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The data from the intelligent round-trip sounding system experimental project carried out in China is used to conduct the corresponding research. The detection process is shown in Fig. 1, including the three stages of rising, flat-floating, and falling, and is able to complete the observation in the vertical direction and the continuous high-frequency observation at a stable height in the horizontal direction. In the ascending stage, the outer ball is used to provide upward buoyancy while carrying a radiosonde for real-time observation and collection of data; the outer ball explodes at a predetermined height, and then the inner ball provides buoyancy in the flat-floating stage to balance gravity. The inner ball is a zero-pressure balloon and reaches a balance between its own gravity and buoyancy at the height of the designed ascent limit. After reaching the predetermined position, the system separates the radiosonde and the inner ball through the fuse device. The radiosonde falls, guided by a parachute, and recording measurements on its way down. In the floating phase, the balloon performs a quasi-Lagrangian measurement with a frequency of 2 s−1. The radiosonde is equipped with a sensor module consisting of sensors for temperature, humidity, and air pressure measurements. The Beidou navigation satellite system is used for longitude, latitude, and altitude measurement, and the horizontal wind speed and direction are calculated from this.
Figure 1. Schematic diagram of the RTISS. L is the distance from the station to the radiosonde, Ω and θ are the azimuth and elevation, respectively, and the black curve is the detection trajectory of WH on 30 October 2018.
The detection system has different working principles in the three stages of rising, flat-floating, and falling (Cao et al., 2019). In the ascending phase, the balloon is subjected to buoyancy, gravity, and air resistance in the vertical direction. In the horizontal floating stage, the adaptive flat-floating process is realized by controlling an appropriate net lift force from the ground. Under this condition, the vertical force is dynamically balanced, and the balloon trajectory can be regarded as an approximate horizontal motion. In the descending stage, the radiosonde descends under the parachute, from the low-density atmosphere into the high-density atmosphere.
We obtained 12 sets of data retrieved in Wuhan, Anqing, Yichang, Ganzhou, and Changsha in 2018, which are: WH1, WH2, and WH3 (22, 23, and 30 October); AQ1 and AQ2 (19 October and 16 November); YC1 and YC2 (18 October and 22 October); GZ1, GZ2, and GZ3 (31 October, 6 November and 9 November); CS1 and CS2 (19 October 19 and 16 November), respectively. The data in the ascending and descending stages are evenly interpolated to a vertical step of 12 m. The balloon trajectory in the flat-floating phase and the height variation with time are shown in Fig. 2. The balloon trajectories in the flat-floating phase are interpolated to x, y coordinates relative to the start of the flat-floating phase in a local geophysical coordinate system (it can also be said to be the projection of the meridional and zonal). In the CS1 data, there is a significant drop in the height after the start of the flat-floating phase, and this segment is deleted in the subsequent calculations. Originally sampled equidistant in time, the sampling distance of the interpolated data is adjusted to the average spatial sampling during the respective flight. Specific information for the flat-floating phase is shown in Table 1.
Figure 2. (a) The trajectory of the flat-floating phase and (b) the floating height variation with time.
Number Direction Step (m) Distance (km) 1-WH1 zonal 13 24.5 2-WH2 zonal 16 67.7 3-WH3 meridional 13 90.3 4-CS1 zonal 13 76.0 5-AQ1 meridional 11 29.0 6-AQ2 zonal 16 53.6 7-YC1 meridional 12 105.5 8-YC2 meridional 8 61.9 9-GZ1 meridional 15 87.6 10-GZ2 meridional 9 37.7 11-GZ3 meridional 9 54.9 12-CS2 meridional 11 50.4 Table 1. Data information after decomposition and re-interpolation in the flat-floating phase.
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The perturbation profile of atmospheric elements contains abundant fluctuation information. The energy corresponding to different scales can be obtained intuitively and clearly using Fourier spectral transformation, and the spectral amplitude and spectral slope can quantitatively describe the spectral structure, reflecting the disturbance characteristics of the atmosphere. Here we use the potential temperature perturbation profile to perform spectral transformation. For non-stationary random processes with stationary increments, the statistical characteristics of increments can be defined as (Marshak et al., 1997):
Since the turbulence theory focuses on the increment of velocity, the velocity increment between
$ {x} $ and$ x + r $ is defined as$ {\text{d}}{u_L}\left( {x,r} \right) $ and$ {\text{d}}{u_T}\left( {x,r} \right) $ , where$ {u_L} $ and$ {u_T} $ represent the velocity components parallel and perpendicular to the separation distance r (consistent with decomposition direction), respectively. The second-order velocity structure function can be defined as:where
$ \left\langle . \right\rangle $ is the ensemble average. Considering that the Fourier power spectrum alone cannot distinguish different theories, based on Kolmogorov theory, the third-order structure function is used here to quantify and compare the disturbance information contained in the atmospheric wind field (Lindborg, 1999; Cho and Lindborg, 2001). The third-order structure function not only can eliminate the arbitrariness of the universal constant in the power law expressed by the second-order structure function in physical space, but it also can reflect the direction of the energy cascade through the sign of the value, where negative values represent downscale energy cascades and positive values represent upscale energy cascades. Considering that transition in the stratosphere occurs within a thin layer (Benavides and Alexakis, 2017), the third-order structure function can be written as (diagonal part):where
$ \varepsilon $ is the energy dissipation rate. In order to systematically describe the random atmospheric process, referring to the multi-order structure function and singularity measurement method (Davis et al., 1994; Marshak et al., 1997), the q-order structure function can be written as:Through multi-order structure function analysis and singularity measurement, the Hurst index and intermittent parameter are obtained. The specific calculation method is described in Lu and Koch (2008).
Number | Direction | Step (m) | Distance (km) |
1-WH1 | zonal | 13 | 24.5 |
2-WH2 | zonal | 16 | 67.7 |
3-WH3 | meridional | 13 | 90.3 |
4-CS1 | zonal | 13 | 76.0 |
5-AQ1 | meridional | 11 | 29.0 |
6-AQ2 | zonal | 16 | 53.6 |
7-YC1 | meridional | 12 | 105.5 |
8-YC2 | meridional | 8 | 61.9 |
9-GZ1 | meridional | 15 | 87.6 |
10-GZ2 | meridional | 9 | 37.7 |
11-GZ3 | meridional | 9 | 54.9 |
12-CS2 | meridional | 11 | 50.4 |