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Spatial analysis: A critical tool for tourism geographies C. Michael Hall, Department of Management, University of Canterbury, Christchurch, New Zealand michael.hall@canterbury.ac.nz Introduction All events happen somewhere at some time. Therefore, all tourism related events can have space and time coordinates attached to them (Dietvorst, 1995). In observational social and environmental science, including geography, noting the place and time of individual events and creating a database of observations is integral to research. Such information allows the study of processes in different types of locations, which may provide insights into the interrelationships between structure and process (Goodchild and Janelle, 2004). Spatial data can also be linked to other data sets thereby potentially increasing explanatory power (Haining, 2003; Goodchild, 2010). As Kim et al. (2005: 273) concluded with respect to their study of amenity driven economic growth and development ‘“place in space” matters’. Nevertheless, different traditions in tourism studies have different understandings of space and how it should be studied. For example, even though Nepal (2008: 138) concludes that a spatial approach is one of the hallmarks of contemporary tourism geography research, he also notes that the full potential of spatial technologies ‘in examining form and processes of touristic development, travel flows and tourist movement, and tourism impacts, has not been realised yet.’ It is also perhaps significant that while the Blackwell Companion to Tourism (Lew et al., 2004), which was edited by geographers, included several review chapters with a significant spatial analysis component (Farsari and Prastacos, 2004; McKercher and Lew, 2004), the equivalent Sage Handbook of Tourism Studies (Jamal and Robinson, 2008) provides no such element, even though the Handbook offers ‘a record of the field’s theoretical and methodological evolutions, emerging cultural critiques, sustainability challenges being addressed, types of tourism that illustrate new theoretical insights and ethical criticisms, and hence a window into the future possibilities awaiting tourism studies’ (Jamal and Robinson, 2008: 16). A review of the contribution of spatial analysis to tourism therefore potentially offers not only insights into divergences in philosophical, theoretical and methodological emphasis in tourism research but also future possibilities. This chapter is divided into three main sections. The next section provides a definition of spatial analysis and its scope, which includes spatial data analysis, spatial statistical analysis, spatial modelling and spatial data manipulation, usually in a geographic information system (GIS) (Kwan, 2000; Maguire et al., 2005). However, despite its potential to contribute to understandings of mobility (Shoval and Isaacson, 2010), and its relationship to time-geography in tourism (Hall, 2005a), perceptions of spatial analysis as an uncritical geography may be influenced by its strong quantitative emphasis. The chapter then goes on to discuss some of the major research contributions in contemporary spatial analysis with respect to spatial interaction and modelling tourist movement before examining the utilisation of GIS and advanced tracking technologies. The chapter concludes by noting the critical function of spatial analysis and its value in policy arguments. Elements of Spatial Analysis In broad terms spatial analysis is ‘the quantitative study of phenomena that are located in space’ (Bailey and Gatrell, 1995: 7). Spatial analysis has a long tradition in human and physical geography and, although the quantitative dimension of physical geography, biogeography and spatial environmental studies is well recognised, it also arguably underpins human geography’s claims to be regarded as a social science rather than a subject of the humanities (Johnston, 2003). Spatial analysis has been hugely influential in a number of fields of relevance to tourism studies including retailing, housing studies, marketing, economics, transport studies, urban and regional planning (Maguire et al., 2005; Stilwell and Birkin, 2008; Wilson and Fotheringham, 2008), as well as on particular themes such as regional development, peripheral areas and visitor behaviour (Brülhart, 2006; Törmä, 2008; Gruber and Soci, 2010). In addition, the development of spatial analysis as a field of study has been given much impetus by the growing demands for spatial data accuracy and quality given the increased amount of spatially referenced data held by the public and private sectors as well as the use of GIS as an interactive decision-making and planning tool.

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According to O’Sullivan and Unwin (2003) there are at least four broad overlapping areas in the spatial analysis literature.

1. Spatial data analysis, which is often descriptive and exploratory, is involved when data are spatially referenced and ‘explicit consideration is given to the possible importance of their spatial arrangement in the analysis or in the interpretation of results’ (Bailey and Gatrell, 1995: 8).

2. Spatial statistical analysis refers to the use of statistical methods ‘to interrogate spatial data to determine whether or not the data are “typical” or “unexpected” relative to a statistical model’ (O’Sullivan and Unwin, 2003: 2).

