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The velocity series documented by the dropwindsonde can derive a wind spectrum, but the interpretation of this spectrum is not thoroughly investigated. Since the wind velocity is not measured in a conventional way by the dropwindsonde, this spectrum can not be interpreted as a usual wind spectrum, e.g. one derived from tower measurements. Meanwhile, the spectral tensor describes the spectral information of the wind field uni- formly in three spatial directions, and therefore is one of appropriate interpretations of this wind spectrum. To explore the possibility of extracting spectral information of the measured wind field from dropwindsonde measurements, the pseudo-stochastic wind field generated based on the spectral tensor, instead of that based on the POD simulation, is used as the driving wind in numerically simulating the dropwindsonde motion. Com- paring the wind spectrum derived from pseudo dropwindsonde measurements to the one calculated using spectral tensor will shed some lights on the interpretation of the spectral information revealed by the dropwindsonde.

The ”true” wind spectrum should be calculated, in theory, by integrating the tensor along two directions perpendicular to the falling track of the dropwindsonde. However, it is extremely difficult to define a calculable falling track since the dropwindsonde changes directions substantially during its fall and different dropwindsondes give significantly different directions. Moreover, when Taylor’s hypothesis is invoked, all dropwindsonde falling tracks can be approximated by the vertical axis. Therefore, the ”true” wind spectrum, used to compare the spectrum calculated based on pseudo dropwindsonde measurements, is calculated by integrating the spectral tensor alongk1and k2 axis which

represent two horizontal directions, x and y, in the physical space.

A general agreement shown in Fig. 3.15(a) indicates that the wind spectrum derived from dropwindsonde measurements can reflect the spectral energy distribution of the measured wind field. It is obvious that the spectrum derived from the dropwindsonde velocity alone deviates from that calculated based on the ”corrected” wind velocity pro- duced by the wind finding equations, around the wave number of 0.05m−1_{. Given that}

the ”corrected” wind spectrum is closer to the ”true” wind spectrum, the dropwind- sonde velocity alone keeps underestimating the spectral intensity of the measured wind field in the region where it deviates from the ”corrected” wind spectrum. This feature directly substantiates the finding made in the theoretical analysis detailed in appendix A (see page 206). Through analytically analyzing the linearized dropwindsonde motion equation in the appendix, it has been found that the dropwindsonde hardly responds to high frequency excitations while the acceleration terms in the wind finding equations, i.e. ( ˙z/g)¨xand ( ˙z/g)¨y, are sensitive to high frequency excitations. The significant differ- ence between the measured and ”true” wind spectrum in really low wave number region may be due to the combination of the lack of pseudo measurements in that region and the impact of integrating the spectral tensor along two horizontal directions rather than following the track of simulated dropwindsonde motions. It is worth mentioning that the wind spectrum calculated following the same composition methodology but using the ”true” wind velocity interpolated from the known pseudo-stochastic wind field is in reasonable agreement with the wind spectrum derived from pseudo measurements in both the low wave number region, under 0.05m−1_{, and high wave number region, above}

0.2m−1_{, despite that the ”true” wind spectrum calculated by integrating the spectral}

tensor gives different spectral intensity estimates in these two regions. This implies al- though the dropwindsonde is able to reveal the spectral information of the measured wind field with a satisfactory accuracy in the whole calculable wave number region, only a relatively small portion of the dropwindsonde measured line spectrum should be used to derive the governing spectral tensor.

Shown in Fig. 3.15(b) is a similar comparison of the cross spectrum of the longitu- dinal and vertical wind. The agreement is not as good as that shown in Fig. 3.15(a), especially in the low wave number region. The major reason for this may be that the cross spectrum of u and w are more sensitive to the integration direction since the u,

w interaction is the main mechanism, according to the spectral tensor model currently employed (Mann, 1994), distorting the spectral tensor from the isotropic state to the sheared state. Nevertheless, the spectrum derived from pseudo measurements starts to

0.1 1 10 100 1000 0.001 0.01 0.1 1 Spectral Intensity (m 3 /s 2 ) Wave Number (m-1) Target Ref Drop Wind

(a) Spectral Density Comparison

-140 -120 -100 -80 -60 -40 -20 0 0.001 0.01 0.1 1 Spectral Intensity (m 3 /s 2 ) Wave Number (m-1) Target Ref Drop Wind

(b) Cross Spectral Density Comparison

Figure 3.15: Comparisons of the longitudinal wind spectral density and cross spectral density for the longitudinal and the vertical wind, in which ”Target” equals to the spec- trum integrated from the spectral tensor, ”Ref” equals the spectrum calculated using the wind finding equation, ”Drop” equals to the spectrum derived based on the drop- sonde velocity alone, and ”Wind” refers to the ”true” wind spectrum calculated from the pseudo-stochastic wind field.

give good estimates of the spectral intensity, comparing with the ”true” spectrum, in the high wave number region (above 0.05m−1_{). This supports the use of dropwindsonde}

measurements to get cross turbulence statistics, at least for local turbulence correlations.