Modelling a single type of environmental impact ... - Semantic Scholar

Environment and Planning A 2003, volume 35, pages 931 ^ 946

DOI:10.1068/a35164

Modelling a single type of environmental impact from an obnoxious transport activity: implementing locational analysis with GIS Antonio Moreno-Jime¨nez

Department of Geography, Autonomous University of Madrid, Cantoblanco, 28049-Madrid, Spain; e-mail: [email protected]

Robert Lindsay Hodgart

Department of Geography, The University of Edinburgh, Drummond Street, Edinburgh EH8 9XP, Scotland; e-mail: [email protected] Received 21 June 2002; in revised form 17 October 2002

Abstract. Many facilities have negative impacts on neighbouring areas, and an obvious social and political concern is therefore to assess and minimise such impacts. The authors address this type of problem in relation to the dispersion of aircraft noise near airports. The approach involved brings together two basic components. First, two spatial models are presented. These are developed from existing concepts in location theory and modelling, but the authors attempt to overcome some of the limitations of previous models. Second, a geographical information system is used to obtain a better representation of the spatiotemporal processes involved in the dispersion of aircraft noise and to evaluate the functions of the two models. A case study is used to illustrate the methodology and helps to indicate how this approach could facilitate improved spatial decisionmaking.

1 Introduction The environmental concerns pervading contemporary societies pose a central problem: how can various forms of welfare and infrastructure provision be made compatible with the negative side effects that many of the human activities supplying these also produce? Societies face such dilemmas as the social rejection of dangerous, disturbing, or annoying activities which are, nevertheless, necessary, and the need to allocate land uses in such a way that some social groups or places are penalised while others are benefited. Such questions are highly controversial and the associated conflicts have generated acronyms and slogans like LULU (locally unwanted land uses), NIMBY (not in my backyard), and NIABY (not in anybody's backyard), which are now common in the literature. This social concern has, of course, spread into the political arena and public bodies are under pressure to scrutinise more carefully the unwanted effects both of governmental and of private decisions. In geography, this has fostered the growth of a focus on `malaise' or `bad-being' in addition to that on well-being. Major contributions to the field have been concerned with several issues: the sociospatial conflicts generated and their dynamics; the concept and measurement of spatial fields of negative impacts or externality cones; and methods for addressing or solving these spatially rooted problems which may also aid decisionmakers. A promising line of research is now emerging at an intersection of location theory and environmental concern. The traditional interest of location theory in desirable facilities, like retail, educational, or recreational centres, has recently been extended both to obnoxious facilities (which threaten way of life and amenities) and to noxious facilities (which are likely to damage health and well-being). One of the most promising aspects of this work involves attempts to build operational models which focus on the location of undesirable facilities. Since the 1980s, a number of authors have addressed some basic issues of this general problem, and in this paper

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we intend to contribute by bringing several research methods together to address the complex environmental impact of a particular activity. The basis for our research comes from two different areas; first, location theoryöparticularly models for optimising the location of facilities; and second, geographical information systems (GIS), which provide powerful capabilities for representing and analysing geographical processes. Stated briefly, the problem is to model the impact of an obnoxious facility, such as an airport, on the surrounding area. The modelling process is intended to provide quantitative measures and map images of this impact in order to evaluate it and to help planning and management decisions. The general case could be described as a human activity operating in a specific area and for certain periods that produces only one type of pollution or emission of fixed amount (although this might be variable depending on managers' decisions). This emission diffuses from a mobile origin according to a known function (usually decreasing with distance), so the emissions received (immissions) elsewhere are variable, but predictable. The mobile pollutant source moves along routes with some degree of flexibility in a two-dimensional or three-dimensional space. Consequently, along the route a corridor is affected by the externality for some period and according to the displacement. The effect on each place is intrinsically temporal in nature and it depends on the emission, location, and speed of the source. For each affected place the temporal externality cone looks like a curve, first rising to a maximum as the pollutant source approaches, then decreasing as it moves away. From another perspective, each instantaneous location of the mobile source forms an externality cone accompanying its displacement. In some places in the surrounding area there are entities which are sensitive to some levels of these immissions, and for several reasons there is an interest and need to evaluate the extent of these impacts and to choose routes which minimise them. So, the problem can be characterised by the following components: emissions from a mobile source leaving or arriving from or to a fixed facility along eligible routes during a specific period; a spatiotemporal dispersion process; and a spatial distribution of entities affected (people or activities). In addition, because it is common for regulations or technical standards to set certain acceptable or unacceptable levels of pollution or disturbance for different land uses and for different time periods, there is a priority to focus specifically on the area in which some specific threshold is exceeded. In the next section the background to this area of modelling is reviewed briefly as an introduction to the two models proposed here. The elements of the case study and the way it has been managed in a GIS are then discussed in subsequent sections, and we then describe the procedure used to implement these models with GIS tools and the results obtained for the sample case study. We conclude with a discussion of the methodology employed and suggestions for further developments. 2 Previous approaches and their limitations The environmental issues posed by many human activities have been tackled with different objectives. Those interested in the diagnosis of present or simulated situations have preferred impact assessment approaches, and those focusing on decisionmaking have mainly drawn on optimisation models (Daskin, 1995). The evaluation of environmental impact generated by transport operation has proved difficult, and it remains an ongoing field of research (Mills and Neuhauser, 2000). Risk, equity, or cost are criteria commonly guiding the search for accurate indicators of impact. One of the most interesting problems here is to choose between alternative routes, considering the numbers and types of persons, activities, or land uses affected along the route (see, for example, Wadden et al, 1976). However, the issue concerning the length of people's exposure to risk, for instance, is not usually considered.

