## 3 Results
In addition to the footprints shown in Table 1, we extracted all CERES footprints of the years 2000-2005 which satisfied \(f\tau\approx 10\) and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Median Anisotropy**} & \multicolumn{2}{c}{**Median Anisotropy**} & \multicolumn{2}{c}{**Median Ratio**} \\ \hline  & \multicolumn{2}{c}{**Spread (\%)**} & \multicolumn{2}{c}{**Uncertainties (\%)**} & \multicolumn{2}{c}{**CERES/**} \\ \hline \(\theta_{s}\) (\({}^{\circ}\)) & **Cloud-Top \(R_{e}\)** & **Cloud-Topped WV** & **Refined** & **CERES-Like** & **Refined** \\ \hline
16.2 & 3.9 & 2.0 & 3.2 & 6.0 & 1.7 \\
18.8 & 3.9 & 1.9 & 3.7 & 5.9 & 1.5 \\
21.4 & 3.5 & 1.6 & 4.0 & 6.1 & 1.5 \\
23.9 & 3.2 & 1.5 & 4.0 & 6.0 & 1.5 \\
26.5 & 2.9 & 1.3 & 4.0 & 5.7 & 1.4 \\
29.1 & 2.9 & 1.3 consisted only of liquid condensate, roughly quadrupling the number of samples. As for refined ADMs, we supplemented angular bins which lacked sufficient CERES observations with simulations. Instead of supplementing an angular bin with all simulated reflectances (i.e., one reflectance from each cloud scenario and moisture profile), we sampled from simulations such that the distribution in cloud-top \(R_{e}\) and their level of cloud-topped water vapor corresponded to respective distribution and level of CERES observations within the same \(\theta_{s}\) interval. Since footprints had near constant \(f\tilde{\tau}\), we skipped the sigmoidal fitting (Section 2.3) and simply averaged reflectances per bin. Resulting CERES-like anisotropies compared well with original CERES SSF estimates, and--as expected from the use of simulations beyond \(\theta_{v}\) of 70\({}^{\circ}\)--were also biased by about \(-0.98\%\) (at \(\theta_{s}\) of 29\({}^{\circ}\) for \(\theta_{v}\) within 0-70\({}^{\circ}\)). We recomputed theoretical flux deviations using refined and CERES-like ADMs and found the positive bias successfully removed for a cloud-top \(R_{e}\) of 10 um, as shown in Figure 7. Remaining residuals were mostly within 5 W m\({}^{-2}\). We found that gathered samples increased in \(CTWV\) with lower \(\theta_{s}\) (Table 2) and reached angular bin medians of up to 16.3 kg m\({}^{-2}\) (at \(\theta_{s}\) of 29\({}^{\circ}\)). Again, CERES-like ADM construction could have been subject to such sampling and therefore produced ADMs fit to moisture levels higher than 4 kg m\({}^{-2}\). Observed flux deviations potentially reflected this CERES sampling bias in cloud-topped moisture. Figure 6: Using TOA SW reflectances predicted from linear models of refined ADMs for three droplet effective radii (varying across panels horizontally) and three \(\theta_{s}\) (varying across panels vertically), we applied both refined and CERES SSF 4 ADMs to obtain differences in flux estimates (shown in color). Differences beyond \(\pm 20\) are not further resolved. Linear models were given a constant cloud-topped water vapor of 4 kg m\({}^{-2}\). Figure 7: Analogous to Figure 6, we compare refined ADMs with CERES-like ADMs at a \(\theta_{s}\) of 29\({}^{\circ}\). The CERES cross-track mode collects flux estimates which--when assembled to monthly statistics--provide optimal spatial sampling [30] and allow for benchmark comparisons with global climate model simulations. To examine whether cross-track sampling and the use of refined rather than CERES-like ADMs could produce systematic flux differences, we applied both ADMs to the center months of winter (January) and summer (July) of 2007. Figure 8 shows largely positive biases across the globe, reaching significant large-scale biases of about 1-2 W m\({}^{-2}\) and local levels of up to 10 W m\({}^{-2}\). Figure 8: Applied to CERES cross-track measured TOA SW reflectances in January (**top**) and July (**bottom**) 2007 over selected conditions (\(\hat{\tau}\) of 10, 100% cloud cover, homogeneous conditions), we found that refined angular distribution models produced mostly higher flux estimates than CERES-like ADMs, shown as positive regional flux biases.