EXAMINING URBAN EXPANSION USING MULTI-TEMPORAL LANDSAT IMAGERY : A CASE STUDY OF THE MONTREAL CENSUS METROPOLITAN AREA FROM 1975 TO 2015 , CANADA

Urban expansion, particularly the movement of residential and commercial land use to sub-urban areas in metropolitan areas, has been considered as a significant signal of regional economic development. In 1970s, the economic centre of Canada moved from Montreal to Toronto. Since some previous research have been focused on the urbanization process in Greater Toronto Area (GTA), it is significant to conduct research in its counterpart. This study evaluates urban expansion process in Montréal census metropolitan area (CMA), Canada, between 1975 and 2015 using satellite images and socio-economic data. Spatial and temporal dynamic information of urbanization process was quantified using Landsat imagery, supervised classification algorithms and the post-classification change detection technique. Accuracy of the Landsat-derived land use classification map ranged from 80% to 97%. The results indicated that continuous growth of built-up areas in the CMA over the study period resulted in a decrease in the area of cultivated land and vegetation. The results showed that urban areas expanded 442 km both along major river systems and lakeshores, as well as expanded from urban centres to surrounded areas. The analysis revealed that urban expansion has been largely driven by population growth and economic development. Consequently, the urban expansion maps produced in this research can assist decision-makers to promote sustainable urban development, and forecast potential changes in urbanization growth patterns. * Corresponding author The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B8, 2016 XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic This contribution has been peer-reviewed. doi:10.5194/isprsarchives-XLI-B8-965-2016 965


INTRODUCTION
Urban expansion, particularly the increase of built-up areas in sub-urban areas in metropolitan areas, has been regarded as an important signal of regional economic development (Yuan et al., 2005).However, along with fast economic development and rapid urbanization process, its benefits are increasingly balanced against environmental impacts (Squire & Kubrin, 2005), such as the decreasing watersheds, land reclamation, coastline change and prominent food production.Therefore, determining how to balance economic benefits maximum and environmental impacts minimum is a challenging task for decision makers for planning, environmental management and land resources integration in the process of urban expansion (Yuan et al., 2005;Wang et al., 2015).
Remote sensing technology plays a significant role that can provide a great amount of data of the Earth surface (Jensen, 2004).Moreover, satellite images can quantitatively describe the spatial structure of urban environment, and provide a costeffective and visualized tool to detect urbanization footprints (Gutman et al., 2004).Multi-temporal and multi-spectral data can be obtained for analysing and monitoring urban expansion patterns using remotely sensed imagery (Weng, 2002).For example, Alberti et al (2004) indicated that the remote sensing technology has the capability to describe changes of land use based on timely and accurate geospatial data.Furthermore, in combination with geographical information system (GIS) that can provide an effective tool to store, analyse, integrate, and display geographical information (Malczewski, 1999), remote sensing and GIS technologies have been widely applied in detecting land use and land cover changes and monitoring urbanization process over the last decades (Dewan et al., 2009).
In this study, combined with GIS technique, temporal analysis is conducted to detect urbanization process using Landsat series imagery from 1975 to 2015 in the Montré al Census Metropolitan Area (CMA).Six level-2 classes are assigned: residential, commercial, barren cropland, water body, forest, and vegetation.The post-classification comparison change detection approach is applied, necessitating the selection of an appropriate classification algorithm.Since unsupervised classifiers need a great amount of work to refine results during the post-classification comparison period, several supervised classification and machine learning methods have been used, such as Maximum Likelihood Classifier (MLC) (Otuker et al., 2010), Support Vector Machine (SVM) (Schneider, 2012), and Artificial Neural Network (ANN) (Erbek et al., 2004).Compared with traditional classification classifiers (e.g.MLC), the Decision Tree (DT) classifier is a different classification algorithm, which is an ensemble consisting of a large number of diverse criterions aiming to separate and identify various classes (Joelsson et al., 2006).Based on the previous studies, the performance of MLC, SVM, ANN and DT classifiers are tested according to accuracy assessment, and their relative performances are evaluated.
Compared with existing work, there are few studies focusing on urban expansion issue in the Montré al CMA using satellitebased approach.This research intends to examine the dynamic change patterns in the urbanization process of the Montré al CMA over a period of 40 years.Multiple classification approaches are used and urban expansion patterns are evaluated in terms of bi-temporal (i.e. between years) and multi-temporal (i.e.across all years) analysis from Landsat imagery at 5-year intervals from 1975 to 2015.Consequently, quantitative and qualitative results of the Montré al CMA urban expansion can be examined.The objectives of this study are thus to identify the urban expansion patterns and characterize the potential driving forces contributing to these changes in the CMA using remotely sensed data and socio-economic data.Specifically, the objectives are (1) to map temporal land cover categories through classification of Landsat series imagery; (2) to assess the accuracy of Landsat series classification results derived by applying MLC, SVM, ANN and DT algorithms; (3) to analyse the tendency of urban expansion in CMA, and to evaluate major driving forces that contribute to relevant changes.

