Evaluating enclosure in urban sites

Landscape and Urban Planning 57 (2001) 25±42

Evaluating enclosure in urban sites Arthur E. Stamps III* Institute of Environmental Quality, 290 Rutledge Street, San Francisco, CA 94110, USA Received 26 March 2001; received in revised form 11 June 2001; accepted 12 August 2001

Abstract This paper compares two mathematical models for evaluating a strong physical correlate of enclosure in urban sites. The physical correlate is the proportion of views covered by physical features which block vision or motion. The Station Point Method mimics how views are perceived from many station points within a geographical area. The Abstract Method uses GIS data to create two variables: average height of features (h) and average distance between features (d). It was hypothesized that the simple Abstract Model would be as accurate as the much more complex Station Point Model. The hypothesis was tested on two sets of data covering 750 views in 25 urban sites. In the ®rst set, the multiple correlation between Station Point and Abstract estimates of proportion of views covered by features which block vision or motion was R ˆ 0:92. Replication was achieved in the second set (R ˆ 0:92). # 2001 Elsevier Science B.V. All rights reserved. Keywords: Landscape assessment; Urban planning; GIS

1. Introduction This paper presents two methods for measuring a physical variable which is very strongly correlated with subjective impressions of environmental enclosure. The variable is the proportion of views covered with physical features which block vision and motion. The two methods are the Station Point Method and the Abstract Method. Both methods were applied to two different samples of urban sites, so it was possible to determine if the ®ndings were reproducible. This paper is organized as follows. First, the importance of enclosure is discussed using evolutionary theory and literature reviews of previous experimental work. Second, a mathematical model (the Station Point Method) is proposed for measuring the extent to which blocking features occupy a view as perceived * Tel.: ‡1-415-641-4998. E-mail address: [email protected] (A.E. Stamps III).

0169-2046/01/$20.00 # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 2 0 4 6 ( 0 1 ) 0 0 1 8 6 - 4

by someone located in an urban site. Third, a mathematical model is developed for measuring, from GIS data, the extent to which blocking features occupy many views as seen by someone located in an urban site (the Abstract Method). Fourth, the relationship between the Station Point measures and the Abstract measures is tested in one data set, and ®fth, replication is attempted in a second data set. Sixth, some possible extensions and future work are described. 1.1. Importance of enclosure Enclosure is such a fundamental component of physical environments that there is a speci®c region in the brain which responds directly to images of walls which enclose space but not to the same walls if they do not enclose space (Holden, 2000). The presence of this physiological response suggests that this ability to recognize enclosure is a consequence of natural selection. Natural selection also works on other mental

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A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

capabilities (Darwin, 1887, p. 89). One important capability is attention. Attention is allocation of perception. Under evolutionary theory, attention in the environment should be focused on physical features which have survival value. For instance, the ability to recognize and avoid regions where one might be physically trapped would have survival value. Such an ability would be indicated, for instance, by the aforementioned innate physiological response to enclosure. Another important ability would be to identify regions which permit or obstruct physical movement, either by one's self or by other organisms. Self-locomotion will be important if it becomes necessary to ¯ee. Regions which allow locomotion by others are regions from which one can be attacked. Consequently, there are clear reasons why environmental enclosure, or a lack thereof, should be important under the theory of evolution. A third physical feature with obvious survival value is visibility. If one can see over a large range and there are no blind spots, then it is possible to extend the range of one's detection of potential attacks. Conversely, if the range of vision is limited, or if there are blind spots, then potential predators could be located nearby. Again, the evolutionary implications should be clear. A fourth ability is the capacity to identify and locate objects in a physical environment. There are many names for this capacity. This article uses a name from computer science: parsing. If one cannot parse an environment (determine what objects are present in an environment and where they are), then one is unable to determine if those objects would enhance or diminish one's safety. For instance, in simple environments where all surfaces are solid, opaque, with discrete boundaries, and are either horizontal or vertical, parsing is simple. Physical and visual access are co-extensive. There is a ground plane below which attacks cannot come. In a deep jungle canopy, on the other hand, there are no surfaces, but rather variations in spatial densities of leaves, twigs, branches, stems, and trunks. There is no clear geometric distinction between one tree and another. Lighting is apt to be dim, making discrimination even more dif®cult. Threats are possible from any direction. In other environments (oceans, the atmosphere, space), there are even fewer geometric distinctions; in landscapes, objects and locations might be well de®ned (a hedge row) or not

(the boundary of a moor in the morning mist). One cannot respond appropriately in an environment where one does not know what is located where, so there is a connection between evolutionary theory and environmental perception. There is also an evolutionary explanation for a relationship between physical features with survival value and environmental preference. The relationship is positive feedback of attention. Some features of a physical environment draw and retain attention because, at one time, those features indicated where there were regions of safety or danger. Examples would be distant vistas, which indicate regions of safety, paths which turn out of sight, indicating regions of possible attack without visual warning, and darklylit, unorganized masses of plant materials, in which it is not possible to determine if it harbors a predator. Much more expansive presentations of the connections between evolutionary theory and environmental preferences have already been published by Appleton (1996) and Kaplan (1987). Typical qualities are prospect (how much and how far one can see), refuge (the ability to hide), and whether something might be hidden as seen from one's present location (mystery). Herzog (1984) extended this line of thought to impressions of spaciousness and impressions of smoothness of ground texture. To sum up: under evolutionary theory, the ability to recognize aspects of the physical environment which either block or permit either visual or physical access should have very strong effects on environmental perception and preference. There is, accordingly, a strong theoretical reason for inquiry on the issue of what features of the environment either block or permit visual or physical access. 1.2. Literature reviews of previous experimental work 1.2.1. General This paper presupposes acquaintance with the current empirical literature on environmental perception and preference. Major themes on which there are now substantial bodies of data include (a) equivalence of scaling techniques, (b) use of images to represent environments, (c) demographic differences, (d) number of respondents, and (e) representation of affective responses. (Supporting data for the claims in this

