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Fractal and multifractal characteristic of spatial pattern of urban impervious surfaces

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Abstract

Urban impervious surface (UIS) has been widely utilized to quantify urban expansion and assess environmental impacts of urbanization. In order to understand the complexity of spatio-temporal change of UIS spatial pattern, we investigated the fractal and multifractal characteristics of UIS spatial pattern in the downtown area of Shanghai, China during 1997–2010. Results suggested that UIS spatial pattern is a typical fractal structure with self-similarity during the study period. The fractal dimension reveals the spatio-temporal complexity of UIS pattern. With the threshold changing from small to large, the spatial complexity of UIS pattern is decreased. The increasing dimension values over time showed the UIS pattern becomes more complex and the spatial distribution becomes more clustered form 1997 to 2010. The multifractal approach transforms irregular UIS fraction data into a compact form and amplifies small differences between different data series. We also specially selected the W-E profile and the N-S profile to check the multifractality of UIS pattern. The results showed that the multifractality was detected in 1997 and 2002 on the W-E profile and only in 1997 on the N-S profile. The UIS pattern is more irregular on the W-E profile than that on the N-S profile according to the probability distribution, and the high fraction pixels are dominant on the two selected profiles by the positive ratio between the regions that the probability measure distributed most concentrated and most rarefied.

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References

  • Ariza-Villaverde AB, Jiménez-Hornero FJ, Ravé EGD (2013) Multifractal analysis of axial maps applied to the study of urban morphology. Comput Environ Urban Syst 38:1–10

    Article  Google Scholar 

  • Arnold CL, Gibbons CJ (1996) Impervious surface coverage-the emergence of a key environmental indicator. J Am Plan Assoc 62(2):243–258

    Article  Google Scholar 

  • Batty M (2008) The size, scale, and shape of cities. Science 319:769–771

    Article  Google Scholar 

  • Batty M, Longley PA (1994) Fractal cities: a geometry of form and function. Academic, London

    Google Scholar 

  • Bauer ME, Heinert NJ, Doyle JK, Yuan F (2004) Impervious surface mapping and change monitoring using satellite remote sensing. In: Proceedings of the American society of photogrammetry and remote sensing annual conference, Denver, Colorado, 24-28 May 2004

  • Benguigui L, Czamanski D, Marinov M, Portugali J (2000) When and where is a city fractal? Environ Plann B Plann Des 27(4):507–519

    Article  Google Scholar 

  • Benguigui L, Blumenfeld-Lieberthal E, Czamanski D (2006) The dynamics of the Tel Aviv morphology. Environ Plan B 33(2):269

    Article  Google Scholar 

  • Chen YG (2012) Fractal dimension evolution and spatial replacement dynamics of urban growth. Chaos, Solitons Fractals 45:115–124

    Article  Google Scholar 

  • Chen YG (2013) Fractal analytical approach of urban form based on spatial correlation function. Chaos, Solitons Fractals 49:47–60

    Article  Google Scholar 

  • Chen YG, Feng J (2012) Fractal-based exponential distribution of urban density and self-affine fractal forms of cities. Chaos, Solitons Fractals 45(11):1404–1416

    Article  Google Scholar 

  • Chen YG, Jiang SG (2009) An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas. Chaos, Solitons Fractals 39(1):49–64

    Article  Google Scholar 

  • Chen YG, Lin JY (2009) Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals. Chaos, Solitons Fractals 41(2):615–629

    Article  Google Scholar 

  • Chen YG, Zhou YX (2004) Multi-fractal measures of city-size distributions based on the three-parameter Zipf model. Chaos, Solitons Fractals 22:793–805

    Article  Google Scholar 

  • Dougherty M, Dymond RL, Goetz SJ, Jantz CA, Goulet N (2004) Evaluation of impervious surface estimates in a rapidly urbanizing watershed. Photogramm Eng Remote Sens 70:1275–1284

    Article  Google Scholar 

  • Feng J, Chen YG (2010) Spatiotemporal evolution of urban form and land use structure in Hangzhou, China: evidence from fractals. Environ Plann B Plann Des 37(5):838–856

    Article  Google Scholar 

  • Grau J, Médez V, Tarquis AM, Saa A, Díaz MC (2006) Comparison of gliding box and box-counting methods in soil image analysis. Geoderma 134:349–359

    Article  Google Scholar 

  • Islam Z, Metternicht G (2003) Fractal dimension of multiscale and multisource remote sensing data for characterising spatial complexity of urban landscapes. IEEE Int Geosci Remote Sens Symp 3:1715–1717

    Google Scholar 

  • Kalnay E, Cai M (2003) Impact of urbanization and land-use change on climate. Nature 423(6939):528–531

    Article  Google Scholar 

  • Lee CK (2002) Multifractal characteristics in air pollutant concentration time series. Water Air Soil Pollut 135(1–4):389–409

    Article  Google Scholar 

  • Li J, Du Q, Sun C (2009) An improved box-counting method for image fractal dimension estimation. Pattern Recogn 42(11):2460–2469

    Article  Google Scholar 

  • Liu MH, Chen YG (2001) Methods of characterizing urban land-use form using fractal dimension. J Xinyang Teach Coll (Nat Sci Ed) 14(2):209–213 (in Chinese)

