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Special Issue "Entropy and Scale-Dependence in Urban Modelling"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 31 August 2019.

Special Issue Editors

Guest Editor
Prof. Dr. Darren Robinson

School of Architecture, The University of Sheffield, Sheffield S10 2TN, UK
Website | E-Mail
Interests: statistical modelling; energy modelling; multi-agent simulation; integrated urban modelling
Guest Editor
Dr. Yong Mao

School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
Website | E-Mail
Interests: statistical modelling; spatial analysis; urban land use and transport modelling

Special Issue Information

Dear Colleagues,

Cities are complex systems that require resources to function. They are maintained in more or less stable states by exchanging entropy across their boundaries: Relatively low entropy resources are imported, processed and higher entropy wastes are exported. Entropy, as originally developed by Boltzmann, measures all microscopic-scale configurations of the universe, and in combination with the second law of thermodynamics, provides a robust metric for assessing universal irreversibility, and therefore future sustainability. This thermodynamic entropy, is dominated in practice by energy use. At macroscopic scales, cities exhibit non-trivial patterns and configurations, e.g., in land use and traffic flows. Information entropy, as developed by Shannon and Von Neumann, assesses the variations within these patterns and configurations without explicitly addressing the underlying variations at microscopic scales. This macroscopic information entropy plays a prominent role in urban modelling and optimization. In his seminal 1970 book ‘Entropy in Urban and Regional Modelling’, Alan Wilson established entropy maximization as a versatile method for a range of urban studies.

This Special Issue focuses on the application of entropy in modelling and evaluating urbanisation at multiple scales. The aim is to clarify the boundaries of applicability of thermodynamic and information entropies, to demonstrate their utility and to identify promising avenues for future exploration.

Prof. Darren Robinson
Dr. Yong Mao
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • thermodynamic entropy
  • information entropy
  • spatial scales and metrics
  • geographical information systems
  • sustainability
  • urban modelling

Published Papers (7 papers)