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Occasionally, the temporal dimension has been envisaged synthetically as medium-term or long-term average situations (for example, Chakraborty and Armstrong, 1995). In the field of optimisation methods there is a growing literature on spatial modelling, focusing on the problem of siting undesirable facilities [for example, Location Science 1995, 3(3) provides a special issue on the location of facilities concerned with hazardous materials] or semidesirable facilities (Brimberg and Juel, 1998; Church and Bell, 1981). Also, some papers give state-of-the-art reviews; see, for instance, Chaudhry and Moon (1987), Erkut and Neuman (1989), List et al (1991), and Schilling et al (1993). The available models for siting undesirable facilities affecting population can be divided into two groups. (a) Single-objective models; these include the maximin or anticenter problem, which maximises the minimum (weighted or not) distance from any population site to any facility; the maxisum, maxian, or antimedian problem which involves maximising the sum of distances to the obnoxious source weighted by the population affected; and the anticover problem that attempts to find solutions minimising the population within a specified distance from the source of pollution. Each model searches for the solution of minimum impact according to a different criterion. See the aforementioned references for examples and further description. (b) Multiple objective models involve several criteria simultaneously: attraction and repulsion (Chen et al, 1992); production and transportation costs; opposition and disutility (Erkut and Neuman, 1992); facility cost, opposition, and equity (Ratick and White, 1988); and total impact and disequity (Falit-Baiamonte and Osleeb, 2000). Models for routing problems considering the negative impact derived from hazardous material transport also offer interesting insights (for example, Current and Ratick, 1995; Drezner and Wesolowsky, 1989; List et al, 1991; List and Mirchandani, 1991). These models usually address the minimisation of different risk measures such as total risk, maximum risk, perceived risk, and so on (Erkut and Verter, 1998); avoiding catastrophes (Erkut and Ingolfsson, 2000); or finding compromise solutions between cost and risk (Go¨mez and Bosque, 2001). See Erkut and Verter (1995) for a literature survey. Because some of the locational models formulated to minimise impacts on a surrounding area are revised versions of classical location ^ allocation models, they tend to inherit their strengths and weaknesses. Models of this type have made a seminal contribution to this area of work but they usually involve considerable simplification of real-world processes, and their implementation often puts more emphasis on mathematical and algorithmic issues than on empirical or practical ones. In another paper one of us has argued that these formulations can be significantly improved in order to model the actual processes involved in a more realistic way (Moreno, 1998). Some important limitations are that these models are usually static, in the sense that the duration of the effect is not considered, and that they rely heavily on simple distance measures to represent how the externality declines away from the pollutant source. In practice, how these effects are spread over space is itself a complex process requiring consideration in its own right. Thus, a wider perspective on spatial externalities could consider such relevant components as: the amount of emission or production from the source; the dispersion of effects through each specific medium to estimate the immission, or amount received at each place; the people and activities possibly affected; and the emission ^ reception period. Obviously, such an approach would aim to achieve a better fit between spatial models and the specific physical or human processes generating disturbances. In this paper we attempt to address this task through a closer analysis of a type of environmental problem generated by human activities which is usually located near urban areas.

