usually represents different types of land cover/use. The model moves from one
state (e.g., land cover/use type) to the other with some transition probability
depending on the current state but not the previous ones (often called a process
without memory). Transition probabilities are computed based on the observed land
change data which represent the probability that the land cover/use type within a
cell (i.e. spatial unit) will convert (or, move) to another land type within the same
period of time in the future. For example, Muller and Middleton (1994) applied
Markovian analysis to time series data to quantify land use changes over a humandominated landscape. Markovian analysis can represent all the multi-directional
land use changes between land use categories. Sequential time series data were used
to simulate land use change over a longer time period.
Markov models usually do not account for specific drivers of land changes,
which assume that collective forces functioning to produce the observed patterns in
the past will continue to do so in the future. In other words, Markov models are used
to project future land changes based on the assumption of stationarity. Markov
model can be dynamic by changing the transition probabilities in some sort of
regular patterns over time (Howard et al. 1995). Given the capability of automatically computing land transition probability with time series data, Markov chain
models are often integrated with more complex forms of models such as cellular
automata and agent-based model that will be discussed shortly.
1.2.4 Cellular Automata
A conventional modeling framework describes systems in equilibrium or as moving
between equilibriums. However, the evolution of land changes usually does not
reach a stable equilibrium but exhibits features of complexity (e.g., edge of chaos,
emergence, and non-linearity). The concept of complexity emphasizes on the
interdependence among constituent parts. Therefore, complex adaptive system
(CAS) is a system composed of interconnected parts that as a whole exhibits one
or more properties that are not obvious from the individual parts. Cellular automata
(CA) models are built upon static cell-based environment where each cell has a
state and can transfer to others based on the current state and the interactions with
its neighborhoods using a set of transition rules (Batty and Xie 1994; Clarke
et al. 1997; Miller and Page 2007). The four major components of CA therefore
are state, landscape/space, neighborhoods and transition rules. For each of the four
components, their structures vary from simple to more complex forms (e.g., Stevens
and Dragicevic 2007). The transition rules are usually set to represent spatial and
temporal constraints (Sante et al. 2010). One of the well tested CA models is the
SLEUTH (Slope, Land use, Exclusion, Urban extent, Transportation, Hillshade)
model developed by Clarke et al. (1997) for simulating urbanization. This model
defines complex rules representing control parameters that allow the model to selfmodify under the circumstances it generates. More applications of this model are
1 Land Change Modeling: Status and Challenges
7
state (e.g., land cover/use type) to the other with some transition probability
depending on the current state but not the previous ones (often called a process
without memory). Transition probabilities are computed based on the observed land
change data which represent the probability that the land cover/use type within a
cell (i.e. spatial unit) will convert (or, move) to another land type within the same
period of time in the future. For example, Muller and Middleton (1994) applied
Markovian analysis to time series data to quantify land use changes over a humandominated landscape. Markovian analysis can represent all the multi-directional
land use changes between land use categories. Sequential time series data were used
to simulate land use change over a longer time period.
Markov models usually do not account for specific drivers of land changes,
which assume that collective forces functioning to produce the observed patterns in
the past will continue to do so in the future. In other words, Markov models are used
to project future land changes based on the assumption of stationarity. Markov
model can be dynamic by changing the transition probabilities in some sort of
regular patterns over time (Howard et al. 1995). Given the capability of automatically computing land transition probability with time series data, Markov chain
models are often integrated with more complex forms of models such as cellular
automata and agent-based model that will be discussed shortly.
1.2.4 Cellular Automata
A conventional modeling framework describes systems in equilibrium or as moving
between equilibriums. However, the evolution of land changes usually does not
reach a stable equilibrium but exhibits features of complexity (e.g., edge of chaos,
emergence, and non-linearity). The concept of complexity emphasizes on the
interdependence among constituent parts. Therefore, complex adaptive system
(CAS) is a system composed of interconnected parts that as a whole exhibits one
or more properties that are not obvious from the individual parts. Cellular automata
(CA) models are built upon static cell-based environment where each cell has a
state and can transfer to others based on the current state and the interactions with
its neighborhoods using a set of transition rules (Batty and Xie 1994; Clarke
et al. 1997; Miller and Page 2007). The four major components of CA therefore
are state, landscape/space, neighborhoods and transition rules. For each of the four
components, their structures vary from simple to more complex forms (e.g., Stevens
and Dragicevic 2007). The transition rules are usually set to represent spatial and
temporal constraints (Sante et al. 2010). One of the well tested CA models is the
SLEUTH (Slope, Land use, Exclusion, Urban extent, Transportation, Hillshade)
model developed by Clarke et al. (1997) for simulating urbanization. This model
defines complex rules representing control parameters that allow the model to selfmodify under the circumstances it generates. More applications of this model are
1 Land Change Modeling: Status and Challenges
7