A geographical approach to identifying vegetation ...

Environment and Planning B: Planning and Design 2010, volume 37, pages 1040 ^ 1056

doi:10.1068/b36044

A geographical approach to identifying vegetation-related environmental equity in Canadian cities Thoreau R Tooke

Department of Forest Resources Management, 2424 Main Hall, University of British Columbia, Vancouver V6T 1Z4, Canada; e-mail: [email protected]

Brian Klinkenberg

Department of Geography, 1984 West Mall, University of British Columbia, Vancouver V6T 1Z4, Canada; e-mail: [email protected]

Nicholas C Coops

Department of Forest Resources Management, 2424 Main Hall, University of British Columbia, Vancouver V6T 1Z4, Canada; e-mail: [email protected] Received 4 April 2009; in revised form 18 December 2009; published online 18 August 2010

Abstract. The research in this paper addresses human ^ environment interactions in Canadian cities by examining the spatial distribution of vegetation in relation to various socioeconomic indicators. Specifically, intercity and intracity comparisons are evaluated using correlation analysis and geographically weighted regression (GWR). Vegetation abundance estimates derived from spectral mixture analysis of Landsat imagery are compared with Canadian census data for the cities of Montreal, Toronto, and Vancouver to quantify vegetation-related environmental equity in Canada's largest urban centres. Results exhibit strong and consistent correlations between median family income and vegetation fraction for Montreal (r 0:473), Toronto (r 0:467), and Vancouver (r 0:456). Furthermore, examining the GWR results suggests that employing an adaptive bandwidth kernel technique with a manual selection of ten neighbours for each observation provides a greater range and higher median values for local regression estimates (Montreal: 0.69; Toronto: 0.74; Vancouver: 0.73) as compared with the Akaike information criterion-selection method. Finally, we discuss the potential application of the presented analysis techniques for urban planning and community-development initiatives, specifically associated with managing vegetation-related environmental equity at various scales. Possible applications of these techniques for urban planning purposes are discussed, and key methodological considerations for performing such an analysis are highlighted.

Introduction The notion of environmental equity was first raised by leaders in the civil rights movements in the 1960s. It did not receive significant public attention, however, until the 1980s when the release of several landmark studies highlighted the increased exposure to hazardous wastes faced by minority-dominated communities in the United States (UCC, 1987; USGAO, 1983). Since the publication of those reports many academic studies and government initiatives have recommended and implemented initiatives to promote environmental equity. Recently, the term environmental equity has been conventionally replaced by environmental justice, the definition of which includes the specification of both distributive justice (the distribution of environmental quality across space) and procedural justice (the access of citizens to environmental planning processes) (Holifield, 2001). In this paper we use the more primary term ènvironmental equity' since our research is explicitly concerned with the distribution of vegetation across urban environments. Furthermore, the research in this paper addresses outcome equity (Cutter et al, 1996) by quantifying the spatial distribution of environmental benefits. Much of the early literature examining environmental equity in the US has tended to focus on the distribution of environmental burdens; namely toxic and hazardous

