# Variability of Interpolation Errors and Mutual Enhancement of Different Interpolation Methods
## 5 Conclusions  
Interpolation methods are crucial for data visualization and understanding underlying data patterns, making accuracy essential for reliable analysis. This study focuses on two regions: Xinyang City in Henan Province and Shadikou Village in Yuanmou County, Yunnan Province. Using PM\({}_{2.5}\) concentration data from May in Xinyang City and elevation point data from Shadikou Village, we investigated four interpolation methods--OK, UK, IDW, and RBF--by comparing interpolation errors using relative difference coefficients and hotspot analysis. Additionally, a global weighted fusion method was employed to assess the accuracy improvement of two interpolation methods with significant differences.  
The analysis based on relative difference coefficients and hotspot identification led to the following conclusions. While all four methods exhibit some variation in interpolation errors, the differences are minimal between UK and OK, both of which are kriging-based methods. The greatest discrepancies in interpolation errors were found when comparing IDW interpolated PM\({}_{2.5}\) data and RBF interpolated elevation data with UK interpolation. The interpolation error for PM\({}_{2.5}\) concentration data, which has a low interpolation point density (0.009 points per square kilometer), is smaller than that for gully elevation data (756,409.05 points per square kilometer). This suggests that data accuracy--affected by point density--has a considerable impact on interpolation error outcomes.  
Based on global weighted fusion analysis, the following conclusions were drawn. For the PM\({}_{2.5}\) concentration data, the fusion of IDW and UK interpolation error data, which showed the largest differences, resulted in a significant reduction in error. The MAX error decreased from 16.329 and 15.20 to lower values, while the MIN error increased by 15.564 and 15.899, respectively. The STD also increased by 4.726 and 4.813. For the gully elevation point data, global weighted fusion was applied to the RBF and UK interpolation error data with the largest differences. The fusion reduced these differences, resulting in more stable and accurate data. However, the accuracy improvement was less pronounced compared to PM\({}_{2.5}\) data. The MIN error improved by 5.037 and 4.607, and the STD increased by 0.135 and 0.151. The MAX error for RBF and UK, however, decreased by 1.936 and 1.967, respectively. This suggests that for high-precision, high-density data, interpolation fusion has a limited impact on improving interpolation accuracy.  
This experiment demonstrates that interpolation fusion significantly enhances accuracy for data with high point density. However, its limitation lies in the small sample area, which prevents the establishment of a specific point density range for improved accuracy. Future work should focus on expanding the sample area and determining the point density threshold beyond which interpolation fusion has minimal or no effect. Identifying this threshold will provide a clearer reference for choosing when to apply interpolation fusion.  
Conceptualization, M.L. and Y.H.; methodology, M.L.; software, Y.H.; validation, H.Y., Y.H. and L.B.; formal analysis, Y.H.; investigation, Y.H.; resources, M.L.; data curation, Z.C.; writing--original draft preparation, Y.H.; writing--review and editing, L.B.; visualization, L.B.; supervision, Z.C.; project administration, L.B. All authors have read and agreed to the published version of the manuscript.  
This research was supported by two fundings: one from the National Natural Science Foundation of China (grant number: 41871324) and the other from the Doctor Research Program of China West Normal University (grant number: 22 KE001).  
Not applicable.  
The data that support the funding of this study are available from the corresponding author upon reasonable request. This data has not been made public because private data is authorized for use only, not for public disclosure.  
The authors declare no conflicts of interest.  
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