Study area
The study area is the Montré al Census Metropolitan Area shown in Figure 1, which is the second most populous metropolitan area in Canada after the Greater Toronto Area (GTA).This project focuses on the urban expansion and population explosion, according to the Statistics Canada, it reported that the CMA had a population of 3,824,221, an increase of 5. 2% from 2006(Canada 2011 Census).This leads to a population density of about 898 people per square kilometer.As the total population and population density of the Montré al CMA is increasing rapidly, it is suitable for urban expansion analysis.The time period chosen are from 1975 to 2015 because it is a highly developed period of the area.Therefore, significant changes of urbanization can be seen directly.The Montré al CMA also includes a diversity of land use categories interspersed with large scales of buildings, watersheds and more than hundreds of hills.Both high and low densities of population are found in the specific portions of the Montré al CMA in the past decades (Canada 2011 Census).
These features indicate the high potential of urbanization process in the Montré al CMA.

Data sources and pre-processing
Imagery from Landsat-1 and Landsat-2 Multispectral Scanner (MSS), Landsat-5 Thematic Mapper (TM), Landsat-7 Enhanced Thematic Mapper Plus (ETM+), and Landsat-8 Operational Land Imager (OLI) were acquired and mainly used to analyse land cover changes and urban expansion in the Montré al CMA (Table 1).MSS images were resampled to 30m resolution, and all reflective bands were applied in image classification excluding the thermal band.All these images were obtained from USGS with level-one product format, sometimes over two images were applied to improve classification accuracy (Table 2).In order to avoid the influence of snow, most of images were acquired from May to October.The World Geodetic System of 1984 (WGS84) and Universal Transverse Mercator (UTM) were selected as coordinate systems.The software Environment of Visualizing Images (ENVI) and ArcGIS version 10.3 were used to conduct image pre-processing.Layer stacking for all images was performed first, followed by images registration.Dark pixel subtraction approach was then used to carry out atmospheric correction based on unique digital number values of each image.Finally, seamless mosaic tool in ENVI was selected for mosaicking images with colour balance, and all mosaicked images were clipped by the boundary of the study area.The Montré al CMA boundary and census division's boundaries were obtained from Statistics Canada (2011).
Census statistical data from 1971 to 2011 provided by Statistics Canada were used to help understanding of urbanization process of the Montré al CMA.The population data were released every 5 years by Statistics Canada (2011).These data were thus used to analyse the relationship between urban expansion and population; in addition, both Consumer Price Index (CPI) and Industrial Production Price Index (CPPI) were acquired from Statistics Canada to explore their potential relationships with urban expansion.A set of full-colour QuickBird 0.6m resolution digital orthoimages in 2006 were provided by the Geospatial Centre, University of Waterloo as a reference map for accuracy assessment after image classification.Moreover, Google Earth very high resolution imagery for the Montré al CMA in 2015 was also used as reference map.

