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The Principle of Scaling of Geographic Space and its Application in Urban Studies
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management. KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Samhällsplanering och miljö, Geoinformatik och Geodesi.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Geographic space is the large-scale and continuous space that encircles the earth and in which human activities occur. The study of geographic space has drawn attention in many different fields and has been applied in a variety of studies, including those on cognition, urban planning and navigation systems. A scaling property indicates that small objects are far more numerous than large ones, i.e., the size of objects is extremely diverse. The concept of scaling resembles a fractal in geometric terms and a power law distribution from the perspective of statistical physics, but it is different from both in terms of application. Combining the concepts of geographic space and scaling, this thesis proposes the concept of the scaling of geographic space, which refers to the phenomenon that small geographic objects or representations are far more numerous than large ones. From the perspectives of statistics and mathematics, the scaling of geographic space can be characterized by the fact that the sizes of geographic objects follow heavy-tailed distributions, i.e., the special non-linear relationships between variables and their probability.

In this thesis, the heavy-tailed distributions refer to the power law, lognormal, exponential, power law with an exponential cutoff and stretched exponential. The first three are the basic distributions, and the last two are their degenerate versions. If the measurements of the geographic objects follow a heavy-tailed distribution, then their mean value can divide them into two groups: large ones (a low percentage) whose values lie above the mean value and small ones (a high percentage) whose values lie below. This regularity is termed as the head/tail division rule. That is, a two-tier hierarchical structure can be obtained naturally. The scaling property of geographic space and the head/tail division rule are verified at city and country levels from the perspectives of axial lines and blocks, respectively.

In the study of geographic space, the most important concept is geographic representation, which represents or partitions a large-scale geographic space into numerous small pieces, e.g., vector and raster data in conventional spatial analysis. In a different context, each geographic representation possesses different geographic implications and a rich partial knowledge of space. The emergence of geographic information science (GIScience) and volunteered geographic information (VGI) greatly enable the generation of new types of geographic representations. In addition to the old axial lines, this thesis generated several types of representations of geographic space: (a) blocks that were decomposed from road segments, each of which forms a minimum cycle such as city and field blocks (b) natural streets that were generated from street center lines using the Gestalt principle of good continuity; (c) new axial lines that were defined as the least number of individual straight line segments mutually intersected along natural streets; (d) the fewest-turn map direction (route) that possesses the hierarchical structure and indicates the scaling of geographic space; (e) spatio-temporal clusters of the stop points in the trajectories of large-scale floating car data.

Based on the generated geographic representations, this thesis further applies the scaling property and the head/tail division rule to these representations for urban studies. First, all of the above geographic representations demonstrate the scaling property, which indicates the scaling of geographic space. Furthermore, the head/tail division rule performs well in obtaining the hierarchical structures of geographic objects. In a sense, the scaling property reveals the hierarchical structures of geographic objects. According to the above analysis and findings, several urban studies are performed as follows: (1) generate new axial lines based on natural streets for a better understanding of urban morphologies; (2) compute the fewest-turn and shortest map direction; (3) identify urban sprawl patches based on the statistics of blocks and natural cities; (4) categorize spatio-temporal clusters of long stop points into hotspots and traffic jams; and (5) perform an across-country comparison of hierarchical spatial structures.

The overall contribution of this thesis is first to propose the principle of scaling of geographic space as well as the head/tail division rule, which provide a new and quantitative perspective to efficiently reduce the high degree of complexity and effectively solve the issues in urban studies. Several successful applications prove that the scaling of geographic space and the head/tail division rule are inspiring and can in fact be applied as a universal law, in particular, to urban studies and other fields. The data sets that were generated via an intensive geo-computation process are as large as hundreds of gigabytes and will be of great value to further data mining studies.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2012. , xii, 90 p.
Keyword [en]
geographic space, scaling, GIScience, VGI, OSM, heavy-tailed distribution, the head/tail division rule, space syntax, nature street, urban sprawl, floating car data, hierarchical spatial structure
National Category
Geotechnical Engineering
Identifiers
URN: urn:nbn:se:hig:diva-18932ISBN: 978-91-7501-277-3OAI: oai:DiVA.org:hig-18932DiVA: diva2:786271
Public defence
2012-03-15, D2, Lindstedtsvägen 5 Entreplan, Royal Institute of Technology, 13:30 (English)
Opponent
Supervisors
Projects
Hägerstrand project entitled “GIS-based mobility information for sustainable urban planning and design”
Available from: 2015-02-05 Created: 2015-02-05 Last updated: 2015-12-11Bibliographically approved
List of papers
1. Defining and generating axial lines from street center lines for better understanding of urban morphologies
Open this publication in new window or tab >>Defining and generating axial lines from street center lines for better understanding of urban morphologies
2012 (English)In: International Journal of Geographical Information Science, ISSN 1365-8816, E-ISSN 1362-3087, Vol. 26, no 8, 1521-1532 p.Article in journal (Refereed) Published
Abstract [en]

