## 5 Results
### Evolution of Earth's TOA Radiative Fluxes and EEI Since 2013
The NET radiative flux (NET\({}^{*}\)) was therefore calculated according to Equation (6), incorporating the offset-corrected values for TSI (Sun), OSR (SW\({}^{*}\)), and OLR (LW\({}^{*}\)). \[\mathrm{NET}^{*}=\left(\frac{\mathrm{TSI}}{4}-\left\langle\frac{\mathrm{TSI}} {4}\right\rangle+0.17\right)-\left(\mathrm{OSR}-\left\langle\mathrm{OSR} \right\rangle-1.10\right)-\left(\mathrm{OLR}-\left\langle\mathrm{OLR}\right\rangle +0.40\right) \tag{6}\]  
These corrections ensured that the initial Uvsq-Sat measurements, starting from early 2021, were aligned with CERES reference levels. This adjustment allowed for a more meaningful assessment of the variability in radiative fluxes over time. Figure 6 shows the temporal evolution of the various time series from both Uvsq-Sat and CERES (EBAF and SSF1 deg). Satellite-based observations from CERES indicate that EEI was approximately +0.8 Wm\({}^{-2}\) in January 2013. While this value was not used as a fixed reference, it served as the starting point of the time series (Figure 6). To better analyze temporal variability, the EEI was set close to zero in January 2013, providing a relative baseline for assessing subsequent changes. Between January 2013 and October 2024, CERES data reveal an increase in EEI at TOA of +0.7 Wm\({}^{-2}\), corresponding to a linear trend of about +0.06 Wm\({}^{-2}\) per year. Between 2021 and 2024, the CERES and Uvsq-Sat data generally agree well. However, a temporal offset of approximately six months was observed between Uvsq-Sat and CERES measurements of OSR, OLR, and NET fluxes during 2022-2023, with Uvsq-Sat showing earlier variations. This discrepancy may be attributed to differences in instrument characteristics, such as angular sampling, retrieval algorithms, data filtering methods, and the fact that the satellites do not observe exactly at the same local solar time. Additionally, the relatively small amplitude of flux variations increases the sensitivity of the comparison to minor differences. Despite this offset, Uvsq-Sat data follow CERES general trends and confirm a peak in EEI in mid-2023, followed by a decline starting in late 2023 and continuing into 2024. This suggests the activation of stabilizing feedback mechanisms after the 2023 El Nino event. This pattern mirrors the post-El Nino response observed after the 2009/2010 event, although the decline was less pronounced following the 2015/2016 El Nino. It is important to note, however, that the decline observed in 2024 still occurred within an overall upward trend in EEI over the past decade, with solar activity and the 2022 eruption of the Hunga Tonga volcano playing a negligible role. EEI fluctuates over time, exhibiting periods of increase and decrease, but follows a persistent upward trend that has intensified notably since the 1980s. [PERSON] et al. (2024) [45]  
Figure 6: 12-month running means of global relative anomalies in ERB from Uvsq-Sat and CERES data (EBAF and SSF1 deg products). The grey area represents the uncertainty range of the Uvsq-Sat data. The overall patterns of the EBAF and SSF1 deg time series are broadly consistent. However, beginning in mid-2021, notable discrepancies emerge in both OSR and OLR. reported a rise of +0.96 Wm\({}^{-2}\) over the 2011-2023 period, while [PERSON] et al. (2024) [46] attributed both the trend and inter-annual variability in EEI to a combination of radiative forcing and surface temperature changes. The doubling of the EEI over the past decade can be explained by a combination of anthropogenic forcing--primarily GHGs emissions--and feedbacks such as increased water vapor, reduced cloud cover, and diminishing sea ice, all of which enhance solar absorption. Internal variability also played a major role: a shift in the PDO from a cold to a warm phase around 2014 likely amplified the EEI by decreasing cloud cover over the Pacific Ocean, leading to greater solar radiation absorption. This warm phase persisted until about 2020, overlapping with the period of rapid EEI increase.