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3 The models proposed for a single period and their components The main contribution of the modelling approach presented here involves considering more fully how externalities diffuse in order to draw more realistic impact fields, as discussed in a previous paper (Moreno, 1995). The following improvements are proposed. (a) A production variable is included which allows the amount of emission generated by the source to vary (or, alternatively, be constant). (b) A spatial spread function is defined which permits us to model how much of the noxious emissions produced at the sources are received at each place (the immissions), by allowing for some decline over space. The spatial spread, usually decay, of externalities (causing opposition or repulsion) has been tackled in several papers. Church and Roberts (1983) proposed a set of continuous functions, and several authors have used different exponential formulations (for example, Chen et al, 1992; Ferna¨ndez et al, 2000; Hansen et al, 1981) or distance-related step functions (Church and Bell, 1981; Falit-Baiamonte and Osleeb, 2000), usually decaying monotonically. All of these suffer from the same flaw: the function is not empirically estimated and it may be somewhat inappropriate for the representation of the pollution spread or population repulsion. Human attitudes towards facilities causing environmental problems are very complex and difficult to model as a simple distance function (see, for example, a case study by Moreno, 1992). In contrast, there are only few studies in which the question is dealt with in a more realistic way. The works of Karkazis and Papadimitriou (1992) and Karkazis and Boffey (1994), for instance, provide a better grounded contribution because they search for optimal locations of facilities involving the dispersion of airborne pollutants and consider, for example, factors such as the predominant wind patterns. Similarly, Chakraborty and Armstrong (1995; 1997) have assessed the area and population impacted by means of a dispersion model from point sources. Taking into consideration the averaged weather conditions, they generate a composite plume `footprint' of emissions for each source, as an alternative to traditional circular buffers. (c) Unlike some location ^ allocation models, these effects are not restricted to the `demand points' or residential areas nearest to each facility (Church and Bell, 1981; Church and Roberts, 1983). Instead, each pollution source is allowed to impact on many places and with different intensities. (d) The areas affected by pollution sources are not defined by a simple radius. Instead, the most seriously affected zone (the `covered' area) is determined by some specific immission level at the destination. This threshold can be set either by technical criteria or by normative standards. (e) The externalities are produced over a period of time and during this period they may change, so measures both for single and for multiple periods are devised. A single period or instant is considered to be homogeneous in the sense that the externalities emitted within it are constant. This implies that the production, spread, and reception of the externality by the entities affected do not change. In addition, some restrictive assumptions have been made: only a single type of emission (and effect) is produced; the entities affected are equally sensitive to this emission (that is, personal differences are not considered); and the sensitivity of the affected entities does not change over time. Taking into account the logic of common land-use regulations, two models have been developed. Single-period or instantaneous versions of the two models will be introduced first; these are then extended to multiple periods. The first model addresses what can be called the maxisum within covered area problem (MWCAP). Stated simply, this is an attempt to compute the weighted sum of the population affected in each place times the effects received, considering only the

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places where some unacceptable threshold of pollution is exceeded. Let us assume the mobile pollutant source is in a specific moment (place) j of its route. The instantaneous impact caused on the covered area may be written as follows: X Fj ˆ wi qj f…dij † , (1) i 2 Cj

where i wi qj f(dij )

are the points affected, for example, populated places, i ˆ 1, ... , n, is the number of persons in place i, is the emission level of the source in the moment (site) j, is the spread function of emissions over space which will depend on dij , the distance between production source and the surrounding populated places, Cj is, for each moment (site) j, the subset of the i places which receive an immission higher than a critical threshold, T, that is Cj ˆ fi j qj f(dij ) 5 T g. The measure of impact underlying this function roughly corresponds to one proposed some time ago by Smith (1997), as it represents a sum of the utility/disutility felt at each place weighted by the population of that place. Formulated in this way, the model can be included in the so-called maxisum problem category(1) in that it only considers the interaction between producers and receivers (not the mutual interaction among the producing sources), but with the modification that it is only computed over the most severely affected zones (the `covered' area) önot over the whole externality field. In broad terms it is mainly based on an efficiency principle. The second model is a modified version of the anticover problem (AP) where the usual aim is to minimise the entities (for example, population) inside a proximal area of facilities, defined by a certain radius (see Erkut and Neuman, 1989; Moon and Chaudhry, 1984; Murray et al, 1998). Our model computes the population inside the zone exceeding some unacceptable pollution level. As before, for a moment (site) j the model can be expressed as follows: X Gj ˆ wi . (2) i 2 Cj

This model involves the modification of previous anticover models such that the area covered is defined by a critical threshold of immissions. Like the related models for desirable facilities that maximise the population covered within a specific range, this indicator can be seen as also paying attention to the principle of efficiency, although in a different way from model (1), in that it tries to minimise the population adversely affected. 4 Application of the models to a specific case study The situation used to illustrate the implementation of these models concerns the noise disturbance produced by aircraft around an airport, and its impact on surrounding population. It can also be seen, therefore, as a contribution to the geography of noise discussed recently by Roulier (1999), although the focus here is not on description and explanation, but on evaluation oriented to decisionmaking. Another feature of the case study is that, because only one source of pollution is considered, the calculations are fairly simple. However, a complication is introduced by the fact that the source movesöwhich produces temporal variations in the externality level.