Identifying vegetation-related environmental equity

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waste emissions (Anderton et al, 1994; Bowen et al, 1995; Cutter et al, 1996; Jerrett et al, 1997). Similar studies relating hazardous emissions and socioeconomic status have also been examined in Canadian cities (Buzzelli et al, 2003; Jerrett et al, 1997; Jerrett et al, 2001); however Su et al (2009) note that environmental inequities in Canada are observed not in terms of race, as in the paradigm in many US cities, but in terms of areas characterized by low incomes. Urban areas in Canada provide an optimal forum for analyzing environmental equity due to the heterogeneous composition of both the anthropogenic and biogenic components of these landscapes. In addition, over 75% of Canadians reside in urban areas, with the health and wellbeing of these residents dependent on the quality of their local environments (Brulle and Pellow, 2006; Comber et al, 2008). One of the critical indicators of the urban quality of life in Canada is the abundance and distribution of vegetation. For example, areas with parks, street trees, and lawns have been demonstrated to produce spaces with positive social outcomes including reductions in crime (Kuo and Sullivan, 2001), increased health benefits (Coen and Ross, 2006), and advanced childhood development (Taylor et al, 1998). Therefore, understanding the distribution of vegetation across the city in relation to socioeconomic indicators is essential to mitigate urban environmental inequalities. Recent studies relating the distribution of vegetation to socioeconomic data have extended the application of remote-sensing products, GIS, and spatial statistics to urban planning and policy-related research. A number of motivating factors have driven this trend in land-use planning, including advances in computational technologies, global increases in urbanization, and an increased recognition that vegetated areas in cities have important associated social benefits (Comber et al, 2008; Grove et al, 2006). One common approach to assessing the relationships between socioeconomic variables and vegetation has been to integrate national census data with vegetation estimates derived from remotely sensed imagery. Remote-sensing technologies, namely satellite multispectral data, provide effective and efficient methods for monitoring vegetated features of urban surfaces. These technologies offer advantages over field-based surveys by enabling spatial coverage and frequent data collection over many inaccessible areas at a relatively low cost. In recent decades remote sensing has been applied to various urban-vegetation analyses, and applications continue to evolve alongside technological advancements. Early studies exploring environmental equity in relation to vegetation cover derived from remote-sensing datasets have focused on correlations with socioeconomic data representing income (Jensen et al, 2004; Li and Weng, 2007; Lo and Faber, 1997; Mennis, 2006a), housing values (Li and Weng, 2007; Lo and Faber, 1997; Jensen et al, 2004), education (Li and Weng, 2007; Lo and Faber, 1997; Mennis, 2006a), and minority status (Mennis, 2006a). In the majority of these studies the correlations tend to be strongest between vegetation and income, with r-values ranging from 0.27 (Mennis, 2006a) to 0.56 (Lo and Faber, 1997). Employing a global statistic, as in the studies mentioned above, provides insightful information regarding the overall environmental equity within a city; however urban areas are heterogeneous environments well suited to locally focused analyses (Mennis, 2006b; Mennis and Jordan, 2005). Specifically, when conducting geographic studies in urban areas it is important to consider that spatial analysis using a global statistic can result in an oversimplification of the relationships across space, consequentially neglecting informative internal variability between ecological and socioeconomic variables (Brundson et al, 2002; Openshaw, 1991). In response to issues of spatial nonstationarity in the strength of the relationship between vegetation and socioeconomic variables recent studies have employed geographically weighted regression (GWR) as a local regression technique

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T R Tooke, B Klinkenberg, N C Coops

to help quantify intracity variations (Lafary et al, 2008; Ogneva-Himmelberger et al, 2009). Furthermore, the benefits of using GWR have been demonstrated not only as a model for quantifying the internal variability of relationships between greenness and many of the socioeconomic variables highlighted in previous studies, but also as a technique for effective visualization of human ^ environment interactions in urban areas (Lafary et al, 2008). In this study, our objective is to elaborate upon processes for assessing spatial aspects of environmental equity within the context of vegetation distribution in major Canadian cities. To accomplish this objective we apply novel techniques for extracting vegetation estimates from satellite imagery while focusing on both intercity and intracity variations in the relationships between vegetation and socioeconomic status. Using vegetation abundance estimates from Landsat satellite imagery we assess all urban vegetation, recognizing that the range of benefits originating from environmental amenities can be derived from both public and private spaces. Using socioeconomic variables from Canadian census data for Montreal, Toronto, and Vancouver, we then quantify the relationship with vegetation estimates (1) between citiesöusing correlation analysis; and (2) within each city öusing GWR. This study endeavors to emphasize those factors that appear to support environmental inequality in major Canadian cities while contributing novel geographic methods for informing initiatives to ensure the equitable distribution of vegetation in urban areas. Study area The cities of Montreal, Toronto, and Vancouver were selected as study areas for this analysis (figure 1) as they represent the largest urban populations in Canada and contain a variety of vegetated areas. Major urban parks are present in all three cities as well as a wide range of land-cover types and building densities. Significant international migration to Canada in the last fifty years has resulted in these three cities representing important examples of multicultural urban centers with social, cultural, and economic diversity. In addition, all three cities have been recognized as world cities by the Globalization and World Cities Group and Network (http://www.lboro.ac.uk/ gawc) as a result of their direct cultural, political, or economic influence on global affairs. Montreal is the second largest city in Canada and the most eastern in this study. Located in the province of Que¨bec and situated on the Island of Montreal at the confluence of the Saint Lawrence and Ottawa Rivers, Montreal has a variable climate with abundant precipitation and average daily temperatures that vary between ÿ15 8C in winter to 27 8C in summer. The urbanized core of Montreal is concentrated in the center and east of the island, while the west of the island is characterized by lower population densities and more vegetated areas. The general socioeconomic trend in Montreal involves a concentric pattern with wealthier residents located in the central parts of the city. This study includes the entire island in the analysis as it forms an easily recognizable and cohesive geographic boundary. The city of Toronto is Canada's largest urban area and represents the dominant economic centre in Canada. Toronto, situated around the north shore of Lake Ontario, is located in the highly urbanized region of Southern Ontario and experiences a slightly milder climate than Montreal. Toronto has been recognized as one of the world's most diverse cities and is an important destination for immigrants to Canada. The general socioeconomic trend is characterized as an east ^ west divide with more affluent residents residing in the western regions of the city. The bounding area for this study represents the census metropolitan area (CMA) and includes the districts of East York, Etobicoke, North York, Old Toronto, and Scarborough, and York.


