## 3 Method
### Part 3: Processing of Instantaneous Albedo to Daily Mean RSF (Level-3)
#### 3.3.2 Twilight Conditions (84\({}^{\circ}\leq\theta_{0}<100^{\circ}\))  
The typical AVHRR/MetOp constellation does not have any orbits near the terminator, and consequently (sub-)tropical and midlatitude regions lack observations around sunrise and sunset (i.e. twilight). The discretized \(\theta_{0}\)-dependent albedo models that were used to interpolate the RSF diurnal cycle during daytime (Section 3.3.1) are not suitable for extrapolation beyond solar zenith angles of 84\({}^{\circ}\). In (sub-)Polar regions, however, observations near the terminator are common, but the low illumination conditions make observation-based RSF retrievals difficult, for instance it complicatesthea proper scene type identification required for the narrowband-to-broadband conversion and for the ADM. Hence, rather than relying on observations, RSF in twilight conditions needs to be simulated using a model. Such models can simulate the physical processes, for example, RTMs. However, their disadvantages, as mentioned in Section 1, are only aggravated in twilight conditions: first, the computational complexity increases (it becomes harder to achieve stable solution for the equations); furthermore, the illumination geometry becomes fully three-dimensional which requires a different kind of calculation and input data (e.g., cloud profiles); also, the nature of the required parameters changes, for example, surface parameters become less important at the cost of atmospherical parameters. Finally, radiative transfer simulations in twilight conditions should account for the Earth's curvature and the Earth's tangent radiation (radiation that goes through the atmosphere without touching the surface). These effects are not simulated in most of the (plane parallel) radiative transfer models. The above mentioned obstacles were avoided by making use of a \(\theta_{0}\)-dependent empirical twilight model which needs very few input data (static surface map and easily retrievable binary cloud mask). In contrast to the Level-2 albedo retrieval, the twilight coefficients \(A\) (intercept) and \(B\) (slope) (Table 2) were calculated for each observation, regardless of day- or nighttime. This was done based on its observed scene type, that is, the combination of _TWL surface type_ (Table 4) and cloud cover. There was no cloud cover weighting, since the cloud mask is binary (either overcast or clear-sky). However, for surface type there is some need for weighting, more specifically for the sea ice: the TWL surface type \"(1) sen ice, 100%\" is for pure sea ice surfaces. Hence, a weighted average was made for sea ice and water depending on their relative areal share of sea ice in the pixel. For each observation, the associated twilight coefficients were assigned to the temporally closest 5 min bin (Figure 9). Because the pixel's scene type may vary between subsequent observations throughout the day (changing cloud cover, sea ice concentration), these scene type dependent coefficients were linearly interpolated (orange and cyan lines in Figure 9). Finally, for each twilight 5 min bin (purple boxes in Figure 9), a flux was calculated (\(F_{twilight}\); Wm\({}^{-2}\)) by combining the interpolated \(A\) and \(B\) coefficients with their corresponding bin-specific Solar Zenith Angle (\(\theta_{0}\), degrees) in Equation (1). When the result was lower than the all-sky twilight model by [PERSON] and [PERSON] (2017), cfr. the dotted lines in Figure 3, it was matched to the latter. This was done because the linear Flux-\(\theta_{0}\) relation is not valid anymore for very small fluxes (\(\theta_{0}>90^{\circ}\)) where it is characterized by a smooth asymptotic transition to the nighttime zero flux. Figure 9: Conceptual example of interpolating Twilight Coefficients \(A\) and \(B\). 3.3.3. Nighttime Conditions (\(\theta_{0}>100^{\circ}\))  
For all the 5 min bins with nighttime conditions (\(\theta_{0}>100^{\circ}\)) the flux was set to zero. \[F_{night}=0.0\,\mathrm{Wm}^{-2}. \tag{7}\]  
3.3.4.