A kriging interpolation model for geographical flows

The kriging model can accommodate various spatial supports and has been extensively applied in hydrology, meteorology, soil science, and other domains. With the expansion of applications, it is essential to extend the kriging model for new spatial support of high-dimensional data. Geographical flows can depict the movements of geographical objects and imply the underlying mobility patterns in geographical phenomena. However, due to the bias, sparsity, and uneven quality of flow data in the real world, research about flows remains hindered by the lack of complete flow data and effective flow interpolation methods. In this study, we design a kriging interpolation model for flows based on several flow-related concepts and the autocorrelation of flows. We also analyze the second-order stationarity and anisotropy in the flow spatial random field. To illustrate the effectiveness and applicability of our method, we conduct two case studies. The former case study compares several experiments of flow density interpolation using Beijing mobile signaling data and illustrates the conditions of applicable areas. The latter case study extends our model to other flow attributes, such as travel time uncertainty, using Beijing taxi origin-destination flow data. The results of these cases demonstrate the effectiveness and high accuracy of our model.