## 2 Materials and Methods
### Retrieval Method
#### 2.3.2 Integrated Retrieval Technique Using Multimode Doppler Spectra  
To effectively use the Doppler spectra from the TIPEX-III cloud radar for retrieving vertical air motions in convective clouds, the following three aspects require further consideration:  
1. The three operational modes have different sensitivities, detectable height ranges, Nyquist velocities, and spectral velocity resolutions. These key performance parameters are crucial for the estimation of vertical air velocity. Thus, comprehensive usage of the multimode data needs to be considered to obtain more reasonable and accurate results. Figure 3: A velocity dealiasing case made from a convective cloud collected at 10:00 UTC on 5 July 2014 by CI mode; (**a**) is the original Doppler spectra at different heights; (**b**) is the corresponding corrected spectra after dealiasing; (**c**) is the estimated MV from (**a**,**b**); and (**d**) is the \(\sigma_{\rm v}\) estimated from (**a**,**b**). The power of Doppler spectra denoted by dB, which represents an analog-to-digital (A/D) converter count and can be converted to dBm by 10 \(\times\ log_{10}\) dB minus the radar receiver gain. 2. Convective clouds over the TP commonly vary rapidly with small scales, and, thus, the measured radar Doppler spectra in a sampling volume can be broadened by the active turbulence, wind shear, and inhomogeneous horizontal wind, which will cause bias to the retrieval results. Therefore, spectral broadening needs to be further revised. 3. Because of a low melting layer altitude of approximately 1 km on the TP, hydrometeors in the interior of convective cells exist mostly in the ice phase, which typically involves greater diameters than the liquid phase. Furthermore, the rain droplets under the cloud base also have relatively large diameters. Therefore, as the fall velocities of the traced targets in the radar sampling volume cannot be neglected, the possible biases that this introduces to the small-particle-traced idea need to be documented. Based on these three considerations, an integrated technique using multimode Doppler spectra is proposed for comprehensive retrieval of vertical air velocity. Figure 5 shows a flow diagram of the method. For the height range 2.01-15.3 km, Doppler spectra from CI are used, because this mode is more sensitive at detecting smaller cloud targets and has a higher detectable range. For the height range below 2.01 km (0.12-1.98 km), Z is utilized to judge whether BL or PR would be more appropriate for the retrieval. If Z is greater than \(-\)10 dBZ or the echo base has approached the near-ground level, then Doppler spectra of PR are selected, because the measurements correspond to a relatively strong or precipitating cloud and PR has a wider velocity range and a robust dynamic range. However, if Z is lower than \(-\)10 dBZ and the echo base is above the near-ground, then the measurements correspond to a relatively weak cloud, and Doppler spectra of BL are chosen because of their higher velocity resolution and better sensitivity. After data selection, \(\omega\) can be derived from the three modes by the small-particle-traced idea and its necessary data processing. Under actual conditions, radar-measured spectra are broader than expected from the cloud particle size distribution alone because of the temporal and spatial filters that introduce additional broadening. The Doppler spectrum variance for a vertically pointing radar can be written as [27]  
\[\sigma_{\mathrm{V}}^{2}=\sigma_{\mathrm{DSD}}^{2}+\sigma_{\mathrm{T}}^{2}+ \sigma_{\mathrm{S}}^{2}+\sigma_{\mathrm{B}}^{2} \tag{1}\]  
where \(\sigma_{\mathrm{DSD}}^{2}\) is the variance induced by the particle size distribution, \(\sigma_{\mathrm{T}}^{2}\) is the variance caused by turbulence, \(\sigma_{\mathrm{S}}^{2}\) is the variance due to wind shear, and \(\sigma_{\mathrm{B}}^{2}\) is the variance introduced by a finite radar beamwidth.