## 3 UVSQ-SAT Data Method and Map Reconstruction of the Variables (Observations and Model)
### Reconstruction Method of the ERA 5 Maps to Compare with the UVSQ-SAT Maps  
To compare the UVSQ-SAT measurements and a model (ERA 5), it is necessary to have similar inputs that means, i.e., to have the same observations time series (temporal) and similar FOV (spatial) at TOA. Figure 9 shows the monthly averaged maps of the albedo and the OLR in February 2021 (for the ERA 5 model). All data of the ERA 5 model were used to obtain these maps (temporal resolution of 1 h and a pixel resolution of 721 \(\times\) 1440). Figure 9: (**Top**) Albedo from ERA 5 during the month of February 2021. (**Bottom**) OLR from ERA 5 during the month of February 2021. Albedo is computed by the ratio of the difference of the incident shortwave radiation and the net shortwave radiation by the incident shortwave radiation. Surfaces that reflect a lot of the light falling on them have a high albedo. Surfaces that don't reflect much light have a low albedo. Albedo values vary across the globe with latitude. At the poles, it can be greater than 0.7 in some areas. This is a result of the lower solar angle present at the poles but also the higher presence of fresh snow, ice, and smooth open water. In the tropics (23.5\({}^{\circ}\)N to 23.5\({}^{\circ}\)S), albedo is between 0.1 to 0.4. OLR values vary also across the globe with latitude, and is primarily sensitive to near-surface and atmospheric temperatures, the air humidity, and the presence of clouds, which are related to the intensity of convective activity as well as the latitude and altitude dependence of the variability. Low OLR values (\(<\)200 Wm\({}^{-2}\)) associated with deep atmospheric convection are found over the equatorial land masses, Amazon basin, and in the western equatorial Pacific. These maps highlight the finesse of the observations (notably in equatorial Atlantic ocean). These details will disappear when increasing the FOV, and consequently degrade the spatial resolution. Considering the ground track of UVSQ-SAT in February 2021 (with same spatio-temporal observations), it is possible to reconstruct new albedo and OLR maps from the ERA 5 model. The impact of the FOV (related to \(\sigma\)) also has a significant effect on the map reconstructions. Figure 10 shows the reconstructed map of the albedo for the ERA 5 model for \(\sigma=1^{\circ}\) and \(\sigma=180^{\circ}\). Figure 11 shows the reconstructed map of the OLR for the ERA 5 model for \(\sigma=1^{\circ}\) and \(\sigma=180^{\circ}\). Figure 10: (**Top**) Albedo (ERA 5) during the month of February 2021 from same observation than UVSQ-SAT (\(\sigma=1^{\circ}\)). (**Bottom**) Albedo (ERA 5) from same observation than UVSQ-SAT (\(\sigma=180^{\circ}\)). These reconstructed maps are slightly different from the ERA 5 monthly averaged data (Figure 9). The selected data (same spatio-temporal resolution than UVSQ-SAT) related to the ground track of the satellite (Figure 7) have an impact on the reconstructed maps (clearly visible for albedo when increasing \(\sigma\)). Low OLR values in the equatorial Atlantic ocean disappear (Figure 11 Bottom) due to the lack of data and low spatial resolution. These simulations show the importance for doing the right comparisons between model and observations (same spatio temporal resolution). That's why, other methods are under investigation to improve the finesse of the details to be restored (albedo and OLR maps). In a second approach, it is planned to use the spherical harmonics method developed by [PERSON] et al. (2017)([PERSON] et al., 2017) to reconstruct the maps of the quantities of interest.