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Quantitative Representation of Distribution and Mixture of Urban Land Use Through Spatial Autocorrelation and Information Entropy

Quantitative Representation of Distribution and Mixture of Urban Land Use Through Spatial... The distribution and mixture of urban land use in Japanese cities was quantitatively represented by using two indexes of texture analyses, spatial autocorrelation and information entropy. The spatial autocorrelation was calculated as Moran's I, and the entropy acquired by considering not only the composition of the areas of each land use class, but also the relation of adjacent cells. Land use data in urban areas except green areas were obtained from a digital land use map, and green areas by processing remote sensing data using an Aster GDS. These data were compiled by GIS, and the two indexes of each land use were calculated in each class. It was concluded that both indexes indicate different states of land use, and their relation was different in each land use class. In some it was sufficient to consider only the entropy, but in other cases, it was not sufficient. Using these indexes together gave a more accurate portrait than one alone for grasping the distribution and mixture of urban land use. Keywords: distribution and mixture of urban land use; spatial autocorrelation; information entropy; GIS; remote sensing 1. Introduction and economic circulation among various sectors, Improving diversity of urban land use has become the significance of which, from the environmental one of the most significant issues in Japan. There is a standpoint, has recently been stated. trend for relatively monotonous land use areas such as Thus, it is thought that mixing several land use seaside industrial areas or newly developed residential classes and proposing indexes that are able to express areas to be given diversity by intentionally allocating the distribution and mixture of land use are meaningful various facilities or land use to such areas from the not only for grasping regional characteristics, but point of view of regional diversity. In many cases, also for making plans that take into consideration a the diversity of regions is discussed according to the diversity of land uses. area ratio of each land use class. It is true that the ratio S o m e s t u d i e s i n t h e f i e l d s o f u r b a n p l a n n i n g is one of the most important and essential factors. o r s p a t i a l a n a l y s i s h a v e p r o p o s e d m a n y k i n d s o f However, it cannot solely express the "diversity" of methods for evaluating the diversity of land use, and land use in some areas, because it merely indicates have obtained meaningful results. One of the most the ratio of the considered land use by focusing the popular indexes in Japan is entropy, which is based means or sums, and never represents the mixture of on Shannon's information entropy. Koide (1977), the distribution. It is obviously different from a case in Tamagawa (1982) and Moon et al. (1991) implemented which commercial areas are clustered into one mass, in studies regarding the mixing of land use in large areas 1)-3) that the areas are dispersed in a checkerboard pattern, by employing the index . There are also studies even though the ratios of both areas are the same. in which remote sensing data were analyzed by use Large masses may be effective for creating large open of the index, and the environmental changes were 4)-7) spaces or networked green areas, because big clusters inspected . of monotonous land use enable the generation of open M o r a n ' s I , w h i c h i s a n i n d e x o f s p a t i a l spaces or green areas. On the other hand, dispersed autocorrelation, has been increasingly employed in l a n d u s e w i l l e n c o u r a g e d i v e r s i t y o f l a n d s c a p e analyses of remote sensing data or GIS data. The advantages of the index are as follows. First, it is a robust index, and is not too sensitive for slight *Contact Author: Takashi Kyakuno, Senior Researcher, differences of distribution. Second, the value obtained Museum of Nature and Human Activities, Hyogo from the index can be easily interpreted and understood Yayoigaoka 6 Sanda, Hyogo, 669-1546 Japan at a glance in analogy with the normal correlation Tel: +81-79-559-2001 Fax: +81-79-559-2007 coefficient. Third, it is able to handle both discrete data E-mail: kyakuno@hitohaku.jp and continuous data. The precise characteristics of the ( Received April 7, 2008 ; accepted July 30, 2008 ) Journal of Asian Architecture and Building Engineering/November 2008/434 427 index are discussed in the next section. Some studies have evaluated urban spaces using t h e s e i n d e x e s , a n d h a v e o b t a i n e d m a n y r e s u l t s . However, few studies analyze the land use pattern in large areas on a detailed scale and detached land use classes, and have used both GIS data and remote sensing data to evaluate urban land use. Furthermore, the characteristic of these values in different regions, such as business districts, newly developed residential areas and seaside residential areas has hardly been discussed. The objective of this study is thus to grasp the characteristics of these indexes when adapting Fig.1. Drawing of the Analysis Area them to Japanese cities and to clarify the advantages of Areas surrounded by the black lines are areas for precise a n a l y s i s . T h e u p p e r r i g h t o n e i s t h e N e w l y D e v e l o p e d combining them with precise land use data. In addition, Residential Area, the lower right one the Central Business the author's objective was to clarify the relation of Area, the middle one the Urban Fringe Area and the left one the these indexes to each land use class. Seaside Complex Area. The white is the Outside area". It was drawn by using the Detached Digital Information issued by the 2. Methodology Geographical Survey Institute. 2.1 Data processing In this study, Detached Digital Information of the into this size. The domain for the analysis was set as Kinki area of 1996 issued by the Geographical Survey shown in Fig.1., which has 3120 pixels by 1680 pixels. Institute of Japan was employed to grasp land use and 2.2 The analysis flow its distribution, and six classes, Low-story Houses, All the pixels were covered by tiles, which were High or Middle-story Houses, Industrial Facilities, sized 16 pixels by 16 pixels, and were set as basic Commercial or Business Facilities, Roads and Others units for the analyses. The whole domain was therefore were extracted from the digital map, where Low-story covered by 105 by 195 tiles. If a tile had pixels which Houses means houses of one to three stories, and High corresponded to unclassified land use, like the outside or Middle-story Houses means houses higher than four areas of the original digital maps, they were removed stories. The digital map has a 10m resolution of land from the analysis samples. As a result, 15023 tiles from use in a large area with precise classes. among 20475 tiles remained for analysis. Wi t h r e g a r d s t o g r e e n a r e a s , r e m o t e s e n s i n g The ratio of area, Moran's I and the entropy of each data acquired by Aster GDS (The ID of the scene land use class on each tile were calculated by programs i s 0 3 0 9 1 9 0 1 5 1 4 1 0 3 1 0 0 2 1 0 0 5 . ) w a s a l s o u s e d t o which were written for calculating Moran's I and the determine where green areas were located because entropy, and by the use of GIS. The value of each grid green areas in the digital