A New Method Based on Weighted Cumulative Entropy to Assess the Sprawl Pattern of Urban Growth of Tabriz City in GIS

Urban sprawl or uncontrolled dispersion of the built-in areas brings about different economic, social, and environmental problems in the cities which have high growth of population. Remote sensing and GIS are used for measuring and visualizing the urban sprawl pattern and obtaining information about their temporal and spatial changes. Shannon’s entropy has traditionally been used in the discussions on measuring uncertainties and urban development. One major shortcoming with Shannon and other entropy measures is the fact that the support of the random variables is not taken into account in calculating the amount of information. The present study has offered a location-based measure for measuring density in urban development based on the cumulative distribution function. Such a measure is called weighted cumulative entropy (WCE), which is an extension of Shannon and other measures of uncertainty. In the newly presented measure, the values of the support set and the distribution function are both important. Shannon’s entropy and WCE are used to study the rate of urban sprawl and to visualize sprawl dispersion of Tabriz in 1993 and 2013. The results of this study showed that WCE is a more suitable statistic than Shannon’s entropy for identifying and monitoring the dispersion or concentration of urban constructions. In fact, Shannon’s entropy has failed to show the difference between the areas while WCE has distinguished the dense urban areas from non-dense ones more clearly. Moreover, the map of urban sprawl pattern in Tabriz indicates asymmetric growth, and the most urban dispersion and growth has happened along the roads from Tabriz to Tehran, Maraghe and Marand cities, which demands urban management in order to achieve sustainable development.