Integrating data-to-data correlation into inverse distance weighting

Abstract

As a typical spatial interpolation method with high efficiency and simplicity, inverse distance weighting (IDW) is almost a standard estimator in numerous fields such as geosciences and environmental science. However, it ignores the data-to-data correlation, which directly leads to unfavorable estimates with irregularly distributed samples. To address this issue, we propose a novel approach, termed dual IDW (DIDW). First, the average distance from one sample to others is employed to measure the data redundancy. Second, we impose an additional exponent on the average distance to make its importance adjustable. Last, this data-to-data distance is incorporated into the traditional IDW to account for the spatial configuration of neighborhoods in the interpolation. Consequently, DIDW flexibly takes both data-to-unknown and data-to-data distances into account. Only those samples that are close to the estimated location but apart from other sampled data would be assigned with large estimation weights. Details of its application and the validity are illustrated using a case study based on the public Walker Lake dataset. Our results indicate that the developed methods not only improve the interpolation accuracy significantly compared with the traditional IDW, but also slightly outperform ordinary kriging in the case where the sample dataset is too small to capture an appropriate spatial continuity, demonstrating that DIDW is valuable to be applied in a broader context.