3. Spatial modelling refers to the construction of models to predict spatial outcomes. These are primarily mathematical models ‘where model outcomes are dependent on the form of spatial interaction between objects in the model, or spatial relationships or the geographic positioning of objects within the model’ (Haining, 2003: 4). An additional form of modelling in spatial analysis is cartographic modelling in which ‘each new data set is represented as a map and map-based operations (or implementing map algebras) generates new maps’ (Haining, 2003: 4).

4. Spatial data manipulation, usually in a geographic information system (GIS), which are software systems for capturing, storing, managing and displaying spatial data (Haining, 2003). Such spatial data may be gathered from a variety of sources including census and surveys, geographic positioning systems (GPS), as well as via remote sensing which is defined as measuring a particular quality of a feature without being in physical contact with the feature itself, and usually applied ‘to the measurements acquired from either airborne or orbiting platforms, with the features of interest located on or just above the surface of the Earth’ (Horning et al., 2010: 3). An additional important dimension of spatial data manipulation of direct relevance to tourism is data representation, particularly in terms of the interface with users.

Quantitative geographical research often involves all four elements. ‘Data are stored and visualized in a GIS environment, and descriptive and exploratory techniques may raise questions and suggest theories about the phenomena of interest. These theories may be subjected to traditional statistical testing using spatial statistical techniques. Theories of what is going on may be the basis for computer models of the phenomenon, and their results may in turn be subjected to statistical investigation and analysis’ (O’Sullivan and Unwin, 2003: 2-3). Spatial analysis is an especially dynamic multi-dimensional area not only because of ongoing methodological and theoretical advances but also because of the extent to which the field responds to developments in technology which can provide spatial information, e.g. GPS and mobile phones (O’Connor et al., 2005; Shoval and Isaacson, 2010), and the emergence of new research challenges such as those associated with concerns over environmental, socio-economic and global change (Verburg et al., 2004; Chu et al., 2009), in which tourism is often implicated (Kim et al., 2005; Schmitz et al., 2007). Yet despite the early adoption of spatial analysis as a quantitative approach in tourism geography (see Smith 1995), the field is perhaps not as prominent as might be expected given its relevance to understanding contemporary tourism related mobility (Hall, 2006). However, as the next section discusses this may partly be because of negativity towards its quantitative base. Spatial Analysis as Quantitative Geography Spatial analysis is often understood as the quantitative procedures used in locational analysis and the spatial science paradigm of geography (Johnston, 2000, 2003). Unfortunately, there has often been a tendency to label those involved in spatial analysis as logical positivists or similar, and such work being regarded as inherently uncritical (Unwin, 1992; Ateljevic et al., 2007). Instead, as Fotheringham et al. (2000) emphasise, such a perspective disguises some significant differences in scientific philosophy of those who advocate and utilise quantitative approaches. For example, those who take a ‘geography is physics’ (naturalistic) approach that searches for universal laws and relationships tend to primarily be physical geographers who work with far much more predictable environmental processes than human geographers. Instead, because the subject matter of human geography is by its very nature ‘typically clouded by human idiosyncracies, measurement problems and uncertainty, the search is not generally for hard evidence that global “laws” of human behaviour exist. Rather, the emphasis of quantitative analysis in human geography is to accrue sufficient evidence which makes the adoption of a particular line of thought compelling’ (Fotheringham et al., 2000: 5). A similar