map sometimes include bare was set as 1 if the pixel corresponded to the focused areas like baseball fields or open spaces covered by on land use class, and as 0 if not. This means that the artificial pavement. The green areas were extracted value of a pixel altered as the land use class changed. by the following procedures. First, the green areas C a l c u l a t i o n s w e r e i m p l e m e n t e d b y c h a n g i n g t h e were separated from the other areas by employing focused on land use in each tile. the maximum likelihood method by using data of one 2.3 Definition of areas for comparative studies visible band and three near-infrared bands of Aster These results were separately summarized in four data, in which mountainous areas, forested areas different types of area: a newly developed residential and urban areas were also included as supervisors. area (usually called "New Town" in Japanese), a central Second, cloud areas were removed from areas which business area, a typical urban fringe area and a seaside w e r e c l a s s i f i e d a s n o n - g r e e n a r e a s b e c a u s e t h e y complex area, respectively. The Senri New Town area have high reflectance in all wavelength bands of the was chosen as a newly developed residential area, and remote sensing data. If the pixels of these cloud areas the central part of Osaka, which is one of the largest corresponded to green areas on the digital map, then cities in Japan, was set as a central business area. As an the pixels were redefined as green areas. Since this urban fringe area, Hanshin-kan, which is between two remote sensing image is one of a relatively clear day, large city centers, Osaka and Kobe, was chosen. The the cloudy areas which correspond to green areas on area has been undergoing urban sprawl for about the the digital map were considered to be mountainous past fifty years. Formerly, it was principally composed areas, because in Japan mountainous areas tend to be of agricultural fields. The area is considered to be a covered by clouds even during clear weather. typical Japanese suburban residential area, composed The remote sensing data was projected onto a mainly of relatively new houses, commercial facilities Japanese standard coordinate system and the pixel was and industrial facilities, but still containing the spatial resized into a 17.75m grid. Corresponding to the size, frames or old houses from former agricultural villages. the resolution of the digital map was also reformatted Seaside areas vary in form and land use composition, 428 JAABE vol.7 no.2 November 2008 Takashi Kyakuno but the most typical case is one dominated solely by T h e i n f o r m a t i o n e n t r o p y i s a n i n d e x w h i c h new industrial facilities. Considering the typical case, numerically indicates the variation of areas and their however, may only lead to obvious results, so another dispersion. It shows the maximum number when the case in which there are remnants of former fishing areas of each class are equivalent and the cells are villages or agricultural villages is considered for the adjacent to cells of each class in the same probability. analyses. A rough map of the areas, indicating their On the other hand, it shows 0 if the domain is occupied 1)2) locations, is shown in Fig.1. by only one class. The definition is as follows . 2.4 The spatial autocorrelation and information (2) entropy As has been discussed, Moran's I is an index which Where i, j is the running number of each land use relates to the size and number of clusters, and can be class (defined as 1 in the case that the land use class interpreted in the same way as the normal correlation is focused on, but 0 in the other land use classes), p is coefficient, where 1 means high correlation and 0 the ratio of an area of land use class i in a target tile, q ij means no relation. In the Moran's I index, there are is the probability of which land use class j is adjacent various ways to consider the neighborhood relation. In when considering land use class i. ( w =1, each i). j ij this study, only cells adjacent to any targeted cell were The relation of these two indexes is shown in Fig.2., considered, and cells which were placed in diagonal in which typical patterns of dispersion are shown as places on the map were not considered. The equation is points in the plane consisting of these two indexes. as follows. For example, the checker board pattern of a land use indicates -1 in Moran's I and 1 in entropy. Then, the relation is plotted at the bottom of the plane. (1) T h e r e l a t i o n i s a l s o p l o t t e d i n t h e u p p e r r i g h t hand side when some clusters are formed. Random Where i, j are the running numbers of each cell dispersion patterns are indicated as points in the right (1<=i, j<=256), x is the value of the cell i (it is 1 if hand side, and cases in which a few of the grids of a the cell corresponds to a focusing class, and 0 if not), land use are dispersed are shown as points of the left x is the mean of x in the calculation domain, n is the hand side. Some actual samples are illustrated. total number of cells in a tile (n=256 in this study), w ij is the weighing variable (in this study, it is set as 1 if 3. Results and Discussion cell i and cell j are adjacent to each other in either the 3.1 Land use patterns of each class vertical or horizontal direction, and 0 if not). Seven thousand one hundred and one tiles, which Fig.2. Theoretical Model of Relation between Entropy and Spatial Autocorrelation JAABE vol.7 no.2 November 2008 Takashi Kyakuno 429 contain more than 20% of the urbanized area, are in particular patterns, and it is therefore generally chosen from all tiles. An urbanized area refers to difficult to define their typical dispersion patterns of classes other than water zones and green zones. In each the Commercial or Business Facilities. If business tile, the spatial autocorrelation and entropy of each facilities and commercial facilities are, however, land use class were calculated and are shown as points analyzed separately, other results will be acquired in Fig.3. This illustrates a rough tendency towards because business facilities are likely to form more dispersion of each land use class in urban areas. clusters than commercial facilities due to the zoning Low-story Houses shows widely spread points in system of Japanese urban planning law. It is difficult the plane, and is densely accumulated on the right to precisely distinguish between business facilities and hand side, which means that such houses are placed commercial facilities, because many facilities serve in various forms and show various dispersion patterns both functions. in urban areas. But, most of them tend to be dispersed T h e J a p a n e s e u r b a n p l a n n i n g s y s t e m d o e s n o t randomly in urban areas, as can be seen by comparing usually exclude small commercial facilities, even in the figure with the theoretical model shown in Fig.2. zones for residential areas, therefore such facilities High or Middle-story Houses shows more monotonous can be built in various forms among various land use d i s p e r s i o n p a t t e r n s t h a n L o w - s t o r y H o u s e s . I n classes. They are sometimes isolated in residential particular, there are few randomly dispersed patterns areas or industrial areas, but are sometimes clustered or stripe patterns unlike with Low-story Houses. This together. The exception is the case of the so-called m e a n s t h a t H i g h o r M i d d l e - s t o r y H o u s e s t e n d t o New Town area, because land use plans are strict and aggregate in urban areas. Industrial Facilities show a commercial facilities are encouraged to aggregate at similar tendency as High or Middle-story Houses. town centers in advance. Commercial or Business Facilities show as widely 3.2 Land use characteristics in different types of spread plots in the plane, as do Low-story Houses. area However, there are no densely accumulated domains Figs.4.