Quantitative Evaluation of Spatial Interpolation Models Based on a Data-Independent Method - Advances in Data, Methods, Models and Their Applications in Geoscience - page 63

for the difference of the 'true' volume and the volume between an interpolated surface and
the datum plane whose elevation is 0. All of the results are calculated by Surfer 8.0.
As shown in Fig. 7, when the original data has no error, the absolute volume differences of
MSM, TPS and Kriging are smaller, and by comparison, LP, MC and IDW are relatively
larger, with the minimum belonging to MSM and the maximum belonging to LP. However,
their relationships make changes after adding a certain errors, similar as the variation of
RMSE in Section 4.1. Aside from LP, the absolute volume differences of other interpolation
methods are increased with mounting errors, keeping a consistent sequence of LP < IDW <
Kriging < TPS < MC < MSM. Beyond doubt, the above analysis results are approximately
accordant with the results of RMSE, ME and Moran'I. Moreover, judging from the variation
tendency, MSM changes greatest with LP changing least, which has demonstrated the
powerful robustness of LP to data errors again. Similar conclusions as volume index can be
got from Fig. 8, which presents the absolute differences of the 'true' surface area and
different interpolated surfaces areas.
Fig. 7. Absolute volume differences of S1
Fig. 8. Absolute surface area differences of S1
4.4 Contour matching
Comparison between the contours of the original surface and those of the interpolated
surfaces will be discussed in this section. Fig .9 takes the second surface for instance to
present the comparisons when the original data is without errors. As shown in Fig. 9, the
contours generated by Kriging, MSM and TPS perform preferably smooth, matching with
contours of the original surface well. For NNI and TLI, the inside shapes of the contours
maintain well with smooth lines, however, some abnormalities like figure losses appear on
the boundary, further verifying their boundary effect mentioned above. Though the shapes
of contours produced by LP keep well too, it is easy to notice that their positions shift on the