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

paragraph are referenced in Stamps (2000, Chapter 3.)) A review of scaling techniques (ratings, rankings, raw score, comparative judgment, true score, signal detection) on 1150 stimuli indicated that results from all methods correlated at r ˆ 0:99. Another review on differences between on-site evaluations and evaluations of simulations (n ˆ 553 environments) suggested that static color simulations are adequate facsimiles (r ˆ 0:83). For demographic effects, a review covering 5301 respondents from 21 countries and 1001 scenes revealed that preferences over demographic factors such as gender, cross-cultures, student or non-student, and designers or non-designers all correlated in the middle to high 80s. The only exceptions were general public or special interest groups (r ˆ 0:56), designer or public for avant garde buildings (r ˆ 0:46), and public or children (r ˆ 0:61). Questions of appropriate sample size can be calculated using power analysis (Cohen, 1988; Cohen and Cohen, 1993). For studies of environmental preferences, empirical tests suggest that experiments using dependent variables of semantic scales require about 30 respondents for reliable (r > 0:90) ®ndings (Stamps, 1992). One useful framework for representing affective responses, supported by evidence from over 7000 respondents and 1700 stimuli (Berlyne, 1973, 1974; Bush, 1973; Crozier, 1974; Evans and Day, 1971; Mehrabian, 1995; Mehrabian and Russell, 1974; Osgood et al., 1957, 1975; Russell et al., 1981; Wright and Rainwater, 1962) suggests that affective responses can be described as intensities of three dimensions: pleasure, arousal, and dominance. Degree of pleasure can be measured by semantic differential scales such as pleasant/unpleasant, behavior, such as time spent or approaching rather avoiding something, or physiological measures such as activation of speci®c areas in the brain. (A review of the relationships among feelings and brain activity is given in Davidson et al. (2000).) Degree of arousal can be measured by scales such as excited/calm, behaviors such as being active rather than lethargic, and activity in other parts of the brain. Dominance can be measured by how much one feels more or less powerful than someone or something else. Typical scales which correlate highly with dominance include power, freedom to move, autonomy, and not being con®ned. Recent research in neurophysiology (see Davidson et al., 2000) indicates

27

that there might also be speci®c regions in the brain which indicate how dominant or submissive one feels. 1.2.2. Literature review on environmental enclosure 1.2.2.1. Dependent variable. Since the present paper is concerned with impressions of enclosure, the primary subjective dependent variable is degree of enclosure. However, any other response scales which correlate highly with rated enclosure might also be useful. Under the three dimension model of affective responses, therefore, any articles which report dependent variables which correlate with the dimension of dominance would be acceptable. Specifically, this paper assumes that dependent variables of rated dominance, rated power, rated massiveness, and rated size of space all indicate degree of dominance. This assumption can be checked empirically by conducting a heterogeneity test as described in Hedges and Olkin (1985). 1.2.2.2. Independent variables. In this literature review, the independent variables are regions of the environment which either block or permit either visual or physical access. Depending on the material and geometry of the region, it may be impervious to both visual and physical access (a brick wall), transparent to both (air), impervious to motion but not vision (glass), or impervious to vision but not motion (fog). There can also be degrees of permeability: translucent glass for vision, sloping or roughly textured ground for motion. In simple cases, physical regions can be represented as proportions of an image covered by a horizontal plane on which one could walk (ground plane) and the proportion of an image covered by solid silhouettes of regions which block motion and vision (blocking features). The reason for representing features as solid silhouettes, as distinct from more complicated representations such as surface details or variations in the surface normal to the silhouette plane, is that previous research found a correlation for judged massiveness of r ˆ 0:97 with the visual angle subtended by the silhouette and r's of 0 for surface details and variations normal to the silhouette plane (Stamps, 1998). Accordingly, one way to parse a view is to divide it into three areas: the area covered by the ground plane, the area covered by the blocking features, and

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A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

Fig. 1. View parsing. Both landscape scenes and urban scenes can be parsed into three categories: the part of the scene composed of features which do not block one's movement or vision (dark grey), the part of the scene composed of features which block one's movement and vision (black), and sky (light grey). In urban scenes, the non-blocking features will typically be ¯at, horizontal, solid planes, while the blocking features can be represented as ¯at, vertical, solid planes.

everything else (typically sky). Fig. 1 shows how images of urban and landscape scenes can be parsed into the three categories of ground, blocking features, and other areas (sky). Once an image is parsed into these categories, it is a simple matter to calculate the proportions of the view occupied by each category.1 There are, of course, possible exceptions. Windows are not opaque, and so permit visual but not physical access, and some urban environments (San Francisco, for instance) are built on hills, where the ground surface undulates. These possible re®nements will be discussed afterwards. 1

One simple method for calculating percentages of a view covered by different elements is to scan the view into a bitmap, assign colors to desired categories, count the number of pixels covered by each color, and divide by the total number of pixels in the bitmap.