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1000 km

Data withheld for privacy purposes

0

10

20 km

Figure 1. Location of study-area sites within Canada and the census tract boundaries.

Vancouver is the third largest city in Canada and is located on the western coast of mainland British Columbia. Vancouver's climate is significantly milder than those of Montreal and Toronto, which results in vegetated areas remaining green for a majority of the year. The city is ethnically diverse and continues to receive global attention as a result of its urban planning initiatives and the 2010 Winter Olympics. Similar to Toronto, Vancouver is characterized as having a pronounced east ^ west divide with affluent residents located in the west. Due to data limitations only a portion of the Vancouver CMA was analyzed, although the area considered represents the significant urban core including Vancouver, Burnaby, and New Westminster. Data Satellite imagery

Landsat 7 Enhanced Thematic Mapper (ETM) summer images were obtained for each of the three cities between 1999 and 2001 (table 1). These images represent times in the year when the vegetation exhibits full leaf-on conditions and as a result Table 1. Acquisition information for Landsat 7 Enhanced Thematic Mapper images. City

Date

Raw image number

UL latitude

UL longitude

Montreal Toronto Vancouver

4 August 2001 2 September 1999 30 July 2000

LE7013027000121650 LE7018030009924650 LE7047026000021250

48.403 44.121 49.824

ÿ71.824 ÿ81.012 ÿ123.783

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captures the maximum multispectral channels, the spectrum, is 30 m. each satellite image to reflectance between the


cover of vegetation in each city. The spatial resolution of the ranging from the visible to the shortwave infrared region of A top-of-atmosphere calibration correction was applied to remove the effects of solar elevation and to standardize the scenes (Ouaidrari and Vermote, 1999).

Census data

Socioeconomic data closely matching the collection date of the satellite images are available from Statistics Canada 2001 census data (http://www.statcan.ca). Census tracts (CTs) provide the geographical boundaries for observation and are recognized as relatively stable geographic areas that contain between 2500 and 8000 people. CTs are the second smallest units for which data is disseminated in Canada and are located within larger census metropolitan areas and census agglomerations. In addition, for privacy purposes some CTs are subjected to area suppression, which removes all characteristic data for geographic areas with populations below a specified size. CTs that were included in the analysis for all three cities, and those CTs whose data have been suppressed, are displayed in figure 1. The socioeconomic variables used in this analysis were selected according to their representation of critical indicators of environmental equity including income, education, family status, and immigrant status. Income from Canadian census data is represented as average and median values and for individuals and families. As a result, four combinations of income representations are available, each requiring a unique interpretation. Average income provides an appropriate representation of the total income within the geographically bounded area, while median income values are a closer representation of the actual received income for the majority of the population. In addition, summarizing income data for the individual provides an indication of the income distribution throughout the entire population, while summarizing income data for families provides an indication of the economic wellbeing of households. Income variables initially selected for analysis include average individual income (AVG INC), median individual income (MED INC), average family income (AVG FAM INC), median family income (MED FAM INC), and the percentage of low income individuals (LOW INC), which is defined as those respondents who spend 20% or more of their average income on food, shelter and clothing. Education variables report the highest level of attained education and include no high school (NO HS), high school (HS), college certificate (CLG CERT), and bachelor degree (BAC). Family status relates to children and includes families and individuals with no children (NO CHILD) and the average number of children per household (CHILD P FAM). Finally, immigrant status is analyzed according to whether respondents recognized themselves as nonimmigrant (NON IMG) or Canadian (CDN). Methods Linear spectral-mixture analysis (SMA)

In the last decade SMA has become the primary method for extracting multiple land covers from a single pixel value over urban areas (Rashed et al, 2001; Ridd, 1995; Small, 2001; Tooke et al, 2009). The approach allocates a representative fraction of selected endmember spectra to each pixel of an image. Each endmember represents a land cover with uniform spectral properties, and linear mixing assumes that the spectral-reflectance profile of each pixel can be described as a linear combination of the selected endmembers (Goodwin et al, 2005). Early urban land-cover classifications using SMA were originally proposed according to Ridd's (1995) vegetation-impervious surface-soil classification scheme.