-1, 5.-1, 6.-1 and 7.-1 show land use maps of in the plane as in Low-story Houses, which means the four different types of areas and Figs.4.-2, 5.-2, 6.-2 that Commercial or Business Facilities do not always and 7.-2 are graphs showing the composition of each assume a particular dispersion pattern but quite varied land use class in the areas. The ratio of green areas ones, including random, clustered and isolated patterns. to the whole area is also displayed as a number. The The patterns of dispersion of Roads represent the reason why the green areas are dealt with separately basic framework of urban areas. The graph shows that from the other land use classes is that green areas various dispersion patterns can be taken. In particular, are found in all the land use classes mentioned in a lot of points are concentrated on the right hand side this study, and places which contains green areas of the vertical middle place of the plane, which means sometimes also have houses, roads and commercial roads tend to form striped patterns in urban areas. facilities. Figs.4.-3, 5.-3, 6.-3 and 7.-3 show the spatial Comparing these graphs, it is supposed that the autocorrelation and entropy of each land use class at locations of Commercial or Business Facilities show each tile of each area. d i v e r s e p a t t e r n s a n d a r e u n l i k e l y t o c o n c e n t r a t e A r o u g h t e n d e n c y c a n b e g r a s p e d t h r o u g h a n Fig.3. Entropy and Spatial Autocorrelation of Each Tile Class of Each Landuse Class 430 JAABE vol.7 no.2 November 2008 Takashi Kyakuno overview of the compositions of the areas. In the I n t h e ' C e n t r a l B u s i n e s s A r e a ' , C o m m e rc i a l o r ' N e w l y D e v e l o p e d R e s i d e n t i a l A r e a ' , t h e a r e a o f B u s i n e s s F a c i l i t i e s c a n b e r e g a r d e d a s f o r m i n g Roads, Low-story Houses and High or Middle-story vermicular clusters by referring to Fig.5.-3, which Houses are large as are Others. Others are thought to is also shown in the land use map. Commercial or be mainly green areas. In the 'Central Business Area', Business Facilities are connecting until roads cut Commercial or Business Facilities and Roads prevail them off. Roads shows similar patterns as Commercial because the land use of these areas is simplified, and or Business Facilities, and can be thought to form several classes characterize the whole area. In the vermicular cluster patterns as well. Different from 'Urban Fringe Areas', there are more Low-story Houses ' N e w l y D e v e l o p e d R e s i d e n t i a l A r e a s ' , n a r r o w and Roads than other classes since the area is typical of networked roads which are indicated as points around suburban residential areas in Japan, and mainly consist x=1.8-2.0 and y=0 are never seen. This indicates that of a variety of houses. In the 'Seaside Complex Area', these two land use classes form many clusters in micro various land use classes exist almost equally, and there perspective, and these clusters are mixed in macro are no conspicuous characteristics. perspective. In the area, the Roads areas tend to be I n o r d e r t o g r a s p t h e m i x i n g o f l a n d u s e , i t i s wider than most roads in usual residential areas, and effective to refer to the spatial autocorrelation and the density of Roads is high. There are only two main entropy. Figs.3.-3, 4.-3, 5.-3 and 6.-3 show a different land use classes and the land use patterns can be almost tendency of distribution of each land use class. Land regarded as simplified in small scale but mixed in large use classes sharing more than 5 percent in each area scale. are plotted in each figure. In the 'Newly Developed I n t h e ' U r b a n F r i n g e A r e a ' , L o w - s t o r y H o u s e s Residential area', Low-story Houses tends to show a show a variety of patterns as can be seen from the vermicular cluster pattern or to form small clusters, dispersed pattern in Fig.6.-3. Some Low-story Houses whereas High or Middle-story Houses are likely to form clusters vermiculated by Roads, and other Low- form big clusters, compared with the figure in the story Houses form line patterns. Several Low-story theoretical model in Fig.2. Roads are distributed in Houses are isolated. As discussed before, this area various ways, including line-like patterns in the area. is a typical suburban area of Japan, in which some It is interesting that Green shows a similar pattern zones have been developed using deliberate plans, t o L o w - s t o r y H o u s e s . I n t h e ' N e w l y D e v e l o p e d but most zones were created without any total plan so Residential Area', the lot size of each low story house that urban sprawl occurred. The former land use and is large and there are generally relatively large gardens periods of development of each zone are also different, in them. Furthermore, in the area there are some large which cause inconsistent land use patterns of the parks, including a mass of green areas in addition to area. This tendency also relates to the pattern of the many trees on the street. Green areas sometimes form roads. Generally, narrow networked roads prevail over big clusters, and sometimes form vermicular clusters other types. The spatial frames of former agricultural like Low-story Houses. On the other hand, High or villages can still be seen in these forms of road. It is Middle-story Houses have an obvious tendency to a typical phenomenon of the area that Commercial or form clusters. In the 'Newly Developed Residential Business Facilities are not clustered, but form line-like Area', high story buildings like apartment houses were patterns. This is because the sizes of lots in the area are separated from other types of buildings according to generally small and the roads are narrow. Therefore, it precise land use plans, and therefore High or Middle- is prohibited by the building standard law in Japan to story Houses were regulated in designated zones. There build large-scale buildings in these areas. It is a matter are some points which are located in the left hand side of course that Commercial or Business Facilities form of the vertical middle place in Fig.4.-3, which means lines along roads. that High or Middle-story Houses are isolated in some In the 'Seaside Complex Areas', each land use forms tiles but not clustered. There are no isolated Low-story various patterns of distribution, the same as the 'Urban Houses, which means that they are never isolated in Fringe Area'. Low-story Houses are located in various such a planned area. Vermicular clusters of Low-story patterns as well as Commercial or Business Facilities. Houses are the result of the existence of narrow streets They sometimes form lines, clusters, vermicular running through a Low-story Houses area. Roads show clusters, or are isolated. High or Middle-story Houses a variety of values in the figure. One characteristic is form either large clusters or small clusters, the same that roads make some clusters, which are indicated as Industrial Facilities. Their sizes may depend on by points on the upper right hand side of Fig.4.