(1) Although the interest is obviously in minimising the impact, the term `maxisum' has been retained because this model belongs logically to the latter class of problems.

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The geographical context is an area adjacent to Madrid Airport. Although efforts have been made to represent the local environment accurately, the real situation is more complex than the representation of the model and some of the data needed for a more realistic treatment are not available. Hence, it cannot be claimed that the conclusions drawn are necessarily valid for this specific situation öthe emphasis here is primarily on methodological issues. The current noise-monitoring system is based on a set of ground stations in and around the airport facility which record the sound level according to a temporal sampling scheme. The results include different statistical summaries for each station. The analysis based on these data is limited for two reasons: first, noise level in the rest of the affected area should be estimated through spatial interpolation; and, second, the impact is not related to population affected, but only, crudely, to space. Our approach, as explained above, represents an attempt to overcome these limitations. Typically, solutions to optimisation models for problems closely similar to those outlined here have been found either by mathematical programming or by heuristic algorithms. But these solutions would require adapting the formulation to each specific spread function, to a temporal process, and to a displacement of the pollutant source in three-dimensional space, which would increase its complexity excessively. Alternatively, because GISs allow the situation outlined above to be represented in a more realistic and detailed way, and also give a convenient means of handling the temporal variation in noise, it was felt that these models could be implemented more effectively here within a GIS environment, even if some mathematical efficiency was thereby sacrificed. 5 The components of the models and the problems of operationalising them in a GIS environment To build an operational representation of the impact produced by the pollution source, a number of components need to be considered. First, the emission source could be an aircraft taking off and moving along a route defined in three-dimensional space. Along its flight path, a constant amount of noise is emitted which diffuses through the atmosphere and reaches the ground. The immission received at each place on the surface is affected by several factors, including distance from the source (hence the altitude of the ground can have a significant role). Because the entities affected on the surface, for example, population, are distributed unevenly, the measures of impact have to take this into account. Although GIS offer quite a flexible environment for representing the real world, because they are general-purpose systems, both of our functions have to be evaluated through a sequence of steps based on a cartographic modelling process, which is less efficient and less elegant in some respects than mathematical optimisation procedures. We now consider how the different components involved are represented in a GIS with raster and vector capabilities. 5.1 The source of pollution

Modelling the externality field of a mobile source is complex, not least because the aircraft moves in a true three-dimensional space of x, y, and z (height) coordinates, and its speed changes continuously, so tracking it is potentially a research task in itself. Moreover, because many GIS are designed to handle only two dimensions, they are not well suited to representing processes in three dimensions. For the sake of simplicity, therefore, only one set of instantaneous locations along two hypothetical routes (A and B) will be considered: that is, only the impact fields generated by these points will be investigated (see figure 1). Both paths have been designed to reflect the flight of an aircraft taking off, although landings may be dealt with in a similar way. Because route A (the more southerly) is closer to the airport, aircraft are lower on this route than on

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Route B

Route A

N

1875 m

Figure 1. The study zone (northeast of Madrid metropolitan area) and two hypothetical routes for aircraft taking off from Madrid Airport.

route B (the more northerly path). The instantaneous sample points were set at roughly 1 km intervals along the routes to help comparison between these paths. The density of points along the route could be increased to create a more `continuous' sequence of locations described by the moving source. It is worth noting that such equally spaced points do not necessarily mean equal periods of noise impact because, when landing and taking off, the speed of the aircraft is continuously reduced or increased. However, to simplify analysis, it is assumed here that the sample locations of the source have been taken at a constant space ^ time interval; that is, the aircraft speed is constant. In addition, the location of the pollution source at each point selected along the route is defined by three items of data: longitude, latitude, and height above the ground. Additionally, the amount of noise emitted by the source is set constant at the reasonably typical level of 125 dB. 5.2 The dispersion function

The spread of sound through the atmosphere is also a complex process (see Magrab, 1975; Warring, 1983), being affected by wind, turbulence, the physical properties of the air (for instance, absorption varies with moisture and temperature and other factors, but at different rates for different sound frequencies). Again, for the sake of simplicity, a general function for noise dispersion will be used which assumes that acoustic power radiates uniformly in all directions through an isotropic atmosphere under standard

