# Turbulence: A Significant Role in Clear-Air Echoes of CINRAD/SA at Night
## 5 Discussion  
Many scholars deny or reject the domination of turbulence in clear-air echoes. First, they propose that a nonzero \(Z_{DR}\) indicates that the scattering is due to creatures rather than turbulence because, according to the statement of [PERSON]'s theory that turbulence is homogeneous and isotropic, the \(Z_{DR}\) of turbulent echoes should be zero. However, a problem with this viewpoint is that non-Kolmogorov turbulence widely exists in the atmospheric boundary layer. Some observations have already shown that the atmospheric structure constant of the refractive index differs between the horizontal direction and the vertical direction. Therefore, the \(Z_{DR}\) cannot support their rejections. We agree that biological scatterers cause large values of \(Z_{DR}\), but the contribution from the effect of turbulence still needs to be investigated. Second, some scholars believe that because the \(C_{n}^{2}\) calculated from echoes is larger than the high end of the observed values, clear-air echoes should not be attributed to turbulence. For example, clear-air echoes of a 10 to 20 dB \(Z\) require \(C_{n}^{2}\) to be greater than \(10^{-11}\)\(m^{-2/3}\), which is far above the observed \(C_{n}^{2}\). The phenomenon of clear-air echoes cannot be explained by Bragg scattering. Therefore, it is assumed that the domination of clear-air echoes is not turbulence. However, scholars have ignored the effect of another scattering mechanism. We found another reasonable scattering mechanism to explain clear-air echoes in communication and wireless areas. In communication, tropospheric scattering (also known as troposcatter) is admitted as an efficient propagation method by the Radiocommunication Sector of the International Telecommunication Union, which describes the mechanism by which microwave radio systems inadvertently achieve beyond-the-horizon communications [53]. One of the three models of the troposcatter is the reflecting-layers model. The other two models are scattering from turbulence and reflections from an exponential atmosphere. Troposphericscattering is the result of the combination of these three models. [PERSON] points out that the reflectivity of the troposcatter can be written as follows [54]:  
\[\eta=B\overline{\left(\frac{\mathrm{d}\varepsilon_{r}}{\mathrm{d}h}\right)^{2}} \lambda^{n}(2\varphi)^{-m} \tag{11}\]  
where \(B\), \(n\), and \(m\) are constants and are measured by experiments; \(\varepsilon_{r}\) is the dielectric constant; \(h\) is the height; \(\varphi\) is the glancing angle; the bar is the sign of the mean; and the relationship between \(\varepsilon_{r}\) and \(h\) can refer to the assumption by [PERSON] [55]. Interestingly, the scattering from turbulence is essentially the same as Bragg scattering, but few studies have highlighted the role of reflecting layers in clear-air echoes. To demonstrate how reflecting layers affect clear-air echoes, we calculated the gradient Richardson number and the intensity of the turbulence (expressed by the ratio of the standard deviation of the wind speed to the mean wind speed) using a microwave radiometer and a wind lidar [56; 57]. Moreover, the atmospheric profiles were collected by a microwave radiometer. Although the geometrical structure of the reflecting layers remains obscure, it can be inferred that turbulent mixing is detrimental to the reflecting layers because a reflecting layer in the atmosphere is formed by relatively sharp gradients of the refractive index, but turbulent mixing makes the temperature and humidity homogeneous and reduces the gradient of the refractive index. Thus, the Richardson number and the turbulence intensity, which indicate turbulent mixing, are shown in Figure 16 to give the relationship between clear-air echoes and turbulent mixing. In Figure 16, large values of \(Z\) correspond to large Richardson numbers and turbulent mixing. When the sun sets in the west, the turbulent mixing rapidly weakens.