Application of Spatial Autocorrelation Techniques to Measure Urban Sprawl, Case Study: Gorgan City

Document Type : Research Paper

Abstract

Introduction
In 1950s, only 30% of the world's population lived in urban areas. By 2000, that proportion increasedup to 47%, and by 2050 the estimated number will be around 72%. Urban sprawl, an undesirable type of urban growth, is one of the major concerns ofthe city planners and administrators. Understanding urban patterns, dynamic processes, and their relationships is a primary objective in the urban research agenda.It isbenefitedfrom a wide consensus among scientists, resource managers, and planners. The reason for this consensus is that future development and management of urban areas requires detailed information about ongoing processes and patterns. To describe these different patterns intelligently, to understand how they change over time, to compare one area with others, or to explain the variations among these patterns statistically, we need to select quantitative measures tosummarize the properties of the urban areas changed during the development process. A continuous monitoring of urban growth evolution in terms of type and extent of changes over time is essential tosupport planners and decision makers in future urban planning.
Therequirement forunderstanding and monitoring urban expansion processes is the availability of both (i) time-series data set and (ii) updated information relatedto the current urban spatial structure to define and to locate evolution trends. In this context, multi-temporal analysis based on remotely sensed data has played an important role in detection ofurban growth. Remotely sensed imagery is an effective data source for urban environment analysis.Itis also suitabletoprovideinformation on urban land cover characteristics and their changes over time at various spatial and temporal scales. In general, urban change detection involves the application of multi-temporal datasets to quantitatively (or visually) analyze the temporal effects of the phenomenon. Effective and sustainable urban management increasingly requires advanced techniques to obtain various and up-to-date information on the pattern, state, characteristics, and development of an urban environment. Recently, more attention has been paid to the use of spatial autocorrelation in measuring urban growth. The use of satellite imagery coupled with autocorrelation techniques can be used for monitoring and planning purposes. These enable the reporting of ongoing trends of urban growth at a detailed level. The spatial autocorrelation can be employed for measurementsand analyses of the degree of dependency among observations in a geographical space. In urban studies, this often means that high values are found near other high values and low values appear in geographical proximity.
The aim of this paper is to show the potential application of the spatial autocorrelation techniques to detect fragmentation over the landscape. This study analyzes urban expansion over time using satellite images and spatial autocorrelation.
 
Materials and methods
 
The spatial autocorrelation here is separated in six sections.
Spatial autocorrelation statistics
Spatial autocorrelation: basic concepts
The concept of the spatial autocorrelation is rooted in Waldo Tobler’s first law of geography: “everything is related to everything else, but near things are more related than distant things”. A non-random spatial pattern may show either positive or negative spatial autocorrelation. In the case of positive spatial autocorrelation, the value of a variable at a given location tends to be similar to the values of that variable in nearby locations. In other words, if the value of some variable is low in a given location, the presence of positive spatial autocorrelation indicates that nearby values are also likely to be relatively low. Conversely, negative spatial autocorrelation is characterized by a tendency for dissimilar values to cluster in proximate locations. For example, the areas exhibiting low values for a particular variable may be surrounded by high values when negative spatial autocorrelation exists. The absence of spatial autocorrelation indicates that the spatial arrangement of the variable values is random.
Global indicators of spatial autocorrelation
Global indicators of autocorrelation can measure if and how much the dataset is auto-correlated throughout the study region. These indicators provide a single statistic that summarizes the spatial pattern of the region and the two main indicators are Moran I and Geary C Ratio indices. Moran’s index I is defined in the following formula 1:
 
 
 
 





(1)





 
 
 
 
Where N is the total pixel number, Xi and Xj are intensities in points i and j (with i / = j),  is the average value, and wij is an element of the weight matrix. Moran index shows a trend similar to the correlation coefficient, consequently it can have values d between -1 and 1.
Geary C Ratio is quite similar to Moran’s I index and it is defined by the following equation 2:
 
 





(2)





 
 


 
Parameters are very similar to the prior equation: the main difference is represented by the cross-product term in the numerator, which in Moran’s it is calculated using deviations from the mean, while in Geary’s it is directly computed. The Geary’s C Ratio israngedbetween 0 and 2. The values between 0 and 1 define positive autocorrelation, while thosegreater than 1 and smaller than 2 indicate negative autocorrelation. Value 0 represents a perfect positive autocorrelation, the same asneighboring values with cross-product equal to 0. Value 2 defines a perfect negative spatial autocorrelation.
Local indicators of spatial autocorrelation
 
 





(3)





 
Local indicators of the spatial autocorrelation allow us to locate clustered pixels, by measuring how much features inside the fixed neighborhood are homogeneous. In this study, we used the Getis–Ord Local Gi, as defined according to the formula:
 
