles of City Land Values. The Record and Guide, New York.. HPS Serial No. 18, 1970 * Vancouver Regional Simulation Project. Roneod report, Resource Science Centre, University of British Columbia-, Vancouver. Ingram, D.R. 1971 "The Concept of Accessibility: A Search for an Operational Form", Regional Studies 5: 101-107. Isard, W. 1960 Methods of Regional Analysis: An Introduction to Regional Science. The'M.I.T. Press, Cambridge, Mass. Isard, W. 1969 General Theory. The M.I,T, Press, Cambridge, Mass. Jones, G.I.H. 1966 "The Urbanisation of the-Fraser Valley", in Lower Fraser Valley: Evolution of a Cultural Landscape (A.H. Siemens, ed.). • B.C. 'Geographical Series Number 9, Tantalus Research Ltd., Vancouver, 1968 pp.139-161. Kaplan, A. - 1964 The Conduct of Inquiry, Chandler, San Francisco, Kilbridge, M,D., R.P. O'Block and P.V. -Teplitz, 1970 Urban Analysis. • Graduate School of Business Administration, Harvard University, Boston. Literature Cited 171 Koreelli, P.; 1970 "A Wave-Like -'Model of Metropolitan Spatial Growth", Regional Science Association, Papers of the 9th. European Congress, Copenhagen 1969, 24:127-138. Lean, W. 1970 "On the Validity of Urban Threshold Theory: A Rejoinder", Journal of the Town Planning Institute 56C3): 106-107. Lean, W., and B. Goodall, 1966 Aspects of Land Economics. " The Estates Gazette Ijirnited, London. Leven, C.L. 1968 "Deteriuinants of the Size and Spatial Form of Urban Areas", Regional'Science Association, Papers of the 22nd. European Congress, 1968 pp..7-28. Lithwick, N.H. 1970 Urban Canada: Problems and Prospects. Central Mortgage and Housing Corporation, Ottawa. Lower Mainland Regional Planning Board, 1963 Land For Living. Lower Mainland Regional Planning Board of British Columbia, New Westminster. Lower Mainland Regional Planning Board, 1963 The Urban Frontier. Lower Mainland Regional Planning Board of British Columbia, New Westminster, " Lowry-, I..S, 1964 ' A Model of Metropolis. The Rand Corporation, Santa Monica., Calif..-Lowry, I.S, • 1965 "A Short Course in Model Design", Journal of the American Institute of Planners 31: 158-166. McKenzie, R.D. • 1925 "The Ecological Approach to the-Study of the Human Community",- in The City CR.E. Park and E.W. Burgess, eds.). University of Chicago Press, Chicago. 1967 pp.63-79. McLuhan, M. • 1965 Understanding Media: The Extensions of Man.- McGraw-H i l l , New York. McLoughlin, J,B, • 1969 Urban and Regional Planning - A Systems Approach. Faber and Faber, London. McMillan, C,, and R. Gonzalez, 1965 * Systems Analysis. Richard D. Irwin Inc., Illi n o i s . • Malisz, B, 1963 The Economics of Shaping Towns. Polish Academy of Sciences. Malisz, B, 1969 "Implications of Threshold Theory for Urban and Regional Planning", Journal of the Town Planning•Institute 55: 108-110. Literature Cited 172 Malm, R., G. 01sson-and 0. Warneryd, 1966 "Approaches to Simulations' of Urban Growth'% Geografiska Annaler 48(B): 9-22.' Malm, R., and 0. Warneryd, 1965 "Urban Growth and Barrier Effects", Proceedings Scandinavian-Polish Regional Science Seminar, Warsaw, pp.185-192.-Mathieson,JR. A. 1970 Land For Housing.. Unpublished paper for Commerce 508 (Professor R.U. Ratcliff), University of British Columbia, Vancouver, November 1970V Mathieson, R.A. 1971 A New Land Ethic: Prerequisite for Resource Planning. - Unpublished paper for Planning 525 (Dr. W. Rees) "' School, of^Community and Regional Planning, U.B.C. November 1971. Mathieson, R.A., M.G. Powers, W. Rees, J, Spencer, K. Verburg and E. Yirenkyi, 1972 . Land Evaluation for Regional Planning:. An Analysis of the  Canada Land Inventory..-" Regional Workshop Study, School of Com-munity and Regional Planning, U.B.C. Vancouver. Meyer, R.K. 1966 "The Evolution of Roads in the Lower Fraser Valley", in Lower Fraser Valley:" Evolution of a Cultural Landscape CA.H. Siemens, ed.). - B.C. 'Geographical Series Number 9, Tantalus Research Ltd.,•Vancouver. 