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position was also articulated by Bradley and Schaefer (1998: 71) who argued that ‘Visions of a positive social science and a ‘social physics’ are unattainable, because so many social phenomena do not satisfy the assumptions of empirical science. This does not mean that scientific techniques, such as careful observation, measurement, and inference ought to be rejected in the social sciences… The goals of investigation are … the creation of… compelling explanations rather than the formation of nomothetic laws’, The above comments are significant given the calls for ‘a new “social physics” based around the notion of “network” might be established in an era in which time and space seem increasingly warped, bent and twisted into strikingly new topologies’ (Urry, 2004: 109). However, Urry’s position can be construed as demonstrating a substantial misunderstanding of the value of quantitative analysis of networks as well as other mobilities, as Hall (2005a: 96) argued, ‘it is important that in developing a new social physics of mobility that we do not ignore the old one,’ if the physics analogue ‘is to be maintained we can argue that macro-level quantitative accounts of patterns of human mobility can be regarded as classical Newtonian physics while micro level accounts of individual human behaviour can be likened to quantum physics. The task in physics, as it is in examining human mobility, is to unify these understandings into a comprehensible whole’. Within the spatial analysis literature there is often a sentiment that much of the criticism of quantitative geography came from individuals who had little or no understanding of mathematical methodologies (Robinson, 1998; Fotheringham et al., 2000). Given such a perspective, it is therefore valuable to review different approaches to spatial analysis and interaction while noting their continued relevance to contemporary tourism geography. Spatial Interaction The various stages of the evolution of spatial theory put forward by Fotheringham et al. (2000) provide a useful outline of the way in which traditions of spatial analysis in tourism geography has developed. Spatial interaction as social physics In this approach the movement of people between locations was regarded as analogous to the physical model of gravitational attraction between celestial bodies (Ravenstein, 1885). Although this version of the model was ‘theoretically empty’ (Fortheringham et al., 2000), it has been long noted that the model produces reasonably accurate estimates of spatial flows in what was termed ‘social physics’ (Zipf, 1949; Stewart and Warntz, 1958). One of the simplest and most common ways of describing the curves that relate flows and distance is with the Pareto function of the form: (1) F = aD-b Where F = the flow, D = the distance and a and b are constants. Low b values indicate a curve with a gentle slope with flows extending over a wide area. High b values indicate a curve with a steep slope with flows confined to a limited area (Haggett, 1975). Behind the Pareto form of the distance-decay function is the gravitational concept which suggests that spatial interaction falls off inversely with the square of the distance (2) F = aD-2 which can be rewritten as

(3) 2

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DaF !=

This inverse square relationship is analagous to that used by physicists in estimating gravitational attraction. The inverse ‘distance effect’ is capable of a series of mathematical transformations which have usually been addressed as logarithmic functions (Taylor, 1971). However, constants tend to be different in different regions and in expressing different sets of spatial interactions (Smith, 1985). Nevertheless, despite its problems the gravity model remains widely used in transport planning and retail analysis, ‘the great variety of forms means that an

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approximate fit can nearly always be made and the model then used to predict future flows’ (Hay, 1986: 186). Gravity models (Malamud, 1973), locational analysis and the role of distance and distance decay (Taylor, 1971) in economic and tourist behaviour played a significant role in early tourism related economic geography, including the influential work of Christaller (1963) (Hall and Page, 2006); as well as research based on the travel cost method (e.g. Font, 2000) and distance decay functions in tourism (e.g. Zhang et al., 1999; McKercher and Lew, 2003). Also connected to this period of spatial analysis, and still strongly resonating in tourism geography, is Butler’s (1980) Tourist Area Cycle of Evolution (TACE) the origins of which was heavily influenced by location analysis and Christaller’s work in particular (Butler, 2006; Hall, 2006), with the first version of the model (Brougham and Butler, 1972) suggesting that the destination development process ‘may be satisfactorily approximated by the solution of the logistic equation (4) Dv = kV(M-V) Dt Where V is the number of visitors, T is time, M is the maximum number of visitors and K is an empirically derived parameter representative of the telling rate, or the spread of knowledge of the resort from tourists to potential tourists’ (Brougham and Butler, 1972: 6 in Butler, 2006: 17). The solution was proposed as V = MV (5) O V + (M – V) - Mkt Where V is the number of tourists at time t. The comment with respect to the ‘telling rate’ also provides a strong connection to the work of Hägerstrand (1968) on the formal analysis of innovation diffusion as a spatial process, which later developed into his influential work on time geography (discussed below). Indeed, in stressing the importance of a mathematical approach to tourism space, Hall (2006: 99) argued that ‘the product life-cycle so influential in consideration of [TACE] is itself a space-time wave analog related to innovation diffusion processes… a point seemingly lost in nearly all of the discussion which has taken place on tourism destination product life-cycles. Such an observation also highlights the potential for spatial interaction modelling to provide a better understanding of the development of information regarding potential destinations’. Spatial interaction as statistical mechanics The next major theoretical framework came with the work of Wilson (1967, 1974, 1975) who produced a family of spatial interaction models, initially rooted in entropy maximizing methods, which also functioned as location models, and which were particularly influential with respect to retailing flows, transportation analysis and regional economics (O’Kelly, 2010). These models were significant because they provided a theoretical justification for what had hitherto been an empirical observation. Although they have been criticised on the basis that one analogy, that of gravitational attraction, has merely been replaced by another, statistical mechanics (Fotheringham et al., 2000). However, from the 1970s on substantial attention has been given to issues of distance and accessibility in the tourism and recreation literature which continue to the present-day (McAllister and Klett, 1976; Baxter, 1979; Smith, 1985; McKercher et al., 2008; Cai and Li, 2009). Spatial interaction as aspatial and spatial information processing From the 1980s on spatial interaction models provided a theoretical foundation that was based more on human behaviour and information processing and which recognised the significance of ‘share’ models and logit (logistic regression) formulation. Nevertheless, many of these spatial interaction models had been ‘borrowed’ from economics, a predominantly aspatial discipline. For example, the discrete choice framework was developed primarily for aspatial contexts such as brand choice and choice of transportation mode. In particular, the assumption that an individual is omniscient and able to evaluate all alternatives is clearly untenable. Therefore, emphasis was given to the importance of the type of information processing which is likely to

