**3. Methods**

#### *3.1. Urban Area Extraction*

Based on DMSP/OLS data, the urban areas in 2000 and 2010 were extracted using a clustering algorithm [61]. Urban core area, fringe area, and rural area are characterized by metropolitan morphology, and urban fringe is a transition zone from urban to rural areas [70–72]. In this study, the core areas and the fringe areas are studied in urban expansion. Core Area is extracted by DMSP/OLS in 2000, and it is the place where the central part of the city is located. The area where the fringe area in 2000 turned into the core area in 2010 was named the Expanded Area. In order to identify this urban sprawl process of each city, the Expanded Area was defined as the urban area extracted in 2010 (excluding the Core Area). The Fringe Area in this study was defined as the buffer zone whose areas were equal to the urban areas extracted in 2010 (Figure 1). The Core Area, Expanded Area, and Fringe Area can represent not only the old urban area, the new urban area, and the suburbs, but also the initial stage, middle acceleration stage, and final stage of the urbanization process, respectively.