1968 pp.69-88. Milgram, G. 1967 "The City Expands. Institute for Environmental Studies, University of Pennsylvania, Philadelphia. Morrill, R.L. 1965- "Expansion Of the Urban Fringe: A Simulation Experi-ment", Proceedings,-Regional Science Association 15: 185-199. Morrill, R.L. 1965b "The Negro Ghetto: Problems and Alternatives", Geographical Review 55: 339-361. Morrill, R.L. 1968 "Waves of Spatial Diffusion", Journal of Regional Science 8:1-18. Mumford, L. 1961 The City in History. Penguin Books, Harmondsworth. Nagel, E. - 1961 The Structure of Science. Harcourt, Brace and World, New York. Neyman,- J. 1960 "Indeterminism in Science and New Demands on Statisticians", Journal of the American Statistical Association 55: 625-639. Qlsson,-G. 1966 "Central Place Systems, Spatial Interaction, and Stochastic Processes", Regional Science Association, Papers of the Vienna Congress 18: 13-45. Literature Cited 173 Olsson, G, . 19.6.8 "ComplementaryModels: A Study of Colonisation Maps", Geografiska Annaler 50CB): 115-132. Parker, V.J. 1966 "Problems and Progress in Rationalizing the Use of the Resources of the Lower Fraser Valley",• in Lower Fraser Valley:  Evolution of a Cultural Landscape (A;H. Siemens, ed.). B.C.' Geographical Series 'Number 9, Tantalus Research Limited, Vancouver. 1968 pp.. 16 3-171. Pearson,,N. 1967 What Price Suburbia? Lower Mainland Regional Planning Board, New Westminster, B.C. Perry, T.M. 1963 Australia's First Frontier. Melbourne University Press, Calton,.Vic. Piaget, J , 1970 Structuralism. Translated and edited by C. Maschler, Harper and Row, New York. Ratcliff, R.U. 1961 Real Estate Analysis. McGraw-Hill, New York. Rawson, M., and A. Norville, 1963' ' Subdivision Casebook.. The Planning Institute of British Columbia, Vancouver.. Robinson, J.L. 1971 Vancouver: Evolution' of Settlement Patterns. Roneod materials, Department of Geography, University of British Columbia, Vancouver. Robinson, J.L. and W.G. Hardwick, 1968 "The Canadian Cordillera", in Canada: A Geographical' Perspective (J. Warketin, ed.). Methuen, Toronto. Rogers, A. 1967 "Theories of Ihtra-Urban Spatial Structure:. A Dissenting View", Land Economics 43:' 108-112. Rogers, A. 1969 "Quadrat Analysis of Urban Dispersion: 1. Theoretical Techniques", Environment and Planning 1: 47-80. Rose, A.J, 1966 "Metropolitan Primacy as the Normal State", Pacific View-point, 7 CD: 1-27. Roy, P,E. ' 1966 "The Changing Role of Railways in the Lower Fraser Valley", in Lower Eraser' Valley:"'Evolution of a Cultural Landscape. OL.A. Siemens, ed,). B.C. Geographical Series Number 9, Tantalus Research Ltd., Vancouver, 1968 pp.51-67. Rutherford, J., H. Burdekin and I. MacGregor, 1971 Case' Studies of Changing  Population and Land Use on the'Periphery of Metropolitan Sydney. Research.Paper Number 16, Geographical Society of New South Wales, Sydney. Literature Cited 174 Scheffler,-. I. 1957 "Explanation, Prediction and Abstraction", The British Journal for the Philosophy of Science Vol. VII (28). Extracted in Philosophy of Science CA, Danto and S. Morgenbesser, eds.). The World Publishing Col,-, Cleveland. 1960. Scottish Development Department, 1968 Grangemouth-Falkirk Regional Survey  and Plan. Volume 2 - Physical Planning Aspects. Her Majesty's Stationery Office, Edinburgh. Seastone,-D. • 1970 "The Regional Dependency Effect of Federal Land Owner-ship", Land Economics 46: 394-403. Seastone.,. D. 1971 "Implications of the Regional Dependency Effect for Federal Land Use and Program Planning", Land Economics 47: 158-167. Siemens, H.A. 1966 "The Proces s.of Settlement in the • Lower -Fraser Valley -In Its Provincial Context", in Lower Fraser Valley:' " Evolution  of a Cioltural Landscape (R.A. Siemens, ed.). B.C. Geographical Series Number 9, Tantalus Research Ltd., Vancouver.- 1968 pp.27-49. Simmons,-J.W'. 1965 "Descriptive Models of Urban Land Use", Canadian Geographer 9: 170-174. Simon,. H.A. 1957 ' Models Of Man.