1.2.2.3. Summary of studies. Table 1 lists findings from previous studies of physical environments which reported dependent variables of rated dominance, power, enclosure, or subjective estimates of how small or large a space appeared, and also reported image data sufficient for calculating the amounts of ground plane and blocking features in each image. For example, Coeterier (1994) had respondents assess the size of 18 landscapes on a scale of 1 (very small) to 100 (very large). Images of the 18 landscapes and the mean estimates of the sizes of the landscapes were published. The present author analyzed each of the 18 images as shown in Fig. 1 and calculated the correlation between areas of ground plane, blocking features, and mean assessments of size of space. The signs of the results were reversed in the present paper in order to make the results comparable to ratings of

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

enclosure rather than openness. The results for the 18 landscapes were, accordingly, r ˆ 0:74 for blocking features, which means that increasing the amount of view occupied by blocking features makes the space seem smaller, and r ˆ 0:83 for ground plane, which means that increasing the amount of ground areas makes the space seem larger. If studies report correlations and sample sizes, it is possible to use statistics to analyze data over more than one study. The statistical method is called metaanalysis.2 For instance, using the data in Table 1, it is possible to calculate collective estimates of the correlations between measure of dominance and either ground plane or blocking features, the 0.05 con®dence intervals on those correlations (0.05 ci), 2

In 1976 (Glass, 1976), coined the term ``meta-analysis'' to describe ``the statistical analysis of a large collection of results from individual studies for the purpose of integrating the findings''. Meta-analysis is an extension of statistical practice from sets of data within an experiment to sets of data from multiple experiments. For instance, an experiment might report a correlation between preferences obtained on-site and preferences obtained from static color simulations of r ˆ 0:50 on an n of 10. Because of the small n, this finding would not reach statistical significance. However, if there were 10 such studies, then the combined finding, now based a collective n of 100, would be significant. Metaanalysis is appropriate when studies report focused (d:f: ˆ 1), effect sizes (correlation, standardized mean difference, odds ratio) and the sample size from which that effect was obtained. Typical outputs from a meta-analysis are the collective effect size, the collective confidence interval, and the size of a study needed to make the collective effect non-significant. Uses for meta-analysis include understanding literatures, planning future research, and mediating scientific disputes scientifically. Since Glass's article, use of meta-analysis has become widespread. A search on the term ``meta-analysis'' in the PsychInfo database during the summer of 2000 found 3206 articles. Meta-analyses have been published on several topics of relevance to landscape planning and management: conservation behavior (deYoung, 1996; Hines et al., 1986±1987; Hornik et al., 1995; Winkler and Winett, 1982; Zelezny, 1999), lighting levels on office task performance (Gifford et al., 1997), alternate scaling methods (Stamps, 1997a), simulation effects (Stamps, 1990), demographic effects on environmental preferences (Stamps, 1999), and managing scientific disputes (Stamps, 1997b). Relevant sources are Light and Pillemer (1984) and, on a slightly more detailed level, Cooper (1989). Basic quantitative protocols are presented concisely by Rosenthal (1991), Hedges and Olkin (1985), and Wolf (1986). Wachter and Straf (1990) and Rosenthal (1998) provide overviews and examples of meta-analyses, and the chapters in Cooper and Hedges (1994) discuss all the steps in metaanalysis at a somewhat more advanced level. Finally, Cook et al. (1994) present an annotated bibliography of books and journals on meta-analysis and a series of very high-end meta-analytic articles.

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and whether the data are suf®ciently similar to justify the assumption that the dependent variables can be used interchangeably. Overall, there is suf®cient data to accept blocking features and ground plane as factors which in¯uence judgments of enclosure (r ˆ 0:80; 0:05 ci ˆ ‰0:69; 0:87Š for blocking features and r ˆ 0:52; 0:05 ci ˆ ‰ 0:68; 0:34Š for ground plane). Homogeneity tests were non-signi®cant for the blocking features (w2 ˆ 8:3 on 5 d.f., a ˆ 0:14), but were marginally signi®cant for the ground plane (w2 ˆ 11:8 on 5 d.f., a ˆ 0:04). The homogeneity tests mean that one cannot reject the assumption that the various dependent measures are interchangeable for blocking features. In less formal terms, it is all right to assume that the measures used for dominance in this review are interchangeable for blocking features. Thus, the empirical literature already suggests that (a) photographic simulations are acceptable substitutes for real environments for the purpose of predicting affective responses, and (b) there are strong relationships between the amount of eye-level view occupied by ground plane or blocking features and subjective impressions of enclosure and spaciousness. 2. Measuring enclosure of urban sites A subsequent step in this line of thought is to develop techniques for ef®cient measurement of amount of eye-level view occupied by ground plane or blocking features over geographical regions which are not visually or physically convex. Because of the concavity, it will be necessary to have methods for calculating proportions of views covered by ground plane or blocking features over many different views. It will be highly desirable to have methods which are ef®cient, because computing time will be proportional to at least the square of the data set, and the size of the data set for a three-dimensional region will be proportional to the cube of the linear resolution, so computational time will be proportional to at least the 6th power of the linear resolution. On the other hand, measuring proportions of views of ground plane and blocking features is apt to be simpler in urban regions than in landscape regions, because urban sites are largely composed of ¯at, opaque planes with discrete edges and with either horizontal (ground) or vertical (wall) orientations.

