**CA Markov Model for Land use and Land Cover modelling and prediction**

The Markov model is based on the theory of random processes. In this model, given the initial state

and state-transition probabilities, simulation results have nothing to do with the historical condition

before the current condition, which can be used to describe land-use changes from one period to

another. We can also use this as a basis to predict future changes. Change was found by creating a

land-use-change transition-probability matrix from periods t to t + 1, which is the basis to predict

future land-use changes.

S(t + 1) = Pij × S(t) |

S(t + 1) denotes the state of the land-use system at times t + 1 and t, respectively. Pij is the

state-transition matrix.

CA has four basic components: Cell and cell space, cell state, neighborhood, and transition rules. The CA model can be expressed as follows

S(t + 1) = f(S(t), N)

In the formula, S is a state set of a finite and discrete state, t and t + 1 are different moments, N

is the neighborhood of the cell, and f is the cell-transition rule of the local space.

Usually, in order to make cellular automata better simulate a real environment, space constraint

variable Î² needs to be introduced to express the topographic terrain, as well as the adaptive

constraints and restrictive constraints of the spatial-influence factors on the cells.

S(t + 1) = f(S(t), N, Î²) |

The separate Markov model lacks spatial knowledge and does not consider the spatial

distribution of geographic factors and land-use types, while the CA-Markov model adds spatial

features to the Markov model, uses a cellular-automata filter to create weight factors with spatial

character, and changes the state of the cells according to the state of adjacent cells and the transition rules.

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