###### Abstract  
Clear-air echo studies are usually based on isotropic turbulence theory. But the theory has been considered incomplete by modern turbulence theory. The intermittence of turbulence can reveal obvious shortcomings in the existing studies of clear-air echoes. The mechanism of clear-air echo scattering needs to be supplemented. This paper introduces the troposcatter theory, normally used in over-the-horizon communication, to fill the gap left by Bragg scattering. By treating radar as a self-transmitted and self-received device, the equivalent transmission loss of weather radar is established and compared with the recommendations of the Radiocommunication Sector of the International Telecommunication Union (ITU-R). The results show that the S-band radar transmission loss aligns with ITU-R recommendations. There is also a linear regression relationship between the radar transmission loss and height, which conforms to the troposcatter theory. This means that the theory of troposcatter scattering is a supplement to the theory of Bragg scattering. Tropospheric scattering can be thought of as general Bragg scattering. Meanwhile, based on ITU-R recommendations, this study also provides a new way for the recognition of biological echoes. weather radar; clear-air echo; transmission loss; troposcatter; turbulence +
Footnote †: journal: remote sensing  
0000-0002-4660-339X/  
However, the structure constant, \(C_{n}^{2}\), calculated from clear-air echoes, surpasses the upper range of observed values. Hence, as the current atmospheric scattering theory cannot provide evidence that turbulence causes clear-air echoes, researchers tend to attribute them to biological activities. However, many studies do not consider the fact that these two pieces of evidence are flawed. Much research has revealed the extensive existence of non-Kolmogorov turbulence. [PERSON] and [PERSON] were the first to observe the uneven distribution of turbulence and its energy dissipation over space, with intermittent velocity gradients increasing as the Reynolds number increased [5]. [PERSON] conducted numerical simulations and discovered that a small region of space accounted for 95% of the energy dissipation [6]. [PERSON]'s team demonstrated the presence of turbulent anisotropy using laser beams in laboratory experiments [7]. [PERSON]'s theory was found to be incomplete in describing atmospheric statistics properly, particularly in segments of the troposphere and stratosphere [8]. The above findings suggest that non-Kolmogorov turbulence plays a significant role in atmospheric dynamics. Thus, clear-air echoes can have a non-zero \(Z_{\text{DR}}\) according to non-Kolmogorov turbulence. Several experimental campaigns have also investigated the turbulent air anisotropy in the real atmosphere. One experimental study involved a laser beam propagating horizontally through the near-ground atmosphere, and showed that the intensity correlation function captures the anisotropic turbulence information, corresponding to the refractive index anisotropy ellipse of atmospheric fluctuations [9]. A similar measurement campaign was used to obtain the intensity covariance function of a propagating plane wave and showed that the anisotropy ratio \(\mu_{x}/\mu_{y}\) ranged from 0.6/1 to 1/0.6 at different times, where the magnitudes of \(\mu_{x}\) and \(\mu_{y}\) affected the horizontal and vertical strength of turbulence through the refractive index structure constant [10]. The results of these measurements suggest that the \(Z_{\text{DR}}\) value of turbulent air can vary over a wide range of the actual atmosphere. Based on the studies mentioned above, this range is between \(-2\) dB and 2 dB. This explains the non-zero differential reflectivity of clear-air turbulence echoes. However, Bragg scattering, as another piece of evidence, has not been updated since it was first introduced.