Validation of the Wind Finding Equation

In addition to validating the wind finding equations theoretically, numerical simulation results are employed in the re-investigation process. Simulations are conducted in the same pseudo-stochastic wind field based on both the simple model, in which the drop- windsonde is treated as a point object with a constant drag coefficient regardless of angles of attack, and on the alternative model. Once the improvement of using the wind finding equations in deriving desired wind statistics from pseudo measurements simulated using the alternative motion model is found similar to that using the simple motion model, the conclusion can be drawn that the wind finding equations are still valid even through the variation of the drag coefficient with angle of attack is not negligible.

20 40 60 80 100 120 140 160 180 200 26 28 30 32 34 36 38 40 Height (m)

Mean Wind Velocity (m/s) Mean Wind Comparison

True Raw Find1

(a) Simple Model

20 40 60 80 100 120 140 160 180 200 26 28 30 32 34 36 38 40 Height (m)

Mean Wind Velocity (m/s) Mean Wind Comparison

True Raw Find1 Find2

(b) Alternative Model

Figure 3.26: Comparison of the mean wind velocity profiles, ”Raw” refers to the com- position results based on raw dropwindsonde measurements, ”Find1” refers to the wind retrieved by the wind finding equations, ”Find2” refers to the calculation results of equa- tion (3.42) and ”True” refers to the preset value of the pseudo-stochastic wind field.

Shown in Fig. 3.26 is the comparison of the mean wind profile composited from pseudo dropwindsonde measurements generated based on two different motion models. Comparing Fig. 3.26(a) to Fig. 3.26(b), it is obvious that the wind finding equations are still valid to correct the dropwindsonde deficiency in reproducing the mean profile in a sheared wind field. The similar improvement seen in these two figures substantiates that the variation of the drag coefficient with angle of attack does not invalidate the use of the wind finding equations to find the correct mean wind profile. In addition, a similar improvement is also seen in Fig. 3.27 which compares the turbulent wind velocity profile. This demonstrates the wind finding equations are still valid to recover the turbulence intensity profile of the measured wind field, which was underestimated by raw dropwindsonde measurements.

In the theoretical discussion of the validity of the wind finding equation detailed in the previous subsection, there is an additional correction appeared, comparing with the conventional wind finding equation, to take into account the influence of the dropwind- sonde vertical acceleration (see equation (3.43 and equations (3.13), (3.14)). The effect of using the term ¨z− g to replace− g in the wind finding equations is illustrated in Figs. 3.26(b) and 3.27(b). It is found that the improvement is insignificant. Moreover, since the dropwindsonde acceleration is not directly reported by the dropwindsonde but must be calculated by differentiating the dropwindsonde falling rate, the improvement of this additional correction will be easily buried by extra errors introduced by the differentia- tion. Besides, since the dropwindsonde acceleration is relatively small comparing with the gravity acceleration, g, its influence is expected to be minimal in the term ¨z − g. As evidence of this statement, the vertical acceleration solved directly from simulations concentrates in the range of (− 1m/s2_,1m/s2_{) (more than 70%), as shown in Fig. 3.28.}

In conclusion, this additional correction is not recommended in processing actual drop- windsonde measurements.

It can be noticed that pseudo measurements produced by the alternative motion model, after dynamically corrected using the wind finding equations, overestimate the turbulence

100 200 300 400 500 2 3 4 5 6 7 8 Height (m)

Turbulent Wind Velocity (m/s) Turbulent Wind Comparison

True Raw Find1

(a) Simple Model

100 200 300 400 500 2 3 4 5 6 7 8 Height (m)

Turbulent Wind Velocity (m/s) Turbulent Wind Comparison

True Raw Find1 Find2

(b) Alternative Model

Figure 3.27: Comparison of the turbulent wind velocity profile, ”Raw” refers to the composition results based on raw dropwindsonde measurements, ”Find1” refers to the wind retrieved by the wind finding equations, ”Find2” refers to the calculation results of equation (3.42) and ”True” refers to the preset value of the pseudo-stochastic wind field.

0 0.05 0.1 0.15 0.2 0.25 -10 -8 -6 -4 -2 0 2 4 6 8 10 Distribution Vertical Acceleration (ms-2)

Figure 3.28: Distribution of the dropsonde vertical acceleration over a range

[− 10ms−2_,10ms−2_{], boxes show the probability density.}

intensity of the measured wind field for both the original equation introduced by Hock and Franklin (1999) and for equation (3.42) with the additional correction. This can be explained by the alternative model nature which includes the variation of the dropwind- sonde aerodynamics with angle of attack. From equations (3.37) and (3.38), it can be seen that the influence of the driving wind is not only on the driving forces but also on the angle of attack, which in turn influences the dropwindsonde aerodynamic values. Thus, the dropwindsonde motion described by the alternative model is more sensitive to fluc- tuations of the driving wind comparing with the simple model described dropwindsonde motions. This effect is illustrated in Fig. 3.27, as the turbulent wind velocity calculated by compositing raw dropwindsonde measurements is higher in the simulations using the alternative motion model than in the simulations using the simple motion model. More- over, the dynamic correction in the wind finding equations duplicates the influence of fluctuating winds since both the horizontal dropwindsonde velocity ˙x, ˙y and dropwind- sonde falling rate ˙z implicitly contains this influence. As a result, the use of the wind finding equations overestimates the turbulent wind velocity if the variation of the drop- windsonde aerodynamics with angle of attack is not neglected. However, a low-pass filter is often utilized in processing actual dropwindsonde measurements which reduces fluctu- ations of both horizontal and vertical dropwindsonde ”reported” wind velocities. As a

result, the overestimation seen in Fig. 3.27 is not expected in processing dropwindsonde measurements in practise, at least not with a similar magnitude.