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meteorological conditions and free of barriers. The formula (Dom|¨ nguez Bustabad and Garc|¨ a Senchermes, 1983, page 87) is: li ˆ pj ÿ …20 ln dij ÿ 11† …dB† , where is the sonorous (acoustic) pressure level (SPL) in place i; li pj is the SPL in the source (place j ), dij is the distance between places i and j. For instance, if the SPL in the source is 110 dB, at 50m the SPL should be:

(3)

l50 ˆ 110 ÿ …20 ln 50 ÿ 11† ˆ 87:0206 …dB† . According to this, the SPL decreases roughly at a rate of 6 dB as distance doubles. 5.3 The location of entities affected

To identify all the activities and beings affected by a source of pollution also constitutes a substantial research problem in itself, but given that this paper is not focused on the second of these problems, only one aspect is considered hereöpopulation. Even so, the spatial representation of population poses problems, because of its mobility and variations in personal sensitivity. To identify all the population likely to be affected over a 24-hour period properly requires data on the approximate location of people at their residences, educational institutions, places of work, etc for appropriately defined periods throughout the day. Here, a crude approximation of treating only residential locations is made by using the 1996 Census data for small, fairly homogeneous, areas called `urban sectors' by the Statistics Institute of the Madrid Autonomous Community. The population is assumed to be evenly distributed among the pixels included in each sector, but in the future, data at building level, which have recently been made available, could be used, so avoiding the need of spatial interpolation adopted here. These population data, which are for the irregular polygons formed by the urban sectors, have been transformed to estimate the average number of people in small grid cells within them. This procedure involved two steps: first, population density was computed for each polygon as persons per ha; second, the polygons for urban sectors were rasterised, breaking them down into a detailed and regular pattern of square pixels, each 1 ha in area. Each pixel was then assumed to contain the average number of people per ha of the sector in which it lies, which enables the impact to be evaluated in a more spatially detailed way. Obviously, at each pixel on the ground, as the source approaches the noise will increase to a maximum when its distance from the aircraft is at its shortest, then fall off as the source moves away, giving a characteristic `dome' pattern. 5.4 Estimating the distance between the source of pollution and the places affected

In two-dimensional GIS and virtually all locational models, distances are usually computed in map-projection space, that is, either on a flat plane or through network links such as roads or streets. However, three-dimensional data are required in our case study, because these are a fundamental factor in the spread of noise pollution. To this end, the basic data are taken from a digital elevation model (DEM) of the area obtained from the Regional Mapping Service of the Madrid Autonomous Community. The DEM selected contains the heights for pixels at 100 m resolution. To help compute the Euclidean distances from the aircraft to each pixel, first, data on the height of the aircraft measured vertically above the point selected on its route (ha g ), and the altitude of the corresponding ground pixel (hg ) directly below the aircraft, are needed. The vertical separation between the height of the aircraft and each pixel, haj (taking into account the altitude of each pixel) can then be calculated as ha j ˆ hag ‡ …hg ÿ hj † ,

(4)

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3

Pollutant source

da j ha j

da j hag

ha j

dg j

Earth surface

dg j hj

hg

hj

Sea level (reference)

3

Figure 2. Components used for computing three-dimensional distances between the ground surface and a flying source of pollution in a two-dimensional raster GIS environment.

where hag is the height of the aircraft above the ground, hg is the altitude of the ground point exactly beneath the source of noise, and hj is the altitude of pixel j (see figure 2 for explanation). The horizontal linear distances, dg j , between the ground x and y coordinates of the aircraft and each pixel j are computed by standard GIS operations (using Pythagoras). Thus, three-dimensional distances between the source of pollution and the ground pixels, da j can then be computed (again, using Pythagoras as shown in figure 2) from daj ˆ …dg2j ‡ ha2j †

1=2

.

(5)

6 Basic steps for computing the functions of the models using standard GIS capabilities Both of the models employed pay special attention to areas where the immission level exceeds some specified threshold. In the literature on noise, the levels suggested as bearable for many human activities range from 60 dB to 70 dB. It was therefore decided to use 65 dB as a reasonable compromise figure. A sequence of operations was then carried out, both to evaluate the functions and to obtain some illustrative results which could be displayed in map form. The main operations carried out to obtain the functions, using standard GIS procedures, are as follows. (a) Specify the location of the pollution source whose impact is to be evaluated. (b) Compute the distances between the pollution source and each point on the ground within the study zone treated as the central point in a pixel, as explained earlier (this calculation can be done in a single raster operation). (c) Using the dispersion function, compute the noise received at each ground pixel, again employing raster calculations. (d) Determine the field affected by a noise of 65 dB and above as a spatial query operation, and then convert this field into a vector polygon. (e) Compute the noise received at each pixel times its population density as a layer product. (f ) The two functions can then be evaluated for the specified location of the source as follows:

