# Variability and Trends in Earth's Radiative Energy Budget from Uvsq-Sat (2021-2024) and CERES Observations (2013-2024)

Mustapha Meftah, Christophe Dufour, Philippe Keckhut, Alain Sarkissian, Ping Zhu

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Mustapha Meftah, Christophe Dufour, Philippe Keckhut, Alain Sarkissian, Ping Zhu. Variability and Trends in Earth's Radiative Energy Budget from Uvsq-Sat (2021-2024) and CERES Observations (2013-2024). Remote Sensing, 2025, 17 (16), pp.2751. 10.3390/rs17162751. hal-05206886

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# Variability and Trends in Earth's Radiative Energy Budget from Uvsq-Sat (2021–2024) and CERES Observations (2013–2024)

Mustapha Meftah<sup>1,*,† ID</sup>, Christophe Dufour<sup>1,† ID</sup>, Philippe Keckhut<sup>1,† ID</sup>, Alain Sarkissian<sup>1,† ID</sup> and Ping Zhu<sup>2,3,† ID</sup>

## Abstract

The Earth's Radiation Budget (ERB) is a critical component for understanding the planet's climate system, as it governs the balance between incoming solar energy and outgoing thermal radiation. Accurate monitoring of the ERB, combined with Ocean Heat Content (OHC) measurements, is essential to assess Earth's Energy Imbalance (EEI) and its implications for global warming. This paper presents new results on the ERB based on data from the Uvsq-Sat and Inspire-Sat nanosatellite missions, which operated from 2021 to 2024. These satellites constitute the first European constellation demonstrator designed for broadband, Wide Field-Of-View (WFOV) measurements of the ERB. While WFOV instruments provide enhanced temporal and spatial coverage, they do not replace the need for Narrow Field-Of-View (NFOV) measurements, such as those provided by the established Clouds and the Earth's Radiant Energy System (CERES) instruments. Instead, they are designed to complement them. By using data from both the WFOV constellation and CERES instruments to measure Reflected Solar Radiation (RSR) and Outgoing Longwave Radiation (OLR), we estimate the EEI and monitor its evolution. Our analysis reveals a generally good agreement between Uvsq-Sat and CERES data for EEI from 2021 through the end of 2024. Over this period, EEI derived from Uvsq-Sat averaged +0.87 ± 0.23 Wm⁻<fnref n="2" />, closely matching the recent CERES trend. Both datasets indicate a peak in EEI in mid-2023, followed by a decline throughout 2024, likely reflecting stabilizing feedbacks triggered by the 2023 El Niño event. Importantly, this short-term decline occurred within a sustained upward trend in EEI since 2013, as shown by CERES observations, with solar activity having a negligible impact. Comparisons with OHC measurements confirm ongoing ocean heat accumulation, consistent with the rising decadal trend in EEI. These insights underscore the importance of continuous, high-frequency observations to capture the complex and rapidly evolving processes influencing Earth's energy balance. Demonstrations using nanosatellites at different local times illustrate the advantages of small satellite constellations for improved monitoring frequency and coverage, particularly for variables that change over short time scales, such as RSR, also known as Outgoing Shortwave Radiation (OSR).

**Keywords:** Earth's Radiation Budget; Earth's Energy Imbalance; climate change; satellites

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Academic Editors: Manuel Antón, Zhuosen Wang, Dominique Carrer, Christian Lanconelli and Angela Erb

Received: 22 June 2025

Revised: 2 August 2025

Accepted: 5 August 2025

Published: 8 August 2025

**Citation:** Meftah, M.; Dufour, C.; Keckhut, P.; Sarkissian, A.; Zhu, P. Variability and Trends in Earth's Radiative Energy Budget from Uvsq-Sat (2021–2024) and CERES Observations (2013–2024). *Remote Sens.* **2025**, *17*, 2751. https://doi.org/10.3390/rs17162751

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ LATMOS/IPSL, UVSQ Université Paris-Saclay, Sorbonne Université, CNRS, 78280 Guyancourt, France; christophe.dufour@latmos.ipsl.fr (C.D.); philippe.keckhut@latmos.ipsl.fr (P.K.); alain.sarkissian@latmos.ipsl.fr (A.S.)</footnote>

<footnote n="2">² Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China; pzhu@szu.edu.cn</footnote>

<footnote n="3">³ Tiandu-Shenzhen University Deep Space Exploration Joint Laboratory & Space Science Center, Shenzhen University, Shenzhen 518060, China</footnote>

<footnote>* Correspondence: mustapha.meftah@latmos.ipsl.fr; Tel.: +33-1-80-28-51-79</footnote>

<footnote>† These authors contributed equally to this work.</footnote>
# 1. Introduction

