Novel spatial and temporal interpolation algorithms based on extended field intensity model with applications for sparse AQI

Bo Cai, Zeyuan Shi, Jianhui Zhao

Abstract: For the sparsely distributed air quality index (AQI), existing techniques have low efficiency to interpolate the value of a non-given point. Thus, an extended field intensity model (EFIM) is proposed based on Coulomb’s law. Single parameter based EFIM is designed for spatial and temporal interpolations, and parameter $c$ is used to control the attenuation of field intensity, while a binary search method is adopted to calculate the optimal $c$. Next, double parameters based EFIM is designed, and parameter $k$ is added to control the range of influence, while an iterative bilinear interpolation method is used to compute the optimal set of $c$ and $k$. Then, spatio-temporal interpolation is provided using spatial and temporal information simultaneously. The monitored AQIs from 4 cities of China are randomly collected as experiment data. Taking RMSE, AME, AEE as evaluation criterions and using 10-fold cross-validation, the new EFIM based algorithms perform better for spatial interpolation of sparse AQI than current methods, while double parameters based EFIM algorithms have higher precision than single parameter. Temporal related EFIM algorithms are also tested for their efficiency, and the normalized absolute error is defined to help indicate when spatio-temporal interpolation should be used. As a new approach for interpolation of sparse samples, our EFIM and algorithms have potential application in related fields.