Trend surface analysis of geographic flows

Abstract

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.

Keywords:

• origin-destination (OD) flow
• flow space
• flow trend
• trend surface analysis

Acknowledgment

The authors thank the editors and the anonymous reviewers for their helpful comments on an earlier draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data and codes availability statement

The data and codes that support the findings of this study are available in ‘figshare.com’ with the identifier(s): https://doi.org/10.6084/m9.figshare.21191209.v1

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant Nos. 42071436, 42101431; the National Key R&D Program of China under Grant No. 2017YFB0503604.

Notes on contributors

Beiyang Guo

Beiyang Guo is a Master Degree candidate at Nanjing University. Her research interests include spatial analysis and big geodata mining.

Tao Pei

Prof. Tao Pei is a professor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include big geodata mining and geostatistics.

Ci Song

Dr. Ci Song is an assistant professor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial statistics and spatial analysis.

Hua Shu

Dr. Hua Shu is a post doctor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial statistics and big geodata mining.

Mingbo Wu

Mingbo Wu is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. His primary research interest is machine learning in big geodata.

Sihui Guo

Sihui Guo is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. Her primary research interest is the commuting pattern mining in cities.

Jingyu Jiang

Jingyu Jiang is a Master Degree candidate at Nanjing University. Her research interests include big geodata mining and topological structure of flow data.

Peijun Du

Prof. Peijun Du is a professor at Nanjing University. His research interests include machine learning and geoscientific analysis in remote sensing images.