Axial lines are defined as the longest visibility lines for representing individual linear spaces in urban environments. The least set of axial lines that cover the free space of an urban environment or the space between buildings constitute what is often called an axial map. This is a fundamental tool in space syntax, a theory developed by Bill Hillier and his colleagues for characterizing the underlying urban morphologies. For a long time, generating axial lines with the help of some graphic software has been a tedious manual process that is criticized for being time consuming, subjective, or even arbitrary. In this article, we redefine axial lines as the least set of individual straight line segments mutually intersected along natural streets that are generated from street center lines using the Gestalt principle of good continuity. Based on this new definition, we develop an automatic solution for generating the newly defined axial lines from street center lines. We apply this solution to six typical street networks (three from North America and three from Europe) and generate a new set of axial lines for analyzing the urban morphologies. Through a comparison study between the new axial lines and the conventional or old axial lines and between the new axial lines and natural streets, we demonstrate with empirical evidence that the newly defined axial lines are a better alternative for capturing the underlying urban structure.

National Category
Computer and Information Science
Identifiers
urn:nbn:se:hig:diva-12984 (URN)10.1080/13658816.2011.643800 (DOI)000306976000009 ()2-s2.0-84864696253 (ScopusID)
Available from: 2012-09-20 Created: 2012-09-20 Last updated: 2015-12-11Bibliographically approved
2. A novel approach to the identification of urban sprawl patches based on the scaling of geographic space
Open this publication in new window or tab >>A novel approach to the identification of urban sprawl patches based on the scaling of geographic space
2011 (English)In: International journal of Geomatics and Geosciences, ISSN 0976-4380, Vol. 2, no 2, 415-429 p.Article in journal (Refereed) Published
Abstract [en]

This paper introduces a novel approach to identifying urban sprawl patches based on the statistics of blocks and natural cities under the principle of scaling of geographic space. Blocks are the minimum cycles decomposed from a road network and the important geographic elements in the process of urbanization. Scaling of geographic space refers to the phenomenon that small geographic objects are far more numerous than large ones. In this study, the measurements of block area, morphology and structure are found to demonstrate scaling property and follow heavy tailed distributions. Because of this, the mean values of these measurements can clearly divide all blocks into a two-level hierarchical structure, of which each hierarchy represents different geographical implications. For instance, small blocks imply the urban area while large ones imply rural area. Based on these findings, an improved method is proposed to aggregate the small blocks into natural cities in Texas. We further identify the abnormal blocks inside the natural city of Dallas, Texas as sprawling blocks, which constitute what we call urban sprawl patches. Multiple levels of urban sprawl are classified by performing the above process iteratively. This approach provides a quantitative and natural way to assess urban sprawl in the context of the urban environment.

National Category
Computer and Information Science
Identifiers
urn:nbn:se:hig:diva-12986 (URN)
Available from: 2012-09-20 Created: 2012-09-20 Last updated: 2015-12-11Bibliographically approved
3. Uncovering urban mobility patterns with massive floating car data
Open this publication in new window or tab >>Uncovering urban mobility patterns with massive floating car data
(English)In: Computers, Environment and Urban Systems, ISSN 0198-9715Article in journal (Other academic) Submitted
Abstract [en]

