# Turbulence: A Significant Role in Clear-Air Echoes of CINRAD/SA at Night
## 4 Results
### 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.  
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  
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%. 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.  
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 \(Z_{DR}\) 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; 49; 50]. 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 \(22^{\circ}\) and \(188^{\circ}\) 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.