Global warming results from anthropogenic GreenHouse Gases (GHGs) emissions, which disrupt the delicate balance between incoming solar radiation and the Earth's reflected shortwave and emitted longwave (thermal) radiation. Understanding these energy exchanges within the Earth-atmosphere system is therefore essential. One of the earliest relatively comprehensive assessments of these exchanges was presented by Kiehl and Trenberth (1997) [1], as illustrated in Figure 1. This energy budget was later thoroughly revised by Stephens et al. (2012) [2]. The Earth's climate is fundamentally governed by radiative energy fluxes at the Top-Of-Atmosphere (TOA) boundary. The Earth's Radiation Budget (ERB) quantifies both the incoming and outgoing radiative energy at the TOA and comprises three principal components: the Incoming Solar Radiation (ISR), also known as Total Solar Irradiance (TSI); the Reflected Solar Radiation (RSR), also referred to as Outgoing Shortwave Radiation (OSR); and the Outgoing Longwave Radiation (OLR), which represents thermal energy emitted by the Earth. Due to their critical importance for understanding and predicting climate change, these ERB components are classified as Essential Climate Variables (ECVs), whose continuous monitoring is mandated by the Global Climate Observing System (GCOS) under the coordination of the World Meteorological Organization (WMO). Among these parameters, the Earth's Energy Imbalance (EEI) is particularly significant, as it provides a direct measure of the net radiative forcing driving climate change [3,4]. Defined as the residual between incoming and outgoing energy fluxes—EEI = ISR – OSR – OLR—this imbalance reflects the energy state of the Earth system and serves as a critical metric for assessing the current status and progression of global climate change. One of the latest Earth heat inventories [5] reveals that the Earth system has persistently accumulated heat, with an estimated total of 381 ± 61 ZettaJoules (ZJ) added between 1971 and 2020. This corresponds to a heating rate, or EEI, of 0.48 ± 0.1 Wm⁻². The vast majority of this accumulated heat—approximately 89%—is stored in the oceans, followed by about 6% on land, 1% in the atmosphere, and roughly 4% contributing to the melting of the cryosphere.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Earth's annual global mean energy budget based on the Kiehl and Trenberth study (1997) [1].</figcaption></figure>
The Earth's radiation budget can be monitored using two complementary approaches: in situ ocean measurements and space-based satellite observations. In situ measurements, such as those from the Argo network [6], provide highly accurate estimates of EEI over long timescales but are limited in capturing short-term variations due to sampling constraints. Alternatively, satellite instruments offer continuous and global coverage of the ERB by measuring both incoming solar radiation and outgoing Earth radiation with higher temporal resolution and stability. Together, these methods provide a comprehensive picture of the Earth's radiative energy exchanges. Among these, satellite measurements play a crucial role in monitoring the ERB, particularly at the TOA boundary, where incoming solar and outgoing terrestrial radiation are most directly observed. To date, seven Clouds and the Earth's Radiant Energy System (CERES) instruments have been launched aboard five satellites—the Tropical Rainfall Measuring Mission (TRMM), Terra, Aqua, Suomi National Polar-orbiting Partnership (S-NPP), and NOAA-20—providing essential diurnal and angular sampling of the Earth's radiative fluxes. To capture the full diurnal cycle, the seven CERES instruments have operated over time from two complementary satellite orbital configurations, one with a Local Time of Descending Node (LTDN) around 10:00 a.m. and another with a Local Time of Ascending Node (LTAN) near 2:00 p.m., with some missions still ongoing and others now completed. Thanks to multiple CERES instruments aboard different satellites operating at varying local times, a robust understanding of Earth's radiation budget has been established. While significant progress has been made in sampling the diurnal cycle, improving the absolute accuracy of EEI measurements remains a key challenge—alongside the need for broader coverage across a wider range of local observation times. To address these issues, innovative approaches have been explored. Gristey et al. (2017) [7] demonstrated that a notional Earth Observation Radiometer constellation using Wide Field-Of-View (WFOV) broadband radiometers can retrieve both spatial and temporal information with high fidelity. However, despite the improved sampling such constellations offer, Wong et al. (2018) [8] argued that ensuring precise calibration and inter-calibration among WFOV radiometers remains a major obstacle—drawing on lessons from instruments like those flown on the Earth Radiation Budget Experiment (ERBE) [9]. In particular, Wong et al. (2018) [8] identified several sources of uncertainty in non-scanner radiometers, including on-orbit gain and offset variations due to thermal effects, radiometric degradation (especially in the shortwave), uncertainties from flux inversion for anisotropic radiance fields, inter-satellite calibration inconsistencies due to footprint mismatches, and biases introduced by changes in satellite altitude. These limitations, inherent to WFOV non-scanner instruments and the complexity of radiative flux retrieval, highlight the persistent challenge of achieving the radiometric precision necessary for climate monitoring. Consequently, several methods have been proposed to determine the EEI, but none have yet achieved the required accuracy [4]. Nevertheless, recent advances in instrument technology and the growing availability of small satellite platforms have renewed interest in employing broadband non-scanning WFOV instruments for EEI measurements. As part of our effort to monitor the ERB, we have developed and deployed a series of small satellite demonstrators in orbit since 2021. This initiative led to the design and implementation of a heterogeneous constellation of satellites with WFOV instruments, representing the first European program specifically dedicated to such measurements. Uvsq-Sat, the inaugural mission [10], was launched on 24 January 2021 into a Sun-Synchronous Orbit (SSO) with an LTDN of approximately 9:30 a.m., and remained operational until its atmospheric reentry on 30 October 2024. The second mission, Inspire-Sat [11], was launched on 15 April 2023, with an LTAN of 10:30 a.m. and re-entered the atmosphere on 18 September 2024. Most recently, the third satellite, Uvsq-Sat NG [12–14], was launched on 15 March 2025 into a similar orbit, with an LTAN close to 10:25 a.m. at an altitude of 600 km. This new mission
is expected to ensure the continuity of the measurement series initiated by the previous
satellites, strengthening our long-term commitment to ERB monitoring.