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take place in spatial choice (Fotheringham, 1983, 1984). Nevertheless, the behavioural dimension has had significant impact in tourism research because of the increasing recognition of cultural distance (Bowden, 2006) and perceived distance as a behavioural constraint and destination attributes (McKercher and Wong, 2004; Bao and McKercher, 2008; McKercher, 2008; Nyaupane and Andereck, 2008) as well as on broader understanding of the importance of spatial interaction in international trade and regional economic development (Krugman, 1997; Pohl, 2001). Indeed, issues of geographical concentration and spillover effects are extremely important with respect to tourism’s role in innovation (Hall and Williams, 2008). In contrast, the generic spatial information choice problem can be stated as: ‘How does an individual at location i make a selection from a set of N spatial alternatives?’ (Fotheringham et al., 2000, p.227). This type of spatial choice must precede engaging spatial interaction such as going on a vacation. According to Haynes and Fotheringham (1990), the spatial choice process has three characteristics. First, it is a discrete, rather than a continuous, process. That is, either a destination is selected or it is not and there are a finite number of alternatives. Second, the number of alternatives is often large, and in some cases, extremely large. Third, the alternative destinations all have fixed spatial locations, which limits the degree to which alternatives are substitutes for one another. It also means that, unless the spatial distribution of alternatives are perfectly regular (which they almost invariably never are), each alternative faces a unique spatial distribution of competing alternatives (Fotheringham et al., 2000). As a result of these conditions Fotheringham (1983, 1984, 1991) developed a competing destinations model of spatial interaction. That model takes the general form: (6) Iij=(Oi, Dj, Sij, Aj) where Iij is the interaction between the ith origin and the jth destination; O is the ith place's ability as an origin to contribute to interaction, Sj is the attractiveness of j as a destination, D is intervening distance between the origin and the destination; and Aj, the “competing destinations” variable, is the accessibility of the jth place relative to all others that may interact with the ith origin. This model has then provided impetus for the development of variations of the competing destinations model, a number of which have been applied to tourism research. For example, Hanink and Stutts (2002) adapted the competing destinations model to develop a specific demand model for national battlefield parks in the US. (7) Ui=(Mi, Ai, Ci) where Ui is the use of the ith battlefield park, M is the park's location relative to the population of potential users, A is its location relative to other national battlefields, and C is a vector of recreational facility characteristics variable across the parks. Although the competing destinations model has had its critics (Ubøe et al., 2008), particularly with respect to achieving its aim of removing the map pattern from distance decay parameters, it is nevertheless recognised as being superior to previous models with respect to both reproducing the interaction flows and giving behavioural explanation to distance decay parameters (Pingzhao and Pooler, 2002). In addition, the spatial information processing approach has proven influential on research on tourist destination choice (Lin and Morais, 2008) as well as tourist shopping behaviour (Kemperman et al., 2009). Spatial Modelling of Tourism Related Mobility The modelling of tourist mobility and the movement of tourism related populations has long been of interest to geographers (e.g. Oppermann, 1995; Flognfeldt, 1999; Bell and Ward, 2000; Forer, 2002; McKercher and Lew, 2004; Hall and Page, 2006; Lew and McKercher, 2006). Model development has generally taken three, often related, forms. First, the use of mathematical models, such as spatial interaction models discussed above. Second, the generation of visual representations of spatial data in the form of maps and models. Third, descriptive models developed from empirical analyses and case studies. One of the most influential frameworks for describing tourism mobility has been that of time-geography. Originally developed by Hägerstrand (1970) and colleagues at Lund University, Sweden (Pred, 1981), time geography focuses on the movement and interaction of individuals

