Quantitative Evaluation of Spatial Interpolation Models Based on a Data-Independent Method - Advances in Data, Methods, Models and Their Applications in Geoscience - page 66

4.5 Comprehensive evaluation
Combing the various evaluation indices discussed above, Tab. 4 gives a comprehensive
evaluation for various interpolation models. The levels of interpolation accuracy are defined
as: lowest, lower, high, higher and highest, while the levels of robustness to errors are set as:
weakest, weaker, strong, stronger and strongest. When the original data has no errors, the
interpolation accuracy of TPS is the highest, followed by MSM, and MC is the lowest. After
higher errors being added to the original data, the interpolation accuracy of TPS changes
from the highest to the lowest, while the precision of LP alters from lower to the highest. As
a result, the strongest robustness to errors is LP, and the weakest is MSM by contrast. As for
MC, regardless of the original data with errors or not, its interpolation accuracy always
keeps lower.

Accuracy with
non-error data

Accuracy with
error data

Models Robustness

IDW lower higher stronger

Kriging high higher strong

MC lowest lower weaker

NNI high high stronger

MSM higher lowest weakest

LP lower highest strongest

TLI high lower weaker

TPS

highest lower weaker

Table 4. Comprehensive Evaluation for interpolation models

5. Conclusions

From the mechanism of spatial interpolation, weight allocation and its corresponding spatial
relationship between interpolated points and known points, this article proposes an
evaluation and analysis approach of spatial interpolation in GIS based on data-independent
method, with the construction of mathematical surfaces without errors to objectively reflect
the precision of different interpolation algorithms and with the addition of varying degree-
errors to examine their robustness to errors. Based on our study, following conclusions can
be given: (1) when the quality of original data is relatively well, TPS and Kriging can acquire
more reliable results; (2) when the quality of original data becomes worse, for its resistance
to data errors, LP can maintain a preferable interpolated precision, showing a powerful
robustness to errors; (3) the validity of weight function and its corresponding spatial
relationship are the kernel for design and analysis of weight function; (4) a kind of data