# Study of the Algorithm for Wind Shear Detection with Lidar Based on Shear Intensity Factor
## 2 Methods
### Improvement of Ramp Length Extension and Contraction Strategy  
The value of wind shear itself reflects the change of wind speed at a certain distance. However, the impact of wind shear on a flight depends not only on the change of wind speed, but also on the ramp length corresponding to the change of wind speed. If the change of wind speed is significant and the corresponding ramp length is small, the wind shear could significantly impact the flight. However, if the change of wind speed is significant and the corresponding ramp length is also large enough, the impact of wind shear on the flight is likely to be small. Therefore, the ramp length determined only based on the change of wind speed itself cannot effectively find the location that has a high impact on flight safety. [PERSON] and [PERSON] put forward the concept of wind shear intensity factor in 1983 [20], and their definition considered the variability of wind speed and the corresponding ramp length simultaneously, which can more objectively reflect the impact of wind shear on the flight. The wind shear intensity factor can be defined as follows:  
\[S=\ \ \ \ \frac{dV}{dt}\ \ g\ \ \ \frac{\Delta V}{V_{a}}^{2}=\ \ \ \ \frac{\Delta V}{R^{1/3}}^{3}gV_{a}\ \ 1 \tag{3}\]  
where \(dV/dt\) represents the change rate of wind speed; \(\Delta V\) represents the variation of wind speed; \(V_{a}\) represents the aircraft's approach speed when landing, which is usually constant, but different aircraft's \(V_{a}\) varies; and \(R\) represents the ramp length corresponding to \(\Delta V\). It can be noted from Equation (3) that the contribution of the total change in the degree of wind speed to the wind shear intensity factor is greater than that of the wind speed's change rate. This may explain why the traditional ramp detection algorithm only releases the wind shear alert based on the total change value of wind speed. Considering that the approach speeds of different aircraft vary during landing, this paper simplifies the calculation of the wind shear intensity factor. The simplified wind shear intensity factor  
Figure 3: The principle of the ramp length extension and contraction strategy of conventional single ramp wind shear detection algorithm. \(S_{simple}\) is defined as follows. Note that the wind shear intensity factors mentioned below all refer to \(S_{simple}\)  
\[S_{simple}=\frac{\Delta V^{3}}{R} \tag{4}\]  
Since the wind shear intensity factor can better reflect the impact of wind shear on flight safety, this paper improved the ramp detection algorithm by determining the best ramp length based on the wind shear intensity factor. Concurrently, the ramp length determined only based on the changing trend of wind shear intensity within the length range of a single ramp cannot guarantee its global optimality. For example, we assume that the wind shear intensity gradually increases within the range of ramp length D. In that case, the wind shear intensity in the location of data point D + L1 decreases, while in the location of data point D + L2 it continues to increase. At the same time, the wind shear intensity in the location of data point D + L2 is higher than that within the range of D. The wind shear intensity in D + L2 is the maximum value of all data points. At this time, if the final ramp length is determined only based on the changing trend of wind shear intensity within the range of a single ramp, the ramp length should be D, but the real optimal ramp length is D + L2 (Figure 4). Therefore, the optimal ramp length determined only based on the changing trend of wind shear intensity within the range of a single slope cannot guarantee its global optimality.