3. The Application
TM satellite images dated 10 December 1988. 13 October 1990 and November 1993 were used to estimate the amount or urban expansion and to measure and compare the spatial pattern of urban sprawl during the period. Principal component analysis of stacked multi-temporal images technique was used to obtain the land use classes and land use change ( Li and Yeh, 1988). It was found that the area for urban land use rapidly expanded from 18,351.4 ha. In 1988 to 19,604 ha. In 1990 and to 39,636.4 ha. in 1993. the annual growth rate of urban area was only 3.4% in 1988-90, but it surpassingly became 34% in 1990-93. spacious use of land resources has been identified as the land consumption per capita increased substantially from 128.4 m2 during 1988-1993, which were both much higher that athe national standard of 100m2. urban expansion had resulted in the loss of 13.2% of its total agricultural land.

It is easy to find that the urban sprawl is affected by some location factors-distance to urban centers and roads. Entropy should be calculated based on the distance variables to address the distance decay properties or urban sprawl. The influences of these locations factors was measured using the buffer functions of GIS. Two types of buffer zones wire devised o calculate densities of land development with regard to the two distance variables. Entropy based on the buffer functions is given as:

Where PDEN_i = DEN_i/DENi and DENi is the density of land development. DEN_i equals to the amount of land development divided by the total amount of land in the ith buffer in the ith buffer in a total of n buffer .

Two types of thematic layers are needed for the calculation of densities of urban sprawl in each buffer. The thematic layer or urban sprawl of each period were obtained by the classification of multi-temporal satellite images. The thematic layers of buffers were created respectively based on the proximity to town centers and roads using the buffer function s of GIS. The width of each buffer is 250 m , and each town has about 15-30 zones on average. The overlay of the urban images and the buffer images can capture the densities of urban sprawl in each buffer. The distribution of the densities over the buffers was obtained using the summary function of ERDAS IMAGINE 8.3. the summary function was used to produce cross-tabulation statistics that compare class value areas between tow thematic layers, including number of pixels ( or hectare ) in common and percentages. The entropy in terms or urban sprawl for each town in 1988, 1990 and 1993 was calculated according to the equation 3.

Three typical urban sprawl patterns can be identified in the towns of Dongguan from the analysis ( Figure 1). The first type is concentrated ( Low Development ) as represented by Hongmei which has only very limited land development in 1988-93 . the second type is Dispersed ( Medium Development ) as represented by Dalang which exhibited some dispersal away from the town center. The third type is Highly Dispersed 9 High Development ) as represented by Tangsha. It has an upward increase in the density of land development and dispersal of urban development away from the own center. There three types of urban sprawl patterns can be reflected from the entropy. In the first type of urban sprawl ( concentrated ), most of the land development is near the town center and the entropy is relatively small. Area farther away format he town center is not so favorable for land conversion and most of the land development is carried out only with in the distance very close to the town center. There is more spread land development in the second type ( Dispersed ) . the entropy is higher than that of the first type. For the third type or urban sprawl (Highly Dispersed ), land development spreads over the urban fringe and to the surrounding rural area and the entropy is the highest among the three types of urban sprawl.

Figure 1. Three typical urban sprawl patterns
The temporal change of spatial patterns of urban development can be easily measured from the change in entropy. The increase of the value of at entropy indicates that there is an increase in urban sprawl and development tends to be more dispersed. It is found that the average increase in entropy was only 2.7% for the whole region during 1988-90. this means that there was only a slight trend of urban sprawl in this periojd. However, the average increase in entropy increased to 8.9% in 1990-93 as a result of rapid land development and property boon in 1992-93. there were some towns with negative figures during these periods, indicating relatively more concentrated development rather that dispersed development. Theses towns were minority among the 29 towns were minority among the 29 towns of Dongguan. There were 11 towns in 1988-90 and only 4( including the city proper ) in 1990-93 that had negative increases. This indicates that the majority of development is towards dispersed development rather than concentrated development. Zhangnutou, a town which is recently famous for the development of property markets for Hong Kong;s residents, had an increase of entropy as high as 24.1% in 1990-93,as compared with the average of 8.9% for the whole area. Two other towns, . Tangsha and Qingxi which are very close to Hong King, were also among those with a ahigh; ;increase of entropy with the rates of 18.1% and 24.9% respectively. Dalingshan and Dalang which are located in the hilly areas, however, also witnessed a high increase of entropy in 1990-93. the development sites in theses tow towns are scattered in the satellite images. The four towns that had negative increase of entropy in 1990-93 were Wangniudun, Daojiao, Hongmei and Xinwan. This means that land development in these towns was less dispersed this period.

4. Conclusion
The study shows that entropy is a good indicator to identify the spatial problems of land development. For the example, entropy based on distance from roads can be used t monitor urban sprawl along roads. Many development sites area just located along roads without a compact development pattern, resulting in wasteful user of land resources and increasing consumption of energy. Entropy is capable of identifying which town has better spatial efficiency in land development. Further more, the two-dimensional entropy space can be used to differentiate various growth patterns clearly. This provides a useful tool for government officials and planners to monitor land development process and find out land user problems.

The application of the method reveals that the Pearl River Delta has experienced severe urban sprawl in the early 90s with the lack or proper development control and management. The dispersed pattern of land development it identified by calculating the entropy from multi-temporal satellites images. The entropy of land development has increased from 2.75 in 1988-90 to 8.9% in 1990-93 as urban areas quickly dispersed to the agricultural areas. Rapid urban expansion is inevitable in the Pearl River Delta during the fast growing period, both the patterns of urban sprawl should be under control to conserve land resources. Urban sprawl which does not take into considerations of physical properties of land, such as soil fertility, has produced severe impacts on agricultural production. According to the findings using entropy. Some towns of the study area have unusual high degree or urban sprawl. There is an urgent need to control such development patterns so that further economic growth in the region can be sustained.

Acknowledgement
This study is supported by the funding from the Croucher Foundation, Hong Kong.

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