# Effect of Topography Truncation on Experimental Simulation of Flow over Complex Terrain
## 5 Quantitative Analyses on Effect of Topographic Truncation  
### Metrics on Profiles Differences  
Based on the previous analysis, topographic truncation had significant effects on mean wind characteristics and turbulence characteristics when simulating flow over an island in the wind tunnel. Hence, to quantify the differences in mean velocity, inclination angle, and turbulence intensity, the special indicators proposed by [PERSON] et al. [17] were used, which are defined as:  
\[U_{x}=\sum_{i=1}^{N}\frac{|U_{i}-U_{iOT}|}{U_{iOT}}\cdot\frac{\Delta h_{i}}{H _{w}} \tag{2}\]  
Figure 9: Special indexes at measurement locations: (**a**) mean velocity; (**b**) inclination angle; (**c**) turbulence intensity.  
\[A_{x} =\sum_{i=1}^{N}\frac{|A_{i}-A_{i,OT}|}{|A_{i,OT}|}\cdot\frac{\Delta h _{i}}{H_{w}} \tag{3}\] \[I_{x} =\sum_{i=1}^{N}\frac{|I_{i}-I_{i,OT}|}{I_{i,OT}}\cdot\frac{\Delta h _{i}}{H_{w}} \tag{4}\]  
where \(N\) is the total number of measurement points along height at each measurement location, \(U_{i}\) is the normalized streamwise mean velocity at \(i\)-th point above the ground, \(U_{i,OT}\) is the normalized mean velocity at \(i\)-th point above the ground in the case of \(OT\), \(\Delta h_{i}\) is the height difference between \(i\)-th point and (\(i\)-1)-th point, \(H_{w}\) is the total height at the measurement location, \(A_{i}\) is the inclination angle at \(i\)-th point above the ground, \(A_{i,OT}\) is the inclination angle at \(i\)-th point above the ground in the case of \(OT\), \(I_{i}\) is the turbulence intensity at \(i\)-th point above the ground, and \(I_{i,OT}\) is the turbulence intensity at \(i\)-th point above the ground in the case of OT. It should be noted that in contrast to previous work [17], the absolute value is applied to Equations (2), (3), and (4) to quantify the overall differences. We also define a mean indicator (\(MI\)) to evaluate the topographic truncation effect in different cases, which can be calculated as:  
\[MI=\sum_{j=1}^{M}a_{x}\cdot\frac{1}{M} \tag{5}\]  
where \(M\) is the total number of measurement locations and \(a_{x}\) means special indicators: \(U_{x}\), \(A_{x}\), and \(I_{x}\).  
Special indicators of the mean velocity, inclination angle, and turbulence intensity at each measurement location are plotted in Figure 9. The special indicator of the inclination angle shows the largest magnitude compared with the other two, while the special indicators of the mean velocity and turbulence intensity show similar magnitudes. This supports the fact that the inclination angle is likely the characteristic most influenced by topographic truncation. Hence, structures sensitive to the inclination angle should be emphasized when obtaining wind characteristics by wind tunnel simulation. As illustrated in Figure 9, the MIs of the cases with transition sections are much lower than that of the WTC in terms of the mean velocity and inclination angle. However, in terms of the inclination angle, the MIs of the cases with transition sections are slightly higher than that of the WTC. From the point of view of mean velocity and turbulence intensity, installing the transition section at the edge of the terrain model can improve the accuracy of a simulation to some extent, but only to a very limited extent. In contrast, installing transition sections at the edges of the terrain model could not improve the accuracy of the inclination angle in the wind tunnel simulation but brought additional errors in the simulation.