  • Liu ZH, Wang YL, Peng J, Xie MM, Li Y (2011) Using ISA to analyze the spatial pattern of urban land cover change: a case study in Shenzhen. Acta Geograph Sin 66:961–971

    Google Scholar 

  • Liu ZH, Wang YL, Peng J (2012) Quantifying spatiotemporal patterns dynamics of impervious surface in Shenzhen. Geogr Res 31:1535–1545

    Google Scholar 

  • Rashed T (2008) Remote sensing of within-class change in urban neighborhood structures. Comput Environ Urban Syst 32:343–354

    Article  Google Scholar 

  • Relly J, Maggio P, Karp S (2004) A model to predict impervious surface for regional and municipal land use planning purposes. Environ Impact Assess Rev 24:363–382

    Article  Google Scholar 

  • Saa A, Gascó G, Grau JB, Antón JM, Tarquis AM (2007) Comparison of gliding box and box-counting methods in river network analysis. Nonlinear Process Geophys 14(5):603–613

    Article  Google Scholar 

  • Seto KC, Fragkias M, Güneralp B, Reilly MK (2011) A meta-analysis of global urban land expansion. PLoS ONE 6(8):e23777. doi:10.1371/journal.pone.0023777

    Article  Google Scholar 

  • Shao Q, Sun C, Liu J, He J, Kuang W, Tao F (2011) Impact of urban expansion on meteorological observation data and overestimation to regional air temperature in China. J Geogr Sci 21(6):994–1006

    Article  Google Scholar 

  • Shen G (2002) Fractal dimension and fractal growth of urbanized areas. Int J Geogr Inf Sci 16(5):419–437

    Article  Google Scholar 

  • Small C (2001) Estimation of urban vegetation abundance by spectral mixture analysis. Int J Remote Sens 22:1305–1334

    Article  Google Scholar 

  • Stow DA, Chen DM (2002) Sensitivity of multitemporal NOAA AVHRR data of an urbanizing region to land-use/landcover changes and misregistration. Remote Sens Environ 80:297–307

    Article  Google Scholar 

  • Tél T, Fülöp Á, Vicsek T (1989) Determination of fractal dimensions for geometrical multifractals. Physica A 159:155–166

    Article  Google Scholar 

  • Thomas I, Frankhauser P, Frenay B, Verleysen M (2010) Clustering patterns of urban built-up areas with curves of fractal scaling behavior. Environ Plann B Plann Des 37(5):942–954

    Article  Google Scholar 

  • Walsh CJ, Roy AH, Feminella JW, Cottingham PD, Groffman PM, Morgan RP (2005) The urban stream syndrome: current knowledge and the search for a cure. J N Am Benthol Soc 24(3):706–723

    Article  Google Scholar 

  • White R, Engelen G (1993) Cellular automata and fractal urban form: a cellular modeling approach to the evolution of urban land-use patterns. Environ Plan A 25:1175–1199

    Article  Google Scholar 

  • Wu CS (2009) Quantifying high-resolution impervious surfaces using spectral mixture analysis. Int J Remote Sens 30:2915–2932

    Article  Google Scholar 

  • Wu J, Thompson J (2013) Quantifying impervious surface changes using time series planimetric data from 1940 to 2011 in four central Iowa cities, U.S.A. Landsc Urban Plan 120:34–47

    Article  Google Scholar 

  • Xian G, Crane M (2006) An analysis of urban thermal characteristics and associated land cover in Tampa Bay and Las Vegas using Landsat satellite data. Remote Sens Environ 104:147–156

    Article  Google Scholar 

  • Xie MM, Wang YL, Li GC (2009) Spatial variation of impervious surface area and vegetation cover based on SubPixel model in Shenzhen. Resour Sci 31:257–264

    Google Scholar 

  • Yue W (2009) Improvement of urban impervious surface estimation in Shanghai using Landsat7 ETM + Data. Chin Geogr Sci 19:283–290

    Article  Google Scholar 

  • Yue W, Xu J, Tan W, Xu L (2007) The relationship between land surface temperature and NDVI with remote sensing: application to Shanghai Landsat 7 ETM + data. Int J Remote Sens 28:3205–3226

    Article  Google Scholar 

  • Yue W, Liu Y, Fan P, Ye X, Wu C (2012) Assessing spatial pattern of urban thermal environment in Shanghai, China. Stoch Env Res Risk A 26:899–911

    Article  Google Scholar 

  • Zeleke TB, Si BC (2005) Scaling relationships between saturated hydraulic conductivity and soil physical properties. Soil Sci Soc Am J 69(6):1691–1702

    Article  Google Scholar 

  • Zhao J, Xu JH, Mei AX, Wu JP, Zhou JH (2004) A study on the information entropy and fractal dimension of land use structure and form in Shanghai. Geogr Res 23:137–146

    Google Scholar 

Download references

Acknowledgments

This study was supported by the National Natural Science Foundation, China (Grant No. 41130525).

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Correspondence to Qin Nie.

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Communicated by: H. A. Babaie

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Nie, Q., Xu, J. & Liu, Z. Fractal and multifractal characteristic of spatial pattern of urban impervious surfaces. Earth Sci Inform 8, 381–392 (2015). https://doi.org/10.1007/s12145-014-0159-1

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  • DOI: https://doi.org/10.1007/s12145-014-0159-1

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