A Spatiotemporal Interpolation Method Using Radial Basis Functions for Geospatiotemporal Big Data

This research designs and implements the Radial Basis Function (RBF) spatiotemporal interpolation method to assess the trend of daily PM_2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. This research also compares the performance of the RBF spatiotemporal interpolation with the Inverse Distance Weighting (IDW) spatiotemporal interpolation. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM_2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. The RBF-based spatiotemporal interpolation methods are evaluated by leave-one-out cross validation. More importantly, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure named k-d tree are adapted in this paper to address the computational challenges.