Abstract
The inverse-distance weighting (IDW) method is considered as one of the most popular deterministic methods and is widely applied to a variety of areas because of its low computational cost and easy implementation. In this paper, we show that the classical IDW is essentially a zeroth-order local kernel regression method with an inverse distance weight function. Thus, it suffers from various shortcomings, such as the boundary bias. Considering the advantages of the local polynomial modeling technique in statistics, the classical IDW was generalized into a higher-order regression by the Taylor expansion and then computed by means of a weighted least-squares method. Surface modeling of rainfall fields in China indicated that the generalized IDWs with the first- and second-orders are more accurate than the classical IDW in terms of root mean square error (RMSE). The example of digital elevation model construction with a group of sample points showed that the two generalized IDWs have better RMSE and mean error than the classical IDW. Furthermore, the second-order IDW has a better performance than the ordinary kriging in terms of RMSE. A theoretical analysis demonstrated that the gradient-plus-inverse distance squared method presented by Nalder and Wein (Agric For Meteorol 92(4): 211–225, 1998) is a first-order form of the generalized IDW expanded on spatial coordinates and elevation. In a word, the generalized IDW can incorporate multiple covariates, which can better explain the interpolation procedure and might improve its accuracy.
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Acknowledgments
The 1-km SRTM data used in this paper were provided by Environmental and Ecological Science Data Center for West China, National Natural Science Foundation of China (http://westdc.westgis.ac.cn). This work is supported by National Natural Science Foundation of China (Grant No. 41101433, 41371367), by Young and Middle-Aged Scientists Research Awards Fund of Shangdong Province (Grant No. BS2012HZ010), by Qingdao Science and Technology Program of Basic Research Project (Grant No. 13-1-4-239-jch), by the Key Laboratory of Marine Surveying and Mapping in Universities of Shandong (Shandong University of Science and Technology) (Grant No. 2013B03), by SDUST Research Fund, and by Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources.
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Chen, C., Zhao, N., Yue, T. et al. A generalization of inverse distance weighting method via kernel regression and its application to surface modeling. Arab J Geosci 8, 6623–6633 (2015). https://doi.org/10.1007/s12517-014-1717-z
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DOI: https://doi.org/10.1007/s12517-014-1717-z