# First Observations of Cirrus Clouds Using the UZ Mie Lidar over uMhalthuze City, South Africa
## 3 Methods and Data  
### UZ Lidar  
The ground-based lidar system was commissioned at UZ in 2018 with the purpose of studying the vertical distribution of aerosols and clouds over the area. The UZ lidar has the same specification as the previously reported lidar system by [PERSON] [17], and the specifications are summarized in Table 1. The lidar system is made up of three sections, namely the transmission, receiver, and data acquisition, as seen in Figure 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & \\ \hline Wavelength & 532 nm: Nd: YAG \\ Maximum pulse energy & 160 mJ \\ Telescope & 404 cm \\ Detector & PMT \\ Field of View & 500 \(\upmu\)rad \\ Vertical and temporal resolutions & 10 m and 10 s \\ \hline \hline \end{tabular}
\end{table}
Table 1: UZ lidar specification.  
Figure 1: Map of South Africa with the location of the study area. The University of Zululand is located in the south-west of Richards Bay.  
The lidar measurements were carried out on 10 and 11 April 2019 in the early evenings until the night. The UZ lidar has the capability to operate during the day or night. However, because the overpass of CALIPSO over the Empangeni region is during the night, the UZ lidar was operated during the night to be able to compare UZ lidar and CALIPSO retrievals. The backscattered photons from the atmosphere were collected by the telescope, and the backscatter coefficient, extinction coefficient, and COD were retrieved using an analytical method.  
The received intensity, \(I(r)\) in terms of photon counts, is obtained over 256 range bins with a pulse width of 7 ns which is provided by the standard LIDAR equation [18] as  
\[I(r)=I_{0}C\beta(r)r^{-2}e^{-2\int_{0}^{r}\sigma(r)dt} \tag{1}\]  
where \(I_{0}\) is the transmitted laser intensity in terms of photon counts at 532 nm, \(C\) is the system constant, \(\beta(r)\) is the backscattering coefficient, \(\sigma(r)\) is the extinction coefficient and \(r\) is the range. The system constant \(C\) is provided by  
\[C=\frac{\eta A_{r}c\tau}{2} \tag{2}\]  
where \(\eta\) is efficiency of receiver system, \(A_{r}\) is receiving telescope area, \(c\) is the speed of light and \(\tau\) is the pulse width of the transmitted laser beam. The single-wavelength lidar equation has two unknowns and can then be solved assuming proportionality between extinction and backscatter. The backscattering and extinction coefficients are provided by contribution of both aerosols and molecules and are expressed as:  
\[\beta(r)=\beta_{aar}(r)+\beta_{mol}(r) \tag{3}\]  
\[\sigma(r)=\sigma_{aar}(r)+\sigma_{mol}(r) \tag{4}\]  
where subscript \((aer)\) and \((mol)\) indicate aerosols/clouds and molecules, respectively. Molecular contributions were calculated by taking data from MSIS-E-90 Atmosphere Model. The molecular backscatter coefficient \(\beta_{mol}(r)\) is estimated by considering the theoretical molecular lidar ratio \(S_{mol}=\frac{\sigma_{mol}}{\beta_{mol}}\) as \(\frac{8\pi}{3}\) sr, under the condition of zero molecular absorption [18]. The total backscatter coefficients are derived from the backward inversion method and can be expressed as,  
Figure 2: Schematic diagram for UZ lidar system.  
\[\beta_{aer}(r)+\beta_{mol}(r)=\frac{X(r)\ exp[-2(S_{aer}(r)-S_{mol})]\int_{r_{c}}^{r }\beta_{mol}(r)dr}{\frac{X(r_{c})}{\beta_{aer}(r_{c})+\beta_{mol}(r_{c})}-2S_{aer} \{\int_{r_{c}}^{r}X(r)\ exp[-2(S_{aer}-S_{mol})\int\beta_{mol}(r)dr\prime]dr\}} \tag{5}\]  
where \(X(r)\) is the range normalized signal provided by \(I(r)r^{2}\) and \(r_{c}\) is the reference height [19]. COD is calculated by integrating the extinction coefficient from cloud base to its top.  
\[COD=\int_{Z_{b}}^{Z_{t}}\alpha(r)dr \tag{6}\]  
where \(Z_{t}\) is the cloud top, \(Z_{b}\) is the cloud base, and \(\alpha(r)\) is the extinction coefficient.