## 6 Sensitivity Analysis of Cloud Droplet Effective Radius Retrievals
Based on the cases considered by [PERSON] _et al._[15], the LWP measurements seem to be constrained to a reasonably low values around 120 g\(\cdot\)m\({}^{-2}\) with R\({}_{\mathrm{eff}}\)-6 \(\upmu\)m. Using the approximate relationship of LWP = (2/3) \(\times\) (R\({}_{\mathrm{eff}}\)\(\times\) COD), a representative COD \(\sim\)30 can be obtained. Once the \"reference' cloud state is determined, the variability of the atmosphere and surface albedo needs to be estimated. For the surface, we make use of the MODIS land surface product MODASRVN (accessed through Level 1 and Atmosphere Archive and Distribution System, [[http://ladsweb.nascom.nasa.gov/data/search.html](http://ladsweb.nascom.nasa.gov/data/search.html)]([http://ladsweb.nascom.nasa.gov/data/search.html](http://ladsweb.nascom.nasa.gov/data/search.html))), which provides the best estimate of the surface albedo since it routinely ingests AERONET aerosol properties allowing for the most accurate surface estimate from satellite that can be made. Since the surface albedo is only retrieved at the MODIS land surface channels, an extrapolation is performed on the spectral albedo retrievals to the 415 nm channel. In this analysis, we consider the surface albedo retrievals over the period 2007-2008. The atmospheric variability, on the other hand, comes from the microphysical aerosol retrievals of AERONET. In SBDART, the actual bimodal size distribution is not completely ingested but is approximated using the SSA (\(\omega_{0}\)), asymmetry parameter (g) and AOD (\(\tau_{\mathrm{a}}\)). While this approximation may miss some fine properties, the main variability is mostly determined by these parameters. To demonstrate the sensitivity analysis, we apply the uncertainty approach for ARM SGP site datasets with \"reference\" state of COD\({}_{\mathrm{ref}}\) = 30 and Reff\({}_{\mathrm{ref}}\) = 6 \(\upmu\)m. Figure 9 shows both the 2D distributions (Figure 9(a,c)) and corresponding 1D distributions integrated over the CODs (Figure 9(b,d)) for prevailing atmospheric variability and surface albedo. The convolved variability of both the processes (Figure 9(e,f)), which is broader than the individual processes alone, resulted in a stable standard deviation of \(\pm\)0.47 \(\upmu\)m from the \"reference\" state R\({}_{\mathrm{eff}}\) of 6 \(\upmu\)m.  
One interesting feature of the joint distribution is that there is a general overbias in the individual COD retrievals along with a subsequent underbias in the effective radius. The reason for this can be seen by looking at the dual channel radiometric plot of Figure 1. In particular, we note that the density of the COD retrieval contours increases in the direction of increasing COD. Since the COD parameter is sensitive mainly to the transmission alone, for a given VIS signal uncertainty distribution, the inversions will be distributed unevenly such that higher COD retrievals will occur with greater frequency than lower COD cases. On the other hand, the R\({}_{\mathrm{eff}}\) parameter is inversely correlated to COD through the LWP. Therefore, an unbiased uncertainty on the LWP measurement will result in underestimating bias in the R\({}_{\mathrm{eff}}\) parameter. However, this bias effect is significantly reduced during the convolution of the individual sources of variability. In the above analysis, the conservative estimate of LWP is taken as 30 g\(\cdot\)m\({}^{-2}\) because it roughly represents the detection limit of LWP with dual frequency radiometers [15,50] already existing at SGP site. One of the biggest sources of error in all dual frequency MWR retrieval models is that the variations in the vertical absorption profile are neglected despite the liquid water absorption profile being sensitive to temperature profile. As already indicated in Figure 4, retrieval of water vapor is significantly improved a multispectral radiometer which can better estimate the temperature profile. It has been suggested that LWP retrievals can be similarly improved with a high frequency 50 GHz channel [52].