Simulating urban land growth by incorporating historical information into a cellular automata model

Abstract

The first and second laws of geography have been applied to the simulation of urban growth in many studies. However, by focusing on the spatial complexity of urban growth, these studies have the shared problem of ignoring the temporal complexity of urban growth, which can be solved by incorporating historical information into the simulation of urban growth. In this paper, we describe how we constructed a Logistic-CA model using smoothed transition rules (the SM-Logistic-CA model). Specifically, in this paper, we: 1) propose an expansion similarity index to measure the similarity of the urban expansion processes in two periods; 2) use linear smoothing and exponential smoothing to integrate the historical transition rules; 3) assign smoothing weights to each period based on the expansion similarity index; and 4) compare the SM-Logistic-CA model with the standard Logistic-CA model. The results show that the SM-Logistic-CA model can exhibit good control of urban growth, and can avoid the problem of new urban land expanding blindly along the original urban land when smoothing is performed using the transition rules of appropriate historical periods. The similarity of the expansion processes between the historical period and the target period and the temporal distance of the historical period from the target period affect the simulation accuracy of the SM-Logistic-CA model, and the neighborhood size changes the relative importance of these two factors on the simulation results.