Image classification
Considering major land use categories within the Montré al CMA, and combined with spatial resolution of the imagery (i.e.30m), six separate classes then were identified: residential, commercial, barren cropland, water body, forest and vegetation (Table 3).
Selecting an appropriate classification algorithm to classify the imagery can improve the overall accuracy, as the quality of classification results directly affect the performance of the change detection (Wang et al., 2015).Therefore, determining an appropriate classifier is significant.In this study, supervised classification methods and machine learning algorithms, including MLC, SVM, ANN and DT, were performed on both the 2006 and 2015 mosaicked images.Training samples were selected for the above six categories based on false colour composite of the reflective spectral bands.Based on the Jeffries-Matusita (JM) distance report, which ranges from 0 to 2 and indicates an average distance between a pair of classes contributing to how accurate classification results will be, it can be therefore used to detect the spectral separability of training samples (Schmidt et al., 2003).If the value is asymptotic to 0, the selected training samples are more polymerized.
Several indices were applied to generate DT algorithms to extract specified class from satellite imagery.Consequently, the Soil Adjusted Vegetation Index (SAVI) was used to extract vegetation information, as shown in equations ( 1) to (4); a Normalized Difference Bare Index (NDBI) was applied to select built-up areas; a Modified Normalized Difference Index (MNDWI) was presented to delineate open water features; and a Normalized Difference Bare Index (NDBal) for the bare land (Hua et al., 2012) was also used. (1) (2)  indicate the original raw digital numbers value in the TM/ETM+ mid-infrared and thermal infrared bands; and is soil adjusted factor, ranging in between 0 and 1.In this case, we choose 0.5 to avoid the influence of different backgrounds.
After image classification, a 3 x 3 majority filter is applied in order to eliminate the salt-and-pepper noise to improve classification accuracy (Wang et al., 2015).
After classification, accuracy assessment is generated for all classified imagery to assess the classification accuracy based on testing samples.Congalton and Green (1999) indicated that the testing sample size with a minimum of 50 samples for each class should be selected in terms of cost-effectiveness.In addition, both QuickBird imagery for 2006 and Google Earth imagery for 2015 were used to randomly select testing samples over 600 pixels (100 samples for each Level-2 class) in order to obtain reliable accuracy assessment for both years.Moreover, selected samples are manually validated.The error matrices therefore are generated, which contain the overall accuracy, the user's accuracy and the producer's accuracy (Congalton, 1991).The user's accuracy means the probability that a pixel is class A given that the classifier has determined the pixel into class A, while the producer's accuracy indicates the probability that the classifier has labeled a pixel into class A given that the ground truth is class A (Jensen, 2004).

Change detection
The post-classification comparison change detection technique is applied to detect urban expansion patterns over past 40 years.
Thematic maps (Alphan et al., 2009) are then built based on separately classified multi-temporal imagery, and comparison between the classified images can be implemented in terms of per-pixel basis.This technique can provide detailed "from -to" information for each class in the process of urbanization (Jensen, 2004).Since we only would like to examine urban expansion patterns, the classified classes are merged into the following two main categories before applying the change detection technique: the urban area and the non-urban area, which can avoid the influences of misclassification or classification errors.Urban expansion then can be analysed based on bi-temporal and multi-temporal change detection maps.

Urban expansion statistical analysis
Wang ( 2015) indicated that both urban expansion rate and urban expansion spatial structure can be varying across time.In this study, as shown in Eq. ( 5), we determine the rate of urban expansion using the Land Use Change Index (LUCI) presented by Haregeweyn (2012), which can be a significant index to assess urban expansion. ( where represents the area of urban at Time a; represents the area of urban at Time b; T is the time period between Time a and Time b. LUCI then can describe annual rate of urban areas if T's unit is in years.Consequently, the correlation between the urban areas and population can be calculated using Pearson correlation coefficient analysis (Wang, 2015).

Accuracy assessment
Error matrices were generated to assess the accuracy of classified imagery based on four different classification approaches (i.e., MLC, SVM, ANN and DT) to determine an appropriate classifier over the study time period.As shown in Table 4, the MLC achieved an overall accuracy of 93.79%.In contrast, SVM had an overall accuracy of 96.26%, and the ANN's overall accuracy was the highest value of 97.26%.These three classifiers performed better than DT's overall accuracy of 89.35%.Both user's and producer's accuracies in commercial, barren cropland and vegetation in ANN were slightly better than the results from other classifiers.Thus, ANN classifier was chosen to perform image classification for the remaining imagery.To reduce misclassification, several classified categories were combined together into either urban area or non-urban area.

Change detection maps and analysis
As shown in Fig. 2, the bi-temporal change detection map indicated an increase in urban area in the Montré al CMA from 628 km² in 1975 to 1554 km² in 2015.In addition, extracting and overlaying the urban area of the multi-temporal classified imagery, the 10 year intervals urban expansion change map was generated (Figure 3).According to Fig. 2 and Fig. 3, there were two main spatial urban expansion patterns in the Montré al CMA: centric expansion mode, in which the urban area expands from urban centres to surrounding non-urban areas by a series of concentric circles (Burgess, 2008); ribbon expansion mode, in which urban area grows along major river banks (e.g., St. Lawrence River) and lakeshores (e.g., Lake of Two Mountains).The Montré al CMA mainly expanded outward from the city of Montreal and along St. Lawrence River.Moreover, several major regional city centres, such as Laval, Roussillon, and Deux-Montagnes, also experienced rapid urbanization process within over past decades.As shown in Figure 3, many regional  Therefore, some small regions connected with other cities after 40 years of process, such as Mirabel and Les Moulins.Furthermore, some cities located both along St. Lawrence River and near Lake of Two Mountains, such as Longueuil and Vaudreuil-Soulanges, had a considerable development.
Overall, the urban areas in the Montré al CMA expanded outward from major regional centres, especially from the city of Montreal, and also along St. Lawrence River.

