## 4 Numerical Results of the Proposed Reconstruction Method
### Reconstruction Results Considering Wind Shear Effect  
Considering that the real airflow around the wind farm is much more complex, the final section of this chapter will show the wind farm reconstruction results containing the inlet wind shear effect to enrich the application scope of the proposed reconstruction method. In Section 3.3, based on Equation (14), a wind field database containing wind shear effects has been obtained. To verify the accuracy of wind field reconstruction under different wind shear conditions, three inlet boundary conditions are set in this section for verification, as shown in Table 2:  
In this section, the number of basis vectors, the noise level and the number of sensors are set the same as in Section 4.1. The reconstruction errors of the velocity field and the pressure field under three boundary conditions are summarized in Table 3. It is worth noting that the third boundary condition is to assume that the wind shear exponent (\(\alpha\)), reference height (\(\mathrm{z_{r}}\)), inlet velocity at \(\mathrm{z_{r}}\) and incident angle are not in the prepared database, i.e., the inlet boundary condition is completely unknown. The reconstruction calculation under this condition is of great significance to verify the feasibility of applying this method to the complex airflow around the real wind field. The following conclusions can be drawn from the analysis of errors in the table: (1) Compared with the uniform entrance boundary, the reconstruction error under the boundary condition considering the wind shear effect is significantly larger. (2) The reconstruction errors under the second and third boundary conditions indicate that relatively satisfactory results can still be obtained with limited sensors under complex and unknown inlet boundary conditions. (3) Interestingly, the reconstruction error of the pressure field is smaller than that of uniform wind speed, probably because the pressure field distribution database built considering the wind shear effect is closer to the actual pressure field distribution, which also indicates the importance of database construction in the reconstruction calculation.  
In general, based on the uniform inlet wind speed and the inlet wind speed condition considering wind shear effect, the proposed method is employed to verify the reconstruction under various unknown inlet conditions, and the factors that may affect the reconstruction accuracy are analyzed. The reconstruction results verify the feasibility of the proposed algorithm in a real and complex wind field environment. Sensor location optimization in wind field reconstruction with different inlet boundary conditions will be addressed in the next chapter.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Inlet Boundary** & **Wind Speed** & & & \\
**Conditions** & **(m/s) at \(\mathrm{z_{r}}\)** & **Incident Angle** & \(\mathrm{z_{r}}\) **(m)** & **Exponent (\(\alpha\))** \\ \hline
1 & 5 & 50\({}^{\circ}\) & 0.8 & 0.143 \\
2 & 10 & 90\({}^{\circ}\) & 0.8 & 0.2 \\
3 & 15 & 130\({}^{\circ}\) & 0.7 & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Three inlet boundary conditions containing different wind shear effects.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Inlet Boundary Conditions** & \
\begin{tabular}{c} **Reconstruction Error of** \\ **Velocity Field** \\ \end{tabular} &
\begin{tabular}{c} **Reconstruction Error of** \\ **Pressure Field** \\ \end{tabular} \\ \hline
1 & 0.51 & 5.48 \\
2 & 1.14 & 6.28 \\
3 & 1.21 & 6.41 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Reconstruction errors (%) of velocity and pressure fields under three different wind shear effects.