Variability of Interpolation Errors and Mutual Enhancement of Different Interpolation Methods

Data interpolation methods are important statistical analysis tools that can fill in data gaps and missing areas by predicting and estimating unknown data points, thereby improving the accuracy and credibility of data analysis and research. Different interpolation methods are widely used in related fields, but the error between different interpolation methods and their interpolation fusion optimization have a significant impact on the interpolation accuracy, which still deserves further exploration. This study is based on two different types of point data: PM2.5 (PM2.5 refers to particulate matter in the atmosphere with a diameter of 2.5 μm or less, also known as inhalable particles or fine particulate matter) in Xinyang City, Henan Province, and the elevation of typical gullies in Yuanmou County, Yunnan Province. Using relative difference coefficients and hotspot analysis methods, the differences in error characteristics among four interpolation methods, ordinary kriging (OK), universal kriging (UK), inverse distance weighted (IDW), and radial basis functions (RBFs), were compared, and the influence of interpolation fusion methods on the accuracy of interpolation results was explored. The results show that after interpolation of PM2.5 concentration and gully elevation, the error difference between OK and UK is the smallest in both datasets. For PM2.5 concentration data, IDW and UK interpolation errors have the largest difference; for elevation data, the differences between RBF and UK interpolation are the largest. The weighted fusion results show that the interpolation error accuracy of PM2.5 concentration data with an interpolation point density of 0.009 points per square kilometer is improved, and the root mean square error (RMSE) after fusion is reduced from 0.374 μg/m3 to 0.004 μg/m3. However, the error accuracy of the elevation data of the gully with an interpolation point density of 0.76 points/m2 did not improve significantly. This indicates that characteristics such as the density of the original data are important factors that affect the accuracy of interpolation. In the case of sparse interpolation points, it is possible to consider fusing the interpolation results with different error patterns to improve their accuracy. This study provides a new idea for improving the accuracy of interpolation errors.