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A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

Table 1 Previous ®ndings on environmental enclosurea Stimuli

Dependent variable

Independent variable

1 2 3 4 5

Buildings and landscapes Landscapes Line drawings of rooms Landscapes Dense urban areas

Dominance Power Enclosure Perceived smallness Enclosure

Blocking Blocking Blocking Blocking Blocking

features features features features features

0.66 0.95 0.93 0.74 0.73

6

Dense urban areas

Enclosure

Blocking features

0.58

7 8 9 10 11

Buildings and landscapes Landscapes Line drawings of rooms Landscapes Dense urban areas

Dominance Power Enclosure Perceived smallness Enclosure

Ground Ground Ground Ground Ground

plane plane plane plane plane

0.45 0.25 0.18 0.83 0.50

12

Dense urban areas

Enclosure

Ground plane

0.72

a b

r

Nsubj

Nstim

Source

65 18 20 1219 36

13 9 12 18 18

Stamps (1994) Stamps (2000, p. 87) Hayward and Franklin (1974) Coeterier (1994) Stamps and Smith, submitted for publication Stamps and Smith, submitted for publication Stamps (1994) Stamps (2000, p. 87) Hayward and Franklin (1974) Coeterier (1994) Stamps and Smith, submitted for publication Stamps and Smith, submitted for publication

±b 65 18 20 1219 36 ±b

6 13 9 12 18 18 6

The variable r is the product moment correlation, Nsubj is the number of respondents and Nstim is the number of stimuli. The same respondents were used in the preceding experiment.

2.1. Station Point Method One approach to measuring average amounts of eye-level view occupied by different features over a large geographical area is to develop a method for obtaining the required measures at one location, repeating the process over many locations, and averaging the ®ndings to calculate an overall result. Thiel (1997, pp. 203±208) proposed using spherical geometry to represent the environment as it is visible from a particular location. The advantage of a spherical representation, as compared to the more typical image obtained from a camera, is that the spherical representation covers everything visible from a station point, while camera views automatically clip a substantial amount of information. With spherical geometry (Brannan et al., 1999, Chapter 7), any visible object can be projected onto a region on a unit sphere. (In this paper, this unit sphere, centered at a station point, will be called the ``visibility sphere''.) If the projection of an environment completely covers the visibility sphere, then there is complete enclosure. If only half of the visibility sphere is covered, then the environment will be half open. If techniques were available for calculating the amount of a sphere covered by projections of environmental features, then it

would be possible to obtain a measure of degree of enclosure for any desired station point in a site. The appropriate measure is the solid angle subtended by an object from a given distance. The solid angle is linearly dependent on object's height and width. The solid angle is also dependent on the inverse of the square of the distance from the station point to the object. The requisite computer code for calculating solid angles was published by Miller (1994). The spherical measure of enclosure can be implemented through the following steps. Objects in the site are represented in a plan view in bitmap format. Each object has a location in terms of x, y, and z coordinates. In this paper, sites measured 1 km  1 km and the horizontal resolution was set to 1 pixel equals 1 m. If graphical data input is desired, heights can be indicated in colors. In the presented case, 256 colors are used. The height of the station point was set at 1.5 m to represent a typical person. From each station point, imagine a person's gaze revolving around like a lighthouse (Fig. 2, top). The horizontal limits of vision will be bordered by two angles: the low azimuth and the high azimuth. The difference between those two azimuths will be the angle increment. The smaller the increment, the more accurate the measurement. Sensitivity studies indicated that

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

Fig. 2. Measuring blocking features using the Station Point Method. Top: The site plan of an environment is represented as a bitmap. The observer stands at the station point. The observer's gaze revolves around like a lighthouse (the plane sweep) in small increments (the difference between the low and high azimuths, AZM). Bottom: For each increment, objects are mapped onto a lune of a unit sphere and areas of the sky, blocking features, and nonblocking features are calculated using spherical geometry. Summation over all the increments generates measures of sky, blocking features, and non-blocking features as visible from a station point.

increments below 68 generated results which were identical to three decimal places, so an increment of 68 was used in this paper. Also, within each increment, objects may be visible. If so, then there will be one pixel which has the largest vertical angle (altitude) as seen from the station point, and one pixel which has the lowest altitude. The bottom of Fig. 2 shows the relationship between a horizontal cone of vision, a hypothetical sphere, and an object. The cone of vision, de®ned by the low and high azimuth, is mapped onto slices of the

31

sphere. (These slices are called lunes.) Points with the lowest and highest altitude within each cone of vision are mapped onto the surface of the sphere (black area in lune). The area in the lune above the black area represents the sky as seen from the station point, and the area below the sphere represents the non-blocking features as seen from the station point. The last step is to calculate the proportions of the sphere covered by sky, blocking features, and non-blocking features. For this model, a blocking feature is a spherical polygon (that is, a polygon on the surface of a sphere) with four vertexes. The angles of vertexes are all known: they are the low and high azimuth and low and high altitude for the cone. Sky and non-blocking features are spherical polygons with three vertexes. Application of Miller's (1994) code to the three polygons in each lune (two polygons if there are no objects in that lune) produces the areas of sky, blocking, and non-blocking features for the lune; summation over all the vision cones (60 for each station point in this paper) produces the three areas as seen from a given station point, and averaging over all the station points in a site (30 views per site in this paper) produces the average amounts of blocking features and non-blocking features as seen from views within a site. In terms of units, the solid angle subtended by an object as seen from that station point is the proportion of the surface of a sphere. Solid angles are typically measured in SI units of steradians or in English units by spherical degrees. Some readers may ®nd it more convenient to use the proportion of the area of a unit sphere. Since a unit sphere has an area of 4p sr or 720 spherical degrees, it is simple to convert proportions to other units, but usually it is much easier to think of the sky in Kansas as covering half of the visible environment rather than as 6.28 sr or 360 spherical degrees. Thus, using geometry, it is possible to start with a plan view of a site in bit map format in which colors represent heights and to calculate, on average, the proportions of the eye-level views which will be covered by features which do or do not block vision or movement. 2.2. Abstract Method The Station Point Method for estimating amounts of view occupied by different features has the advantage

