# An Investigation of Optically Very Thin Ice Clouds from Ground-Based ARM Raman Lidars
## 5 Discussion  
The higher sensitivity of the RL allows the opportunity to detect optically very thin ice clouds, which often go undetected by CALIPSO. The optically very thin ice clouds represent a large proportion (22-23%) of ice cloudy profiles. With the focus of this study being on the optically thinest clouds that can be detected by the instruments, a discussion of the uncertainty in the optical depth retrievals is necessary. The optical depth is derived from the particulate extinction (Equation (1)); therefore, the focus will be on uncertainties in particulate extinction. For both the RL and CALIPSO, uncertainty in particulate extinction arises from uncertainties in the lidar ratio and particulate backscatter, which can be expressed as  
\[\Delta\alpha=\ \left\{\sqrt{\left(\frac{\Delta S}{S}\right)^{2}+\left(\frac{ \Delta\beta}{\beta}\right)^{2}}\right\}\alpha \tag{2}\]  
where \(\Delta\alpha\) is the uncertainty in the particulate extinction \(\alpha\) in km\({}^{-1}\), \(\Delta S\) is the uncertainty in the lidar ratio \(S\) in \(sr\), and \(\Delta\beta\) is the uncertainty in the particulate backscatter \(\beta\) in (km sr)\({}^{-1}\). For the RL, the uncertainties for the lidar ratio and particulate backscatter depend on the methods used to determine those quantities. RL lidar ratio and particulate backscatter uncertainties are composed of uncertainties in the signal, overlap function and calibration coefficient. For CALIPSO, the uncertainty for the lidar ratio also depends on the method used to determine the lidar ratio. The lidar ratio uncertainty depends only on the uncertainties in the measured data for constrained retrievals. The lidar ratio uncertainty is assigned a relative uncertainty of 25% for unconstrained retrievals [45]. The uncertainty in particulate backscatter for CALIPSO is composed of the uncertainties  
Figure 8: Cloud fractions of all clouds (left) and ice clouds (right). Cloud fractions are based on (**a**) all profiles and (**b**) transparent profiles for CALIPSO (red) and the RL (blue). Cloud fractions are for SGP (light color), TWP (medium color) and CALIPSO global (dark red). The RL resolution is the CALIPSO-like feature detection resolution (i.e., 5 min/60 m at SGP and 20 min/60 m at TWP). Values are also given above the bars. Data for the RL at the SGP site are from August 2008 to August 2016 and at the TWP site from December 2010 to January 2015. Data for CALIPSO are from June 2006 to August 2016.  
in the molecular backscatter, normalization backscatter, molecular transmittance and particulate transmittance [45; 50]. To gauge the uncertainties in the ice cloud column optical depth, the absolute uncertainty in particulate extinction is expressed as  
\[\Delta\tau_{i,c}=\int_{z_{base}}^{z_{top}}\Delta\alpha_{i}(z)dz \tag{3}\]  
where \(\Delta\tau_{i,c}\) is the absolute uncertainty in the ice cloud column optical depth in km\({}^{-1}\), and \(\Delta\alpha_{i}\) is the uncertainty in the ice cloud particulate extinction in km\({}^{-1}\). This approach of determining the optical depth uncertainty neglects the contribution of the covariance of the lidar ratio and particulate backscatter to the optical depth uncertainty. This contribution, however, is negligible for low optical depths (i.e., the focus of this analysis) with typical SNRs [50]. The median absolute uncertainty for transparent profiles with ice cloud column optical depths below 0.01 is 1.3E\(-\)3 km\({}^{-1}\) (2.3E\(-\)3 km\({}^{-1}\)) and 5.8E\(-\)3 km\({}^{-1}\) (4.8E\(-\)3 km\({}^{-1}\)) for the RL and CALIPSO SGP (TWP). The median relative uncertainty (i.e., Equation (3) divided by Equation (1)) for transparent profiles with ice cloud column optical depths below 0.01 is 82.9% (85.2%) and 91.3% (73.1%) for the RL and CALIPSO SGP (TWP), respectively. The relative uncertainty is large, which is the result of summing various factors contributing to ice cloud extinction uncertainties, and is relative to small values by only considering the ice cloud column optical depths below 0.01.