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in time and space and has been extremely influential in recent years as a way of conceiving tourism and leisure related mobility (Baerenholdt et al., 2004; Coles et al., 2004; Haldrup, 2004, 2010; Hall, 2005b, 2005c, 2008a; Coles and Hall, 2006; Axhausen, 2007). However, there are significant differences in the way the concept is applied, with some researchers utilising it more as a conceptual framework (Baerenholdt et al., 2004; Larsen et al., 2007), than as a formal analytical tool (Zillinger, 2007). Building on basis of personal mobility biographies (Frändberg and Vilhelmson, 2003; Frändberg, 2006, 2009), Frändberg (2008) has used a time-geographical form of notation to represent transnational mobility as paths in time and space, and to demonstrate how such representations can contribute to explaining some of the dynamics of long distance mobility. An advantage of using time-space paths is that several aspects of an individual's travel biography can be represented in a single image (Frändberg, 2008). GIS has been recognised as an excellent platform with which to model the space-time patterns of individuals, including tourists (van der Knaap, 1999), and their actual and potential activity paths (Miller, 1991, 1999, 2005; Miller and Wu, 2000). For example, using GIS software, in a study of Hong Kong McKercher and Lau (2008) identified a total of 78 discrete movement patterns, which were categorized into 11 movement styles. The large number of movement patterns was a reflection of the interaction of six factors: territoriality, the number of journeys made per day, the number of stops made per journey, participation in a commercial day tour, participation in extra-destination travel and observed patterns of multi-stop journeys. In addition, GIS can be combined with employment and economic data to generate an improved understanding of labour market mobility, business development and location issues and the distribution of tourism related employment as part of the tourism space economy (Page et al., 1999; Hall and Page, 2006). For example, Chhetri et al. (2008) employed a spatial econometric approach to modelling the spatial patterns of tourism-related employment for South East Queensland, Australia, while Lundmark (2005, 2006) and Müller and Ullrich (2007) focussed on labour market mobility and seasonal employment in rural Sweden and their significance for regional development. In addition to economic and population modelling the comprehensive geo-referenced database ASTRID (generated by Statistics Sweden) has also been extensively utilised to study various dimensions of second homes in Sweden and their effect on mobility, amenity values and regional development (Müller, 2002a, 2002b, 2006a, 2006b; Marjavaara, 2007; Marjavaara and Müller, 2007), as well as contributing to the broader debate of the implications of seasonal and temporary mobility on estimates of regional populations (Müller and Hall, 2003). Because of the ready availability of time-space data GIS based modelling has also been used in a number of other studies of second homes in the Nordic region (Jansson and Müller, 2003; Overvåg, 2009, 2010). Given the capacity of GIS to integrate spatial and other data as well as chart and illustrate tourist and population flows it is therefore not surprising that it has become increasingly important as a planning tool for both public and private sector. As Miller (2005: 238) commented, ‘The deployment of location-based services… means that the private and public sectors will be collecting and using space-time activity… data to sell and promote their products and programs. Researchers should also use these data and tools to make our transportation, telecommunication and settlement systems more livable and sustainable’. The utilisation of GIS and spatial analysis for tourism planning GIS has been well recognised as a tool for tourism planning because of its capacity to not only integrate spatial data but also because of its potential to represent data to users (Hasse and Milne, 2005; Levy and Dickson, 2006; Boers and Cottrell, 2007; Hultman, 2007; Zhao et al., 2008), including tourists (Zipf, 2002; Chen, 2007). The capacities of GIS as an accessible business and public planning tool have also been greatly advanced by developments in personal computing as well as the availability of GIS platforms on mobile phones and computing devices, which allow members of the public to access maps which may include a variety of different information sources embedded in them to enable improved visitor decision-making (Dickmann, 2005; Dye and Shaw, 2007). The inclusion of visitor monitoring and survey data into GIS can also allow a thorough analysis of visitor use patterns, perceptions, activities and product usage, which can be extremely important in the management of public use pressures at tourist sites and destinations (Arnberge and Hinterberger, 2003; Chhretri, 2006; Connell and Page, 2008; Landré, 2009), as well as identifying tourism and leisure opportunities (Chhetri and Arrowsmith, 2008). Indeed, a significant contemporary development in GIS modelling and mapping is the growth of neogeography (Turner, 2006), also referred to as volunteered or user-generated geographic information (Goodchild, 2007), and how this can be incorporated into