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This scheme provides a conceptual model that divides urban environments into the three classes; however, the approach is problematic in a remote-sensing context as it represents features that cannot necessarily be distinguished on the basis of reflectance values alone (Phinn et al, 2002; Powell et al, 2007). As a result, Small (2001) developed a more applicable model that establishes substrate, vegetation, and dark (SVD) features of the urban environment as components for SMA. Using the SMA process, accurate SVD fractions have been obtained from Landsat 7 ETM imagery (Small and Lu, 2006) and derived for a number of major cities across the globe (Small, 2001). The SMA process involves several steps including transformations to remove noise correlations between bands and a projected six-dimensional scatterplot of the extreme image-reflectance values used to establish endmembers. When selecting image endmembers across several urban landscapes it is important that the spectral signatures of the selected endmembers resemble actual SVD features. The selected endmember spectra for Montreal, Toronto, and Vancouver are plotted in figure 2 to help demonstrate the coherence between images and SVD features. The final step in the SMA procedure is to produce fractional images of SVD features that can be used for further analysis. To generate fractional images with meaningful values sum-to-unity and sum-to-positivity constraints were applied to the analysis, and fractional images were produced for each of the SVD features. As the dark fractional images contain shadow (Small, 2001; Tooke et al, 2009) further analyses using this feature are limited; however, substrate and vegetation fractions can be correlated with other geographic data in order to explore a variety of spatial processes in urban areas (Li and Weng, 2007; Mennis, 2006a). The vegetation fractional images for Montreal, Toronto, and Vancouver are depicted in figure 3.

0.2

(c)

2215

1650

830

(b)

0.4

485 560 660

0.1

Wavelength (nm)

0.3 Substrate

0.2

Vegetation

Dark

2215

1650

0.1

485 560 660

Reflectance value

(a)

0.3

830

Reflectance value

0.4

Wavelength (nm)

Figure 2. Endmember spectra derived from spectral-mixture analysis for (a) Montreal, (b) Toronto, and (c) Vancouver.

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25 km

(a)

(b)

(c)

0

% Vegetation

100

Figure 3. Spectral-mixture-analysis derived vegetation fractional images for (a) Montreal, (b) Toronto, and (c) Vancouver.


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GWR

To quantify relations between land cover and socioeconomic data, spatial statistics are often applied in order to enable meaningful comparison. GWR is an emerging statistical method for analyzing spatially dependent relationships between variables that is becoming increasingly popular for urban geographic analysis (Lafary et al, 2008; Ogneva-Himmelberger et al, 2009) and is now available in many GIS-software packages. Traditional global regression models summarize statistics across an entire area, ignoring any underlying spatial variability. In reality, many processes are spatially nonstationary, resulting in the same independent variable potentially producing different responses across an area of study (Fotheringham et al, 2002). GWR accounts for this spatial variability by extending regular regression, calculating local parameter estimates for every observation using a distance-weighting function. Aspatial regression is expressed as X yî b0 bk xik ei , (1) k

where y^ is the estimated value of the dependent variable for observation i, b0 is the intercept, bk is the parameter estimate for variable k, xik is the value of the kth variable for i, and ei is the error term. To calculate local parameter estimates GWR generates a separate regression equation for each observation using a distance-dependent weighting of the observations contained in the dataset. Each GWR equation can be expressed as X yî b0 ui , ni bk ui , ni xik ei , (2) k

where (ui , ni ) captures the geographical coordinate location of i (Fotheringham et al, 2002). The weight assigned to each observation is based on a distance-decay function centered on observation i (Mennis, 2006b). GWR is particularly useful for studying spatial relationships in urban areas due to the heterogeneous composition of these environments (Mennis and Jordan, 2005). Many of the processes in urban areas are present at a household, block, or neighborhood scale, and using global regression models with spatially rich urban data neglects the potential significance of the underlying spatial variability. In GWR the bandwidth selection is an essential component of the methodology and should be determined according to the objectives of the user. Two styles of bandwidth are available in GWR: a fixed-distance kernel that uses a constant radius centered on each observation to select variables for the analysis, or an adaptive kernel that selects a constant number of neighbors for analysis regardless of distance. In our model we apply an adaptive kernel due to the range in CT sizes that discourage the use of a fixed-distance kernel. For example, the smallest CT in all three cities is 0.02 ha and the largest 2901.6 ha. Such a discrepancy in size would require a fixed bandwidth so large that the results of the GWR would come close to approximating those of a global aspatial regression model. Furthermore, we argue that smaller CTs tend to be located in areas with higher population densities, and therefore people are generally in a position to travel less distance to access basic services, and vice versa for larger CTs. As a result, selecting an adaptive bandwidth inherently acknowledges the realistic distance people regularly travel in relation to their home. After selecting the appropriate bandwidth type, the next step is to assess the number of neighbors that will be used in the regression model at each observation. Techniques, such as cross-validation and Akaike information criterion (AIC), can be used to determine automatically an optimal value for the bandwidth. In contrast,

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Table 2. Geographically weighted regression results for Montreal, Toronto, and Vancouver. Manual bandwidth selection

AIC a bandwidth selection



Number of neighbors 10 0.69 Median local r 2 0 Minimum local r 2 0.99 Maximum local r 2 Monte Carlo p-value < 0.000 a Akaike information criterion.

