CoYangCZ: a new spatial interpolation method for nonstationary multivariate spatial processes

Abstract

In multivariate spatial interpolation, the accuracy of a variable of interest can be improved using ancillary variables. Although geostatistical methods are widely used for multivariate spatial interpolation, these methods usually require second-order stationary assumption of spatial processes, which is difficult to satisfy in practice. We developed a new multivariate spatial interpolation method based on Yang-Chizhong filtering (CoYangCZ) to overcome this limitation. CoYangCZ does not solve the multivariate spatial interpolation problem from a purely statistical point of view but integrates geometry and statistics-based strategies. First, we used a weighted moving average method based on binomial coefficients (i.e. Yang-Chizhong filtering) to fit the spatial autocorrelation structure of each spatial variable from a geometric perspective. We then quantified the spatial autocorrelation of each spatial variable and the correlations between different spatial variables by analyzing the variances of different spatial variables. Finally, we obtain the best linear unbiased estimators at the unsampled locations. Experiments on air pollution and meteorological datasets show that CoYangCZ has a higher interpolation accuracy than cokriging, regression kriging, gradient plus-inverse distance squared, sequential Gaussian co-simulation, and the kriging convolutional network. CoYangCZ can adapt to second-order non-stationary spatial processes; therefore, it has a wider scope of application than purely statistical methods.

Keywords:

• Multivariate spatial processes
• spatial interpolation
• Yang Chizhong filtering
• geostatistics

Acknowledgements

We gratefully acknowledge the comments from the editor and the reviewers.

Author contributions

Qiliang Liu, Yongchuan Zhu, and Jie Yang conceived and designed the presented idea. Yongchuan Zhu and Jie Yang implemented the experiments and analysed the results. Qiliang Liu and Yongchuan Zhu wrote the manuscript. Xiancheng Mao and Min Deng reviewed the manuscript, and provided comments.

Disclosure statement

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

Data and codes availability statement

The findings of this study are backed by data and codes that can be found on ‘figshare.com’, with the identifier at the public link: https://doi.org/10.6084/m9.figshare.24230179.

Additional information

Funding

This study was funded through support from National Natural Science Foundation of China (NSFC) [No. 42271484 and 41971353] and Natural Science Foundation of Hunan Province [No. 2021JJ20058].

Notes on contributors

Qiliang Liu

Qiliang Liu is currently a professor at Central South University, Hunan, China. His research interests focus on multi-scale spatio-temporal data mining and spatiotemporal statistics. He has published more than 30 peer-reviewed journal articles in these areas.

Yongchuan Zhu

Yongchuan Zhu is currently a postgraduate student at Central South University and his research interests focus on spatial statistics.

Jie Yang

Jie Yang is currently a Ph.D. candidate at Central South University and his research interests focus on spatio-temporal statistics.

Xiancheng Mao

Xiancheng Mao is currently a professor at Central South University. His research interests are 3D geological modeling and mineral prospectivity mapping.

Min Deng

Min Deng is currently a professor at Central South University and the associate dean of School of Geosciences and info-physics. His research interests are map generalization, spatio-temporal data analysis and mining.