An object-based cellular automata model to mitigate scale dependency
3.4 Simulation results
polygons produced in the VecGCA model for each study area. In addition, for the Maskoutains region, an overlay of the 2002 vector and 100 m raster land-use/land-cover maps with the simulation outcomes of VecGCA and the raster-based CA models, respectively, was performed to determine the correspondence between the results of the models and the real state of the study area. The same procedure was executed for the Elbow river watershed using the 2001 vector and 30 m raster land-use/land-cover maps and the corresponding simulation outcomes.
Table 1. Proportion of land-use and number of patches/polygons in the outcomes of the VecGCA model, the raster-based CA model and the 2002 raster land-use map in the Maskoutains region
Initial condition
Land-use map 1999 Land-use map
2002 Simulation
outcomes for 2002 Vector
format Raster
format Vector
format Raster
format VecGCA Raster- based CA
Forest[%] 16.57 16.58 14.83 14.86 14.92 14.86
Agriculture
[%] 80.70 80.70 82.45 82.41 82.35 82.41
Total number of patches /
polygons 5247 3118 5702 1371 4666 1569
A spatial overlay analysis shows that the land-use distribution generated by VecGCA for 2002 coincides as an average in 99% with the 2002 land- use map, whereas the distribution produced by the raster-based CA coincides in 89%, although an appropriate cell size has been used (Table 2). 100 % of the forest polygons produced by VecGCA coincide with the real forested patches in the study area, in comparison to only 77%
generated by the 100 m raster-based CA model. These results can by explained by the capacity of VecGCA to reproduce the evolution of the objects by a change of shape, whereas the patches produced by the raster- based CA model are created by the agglomeration of individual cells changing state. In addition, when looking closely at the simulation maps, one can observe that the landscape generated by VecGCA is characterized by large patches of well-defined boundaries, in comparison to the diffuse boundaries and the high level of landscape fragmentation produced by the raster-based CA model (Fig. 3).
Table 2. Proportion of simulated area that coincides with the state of the system in 2002 for each land use in the Maskoutains region
Proportion of simulated land uses [%]
Land uses
VecGCA Raster-based CA
Forest 100.00 77.47
Agriculture 99.00 93.04
Other 98.54 97.86
Average 99.18 89.45
Fig. 3. Detail on the polygons’ boundaries produced by the VecGCA model and the raster-based CA model in the Maskoutains region
Different results were obtained for the Elbow river watershed. In this case, VecGCA generated a land-use distribution that is more similar to the 2001 land-use map in comparison to the results produced by the raster- based CA (Table 3; Fig. 4). The proportions of the land-use classes vegetation, park/golf and developed land in the Tsu Tina Reserve are
Raster land-use map 2002 (resolution 30 m)
VecGCA result in 2002 (neighborhood 30 m)
Raster-based CA result in 2002 (cell size 100 m)
underestimated by the raster CA model, while other classes such as urban and undeveloped land in the Tsu Tina Reserve are overestimated.
Table 3. Proportion of land-use and number of patches/polygons in the outcomes of the VecGCA model, the raster-based CA model and the 2001 raster land-use map in the Elbow river watershed
Initial condition
Land-use map 1996
Land-use map 2001
Simulation outcomes for 2001 Vector
format Raster
format Vector
format Raster
format VecGC A
Raster- based CA
Forest [%] 44.45 44.45 44.34 44.31 45.57 44.21
Agriculture [%] 15.39 15.39 13.47 13.43 15.29 15.02
Vegetation [%] 1.98 1.98 1.68 1.71 1.82 0.28
Park/golf [%] 0.87 0.87 0.82 0.83 0.54 0.23
Urban [%] 1.56 1.56 2.30 2.29 2.09 3.81
Forest in Tsu Tina
Reserve [%] 6.80 6.80 5.87 5.87 6.99 5.90
Developed land in Tsu Tina Reserve
[%] 3.04 3.04 3.22 3.23 3.11 1.40
Undeveloped land in Tsu Tina
Reserve [%] 2.88 2.88 3.52 3.51 2.79 5.42
Total number of
patches/polygons 7195 5837 8306 6686 2986 4321
A spatial overlay analysis of the land-use maps generated by VecGCA and the raster-based CA model with the 2001 land-use maps in vector and raster format reveals that the results obtained with VecGCA highly coincide with the land-use spatial distribution in the study area, whereas the results obtained with the raster-based CA model largely differ for most land-use classes (Table 4). The cell size used for the raster-based CA model was 30 m, which is the same as the resolution of the original land- use data. In that case, no previous sensitivity analysis was done to determine the best cell size to be used, and we might hypothesize that it is not the most appropriate cell size for this study area either.