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A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

of mimicking how people are actually located in a large geographical area, but it is computationally expensive. As the size of the data increases, so does the computation. For the present data, the base map contains 106 elements (1000  1000). If three dimensions are desired, the size of the base data increases to 109, and if higher resolution is desired (10 cm rather than 1 m, for instance), the size of the base data increases to 1012, and the running time is proportional to at least the square of that. Consequently, it would be useful for large-scale users to have access to a more ef®cient way to obtain results, provided, of course, that the more ef®cient way produces the same answers. Geometry provides a possible solution. As was noted above, spherical geometry suggests that the solid angle subtended by an object will be directly proportional to the object's height and width and inversely proportional to the square of the distance from the station point to the object. The question addressed in this section is whether it is also possible to obtain estimates of proportions of views occupied by features which block vision or motion from variables which can be calculated from GIS data. The simplest, most abstract model of features in a given site is that they are all the same size, all the same shape, and all are equidistant from each other. The visual expression of these assumptions generates a hexagonal grid of circles (Fig. 3). The radius of each circle can be calculated directly from the proportion of the site covered by all features and the number of features. For example, if the total area (TA) is 100 m2, the coverage (HC) is 50%, and there are 50 features (number of features, or NF), then all the features cover an area of 50 m2; each feature has an area (feature area, or FA) of 1 m2; and since the area of a circle p ˆ  pr 2 , the radius of the average feature (r) is r ˆ FA=p ˆ 0:564 m. The average distance between features is calculated using the fact that the tributary area for a point in a hexagonal grid is equal to 0.866 times the square of the grid spacing (from plane trigonometry, Abramowitz and Stegun, 1965, Chapter 4). Given the total area of the site (TA), p therefore, the grid spacing is grid ˆ TA=0:866NF. For a site area of 100 m2 and 50 features, the grid size will be 1.52 m. The grid, however, is the distance between the centers of features. In order to ®nd the average distance between features, it is necessary to

Fig. 3. Measuring visible blocking features using the Abstract Method. Top: The assumptions that all objects have the same shape, size, and spacing from each other generates the geometrical interpretation of equal circles in a hexagonal grid. From plane geometry we know that the tributary area of one point in a hexagonal grid equals the grid spacing squared times 0.866. Thus, if we know the total site area and the number of features, we can calculate the grid spacing. If we know how much of the site is covered by features and the number of features, we can calculate the radius of the average feature. Bottom: Once we know the grid spacing and the average radius, we can obtain the average distance between features (d) by subtraction. This distance, plus the average height of features (h), produces a simple model for visible blocking features.

subtract out twice the average radius (Fig. 5, middle). For the example of this paragraph, the average distance between features (d) is 1:52 2  0:564 ˆ 0:392 m. Given the average distance between features, it is simple to calculate the inverse of the square of that distance. The inputs required from a GIS for the purpose of estimating proportions of views occupied by blocking features are (a) total area of the site, (b) amount of the site covered by features, (c) the number of features, and (d) the heights of the features. All these inputs can be readily measured from bit maps of sites. The four inputs are then converted into two variables: average

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

height of features (h), and average distance between features (d), using the equations described in the preceding paragraph. 3. Testing According to the Abstract Method, the proportions of views occupied by blocking features (BLK) should

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be predicable from Eq. (1) 2

BLK  h ‡ d ;

(1)

where h is the average height of features in the geographical region and d is the average distance between features. One way to test how well this equation performs is to create other estimates of proportions of views occupied by blocking features and compare the results

Fig. 4. Sites for the ®rst stimulus set. Site a: suburb in the United States. Sites b and c: college campuses in the United States.

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A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

Fig. 5. Portions of Site c at three heights: height ˆ 6 m (top); height ˆ 12 m (middle); height ˆ 18 m (bottom). Only parts of the site are shown to increase clarity.

of the two methods. Speci®cally, since the Station Point Method also generates estimates of proportions of views occupied by blocking features, it is possible to use the Station Point estimates of proportions of views occupied by blocking features as the dependent variable, the two measures of h and d as calculated from the abstract model as independent variables, and employ regression to determine how well the Abstract Model predicts the results obtained from the Station Point Model. 3.1. First test 3.1.1. Sites Three sites were created using Microstation software. Each site measured 1 km  1 km. One of the sites was based on road patterns in local suburbs. The other two sites were based on campuses of local universities. Buildings were added or deleted to achieve proportions of horizontal coverage (built

area/total area of site) of 0.055, 0.104, and 0.159.3 For each site, the buildings were created at 2, 4, and 6 stories (6, 12, and 18 m), resulting in a balanced experimental design of three horizontal proportions by three heights and a total of nine sites. For these sites, the non-blocking feature was the ¯at, horizontal ground plane, and the blocking features were the solid, opaque, ¯at, vertical walls of buildings. Fig. 4 shows the site plans, Fig. 5 shows axonometric views of a part of Site c, and Fig. 6 shows views of Sites a, b, and c as images obtained by a 35 mm camera with a 28 mm lens. 3.1.2. Views A random number routine selected thirty station points within each of the nine sites, so there was a 3 There is nothing special about the value of 0.055. It happened to be the horizontal coverage of the first site investigated. The horizontal coverages of the other sites were adjusted to be integral multiples of 0.055 in order to match the integral multiples of the heights.

