application of spatial autocorrelation techniques to measure urban sprawl, case study: gorgan city

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.