**5. Discussion**

Many scholars deny or reject the domination of turbulence in clear-air echoes. First, they propose that a nonzero *ZDR* indicates that the scattering is due to creatures rather than turbulence because, according to the statement of Kolmogorov's theory that turbulence is homogeneous and isotropic, the *ZDR* 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 *ZDR* cannot support their rejections. We agree that biological scatterers cause large values of *ZDR*, but the contribution from the effect of turbulence still needs to be investigated.

Second, some scholars believe that because the *C*<sup>2</sup> *<sup>n</sup>* 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*<sup>2</sup> *<sup>n</sup>* to be greater than 10−<sup>11</sup> *m*<sup>−</sup>2/3, which is far above the observed *C*<sup>2</sup> *<sup>n</sup>*. 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. Tropospheric

scattering is the result of the combination of these three models. Zhang points out that the reflectivity of the troposcatter can be written as follows [54]:

$$\eta = B \overline{\left(\frac{\mathrm{d}\varepsilon\_{r}}{\mathrm{d}\hbar}\right)^{2}} \lambda^{n} (2\,\mathrm{q})^{-m} \tag{11}$$

where *B*, *n*, and *m* are constants and are measured by experiments; *ε<sup>r</sup>* is the dielectric constant; *h* is the height; *ϕ* is the glancing angle; the bar is the sign of the mean; and the relationship between *ε<sup>r</sup>* and *h* can refer to the assumption by K. Bullington [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.

**Figure 16.** Turbulence intensities (**a**) and Richardson number (**b**) for 20 h at Daxing, Beijing, 2 May 2021. The black isopleth is the time–height cross-section of *Z* (unit: dBZ), which is the same as the fill color in Figure 6.

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. Additionally, the unmixed air masses with relatively sharp gradients become the reflecting layer and generate the scattering signal of the clear-air echoes. In contrast, in the daytime, the strong turbulent mixing breaks the structure of the reflecting layer, and only the turbulent

scattering remains. Thus, turbulence has a greater impact on the echoes at night than in the daytime.

The same diurnal variation has been observed in the field-strength variation in the short radio wave propagation in Arizona [58]. Other studies have found that troposcatter propagation only occurs when the turbulence scale is larger than the wavelength of the radio signal, and the signal level with a wavelength of 9 cm is much larger than that with a wavelength of 3 cm [58,59]. These phenomena have the same characteristics as clear-air echoes, with the value of the reflectivity factor at the S-band being bigger than that at the X-band. Thus, we propose that the reflecting layers cause a diurnal variation in clear-air echoes and enhance the signal of clear-air echoes at night. Therefore, the coexistence of the reflecting layers and Bragg scattering is the reason why the value of *C*<sup>2</sup> *<sup>n</sup>* calculated from the echoes is larger than the value from the theoretical calculations. Further, the reflecting layers explain some of the characteristics of *ZDR*. For example, the vertical signal of clear-air echoes is weaker than the horizontal signal because turbulent mixing is stronger in the vertical direction, and the vertical reflecting layers cannot easily survive. Thus, the values of *ZDR* are generally greater than zero.

An interesting note is that the high reflectivity area in the upper-left region of Figure 4 analyzes the characteristics of a low correlation coefficient, and in this area, *ZDR* presents a mixture of high and low values. This characteristic is ascribed to the atmospheric response to the underlying surface, which belongs to a mountainous region and is quite different from the others in Figure 1.

The rough terrain of mountains makes the turbulence more chaotic and intense, which produces a stronger refractive index and scattering. A thin layer of shear turbulence excited on the shear plane makes the *ZDR* larger, but the layer is not stable, bringing a mixture of high and low values to the *ZDR*. However, it is noted that, by upthrust, too high mountains may affect the turbulent scales, which are too large to match up to the radar wavelength for scattering. The relationship between the underlying surface and clear-air echoes is worth further exploration in the future.

Another interesting characteristic of the *ZDR* is that its value grows weak and becomes close to zero in the day–night shift scenes. We speculate that the turbulent mixing reaches a quasi-equilibrium state, and this will be further investigated in future studies.

Yet despite all this, some scholars still express a slightly different point of view. They claim that the reflection from turbulent air at the S-band has been studied by some studies [29,60–63], and it has been well established with polarization radars that turbulent air has *ZDR* values close to 0 dB at the S-band. However, these echoes were commonly observed at the top of the convective boundary layer (also called the entrainment layer). The entrainment layer is essentially static in stability. Due to the effects of penetrative convection and entrainment, thermals reciprocate in the layer [64]. The reciprocation brings turbulence generation on the one hand; on the other hand, the stable air brings the turbulence closer to a locally homogeneous isotropic state. Thus, the observed echoes can be regarded as special cases and cannot represent the whole characteristic of clear-air turbulent echoes. Figure 17 shows the vertical profiles of the *Z* values and rawinsonde data. It is observed that there is a layer of enhanced reflectivity at the entrainment layer, which is consistent with the known results [63].

