The CA-Markov model is composed of CA model, Markov chain and multi-criteria evaluation (MCE) [29]. The CA model is a discrete, finite state composition of the meta-cell model. It can simulate complex dynamic systems with spatial-temporal characteristics according to certain local rules [43]. Markov chains create the transfer matrix and probability between land use types for multiple time periods in the past through spatial comparison analysis, which are the basic **data** for predicting future land use patterns. MCE refers to the selection of expansion factors to construct a land use transition suitability image collection. CA-Markov model can effectively predict future land use dynamics [44]. The prediction process equation of the CA-Markov model is shown below [45]:
Ctj + 1 = F[Ctj, N](5)
where C(t j ) and C(t j+1 ) are the states of the cell at time t j and t j+1 , respectively; F is the transition rule; N is the domain of the cellular. In this study, elevation, slope, earthquake, landslide, highway, main road, railroad and population density were selected as the driving factors affecting urban expansion. Among them, elevation, slope, earthquake and landslide are negative indicators, and the rest are positive indicators. The suitability evaluation maps for earthquakes, landslides, highways, main roads and railroads were calculated by the kernel density tool, and finally, the normalized driver maps were obtained ( Figure 5). The Kappa coefficient was applied to check the accuracy of the CA-Markov model simulation results [46]. The formula for calculating the Kappa coefficient is shown below:
Kappa = p a − p c 1 − p c (6) p a = s n (7) p c = a 1 * b 1 + a 2 * b 2 n * n(8)
where n is the total number of cell sizes in the raster; a 1 is the number of cell sizes in the real raster of the urban land; a 2 is the number of cell sizes in the non-urban land; b 1 is the number of cell sizes in the simulated raster of the urban land; b 2 is the number of cell sizes in the non-urban land; s is the number of cell sizes in the real raster and the simulated raster that correspond to each other. 