Urban mobility patterns are crucial to understanding urban structures, with applications ranging from traffic forecasting to urban planning. This paper develops a bottom-up approach to assess urban mobility patterns in a quantitative manner based on over 14,200,000 GPS points obtained from 11,263 moving taxicabs in Wuhan, Hubei, China. These taxicabs are equipped with GPS devices and are continuously being driven; thus, the corresponding mobile data sets (i.e., floating car data) cover the entire urban open space and bear traffic characteristics. Consequently, such mobile data are unique and more suitable for urban mobility analysis. Instead of employing the commonly used trajectory methods, we divided the GPS points into moves and stops, focusing on the latter. We found that the time intervals for all of the stops demonstrate the scaling property; that is, the stops can be separated into far more short ones than long ones, which we believe to be typical of the traffic system. The long stops showed a cluster pattern in a self-organized way at different timelines. We extracted these spatiotemporal clusters in a natural way and found that their sizes bear a heavy-tailed distribution. We further analyzed their evolution in both time and space and then categorized them into hotspots and traffic jams, of which the distributions objectively and quantitatively suggest the dynamic and multiple nuclei of urban mobility patterns. This study also provides insights into research on mobile data from the perspective of a complex system.

Keyword
Urban mobility patterns, floating car data, self-organized, heavy-tailed distribution, bottom-up, spatiotemporal cluster
National Category
Civil Engineering
Identifiers
urn:nbn:se:hig:diva-18934 (URN)
Available from: 2012-02-14 Created: 2015-02-05 Last updated: 2015-02-05Bibliographically approved
4. An across-country comparison of hierarchical spatial structures of cities
Open this publication in new window or tab >>An across-country comparison of hierarchical spatial structures of cities
2014 (English)In: Geomatica, ISSN 1195-1036, Vol. 68, no 3, 207-217 p.Article in journal (Refereed) Published
Abstract [en]

This paper investigates the hierarchical structures of twenty-nine selected European countries from the perspectives of blocks and natural cities, and further makes an across-country comparison among them. Blocks are minimum cycles consisted of road segments in the road network of a whole country, and natural cities are defined as the aggregations of small blocks. We test the size distributions of blocks and natural cities at country level and find both exhibit heavy tailed distributions. Especially, the power law distribution of city sizes indicates the scaling property. Therefore, the cities in a country can be repeatedly grouped into a similar two-tier structure of head and tail via the head/tail division rule. The ascending tiers represent the small, middle, big and mega cities, respectively. Accordingly, a simple model is developed to evaluate and cross compare the degree of similarity and stability of the hierarchical structures of cities. Moreover, cities and blocks are the functional units of a country and the correlation coefficients between city sizes/number of blocks and the economic factors (i.e. GDP/population) are up to 0.87. We further conjecture that the compared results of hierarchies can serve as an indicator to assess that of country’s economic system.

Keyword
Hierarchical spatial structure, heavy tailed distribution, scaling of geographic space, the head/tail division rule, road networks
National Category
Civil Engineering
Identifiers
urn:nbn:se:hig:diva-18935 (URN)10.5623/cig2014-305 (DOI)
Available from: 2012-02-14 Created: 2015-02-05 Last updated: 2015-02-05Bibliographically approved
5. Computing the fewest-turn map directions based on the connectivity of natural roads
Open this publication in new window or tab >>Computing the fewest-turn map directions based on the connectivity of natural roads
2011 (English)In: International Journal of Geographical Information Science, ISSN 1365-8816, E-ISSN 1362-3087, Vol. 25, no 7, 1069-1082 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we introduce a novel approach to computing the fewest-turn map directions or routes based on the concept of natural roads. Natural roads are joined road segments that perceptually constitute good continuity. This approach relies on the connectivity of natural roads rather than that of road segments for computing routes or map directions. Because of this, the derived routes possess the fewest turns. However, what we intend to achieve are the routes that not only possess the fewest turns but are also as short as possible. This kind of map direction is more effective and favored by people because they bear less cognitive burden. Furthermore, the computation of the routes is more efficient because it is based on the graph encoding the connectivity of roads, which is substantially smaller than the graph of road segments. We experimented on eight urban street networks from North America and Europe to illustrate the above-stated advantages. The experimental results indicate that the fewest-turn routes possess fewer turns and shorter distances than the simplest paths and the routes provided by Google Maps. For example, the fewest-turn-and-shortest routes are on average 15% shorter than the routes suggested by Google Maps, whereas the number of turns is just half as much. This approach is a key technology behind FromToMap.org – a web mapping service using openstreetmap data.