Some scholars also conject that dust and other particulate matter can be the cause of the clear-air echoes. At the beginning of this study, we also inferred that nocturnal pollutant accumulation is the reason for the echo diurnal variation because of the uncleanliness of the atmosphere of the megacities. Yet, it is hard to explain the variation in the echo signal.

One piece of evidence is based on seasonal variation. In winter, the air quality is the worst because of heating, which uses fossil fuels, but the clear-air echo is hardly observed by radars during winter. The annual and monthly variation in the sand and dust also showed that the sand and dust weather is most frequent in spring, whereas the signal of the spring clear-air echo was generally weaker than summer and autumn.

**Figure 17.** Time–height cross-section of the Z values (**a**) from 22:30 to 24:00, and the vertical profiles of the radar products (**b**,**c**) and rawinsonde products (**d**,**e**) at 23:15 UTC on 2 May 2021. The profiles of (**d**,**e**) are measured by rawinsondes. The estimated entrainment layer is based on the maximum vertical gradient in each variable (orange line).

The other piece of evidence comes from the daily change in pollutants. The concentration of pollutants has two peaks because of traffic congestion in the metropolis, which is different from the *Z* value. The wind, which is related to pollutant diffusion and dust, also does not show a significant correlation with the clear-air echoes. Although it is known that fire plumes can cause clear-air echoes [65,66], it is unrealistic to detect plumes of wild fires in an urban area. Thus, dust and the pollutants are unlikely to be the main causes of clear-air echoes.

The issue of the influence of meteorological factors on troposcatter communication remains unknown and requires future examination. In troposcatter, the value of the signal level depends on the refractive index and its gradient, which are affected by the intensity of the turbulence fluctuation and atmospheric stratification. Thus, Gaoming Zhang proposed that the inversion of temperature leads to the diurnal variation in the signal [54]. However, few studies focus on the effect of turbulent mixing on signals level. Thus, we plan to provide a more in-depth explanation of reflecting layers forming and the structure of the nocturnal boundary layer in future studies. Meanwhile, Guifu Zhang pointed that bistatic radars have an advantage in the sensitivity of clear echoes [67]. Technically, experiments using bistatic radars are closer to the principle of troposcatter propagation. Moreover, experiments with bistatic radar data would provide more information for the analysis in future research.

#### **6. Conclusions**

In this study, clear-air echoes detected by CINRAD were analyzed to find their causes. Some observations diverge from the previous conclusion that bio-scatterers are the main reason for clear-air echoes.

Echoes with a larger Z are not deformed in the air, even if the scatterers are moving. The change in echoes in the vertical direction is also closer to the switching of the physical mode rather than biological flying. The analysis results of the DWR and the VAD support that turbulence plays an important role in clear-air echoes. In the case of May 2, the frequency distribution of the DWR peaks at 21.5 dB, which is consistent with the theory of turbulence. From 1 May to 20 May, 58% of the DWR between the S-band and the X-band is distributed between 18 dB and 24 dB, which means that more than half of the echoes at night were caused by turbulence. It was confirmed that the influence of turbulence is erroneously ignored in clear-air echoes. The reflecting-layers model of troposcatter propagation is the cause of the clear-air echoes, and this model can explain the main phenomena of the radar observations.

This study provides initial evidence for a case study in Beijing that the model based on Kolmogorov's theory may not be tenable for all clear-air echoes, highlighting the need for an expanded set of causes of clear-air echoes. The reflecting-layers model, which is one of the three models of tropospheric scattering, cause a diurnal variation in clear-air echoes and enhances the signal of clear-air echoes at night. Unmixed air masses with relatively sharp gradients become the reflecting layer and generate the scattering signal of clear-air echoes.

With the help of the theory of troposcatter propagation, rapid progress will be made in the ecological monitoring method of weather radars. A more objective and comprehensive study of clear-air echoes can effectively make weather radars acceptable in biological research instead of ignoring irrationalities. With the help of weather radars, ecology will be able to develop strongly and continuously in the near future.

**Author Contributions:** Conceptualization, Y.T. and S.M.; methodology, Y.T.; software, Y.T.; validation, Y.T.; formal analysis, Y.T.; investigation, Y.T.; resources, S.M. and H.C.; data curation, S.M. and H.C.; writing—original draft preparation, Y.T. and T.L.; writing—review and editing, Y.T. and T.L.; visualization, Y.T. and T.L.; supervision, S.M. and H.C.; project administration, Y.T., S.M. and H.C.; funding acquisition, Y.T., S.M. and H.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 42205145 and 31727901.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors thank Yunjie Xia, Beijing Meteorological Observation Center, China, for providing the RPG-HATPRO-G5 and the Windcube 100 s data.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of this study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **References**


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