Science China Technological Sciences

, Volume 62, Issue 4, pp 687–697

# Mathematical analysis of urban land use change in Xi’an city wall area by using parcel-level data

• ShuSheng Wang
• ZiLiang Zhao
• YuQian Xu
• XiaoLong Li
Article

## Abstract

Nowadays, more and more interdisciplinary approaches have been applied in urban planning, such as computer, mathematics and geography. However, the sophisticated mathematical methods such as transition matrix, joint-count, Bayes rules and Markov chain have not been deeply utilized in urban land use analysis. Furthermore, the newborn parcel-level urban land use data method has just been tested in a few cases and has not yet been adopted in ancient city area. Based on the above, this paper uses a series of mathematical methods and parcel-level urban land use data for quantification study in the Xi’an city wall area. Digitizing the maps compiled in 1935, 1963, 1995, 2007 and 2017 of the study area leads to the acquisition of the parcel-level urban land use data concerning the following four categories: Residential (R), Service (S), Culture (C) and Other (O). Then five parcel maps of different times will be built up. Through a series of mathematical analysis, the result shows that urban land use change in this area has three kinds of characteristics. For urban land use change speed, the period between 1995 and 2007 is the fastest while the period from 1963 to 1995 is the slowest. For the transition of urban land use, R and S are the main categories, and transition from R to S is the dominant change. Besides, dominated neighbors have positive effects on their transition. C is consistently increasing and has a clustering distribution. For the influence of other factors such as environment and policy, C is a special category that has the highest sensitivity to policies. The result clearly explains the data from the research into the evolution of urban land use in the study area work as a powerful support for land use planning and policy. The mathematical methods would provide a new perspective for the study in ancient Chinese cities.