Place, publisher, year, edition, pages
London: Taylor & Francis, 2011
National Category
Other Earth and Related Environmental Sciences Environmental Analysis and Construction Information Technology Other Civil Engineering
Identifiers
urn:nbn:se:hig:diva-10007 (URN)10.1080/13658816.2010.510799 (DOI)000295467600002 ()2-s2.0-79961243742 (ScopusID)
Funder
Formas
Available from: 2011-09-02 Created: 2011-09-02 Last updated: 2015-12-11Bibliographically approved
6. Scaling of geographic space from the perspective of city and field blocks and using volunteered geographic information
Open this publication in new window or tab >>Scaling of geographic space from the perspective of city and field blocks and using volunteered geographic information
2012 (English)In: International Journal of Geographical Information Science, ISSN 1365-8816, E-ISSN 1362-3087, Vol. 26, no 2, 215-229 p.Article in journal (Refereed) Published
Abstract [en]

Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This article develops a novel perspective to the scaling of geographic space using large street networks involving both cities and countryside. Given a street network of an entire country, we decompose the street network into individual blocks, each of which forms a minimum ring or cycle such as city blocks and field blocks. The block sizes demonstrate the scaling property, that is, far more small blocks than large ones. Interestingly, we find that the mean of all the block sizes can easily separate between small and large blocks –a high percentage (e.g., 90%) of smaller ones and a low percentage (e.g., 10%) of larger ones. Based on this regularity, termed as the head/tail division rule, we propose an approach to delineating city boundaries by grouping the smaller blocks. The extracted city sizes for the three largest European countries (France, Germany, and United Kingdom) exhibit power law distributions. We further define the concept of border number as a topological distance of a block far from the outmost border to map the center(s) of the country and the city. We draw an analogy between a country (or a city or geographic space in general) and a complex organism like the human body or the human brain to further elaborate on the power of this block perspective in reflecting the structure or patterns of geographic space.

Keyword
power law distribution, scaling of geographic space, data-intensive geospatial computing, street networks
National Category
Computer and Information Science
Identifiers
urn:nbn:se:hig:diva-12971 (URN)10.1080/13658816.2011.575074 (DOI)000300611200002 ()2-s2.0-84863339304 (ScopusID)
Available from: 2012-09-19 Created: 2012-09-19 Last updated: 2015-12-11Bibliographically approved
7. Automatic generation of the axial lines of urban environments to capture what we perceive
Open this publication in new window or tab >>Automatic generation of the axial lines of urban environments to capture what we perceive
2010 (English)In: International Journal of Geographical Information Science, ISSN 1365-8816, E-ISSN 1365-8824, Vol. 24, no 4, 545-558 p.Article in journal (Refereed) Published
Abstract [en]

Based on the concepts of isovists and medial axes, we developed a set of algorithms that can automatically generate axial lines for representing individual linearly stretched parts of open space of an urban environment. Open space is the space between buildings where people can freely move around. The generation of the axial lines has been a key aspect of space syntax research, conventionally relying on hand-drawn axial lines of an urban environment, often called axial map, for urban morphological analysis. Although various attempts have been made towards an automatic solution, few of them can produce the axial map that consists of the least number of longest visibility lines, and none of them really works for different urban environments. Our algorithms provide a better solution than existing ones. Throughout this article, we have also argued and demonstrated that the axial lines constitute a true skeleton, superior to medial axes, in capturing what we perceive about the urban environment.

Place, publisher, year, edition, pages
London: Taylor & Francis, 2010
National Category
Environmental Analysis and Construction Information Technology Other Earth and Related Environmental Sciences Other Civil Engineering
Identifiers
urn:nbn:se:hig:diva-10005 (URN)10.1080/13658810902950351 (DOI)000275655500004 ()2-s2.0-77949493384 (ScopusID)
Available from: 2011-09-02 Created: 2011-09-02 Last updated: 2016-07-04Bibliographically approved

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