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urban growth model. 
2.1 SA method for CA modeling 
In this study, univariate sensitivity analysis was performed in 
which the parameters i.e. the basic CA elements were assumed 
independent. This is mainly because of the fact that complicated 
mathematical operations are difficult to derive for the analysis 
of uncertainties and errors in CA simulation testing as stated by 
Yeh and Li (2003). Furthermore, KAPPA statistic can be used 
(Congalton and Mead, 1983) for the analysis of simulation 
outcomes since CA operates in raster environment. However, 
KAPPA statistic has some disadvantages since it does not 
quantify the patterns of map land-use classes, thus even a small 
difference of classes between two maps is shown as an 
inconsistency (White et al. 1997; Barredo et al. 2003; Straatman 
et al. 2004). In order to overcome these shortcomings this study 
proposes an integrated SA method that employs qualitative and 
quantitative approaches of cross-classification map, KAPPA 
index with coincidence matrices and spatial metrics. The 
effective SA was accomplished by varying the CA basic 
elements one at the time, more specifically neighborhood size 
and type. Subsequently, the model outputs i.e. the simulated 
maps were compared with each other in terms of the 
combination of different approaches to provide the quantitative 
and qualitative measures and achieve the high accuracy in map 
comparisons. 
Under the heading of qualitative part of the approach, the visual 
comparison of the outcomes was used. The advantage of this 
method is in its capability to detect the uncertainties and 
inconsistencies while comparing the simulation results. White et 
al. (1997) and Mandelbrot (1983) pointed out that visual 
similarity is an important factor for comparison of complex 
fractal forms. Therefore, the cross-classification map, which is 
the result of multiple GIS overlay analysis showing all 
combinations, was produced to enable visual comparison and 
the analysis of visual similarities and differences between 
model outputs. The cross-classification map depicts the 
locations of the combinations of the map land-use classes of 
urban growth model output for the two maps that were being 
compared. The advantage of a cross-classification map is 
reflected in its capability to easily determine the locational 
differences of map land-use classes between the two maps. 
Quantitative part of the developed approach relics on the 
following two categories: a coincidence matrix with KAPPA 
index and spatial metrics. The KAPPA index is computed with 
the coincidence matrix to compare the results of changing CA 
element values. It was introduced by Cohen (1960) and adapted 
for accuracy assessment in the remote sensing applications by 
Congalton and Mead (1983). It ranges from 0 to 1, and when it 
approaches | it indicates that the two maps are similar. In this 
study, the overall KAPPA index (Lillesand and Kiefer, 1994) 
was calculated in order to analyze the degree of similarity 
between outputs when varying different CA element 
configurations. 
Landscape indices or metrics are quantitative indices that can 
measure the structure and pattern of a landscape (McGarigal 
and Marks, 1994; O'Neill et al., 1988). Their origins can be 
found in the information measures theory and fractal geometry 
(Mandelbrot, 1983). Recent studies use the term spatial metrics 
for the analysis of the urban phenomena. It has been shown that 
spatial metrics have significant advantages when applied in the 
analysis of heterogeneous urban areas (Parker and Meretsky 
2004; Alberti and Waddell 2000; Barnslev and Bair 1997; 
87 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
Herold et al. 2002). In addition. Herold et al. (2003) stated that 
spatial metrics can be utilized for the accuracy assessment of 
CA model simulations. In turn, they have applied spatial metrics 
to test the accuracy of SLEUTH CA model. 
In this study, fractal dimension (FD) and class area spatial 
metrics were employed to analyze the CA model output results. 
Fractal dimension (FD) illustrates the complexity and the 
fragmentation of a land-use class patch by a perimeter-area 
proportion. The derived version of FD, which is called Area 
Weighted Mean Patch Fractal Dimension (AWMPFD), is used 
in this study since it eliminates the overestimation of smaller 
land-use class patches (Milne, 1991). In addition to FD, class 
area metric compares the change in area of each class by 
varying radius from the city center. Class area is a measure used 
to calculate the surface of overall change for each class type. In 
order to analyze results of spatial metrics, radius zones were 
created to divide study area into subareas with the increasing 
radius of 10 km from the city center, and FD value is calculated 
for each sub-area. To compute metrics, PATCH ANALYST 
3.1, an extension of ESRI ArcView GIS software, was used to 
facilitate the spatial analysis of landscape patches calculations 
and modeling of attributes associated with patches (Elkie et al., 
1999). 
3. SIMULATION FRAMEWORK 
3.1 Study area and CA model 
San Diego region, USA, was chosen for the study arca. The 
digital map data for the study area was obtained from San 
Diego’s Regional Planning Agency public Internet site 
(SANDAG, 2004). The vector map was rasterized to 
appropriate spatial resolutions in order to apply the CA model. 
The raster map represents the digital image of the city classified 
in nine land use classes, which are: housing area, commercial 
area, public area, industrial areas. recreational areas, water 
arcas, transportation network, agricultural areas, and vacant 
land. : 
Since it is important to analyze different urban land use classes 
that change over time, housing and commercial areas were 
chosen as the most dynamic. Land uses such as agricultural 
areas and public areas, which would impose more constraints on 
urban growth pattern, were classified as other land use classes. 
Nonetheless, these areas are considered to be changed to 
housing throughout the simulation. Water areas and roads 
represent fixed land use types, which are assumed not to grow 
or change the location over time. Therefore, the simulation was 
configured to ensure that urban area can grow in any direction 
without limitations except for roads and water areas, in which 
urban growth is assumed to be impossible. 
The constrained CA-based simulation model developed by 
White et al. (1997) was selected due to the fact that it has been 
widely adapted to simulation of different real cities growth. 
Simulations based on the CA model were performed by Cellular 
Automata extension of ESRI ArcView GIS software (Heuegger, 
2002). The GIS-based CA simulations of urban growth of San 
Diego region were used to obtain different model outcomes 
when varving different CA elements more specifically 
neighborhood size and type.