Fig. 6. Images of Site a (top row), Site b (middle row) and Site c (bottom row) at three heights (6, 12 and 18 m) as visible by a 35 mm camera with a 28 mm lens. Table 2 Data for the ®rst experimenta Stim

Site

HC

NF

h

Station Point Method BLK1

1 2 3 4 5 6 7 8 9

a a a b b b c c c

0.055 0.055 0.055 0.108 0.108 0.108 0.159 0.159 0.159

268 268 268 30 30 30 80 80 80

6 12 18 6 12 18 6 12 18

Abstract Method BLK1

m

s

m

s

0.052 0.089 0.122 0.026 0.044 0.081 0.070 0.075 0.096

0.042 0.080 0.075 0.028 0.064 0.095 0.081 0.073 0.076

0.488 0.485 0.487 0.494 0.493 0.490 0.483 0.489 0.490

0.011 0.018 0.009 0.006 0.010 0.016 0.024 0.013 0.008

d

BLK2

49 49 49 129 129 129 69 69 69

0.066 0.091 0.116 0.030 0.055 0.081 0.045 0.070 0.095

a ``Stim'' indicates the stimulus. ``Site'' indicates which of three site plans (a, b, or c) was used in the stimulus. ``HC'' is the horizontal coverage of the site. ``NF'' is the number of features in the site. ``h'' is the average height of features in the site. ``Station Point Method'' is the ®rst method used to estimate proportions of views occupied by either blocking features (BLK1) or non-blocking features (BLK1). ``m'' is the mean. ``s'' is the standard deviation. Abstract Method is the second method used to estimate proportions of views occupied by blocking features. ``d'' is the average distance between blocking features as calculated using the Abstract Method. The last column is the estimate of proportions of views occupied by blocking features (BLK2) as calculated by the Abstract Method.

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total of 270 views. Amounts of non-blocking features and blocking features were measured as solid angles subtended from each station point. Table 2 lists the relevant variables from the 270 views. The suburban site (Site a) had a horizontal coverage of about 5%, 268 features, and an average distance between features of 49 m. The campus sites (Sites b and c) had larger horizontal coverages (about 10 and 15%), fewer features (30 and 80), and larger average distances between features (129 and 69 m). 3.1.3. Results One result was immediately obvious from the data in Table 2: there was almost no variation in amount of ground for these stimuli. There was no evidence to suggest that the proportion of views covered by ground was related to the low density of the buildings (r ˆ 0:05, t ˆ 0:35, a ˆ 0:73). Accordingly, the variable of ground was dropped. Table 3 shows the regression between proportion of view covered by blocking features as measured from the Station Point

Table 3 Regression for the ®rst experimenta Source

d.f.

SS

ms

F

a

h d Residual

1 1 6

0.037 0.019 0.010

0.037 0.019 0.0017

20.7 10.6

0.003 0.017

Total

8

0.067

a

The dependent variable was the proportion of eye-level views occupied by blocking features as calculated by the Station Point Method. The independent variables were estimates of average height (h) and average distance between features (d) as estimated by the Abstract Method.

Method and as measured from the Abstract Method. The multiple correlation was R ˆ 0:92. 3.2. Replication A second set of sites was created in order to determine if the preceding results could be replicated

Table 4 Data for the second experimenta Stim

Site

HC

NF

h

s(ht)

Station Point Method BLK1

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

d d d d e e e e f f f f g g g g

0.343 0.343 0.343 0.343 0.444 0.444 0.444 0.444 0.558 0.558 0.558 0.558 0.811 0.811 0.811 0.811

100 100 100 100 102 102 102 102 70 70 70 70 86 86 86 86

15.8 16.2 32.4 31.0 15.9 14.7 32.3 31.5 17.4 17.1 33.2 31.6 15.4 15.9 31.8 32.0

2.70 6.17 2.49 8.00 2.71 6.67 3.21 6.23 3.60 6.46 2.78 5.94 3.19 6.72 2.69 7.57

Abstract Method BLK1

m

s

m

s

0.314 0.330 0.395 0.310 0.354 0.307 0.399 0.409 0.339 0.313 0.419 0.427 0.542 0.416 0.586 0.544

0.153 0.137 0.125 0.145 0.113 0.092 0.138 0.093 0.142 0.130 0.131 0.124 0.068 0.049 0.028 0.074

0.447 0.441 0.449 0.460 0.440 0.451 0.404 0.443 0.445 0.447 0.436 0.438 0.380 0.370 0.381 0.393

0.035 0.036 0.037 0.034 0.028 0.025 0.032 0.027 0.038 0.031 0.039 0.033 0.022 0.022 0.017 0.027

d

BLK2

41 41 41 41 32 32 32 32 27 27 27 27 6 6 6 6

0.318 0.320 0.394 0.388 0.321 0.316 0.396 0.392 0.331 0.329 0.402 0.395 0.483 0.486 0.558 0.559

a ``Stim'' indicates the stimulus. ``Site'' indicates which of four site plans (d, e, f, or g) was used in the stimulus. ``HC'' is the horizontal coverage of the site. ``NF'' is the number of features in the site. ``h'' is the average height of features in the site. ``s(ht)'' is the standard deviation of height within the stimulus. ``Station Point Method'' is the ®rst method used to estimate proportions of views occupied by either blocking features (BLK1) or non-blocking features (BLK1). ``m'' is the mean. ``s'' is the standard deviation. Abstract Method is the second method used to estimate proportions of views occupied by blocking features. ``d'' is the average distance between blocking features as calculated using the Abstract Method. The last column is the estimate of proportions of views occupied by blocking features (BLK2) as calculated by the Abstract Method.