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First, summing the pixel values from the previous product within the 65 dB polygon yields the function value for the maxisum problem within covered area for that aircraft position. Second, summing the population densities inside the 65 dB polygon gives the corresponding function value for the anticover model (that is, the estimated total number of people affected by an unbearable noise). 7 Detailed results for some hypothetical source locations and paths The sample application enables some results from the models to be examined both in local detail and at a more general level. Table 1 displays the main indicators of the impact produced by the pollution source for three instantaneous sample positions on the two different paths, including the values of the two functions obtained by summing the appropriate values in each pixel of the area affected. These last results therefore give overall measurements of the strength of the externality effects produced at each position of the aircraft, and thus allow comparisons to be made between different points on the two routes. Table 1. The areas affected and the values of the two functions for three selected locations of the pollutant source on routes A and B. Affected area with 65 dB and above (km2 )

Value of Fj function for maxisum problem within covered area (person decibels)

Value of Gj function for anticover problem (that is, population affected)

Route A 1 700 2 900 3 1 080

38.71 37.81 35.76

8 718 036 8 849 142 8 727 476

124 319.8 125 487.5 124 157.5

Route B 4 975 5 1 195 6 1 380

36.38 35.32 33.91

5 325 896 5 881 151 6 103 803.5

Point

Height of pollutant source above the ground (m)

79 490.0 88 283.5 92 307.5

By use of the mapping capabilities of GIS, a picture of each instantaneous externality field can also be obtained; figure 3 shows an example for point 1 on route A. If noise diffuses evenly in all directions and the ground is perfectly flat, the area on the ground receiving 65 dB or more from a specific (that is, `instant') source location will be circular, as shown in figure 3. However, in similar maps for other positions where the height of the ground is more variable, slight elongations appear in the direction of higher ground and the radius of the field can be slightly curtailed towards lower ground. The radius and areal extent of these fields on the ground get smaller, of course, as the aircraft gains height. In examining these results it is worth recalling that the first function is based on multiplying the noise received at each pixel on the ground by the population of that pixel, which provides a quantity measured in units of `person decibels'. Thus, in the present context, it seems reasonable to argue that a pixel recording 20 000 person decibels is twice as strongly affected by noise as one with 10 000 person decibels. The second function is probably easier to interpret as it simply gives the total number of people in the region receiving 65 dB or more when the aircraft is at the specific location concerned.

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Route A Urban sectors Municipal boundary 65 dB-and-above zone Noise from point 1 50 ^ 55 db 55 ^ 60 dB 60 ^ 65 dB 65 ^ 70 dB 70 ^ 75 dB 75 ^ 79.098 dB no data N W

E S

3

0

3

6

km

Figure 3. Estimated noise field generated from point 1 at a height of 700 m on route A.

8 Developing functions which take account of the temporal dimension A key feature of the impact from a mobile source is the duration involved, that is, the period during which each place or entity suffers disturbance. Because in the approach taken here we are concerned with the zone over a critical threshold, the estimation of this duration implies taking into account only the period for which each place remains in the critical zone. It may be worth noting at this point that obtaining a visual picture of the whole zone affected for each route is only a matter of using GIS capabilities to merge the impact-field polygons for each sample location of the source. Figure 4 (see over) displays the externality fields generated by the three sample locations on routes A and B, that is, the areas affected by a noise of 65 dB or more. The extent of these composite fields is very slightly curtailed towards the west as the aircraft gains height after take off, reducing the area affected below. To obtain a more complete evaluation of the noise disturbance, it is therefore necessary to devise functions which take account of how that disturbance varies over time as well as over space, and also of how long it exceeds the threshold. Incorporation of the temporal dimension into the maxisum model within covered area is quite simple if it is assumed that the sample three-dimensional locations of the pollution source have been taken at equal time intervals (or equal space ^ time intervals, assuming a constant speed for the mobile source). In this case each location of the aircraft represents an infinitesimal interval (for example, a crude second or another, convenient, smaller period) during which each place on the ground receives a certain volume of noise. Over any duration of time under consideration (defined, say, by the total number of seconds), at a particular pixel on the ground the noise impacts in person decibels at each of the instantaneous, equally spaced, points in time composing that duration can then be summed to obtain

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Route A Route B Affected zone öroute B Affected zone öroute A Municipal boundary Urban sectors Population haÿ1 0 ^ 131.813 131.813 ^ 263.627 263.627 ^ 395.44 395.44 ^ 527.253 527.253 ^ 659.067 659.067 ^ 790.88 no data

