## 4 Results
### Transmission Loss Comparisons  
In Equation (25), a relationship was established between the transmission loss of radar and troposcatter via the derivation and ITU-R recommendations. The clear-air echo signal caused by troposcatter should follow the ITU-R propagation model. Detailed guidance on the prediction of transmission loss can be found in ITU-R P.617 and P.2001, which were introduced in Section 2.3.2. To demonstrate the substantial role of troposcatter in radar observations, the transmission loss obtained via radar and the ITU-R recommendations are compared in Figure 18.  
In Figure 18, different ITU-R standards are represented by different line types, and line colors indicate various non-exceedance percentages. The radar transmission loss is colored to reflect its frequency distribution from 12:30 to 16:00 UTC everyday throughout May. The results show that the radar transmission loss aligns with ITU-R recommendations, with ITU-R P.2001 being more consistent with radar transmission loss than ITU-R P.617. As the distance increases, the transmission loss of the radar also increases, and the rate of increase gradually accelerates, which is consistent with the transmission loss variation characteristics of ITU-R recommendations.  
Although the scattering coefficient is an estimated value, resulting in a potential error, the radar transmission loss is still primarily distributed near the ideal loss recommended by the ITU. Therefore, the actual non-exceedance percentage corresponding to radar is undetermined. Overall, the radar transmission loss is consistent with ITU-R's transmission loss for troposcatter, which proves the role of troposcatter in clear-air radar echoing. Moreover, there should be a linear regression relationship between the transmission loss (in dB) and height.  
Figure 17: Range–height cross-sections of reflectivity factor in S-band (**a**) and X-band (**b**). The black dashed lines in (**a**,**b**) represent the radar beams of VCP21. The positive direction of cross-sections in (**a**,**b**) is on the azimuth of 78\({}^{\circ}\) (**a**) and the azimuth of 282\({}^{\circ}\) (**b**), respectively, which means that (**a**,**b**) are facing each other.  
In general, the dielectric constant tends to be exponentially distributed. As shown in Equation (5), the variation in the scattering cross-section for troposcatter with height is the same as the variation in the dielectric constant. It makes the transmission loss also exponentially distributed like the dielectric constant. In Figure 19 we found that the transmission loss (in dB) has a linear relationship with height. Therefore, we deem that most clear-air echoes are caused by tropospheric scattering due to turbulence because the S-band weather radar transmission loss of clear-air echoes is consistent with the value of tropospheric scattering. The theory of tropospheric scattering is a supplement to the theory of Bragg scattering. Based on the theory of tropospheric scattering, we can explain the problem of the excessive signal strength of clear-air echoes. The original misunderstanding was caused by neglecting the impact of incoherent reflection by irregular layers.  
Notably, in Figure 19, there is a disorder in the loss below the height of 500 m. This may be caused by biological scattering. The feature of biological scattering can also be found in the echoes close to the radar (i.e., the heights of the echo are low) in Figures 7 and 8. In these two figures, the echoes close to the radar have different characteristics from the other echoes, such as more discrete velocities and \(K_{\text{DP}}\) values, which are characteristic of biological activity. Therefore, biological scattering is still one of the causes of the clear-air echoes below 500 m.  
Figure 18: Radar transmission loss with range for elevation angles of 0.5\({}^{\circ}\) (**a**) and 1.45\({}^{\circ}\) (**b**) every day from 12:30 to 16:00 UTC in May. The transmission loss predictions of ITU-R are the lines in each subgraph.