Fig. 4. Sub region of the Elbow river watershed showing the land-use spatial distribution generated by the two models
Table 4. Proportion of simulated area that coincides with the state of the system in 2001 for each land use in the Elbow river watershed
Proportion of simulated land uses [%]
Land uses
VecGCA Raster-based CA
Forest 93.79 88.96
Agriculture 98.67 85.67
Vegetation 83.13 21.19
Park/golf 100.00 60.93
Urban 80.80 54.45
Forest in Tsu Tina
Reserve 92.69 87.33
Developed land in Tsu
Tina Reserve 96.45 73.90
Undeveloped land in Tsu
Tina Reserve 100.00 60.42
Average 91.34 66.60
Raster-based CA result in 2001 (cell size 30 m)
VecGCA result in 2001 (neighborhood 30 m) Raster land-use map 2001
(resolution 30 m)
When varying the neighborhood size in VecGCA, the results for the Maskoutains region reveal that for the neighborhood sizes of 10 m and 30 m, the simulated proportion of forested and agricultural land for 2002 differs in less than 2% of the proportion calculated from the 2002 land-use map; for the neighborhoods of 60 m and 120 m, the difference might exceed 8% (Table 5). However, for the Elbow river watershed the variation of the neighborhood size does not produce significant variation in the simulation outcomes (Table 6). These results can be explained by the fact that the influence function (Equation 4) and the transition function (Equation 5) are directly proportional to the neighbors’ area within the neighborhood and this area varies with the neighborhood size and the landscape configuration. In the Maskoutains region, the majority of the objects are small forested patches having only one agricultural neighbor (Fig. 5a). The influence of this neighbor and the area to change from forest to agriculture increase when the neighborhood size increases. In the Elbow river watershed, the geographic objects have several neighbors of different states (Fig. 5b). In this case, an increase of the neighborhood size produces a small increase of the neighbors’ area within the neighborhood in comparison to the objects that have only one neighbor. In addition, when the neighborhood increases, new neighbors appear which influence and area to change are not significant because they are distant geographic objects separated by other objects. Therefore, in this landscape configuration the simulation outcomes are less sensitive to the neighborhood size.
Table 5. Proportion of land-use/land-cover (%) in the Maskoutains region using different neighborhood sizes
Land uses Neighborhood 1999 2000 2001 2002 a
10 m 16.57 16.38 16.30 16.22 1.40 30 m 16.57 16.03 15.44 14.59 0.23 60 m 16.57 16.02 14.90 12.16 2.66 120 m 16.57 12.40 9.43 6.37 8.46 Forest[%]
Original 16.57 - - 14.83 -
10 m 80.70 80.89 80.98 81.05 1.40 30 m 80.70 81.25 81.84 82.68 0.24 60 m 80.70 81.25 82.38 85.11 2.67 120 m 80.70 84.88 87.84 90.91 8.46 Agriculture[%]
Original 80.70 - - 82.45 -
a Variation between the simulation outcomes and the 2002 land-use/land-cover map in the Maskoutains region
Fig. 5 (a) Schematic representation of the landscape configuration of the Maskoutains region where the objects have only one neighbor for different neighborhood sizes. (b) Schematic representation of the Elbow river landscape configuration where the objects have several neighbors; when the neighborhood size increases the number of neighbors and the neighbors’ area within the neighborhood also increase
Table 6. Proportion of land-use/land-cover (%) in the Elbow river watershed using different neighborhood sizes
Neighborhood 1996 1997 1998 1999 2000 2001 a 10 m 44.45 44.62 44.58 44.44 44.42 44.39 0.04 30 m 44.45 44.49 44.36 44.15 44.11 43.46 0.89 60 m 44.45 44.97 44.84 44.72 43.62 43.58 0.77 120 m 44.45 45.53 45.35 45.08 44.86 43.53 0.82
Forest
Original 44.45 44.35 10 m 15.39 15.33 15.28 15.26 15.24 15.21 1.73 30 m 15.39 15.41 15.30 15.40 15.36 15.35 1.87 60 m 15.39 15.58 15.51 15.40 15.35 15.32 1.84 120 m 15.39 15.74 15.77 15.60 15.56 15.56 2.09
Agriculture
Original 15.39 13.48 10 m 1.98 1.85 1.82 1.82 1.80 1.79 0.11 30 m 1.98 1.61 1.48 1.45 1.43 1.54 0.14 60 m 1.98 1.32 1.19 1.18 1.39 1.36 0.32 120 m 1.98 0.82 0.48 0.28 0.25 0.33 1.35
Vegetation Original 1.98 1.68
10 m 0.87 0.81 0.78 0.75 0.73 0.74 0.08 30 m 0.87 0.74 0.67 0.62 0.61 0.60 0.23 60 m 0.87 0.72 0.67 0.66 0.64 0.56 0.27 120 m 0.87 0.71 0.66 0.62 0.62 0.61 0.22
Parkrs
Original 0.87 0.82
a
b
c d
(a)
a b
c
e d f
g h
i
j k m
l n
p o
(b)
10 m 1.56 1.60 1.61 1.63 1.63 1.67 0.63 30 m 1.56 1.66 1.69 1.71 1.72 1.72 0.58 60 m 1.56 1.67 1.69 1.69 1.70 1.75 0.55 120 m 1.56 1.66 1.68 1.70 1.70 1.70 0.60
Urban
Original 1.56 2.30
10 m 6.80 6.78 6.75 6.74 6.72 6.73 0.86 30 m 6.80 6.79 6.66 6.61 6.60 6.59 0.72 60 m 6.80 6.79 6.71 6.64 6.63 6.62 0.75 120 m 6.80 6.81 6.77 6.72 6.50 6.46 0.59
Forest in TTNRb
Original 6.80 5.87
10 m 3.04 3.03 3.01 2.99 2.99 2.97 0.25 30 m 3.04 3.01 3.07 3.07 3.06 3.05 0.17 60 m 3.04 3.03 2.95 2.97 2.96 2.97 0.26 120 m 3.04 3.00 2.94 2.94 2.78 2.64 0.58
Developed land in TTNR
b
Original 3.04 3.22
10 m 2.88 2.92 2.96 2.99 3.01 3.05 0.47 30 m 2.88 2.92 3.00 3.05 3.07 3.09 0.43 60 m 2.88 2.91 3.07 3.11 3.13 3.14 0.38 120 m 2.88 2.92 3.01 3.07 3.44 3.63 0.11
Undeveloped
land in TTNR
b
Original 2.88 3.52
a Variation between the simulation outcomes and the 2002 land-use/land-cover map in the Elbow river watershed
b TTNR: Tsu Tina Nation Reserve