This is very similar to Moran’s index, except for wij (d) which, in this case, represents a weight that varies according to distance. The interpretation of Getis and Ord’sGi meaning is not immediate, but it needs a preliminary classification that should be done in comparison withGi to intensity the values. In particular, a high value of the index means positive correlation for high values of intensity, while a low value of the index means positive correlation for low values of intensity.
Local versions of the spatial autocorrelation are used to measure the magnitude of the spatial autocorrelation within the immediate neighborhood. Values indicating the magnitude of the spatial association can be derived and located for each areal unit. The local version of the statistic employs distance information to identify local clusters and relies on the distance information captured in distance matrix.
The Local Indicator of Spatial Association (LISA) represents the local version
 
 





(4)





 
 
of Moran’s index I. Itis defined by the relation 4:
 
Where X is the intensity mean of all events, Xi is the intensity of event “i”, Xj is the intensity of event “j” (with j≠i),  is the variance of all events and wij is the weight matrix.
 
AnalysisUrban Sprawl using NDVI index
In our analysis, we adopted the Normalized Difference Vegetation Index (NDVI), which is the most widely used index for a number of different applications, ranging from vegetation monitoring to urban sprawl. The NDVI is computed using the following formula 5:
 
 
 





(5)





 
This index was computed for the years 1986 and 2010 to emphasize on changes and improve change detection.
Resultsand discussion
All of the spatial autocorrelation statistics discussed so far havea common characteristic; they are global because they are summary values for the entire study region. It is reasonable to suspect that the magnitude of the spatial autocorrelation does not have to be uniform over the region (spatial homogeneity), but rather they are variable according to the location. In other words, it is likely that the magnitude of the spatial autocorrelation is high in some sub regions but low in other sub regions within the study area. It may even be possible to find positive autocorrelation in one part of the region and negative autocorrelation in another part. This phenomenon is called spatial heterogeneity. Results of the local Moran indicatedthat the highest spatial autocorrelation was found in forest areas. This isbecause of their uniformity and homogeneity compared to the other covers. Urban cover in outputs of local Moran has moderate spatial autocorrelation and it means that pixels of the built-up places have moderate similarity. The minimum spatial autocorrelation was seen in agricultural areas.
Results of Getis’sGi statistic show that forest cover has positive spatial autocorrelation and urban cover has negative spatial autocorrelation. In contrast to the local Moran’s, Getis’sGistatistic, we consider low values in NDVI as negative spatial autocorrelation. The urban cover in NDVI map has low values, and outputs of Getis’sGi statistic show negative spatial autocorrelation. In general, comparison of output maps of the local Moran and Getis’sGi statistic indicatedthat both indices can detect and measure built-up places and forest covers but, the Getis’sGi statistic was better for measuring urban sprawl because of its capability in representation of negative values as distinct clusters.
 
 
Most studies onmeasurement ofurban sprawl in Iran apply discrete approach or land use classification from Landsat images. According to this fact that Landsat images have moderate spatial resolution, it is necessary to evaluate the data set todetect and separatebuilt-up areas. Spatial resolution is a function of sensor altitude, detector size, focal size and system configuration. It defines the level of spatial detail depicted in an image, and it is often related to the size of the smallest possible feature that can be detected from an image. This definition implies that only the objects larger than the spatial resolution of a sensor can be picked up from an image. Another meaning of the spatial resolution is that a ground feature should be distinguishable as a separate entity in the image. For any feature to be identifiable in an image, it should be consistent with the spatial resolution, spectral contrast, and the feature’s shape. In this study, to overcome these problems, we used the local spatial autocorrelation that measure urban sprawl continuously. The NDVI map was used as input of local spatial autocorrelation statistics, outputs of local Moran’s and Getis’sGi statistics were compared using kernel density graph of the indices. In general, the results of this study indicatedthat the use of continuous approaches to measurethe growth of the city using spatial autocorrelation techniques is appropriate and efficient. Therefore, in order to survey urbanization in different areas we can use the spatial autocorrelation indices, since these indicators don't need classification of the satellite images that is very time-consuming and costly accompanied with errors and uncertainties.
 
Conclusion
In general, change detection of urban landscape requires multi-temporal data for quantitative analysis.Several approaches have been developed that consider this problem. Regardless of the classification methods of urban environments including pixel-based or object-based, it is believed that the classification method has major drawbacks, because the classes are separated by discrete boundaries. Thus, the process of classification of images due to the conversion of continuous data to discrete classes reduces the information. Withthe spatial heterogeneity of urban environments, remote sensing analysis of these areas is challenging, but still the most important study source of the urban landscape is remote sensing. In this regard, remote sensing imagery coupled with spatial autocorrelation techniques can be used for monitoring and planning purposes. These enable the reporting of ongoing trends of urban growth at a detailed level.

