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AMIS: Development of a GIS/Multicriteria Corridor Planning Methodology
To generate the final Analytic Impedance Value (AIV, or f) for each element a weighting process was used. To avoid affinity groupings with more elements potentially registering higher total impedances an isotropic layer approach was used. Each affinity grouping was considered to offer a maximum possible impedance which could be generated only if all of its constituent elements were present (Table 4). The summed elemental impedances were then fitted into this layer. Where there were few elements, such as in the "Socioeconomic" affinity grouping, each element represented a larger % of the affinity grouping’s total impedance. In other groupings with many elements, some registered very small percentages of the sum impedance.
This process can be specified mathematically. Consider the preference matrix [1]. Here, each Purpose and Need category, represented by PNi where i = 1 to 8, contains a specific priority ordering of the affinity groupings. The priority coefficients (b) that weight each affinity grouping within PNi are given by bij, where j = 1 to 5 for the five affinity groupings defined (see Table 1). Since AHP computation was employed for each P/N, for PNi it is given that  .
The complete matrix of 8 P/N’s each comprised of 5 affinity grouping priorities was not used in this case. Instead the meeting participants were asked which P/N’s applied to this highway. Three specific P/N’s were identified and ranked through pairwise comparison for this project using AHP. To perform the AHP computations the Java-based web software HIPRE was used [11]. This offered an advantage over proprietary software such as ExpertChoice [12] in that being web-based and remote-site hosted it was accessible by all stakeholders at all times. Regardless of location, each stakeholder could view graphically the preference orderings generated by the AHP and even perform dynamic sensitivity analysis (see Figure 3). Password protection was used. Combinatorial scoring was then employed to compute a scaling factor that was applied to each attribute. A second, independent AHP prioritization was performed on the three selected P/N’s. This yielded: 
where g1 is the AHP-derived priority coefficient for the first P/N, g2 the coefficient for the second selected P/N and g3 applies to the final P/N1. The final weighting was computed on the basis of the following distribution: 65% from the "Legislation" P/N, 19.9% from the "Economic/social development" P/N and 15.2% from the "System Linkage" P/N (Figure 3). The affinity grouping priorities derived by AHP were then multiplied by the appropriate scaling factors. Substituting for PN1, PN2 and PN3 from the matrix 1, the b coefficients were resolved. Each affinity grouping therefore possessed an affinity grouping (category) impedance multiplier (termed s), representing a relational impedance (Table 4). To interpret s, consider for example all of the elements in the affinity grouping "Dirt and Rock" sum to give about 1/6 of the impedance of all the elements in the "Regulatory Practices" affinity grouping. But all of the possible elements in each group are unlikely to be spatially copresent in one location, so individual elemental impedances, termed Analytic Impedance Values or f, must be computed. With a and s given, f was computed as given in Equation 3. For the elements belonging to the SocioEconomic affinity group, for example, faSE is the final Analytic Impedance Value for element a,aaSE is the raw impedance score for element a and represents the AHP-derived affinity group total impedance for the "SocioEconomic" affinity group. 
To give some idea of the range of f values the element with the highest impedance, f = 7138.8 units, was Four F National Properties. This element was assigned the highest raw score and since it belonged to the “Regulatory” affinity group it also received the highest categorical impedance rating. Every participant felt that such properties (National Historic Register) were very difficult and expensive to acquire, and even if legally and economically feasible, the acquisition process often faced significant and widespread community opposition. Therefore they felt that the Four F properties should be avoided when planning this road corridor. The lowest f was assigned to element Slope Categories 0-5% in the "Dirt and Rock" affinity group (f = 175.0). This reflected a rather low level of impedance assigned to engineering concerns in this case. The final f value for each data element was then ready for input into the GIS2. The GIS database for AMIS was constructed to the same resolution as the underlying terrain data, USGS 30 meter digital elevation models (DEMs). This was selected to simplify data conversion and also to approximate an absolute minimum width for an interstate highway corridor. Although a larger cell size would have depicted the actual right of way required for a highway corridor more accurately, it would also have meant that the effective scale of the data would be reduced with concomitant accuracy loss. The 30 meter size was therefore selected as a necessary compromise. Data for the GIS came from a variety of sources within the state and federal government. (see Figure 3 and 4 for examples). All of the vector data was converted to raster grids within Arc/Info. The integer value of each grid cell was taken directly from the calculated AHP values for that data layer. For cell A, where n elements are present, net cellular impedance ma is given by: 
Once all the raster layers were completed, Arc/Info then added the values of all cells in the corridor study area. The result is an impedance surface, representing the sum of all the calculated costs on a per-cell basis (Figure 5). Using Avenue scripts within Arcview, the routing function is invoked with a button which then allows the user to specify where the route should terminate. Arcview then determines the least cost route to that cell and draws it onscreen as a graphic element (Figure 6). |