Trend surface analysis of geographic flows

An origin-destination (OD) flow is the movement of objects from an origin to a destination. Determining how the flows vary across geographic locations helps understand the mechanism of flow distributions; however, it has rarely been studied. Here, we propose a trend surface model with polynomial functions to quantify the flow distribution with coordinates in the flow space. This model assumes that an observed data-record is composed of the trend value and the residual, and is represented by the orthogonal polynomial with O and D coordinates as independent variables and flow properties as dependent variables. The simulation experiments based on the linear and quadratic models indicated that the trend surface function could reflect the increasing/decreasing variation of flows with OD locations (i.e. flow trends) in different patterns. Applying this model to a case study of taxi OD flows in the broad Central Business District of Beijing, we found that the flows exhibited a rising trend toward the southwest. The trend surface characteristics are associated with the distributions of urban functional patches, where the workplaces and residences increased toward the southwest in the study area. Notably, the spatial deviations of trend surface model can help in identifying site pairs that attract flows at a high density (e.g. commerce centers and big communities), facilitating the planning of public transportation to mitigate the congestion.