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Accuracy assessment of interpolation methods in grid DEMs based on a variance-scale relation

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Abstract

The theoretical variance-scale relation has been widely used in detecting scale phenomena in ecology. Mathematical derivation and verification in mathematical functions have been demonstrated in this paper that the inherent law, e.g., variance of an independent variable, decreases while scale (resolution) increases. Based on this variance-scale relation and the attribute of grid DEM, an accuracy assessment approach for interpolation methods applied to generating grid DEMs was developed. A numerical test and two real-world examples were employed as a means of examining the feasibility of this accuracy assessment approach by comparing four interpolation methods, i.e., HASM, Spline, Kriging, and IDW. A scale-based error model of DEM was obtained in the numerical test and interpolation accuracy could be compared based on the matching scales. Both the regular sampling case and the random sampling case showed that all of the calculated variance-scale relations of all four methods broke the theoretical law because of synthetic effect of sampling density, terrain characteristics, scale and smoothing effect of interpolators in the real-world test. The overall level of variance at most scales was thus used as an accuracy assessment criterion. After perfecting the second assumption, we established the final assessment criteria. Based on the new accuracy assessment framework, all the results indicated that HASM and Spline were more accurate than Kriging and IDW. The new accuracy assessment approach provides an alternative framework for comparing different interpolation methods in grid DEMs.

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Acknowledgments

Special thanks go to the three reviews’ comments and suggestions. This work is supported by the State major project of water pollution control and management (Grant No. 2014ZX07101-011), and by Special Research Foundation for the Public Welfare Industry of Ministry of Water Resources (201301075).

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Authors and Affiliations

  1. College of Hydrology and Water Resources, Hohai University, Nanjing, China

    Hai Yang, Chuanhai Wang, Tengfei Ma & Weijian Guo

  2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China

    Hai Yang, Chuanhai Wang, Tengfei Ma & Weijian Guo

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  1. Hai Yang
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Correspondence to Hai Yang.

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Yang, H., Wang, C., Ma, T. et al. Accuracy assessment of interpolation methods in grid DEMs based on a variance-scale relation. Environ Earth Sci 74, 6525–6539 (2015). https://doi.org/10.1007/s12665-015-4388-5

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