Application of Inverse Distance Weight Interpolation Taking into Account Anisotropy to the Reconstruction of Temperature Field

Abstract The reconstruction of temperature field has important practical significance for analyzing the spatial distribution characteristics of temperature. The inverse distance weighting (IDW) is one of the most widely used methods for this purpose. However, the temperature data exhibit anisotropic characteristics, so the anisotropic characteristics of the temperature need to be taken into account during IDW interpolation. Currently, the IDW method typically accounts for anisotropic characteristics by defining an elliptical search range based on directional differences in the range. However, the ellipse is used solely to filter reference points, while the sample points inside and outside the ellipse still exhibit anisotropic spatial properties. Nevertheless, the weighting process is still based on the assumption of isotropy. This inconsistency limits the interpolation accuracy and leads to reduced precision in the reconstruction of temperature fields. Therefore, this study proposes a structure-aware anisotropic IDW (SA-IDW) method, which models the spatial structural characteristics of the data. The approach first investigates the anisotropy of temperature data, constructs rotation and stretching matrices, and then transforms the temperature data from anisotropic to isotropic spatial features using these matrices. Subsequently, the IDW method is applied to reconstruct the temperature field. The accuracy of SA-IDW is verified and compared with IDW, four-quadrant IDW (FQIDW), adaptive IDW (AIDW), and search-range anisotropic IDW (SERI-IDW). The experimental results show that SA-IDW has significantly improved interpolation accuracy compared with other IDWs and can better reflect the spatial variation of temperature data. Significance Statement This study introduces a structure-aware anisotropic IDW (SA-IDW) method to improve the reconstruction accuracy of temperature fields, which are often impacted by anisotropic characteristics in temperature data. Traditional IDW methods fail to fully account for these anisotropies, leading to lower accuracy in temperature field reconstruction. The proposed SA-IDW method effectively addresses this issue by transforming anisotropic temperature data into isotropic characteristics, enhancing interpolation accuracy, and better reflecting spatial temperature variations. This advancement has significant implications for more accurate climate modeling and environmental monitoring.