## Keywords

urban space land use parcel maps transition matrix probability Markov chain

## References

1. 1.
Li Z, Huang J N, Zhang T J. A brief review on the centennial study of urban morphology (in Chinese). New Architecture, 2014, 157: 131–135Google Scholar
2. 2.
Debbage N, Bereitschaft B, Shepherd J M. Quantifying the spatiotemporal trends of urban sprawl among large U.S. metropolitan areas via spatial metrics. Appl Spatial Anal, 2017, 10: 317–345
3. 3.
Tian L, Li Y, Yan Y, et al. Measuring urban sprawl and exploring the role planning plays: A shanghai case study. Land Use Policy, 2017, 67: 426–435
4. 4.
Theobald D M. Land-use dynamics beyond the American urban fringe. Geographical Rev, 2001, 91: 544–564
5. 5.
Rodewald A D. The importance of land uses with in the landscape matrix. Wildlife Soc Bull, 2003, 31: 586–592Google Scholar
6. 6.
Jiang B, Claramunt C. Integration of space syntax into GIS: New perspectives for urban morphology. Trans GIS, 2002, 6: 295–309
7. 7.
Tannier C, Thomas I. Defining and characterizing urban boundaries: A fractal analysis of theoretical cities and Belgian cities. Comput Environ Urban Syst, 2013, 41: 234–248
8. 8.
Chen Y. Derivation of the functional relations between fractal dimension of and shape indices of urban form. Comput Environ Urban Syst, 2011, 35: 442–451
9. 9.
Li X, Yeh A G O. Analyzing spatial restructuring of land use patterns in a fast growing region using remote sensing and GIS. Landscape Urban Planning, 2004, 69: 335–354
10. 10.
Ma R, Gu C, Pu Y, et al. Mining the urban sprawl pattern: A case study on Sunan, China. Sensors, 2008, 8: 6371–6395
11. 11.
Adams J S. Residential structure of midwestern cities. Ann Assoc Am Geograp, 1970, 60: 37–62
12. 12.
Batty M. Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models and Fractals. Cambridge: MIT Press, 2005Google Scholar
13. 13.
Verburg P H, Schot P P, Dijst M J, et al. Land use change modelling: Current practice and research priorities. GeoJournal, 2004, 61: 309–324
14. 14.
Costanza R, Ruth M. Using dynamic modeling to scope environmental problems and build consensus. Environ Manage, 1998, 22: 183–195
15. 15.
Waddell P. UrbanSim: Modeling Urban development for land use, transportation, and environmental planning. J Am Planning Association, 2002, 68: 297–314
16. 16.
Chakir R, Le Gallo J. Predicting land use allocation in France: A spatial panel data analysis. Ecol Economics, 2013, 92: 114–125
17. 17.
Zhu J, Zheng Y, Carroll A L, et al. Autologistic regression analysis of spatial-temporal binary data via monte carlo maximum likelihood. JABES, 2008, 13: 84–98
18. 18.
Baker W L. A review of models of landscape change. Landscape Ecol, 1989, 2: 111–133
19. 19.
Lambin E F. Modelling and monitoring landcover change processes in tropical regions. Prog Phys Geography, 1997, 21: 375–393
20. 20.
Theobald D M, Hobbs N T. Forecasting rural land-use change: A comparison of regression and spatial transition-based models. Geograp Environ Model, 1998, 2: 65–82Google Scholar
21. 21.
Landis J D. The California urban futures model: A new generation of metropolitan simulation models. Environ Plann B, 1994, 21: 399–420
22. 22.
Turner M G, Wear D N, Flamm R O. Land ownership and land-cover change in the southern Appalachian highlands and the Olympic peninsula. Ecol Appl, 1996, 6: 1150–1172
23. 23.
Geoghegan J, Wainger L A, Bockstael N E. Spatial landscape indices in a hedonic framework: An ecological economics analysis using GIS. Ecol Economics, 1997, 23: 251–264
24. 24.
Clarke K C, Hoppen S, Gaydos L. A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area. Environ Plann B, 1997, 24: 247–261
25. 25.
Clarke K C, Gaydos L J. Loose-coupling a cellular automaton model and GIS: Long-term urban growth prediction for San Francisco and Washington/Baltimore. Int J Geographical Inf Sci, 1998, 12: 699–714
26. 26.
Herold M, Couclelis H, Clarke K C. The role of spatial metrics in the analysis and modeling of urban land use change. Comput Environ Urban Syst, 2005, 29: 369–399
27. 27.
Mas J F, Kolb M, Paegelow M, et al. Inductive pattern-based land use/ cover change models: A comparison of four software packages. Environ Model Software, 2014, 51: 94–111
28. 28.
Kolb M, Mas J F, Galicia L. Evaluating drivers of land-use change and transition potential models in a complex landscape in Southern Mexico. Int J Geographical Inf Sci, 2013, 27: 1804–1827
29. 29.
Tepe E, Guldmann J M. Spatial and temporal modeling of parcel-level land dynamics. Comput Environ Urban Syst, 2017, 64: 204–214
30. 30.
Long Y, Shen Y, Jin X. Mapping Block-Level urban areas for all Chinese cities. Ann Am Association Geographers, 2016, 106: 96–113
