## 5 Results
### OHC and EEI as Complementary Measurements  
OHC measurements and TOA EEI observations provide complementary and interconnected perspectives on Earth's energy budget. While EEI quantifies the net radiative flux entering and leaving the Earth system, OHC reflects the cumulative storage of this energy, primarily in the oceans, which absorb over 89% of the excess heat from global warming. Between 2013 and 2024, the ocean heat content (0-2000 m) increased steadily from approximately 160 to 300 ZJ, indicating a nearly doubling of accumulated heat. This gradual rise highlights OHC's role as a robust long-term climate indicator, less sensitive to short-term atmospheric variability such as EI Nino events. It is physically more meaningful to compare the rate of change of ocean heat content, \(\partial\)OHC/\(\partial t\), with EEI, as the latter represents the instantaneous net energy flux into the Earth system, while the former represents its dominant heat sink [48; 49]. Direct comparison of absolute OHC and EEI time series may obscure their dynamical relationship due to OHC's cumulative nature and differing response timescales. Studies consistently show a strong correspondence between \(\partial\)OHC/\(\partial t\) and EEI: [PERSON] and [PERSON] (2021) [48] demonstrated near one-to-one tracking of these quantities through 2019; [PERSON] et al. (2021) [49] estimated average ocean heat uptake at \(0.62\pm 0.10\) Wm\({}^{-2}\) compared to CERES EEI of 0.77 \(\pm\) 0.10 Wm\({}^{-2}\) over 2005-2019; [PERSON] et al. (2022) [50] used satellite altimetry and gravimetry to derive OHC changes and confirmed strong agreement with CERES EEI over 2002-2016. Furthermore, [PERSON] et al. (2021) [24] reported a near doubling of EEI from 2005 to 2019, consistent with ocean heat uptake trends. The Copernicus Ocean State Report 2024 [51] extended this OHC-EEI comparison to 1993-2022, further confirming the close linkage. [PERSON] et al. (2019) [52] provide a comprehensive review of multiple methods to estimate OHC and EEI, emphasizing \(\partial\)OHC/\(\partial t\) as the primary physical linkage between ocean and TOA energy measurements. Figure 8 presents the temporal evolution of \(\partial\)OHC/\(\partial t\) and EEI from CERES since 2013, along with EEI from Uvsq-Sat since 2021, highlighting their agreement and reinforcing the critical role of ocean heat uptake in modulating Earth's energy imbalance. EEI derived from satellite observations provides a global, integrated measure of the Earth's energy budget, quantifying the difference between incoming solar radiation and outgoing long-wave (infrared) radiation at TOA. This approach captures energy exchanges across all Earth system components--including the ocean, atmosphere, cryosphere, and land--and enables near-real-time monitoring of the energy imbalance. The CERES historical record indicates that EEI has approximately doubled over the course of its observational period [35]. During the first decade of CERES measurements (March 2000 to February 2010), the average EEI was +0.5 \(\pm\) 0.2 Wm\({}^{-2}\). In contrast, during the most recent decade (January 2013 to December 2022), it increased to +1.0 \(\pm\) 0.2 Wm\({}^{-2}\), reflecting an intensification of net energy accumulation in the Earth system. Between 2021 and 2024, EEI derived from Uvsq-Sat averaged +0.87 \(\pm\) 0.23 Wm\({}^{-2}\), closely aligning with the recent CERES trend with clear responses to EI Nino and La Nina events. However, as previously mentioned, a temporal offset of approximately six months occurred during the 2022-2023 period between Uvsq-Sat and CERES measurements of OSR, OLR, and NET radiative flux, with Uvsq-Sat capturing these variations earlier. Furthermore, \(\partial\)OHC/\(\partial t\) data over the same period exhibit partially divergent behavior, both in the timing and magnitude of heat uptake.