-3. the sizes of the lots in which the facilities are located. This means that there are very wide roads in the area. Roads also show various forms; some are narrowly Each type of land use tends to cluster in the 'Newly networked, others are wide. The crossing points of Developed Residential Area', and the types of land wide roads can be regarded as a kind of "cluster" of use that are not Roads are clearly separated from each Roads pixels, and this is indicated as points in the other. upper right hand side in Fig.7.-3. JAABE vol.7 no.2 November 2008 Takashi Kyakuno 431 Fig.4.-1 Land Use Map of 'Newly Developed Residential Area' Fig.5.-1 Land Use Map of 'Central Business Area' Fig.4.-2 Percentages for Areas of Each Land Use Class and Ratio Fig.5.-2 Percentages for Areas of Each Land Use Class and Ratio of Green Area to the Whole Area in 'Newly Developed of Green Area to the Whole Area in 'Central Business Area' Residential Area' Fig.4.-3 Plots by Entropy and Spatial Autocorrelation of Each Fig.5.-3 Plots by Entropy and Spatial Autocorrelation of Land Use Class in 'Newly Developed Residential Area' Each Land Use Class in 'Central Business Area' 432 JAABE vol.7 no.2 November 2008 Takashi Kyakuno Fig.6.-1 Land Use Map of 'Urban Fringe Area' Fig.7.-1 Land Use Map of 'Seaside Complex Area' Fig.6.-2 Percentages for Areas of Each Land Use Class in Fig.7.-2 Percentages for Areas of Each Land Use Class in 'Urban Fringe Area' 'Seaside Complex Area' Fig.6.-3 Plots by Entropy and Spatial Autocorrelation of Each Fig.7.-3 Plots by Entropy and Spatial Autocorrelation of Each Land Use Class in 'Urban Fringe Area' Land Use Class in 'Seaside Complex Area' JAABE vol.7 no.2 November 2008 Takashi Kyakuno 433 Using these two indexes led to interesting results. space. Another grid system like a pentagon system or Planes spanned by these indexes express various forms triangle system may lead to another result. This study of the mixture of land use. For example, big clusters is a first step for quantitatively describing urban land and vermiculated big clusters can be distinguished from use pattern. Based upon the fact that many patterns each other by referring to the spatial autocorrelation. of dispersion were well comprehended by the scheme Using the two indexes enables us to clearly represent of this study, these problems will be discussed with the difference in the features of land use patterns various cases and various methodologies. between Low-story Houses and High or Middle–story Houses in the 'Newly Developed Residential Area' Acknowledgement well. Furthermore, one cluster can be distinguished The author is grateful for the support by Grant-in- from several small clusters by referring to the spatial Aid for Scientific Research (18700239) of Japan. autocorrelation. On the other hand, vermicular clusters can be distinguished from small clusters or line-like References 1) Koide, O. (1977) 'Tochiriyoukonngoudo no Tekiyou Narabini patterns by referring to the entropy. Differences in Sono Kentei' (in Japanese), City planning review, 12, pp.79-84 (in the road pattern of the 'Central Business Area' and Japanese). 'Urban Fringe Area' are well represented by using 2) Tamagawa, H. (1982) 'Tochirinoyou no Titsujosei no Suuriteki entropy. The land use patterns of Low-story Houses of Hyogen ni Kansuru Kenkyu' (in Japanese), City planning review, different areas can also be distinguished by employing 17, pp.73-78 (in Japanese). 3) Moon, T. et al. (1999) A study on the Indicator of Mixed Degree entropy. In 'Newly Developed Residential Areas', Low- of Land Use, City planning review, 26, pp.505-510 (in Japanese). story Houses tend to form vermicular clusters, but are 4) Tsunekawa, A. et al. (1991) Quantitative Analysis Methods of sometimes isolated or form small clusters in 'Seaside Mixed Land Use, Environmental Information Science, 20(2), Complex Areas'. Entropy plays an important role in pp.115-120 (in Japanese). 5) Kumagai, J. (2000) Development of a Spatial Analysis Method distinguishing these differences. for Land Cover taking into account the Complexity of Local Distributions,Environmental Information Science, 14, pp.1-5 (in 4. Conclusion Japanese). Applying both entropy and spatial autocorrelation in 6) Kyakuno, T. and Sotoma, M. (2004) Study on the change of order to understand urban land use is a more effective land use and the degree of mixture of it focusing on distance from coastal line in waterfront area. Journal of Architecture and method for comprehending land use classes than using Planning, 579, pp.75-80 (in Japanese). either index alone. Applying both indexes offers a 7) Kyakuno, T. and Miyazaki, H. (2005) Texture analysis of SAR new way for describing the morphology of urban land data and its relation to land coverage in urban area. Journal of use. Entropy is targeted at diversity and complexity, Architecture and Planning, 590, pp.111-116 (in Japanese). while spatial autocorrelation is targeted at representing 8) Zhang, C. (1999) Development of a Spatial Analysis Tool for Irregular Zones Using the Spatial Data Framework,Graphical spatial similarity on a local scale. Using both indexes Review of Japan, 72A-3, pp.166-177 (in Japanese). enabled the author to grasp urban land use from the 9) Yoon, J. et al. (2004) A Study on the Planning Utilization Based perspective of diversity and similarity. by the Spatial Cognition of Mental Evaluation, Journal of There are still some problems with this scheme. Architecture and Planning, 585, pp.61-67 (in Japanese). First, some spatial situations which look different 10) Myint, S. W. (2003) Fractal approaches in texture analysis and classification of remotely sensed data - comparisons with spatial from each other have close values in both indexes. autocorrelation technique and simple descriptive statistics-, Int. J. T h i s t e n d e n c y b e c a m e c o n s p i c u o u s i n l i n e - l i k e Remote Sensing, 24(9), pp.1925-1947. dispersion patterns. The second problem concerns 11) Myint, S. W. et al. (2004) Wavelets for Urban Spatial Feature scale dependency. In this study, the scale of the basic Discrimination -Comparisons with Fractal, Spatial Autocorrelation, and Spatial Co-occurrence Approaches-, Photogrammetric & grid was set to 17.75m due to the pixel size of the Remote Sensing, 70(7), pp.803- 812. remote sensing data, and the analysis tiles were set to 12) Cliff A.D. and Ord J.K.: Spatial processes -models & applications- 16 pixels by 16 pixels. The reason why this tile size Pion, 1981. is employed is that in future studies these results will be compared with results by the fractal analysis in which it is desirable that the analysis tiles have a size of 2 pixels and the tile size is not excessively large for usual Japanese cities. The result will differ if these basic values are different. In particular, making the grid size smaller will lead to a change of the result. The third problem originates in the way in which adjacent cells were considered. In this study, for the purpose o f r e d u c i n g c o m p u t i n g t i m e , d i a g o n a l c e l l a r e a s were not regarded as adjacent. When taking this into account, different results may occur. Furthermore, the Euclidian system is not the only way to address urban 434 JAABE vol.7 no.2 November 2008 Takashi Kyakuno http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Asian Architecture and Building Engineering Taylor & Francis

Quantitative Representation of Distribution and Mixture of Urban Land Use Through Spatial Autocorrelation and Information Entropy

