## 4 Results
### Paradox of Biology and Clear-Air Echo
#### 4.1.1 Velocity Analysis  
The clear-air echoes in Figure 5 are similar to the echoes caused by the migration of many different species of scattering birds [41]. It is unlikely that these echoes are caused by insects, as an insect has a higher differential reflectivity and a relatively lower differential phase. It is also unlikely that these echoes are caused by birds because of the velocity-azimuth display (VAD). VAD analysis is used to determine spatially averaged kinematic properties of the velocity field. The VAD of the wind field resembles a sine function of the radar azimuth angle. The large differences in the observed radial velocity are usually regarded as the result of the creatures' own flight speeds during bird migration. Figure 7 shows a velocity field close to a sine function, which was the same passage of a cold front as observed using an operational weather radar at De Bilt [42]. Only a small part of the residual error near and to the west of the radar shows signs of bird activity in Figure 8. And most of the echoes show no sign of biological activity. To prove our point, we used two wind lidars (Windcube 100S) to check the wind field differences between the wind lidars (WLSs) and the weather radar (CINRAD). One wind lidar is located at the same site as the weather radar, as shown by the red dots in Figure 9a,b. The location of the other lidar is shown by the blue dot in Figure 9a,b. Reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF) showed that the wind field was uniform at that time. Since the radial velocity field of the radar behaves as a sine function in Figure 9, we can substantially simplify the computation of the velocity, based on the meaning of radial velocity. The sine function at any range represents the radar radial component of the velocity field at that altitude, which means the extreme value of the sine function is the velocity and the direction in which the extreme value is located is the direction of motion. Notably, as the wind lidar is a device of vertical observation, the accuracy of comparison between weather radar and lidar will decrease with increasing distance between them. Therefore, the range of valid data is limited to 50 km in the calculation of weather radar wind profiles empirically. Figure 7: The gradient of \(\mathcal{O}_{\text{DP}}\) in range (**a**) and the root-mean-square (RMS) deviation of \(\mathcal{O}_{\text{DP}}\) over 9 pixels in range (**b**), on 7 May 2021, at 15:00 UTC for an elevation angle of \(1.45^{\circ}\). Figure 8: Doppler velocity fields (**a,d**) and fields fitted by sinusoidal function (**b,e**), on 7 May 2021, at 15:00 UTC. Panels (**c,f**) show the difference between the velocity field and the field of sinusoidal fitting. The elevation angles of (**a–c**) and (**d–f**) are \(1.5^{\circ}\) and \(2.4^{\circ}\), respectively. Figure 9: (**a,b**) are locations of the WLSs and CINRAD. (**c,d**) are profiles of mean wind speed and wind direction from 13:30 to 15:30 UTC on 7 May 2021. The WLSs are located separately in the DX and TZ stations. CINRAD is also located in the DX station. In (**a,b**), the arrow represents the wind field of the ECMWF reanalysis data at a height of 900 hPa at 14:00 (**a**) and 15:00 (**b**). It is clear that if the movement of the CINRAD echo is similar to the wind field observed with the lidar, then most of the clear-air echoes are not generated by bird activity because there is no corresponding speed of bird movement. In Figure 9c there are no significant differences except for a top-down systematic deviation of less than 5 m/s, which is too small for bird flight speeds as migrating birds fly at air speeds slightly above 10 m/s [43]. However, the flight of birds may also contaminate the laser wind radar observations. We therefore show the laser wind radar results for a longer period of time. Due to the nature of lasers, they cannot bypass bird bodies, and bird activity will directly block the laser beam.