Submitted as: development and technical paper
19 Sep 2022
Submitted as: development and technical paper | 19 Sep 2022
Status: a revised version of this preprint is currently under review for the journal GMD.

A generalized spatial autoregressive neural network (GSARNN) method for three-dimensional spatial interpolation

Junda Zhan1,, Sensen Wu1,2,, Jin Qi1,2, Jindi Zeng1, Mengjiao Qin1,2, Yuanyuan Wang3,2, and Zhenhong Du1,2 Junda Zhan et al.
  • 1School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
  • 2Zhejiang Provincial Key Laboratory of Geographic Information Science, Hangzhou 310028, China
  • 3Ocean Academy, Zhejiang University, Zhoushan 316022, China
  • These authors contributed equally to this work.

Abstract. Spatial interpolation, which is one of the most important spatial analysis methods, predicts unsampled spatial data from the values of sampled points. Generally, the core of spatial interpolation is fitting spatial weights via spatial correlation. Traditional methods express spatial distances in a conventional Euclidean way and conduct relatively simple spatial weight calculation processes, limiting their ability to fit complex spatial nonlinear characteristics in multidimensional space. To tackle these problems, we developed a generalized spatial distance neural network (GSDNN) unit to generally and adaptively express spatial distances in complex feature space. By combining the spatial autoregressive neural network (SARNN) with the GSDNN unit, we constructed a generalized spatial autoregressive neural network (GSARNN) to perform spatial interpolation in three-dimensional space. The GSARNN model was examined and compared using two three-dimensional cases: a simulated case and a real Argo case. The experiment results demonstrated that exploiting the feature extraction ability of neural networks, the GSARNN achieved superior interpolation performance and was more adaptable than inverse distance weighted, ordinary Kriging, and SARNN methods.

Junda Zhan et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2022-198', Anonymous Referee #1, 03 Oct 2022
    • AC1: 'Reply on RC1', Zhen Hong Du, 31 Oct 2022
  • RC2: 'Comment on gmd-2022-198', Anonymous Referee #2, 10 Oct 2022
    • AC2: 'Reply on RC2', Zhen Hong Du, 31 Oct 2022
  • CEC1: 'Comment on gmd-2022-198', Juan Antonio Añel, 25 Oct 2022
    • AC3: 'Reply on CEC1', Zhen Hong Du, 31 Oct 2022
  • RC3: 'Comment on gmd-2022-198', Anonymous Referee #3, 28 Oct 2022
    • AC4: 'Reply on RC3', Zhen Hong Du, 31 Oct 2022

Junda Zhan et al.

Junda Zhan et al.


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Short summary
We developed a generalized spatial autoregressive neural network used for three-dimensional spatial interpolation. Taking the different changing trend of geographic elements along various directions into consideration, the model defined spatial distance in a generalized way and integrated it into the process of spatial interpolation with the theories of spatial autoregression and neural network. Compared with traditional methods, the model achieved better performance and was more adaptable.