Keywords

Main Subjects

References

پوراحمد، ا.، حسام، م.، آشور، ح. و محمدپور، ص. 1389. تحلیل بر الگوی گسترش کالبدی- فضایی شهر گرگان با استفاده از مدل­های آنتروپی شانون و هلدرن. مجله پژوهش و برنامه­ربزی شهری. سال اول، شماره سوم.
صادقی­نیا،ع.ر.،علیجانی،ب.،ضیائیان،پ. وخالدی،ش. 1392. کاربردتکنیکهایخودهمبستگیفضاییدرتحلیلجزیرهحرارتیشهرتهران. نشریه تحقیقات کاربردی علوم جغرافیایی، سال سیزدهم، شماره 30. 90-67.
کامیاب، ح.ر. و سلمان­ماهینی، ع.ر. 1391. الگوهای مکانی- زمانی تغییرات سیمای سرزمین و توسعه شهری (مطالعه موردی: گرگان). مجله کاربرد سنجش از دور و GIS در علوم منابع طبیعی. سال سوم. شماره دوم.
Anselin, L. 1995. Local indicators of spatial association – LISA. Geographical Analysis, 27(2), 93–115.
Bailey, T.C., and Gatrell, A.C. 1995. Interactive Spatial Data Analysis. Longman Higher Education, Harlow.
Batty, M. 1997. Cellular automata and urban form: a primer” Journal - American Planning Association, Volume 63, Issue 2, pp. 266-274.
Bowman, A. W., and Azzalini, A., 1997. Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations. Oxford: Oxford University Press.
Chu, H.J. Wu, CH.F. and Lin, Y.P. 2013. Incorporating spatial autocorrelation with neural networks in empirical land-use change models. Environment and Planning B: Planning and Design, volume 40, pages 384 – 404.
Cockx, K., Van de Voorde, T. and Canters, F. 2014. Quantifying uncertainty in remote sensing-based urban land-use mapping. International Journal of Applied Earth Observation and Geoinformation. 31, 154–166.
Danese, M., Lazzari, M., and Murgante, B., 2009. Geostatistics in historical macroseismic data analysis. Transactions on Computational Sciences Journal VI LNCS vol. 5730, 324–341.
Donnay, J.P., Barnsley, M.J. and Longley, P.A. 2001. Remote sensing and urban analysis. In: J.P. Donnay, M.J. Barnsley and P.A. Longley (eds.), Remote Sensing and Urban Analysis, Taylor & Francis, London and New York, pp 3–18.
Esch, T., Taubenböck, H., Heldens, W., Thiel, M., Wurm, M., Geiss, C. and Dech, S. 2010. Urban Remote sensing—How can earth observation support the sustainable development of urban environments? In Proceedings of the 15th International Conference on Urban Planning, Regional Development and Information Society, Vienna, Austria, 18–20; pp. 837–847.
Fan, c., and Myint, s. 2014. A comparison of spatial autocorrelation indices and landscape metrics in measuring urban landscape fragmentation. Landscape and Urban Planning 121 117– 128.
Fichera, C., Modica, G. and Pollino, M. 2011. GIS and remote sensing to study urban-rural transformation during a fifty-year period, Lecture Notes in Computer Science LNCS, Volume 6782, pp. 237-252.
Foody, G., 1996. Approaches for the Production & Evaluation of Fuzzy Land Cover Classifications From Remotely-Sensed Data. International Journal of Remote Sensing 17: 1317–1340.
Foody, G.M. 2000. Estimation of sub-pixel land cover composition in the presence of untrained classes. Computers & Geosciences 26, 469–478.
Gatrell, A.C., Bailey, T.C., Diggle, P.J. and Rowlingson, B.S., 1996. Spatial point pattern analysis and its application in geographical epidemiology. Transaction of Institute of British Geographer 21, 256–271.
Geary, R., 1954. The contiguity ratio and statistical mapping. The Incorporated Statistician, volume 5.
Getis, A., and Ord, J., 1992. The analysis of spatial association by distance statistics. Geographical Analysis, volume 24, pp. 189-206.
Janzen, J. 1986. Introductory digital image processing, Prentice-Hall, Englewood Cliffs, New Jersey.
Herold, M., Goldstein, N.C. and Clarke, K.C. 2003. The spatiotemporal form of urban growth: Measurement, analysis and modeling. Remote Sensing of Environment, Volume 86, Issue 3, 286-302.
Herold, M., Roberts, D., Gardner, M. and P. Dennison 2004. Spectrometry for urban area remote sensing—development and analysis of a spectral library from 350 to 2400 nm. Remote Sensing of Environment, 91, 304–319.
Jensen, J. R., and Cowen, D. C. 1999. Remote sensing of urban/suburban infrastructure and socioeconomic attributes. Photogrammetric Engineering and Remote Sensing, 65, 611–622.
Jensen, J. R. 2005. Introductory digital image processing: A remote sensing perspective (Third Edition). Upper Saddle River, NJ: Prentice Hall.