N W

E S

3

0

3

km

Figure 4. Sample locations of the pollution source and the associated impact fields with 65 dB or above for routes A and B, overlaid on population density.

a measure of the total `dose' of noise received by that pixel as the aircraft moves over the region. The appropriate formula then is m X X F ˆ wi qjm f…dij † , (6) L

mˆ1

i 2 Cjm

where m are the time units expressing the duration of the route L, m ˆ 1, ... , mL ; the mL limit can be thought of as determined either by the end of the route or by the definite absence of population inside the covered area of this route. qjm is the emission level in the site j and moment m, Cjm for each site j, is the subset of the i places which receive an immission higher than a critical threshold, T, in the moment m, that is, Cjm ˆ fijqjm f(dij ) 5 T g. By summing the values thus computed for all pixels we obtain a measure of the dose of noise received across the whole region during the time period concerned. Comparison of such `global' values for routes A and B (column 1 in table 2) affords an appreciation of how much greater the overall noise impact of the more southerly route is. (It may be helpful to note that these figures are simply obtained by summing the noise impacts for the three sample points on each route given in column 3 of table 1, Table 2. Spatiotemporal impact indicators or global functions for the two models. Route

F function for maxisum model within covered area

G function for anticover model

Total area affected (km2 )

A B

26 294 654 17 310 850.5

372 283.06 236 609.72

50.73 48.23

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Duration of effects

1

2

3

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3 ...

Affected zone from a sample location of the source Populated places

Figure 5. The underlying logic of the space ^ time indicator of impact for a source moving steadily along a route, illustrating the instantaneous impact fields, the places affected, and the periods during which each place is covered.

and that, of course, only situations in which a pixel received over 65 dB are included.) In this modified form, the first function can now be seen as providing a quantitative spatiotemporal measure of externality impact for the region, that is, as an overall index which combines the strength and duration of noise. Extending the anticover model into the temporal dimension is less direct and requires some explanation. The key variable here is obviously the period during which any populated place is in the covered zone. If the sample locations of the pollution source are again taken at equal time intervals, then the period for which each place on the ground is affected is given by the number of times it lies in the impact zone of any of these discrete sample locations. For instance, if the intervals are seconds, a place might be affected (that is, be included in the critical zone) by 10, 11, 12, etc sample locations, which would be equivalent to the corresponding number of seconds affected. Figure 5 explains the logic of this measure: along the route shown, the equal time intervals between the source locations produce overlapping impact areas. It is then a matter of counting the number of times each ground point is inside any impact zone to obtain the period affected. With the aid of simple GIS operations (a sum of the raster layers identifying each individual impact zone) it is possible to calculate the length of time that each place remains affected. Figure 6 (see over) displays such a map for route A. However, given that each place has a different population, it is necessary to weight this indicator accordingly. This involves, first, multiplying the population located at each place (wi ) by the duration for which it is affected (ti ), and, second, summing these products for all pixels in the zone affected. Hence, a spatiotemporal indicator of impact or global function for this model can now be written: m n X X X G ˆ wi ti ˆ wi . (7) L

iˆ1

mˆ1

i 2 Cjm

The second expression states that the impact for route L involves summing the function (2) for all the moments of this route. Evaluating this function using the first expression with a raster GIS is a simple task which requires only the following steps: (a) Overlay (sum) the raster layers identifying the individual (or `instantaneous') zones affected for each sample source location. (b) Overlay (product) the resulting layer and the layer for population location. (c) Sum the previous product over the whole zone affected. The results produced from such calculations for the two sample routes are shown in the second column of table 2.

A Moreno-Jime¨nez, R L Hodgart

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Municipal boundary Urban sectors Affected zone öroute A 1 Affected period öroute A 0 1 2 3

N W 3

0

3

E S

km

Figure 6. Length of period affected for each place on the ground by the set of sample locations on route A.

