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<p>While the Kriging method is widely employed for the spatial interpolation of air pollution, its original design lies in geostatistics, focusing solely on the impact of distance on the target values. In the spatial interpolation of air pollution, factors such as wind speed, wind direction, and underlying surface parameters exert a greater influence on the spatial distribution of pollutants compared to distance alone. To account for these impacts, this study proposed an LSTM-Kriging model that replaced the semi-variance function fitting process with the time-series deep learning long short-term memory (LSTM) model. This model preserved the structure of the Kriging model while considering the physical mechanism and time-series characteristics of regional air pollution using the proposed LSTM-based optimization method. The proposed LSTM-Kriging model was validated using time-series meteorological and PM<sub>2.5</sub> data from 61 atmospheric monitoring stations in Guilin, China. The model employs a sliding window of 12&#xa0;h and selects the 13 nearest neighboring stations. With 80% of the temporal data used for training and 20% for validation. The results indicated that replacing the kernel function with the LSTM model significantly improved prediction accuracy, with average errors of PM<sub>2.5</sub> concentration prediction being 6.268–15.903%, compared to 14.022–23.625% for the traditional Kriging method. More importantly, the established method has the capability to characterize the influence of wind direction on the dispersion and distribution of air pollutants. The proposed LSTM-Kriging model with Root Mean Square Error, Mean Absolute Error, and Symmetric Mean Absolute Percentage Error values of 7.151, 5.388, and 19.762% respectively, outperforms other models, providing more accurate and robust estimation performance. The proposed model considers the characteristics of the application domain within the core calculation of Kriging, enhancing its interpolation accuracy and enabling generalization to other spatial evaluation domains.</p>

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A novel LSTM-Kriging model for spatiotemporal interpolation of air pollution

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Rui Xu,
  • Jiaming Zou,
  • Yuanfeng Sun,
  • Jian Li,
  • Liyi Guo,
  • Shiming Shen,
  • Hang Wan

摘要

While the Kriging method is widely employed for the spatial interpolation of air pollution, its original design lies in geostatistics, focusing solely on the impact of distance on the target values. In the spatial interpolation of air pollution, factors such as wind speed, wind direction, and underlying surface parameters exert a greater influence on the spatial distribution of pollutants compared to distance alone. To account for these impacts, this study proposed an LSTM-Kriging model that replaced the semi-variance function fitting process with the time-series deep learning long short-term memory (LSTM) model. This model preserved the structure of the Kriging model while considering the physical mechanism and time-series characteristics of regional air pollution using the proposed LSTM-based optimization method. The proposed LSTM-Kriging model was validated using time-series meteorological and PM2.5 data from 61 atmospheric monitoring stations in Guilin, China. The model employs a sliding window of 12 h and selects the 13 nearest neighboring stations. With 80% of the temporal data used for training and 20% for validation. The results indicated that replacing the kernel function with the LSTM model significantly improved prediction accuracy, with average errors of PM2.5 concentration prediction being 6.268–15.903%, compared to 14.022–23.625% for the traditional Kriging method. More importantly, the established method has the capability to characterize the influence of wind direction on the dispersion and distribution of air pollutants. The proposed LSTM-Kriging model with Root Mean Square Error, Mean Absolute Error, and Symmetric Mean Absolute Percentage Error values of 7.151, 5.388, and 19.762% respectively, outperforms other models, providing more accurate and robust estimation performance. The proposed model considers the characteristics of the application domain within the core calculation of Kriging, enhancing its interpolation accuracy and enabling generalization to other spatial evaluation domains.