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spatial analysis and understandings of tourism behaviour (Elwood, 2008; Flanagin and Metzger, 2008). In addition, user generated content also has potential for inclusion in dynamic maps for mobile tourism applications developed by private and public providers (Schilling et al., 2005). GIS has proven to be valuable for studying the effects of changing land use by virtue of being able to not only record resources with a given region but also being able to illustrate the effects of developments, such as the construction of new transport networks or resorts, on other elements in the system. This has made it especially useful, for example, in identifying the wilderness attributes of an area and the effects of developments on wilderness values such as naturalness (Carver et al., 2002; Machado, 2004; Hall and Page, 2006), as well as a tool for site management (Lang and Langanke, 2005). The dynamic element of GIS also allows future scenarios and forecasts to be spatially visualised. For example, Marshall and Simpson (2009) combined GIS with forecasting methods to explore issues of population sustainability in the Cairngorms and Peak District National Parks. Simulation has become an increasingly important planning tool for studying the spatial behaviour of tourists and their impacts that has become increasingly integrated with GIS environments (Cole, 2005; Lundgren et al., 2006; Hunt et al., 2010). Information provided by simulations can allow planners to assess the effects of different management strategies. Both probabilistic simulation and agent-based models (ABM) are used in the development of spatial simulation models (Gimblett and Skov-Peterson, 2008). Probabilistic models are developed via the collection of data from tourists while undertaking their trips and/or from data gained from observation (Sacchi et al., 2001). This approach has been used for example with respect to national park and wilderness camping and recreational behaviour (Lawson and Manning, 2003; Lawson et al., 2003; Lawson et al., 2006). In contrast, ABM are models of a collection of autonomous decision-making entities (agents) in which each agent individually assesses its situation and makes decisions on the basis of a set of rules that have been developed from ‘real world’ data, and which is also used to calibrate and validate spatio-temporal simulation models (O’Connor et al., 2005). The repetitive competitive interactions between agents within the system then provides information on behaviour at different points of time. As a result of incorporating neural networks, evolutionary algorithms or other learning techniques agents may be capable of evolving, thereby allowing unanticipated behaviours to emerge (Bonabeau, 2002). The benefits of ABM over other modeling techniques are (i) ABM captures emergent phenomena; (ii) ABM provides a natural description of a system; and (iii) ABM is flexible. However, it is the ability of ABM to deal with emergent phenomena which drives the other benefits (Bonabeau, 2002; Manning, 2005). ABMs are particularly useful for simulating tourism environments in which visitors are restricted to movement on a network such as roads, trails or rivers and have therefore come to be used in a national park and protected area context (Itami et al., 2003; Cole, 2005). Hunt et al. (2010) also used an ABM of recreational fishing in northern Ontario, Canada, in order to demonstrate the implications of different management scenarios with stakeholders. The use of advanced tracking technologies In the same way that the advent of the personal computer revolutionised use of GIS from a user perspective so further revolutions in informational and communication technology provide new opportunities for spatial analysis. Paramount among the new developments is the use of GPS devices and cellular phones which both allow for the tracking of tourists in space-time (Ahas et al., 2007; Shoval and Isaacson, 2007, 2010; Ahas et al., 2008; Shoval, 2008; van der Spek et al., 2009; Chhreti et al, 2010; Ahas 2011). The method has a range of applications including not only improved collection of data over traditional methods such as diaries, but also management, planning and marketing applications. For example, Shoval (2010) highlighted the possibility to use aggregative data obtained from GPS receivers in order to better understand the impact of visitors on destinations and provided examples from PortAventura amusement park (see also Russo et al., 2010) and the Mini Israel theme park (two enclosed outdoor environments), the Old City of Akko in Israel (a small historic city) and Hong Kong. Tchetchik et al. (2009) demonstrated how high-resolution time-space data recorded by GPS units could be used to segment visitors to the Old City of Acre heritage site in Israel. Mobile phones also provide significant opportunities for analysing tourist behaviour over various scales (Asakura and Iryob, 2007). Girardin et al. (2009) used the distribution and density of digital footprints to examine the attractiveness of urban space to visitors in a case study of the area of the New York City Waterfalls public art project. Tiru et al. (2010) discusses the operation