Statistical analysis of urban expansion and driving force analysis
As shown in Table 5, the mean annual growth rate of urban expansion in the Montré al CMA from 1975 to 2015 was 1.6%.There were several significant urban expansion periods within the past 40 years.The periods among 1980-1985, 1985-1990, and 1995-2000 experienced 4.1%, 3.9% and 4.6% in annual growth rate of urban area, respectively.A decrease in urban area period occurring in between 1975 to 1980 may result in image misclassification, since these images were obtained from Landsat-1 with 60 metres resolution and only 4 bands were available for the classification.From 2006 to 2010, the Montré al CMA experienced a lower annual growth rate of 0.1% in urbanization process, which may be due to low urban expansion rate in this period or lower classification accuracy of both imagery.
To reveal the relationship between urban growth rate and population, urban area was calculated from classified imagery with 5-year intervals from 1975 to 2015 to compare the correlation with census data of the Montré al CMA.As shown in Figure 4, both population and urban area experienced an increased tendency within this study time period.The chart indicated that urban expansion is positively correlated to population growth.The Pearson correlation coefficient (r) between urban area and population was 0.983 (p<0.01), which means strong correlation between these two variables.
When focused on three significant periods of urban expansion accompanied with the population growth over the same time, the mean annual population growth rate in the past 40 years was 0.98%; however, the periods among 1981-1986, 1986-1991, and 1996-2001 experienced annual population growth rates of 0.43%, 1.41% and 0.6%, respectively.It reflected that urban expansion was typically delayed by a few years followed by an obvious increase in population.Bhatta (2010) indicated that urban expansion can be impacted on by a large amount of factors, such as population, economic development, and industrialisation.In addition, Industrial Production Price Index (CPPI) and Consumer Price Index (CPI) were also used to analyse their correlations with urban area; however, both CPPI and CPI mainly focus on economic prosperity, especially for inflation, they have small influences on urbanization process (Chen et al., 2013).

CONCLUSION
In this research, spatial and temporal dynamic changes of the urban area in the Montré al CMA have been successfully detected using Landsat series imagery.The selection of an appropriate classifier was a significant factor to reveal detailed urbanization process, which had impacts on the final change detection results.In our study, ANN was determined to be a superior classifier compared to other classification algorithms, such as MLC, SVM and DT.We found that the urban expansion mainly occurred in a centric expansion mode, in which the city expanded outward from the city of Montreal.The Montré al CMA also experienced an expansion mode along major river systems, such as St. Lawrence River.Furthermore, the urbanization process was strongly correlated with increased population.However, there are still some limitations in this research.For instance, only both QuickBird images in 2006 and Google Earth images in 2015 were available to select the training samples, accuracy assessment therefore may not be pretty reliable due to lack of reference maps.
In conclusion, Landsat series imagery can be successfully applied to identify the urban expansion patterns of the metropolitan areas for a long time period.The extent and spatial patterns of the Montré al CMA 's urban expansion were both identified quantitatively and qualitatively in this research.Moreover, integrating Landsat imagery and census data is feasible to analyse urban expansion in regional scales even global scales.Therefore, according to historical development patterns combined with current urban development policy, these results can be used by decision makers or regional governments to promote the Montré al CMA's economic development in the future.

Fig. 2 .
Fig. 2. Urbanization process change map for the Montré al CMA from 1975 to 2015

Fig. 3 .
Fig. 3. Urbanization multi-temporal change map for the Montré al CMA from 1975 to 2015 with 10-year intervalsTable 5. Annual urban growth rate from 1975 to 2015 in the Montré al CMA

Table 1 .
Introduction of the sensors used in this study

Table 2 .
Satellite imagery with 5-year intervals used in this study

Table 3 .
Classification categories and descriptions