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Taylor & Francis
Copyright
© 2018 Architectural Institute of Japan
ISSN
1347-2852
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1346-7581
DOI
10.3130/jaabe.7.427
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Abstract

The distribution and mixture of urban land use in Japanese cities was quantitatively represented by using two indexes of texture analyses, spatial autocorrelation and information entropy. The spatial autocorrelation was calculated as Moran's I, and the entropy acquired by considering not only the composition of the areas of each land use class, but also the relation of adjacent cells. Land use data in urban areas except green areas were obtained from a digital land use map, and green areas by processing remote sensing data using an Aster GDS. These data were compiled by GIS, and the two indexes of each land use were calculated in each class. It was concluded that both indexes indicate different states of land use, and their relation was different in each land use class. In some it was sufficient to consider only the entropy, but in other cases, it was not sufficient. Using these indexes together gave a more accurate portrait than one alone for grasping the distribution and mixture of urban land use. Keywords: distribution and mixture of urban land use; spatial autocorrelation; information entropy; GIS; remote sensing 1. Introduction and economic circulation among various sectors, Improving diversity of urban land use has become the significance of which, from the environmental one of the most significant issues in Japan. There is a standpoint, has recently been stated. trend for relatively monotonous land use areas such as Thus, it is thought that mixing several land use seaside industrial areas or newly developed residential classes and proposing indexes that are able to express areas to be given diversity by intentionally allocating the distribution and mixture of land use are meaningful various facilities or land use to such areas from the not only for grasping regional characteristics, but point of view of regional diversity. In many cases, also for making plans that take into consideration a the diversity of regions is discussed according to the diversity of land uses. area ratio of each land use class. It is true that the ratio S o m e s t u d i e s i n t h e f i e l d s o f u r b a n p l a n n i n g is one of the most important and essential factors. o r s p a t i a l a n a l y s i s h a v e p r o p o s e d m a n y k i n d s o f However, it cannot solely express the "diversity" of methods for evaluating the diversity of land use, and land use in some areas, because it merely indicates have obtained meaningful results. One of the most the ratio of the considered land use by focusing the popular indexes in Japan is entropy, which is based means or sums, and never represents the mixture of on Shannon's information entropy. Koide (1977), the distribution. It is obviously different from a case in Tamagawa (1982) and Moon et al. (1991) implemented which commercial areas are clustered into one mass, in studies regarding the mixing of land use in large areas 1)-3) that the areas are dispersed in a checkerboard pattern, by employing the index . There are also studies even though the ratios of both areas are the same. in which remote sensing data were analyzed by use Large masses may be effective for creating large open of the index, and the environmental changes were 4)-7) spaces or networked green areas, because big clusters inspected . of monotonous land use enable the generation of open M o r a n ' s I , w h i c h i s a n i n d e x o f s p a t i a l spaces or green areas. On the other hand, dispersed autocorrelation, has been increasingly employed in l a n d u s e w i l l e n c o u r a g e d i v e r s i t y o f l a n d s c a p e analyses of remote sensing data or GIS data. The advantages of the index are as follows. First, it is a robust index, and is not too sensitive for slight *Contact Author: Takashi Kyakuno, Senior Researcher, differences of distribution. Second, the value obtained Museum of Nature and Human Activities, Hyogo from the index can be easily interpreted and understood Yayoigaoka 6 Sanda, Hyogo, 669-1546 Japan at a glance in analogy with the normal correlation Tel: +81-79-559-2001 Fax: +81-79-559-2007 coefficient. Third, it is able to handle both discrete data E-mail: kyakuno@hitohaku.jp and continuous data. The precise characteristics of the ( Received April 7, 2008 ; accepted July 30, 2008 ) Journal of Asian Architecture and Building Engineering/November 2008/434 427 index are discussed in the next section. Some studies have evaluated urban spaces using t h e s e i n d e x e s , a n d h a v e o b t a i n e d m a n y r e s u l t s . However, few studies analyze the land use pattern in large areas on a detailed scale and detached land use classes, and have used both GIS data and remote sensing data to evaluate urban land use. Furthermore, the characteristic of these values in different regions, such as business districts, newly developed residential areas and seaside residential areas has hardly been discussed. The objective of this study is thus to grasp the characteristics of these indexes when adapting Fig.1. Drawing of the Analysis Area them to Japanese cities and to clarify the advantages of Areas surrounded by the black lines are areas for precise a n a l y s i s . T h e u p p e r r i g h t o n e i s t h e N e w l y D e v e l o p e d combining them with precise land use data. In addition, Residential Area, the lower right one the Central Business the author's objective was to clarify the relation of Area, the middle one the Urban Fringe Area and the left one the these indexes to each land use class. Seaside Complex Area. The white is the Outside area". It was drawn by using the Detached Digital Information issued by the 2. Methodology Geographical Survey Institute. 2.1 Data processing In this study, Detached Digital Information of the into this size. The domain for the analysis was set as Kinki area of 1996 issued by the Geographical Survey shown in Fig.1., which has 3120 pixels by 1680 pixels. Institute of Japan was employed to grasp land use and 2.2 The analysis flow its distribution, and six classes, Low-story Houses, All the pixels were covered by tiles, which were High or Middle-story Houses, Industrial Facilities, sized 16 pixels by 16 pixels, and were set as basic Commercial or Business Facilities, Roads and Others units for the analyses. The whole domain was therefore were extracted from the digital map, where Low-story covered by 105 by 195 tiles. If a tile had pixels which Houses means houses of one to three stories, and High corresponded to unclassified land use, like the outside or Middle-story Houses means houses higher than four areas of the original digital maps, they were removed stories. The digital map has a 10m resolution of land from the analysis samples. As a result, 15023 tiles from use in a large area with precise classes. among 20475 tiles remained for analysis. Wi t h r e g a r d s t o g r e e n a r e a s , r e m o t e s e n s i n g The ratio of area, Moran's I and the entropy of each data acquired by Aster GDS (The ID of the scene land use class on each tile were calculated by programs i s 0 3 0 9 1 9 0 1 5 1 4 1 0 3 1 0 0 2 1 0 0 5 . ) w a s a l s o u s e d t o which were written for calculating Moran's I and the determine where green areas were located because entropy, and by the use of GIS. The value of each grid green areas in the digital map sometimes