An object-based cellular automata model to mitigate scale dependency
3.3 Modeling land-use/land-cover changes
VecGCA was tested using real data to simulate land-use/land-cover changes in two regions of different complexity in Canada. The first study area is the Maskoutains region located in Southern Quebec that covers an extent of 1312 km2. In this region, two predominant land use/land covers can be observed: agriculture and forest. The landscape is characterized by small forested patches within a large agriculture matrix. Two land- use/land-cover maps originating from Landsat Thematic Mapper images, acquired at a spatial resolution of 30 m in 1999 and 2002 (Soucy-Gonthier et al. 2003), were used in this study.
The second study area is the Elbow river watershed in Southwest Alberta, which covers approximately 1238 km2. A greater variety of land uses/land covers can be observed in this region, such as forest, agriculture, vegetated land (shrubs and other vegetation different from agricultural land), construction and open area, urban land, a portion of the Alberta's Rocky Mountains, a portion of the Tsuu Tina Nation reserve, and others.
Data used for the study include two land-use maps generated from Landsat Thematic Mapper images acquired in the summer of 1996 and 2001, at 30 m spatial resolution.
The original land use/land cover maps (for both regions) were transformed into a vector format using the function Raster to Polygons of ArcMap (ESRI 2005).
3.3.1 Components of the land use/land cover VecGCA model Several components must be defined in VecGCA: the space, including the set of states, the neighborhood size and influence function, and the transition function. In addition, the transition probabilities and threshold values must be calculated.
For both study areas, space is defined as a collection of patches of different land uses/land covers. Each patch corresponds to a polygon in the vector land-use/land-cover map of the study area. The vector land use/land cover maps for 1999 and 1996 were used as initial conditions for the Maskoutains region and the Elbow river watershed, respectively. In the Maskoutains region, there are four possible states for each object: forest, agriculture, water and road. Only two changes of states are considered,
namely forest to agriculture and agriculture to forest. The dynamics in the Elbow river watershed is more complex; there are nine possible states (forest, agriculture, vegetation, park/golf, urban land, forest and Tsu Tina reserve, developed land in Tsu Tina reserve, undeveloped land in Tsu Tina reserve and other), and 36 possible changes of state.
Transition probabilities were calculated from the comparison between the two land-use maps of different dates according to Eq. 3.3.
∑
= →→ = 4 → 1 i
i X
Y X Y
X
A P A
(3.3) where
PX→Y is the transition probability from state X to state Y AX→Y is the total area that changes from state X to state Y
The influence function was defined using Eq. 3.4, the variables being the same as in Equation 1. The influence value is proportional to the neighbor’s area within the neighborhood, and inversely proportional to the distance between the centroids of the objects.
ab a a t
X b t
X A t d
p
ab
e
g = 1 −
− ( )→ ( +1)* ( ) / (3.4) The transition function that determines the area of change of each geographic object is given by Eq. 3.5.⎩⎨
⎧ ≥
= 0 other case if
* )
( a ab ab ab
b
g g
t
f A
λ
(3.5)
where λab is a threshold value that represents the resistance of the geographic object b to change its state for the state of its neighbor a. This value can be defined as the probability that a geographic object does not change its state from the state X to the state Y although all its neighbors are in state Y. The same transition function was applied to define the dynamics of both study areas.
3.3.2 Definition of the raster-based CA model
A stochastic raster-based CA model was implemented for each study area to compare its results with the simulation outcomes of the VecGCA
models. For the Maskoutains region, space was defined as a regular rectangular grid of 409 columns and 508 rows and a cell size of 100 m.
This size was chosen based on the results previously obtained in a scale sensitivity analysis conducted by Ménard and Marceau (2005), which indicates that 100 m is the cell size that best captures the dynamics of the study area. For the Elbow river watershed, the grid defining space has 2450 columns and 1864 rows and a cell size of 30 m (corresponding to the original resolution of the land-use data). The initial conditions correspond to the 1999 and the 1996 raster-land use maps for the Maskoutains region and the Elbow river watershed, respectively.
For both models, a Moore neighborhood was chosen to represent the influence of the adjacent cells on a central cell. Probabilistic rules were calculated from the comparison between two land-use maps (1999 and 2002 for the Maskoutains region, and 1996 and 2001 for the Elbow river watershed), according to the procedure described in Ménard and Marceau (2005), where a cell in the state X that has n cells in the state Y in its neighborhood has a probability of changing to the state Y equal to the number of cells in the state X with n neighbors in the state Y that have changed to the state Y between t1 and t2, divided by the total number of cells in the state X with the same neighborhood in t1.
To account for a temporal resolution of one year, the probabilistic rules were adjusted using the exponential method presented by Yeh and Li (2006) where the transition probability P calculated for a time step t is substituted by Pn for a time step T where T = n*t.
3.3.3 Model simulations
While it is hypothesized that the use of polygons to define space rather than cells of arbitrary sizes will mitigate the cell size sensitivity when using VecGCA, the potential sensitivity of the model to the neighborhood configuration remains. To address this issue, four simulations, from 1999 to 2002, were performed for the Maskoutains region and four others, from 1996 to 2001 were conducted for the Elbow river watershed. Each simulation was associated to a different neighborhood size: 10 m, 30 m, 60 m and 120 m. The results were compared to the land-use/land-cover maps of 2002 and 2001 for the Maskoutains region and the Elbow river watershed, respectively.
To compare the simulation outcomes produced by the VecGCA models and the raster-based CA models, a landscape analysis using Fragstats 3.3.
(McGarigal et al. 1995) was done on the raster-based CA results. The number of patches for each land use was calculated on the raster map generated by the raster-based CA model and compared to the number of
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.