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of a mobile-positioning-based online tourism monitoring tool that uses as source data mobile operators' log files in which the starting locations of foreign roaming clients' call activities have been stored. (The database is anonymous and the identity of phones, phone owners, and phone numbers are strictly protected pursuant to EU directives). Operator’s data was evaluated to evaluate the extent of repeat visitation to Estonia by mobile phone users (Tiru, Kuusik et al., 2010), thereby providing tourism data that was otherwise unavailable from other data sources. Conclusion: Which Way to Turn? The mathematical modelling of movement over space has been often been criticised because of the perspective that ‘most types of spatial modelling efforts are fatally flawed because they fail to account for the complex attitudes, preferences and tastes of individuals. These latter attributes are influenced not only by personal circumstances and characteristics, but also by the cultural, social and political milieu in which individuals make spatial decisions’ (Fotheringham et al., 2000: 214) Nevertheless, Fortheringham et al. (2000) argue that such criticisms are based on what spatial interaction models once were rather that for what they are now. Indeed, it is becoming increasingly clear that spatial analysis can be usefully integrated with more qualitative methods so as to incorporate both spatial and cultural ‘turns’ (Latham, 2003; Hall, 2011). Indeed, this is also being illustrated by the extent to which user generated content can also provide insights into tourist behaviour and activities. As Latham (2003: 1993) notes, ‘human geography needs to be more imaginative, pluralistic, and pragmatic in its attitude towards both (a) methodology and (b) the kinds of final research accounts it produces’. Issues of methodological preference aside there is also ‘no intrinsic need for this subdisciplinary apartheid’ between mathematical modelling and critical geography (Clarke and Wilson, 2001, p.30). Spatial analysis and geographic information science provides an extremely sound basis to identify differences in relative access to resources within calls for a people-oriented GIS (Miller, 2005a). Space-time activities, including access to leisure and tourism opportunities, are not evenly distributed (Hall, 2005b, 2010). Spatial analysis therefore provides an empirical means to illustrate differences in access that occur as a result of class, socio-economic and demographic differences, ethnicity and gender (Kwan, 1998, 1999; Janelle and Hodge, 2000; Miller, 2005a, 2005b), in a manner which may be more compelling and better understood by policy makers than those derived from qualitative measures based upon small sample sizes (Hall, 2010). The future issues facing spatial analysis and GIS in tourism arguably reflect the broader issues surrounding the field (Miller, 2005a; Goodchild, 2010). Nevertheless, following Clarke and Wilson (2001) several key factors emerge. First, there is a ‘recognition that model-based analysis is but part of a wider process of management and planning rather than the central feature of planning’ (Clarke and Wilson, 2001: 36). Therefore, spatial analysis still needs to be placed within the broader context of tourism planning and policy and the different interests it may serve (Hall, 2008b). Second, the quality and quantity of spatially referenced information is continuing to increase, although there is concern over its commodification and access, along with implications for privacy. Third, improvements and changes in information and communications technology and services, including costs, convergence and miniaturisation, will be a major driver in the use of such technology in spatial analysis. Fourth, there will ongoing methodological development along with better packaging and presentation of outputs for end-users. Indeed, the continued growth of user-generated content is likely to be a major driver in spatial analysis and geographical information systems in the foreseeable future. This is also likely to lead to greater integration of quantitative and qualitative methods in spatial research with respect to tourist behaviours as well as destination marketing and design. It is also possible the methodological integration will also provide for stronger relationships between the human and physical geographical dimensions of research on tourism and the environment. Fifth, it is likely that there will be a continuing growth of interest in spatial analysis from the public and private sector given the spatial dimension of economic and regional development as well as public interest in spatial technologies and representation. Such interest is likely to become a significant driver for both research funding and careers. This chapter has highlighted the increasingly significant role of spatial analysis in tourism geography. After many years of being out of favour quantitative spatial analysis is being adopted again in light of the recognition of the vital role of GIS and spatial data in contemporary tourism planning, management and marketing. However, the critical function of spatial analysis and its value in policy arguments is also being rediscovered particularly because of its

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C. Michael Hall is a professor in the Department of Management, University of Canterbury, New Zealand; Docent in the Department of Geography, University of Oulu, Finland; and a Visiting Professor at Linnaeus University School of Business and Economics, Kalmar, Sweden and the Sheffield Business School, UK.