## 4 Verification and Analysis of Model Accuracy  
To further analyze and validate the rationality and validity of the VIP-cokriging spatial model, the one-dimensional model case from Section 3.1 was used as an example in this section. The aging temperature two-factor cokriging spatial model was compared with the inverse distance weighting model [36], ordinary kriging model [37], and universal kriging model [38], which were more commonly used in the construction of spatial models for dam safety monitoring at present. In this paper, the data of seven measurements from June 2020 to December 2020 of this measuring line were cross-repaired. The error statistics of the single point at typical moments are shown in Table 3, and the overall error is shown in Figure 10. As can be seen from the graph, the inverse distance weighting model was the worst, with the maximum relative error of edge measuring points reaching 178.73%, and the relative error of non-edge measuring points basically exceeding 10%, with the mean absolute error of 22.09 to 23.54 mm. The analysis of the reason should be related to the fact that the method only considered the influence of distance on unknown points while ignoring the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Measuring** \\ **Points** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Measured** \\ **Value (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{**Aging**} & \multicolumn{2}{c}{**Aging + Water Pressure**} & \multicolumn{2}{c}{**Aging + Water Pressure + Rainfall**} \\ \cline{3-8}  & & & **Repaired** & **Relative** & **Repaired** & **Relative** & **Repaired** & **Relative** \\  & & **Value (mm)** & **Error** & **Value (mm)** & **Error** & **Value (mm)** & **Error** \\ \hline EXa1-1 & 15.45 & 11.18 & 27.67\% & 15.57 & 0.80\% & 15.57 & 0.77\% \\ \hline EXa1-2 & 11.68 & 9.42 & 19.35\% & 11.85 & 1.47\% & 11.85 & 1.43\% \\ \hline EXa2-1 & 15.93 & 8.00 & 49.78\% & 15.76 & 1.06\% & 15.75 & 1.13\% \\ \hline EXa2-2 & 12.47 & 7.89 & 36.75\% & 12.41 & 0.45\% & 12.42 & 0.39\% \\ \hline EXa2-3 & 17.27 & 11.30 & 34.55\% & 17.11 & 0.91\% & 17.12 & 0.87\% \\ \hline EXa2-4 & 12.93 & 9.34 & 27.76\% & 12.91 & 0.17\% & 12.91 & 0.18\% \\ \hline EXa3-1 & \(-\)10.82 & \(-\)3.37 & 68.85\% & \(-\)10.86 & 0.41\% & \(-\)10.87 & 0.48\% \\ \hline EXa3-2 & \(-\)9.86 & \(-\)1.89 & 80.80\% & \(-\)9.62 & 2.47\% & \(-\)9.59 & 2.69\% \\ \hline EXa3-3 & \(-\)6.13 & \(-\)0.38 & 93.79\% & \(-\)6.04 & 1.43\% & \(-\)6.05 & 1.25\% \\ \hline EXa3-4 & 1.18 & 4.02 & 240.95\% & 1.47 & 24.68\% & 1.46 & 23.76\% \\ \hline EXa3-5 & 10.87 & 7.92 & 27.18\% & 10.86 & 0.12\% & 10.86 & 0.13\% \\ \hline EXa3-6 & 13.11 & 8.53 & 34.94\% & 13.04 & 0.56\% & 13.04 & 0.56\% \\ \hline EXa4-1 & \(-\)2.57 & 0.69 & 126.76\% & \(-\)2.53 & 1.54\% & \(-\)2.53 & 1.56\% \\ \hline EXa4-4 & \(-\)7.93 & \(-\)3.19 & 59.81\% & \(-\)7.93 & 0.03\% & \(-\)7.93 & 0.02\% \\ \hline EXa4-5 & \(-\)6.09 & \(-\)1.28 & 79.06\% & \(-\)6.17 & 1.36\% & \(-\)6.17 & 1.34\% \\ \hline EXa4-6 & 3.37 & 4.04 & 19.86\% & 3.50 & 3.84\% & 3.50 & 3.84\% \\ \hline EXa4-7 & 3.59 & 4.58 & 27.47\% & 3.67 & 2.27\% & 3.67 & 2.27\% \\ \hline EXa4-8 & 5.86 & 4.56 & 22.15\% & 5.79 & 1.27\% & 5.79 & 1.23\% \\ \hline MAE (mm) & & 4.22 & & 0.10 & & 0.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spatial repair results with selection of different covariates of the two-dimensional model. correlation between measuring points. The ordinary kriging model took into account the autocorrelation between each measuring point in space, and its accuracy was significantly improved compared with the inverse distance weighting model. The relative errors of its non-edge measurement points were controlled within 10%, and the mean absolute error was 16.74\(\sim\)17.79 mm. This method considered that the variables were stationary in the region, that is, there was no trend quantity, whereas the vertical displacement of dam appearance generally had a growing trend.