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

37

Fig. 7. Sites for the second stimulus set. Sites in the top row are based on maps of Edinburgh (Collins, 1999, p. 12 and 19) # Bartholomew Ltd. 2001, reproduced by Kind Permission of HarperCollins Publishers. Sites in the bottom row are based on Paris (Michelin, 2000, p. 15 and 21). # MICHELIN from Michelin Atlas by Arrondissements, Permission No. 01-US-004.

under other conditions. The sites (d±g) were obtained from random samples of maps of Edinburgh (Collins, 1999) and Paris (Michelin, 2000). There were two site plans in each city. Each site measured 1 km  1 km. Horizontal coverages were 34.3, 44.4, 55.8, and 81.1%. There were two height factors: average height (16 or 32 m) and variation in height (standard deviations of 3 or 6 m within each site). The experimental design was, accordingly, a 4  2  2 factorial, for a total of 16 sites. There were 30 station points in each

site, for a total of 480 views. Table 4 lists the variables for the sites. Fig. 7 shows the site plans, Fig. 8 shows versions of a part of Site d at all four combinations of heights and standard deviations of heights, and Fig. 9 shows images of Sites d±g as they would appear by a 35 mm camera with a 28 mm lens. For these sites, the horizontal coverages ranged from 30 to 80%, the number of features was in the range of 70 to 100, and the average distance between features ranged from 41 m down to 6 m.

38

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

Fig. 8. Portions of Site d at four combinations of height and variation in height: average height ˆ 12 m, s ˆ 3 m (top row); average height ˆ 12 m, s ˆ 6 m (second row); average height ˆ 32 m, s ˆ 3 m (third row); average height ˆ 32 m, s ˆ 6 m (bottom row). Only parts of the site are shown to increase clarity.

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

39

Fig. 9. Images of Site d (top left), Site e (top right), Site f (bottom left) and Site g (bottom right) as visible by a 35 mm camera with a 28 mm lens. The clipping effect is obvious in these images.

4. Results and discussion

4.1. Additional terms

Table 5 shows the regression between proportion of view covered by blocking features as measured from the Station Point Method and as measured from the Abstract Method. The multiple correlation was again R ˆ 0:92. The correlation between the proportion of views covered by ground and building density was, again, very low (r ˆ 0:02, t ˆ 0:28, a ˆ 0:78).

Since geographical information systems typically provide a large number of variables, it might be supposed that adding additional variables to the Abstract Method would generate better results. There is a reason why adding more variables might be counter-productive. For example, in the ®rst data set, the multiple R can be increased from 0.92 to 0.95 by adding the variables of horizontal coverage and number of features to the regression in Table 3. However, the appropriate statistical method for deciding if one regression model is better than another is to calculate if the new variables increase the squared multiple correlation by a statistically signi®cant amount (Namboodiri et al., 1975; Overall and Klett, 1972). The difference in ®t due to the horizontal coverage and number of features for the ®rst data set did not achieve statistical signi®cance (F2;4 ˆ 0:67, a ˆ 0:53), which means that the apparent increase in ®t from R ˆ 0:92 to 0.95 was attributable to random variation. Conclusions based on the apparent increase

Table 5 Regression for the second experimenta Source

d.f.

SS

ms

F

a

h d Residual

1 1 13

0.021 0.080 0.018

0.021 0.080 0.001

15.1 57.7

0.001 3E 6

Total

15

0.119

a

The dependent variable was the proportion of eye-level views occupied by blocking features as calculated by the Station Point Method. The independent variables were estimates of average height (h) and average distance between features as estimated by the Abstract Method (d).

40

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

in ®t due to these variables would be classic alpha errors (false positives). This problem is often called ``over®tting''. Over®tting can be avoided by conducting focused experiments and by not multiplying terms beyond necessity. 4.2. Amount of ground and building density In neither experiment there was a relationship between proportion of ground visible in spherical representations of views and the horizontal coverage of features on the sites (r's of 0.02 and 0.05). This may be due to the fact that the spherical representation of a view includes far more ground than is visible in typical views and the scale of the sites. Images obtained from the cameras with horizontal directions of views are typical views. Examples of these types of views can be seen in Figs. 1, 6, and 9. There is a substantial amount of clipping in a typical view. In the spherical representation, the whole ground surface is represented. For instance, if a station point is located 1.5 m above the center of a horizontal disk, and the radius of the disk is 3 m, then the disk would cover about 23% of the visibility sphere. A disk of 5 m radius would cover about 32%, a disk of 10 m would cover about 40%, and a disk of in®nite radius would cover 50%. Given that the average distances between features in the presented cases were usually over 10 m, geometry indicates that the spherical representation of ground planes would not have much variation. There should be larger effects between horizontal coverage and the spherical representation of ground planes for much smaller regions, such as gardens, courtyards, or rooms. 5. Summary, conclusions, and opportunities The literature on environments, evolution and affect suggests that enclosure is very important in environmental perception and preference and that there is a strong relation between the proportion of a view covered by elements which block vision or motion and subjective impressions of enclosure. Accordingly, proportions of views covered by features which block vision or motion is necessary (although perhaps not suf®cient) as a physical index of amount of subjective impression of enclosure. Accordingly, researchers, designers, or managers who work on large geographic