include bare was set as 1 if the pixel corresponded to the focused areas like baseball fields or open spaces covered by on land use class, and as 0 if not. This means that the artificial pavement. The green areas were extracted value of a pixel altered as the land use class changed. by the following procedures. First, the green areas C a l c u l a t i o n s w e r e i m p l e m e n t e d b y c h a n g i n g t h e were separated from the other areas by employing focused on land use in each tile. the maximum likelihood method by using data of one 2.3 Definition of areas for comparative studies visible band and three near-infrared bands of Aster These results were separately summarized in four data, in which mountainous areas, forested areas different types of area: a newly developed residential and urban areas were also included as supervisors. area (usually called "New Town" in Japanese), a central Second, cloud areas were removed from areas which business area, a typical urban fringe area and a seaside w e r e c l a s s i f i e d a s n o n - g r e e n a r e a s b e c a u s e t h e y complex area, respectively. The Senri New Town area have high reflectance in all wavelength bands of the was chosen as a newly developed residential area, and remote sensing data. If the pixels of these cloud areas the central part of Osaka, which is one of the largest corresponded to green areas on the digital map, then cities in Japan, was set as a central business area. As an the pixels were redefined as green areas. Since this urban fringe area, Hanshin-kan, which is between two remote sensing image is one of a relatively clear day, large city centers, Osaka and Kobe, was chosen. The the cloudy areas which correspond to green areas on area has been undergoing urban sprawl for about the the digital map were considered to be mountainous past fifty years. Formerly, it was principally composed areas, because in Japan mountainous areas tend to be of agricultural fields. The area is considered to be a covered by clouds even during clear weather. typical Japanese suburban residential area, composed The remote sensing data was projected onto a mainly of relatively new houses, commercial facilities Japanese standard coordinate system and the pixel was and industrial facilities, but still containing the spatial resized into a 17.75m grid. Corresponding to the size, frames or old houses from former agricultural villages. the resolution of the digital map was also reformatted Seaside areas vary in form and land use composition, 428 JAABE vol.7 no.2 November 2008 Takashi Kyakuno but the most typical case is one dominated solely by T h e i n f o r m a t i o n e n t r o p y i s a n i n d e x w h i c h new industrial facilities. Considering the typical case, numerically indicates the variation of areas and their however, may only lead to obvious results, so another dispersion. It shows the maximum number when the case in which there are remnants of former fishing areas of each class are equivalent and the cells are villages or agricultural villages is considered for the adjacent to cells of each class in the same probability. analyses. A rough map of the areas, indicating their On the other hand, it shows 0 if the domain is occupied 1)2) locations, is shown in Fig.1. by only one class. The definition is as follows . 2.4 The spatial autocorrelation and information (2) entropy As has been discussed, Moran's I is an index which Where i, j is the running number of each land use relates to the size and number of clusters, and can be class (defined as 1 in the case that the land use class interpreted in the same way as the normal correlation is focused on, but 0 in the other land use classes), p is coefficient, where 1 means high correlation and 0 the ratio of an area of land use class i in a target tile, q ij means no relation. In the Moran's I index, there are is the probability of which land use class j is adjacent various ways to consider the neighborhood relation. In when considering land use class i. ( w =1, each i). j ij this study, only cells adjacent to any targeted cell were The relation of these two indexes is shown in Fig.2., considered, and cells which were placed in diagonal in which typical patterns of dispersion are shown as places on the map were not considered. The equation is points in the plane consisting of these two indexes. as follows. For example, the checker board pattern of a land use indicates -1 in Moran's I and 1 in entropy. Then, the relation is plotted at the bottom of the plane. (1) T h e r e l a t i o n i s a l s o p l o t t e d i n t h e u p p e r r i g h t hand side when some clusters are formed. Random Where i, j are the running numbers of each cell dispersion patterns are indicated as points in the right (1<=i, j<=256), x is the value of the cell i (it is 1 if hand side, and cases in which a few of the grids of a the cell corresponds to a focusing class, and 0 if not), land use are dispersed are shown as points of the left x is the mean of x in the calculation domain, n is the hand side. Some actual samples are illustrated. total number of cells in a tile (n=256 in this study), w ij is the weighing variable (in this study, it is set as 1 if 3. Results and Discussion cell i and cell j are adjacent to each other in either the 3.1 Land use patterns of each class vertical or horizontal direction, and 0 if not). Seven thousand one hundred and one tiles, which Fig.2. Theoretical Model of Relation between Entropy and Spatial Autocorrelation JAABE vol.7 no.2 November 2008 Takashi Kyakuno 429 contain more than 20% of the urbanized area, are in particular patterns, and it is therefore generally chosen from all tiles. An urbanized area refers to difficult to define their typical dispersion patterns of classes other than water zones and green zones. In each the Commercial or Business Facilities. If business tile, the spatial autocorrelation and entropy of each facilities and commercial facilities are, however, land use class were calculated and are shown as points analyzed separately, other results will be acquired in Fig.3. This illustrates a rough tendency towards because business facilities are likely to form more dispersion of each land use class in urban areas. clusters than commercial facilities due to the zoning Low-story Houses shows widely spread points in system of Japanese urban planning law. It is difficult the plane, and is densely accumulated on the right to precisely distinguish between business facilities and hand side, which means that such houses are placed commercial facilities, because many facilities serve in various forms and show various dispersion patterns both functions. in urban areas. But, most of them tend to be dispersed T h e J a p a n e s e u r b a n p l a n n i n g s y s t e m d o e s n o t randomly in urban areas, as can be seen by comparing usually exclude small commercial facilities, even in the figure with the theoretical model shown in Fig.2. zones for residential areas, therefore such facilities High or Middle-story Houses shows more monotonous can be built in various forms among various land use d i s p e r s i o n p a t t e r n s t h a n L o w - s t o r y H o u s e s . I n classes. They are sometimes isolated in residential particular, there are few randomly dispersed patterns areas or industrial areas, but are sometimes clustered or stripe patterns unlike with Low-story Houses. This together. The exception is the case of the so-called m e a n s t h a t H i g h o r M i d d l e - s t o r y H o u s e s t e n d t o New Town area, because land use plans are strict and aggregate in urban areas. Industrial Facilities show a commercial facilities are encouraged to aggregate at similar tendency as High or Middle-story Houses. town centers in advance. Commercial or Business Facilities show as widely 3.2 Land use characteristics in different types of spread plots in the plane, as do Low-story Houses. area However, there are no densely accumulated domains Figs.4.