A dynamic continuum modeling approach to the spatial analysis of air quality and housing location choice in a polycentric city

Abstract This study develops a model that integrates land use, transport, and environment factors. Specifically, a continuum modeling approach is used to access how air quality, among other factors influence people’s housing location choices. We assume that pollutants generated by the transport sector are dispersed through turbulent diffusion and advection by the wind and that they affect air quality. Air quality affects people’s housing choices, which in turn changes their travel behavior. A polycentric urban city with multiple central business districts (CBDs) is considered, and the road network within the modeled city is assumed to be sufficiently dense that it can be viewed as a continuum. The predictive continuum dynamic user-optimal (PDUO-C) model is used to describe the traffic flow for a given traffic demand distribution. The dispersion of the vehicle exhaust is modeled with an advection-diffusion equation. In this study, we incorporate departure time choice into the PDUO-C model to describe the traffic flow and show that the departure time choice problem is equivalent to a variational inequality (VI) problem in which housing location choice is determined by travel cost, air quality and rent. The coupled system can be treated as a fixed-point problem. A projection method is adopted to solve the VI problem, and a self-adaptive version of the method of successive averages (MSA) is proposed to solve the whole coupled system. A numerical example is given to illustrate the effectiveness of the proposed model.