Reducing spatial autocorrelation in the dynamic simulation of urban growth using eigenvector spatial filtering

Abstract

In cellular automata (CA) based modeling of dynamic urban growth, non-spatial statistical approaches are usually affected by spatial autocorrelation and fail to describe the spatially non-stationary relationships between urban growth and its drivers. The eigenvector spatial filtering (ESF) is a representative method that can well estimate the regression coefficients in the presence of spatial autocorrelation. In this study, we developed two CA models based on the linear ESF (LESF) and the non-stationary ESF (NESF), of which LESF is featured by spatially stationary coefficients while NESF is featured by spatially varying coefficients. These two models were compared to a conventional logistic regression (LOGR) CA model. The three models (i.e. CALOGR, CALESF and CANESF) were used to simulate rapid urban growth in Suzhou between 2009, 2014 and 2019. The statistics suggest significant reduction in the spatial autocorrelation of the residuals in the CALESF and CANESF land transition maps, as well as an increase in the model reliability. The results show that compared with CALOGR, CALESF and CANESF respectively improved the overall accuracy by 2.0% and 2.2% in 2014, and improved by 0.4% and 0.7% in 2019; they also hit more new-urban-cells, respectively increasing the figure-of-merit (FOM) by 3.8% and 4.3% in 2014, 0.3% and 0.9% in 2019. All three models performed better when integrated spatial heterogeneity into the CA neighborhoods, increasing overall accuracy by over 1% and FOM by over 2%. We concluded that the ESF-based CA models can effectively derive spatially varying land transition rules to capture the urban dynamics, and more accurately predict urban growth featured by spatial autocorrelation.