10 0.74 0.02 0.99 < 0.000

10 0.73 0 0.98 0.95

68 0.34 0.03 0.84 < 0.000

27 0.43 0.01 0.90 < 0.000

24 0.51 0.02 0.85 0.26

the user may specify the bandwidth value that is appropriate for the analysis in question. As a methodological step in this paper we examine and compare both AIC and manual approaches (using ten neighbours) for determining bandwidth values. Since the manual approach demonstrates a greater range in local r 2 values and higher median local r 2 value for each city (table 2), and as a result of its ability to provide a consistent and consequently comparable value across all three cities, this method is utilized for all further GWR models in our study. To select the appropriate variables for analysis multivariate statistics are applied to the initial set of socioeconomic variables with the purpose of isolating single variables that best represent important census characteristics that can be related to the distribution of vegetation. Furthermore, multivariate statistics help in determining those variables that exhibit multicollinearity; a necessary process to ensure that the GWR is properly specified. In our study we apply factor analysis; a technique commonly used in social sciences to enable the identification of groups of elements that can be synthesized into clearly discernable factors. The final step in performing GWR is to test the results to ensure that the model is correctly specified. Several methods can be used to test the validity of the GWR model; Monte Carlo simulations and testing for spatial autocorrelation being two common techniques (Getis, 2007). In this paper, Monte Carlo simulations are used to generate models repeatedly with randomized spatial locations for each observed variable. The results of the simulated models are then compared with the original model to determine the probability of the GWR results demonstrating spatial nonstationarity. Data integration

The socioeconomic variables used in the analysis were joined with the relevant geographic boundaries and non-percentage-based variables were standardized using the total population, total households, or total families for each CT depending on the selected variable. Vegetation and substrate fractions were then summarized for each CT polygon and the mean values were calculated to provide an indication of vegetated and impervious land-surface cover. These values were then added as an attribute along with the selected census variables in order to facilitate global and local regression calculations for individual CTs. GWR mapping technique

A variety of options exist for mapping the results of a GWR analysis, and it is important that the technique adopted clearly represents the objectives of the research. In this study we are concerned with areas in the city that demonstrate environmental inequalities in relation to the vegetation and socioeconomic factors. For illustrative purposes, and to ensure the wide range of available data from GWR analyses are communicated effectively, four distinct classes (situations A ^ D) based on a mean or standard deviation classification (figure 4) are emphasized. The first step in this


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Geographically weighted regresion

Local r 2 > 0:60

Positive relationship Vegetation < ÿ1sd Income < ÿ1sd

Situation A

Negative relationship

Vegetation > 1sd Income > 1sd

Situation B

Vegetation < ÿ1sd Income > 1sd

Vegetation < 1sd Income < ÿ1sd

Situation C

Situation D

Figure 4. Flow chart displaying technique for mapping census tracts which demonstrate four vegetation-related environmental inequalities.

classification is to identify the direction of the relationship between census variables and vegetation to help determine areas with an overabundance and underabundance of vegetation in relation to income. In the second step, the mean local r 2 values are determined, and areas that demonstrate more than 1 standard deviation of separation are selected to represent anomalies in each city. This novel classification technique ensures that directionality, strength of the relation, and internal variability are clearly and effectively communicated for each city. Results Intercity comparison

The results of the correlation analyses between vegetation cover and the socioeconomic variables for Montreal, Toronto, and Vancouver indicate that the highest correlations for all three cities exist between vegetation fractions and income variables (table 3). All the variables that represent income demonstrate significant positive relationships, the highest correlations for all cities belonging to median family income. As mentioned earlier, median family income generally better reflects the actual economic situation faced by the majority of the people in the census tract; therefore, a higher median income would typically suggest that the census tract is overall wealthier than one with a lower median income, while average values may be skewed higher or lower due to extreme values within the population data. Variables representing education also demonstrate significant relationships with vegetation; however more variability can be observed between cities. The strongest relationship with education comes from the variable representing no high school degree, and is negatively correlated with vegetation for each city. Vancouver exhibits a stronger relationship (r ÿ0:387, p < 0:05) than Montreal (r ÿ0:287, p < 0:05) and Toronto (r ÿ0:218, p < 0:05). Familystatus indicators, specifically those families with no children, resulted in a higher positive correlation with vegetation for Montreal (r 0:388, p < 0:05) than Toronto (r 0:138, p < 0:05) and Vancouver (r 0:127, p < 0:05). Finally, immigrant-status indicators were highest in Toronto with those people recognizing themselves as Canadian demonstrating a much higher correlation to vegetation (r 0:316, p < 0:05) than either Montreal (r 0:088, p < 0:05) or Vancouver (r 0:120, p < 0:05). These results clearly indicate the unique socioeconomic circumstances in each city.