• John Wiley, New York. Simon,.H.A. 1968 "Research For Choice", iri Environment arid Policy (W.R. Ewald, ed.). Indiana University Press, Blcomington, 1968 pp.360-380. . . Sinclair, R. 1967 "Von Thunen and Urban Sprawl", Annals of the Association of American Geographers 57: 72-87. Springer, C.H., R.E. Herlihy, R.T, Mall and R.I. Beggs, 1968 Probabilistic •"Models. Richard D, Irwin Inc., Homewood,. I l l . Tornqyist, G. 1968 "Flows of Information and the Location of Economic Activity"',. Geografiska Annaler 50(B): 99-107. Turner, F.J. 1920•' The Frontier iri American History. New York. Vance, J.E. • 1964 Geography arid Urban Evolution in the San Francisco Bay ". Area. Institute Of Governmental Studies, University of California, • Berkeley,.Calif. Vance, J.E, 1971 "Land Assignment in-the Precapitalist, Capitalist and Postcapitalist City"', Economic Geography 47: 101-^ 120, Literature Cited 175 Wartofsky, M... 1968 "Telos and Technique: Models as Modes of Action", in Planning for Diversity arid Choice CS. Anderson ed.). The M.T;T. Press, Cambridge, Mass.. 1968 pp.259-274. Walters, C.J, - 1971 "Systems Ecology: The Systems Approach and Mathe-matical Models in Ecology", in Fundamentals of Ecology (E.P. -Oduml, 3rd. Edition. W.B. Saunders, Philadelphia.' 1971 pp,276-292, Webber, M.M. 1963 "Order in Diversity: Community Without Propinquity", in Environmental Psychology - Man and His Physical Setting (H. M. Proshansky, W.H. Ittelson and L.G. Rivlin, eds.). Holt, Pinehart and Winston, New York. 1970 pp.533-549. Wendt, P.F,, and A.R.- Cerf, 1969 Real Estate Investment Analysis and  Taxation. McGraw-Hill, San-Francisco. Werthman,. C., J,S. Mandel and T. Dienstfrey, 1965 Planning and the Pur-' ghase Decision: Why People Buy in Planned Communities. Institute of Urban and Regional Development, Centre for Plan-ning and Development Research, University of California, Berkeley. Wilson,,A.G. 1969 "Research for Regional Planning", Regional Studies 3: 3-14. Wilson, A.G. 1970 On Some- Problems in Urban and Regional Modelling. Working Paper Number- 59, Centre for Environmental Studies, London. Wolforth, J,R. 1965 Residential Location and the Place of Work. B.C. Geographical Series Number 4, Tantalus Research Ltd., Vancouver. Work, G,L. 1968 "Investment Decision Making for Lenders", in Colloquium on Computer Applications iri Real Estate Investment Analysis (R'.U. Ratcliff, ed.). Faculty of Commerce and Business Administra-tion,. University of British Columbia, Vancouver. 1968 pp.15-24. Y u i l l , R.S. 1965 "A Simulation Study of Barrier Effects in Spatial Diffusion Problems", Research Report Number 5, Department of Geography, Northwestern University, Evanston,-111. Y u i l l , R.S. 1970 A General Model for Urban Growth: A Spatial Simulation. Michegan Geography.Publication Number 2. Department of Geography, University of Michegan, Ann Arbor. APPENDIX I The Vancouver Region: A S e r i e s of Topographic Maps E X C E R P T S P R O M T H E N A T I O N A L S Y S T E M OP T O P O G R A P H I C M A P S L E G E N D SCALE 1:50,000 1.25 Inches to 1 Mile approximately 0 1 2 3 Miles 1000 500 0 1000 2000 3000 4000 Metres 1 pop 500 0 1000 2000 3000 4000Ya rds Varioios contour i n t e r va l s House; Building »• School i Church; Church with spire + t Post Office * Radio Station • Tower; Chimney i U t Well; Tank • Cutting "•••'.••:?' Embankment —wtrm^r-Cliff -i^r^f. Contours: . y»—— elevation .— depression „ » . approximate - — - -*°° Roads: m*, hard surface, all weather •^••HMMH hard surface, all weather..... loose surface, all weather loose surface, all weather . J ; " " ; ' ^ " " " ^ dry weather = = ^ = ^ cart Inch; trait, or cut line Railways: normal gauge, multiple track .. . normal gauge, single track ' t""' • ^ i ,- • abandoned or under construction , .I"1, , underpass, overpass , j | , , Tunnel; Drawbridge , „ ,,,, Power line; Telephone line w. j . j . Foreshore Hats Lighthouse ^ Wharf or pier; Breakwater ^ j u " " " Levee or dyke —»• • Rocky reef -*SE*2a>-Swamp or marsh * " Inundated land, seasonal — ~ ~ ~ — Intermittent lake, stream C— Indefinite shoreline, stream Rapids, large, small; Bridge J==—HI" Oilch or Hume —f Snowfield; Glacier CmSKj- <F?~$ Wooded area; unclassified, scrub Vineyard; Orchard Boundaries; international, with monument Hir''^""03g provincial county or district _ . township or parish _ _ _ township or parish, un surveyed City or town park, reserve, etc . Horizontal control point, with elevation A582 Bench mark, with elevation 13^ Spot elevation; precise, approximate.. .4582 .737; Historical site; Cemetery # Mine or open cul; Quarry.