-1, 5.-1, 6.-1 and 7.-1 show land use maps of in the plane as in Low-story Houses, which means the four different types of areas and Figs.4.-2, 5.-2, 6.-2 that Commercial or Business Facilities do not always and 7.-2 are graphs showing the composition of each assume a particular dispersion pattern but quite varied land use class in the areas. The ratio of green areas ones, including random, clustered and isolated patterns. to the whole area is also displayed as a number. The The patterns of dispersion of Roads represent the reason why the green areas are dealt with separately basic framework of urban areas. The graph shows that from the other land use classes is that green areas various dispersion patterns can be taken. In particular, are found in all the land use classes mentioned in a lot of points are concentrated on the right hand side this study, and places which contains green areas of the vertical middle place of the plane, which means sometimes also have houses, roads and commercial roads tend to form striped patterns in urban areas. facilities. Figs.4.-3, 5.-3, 6.-3 and 7.-3 show the spatial Comparing these graphs, it is supposed that the autocorrelation and entropy of each land use class at locations of Commercial or Business Facilities show each tile of each area. d i v e r s e p a t t e r n s a n d a r e u n l i k e l y t o c o n c e n t r a t e A r o u g h t e n d e n c y c a n b e g r a s p e d t h r o u g h a n Fig.3. Entropy and Spatial Autocorrelation of Each Tile Class of Each Landuse Class 430 JAABE vol.7 no.2 November 2008 Takashi Kyakuno overview of the compositions of the areas. In the I n t h e ' C e n t r a l B u s i n e s s A r e a ' , C o m m e rc i a l o r ' N e w l y D e v e l o p e d R e s i d e n t i a l A r e a ' , t h e a r e a o f B u s i n e s s F a c i l i t i e s c a n b e r e g a r d e d a s f o r m i n g Roads, Low-story Houses and High or Middle-story vermicular clusters by referring to Fig.5.-3, which Houses are large as are Others. Others are thought to is also shown in the land use map. Commercial or be mainly green areas. In the 'Central Business Area', Business Facilities are connecting until roads cut Commercial or Business Facilities and Roads prevail them off. Roads shows similar patterns as Commercial because the land use of these areas is simplified, and or Business Facilities, and can be thought to form several classes characterize the whole area. In the vermicular cluster patterns as well. Different from 'Urban Fringe Areas', there are more Low-story Houses ' N e w l y D e v e l o p e d R e s i d e n t i a l A r e a s ' , n a r r o w and Roads than other classes since the area is typical of networked roads which are indicated as points around suburban residential areas in Japan, and mainly consist x=1.8-2.0 and y=0 are never seen. This indicates that of a variety of houses. In the 'Seaside Complex Area', these two land use classes form many clusters in micro various land use classes exist almost equally, and there perspective, and these clusters are mixed in macro are no conspicuous characteristics. perspective. In the area, the Roads areas tend to be I n o r d e r t o g r a s p t h e m i x i n g o f l a n d u s e , i t i s wider than most roads in usual residential areas, and effective to refer to the spatial autocorrelation and the density of Roads is high. There are only two main entropy. Figs.3.-3, 4.-3, 5.-3 and 6.-3 show a different land use classes and the land use patterns can be almost tendency of distribution of each land use class. Land regarded as simplified in small scale but mixed in large use classes sharing more than 5 percent in each area scale. are plotted in each figure. In the 'Newly Developed I n t h e ' U r b a n F r i n g e A r e a ' , L o w - s t o r y H o u s e s Residential area', Low-story Houses tends to show a show a variety of patterns as can be seen from the vermicular cluster pattern or to form small clusters, dispersed pattern in Fig.6.-3. Some Low-story Houses whereas High or Middle-story Houses are likely to form clusters vermiculated by Roads, and other Low- form big clusters, compared with the figure in the story Houses form line patterns. Several Low-story theoretical model in Fig.2. Roads are distributed in Houses are isolated. As discussed before, this area various ways, including line-like patterns in the area. is a typical suburban area of Japan, in which some It is interesting that Green shows a similar pattern zones have been developed using deliberate plans, t o L o w - s t o r y H o u s e s . I n t h e ' N e w l y D e v e l o p e d but most zones were created without any total plan so Residential Area', the lot size of each low story house that urban sprawl occurred. The former land use and is large and there are generally relatively large gardens periods of development of each zone are also different, in them. Furthermore, in the area there are some large which cause inconsistent land use patterns of the parks, including a mass of green areas in addition to area. This tendency also relates to the pattern of the many trees on the street. Green areas sometimes form roads. Generally, narrow networked roads prevail over big clusters, and sometimes form vermicular clusters other types. The spatial frames of former agricultural like Low-story Houses. On the other hand, High or villages can still be seen in these forms of road. It is Middle-story Houses have an obvious tendency to a typical phenomenon of the area that Commercial or form clusters. In the 'Newly Developed Residential Business Facilities are not clustered, but form line-like Area', high story buildings like apartment houses were patterns. This is because the sizes of lots in the area are separated from other types of buildings according to generally small and the roads are narrow. Therefore, it precise land use plans, and therefore High or Middle- is prohibited by the building standard law in Japan to story Houses were regulated in designated zones. There build large-scale buildings in these areas. It is a matter are some points which are located in the left hand side of course that Commercial or Business Facilities form of the vertical middle place in Fig.4.-3, which means lines along roads. that High or Middle-story Houses are isolated in some In the 'Seaside Complex Areas', each land use forms tiles but not clustered. There are no isolated Low-story various patterns of distribution, the same as the 'Urban Houses, which means that they are never isolated in Fringe Area'. Low-story Houses are located in various such a planned area. Vermicular clusters of Low-story patterns as well as Commercial or Business Facilities. Houses are the result of the existence of narrow streets They sometimes form lines, clusters, vermicular running through a Low-story Houses area. Roads show clusters, or are isolated. High or Middle-story Houses a variety of values in the figure. One characteristic is form either large clusters or small clusters, the same that roads make some clusters, which are indicated as Industrial Facilities. Their sizes may depend on by points on the upper right hand side of Fig.4.