Lanorte, A., Danese, M., Lasaponara, R. and Murgante, B. 2013. Multi-scale mapping of burn area and severity using multi-sensor satellite data and spatial autocorrelation analysis. International Journal of Applied Earth Observation and Geoinformation, Elsevier, Volume 20, Pages 42–51.
Lee, J., and Wong, D.W.S. 2001. Statistical analysis with ArcView GIS. John Wiley & Sons, Inc.
Lu, D., Mausel, P., Brondizios, E. and Moran, E. 2004. Change detection techniques. International Journal of Remote Sensing, 25, 2365–2407.
Moran, P., 1948. The interpretation of statistical maps. Journal of the Royal Statistical Society 10, 243–251.
Murgante, B., Las Casas, G. and Danese, M., 2008. The periurban city: geo-statistical methods for its definition. In: Coors, M., Rumor, V., Fendal, E.M., Zlatanova, ST. (Eds.), Urban and Regional Data Management. Taylor & Francis Group, London, pp. 473–485.
Murgante, B., and Danese, M., 2011. Urban versus Rural: the decrease of agricultural areas and the development of urban zones analyzed with spatial statistics. International Journal of Agricultural and Environmental Information Systems 2 (2).
Murgante, B., and Borruso, G. 2012. Analyzing Migration Phenomena with Spatial Autocorrelation Techniques. Lecture Notes in Computer Science vol. 7334, pp. 670–685. Springer-Verlag, Berlin.
Nole, G., Danese, M., Murgante, B., Lasaponara, R. and Lanorte, A. 2012. Using Spatial Autocorrelation Techniques and Multi-temporal Satellite Data for Analyzing Urban Sprawl. Computational Science and Its Applications. 7335, 512-527.
Nolè, G., Lasaponara, R. and Murgante, B. 2013. Applying spatial autocorrelation techniques to multi-temporal satellite data for measuring urban sprawl. International Journal of Environmental Protection (IJEP), 3(7), 11-21. World Academic Publishing.ISSN: 2226-6437.
Nole, G., Tito, C., Lasaponara, R., Lanorte, A. and Murgante, B. 2014. Quantifying Urban Sprawl with Spatial Autocorrelation Techniques using Multi-Temporal Satellite Data. International Journal of Agricultural and Environmental Information Systems, 5(2), 20-38.
O’Sullivan, D., and Unwin, D., 2002. Geographic Information Analysis. John Wiley & Sons.
Palmer, M.W., Earls, P., Hoagland, B.W., White, P.S. and Wohlgemuth, T., 2002. Quantitative tools for perfecting species lists. Environmetrics 13, 121–137.
PerpinanLamigueiro, O., and Hijmans, R., 2014. R Package rasterVis, Visualization methods for the raster package.
Premo, L.S. 2004. Local spatial autocorrelation statistics quantify multi-scale patterns in distributional data: an example from the Maya Lowlands. Archaeological Science 31, 855–866.
Rocchini, D., Metz, M., Ricotta, C., Landa, M., Frigeri, A. and Neteler, M., 2013. Fourier transforms for detecting multi-temporal landscape fragmentation by remote sensing, International Journal of Remote sensing, 34:24, 8907-8916.
Seto, K.C., and Fragkias, M. 2005. Quantifying spatiotemporal patterns of urban land-use change in four cities of China with timer series landscape metrics. Landscape Ecology, 20, 871–888
Tobler, W.R. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography, Volume 46, Issue 2, pp.234–240.
Tucker, C. J. 1979. Red and photographic infrared linear combinations for monitoring vegetation. Remote sensing of Environment. 8:127-150.
United Nations. 2012. World urbanization prospects. The 2011 Revision. New York.
Yichun, X., Fang, C., Lin, GCS., Gong, H. and Qiao, B. 2007. Tempo-spatial patterns of land use changes and urban development in globalizing china: a study of Beijing. Sensors, 7: 2881-2906
Zhang, Q., Ban, Y., Liu, J. and Hu, Y. 2011. Simulation and analysis of urban growth scenarios for the Greater Shanghai Area, China. Computers, Environment and Urban Systems, 35: 126-139.
Zhou, W., Cadenasso, M.L., Schwarz, K. and Pickett, S.T.A. 2014. Quantifying Spatial Heterogeneity in Urban Landscapes: Integrating Visual Interpretation and Object-Based Classification. remote sensing, 6, 3369-3386.
Journal of Environmental Studies
Volume 42, Issue 1
June 2016
Pages 97-113

Files

Share

How to cite

Statistics