-. V 5^^ ?? Sand or gravel pit Surveyed Line Section Number 16 Lot Number 2 2) Surveyed Timber Licence Number.. T.L. 2071 Surveyed Pulp Licence Number.... P. L. 626 182 u oo 05 w ' fTv ' M/ /L ~ I 'Ti Pitt Lake < PROVINCIAL , L U . A N S 1 I A1J-: .^OQUITLAiyf''>DI§TRICT ^ 1 PORT 'COQUITLAM * *s • Tp 9 PUT MEADOWS-, DISTRICT \ MUNICIPALITY •I: ^ U ETC RESEARCH Tp4 R5 W7 MAPLE L RIDGE' • -BARK l'p"4 R4 W7 H FOpST RESERVE, j | \ | A7 DISTRICT MUNICIPALITY f n T63 L W / W 7 , V|' •" > 187 POPULATION DENSITY, 1966. PERSONS PER GROSS ACRE MORE THAN 2 0 10 - 2 0 NOTE; DENSITY CALCULATED USING I966 CENSUS COUNTS FOR CENSUS TRACTS OR GROUPS OF ENUMERATION AREAS IF DENSITY GREATLY VARIES FROM THAT 'TYPICAL' OF A WHOLE CENSUS TRACT GREATER VANCOUVER REGIONAL DISTRICT PLANNING DEPARTMENT FEBRUARY, I970 SCALE IN MILES DEWDNEY-ALOUETTE REGIONAL DISTRICT A P P E N D I X I I 2 - 5 LESS THAN 2 BRITISH C O L U M B I A C A N A D A . / M A P N o : S 2 0 - 0 0 5 APPENDIX IV OUTLINE FOR OPERATION OF THE MODEL o Iri separate discussions with two computer programmers, (James Kestner, Daniel Purvis) with the University of British Columbia Computer Science Centre, the feasibility of the method of application was established, and the. general form of model notation and operational procedures was developed. The method of application, Monte Carlo simulation of urban expansion as a spatial diffusion process, is described in Chapter 5. In the following, a brief outline of operational procedures is given. Estimates of the time required for the model to be programmed and made fully operational ranged from four to six weeks. 'Model Notation A = Accessibility (Travel time at peak hour in minutes). BAR = Barrier Limitations (Slight, moderate, severe). D = Distance (Kilometres). DDL = Derived Demand for Land (Hectares). 189 TRAFFIC VOLUMES, 1967. A P P E N D I X 5 , 0 0 0 1 0 , 0 0 0 1 5 , 0 0 0 2 0 , 0 0 0 5 0 , 0 0 0 4 0 , 0 0 0 5 0 , 0 0 0 6 0 , 0 0 0 NOTES: • PROVINCIAL HIGHWAY VOLUMES BASED ON DEPARTMENT OF HIGHWAYS COUNTS. OTHER VOLUMES BASED ON MUNICIPAL COUNTS. • GENERALLY ONLY VOLUMES EXCEEDING 3000 VEHICLES PER DAY INDICATED GREATER VANCOUVER REGIONAL DISTRICT PLANNING DEPARTMENT FEBRUARY, 1970 SCALE IN MILES BRITISH C O L U M B I A Mop No K 6 2 - 066 INTRODUCTION GREATER VANCOUVER FLOW PATTERN T R A F F I C F L O W is an expression of life in the ci ty ; the myriad ventures of people between their diverse places of work, study, shopping and leisure and their homes. Because travel is vital to urban life, the process of planning facil ities to facilitate effi-cient movement of people and goods requires that the pattern and nature of this movement be under-stood. A n overall traff ic f low map is one element designed to develop that understanding and is pre-pared as part of a data inventory for a comprehen-sive plan study for Greater Vancouver. Such a study, tentatively t it led the T R A N S P O R T A T I O N A N D U R B A N P A T T E R N S T U D Y is to be carried forward by the G .V .R .D . and is designed to identify the best pattern for future physical development of metropolitan Vancouver. The traff ic f low map is simply a graphic image of the daily sum of vehicular travel counts on our principal traffic routes. It shows the general pattern and orientation of traffic. It thus approximates and measures the activity pattern of the metro com-munity — the journeys of people and the auto-motive vehicles carrying goods to serve them. It depicts the currently preferred routes and the general destination of traff ic movements and thus is a general indicator of the corridors of travel demand. Coupled with more precise data on origins and destinations of travel, the counts can help explain the amount and nature of travel to form a basis for assessing the adequacy of present trans-port facilities and operations and rectifying inade-quacies in the system. By themselves, f low volumes are an inadequate basis for transportation plan-ning. Addit ional data including knowledge of the future urban pattern, the number of trips per person; the purposes, origins, destinations and t iming of these trips; travel mode, time and