*4.2. Time–Height Cross-Section*

Movement is the most important feature of bio-scatterers. To reveal the causes of clear-air echoes, the radar data were displayed as a time–height cross-section. The signal of the clear-air echoes showed significant diurnal variations, as shown in Figure 9. It was thought that the activities of nocturnal creatures caused greater echoes. However, the rapid growth in the signal in the time–height cross-section caught our attention. Surprisingly, the value of *Z* grew fast. The 23 dBZ echo only took 13 min to increase from 500 m to 1000 m, and the increasing velocity was 0.64 m/s. When using the wind lidar, as Figure 10 shows, the vertical velocity of the wind was below 0.5 m/s and was smaller than the velocity of the echoes. This indicates that a small bio-scatterer, which does not fly well, could not be the scatterer. Despite the impractical state of motion, perhaps these clear-air echoes were still caused by large bio-scatterers. However, the vertical profiles of *ZDR* shown in Figure 9 deny this view.

**Figure 9.** Time–height cross-section of radar products for 24 h from the CINRAD/SA at Daxing, Beijing, 2 May 2021. The fill color is *Z* (unit: dBZ); the black isopleths are valid data proportions; and the white isopleths are *ZDR* (unit: dB). The times of sunset and sunrise were 11:08 and 21:13, UTC, respectively.

**Figure 10.** Vertical wind profiles measured using the Windcube 100 s on 2 May 2021. The positive and negative values represent the vertical upward and downward wind speeds (unit: m/s), respectively.

It is known that *ZDR* is the radar reflectivity difference between the horizontal and vertical polarization and represents the dimension of the scatterer. If the measurements of the volumes contain multiple scatterers, *ZDR* will be biased toward the characteristics of the largest scatterers. In Figure 9, the profiles of *ZDR* increased with height and were temporarily greater than 2.5 dB above an altitude of 1200 m. Scatterers with a 2.5 dB *ZDR* do not climb from the ground and do not land. This implies that the echoes did not float from the ground into the air, but they suddenly appeared in the middle of the air without immigration.

#### *4.3. Velocity Analysis*

Although we have preliminarily analyzed the VAD in Section 4.1, to avoid confusion with large insects and birds, the Doppler velocity and the results of the VAD analysis are displayed in Figure 11 again. In Figure 11, the velocity fields, which were obtained from the VAD analysis, are similar to the radar Doppler velocity. The residual values of the velocity fields are shown in Figure 12a. in total, 86.4% of the residual values are less than 4 m/s, and 65.3% of the values are less than 2 m/s. The echoes were unlikely caused by large insects and birds mainly because large insects and birds have quite a great flight speed and would make the speed field messy and produce great deviations.

**Figure 11.** Doppler velocity fields (**a**–**c**) and the fields which were obtained from the VAD analysis (**d**–**f**). The elevation angles of (**a**–**c**) are 0.5◦, 1.5◦, and 2.4◦, respectively, the same as (**d**–**f**). Except for some error points and point targets, the velocity fields (**d**–**f**) which were obtained from the VAD analysis are similar to the Doppler velocity (**a**–**c**).

**Figure 12.** (**a**) Histogram of the residual error of the VAD analysis at different altitudes. The volume of the radar beam is used to calculate the ordinate. (**b**) The profiles of the mean wind speed during 12:30 to 13:30 (UTC) on 2 May 2021.

The comparison of the speed profiles with the RWP and the CINRAD/SA confirms the conclusion. The profiles of the horizontal wind speed which were sensed by the RWP are not different from the speed profiles calculated by the CINRAD/SA, as shown in Figure 12b. Despite the system deviation in Figure 12b, which is common in the results of the VAD wind profile [47], the changes in the speed profiles are consistent, generally. The profiles of the CINRAD/SA indicate that clear-air echoes are moving with the wind speed. However, the speed of biological autonomous movement is not detected by the weather radar. This means that these echoes are unlikely to be caused by creatures with a strong flight ability such as birds and large insects.

#### *4.4. Comparison of the S-Band and X-Band*

In Sections 4.1 and 4.2, some contradictions of bio-scatterers were revealed, and a quantitative analysis of the echoes was thus needed to convincingly demonstrate the cause of the clear-air echoes. A comparison of the reflectivity factors of the two bands is another method that can be used to determine the cause of clear-air echoes. Since the DWR of the turbulence echoes in different bands was more regular than biological, the time–height cross-section of *Z* using the data from BJXFS is shown in Figure 13, and the DWR between the S-band and the X-band is displayed in Figure 14.

**Figure 13.** Time–height cross-section of *Z* (the fill color) and the valid data proportions (the black isopleths) for 24 h from the X-band radar at FS, Beijing, 2 May 2021.