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Table 3. Correlation results for Montreal, Toronto, and Vancouver. Census variables a

AVG INC MED INC AVG FAM INC MED FAM INC LOW INC NO HS HS CLG CERT BAC NO CHILD CHILD P FAM NON IMG CDN

Montreal

Toronto

Vancouver

r

p

r

p

r

p

0.400 0.401 0.450 0.473 ÿ0.378 ÿ0.287 ÿ0.035 ÿ0.108 0.152 0.388 0.210 0.125 0.088

* * * * * * ns ns * * * ns ns

0.363 0.331 0.395 0.467 ÿ0.278 ÿ0.218 ÿ0.148 0.048 0.158 0.138 0.105 0.305 0.316

* * * * * * * ns * * ns * *

0.371 0.187 0.446 0.456 ÿ0.392 ÿ0.387 ÿ0.020 ÿ0.160 0.141 0.127 0.234 0.004 0.120

* ns * * * * ns ns ns ns * ns ns

a See

text for description of variables. * significant at a < 0:05 (Bonferonni adjusted a=n). ns not significant.

Intracity comparison

These correlation results provide a measure of intercity environmental-equity variability. However, trends exist at the neighborhood scale that are ignored in any global statistic. The socioeconomic variability in cities in certain areas displaying more environmental (in)equity than others, and an analysis of local relationships can be more insightful with respect to the mitigation of inequalities through the management of natural resources within individual cities. Table 4. Income (factor 1), education (factor 2), and immigration status (factor 3) analysis results for Montreal, Toronto, and Vancouver. Socioeconomic variables a

Montreal 1

2

3

1

2

MED FAM INC MED INC AVG INC AVG FAM INC CLG CERT HS NO HS BAC CDN NON IMG CHILD FAM NO CHILD LOW INC

0.93 0.94 0.91 0.89 0.42 0.19 ÿ0.02 0.64 0.56 0.42 0.26 0.48 ÿ0.48

ÿ0.27 ÿ0.18 ÿ0.31 ÿ0.32 0.73 0.91 0.90 0.13 0.29 0.08 0.36 0.72 0.38

0.02 ÿ0.08 0.04 0.07 0.25 0.14 ÿ0.03 0.45 ÿ0.72 ÿ0.74 ÿ0.47 0.39 ÿ0.41

ÿ0.93 ÿ0.93 ÿ0.91 ÿ0.89 0.23 0.56 0.65 ÿ0.41 ÿ0.57 ÿ0.78 0.24 0.02 0.72

ÿ0.14 0.11 ÿ0.21 0.05 ÿ0.08 0.08 ÿ0.07 0.10 ÿ0.88 ÿ0.12 ÿ0.72 0.13 ÿ0.59 0.25 ÿ0.58 ÿ0.38 ÿ0.35 0.51 ÿ0.16 0.22 ÿ0.08 0.82 ÿ0.90 ÿ0.25 0.02 0.31

0.39 5.01

0.26 3.37

0.15 1.90

0.45 5.80

Proportion total Exploratory variable a See

Toronto

text for descriptions of variables.

Vancouver 3

0.23 3.01

0.11 1.40

1

2

3

ÿ0.93 ÿ0.92 ÿ0.92 ÿ0.86 ÿ0.09 0.49 0.68 ÿ0.58 ÿ0.46 ÿ0.68 0.16 ÿ0.07 0.84

ÿ0.03 ÿ0.11 ÿ0.07 ÿ0.03 ÿ0.85 ÿ0.74 ÿ0.48 ÿ0.51 0.10 0.06 0.01 ÿ0.93 0.13

ÿ0.20 0.13 ÿ0.27 ÿ0.36 0.35 ÿ0.05 0.14 ÿ0.20 0.39 0.58 ÿ0.68 ÿ0.18 ÿ0.14

0.45 5.81

0.21 2.69

0.11 1.45


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Results from the factor analysis (table 4) support the selection of median family income as the best representation of income. Additionally, factors 2 and 3 identify ancillary variables related to education and immigrant status that could be used in

(a)

(b)

(c) Local r 2 values < 0.2 0.2 ^ 0.4 0.4 ^ 0.6 0.6 ^ 0.8 > 0.8 10 km

Situation

strong local positive relation A low vegetation low income strong local positive relation B high vegetation high income strong local negative relation C low vegetation high income

Color plate 1. Maps displaying results of the geographically weighted regression procedure to highlight vegetation-related environmental inequity in (a) Montreal, (b) Toronto, and (c) Vancouver.