speed, and congestion levels now and in the future are al-so necessary. T R A F F I C T E M P O . The f low of traff ic is dyna-mic-varying with each year, month, week, day, hour and minute reflecting the changing rhythm and tempo of individual and communi ty life in Greater Vancouver. Max imum annual travel occurs in Ju ly and August when tourist and recreational travel is highest. Weekly travel reaches a peak on Friday reflecting the effect of evening shopping and increased recreation added to normal work-to-home commuting. As is typical of urban transport systems, three peaking periods occur each day — the morn-ing rush (home-to-work); the evening rush which is highest because it overlaps work-to-home, shop-ping and business trips; and the early evening surge due to shopping and leisure activity trips. A map of peak-hour traffic f lows for metropol itan Van-couver, while potential ly valuable, could not be prepared due to lack of ready data. The pattern of traff ic f low in metropolitan Vancouver is essentially radial, fanning outward from the small downtown Vancouver peninsula where traff ic movement is strongly focussed. Physiography, particularly major water bodies, plays a key part in shaping the f low pattern be-cause it has determined the location of many links in the major regional road network. The bridge crossings of Burrard Inlet l inking the "Bu r -rard Peninsula" and the " N o r t h Shore" , and those across the Fraser River l inking the peninsula and the " Sou th Shore " serve to channel traff ic into defined corridors. In addit ion, the sea restrains westward growth, and directs the main thrust of metropolitan growth to the south-east along the Burrard Peninsula. The trans-continental highway system enters Vancouver along this peninsula. For these reasons major f lows occur along corridors to the south-east of downtown Vancouver. The heaviest traff ic volumes are concentrated on highways and arterials, which because of their abi l i ty to handle relatively large volumes wi th greater speed and safety, attract and collect vehicles f rom tributary streets and roads. In addit ion to autos, the truck and bus transit movements fo l low arterial streets and highways, adding to their vehicle volumes. However, these heavy volumes on particular routes are not necessarily true lines of travel desire because drivers select the most prac-tical paths offered them by current facilities. In-deed where bridge crossings channel the move-ments, the driver has little or no choice. New facilities added to the network offer new choices and typica l ly result in different f low patterns. Heavy traff ic volumes also mirror the pattern of urban development — particularly the major retail, office, industrial and other employment concen-trations. The convergence on " d o w n t o w n " Van-couver reflects the strong role of that area as a specialized regional retail and service centre. The volume map illustrates heavy movement between the metropolitan core and both the inner and outer suburbs and the urban-rural fringe. This is enhanced by movement generated wi th in the high-er density living areas fringing the metro core. There is a fairly uni form spread of volumes on the routes focussing on the core area f rom the east and south, reflecting a fairly uni form pattern of sub-urban development in the region. The movement pattern is not a funct ion solely of concentrated employment. It reflects the heavy emphasis of single-family housing and the suburban life-style which requires heavy reliance on the auto — particularly for commuting, because the overall development densities are currently too low to sus-tain a strong network of economical publ ic transit services. Considerable movement is in evidence on the more peripheral arterials which accommodate work trips to suburban service, institutional and indus-trial employment areas as well as a large number of shopping, social and recreational trips. TRAVEL TIME - SUMMER 1968 • 5 MINUTE ISOCHRONES FROM INTERSECTION OF GRANVILLE AND GEORGIA IN DOWNTOWN VANCOUVER AT 4 '30 PM BY FASTEST ROUTE. Outline for Operation of the Model 190 DEM = Diffusion