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Research

Open AccessArticle
Delimitating the Natural City with Points of Interests Based on Service Area and Maximum Entropy Method
Entropy 2019, 21(5), 458; https://doi.org/10.3390/e21050458
Received: 17 February 2019 / Revised: 25 April 2019 / Accepted: 26 April 2019 / Published: 2 May 2019
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Abstract
The natural city, which is essential to understand urban physical scale and identify urban sprawling in urban studies, represents the urban functional boundaries of the city defined by human activities rather than the administrative boundaries. Most studies tend to utilize physical environment data [...] Read more.
The natural city, which is essential to understand urban physical scale and identify urban sprawling in urban studies, represents the urban functional boundaries of the city defined by human activities rather than the administrative boundaries. Most studies tend to utilize physical environment data such as street networks and remote sensing data to delimitate the natural city, however, such data may not match the real distribution of human activity density in the new cities or even ghost cities in China. This paper suggests aggregating the natural city boundary from the service area polygons of points of interest based on Reilly’s Law of Retail Gravitation and the maximum entropy method, since most points of interests provide services for surrounding communities, reflecting the vitality in a bottom-up way. The results indicate that the natural city defined by points of interests shows a high resolution and accuracy, providing a method to define the natural city with POIs. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
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Open AccessArticle
Entropy and its Application to Urban Systems
Entropy 2019, 21(1), 56; https://doi.org/10.3390/e21010056
Received: 3 December 2018 / Revised: 8 January 2019 / Accepted: 9 January 2019 / Published: 12 January 2019
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Abstract
Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization [...] Read more.
Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization approach, as applied by Alan Wilson and others from the 1960s, contrasts with considerations from the 1990s of the city as a thermodynamic dissipative system, in the tradition of Ilya Prigogine. By reviewing the relevant mathematical theory, we draw the distinction among three interrelated definitions of entropy, the thermodynamic, the figurative, and the information statistical. The applications of these definitions to urban systems within the literature are explored, and the conflation of the thermodynamic and figurative interpretations are disentangled. We close this paper with an outlook on future uses of entropy in urban systems analysis. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
Open AccessArticle
Scaling Effects of Elevation Data on Urban Nonpoint Source Pollution Simulations
Entropy 2019, 21(1), 53; https://doi.org/10.3390/e21010053
Received: 3 December 2018 / Revised: 23 December 2018 / Accepted: 2 January 2019 / Published: 11 January 2019
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Abstract
The scale effects of digital elevation models (DEM) on hydrology and nonpoint source (NPS) pollution simulations have been widely reported for natural watersheds but seldom studied for urban catchments. In this study, the scale effect of DEM data on the rainfall-runoff and NPS [...] Read more.
The scale effects of digital elevation models (DEM) on hydrology and nonpoint source (NPS) pollution simulations have been widely reported for natural watersheds but seldom studied for urban catchments. In this study, the scale effect of DEM data on the rainfall-runoff and NPS pollution was studied in a typical urban catchment in China. Models were constructed based on the DEM data of nine different resolutions. The conventional model performance indicators and the information entropy method were applied together to evaluate the scale effects. Based on the results, scaling effects and a resolution threshold of DEM data exist for urban NPS pollution simulations. Compared with natural watersheds, the urban NPS pollution simulations were primarily affected by the local terrain due to the overall flat terrain and dense sewer inlet distribution. The overland process simulation responded more sensitively than the catchment outlet, showing prolonged times of concentration for impervious areas with decreasing DEM resolution. The diverse spatial distributions and accumulation magnitudes of pollutants could lead to different simulation responses to scaling effects. This paper provides information about the specific characteristics of the scale effects of DEM data in a typical urban catchment, and these results can be extrapolated to other similar catchments as a reference for data collection. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
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Open AccessArticle
Spatio–Temporal Pattern of the Urban System Network in the Huaihe River Basin Based on Entropy Theory
Entropy 2019, 21(1), 20; https://doi.org/10.3390/e21010020
Received: 18 October 2018 / Revised: 14 December 2018 / Accepted: 18 December 2018 / Published: 27 December 2018
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Abstract
As complex systems, the spatial structure of urban systems can be analyzed by entropy theory. This paper first calculates the interaction force between cities based on the gravity model, the spatial relationship matrix between cities is constructed using the method of network modeling, [...] Read more.
As complex systems, the spatial structure of urban systems can be analyzed by entropy theory. This paper first calculates the interaction force between cities based on the gravity model, the spatial relationship matrix between cities is constructed using the method of network modeling, and the spatial network modeling of urban system can be calculated. Secondly, the Efficiency Entropy (EE), Quality Entropy (QE), and System Entropy (SE) of urban system network are calculated and analyzed by information entropy. Finally, taking the Huaihe River Basin (HRB) as a case study, model verification and empirical analysis are performed. It is found that the spatio–temporal pattern of the urban system network structure in the basin is uneven: in space, the urban system network in the HRB presents a layer-by-layer spatial distribution centered on the core city of Xuzhou; meanwhile, the overall urban system network in the basin presents an orderly development trend. This study has certain theoretical and practical value for the planning of urban and urban systems and the coordinated development of regions. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
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Open AccessArticle
Spatial Measures of Urban Systems: from Entropy to Fractal Dimension
Entropy 2018, 20(12), 991; https://doi.org/10.3390/e20120991
Received: 2 November 2018 / Revised: 29 November 2018 / Accepted: 14 December 2018 / Published: 19 December 2018
Cited by 1 | PDF Full-text (2734 KB) | HTML Full-text | XML Full-text
Abstract
One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different [...] Read more.
One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurements into fractal dimensions for the spatial analysis of scale-free urban phenomena using the ideas from scaling. Urban systems proved to be random prefractal and multifractal systems. The spatial entropy of fractal cities bears two properties. One is the scale dependence: the entropy values of urban systems always depend on the linear scales of spatial measurement. The other is entropy conservation: different fractal parts bear the same entropy value. Thus, entropy cannot reflect the simple rules of urban processes and the spatial heterogeneity of urban patterns. If we convert the generalized entropies into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. Especially, the geographical analyses of urban evolution can be simplified. This study may be helpful for students in describing and explaining the spatial complexity of urban evolution. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
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Open AccessArticle
Cities, from Information to Interaction
Entropy 2018, 20(11), 834; https://doi.org/10.3390/e20110834
Received: 23 August 2018 / Revised: 8 October 2018 / Accepted: 26 October 2018 / Published: 31 October 2018
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Abstract
From physics to the social sciences, information is now seen as a fundamental component of reality. However, a form of information seems still underestimated, perhaps precisely because it is so pervasive that we take it for granted: the information encoded in the very [...] Read more.
From physics to the social sciences, information is now seen as a fundamental component of reality. However, a form of information seems still underestimated, perhaps precisely because it is so pervasive that we take it for granted: the information encoded in the very environment we live in. We still do not fully understand how information takes the form of cities, and how our minds deal with it in order to learn about the world, make daily decisions, and take part in the complex system of interactions we create as we live together. This paper addresses three related problems that need to be solved if we are to understand the role of environmental information: (1) the physical problem: how can we preserve information in the built environment? (2) The semantic problem: how do we make environmental information meaningful? and (3) the pragmatic problem: how do we use environmental information in our daily lives? Attempting to devise a solution to these problems, we introduce a three-layered model of information in cities, namely environmental information in physical space, environmental information in semantic space, and the information enacted by interacting agents. We propose forms of estimating entropy in these different layers, and apply these measures to emblematic urban cases and simulated scenarios. Our results suggest that ordered spatial structures and diverse land use patterns encode information, and that aspects of physical and semantic information affect coordination in interaction systems. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
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Open AccessArticle
Morphogenesis of Urban Water Distribution Networks: A Spatiotemporal Planning Approach for Cost-Efficient and Reliable Supply
Entropy 2018, 20(9), 708; https://doi.org/10.3390/e20090708
Received: 26 July 2018 / Revised: 23 August 2018 / Accepted: 13 September 2018 / Published: 14 September 2018
Cited by 4 | PDF Full-text (6417 KB) | HTML Full-text | XML Full-text
Abstract
Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects [...] Read more.
Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects of demand shifting and flow rearrangements are simulated and assessed with hydraulic performances. With the methodology, it is possible to test various planning and adaptation options of the future WDN, where the unknown (future) network is approximated via the co-located and known (future) road network, and hence different topological characteristics (branched vs. strongly looped layout) can be investigated. The reliability of the planning options is evaluated with the flow entropy, a measure based on Shannon’s informational entropy. Uncertainties regarding future water consumption and water loss management are included in a scenario analysis. To avoid insufficient water supply to customers during the transition process from an initial to a final WDN state, an adaptation concept is proposed where critical WDN components are replaced over time. Finally, the method is applied to the drastic urban transition of Kiruna, Sweden. Results show that without adaptation measures severe performance drops will occur after the WDN state 2023, mainly caused by the disconnection of WDN parts. However, with low adaptation efforts that consider 2–3% pipe replacement, sufficient pressure performances are achieved. Furthermore, by using an entropy-cost comparison, the best planning options are determined. Full article
(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)
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