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subsequent GWR analyses. Furthermore, the Monte Carlo simulations for Montreal and Toronto demonstrated significant results (table 2) suggesting that both these cities exhibit spatially nonstationary relationships between income and vegetation. Meanwhile, the Monte Carlo simulations for Vancouver proved not to be significant, which implies that Vancouver may not exhibit substantial internal variability in the relationship between income and vegetation; however these results are also partly due to the smaller geographic extent of the data used in the GWR analysis. The results of the GWR analysis are displayed for the local relationships between vegetation and income in color plate 1. Situations A (low vegetation and low income), B (high vegetation and high income), and C (low vegetation and high income) are mapped for each city where applicable, while situation D (high vegetation and low income) was not associated with census tracts in any of the cities. Examining the results of the mapped GWR for each city (color plate 1) provides some noticeable trends and differences between the cities. Looking first at the variance in the local r 2 values between income and vegetation, several pockets of high values appear within each city. Considering the location of the various situations provides a more informed interpretation of the results. Each city exhibits a variety of situations with respect to vegetation-related environmental inequality. All three cities contain areas with high vegetation and high income (situation B) and the complementary trend of low vegetation and low income (situation A). Finally, a few census tracts in Toronto and Montreal were identified with the situation exhibiting low vegetation and high income (situation C). Discussion Current government initiatives directed at developing environmentally sustainable economics has placed environmental-equity research focused on contamination in a precarious position. Specifically, evidence demonstrates that reducing environmental hazards does not necessarily reduce environmental inequity (Barlow and May, 2000). This concept has led Buzzelli (2008) to suggest that environmental equity appears to be at odds with the principles of sustainability, since the redistribution of environmental burdens may still compromise the environmental conditions for future generations. However, shifting focus away from environmental burdens to environmental benefits requires that sustainability and environmental equity need not be mutually exclusive. Examining urban vegetation, for example, provides a prime opportunity to balance urban inequalities and promote sustainability. The question then becomes where to implement vegetation-planting strategies to ensure an equal distribution of this essential amenity. Performing both global and local spatial assessments of environmental equity provides a suite of statistics that can be used to analyze various geographic trends in the distribution and abundance of inequalities between socioeconomic variables and vegetation fractions. The global method applied in this study uses the Pearson correlation coefficient; a standard but powerful statistic that enables the quantification of relations between vegetation fraction and socioeconomic variables for selected cities. The results of this study validate long-standing theories that have described classbased environmental inequities and the pronounced existence of these situations in North American cities (Faber, 1998). In this study the strongest relationships with vegetation fraction were observed with those variables related to economic status, in particular various representations of income from national census data. In all three study areas income variables were positively correlated with vegetation fraction, suggesting that the higher an individual's income the greater the chance that he or she lives live in an area with greater amounts of vegetation. This correlation is consistent across Montreal, Toronto, and Vancouver, and is similar to that found


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in other American cities (Jensen et al, 2004; Li and Weng, 2007; Lo and Faber, 1997; Mennis, 2006a). Although the consistently high correlation with income supports the general existence of environmental inequalities across urban areas, the variability in the correlations of the other socioeconomic variables highlights intercity differences with respect to the equitable distribution of vegetation. The global correlations illustrate the difference in socioeconomic and vegetation relationships across three major Canadian cities (table 3). It is important to note that this analysis cannot reveal the process of causation through which these relationships emerge. However, planners and community organizations can use them to help guide policies and initiatives to help mitigate recognized inequalities. In addition, cross-city comparison can help policy analysts examine the successes and failures of urban development processes in these major cities. At the same time, policy differences do not necessarily explain all the facets of urban development. The relationships derived from this analysis are partly a result of cultural and historical influences on urban development patterns that remain important to the diversity, originality, and differentiating characteristics of urban centers. As a result, the methods presented in this study should be viewed as a tool that could be applied by various individuals or organizations interested in the geographic relationships between people and the environment. Global assessments of environmental equity can have valuable applications for intercity comparisons and act as a general tool for recognizing the existence of inequitable relationships between the urban environment and socioeconomic status. However, cities are inherently diverse landscapes composed of blocks, neighborhoods, and districts whose internal variability is masked by a simple global statistic. GWR can highlight relationships at various scales and allows planners and community organizations to quantify the geographic variability across a city. In practice, a local regression analysis enables the determination of location-specific allocation of environmental services and resources to reduce environmental inequalities efficiently. Maps summarizing the GWR results between income and vegetation highlight those areas where inequalities exist within each city (color plate 1). Of interest are those CTs that exhibit an overabundance and underabundance of vegetation in relation to income. By targeting these areas urban planners and community organizations can allocate and manage resources towards alleviating inequalities in the most adversely affected neighbourhoods. Specifically, those mapped areas where income and vegetation are both low are of immediate interest as residents in these locations face a disadvantage with regards to accessibility and availability of proximate vegetation. Local regression parameters from this study exhibited stronger relationships with vegetation than did the global correlation, which exemplifies the power and utility of GWR for analysing the relationships between socioeconomic status and environmental factors including vegetation. Reviewing the maps produced for each city reveals geographic trends that can act as a powerful tool for motivating initiatives to help manage and mitigate environmental inequalities. Mapping inequalities has been recognized as a valuable means of stimulating community members to become actively involved in the laws and policies which govern the distribution of local resources (Hutchinson and Toledano, 1993). In addition, epidemiologists have recently recognized the importance of neighborhood-level social and environmental factors on the health and wellbeing of urban residents (Brulle and Pellow, 2006; Maantay, 2002; Ostfield et al, 2005).

