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4. Results and discussion
4.1 RMSE and ME
As the RMSE statistics of the interpolated results from the three surfaces shown in Tab. 3, it
is not difficult to identify that all of the three interpolated surfaces present similar variation
tendency as a whole. The RMSEs of the interpolated surfaces keep pace with the increasing
errors of the original surface, leading to a decreasing interpolated accuracy.
S1 S2 S3
0
1 10 0 1 10 0 1 10
IDW
0.13
0.46 1.38 1.14 1.19 1.72 0.25 0.50 1.30
Kriging
0.02
0.65 2.13 0.11 0.65 1.99 0.01 0.67 1.98
MC
0.07
0.83 2.79 0.29 0.90 2.53 0.06 0.88 2.51
NNI
0.03
0.62 2.02 0.27 0.67 1.91 0.05 0.64 1.88
MSM
0.02
1.07 3.62 0.29 1.07 3.22 0.01 1.11 3.28
LP
0.22
0.25 0.43 2.51 2.49 2.50 0.56 0.58 0.69
TLI
0.03
0.70 2.31 0.26 0.76 2.17 0.05 0.72 2.14
TPS 0.02 0.84 2.86 0.07 0.87 2.58 0.01 0.90 2.56
* 1) 0, 1, 10 are the RMSE added to the original sample points; 2) For the interpolation methods of NNI
and TLI cannot deal with the boundary problem well, therefore their boundary values which are
replaced with the maximum have been excluded when calculated in statistics.
Table 3. RMSE statistics of the interpolated results from the three surfaces
As shown in Tab.3, Fig. 2 and Fig. 3, when sample points have no errors, the RMSEs of the
interpolated results for different methods have an decreasing sequence as LP > IDW, MC >
NNI, TLI > Kriging, MSM, TPS. However, the interpolated results vary with the augment of
data errors. When the RMSE of sample points increases to 10, the RMSE of the surface
interpolated by MSM achieves the maximum, with the minimum gained by LP and the
sequence of RMSE for different interpolations changes to MSM > TPS, MC > TLI, Kriging,
NNI > IDW > LP. The results show that if the original data has a better quality, the methods
of TPS, MSM and Kriging can get a high precision for the interpolated results, while the
quality of the original data becomes poorly, the result of LP turns to be relatively reliable.
Fig. 2. RMSE statistics of interpolated results from S1
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