Quantitative Evaluation of Spatial Interpolation Models Based on a Data-Independent Method - Advances in Data, Methods, Models and Their Applications in Geoscience - page 54

1. Comparison results: most commonly used methods for evaluation of spatial
interpolation models compare the measured data with the interpolated data. However,
it is no doubt that measured data are always unsatisfactory. This leads to unknown
errors inherent in measured data (Zhou & Liu, 2002). The results may not always keep
consistent and even get some controversial conclusions. For example, Laslett et al.
(1987), Javis & Stuart (2001) and Erdogan (2009) thought Thin Plate Spline interpolation
model can give better interpolated results, while Bater & Coops (2009) argued that
Nature Neighbour Interpolation is with more accurate interpolated value. Meanwhile,
some researchers (Hosseini et al., 1993; Gotway et al., 1996; Zimmerman et al. 1999;
Erxleben et al., 2002; Vicente-Serrano et al., 2003; Attorre et al, 2007; Piazza et al, 2011)
found that Kriging is the best one among all the existing interpolation models. Another
phenomenon should be mentioned is that the frequency of interpolation methods
compared varies considerably among methods and different studies have compared a
suite of different methods, which makes it difficult to draw general conclusions.
2. Assessment indices: there are two typical assessment indices, i.e. statistical measures
and spatial accuracy measures. The statistical measures such as Root Mean Squared
Error (RMSE), Standard Deviation (SD) and Mean Error (ME) are most frequently used
(Weber & Englund, 1994; Weng, 2002; Vicente-Serrano et al., 2003; Hu et al., 2004;
Weng, 2006; Tewolde, 2010), whereas incapable of describing the spatial pattern of
errors. Then the morphological accuracy measures such as accuracy surface and spatial
autocorrelation (Weng, 2002; Weng, 2006; Tewolde, 2010) are employed. However, in
order to obtain full evaluation of the interpolations, following problems should be
further addressed: (1) most of the evaluations are still concentrated on the statistical
measures, while the spatial accuracy ones are likely to be ignored relatively; (2) the
maintenance of integrity of an interpolated surface has attracted little attention and a
suitable quantitative index is still lack; (3) without consideration of the robustness of
interpolation algorithms to data errors.
To overcome the above-mentioned problems, the author (2002, 2003 & 2004) developed a
quantitative, data-independent method to evaluate algorithms in Digital Terrain Analysis.
With this method, six slope/aspect algorithms and five flow routing algorithms were
evaluated properly. Here we hope to employ this method to comprehensively evaluate
spatial interpolation models and identify a set of accuracy measures.
2. Unified interpolation models
So far, more than ten spatial interpolation models have been developed in different fields.
Here eight commonly used interpolation algorithms are examined and discussed, e.g.
Inverse Distance Weighted (IDW), Kriging, Minimum Curvature (MC), Natural Neighbor
Interpolation (NNI), Modified Shepard's Method (MSM), Local Polynomial (LP),
Triangulation with Linear Interpolation (TLI) and Thin Plate Spline (TPS). According to the
range of interpolation, these interpolations can be classified as global interpolation, block
interpolation and point-by-point interpolation. While in view of mathematical mechanism,
they can also be grouped into deterministic algorithms and geostatistical algorithms.
Although there are various spatial interpolation algorithms with diverse functions, they
share the same essential factors, i.e. on the basis of describing the relationships between data
points, and computing the values of unmeasured points through different function
combinations of sample points. In another word, the relationships depict the spatial