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Limitations and future research Many of the limitations of similar studies, including the exploratory nature and restricted ability to determine elements of causation, have been discussed in previous publications (Lafary et al, 2008). However, one substantial issue that has been overlooked in the literature examining spatial assessment of urban environmental equity concerns the static understanding of human ^ environment interactions. Most studies in this field, including the one presented in this paper, focus on a single snapshot of the inherently dynamic nature of urban environments. This method of conceptualizing environmental equity can provide insightful analysis for decision makers. However, it neglects trends over time that indicate changing circumstances. Our primary recommendation for future research prescribes an analysis of the temporal relationship between socioeconomic variables and vegetation in cities. Novel opportunities for conducting studies examining changing environmental equity in Canadian cities are available by integrating census data collected and disseminated at five-year intervals with freely available Landsat satellite imagery. Conclusion The tools and techniques described in this paper, including GWR and the use of vegetation fractions derived from remote sensing, establish novel methods for evaluating the state of vegetation-related equity in Canadian cities. Specifically, we demonstrate the application of global and local analysis techniques for assessing the spatial variability of environmental equity in urban areas. Our results indicate that income provides the strongest correlation with vegetation fractions in Montreal, Toronto, and Vancouver, while education, family status, and immigrant status are appropriate secondary variables for examining environmental equity in these cities. Using a global statistic in this study enabled meaningful comparisons of the vegetation-related environmental equity between Canada's largest urban centers, while GWR provided a local regression model for analyzing the internal variability of environmental equity. Specifically, the GWR provided useful information for locating areas where inequalities are of greater concern in each individual city. Acknowledgements. We would like to thank the Environmental Prediction in Canadian Cities project funded by the Canadian Foundation for Climate and Atmospheric Sciences for their support. We would also like to thank two anonymous reviewers who provided informative critiques on the original draft of this paper. References Anderton D L, Anderson A B, Oakes J M, Fraser M R, 1994, `Ènvironmental equity: the demographics of dumping'' Demography 31 229 ^ 248 Barlow M, May E, 2000 Frederick Street: Life and Death on Canada's Love Canal (HarperCollins, Toronto) Bowen W M, Salling M J, Haynes K E, Cyran E J, 1995, ``Towards environmental justice: spatial equity in Ohio and Cleveland''Annals of the Association of American Geographers 85 641 ^ 663 Brulle R J, Pellow D N, 2006, `Ènvironmental justice: human health and environmental inequalities'' Annals Review of Public Health 27 103 ^ 124 Brunsdon C, Fotheringham A S, Charlton M, 2002, ``Geographically weighted summary statisticsö a framework for localised exploratory data'' Computers, Environment and Urban Systems 26 501 ^ 524 Buzzelli M, 2008, `Ènvironmental justice in Canadaöit matters where you live'', Canadian Policy Research Networks, http://www.cprn.org/doc.cfm?doc=19698/=cn Buzelli M, Jerrett M, Burnett R, Finklestein N, 2003, ``Spatiotemporal perspectives on air pollution and environmental justice in Hamilton, Canada'' Annals of the Association of American Geographers 93 557 ^ 573 Coen S E, Ross N A, 2006, `Èxploring the material basis for health: characteristics of parks in Montreal neighbourhoods with contrasting health outcomes'' Health and Place 12 361 ^ 371


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