## 3 Method
### Part 3: Processing of Instantaneous Albedo to Daily Mean RSF (Level-3)
#### 3.3.1. Daylight Conditions (\(\theta_{0}<84^{\circ}\)): Modeling Albedo Diurnal Cycle
This method assumes that the scene types (cloud properties) evolve linearly between the observations. From sunrise to the first observation, and after the last observation until sunset, there was no interpolation and a single scaled diurnal cycle was used. The final result was obtained by connecting the interpolated diurnal cycles, cfr the blue curve in Figure 8.  
In the example of Figures 7a and 8, the DLB was entirely situated within the 24 h temporal range of the UTC day, and hence, only a single DLB contributed to the daily mean  
Figure 8: Conceptual example of modeling the albedo diurnal cycle. calculation. However, for part of the globe (centered around the antimeridian) the UTC day contained two partial DLBs, typically with the first DLB containing 0 h UTC and the second DLB containing 24 h UTC (Figure 7b). In these cases, an additional last step was required (after the TOA albedo has been interpolated), that is, cutting off the redundant part(s) of the diurnal cycle that did not belong to the current UTC day. Finally, for every 5 min bin in the DLB, the albedo (\(\alpha_{SW}\)) was converted to daylight flux \(F_{daylight}\) (Wm\({}^{-2}\)) as follows:  
\[F_{daylight}=\left(\frac{\alpha_{SW}\cdot TSI\cdot cos(\theta_{0})}{d^{2}} \right)\cdot\left(\frac{r_{c}}{r_{e}+h_{20}}\right)^{2}. \tag{6}\]  
The first term contains the daily Total Solar Irradiance (TSI, Wm\({}^{-2}\)) supplied as input data cfr. Section 2.1. The Sun-Earth distance (d) was calculated using the Bretagnon method and coefficient look-up tables [43]. The second term in Equation (6) is a correction to scale the reference level of the flux to 20 km, according to [PERSON] et al. [35] (Equation (18) in that reference), and equals 0.993751 (\(r_{c}\) is the Earth's equatorial radius). If the DLB did not contain any observations, the entire daily mean was flagged as invalid. This may happen because the Level-2 input data is corrupted or invalid. Another, more frequent reason is that the duration of the DLB is very short, typically occurring in wintertime at high latitudes, which decreases the chance of having an observation falling within its temporal range. To avoid too many daily mean grid boxes being flagged as invalid, an exception was made for these situations: if the minimum solar zenith angle (\(\theta_{0}\)) remained higher than 80\({}^{\circ}\) over the entire DLB, all its 5 min bins would be re-categorized to \"twilight\" and processed as such (Section 3.3.2), meaning that the twilight model was exceptionally extended to the range of 80\({}^{\circ}<\theta_{0}<84^{\circ}\). This exception is a trade-off between data coverage (avoiding too much missing grid boxes) and accuracy (not relying too much on modeling by setting requirements to the minimum contribution of observations). In the example of Figure 8, there would be two shortwave instantaneous Level-2b observations used to create the albedo's diurnal cycle (one from NOAA-17 and one from NOAA-16) from only one DLB. Note that in the case of multiple DLBs, these were added and the total number was higher. An example for the daily mean of 23 July 1983 is shown in Figure 2b. Latitudinal variation is seen in the winter hemisphere (here South) which is characterized by shorter daylight blocks, that is, by more observations falling outside the DLBs limits. In the northern hemisphere, the dominant feature is an increase towards the pole due to overlapping orbits. Furthermore, there is longitudinal variation due to: (1) number of DLBs per UTC day--because each DLB should have at least one observation, regions with two DLBs have at least two observations; and (2) sideways overlap of consecutive orbits, that is, where the swath edges of each orbit overlap with the edges of next orbit, resulting in a double temporal frequency compared to the center part of the swath.