-3. the sizes of the lots in which the facilities are located. This means that there are very wide roads in the area. Roads also show various forms; some are narrowly Each type of land use tends to cluster in the 'Newly networked, others are wide. The crossing points of Developed Residential Area', and the types of land wide roads can be regarded as a kind of "cluster" of use that are not Roads are clearly separated from each Roads pixels, and this is indicated as points in the other. upper right hand side in Fig.7.-3. JAABE vol.7 no.2 November 2008 Takashi Kyakuno 431 Fig.4.-1 Land Use Map of 'Newly Developed Residential Area' Fig.5.-1 Land Use Map of 'Central Business Area' Fig.4.-2 Percentages for Areas of Each Land Use Class and Ratio Fig.5.-2 Percentages for Areas of Each Land Use Class and Ratio of Green Area to the Whole Area in 'Newly Developed of Green Area to the Whole Area in 'Central Business Area' Residential Area' Fig.4.-3 Plots by Entropy and Spatial Autocorrelation of Each Fig.5.-3 Plots by Entropy and Spatial Autocorrelation of Land Use Class in 'Newly Developed Residential Area' Each Land Use Class in 'Central Business Area' 432 JAABE vol.7 no.2 November 2008 Takashi Kyakuno Fig.6.-1 Land Use Map of 'Urban Fringe Area' Fig.7.-1 Land Use Map of 'Seaside Complex Area' Fig.6.-2 Percentages for Areas of Each Land Use Class in Fig.7.-2 Percentages for Areas of Each Land Use Class in 'Urban Fringe Area' 'Seaside Complex Area' Fig.6.-3 Plots by Entropy and Spatial Autocorrelation of Each Fig.7.-3 Plots by Entropy and Spatial Autocorrelation of Each Land Use Class in 'Urban Fringe Area' Land Use Class in 'Seaside Complex Area' JAABE vol.7 no.2 November 2008 Takashi Kyakuno 433 Using these two indexes led to interesting results. space. Another grid system like a pentagon system or Planes spanned by these indexes express various forms triangle system may lead to another result. This study of the mixture of land use. For example, big clusters is a first step for quantitatively describing urban land and vermiculated big clusters can be distinguished from use pattern. Based upon the fact that many patterns each other by referring to the spatial autocorrelation. of dispersion were well comprehended by the scheme Using the two indexes enables us to clearly represent of this study, these problems will be discussed with the difference in the features of land use patterns various cases and various methodologies. between Low-story Houses and High or Middle–story Houses in the 'Newly Developed Residential Area' Acknowledgement well. Furthermore, one cluster can be distinguished The author is grateful for the support by Grant-in- from several small clusters by referring to the spatial Aid for Scientific Research (18700239) of Japan. autocorrelation. On the other hand, vermicular clusters can be distinguished from small clusters or line-like References 1) Koide, O. (1977) 'Tochiriyoukonngoudo no Tekiyou Narabini patterns by referring to the entropy. Differences in Sono Kentei' (in Japanese), City planning review, 12, pp.79-84 (in the road pattern of the 'Central Business Area' and Japanese). 'Urban Fringe Area' are well represented by using 2) Tamagawa, H. (1982) 'Tochirinoyou no Titsujosei no Suuriteki entropy. The land use patterns of Low-story Houses of Hyogen ni Kansuru Kenkyu' (in Japanese), City planning review, different areas can also be distinguished by employing 17, pp.73-78 (in Japanese). 3) Moon, T. et al. (1999) A study on the Indicator of Mixed Degree entropy. In 'Newly Developed Residential Areas', Low- of Land Use, City planning review, 26, pp.505-510 (in Japanese). story Houses tend to form vermicular clusters, but are 4) Tsunekawa, A. et al. (1991) Quantitative Analysis Methods of sometimes isolated or form small clusters in 'Seaside Mixed Land Use, Environmental Information Science, 20(2), Complex Areas'. Entropy plays an important role in pp.115-120 (in Japanese). 5) Kumagai, J. (2000) Development of a Spatial Analysis Method distinguishing these differences. for Land Cover taking into account the Complexity of Local Distributions,Environmental Information Science, 14, pp.1-5 (in 4. Conclusion Japanese). Applying both entropy and spatial autocorrelation in 6) Kyakuno, T. and Sotoma, M. (2004) Study on the change of order to understand urban land use is a more effective land use and the degree of mixture of it focusing on distance from coastal line in waterfront area. Journal of Architecture and method for comprehending land use classes than using Planning, 579, pp.75-80 (in Japanese). either index alone. Applying both indexes offers a 7) Kyakuno, T. and Miyazaki, H. (2005) Texture analysis of SAR new way for describing the morphology of urban land data and its relation to land coverage in urban area. Journal of use. Entropy is targeted at diversity and complexity, Architecture and Planning, 590, pp.111-116 (in Japanese). while spatial autocorrelation is targeted at representing 8) Zhang, C. (1999) Development of a Spatial Analysis Tool for Irregular Zones Using the Spatial Data Framework,Graphical spatial similarity on a local scale. Using both indexes Review of Japan, 72A-3, pp.166-177 (in Japanese). enabled the author to grasp urban land use from the 9) Yoon, J. et al. (2004) A Study on the Planning Utilization Based perspective of diversity and similarity. by the Spatial Cognition of Mental Evaluation, Journal of There are still some problems with this scheme. Architecture and Planning, 585, pp.61-67 (in Japanese). First, some spatial situations which look different 10) Myint, S. W. (2003) Fractal approaches in texture analysis and classification of remotely sensed data - comparisons with spatial from each other have close values in both indexes. autocorrelation technique and simple descriptive statistics-, Int. J. T h i s t e n d e n c y b e c a m e c o n s p i c u o u s i n l i n e - l i k e Remote Sensing, 24(9), pp.1925-1947. dispersion patterns. The second problem concerns 11) Myint, S. W. et al. (2004) Wavelets for Urban Spatial Feature scale dependency. In this study, the scale of the basic Discrimination -Comparisons with Fractal, Spatial Autocorrelation, and Spatial Co-occurrence Approaches-, Photogrammetric & grid was set to 17.75m due to the pixel size of the Remote Sensing, 70(7), pp.803- 812. remote sensing data, and the analysis tiles were set to 12) Cliff A.D. and Ord J.K.: Spatial processes -models & applications- 16 pixels by 16 pixels. The reason why this tile size Pion, 1981. is employed is that in future studies these results will be compared with results by the fractal analysis in which it is desirable that the analysis tiles have a size of 2 pixels and the tile size is not excessively large for usual Japanese cities. The result will differ if these basic values are different. In particular, making the grid size smaller will lead to a change of the result. The third problem originates in the way in which adjacent cells were considered. In this study, for the purpose o f r e d u c i n g c o m p u t i n g t i m e , d i a g o n a l c e l l a r e a s were not regarded as adjacent. When taking this into account, different results may occur. Furthermore, the Euclidian system is not the only way to address urban 434 JAABE vol.7 no.2 November 2008 Takashi Kyakuno

Journal

Journal of Asian Architecture and Building EngineeringTaylor & Francis

Published: Nov 1, 2008

Keywords: distribution and mixture of urban land use; spatial autocorrelation; information entropy; GIS; remote sensing

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