Predicting the expansion of an urban boundary using spatial logistic regression and hybrid raster–vector routines with remote sensing and GIS

This paper presents an urban growth boundary model (UGBM) which utilizes spatial logistic regression (SLR), remote sensing, and GIS to simulate the differentially expanding geometry of a dynamic urban boundary over decadal time periods. SLR is used as the core algorithm in a UGBM quantifying how biophysical factors influence the rate at which all edges of an urban boundary expand over time. Spatial drivers selected from a raster-based environment are used as input predictor variables to the SLR UGBM, the output response variable being the distance between time-separated urban boundary intersections along arcs extending radially from a point centered at the urban core relative to the maximum distance. Percent area match (PAM) quantity and location goodness-of-fit metrics, fit of the predicted distance versus observed distance, and the sensitivity of the SLR UGBM to the contribution of each predictor variable are used to assess the agreement between predicted and observed urban boundaries. The model is built, tested, and validated using satellite images of the city of Las Vegas, United States of America, collected in 1990, 2000, and 2010. We compare urban boundary simulation of full and reduced SLR UGBMs to a null UGBM lacking in specificity of predictor variables. Results indicate that the SLR UGBM has a better goodness of fit compared to a null UGBM using PAM quantity and location goodness-of-fit metrics. Then, we use the SLR UGBM to predict urban boundary expansion between the years 2000 and 2010 and describe how this model can be used to plan ahead for future boundary expansions given what is known about current edge conditions.