**Figure 14.** The DWR between the values of Figures 8 and 12. The time–height cross-section and the histogram of the DWR at nighttime are exhibited in (**a**) and (**b**), respectively. The black isopleth in (**a**) is the proportion of the X-band valid data. The bar chart (**b**) represents the normalized frequency distribution of the DWR from sunset to sunrise, and the data in the histogram from 19 dB to 25 dB occupy 80%.

In Figure 13, intuitively, the signal of the X-band differed from the S-band signal in the value of *Z*; the value of the X-band was much smaller than that of the S-band. The signal of the X-band also did not have an as pronounced diurnal variation as that of the S-band echoes. Although the signal of the X-band echoes appeared as fast as those of the S-band signal at dusk, the signal did not last long and slowly vanished from the top to the bottom after 13:00. Meanwhile, the value of *Z* in Figure 13 is low at lower altitudes and increases with height, which is different in Figure 9. This is due to the minimum scale of turbulence which increases with height. When the minimum scale exceeds the half-wavelength of the X-band, which is still much smaller than the wavelength of the S-band, the scattering vanishes before the refractivity gradient weakens. Hence, the *Z* value of the X-band seems to increase progressively without reducing.

Figure 14a shows the time–height cross-section of the DWR between the *Z* values of the CINRAD/SA and X-POLs, and Figure 14b shows the normalized frequency histograms for the radar fields in Figure 14a. The histogram of the DWR shows the characteristic values near 21.5 dB. Moreover, the *Z* value distributions of the S-band and X-band also show that the peaks of the *Z* values are at intervals of about 22 dB (in Figure 15), whereas the *ZDR* distribution does not peak at 0 dB. In Figure 15, the frequency distribution of the *Z* value resembles the Gaussian distribution and slightly changes with height, which is in line with the condition of the hypothesis in Section 3.2. However, it is not expected that the correlation or other products should follow the Gaussian distribution. The distributions of turbulence variables deviate from normality because of the intermittence [48–50].

**Figure 15.** Histograms of the radar products of the CINRAD/SA (S-band) and X-POL (X-band), respectively, on 2 May 2021 at 13:00 UTC for a height ranging between 300 m and 1.2 km.

The large widths of these distributions match with the characteristics of bird echoes seemingly. However, the echo is unlikely to be mainly caused by birds for the following reasons. First, the analysis of the VAD has already denied the dominance of birds. Second, for north China, May is almost the end of the spring migration and is close to the period of preincubation, yet the scatterers of the clear-air echo still travel to the north until late July [51,52]. Third, there are two international airports located at the azimuth angles of 22◦ and 188◦ and the distances of 31 km and 34 km, respectively. The large numbers of birds migrating would obviously be a threat to the safety of the flights if the clear-air echo was caused by birds. Therefore, the suspicion of birds and large insects has been ruled out.

It is worth noting that the CINRAD/SA and X-POL are located along the same migration path. It means that the two radars should observe the same group of scatterers

with the same scattering characteristic, moving from upstream (XFS) to downstream (SDX) the whole night, continuously. Although *Z* values from atmospheric insects may have asymmetric patterns which depend on the angle between the radar beam and the main orientation of the biological scatterers, the time–height cross-section of the *Z* values will not be affected because the cross-sections are counted by the whole coverage volume of the radar observation and are not dependent on the azimuth. Thus, the asymmetric patterns cannot stain the ratio between the *Z* values of the CINRAD/SA and X-POL.

It is already known that, according to Equation (6) and Equation (10), the *Z* difference in the turbulence of the S-band (2870 MHz, 10.45 cm) and the X-band (9455 MHz, 3.17 cm) is about 19.0 dB and 21.4 dB, respectively. Since many creatures are within the size threshold for Mie scattering and have different RCSs at different wavelengths, the reflectivity relationships to the wavelength are far from straightforward. Meanwhile, wide discrepancies are found between the characteristics of clear-air echoes and the law of biological activities. Therefore, this proves that the Beijing CINRAD/SA echoes are mainly caused by turbulence.

The DWR statistics for the region of Beijing reveal that, from 1 May 2021 to 20 May 2021, 58% of the DWR was distributed between 18dB and 24dB, which is the characteristic interval of turbulence. Moreover, the clear-air echoes maintain the features of the variations in the *Z* values and the VAD analysis. It means that nearly 58% of the echoes were probably caused by turbulence and proves that the influence of turbulence is erroneously ignored in clear-air echoes. Almost all these echoes did not show the classic features of Bragg scattering, such as a low *Z* and zero *ZDR*. These echoes could wrongly be identified as bioscatterers and cause a misestimation of biomass. The number of flying creatures observed by the weather radar was much smaller than previously thought.