regions would ®nd it useful to have methods for ef®ciently calculating degrees of enclosure. Two such methods were presented in this paper. The Station Point Method calculates spherical angles of blocking features as they would appear at a point in the region. The Abstract Method calculates two variables (average height and average distance between objects) from GIS data. Both methods generated the same estimates of proportion of view occupied by features which block movement or vision (R ˆ 0:92) over several different site factors (horizontal coverage ranging from 5 to 80%, heights ranging from 6 to over 32 m, average distances between objects of 6 m (medieval section of Paris) to 129 m (college campus in the United States), and standard deviations in heights from none to s ˆ 6 m. Future work might include applications of either the Station Point or the Abstract Method to issues of landscape or urban design management. For instance, it may be that policy requires retention of the identity of a geographical region, and the identity may be contingent on the enclosure or spaciousness of that region. An example of this application is given in Palmer and Lankhorst (1998). Other future work might include additional validation of the relationship between features which block vision or motion, features which do not block vision or motion, and subjective impressions of enclosure, or application of Eq. (1) to landscapes. The current ®ndings on the relationship between features which block vision and subjective impressions of enclosure are fairly solid (as indicated by the 0.05 con®dence interval on the collective correlation of [0.69, 0.87]), and so it will dif®cult to change the collective result with new data. However, the collective 0.05 ci for ground planes is much wider ([ 0.68, 0.34]), so that issue is more likely to reward current inquiry. Another opportunity for future work is to enlarge the number of parameters in the spherical model of environmental representation. One such parameter is curvature in the ground plane. Two other possible parameters are distance to objects and materials of objects. For instance, it may (or may not) be the case that judged enclosure will differ according to distance, even if the solid angles subtended are held constant. The implication would be whether the solid angle model holds over different scales such as rooms, courtyards, plazas,gardens,parks,andlandscape

A.E. Stamps III / Landscape and Urban Planning 57 (2001) 25±42

vistas. It may also be the case that people would feel less con®ned if the surface were living (hedges) rather than inanimate (brick walls). The azimuth (which re¯ects whether an object is in front of, on the side of, or behind the observer) may matter, or the altitude (below, at eye-level, above) may be important. For these questions, it is simply too soon to tell. References Abramowitz, M., Stegun, I.A. (Eds.), 1965. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York. Appleton, J., 1996. The Experience of Landscape. Wiley, New York. Berlyne, D.E., 1973. Interrelations of verbal and nonverbal measures used in experimental aesthetics. Scand. J. Psychol. 14, 177±184. Berlyne, D.E., 1974. Verbal and exploratory responses to visual patterns varying in uncertainty and in redundancy. In: Berlyne, D.E. (Ed.), Studies in the New Experimental Aesthetics: Steps Toward an Objective Psychology of Aesthetic Appreciation. Wiley, New York, pp. 121±158. Brannan, D.A., Esplen, M.F., Gray, J.J., 1999. Geometry. Cambridge University Press, Cambridge, MA. Bush, L., 1973. Individual differences multidimensional scaling of adjectives denoting feelings. J. Person. Social Psychol. 25 (1), 50±57. Coeterier, J.F., 1994. Cues for the perception of the size of space in landscapes. J. Environ. Manage. 42, 333±347. Cohen, J., 1988. Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum Associates, Hillsdale, NJ. Cohen, J., Cohen, P., 1993. Applied Regression/Correlation Analysis for the Behavioral Sciences. Lawrence Erlbaum, Hillsdale, NJ. Collins, 1999. Edinburgh Street®nder Color Atlas. HarperCollins, London. Cook, T.D., Cooper, H., Cordray, D.S., Hartman, H., Hedges, L.V., Light, R.J., Louis, T.A., Mosteller, F. (Eds.), 1994. MetaAnalysis for Explanation. Russell Sage, New York. Cooper, H., 1989. Integrating Research: A Guide for Literature Reviews. Sage, Newbury Park, CA. Cooper, H., Hedges, L.V. (Eds.), 1994. The Handbook of Research Synthesis. Russell Sage, New York. Crozier, J.B., 1974. Verbal and exploratory responses to sound sequences varying in uncertainty level. In: Berlyne, D.E. (Ed.), Studies in the New Experimental Aesthetics: Steps Toward an Objective Psychology of Aesthetic Appreciation. Wiley, New York, pp. 27±90. Darwin, C., 1887. The Autobiography of Charles Darwin (1993 Edition). W.W. Norton, New York. Davidson, R.J., Jackson, D.C., Kalin, N.H., 2000. Emotion, plasticity, context, and regulation. Perspectives from affective neuroscience. Psychol. Bull. 126 (6), 890±909.

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Wachter, K.W., Straf, M.L. (Eds.), 1990. The Future of MetaAnalysis. Russell Sage Foundation, New York. Winkler, R.C., Winett, R.A., 1982. Behavioral interventions in resource conservation: a systems approach based on behavioral economics. Am. Psychol. 37 (4), 421±435. Wolf, F.M., 1986. Meta-Analysis: Quantitative Methods for Research Synthesis, Vol. 59. Sage, Newbury Park, CA. Wright, B., Rainwater, L., 1962. The meanings of color. J. Gen. Psychol. 67, 89±99. Zelezny, L.C., 1999. Educational interventions that improve environmental behaviors: a meta-analysis. J. Environ. Educ. 31 (1), 5±14. Arthur E. Stamps obtained his PhD from U.C. Berkeley in 1980. Although the degree was given by the Department of Architecture, his research is based on work done on statistics in the Psychology Department, Social Systems Design in the Graduate School of Business, and futures research in the Department of City Planning. He has published over 60 articles in the scientific or professional presses, given presentations at over 20 conferences, and is an associate editor for a psychology journal. A detailed overview of this work, covering over 275 studies, 41,000 respondents, and 12,000 stimuli has been published in book form (Stamps, A.E., 2000. Psychology and the Aesthetics of the Built Environment. Kluwer Academic Publishers, Norwell, MA). He is currently doing research on environmental perception and preference and urban design principles at the Institute of Environmental Quality in San Francisco.