## 2 Input Data
### Narrowband-to-Broadband Coefficients  
Conversion of narrowband to broadband (NTB) reflectance was carried out empirically by creating multivariate linear regressions on matched AVHRR-CERES observations (i.e., collocated, coangular, and simultaneous). The method is explained in detail by [PERSON] and [PERSON] (2017). Achieving a sufficient matching sample size is only possible when the orbital planes of both CERES- and AVHRR-carrying satellites coincide, which limits the amount of useful data to these favorable periods (2004-2005, 2007-2008, 2011-2012). The spatial resolution of AVHRR and CERES is at nadir at about 4 km and 32 km, respectively, which requires a considerable spatial aggregation of AVHRR footprints to match a single CERES footprint. The main objective of [PERSON] and [PERSON] (2020) was to derive regressions with high scene-specific accuracy, which is possible by narrowing down each scene type to a very homogeneous sample. However, there is a trade-off between the regression-specific theoretical accuracy (=internal), and the practical accuracy of the regressions when applied to the entire range of possible scene types (global result), including non-homogeneous scenes. Therefore, it was decided to slightly modify the regressions from Akkermans and Clerbaux (2017) by loosening the cloud cover range, thereby redefining the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cloud Class** & \multicolumn{3}{c}{**Clear-Sky**} & \multicolumn{3}{c}{**Overcast**} \\ \hline
**TWL Surface Type** & \(n\) & **A** [**Wm\({}^{-2}\)**] & **B** [**Wm\({}^{-2/o}\)**] & \(n\) & **A** [**Wm\({}^{-2}\)**] & **B** [**Wm\({}^{-2/o}\)**] \\ \hline Water & 34,283 & 41.749 & \(-5.114\) & 4,969,304 & 83.833 & \(-12.835\) \\ Sea ice 100\% & 141,835 & 83.897 & \(-12.784\) & 375,797 & 92.968 & \(-13.628\) \\ Perm.snow/ice & 1,626,464 & 96.117 & \(-14.699\) & 1,879,264 & 99.274 & \(-15.704\) \\ Fresh snow & 86,142 & 60.456 & \(-8.476\) & 652,909 & 90.565 & \(-13.671\) \\ Land & 7902 & 38.724 & \(-5.501\) & 102,852 & 85.617 & \(-12.739\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Twilight model: sample size (\(n\)) and regression coefficients (\(A\), \(B\)).  
Figure 3: Twilight model with \(\theta_{0}\)-dependent RSF for clear-sky (**left**) and overcast (**right**) conditions; The red dotted lines are the CERES twilight model taken from (K  
\"clear-sky\" and \"overcast\" regressions: (1) \"clear-sky\" is now defined as cloud cover from 0% to 10% (instead of strictly 0%), and (2) \"overcast\" is now defined as cloud cover from 90% to 100% (instead of strictly 100%). Note that the cloud cover thresholds are imposed on both (fractional) AVHRR and CERES cloud masks in the SSF footprint, for example, clear-sky means that both cloud fractions should be below 10%. Furthermore, some small bug fixes in the code were found and solved. Together, the above mentioned adaptations resulted in updated coefficients, listed in Table 3, which is an update compared to [PERSON] and [PERSON] (2017) (Table 3 therein). Overall, the updates are relatively small and did not affect the main analyses, results and conclusions of [PERSON] and [PERSON] (2017).