As one of the major research approach for my dissertation, GIS technique is intensively employed and interactively collaborated with mathematical and statistical operations, in modeling the urban density distribution pattern. The research summarized here is centered around three major formal questions:
1) How could the accessibility of an urban field with multiple centers of different values be correctly reflected in a density distribution model, not only qualitatively but also in a quantitative manner?
2) How could the GIS reasoning, for both raster and vector data, be interactively integrated with mathematical modeling to bridge the abstract quantitative equations with complex spatial reality?
3) How is the significance of GIS reasoning for those area where no established database available?
A concept model is first built to reflect the relationship between housing density and the urban density distribution pattern, and then is quantified as a mathematical model. With the relevant coefficients also generated through the statistical operation, the prototype mathematic model represent the density distribution pattern of urban Shanghai is determined as (n: density, t: accessibility time, the mathematical operations are omitted here)
( Figure 1 ).
In order to examine the validity of the mathematical model, a simplified abstract spatial urban model was built to simulate urban Shanghai. We calculated the accessibility map with each cell assigned a value referring to (t), the traveling time form the center via the old road system. Then, each cell was converted to the corresponding density value (n) by the equation ( Figure 2 ). The coverage of this abstract model is identical to the real urban Shanghai, which suggests the mathematic model correctly reflects the law of the density distribution in urban Shanghai.
In response to the first formal research question, the model is then improved to reflect more complex urban conditions with multiple centers of different value coexisting in a field ( Figure 4-5 ).
After testing and improvement, the model is applied to the real conditions of urban Shanghai to demonstrate the possibility of progressively modifying the urban pattern, by adjusting variables of accessibility and local centers, and to determine further the rational density value for residential development ( Figure 6 ) ( Figure 7-10 ). The model developed ensures that the density of residential development is attuned to the overall urban pattern at the macro level and the land value at the detailed level. The relevant GIS (Arcview) techniques employed here are, standard vector data reasoning, spatial analyst dealing with raster data, and 3-D analyst as a visualization tool. Particularly, functions like map algebra, overlay, reclassification, and cost-distance calculation are intensively employed.
1. The regression analysis between Shanghai's density distribution and its accessibility to the city core indicates that the density distribution is better correlated with the accessibility of the old road system ( Figure 1 ).
2. The mathematical model of the urban density distribution pattern targets the issue of how strategic thinking could be presented quantitatively in the form of physical density distribution patterns, and rationally guide the intensity of residential development, so as to finally realize the proposed strategy of urbanization ( Figure 6 ).
3. The improvement of the model further resolves the technical problem of how the integrated attracting impact could be distinguished for spatial location within a complex urban environment with multiple centers of different density values (Figure 6). It is important that the model provides an interactive way of dynamically examining the feasibility of the physical urban pattern in terms of broad social, economic and environmental goals of sustainability. In this way, the model can be a useful tool in an active approach to urban pattern control. Here, GIS plays a key role in implementing a mathematical equation within a complex urban spatial environment. Theoretically, we could allocate centers anywhere in the urban area with any density value according to our strategic thinking, and modify them until our expectation of the urban pattern is satisfied.
4. In turn, this tool provides a new approach for determining the density of residential development ( Figure 9-10 )., one in which the overall urban pattern could be well defined and the natural land value properly reflected. The model provides a two-way mechanism that allows interactive communications between the residential density and the urban pattern, allowing urban impact to be well reflected in the housing development.
In sum, this study demonstrates that, first, GIS technique has great potential not only in terms of direct application, but also for some theoretical studies, and what interests me most is possibility of making quantitative spatial model, other than the conventional qualitative depiction; second, it is important to recognize the significance of actively integrating other reasoning methods, which could greatly enhance GIS's basic function and thus broaden its sphere of application; third, according to this study, GIS reasoning is not necessary merely a heavily data dependent technique, but could be very applicable even for those places without established database, if its unique spatial power is recognized, in other words, simple data but complicated reasoning.