31. 31.
Waddell P, Wang L, Charlton B, et al. Microsimulating parcel-level land use and activity-based travel: Development of a prototype application in San Francisco. JTLU, 2010, 3: 65–84
32. 32.
Evans T P, Moran E F. Spatial integration of social and biophysical factors related to landcover change. Populat Develop Rev, 2002, 28: 165–186
33. 33.
Mitchell Hess P, Vernez Moudon A, Logsdon M G. Measuring land use patterns for transportation research. Transpation Res Record, 2001, 1780: 17–24
34. 34.
Zhang Y, Li X, Song W. Determinants of cropland abandonment at the parcel, household and village levels in mountain areas of China: A multi-level analysis. Land Use Policy, 2014, 41: 186–192
35. 35.
Evans T P, Manire A, de Castro F, et al. A dynamic model of household decision-making and parcel level landcover change in the eastern Amazon. Ecol Model, 2001, 143: 95–113
36. 36.
Bell K P, Irwin E G, King R L. Spatially explicit micro-level modelling of land use change at the rural-urban interface. Agricult Econom, 2002, 27: 217–232
37. 37.
Biba S, Curtin K M, Manca G. A new method for determining the population with walking access to transit. Int J Geographical Inf Sci, 2010, 24: 347–364
38. 38.
Torrens P M, Alberti M. Measuring sprawl. Centre for Advanced Spatial Analysis. Working Paper. London: University College London. 2000Google Scholar
39. 39.
Weston L M. A methodology to evaluate neighborhood urban form. Planning Forum, 2002, 8: 64–77Google Scholar
40. 40.
Pontius Jr. R G, Shusas E, McEachern M. Detecting important categorical land changes while accounting for persistence. Agriculture EcoSyst Environ, 2004, 101: 251–268
41. 41.
Kane K, Tuccillo J, York A M, et al. A spatio-temporal view of historical growth in Phoenix, Arizona, USA. Landscape Urban Planning, 2014, 121: 70–80
42. 42.
Wang L, Wei H Y, Feng P, et al. Analyzing land-use change of Xi’an region on RS image (in Chinese). Resource Develop Market, 2010, 26: 589–592Google Scholar
43. 43.
Xie X. Study on prediction of land use/cover change-a case study in the Xi’an region. Arid Zone Res, 2008, 25: 125–130
44. 44.
Xue X R, Dang X G. Research on forecast of land use in Xi’an city based on the theory of gray system (in Chinese). Stat Inf Forum, 2009, 24: 40–43Google Scholar
45. 45.
Li F X, Shi H, Feng X G, et al. Study of land use dynamic evolution and driving factors in Xi’an (in Chinese). Bull Survey Mapp, 2015, 374: 41–45Google Scholar
46. 46.
Zhang H L, Jiang J J, Xie X P, et al. Analyzing land use changes and its driving forces in Xi’an region during the past 25 Years (in Chinese). Resource Sci, 2006, 28: 71–77Google Scholar
47. 47.
Jiang Y, Cui L P, Yan S F. A study of the history of protecting the Xi’an city Wall in modern times (in Chinese). Architect Culture, 2014, 119: 60–65Google Scholar
48. 48.
Wang S S. Preliminary analysis of planning methods of Xi’an urban pattern in the beginning of Ming Dynasty (in Chinese). Urban Planning Forum, 2004, 153: 85–88Google Scholar
49. 49.
Xiao L. Study on protection project and protection study of Gulou historic block in Xi’an (in Chinese). Inf China Construct, 2004, 317: 59–62Google Scholar
50. 50.
Bell K P, Irwin E G, King R L. Spatially explicit micro-level modelling of land use change at the rural-urban interface. Agricult Econom, 2002, 27: 217–232
51. 51.
López E, Bocco G, Mendoza M, et al. Predicting land-cover and landuse change in the urban fringe. Landscape Urban Planning, 2001, 55: 271–285
52. 52.
Arsanjani J J, Kainz W, Mousivand A J. Tracking dynamic land-use change using spatially explicit Markov Chain based on cellular automata: The case of Tehran. Int J Image Data Fusion, 2011, 2: 329–345
53. 53.
Zhang R, Tang C, Ma S, et al. Using Markov chains to analyze changes in wetland trends in arid Yinchuan Plain, China. Math Comput Model, 2011, 54: 924–930
54. 54.
Jokar Arsanjani J, Helbich M, Kainz W, et al. Integration of logistic regression, Markov chain and cellular automata models to simulate urban expansion. Int J Appl Earth Observation GeoInf, 2013, 21: 265–275
55. 55.
Ren Y Y. Development of urban planning conception in modern Xi’an —A case study of the file documents by the 1927–1947 Republic of China (in Chinese). J Shaanxi Normal Univ (Philosophy Soc Sci), 2009, 38: 105–112Google Scholar

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

## Authors and Affiliations

• ShuSheng Wang
• 1
• 2
Email author
• ZiLiang Zhao
• 2
• YuQian Xu
• 1
• 2
• XiaoLong Li
• 1
• 2
1. 1.State Key Laboratory of Green Building in Western ChinaXi’an University of Architecture and TechnologyXi’anChina
2. 2.College of ArchitectureXi’an University of Architecture and TechnologyXi’anChina