As expected, the two measures indicate that route B (the more northerly, higher altitude, route) produces a lower impact on the residential areas below. According to these results, the impact of route B is just 63.56% of that of route A in the case of the anticover criterion, and 65.83% for the criterion of the maxisum model within the covered area. Although this result might be clear for the paths compared here, it must be remembered that, because this is a three-dimensional process, the track on a two-dimensional map may be highly deceptive. 9 Conclusions In this paper we have tried to tackle a particular problem involving the analysis of environmental externalities by bringing together different conceptual and technical tools in order to gain a better appraisal of the processes involved in the real world. In doing so, we have suggested that the capabilities of GIS for representing the real world more accurately can provide a powerful basis for examining actual processes in a more realistic and flexible way than can traditional modelling tools (for example, optimisation programs). Hence, this procedure can enable us to examine environmental problems in closer detail. The underlying principles of locational analysis have provided us with a wellestablished basis for devising evaluation criteria, although in this paper we considered only single criterion objectives. Building on the work of previous authors, we have proposed two models concerned with the assessment of externalities. These models offer some meaningful improvements on the older models: namely, the inclusion of a production variable, the case-specific dispersion of the externality effect, and a temporal perspective. These improvements allow us to create more realistic and more relevant measures for evaluating impact, so overcoming both the abstract distance-decay curves of almost all former optimisation models, and the crude noise summaries, which are not related to population, actually used to represent the impact on the space. Combining the principles of some optimisation models with GIS methods of implementation yields an approach which is promising in two senses. First, it provides

Modelling a single type of environmental impact

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better technical procedures for tackling complex problems, so avoiding some of the serious reductionism (that is, simplification) inherent in older models. Second, it provides results which are more easily and widely understood (for example, in the form of maps), both at intermediate steps in the analysis and at the final stage of evaluation; such results are also likely to be seen as more user friendly by nontechnical stakeholders. It has to be acknowledged, nevertheless, that the procedures followed in this paper have been somewhat time consuming and cumbersome, mainly because the programming capabilities of GIS have not really been exploited. Had GIS been used more fully (as could be the case in future applications), this would have greatly speeded the data handling and made the analysis more manageable. The proposed approach can be seen as an improvement which gives better value than older methodologies concerned with assisting both evaluation and decisionmaking. First, in ex-ante evaluation the results can provide information to counter the expected opposition near candidate sites for terminal transportation facilities. Second, they can also be useful in managerial decisionmaking in the choice of routes causing risk or disturbance. The general methodology can be extended in several directions. First, in addition to the case of aircraft routes, the proposed indices might be usefully applied to other mobile pollutant or risk sources such as water, rail, or road transport. Second, indices can also be computed for separate socioeconomic groups (as has been done by Chakraborty and Armstrong, 1997; Mills and Neuhauser, 2000), so allowing a comparison of the burdens for each and, hence, addressing environmental justice concerns during the current policy debates concerning public financial support for soundproofing dwellings near the airport, for example. Third, and as a further development, the indices can also be adapted as objective functions in new optimisation models with widened scope to include the amount of population covered, the immission levels, and the duration of coverage along the route. Acknowledgements. The financial support of Spanish Ministry of Education and Culture for this research in the Department of Geography, University of Edinburgh, is acknowledged. The authors are grateful for comments of two anonymous referees. References Brimberg J, Juel H, 1998, ``A minisum model with forbidden regions for locating a semi-desirable facility in the plane'' Location Science 6 109 ^ 120 Chakraborty J, Armstrong M P, 1995, ``Using geographic plume analysis to assess community vulnerability to hazardous accidents'' Computers, Environment and Urban Systems 19(5 ^ 6) 341 ^ 356 Chakraborty J, Armstrong M P, 1997, ``Exploring the use of buffer analysis for the identification of impacted areas in environmental equity assessment'' Cartography and Geographic Information Systems 24(3) 145 ^ 157 Chaudhry S, Moon I, 1987, ``Analytical models for locating obnoxious facilities'', in Material Disposal: Siting and Management Ed. M Chatterji (Gower, Brookfield, VT) pp 275 ^ 282 Chen P, Hansen P, Jaumard B, Tuy H, 1992, ``Weber problem with attraction and repulsion'' Journal of Regional Science 32 467 ^ 486 Church R, Bell T, 1981, ``Incorporating preferences in location allocation models'' Geographical Perspectives 48 22 ^ 34 Church R, Roberts K, 1983, ``Generalized coverage models and public facility location'' Papers of the Regional Science Association 53 117 ^ 135 Current J, Ratick S, 1995, ``A model to assess risk, equity and efficiency in the facility location and transportation of hazardous material'' Location Science 3(3) 187 ^ 201 Daskin M, 1995 Network and Discrete Location: Models, Algorithms and Applications (John Wiley, Chichester, Sussex) Dom|¨ nguez Bustabad M, Garc|¨ a Senchermes A, 1983 Ru|¨ do de tra¨fico urbano e interurbano: manual para la planificacio¨n urbana y la arquitectura [Noise of urban and interurban traffic: manual for urban planning and architecture] (Ministerio de Obras Pu¨blicas y Urbanismo, Madrid) Drezner Z, Wesolowsky G, 1989, ``Location of an obnoxious route'' Journal of the Operational Research Society 40 1011 ^ 1018

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