# Variability of Interpolation Errors and Mutual Enhancement of Different Interpolation Methods
## 4 Discussion  
This study introduces a direct fusion of interpolation methods to enhance accuracy. By integrating different methods, this approach leverages their strengths to adapt to data variations across regions or densities while compensating for the inherent limitations of each method. The experimental results from two distinct regions with varying data show that this method is not only simple and easy to implement but also highly effective with significant practical value. Interpolation methods are essential analytical and statistical tools, but each has inherent advantages and drawbacks [48; 49; 50]. For example, kernel function interpolation [51] excels at modeling nonlinear data distributions, making it ideal for datasets with complex relationships. Kriging interpolation [52], commonly used for spatial data, accounts for spatial variability, yielding more reasonable predictions of unknown point values. However, it requires the fine tuning of parameters for irregular data distributions, making it more suitable for datasets with regular structures. Consequently, each method can produce varying degrees of interpolation error. Current research on improving interpolation error often focuses on refining individual methods, from parameter selection to methodological adjustments, to make them more versatile. For instance, [PERSON] et al. [53] proposed the optimal method and parameters for the spatial interpolation of rainfall in the Xin'anjiang River basin, while [PERSON] et al. [54] addressed the smoothing issue in ordinary kriging by adopting [PERSON]'s post-processing technique, improving the accuracy of spatial variations. [PERSON] et al. [55] used cross-validation to optimize parameters and models, such as semivariogram selection, partition distance, and spatial variability directionality. [PERSON] et al. [56] improved spatial interpolation by combining GIS technology with the successive interpolation approach (SIA) using long-term precipitation data and terrain variables to derive accurate topographic maps. [PERSON] et al. [57] evaluated various spatial interpolation algorithms for estimating missing rainfall data, optimizing method settings for ideal results. [PERSON] et al. [58] enhanced DEM quality by fine tuning ANUDEM algorithm parameters to correct errors in topographic data. While continuous adjustments to parameters, like silk and nugget, help tailor interpolation methods to specific datasets, they are constrained by the fundamental limitations of each method, which cannot be fully overcome by parameter adjustments alone. When data do not fully meet the requirements of a single interpolation method, can combining two methods yield better results? This is the central question we are exploring. By integrating the results of two interpolation techniques, the strengths of each can be maximized, while their individual limitations are mitigated through mutual fusion [59]. This approach minimizes or eliminates the shortcomings of each interpolation method, enhancing overall performance and expanding the applicability of interpolation techniques. The fusion leverages multiple models, improving both the accuracy and stability of predictions and increasing confidence in the results. Our experiments demonstrate that fusing two interpolation methods can enhance accuracy, particularly with sparse data. Sparse data, due to their low density, typically result in higher interpolation errors, making it challenging for a single method to fully satisfy data requirements. Consequently, fusion proves more effective in improving accuracy for sparse datasets. Further studies, such as those by [PERSON] et al. [60], highlight the significant influence of airborne LiDAR point cloud density and the chosen interpolation method on the accuracy of DEMs and surface roughness. Among the methods, RBF and OK interpolation algorithms perform best, even with sparse data, while IDW shows varied performance in roughness accuracy as data density decreases.