Emissions CNumber of Emissions). INST = Institutional Limitations (Slight, moderate,.severe). LAM = Land Absorption Multiplier CDimensionless). LAR Land Absorption Rate (Hectares/1,0 0 0 persons). LCR Land Consumption Rate (Hectares/l,000 persons). NET : = Network Limitations (Slight, moderate, severe). NODE = Dominant Urban Node. P = Population (persons). PIN = Population Increase (persons). PLC(XY) = Probability of Land'Conversion at Site XY (0 1). PQ = Propinquity (Distance from urban area in kilometres). R = Resilience (Low, Moderate, High). RL = Rural Land (Hectares). RM = Resilience Multiplier (Dimensionless).. RULC = Rural-Urban Land Conversion (Hectares). THL = Threshold Level (number of "Hits" required). TLR = Total Land Required (Hectares). TOP = Topographical Limitations (Slight, Moderate, Severe). TT = Travel Time (Minutes). UL = Urban Land (Hectares). USL = Unsatisfied'Demand for Land (Hectares). XY = Cell in Regional Matrix (Site). Outline for Operation of the Model 191 Generalized Procedures Formulation of the model begins with a given rural-urban land use pattern at time T. Land to be'considered for urban expansion is rep-resented in a regional grid in which each-cell is identified by the appro-priate row (X) and column (Y). Each cell or site (XY) is described in terms of the following characteristics: propinquity to nearest urban area, accessibility to nearest dominant urban node, and barrier restrictions. CD PQ(XY) = f [D(XY- UL)] C21 ACXY) = f [TTCXY' NODE)] (3) • BARCXY) = f [TOP(XY), NETCXY), INST(XY)] In addition, the total urban system has a level of resilience which varies according to the land consumption rate; 0+) R f [LCR] Both the propinquity and accessibility characteristics of each site are. combined to form, a rural land conversion probability matrix for the region-, (5) PLC(XY) ' = f [PQ(XY),A(XY)] Similarly', to determine the number of "hits" required by a site before i t is accepted as' an urban area, resilience and barrier effects are combined to establish a site's conversion threshold; C6) THL(XY) = f [R, BARCXY)] In. order to obtain the number of diffusion emissions required in any diffusion period, i t is necessary to f i r s t translate the population Outline for Operation of the Model 192 increase in the preceding time period, into a derived demand for land; plier (LAM) in Equation 7, are derived by converting the land consumption and land absorption rates, respectively, to constants as shown in the following illustration. For example, a land consumption rate of 40 hectares/ 1,000 persons in this hypothetical, non-linear table function results in a resilience multiplier of 0.75. C7) DDL f [PIN, RM, LAM] Both the Resilience Multiplier (RM) and Land Absorption Multi-Resilience Multiplier 2 1 \ V 20 40 60 80 Hectares/I,000 persons (Land Consumption Rate) (8) RM (9) LAM Outline for Operation of the Model 193 To continue, i t is assumed that in the i n i t i a l time period T, there is no residual demand for land and thus; (10) UDL(T) = 0 However, in the subsequent period the unsatisfied demand for land is found by subtracting the total rural land conversion in time T from the total land required in time T; (11) UDLCT+l) = f [TLR(T) - RLC(T)] Thus i t is now possible to derive the total land required in any diffusion period; (12) TLR = f [DDL, UDL] The next step involves translating the Total Land Required from Equation 12, into the number of diffusion emissions for a time period. This is achieved by employing a table function, such as the one illustrated below. In this hypothetical example, a total land requirement of 800 hectares, in a diffusion period, involves the generation of 65 single emissions. Diffusion Emissions 4 0 0 800 1000 Hectares: Total Land Required Outline for Operation of the Model 194 (131 DEM = f [TLR] Finally, the rate, extent and location of rural-urban land con-version in any diffusion period is a function of three inputs: the number of diffusion emissions, the probability of land conversion and.the thres-hold level for sites. (14). RULC = f [DEM, PLC(XY), THL(XY)] 


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items