# GNSS-Based Vertically Monitoring of Super-Tall Buildings
## 5 Verticality Monitoring Result and Analysis of the W Tower
### Verticality Monitoring Result of the W Tower  
In order to validate/check the result of laser plumbing by comparison with the GNSS result, the GNSS data of the monitoring network consisting of points HG, ZT, LYW, and WT were reprocessed in static mode to obtain the mean coordinate of WT. Then, the systematic bias between the coordinates of a GNSS measurement and a laser plumbing measurement can be calculated by Equations (12) and (13) with the ellipsoidal height of the monitoring point (\(h_{\text{WFT}}=432.477\) m) and the deflection of the vertical components. Table 8 lists the corresponding corrections of the plane coordinates of the monitoring point (WT). The differences between the coordinates of the laser plumbing and GNSS measurements without corrections are listed in Table 9.  
The coordinates of the GNSS measurement can be corrected with the corrections listed in Table 8. The differences between the coordinates of the laser plumbing and GNSS measurements with corrections are listed in Table 10.  
In the \(x\) direction, it can be seen that the difference between the coordinates of the GNSS measurement and the laser plumbing measurement has been reduced by the corrections calculated with the deflections of the vertical. However, in the \(y\) direction, it seems that the corrected difference becomes worse. In fact, there are two possibilities. On one hand, the accuracy of deflections of the vertical leads to the results, with a building height of 432 m, when the accuracy of deflections of the vertical is about 1-2 arc seconds, which may lead to a difference of millimeters. On the other \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**From**} & \multirow{2}{*}{**To**} & \multicolumn{2}{c}{**GZGEOID**} & \multicolumn{2}{c}{**EGM2008**} & \multicolumn{2}{c}{**EGEN-6C4**} \\ \cline{3-6}  & & \(\Delta\)**N/m** & \(\xi\)/\(\eta\)(\(\eta^{\prime\prime}\)) & \(\Delta\)**N/m** & \(\xi\)/\(\eta\)(\(\eta^{\prime\prime}\)) & \(\Delta\)**N/m** & \(\xi\)/\(\eta\)(\(\eta^{\prime\prime}\)) \\ \hline \multirow{4}{*}{XT} & A1 & \(-0.018\) & \(3.80\) & \(-0.014\) & \(3.20\) & \(-0.013\) & \(2.99\) \\  & C1 & \(0.019\) & \(4.25\) & \(0.014\) & \(3.21\) & \(0.013\) & \(2.99\) \\  & B1 & \(0.025\) & \(-6.04\) & \(0.028\) & \(-6.65\) & \(0.028\) & \(-6.69\) \\  & D1 & \(-0.024\) & \(-5.80\) & \(-0.027\) & \(-6.57\) & \(-0.027\) & \(-6.64\) \\ \cline{2-6}  & A2 & \(-0.035\) & \(3.91\) & \(-0.029\) & \(3.21\) & \(-0.027\) & \(3.00\) \\  & C2 & \(0.038\) & \(4.36\) & \(0.029\) & \(3.23\) & \(0.027\) & \(3.01\) \\  & B2 & \(0.050\) & \(-6.04\) & \(0.055\) & \(-6.69\) & \(0.056\) & \(-6.73\) \\  & D2 & \(-0.048\) & \(-5.80\) & \(-0.054\) & \(-6.53\) & \(-0.054\) & \(-6.56\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The deflection of vertical components from the GZGEOID, EGM2008, and EIGEN-6C4 models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Laser Plumbing**} & \multicolumn{2}{c}{**GNSS Measurement**} & \multicolumn{2}{c}{**Differences**} \\ \cline{2-7}  & \(x\) & \(y\) & \(x\) & \(y\) & \(x\) Direction & \(y\) Direction & \(xy\) Directions \\ \hline WT & 8258.284 & 3535.986 & 8258.310 & 3535.976 & +0.026 & \(-0.010\) & \(0.028\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The vertical deflections and the corrections of plane coordinates calculated with different strategies.