This manuscript focuses on observations made by the Uvsq-Sat and Inspire-Sat satel-
lites between February 2021 and October 2024, as well as those from CERES between 2013
and the end of 2024. In Section 2, we emphasize the importance of measuring both the
Earth's radiation budget and the Earth's energy imbalance. Section 3 briefly introduces
the Uvsq-Sat and Inspire-Sat CubeSats, their Earth Radiative Sensors (ERS), calibration
methods, and how they address key challenges in ERB observations. Section 4 presents
the methodology used to process data from the Uvsq-Sat and Inspire-Sat missions based
on orbital time-series. In Section 5, we present new ERB observations at TOA from the
Uvsq-Sat mission, covering the period from February 2021 to October 2024. We analyze
global trends and variability in TOA radiation and compare our findings with those from
the CERES dataset. We further investigate the potential drivers of the observed radiative
changes, including natural variability (e.g., El Niño, La Niña, and the Pacific Decadal
Oscillation (PDO)), GHGs forcing, and the influence of clouds and aerosols. To assess con-
sistency across Earth's energy reservoirs, we compare our radiative flux measurements with
independent Ocean Heat Content (OHC) estimates. Finally, we emphasize the advantages
of deploying a constellation of small satellites equipped with WFOV sensors to enhance
spatial and temporal coverage, paving the way for improved global climate monitoring.

## 2. Importance of ERB at TOA and EEI Measurements for the Next Decades

The GCOS currently identifies 55 ECVs critical for understanding and characterizing
Earth's climate, with approximately 60% relying heavily on satellite Earth observation
data. Collectively, all these variables offer a comprehensive picture of the evolving global
climate system and serve as fundamental indicators for informing climate mitigation and
adaptation strategies, assessing climate risks, attributing climatic events to their underlying
causes, and supporting climate services. Among these variables, ERB is a key component,
as it directly reflects the planet's energy balance and climate dynamics. Variations in
ERB indicate changes in energy accumulation within the climate system, primarily in
the oceans, making it a fundamental metric for assessing global warming. Accurate
ERB measurements are crucial for understanding climate processes, validating climate
models, and guiding mitigation strategies. Observations of ERB at TOA are only achievable
via satellite platforms. Currently, datasets from the CERES Energy Balanced and Filled
(EBAF) Edition 4.2.1 [15] are available, providing monthly mean TOA shortwave, longwave,
and net radiative fluxes on a 1° × 1° spatial grid. These data offer enhanced spatial and
temporal detail for analyzing the Earth's energy budget.

For the period 2000–2010, Stephens et al. (2012) [2], using satellite data primarily
from the CERES mission, estimated the incoming solar radiation at 340.2 ± 0.1 Wm⁻²,
the reflected solar radiation at 100 ± 2 Wm⁻², and the outgoing longwave radiation at
239.7 ± 3.3 Wm⁻². While determining absolute values of Earth's radiative fluxes is impor-
tant—as it allows for direct comparisons—it remains a challenging task due to calibration
uncertainties and instrumental biases. Thus, one can account for inter-satellite biases and
place greater emphasis on analyzing the variability and anomalies in these fluxes, which
are particularly useful for understanding changes in the energy balance and the global
climate system.

Prior to the industrial era, approximately before 1850, Earth's energy balance is as-
sessed to have been close to equilibrium, with net radiative forcing near zero. This conclu-
sion is supported by multiple lines of evidence, including: the synthesis of pre-industrial
energy balance estimates presented in Chapter 7 [16] of Working Group I of the Intergovern-
mental Panel on Climate Change (IPCC)'s Sixth Assessment Report (AR6); observational and model-based updates to Earth's energy budget reported by Stephens et al. (2012) [2]; the conceptual framework of near-equilibrium conditions prior to anthropogenic forcing articulated by Hansen et al. (2005) [17]; historical analyses of surface and TOA energy fluxes reviewed by Wild et al. (2013) [18]; and energy budget constraints on climate response from the pre-industrial state discussed by Otto et al. (2013) [19].

With the onset of industrialization in the mid- to late 19th century, atmospheric concentrations of GHGs such as carbon dioxide ($CO_2$) and methane ($CH_4$) began to rise. However, the increase in EEI during this period remained small or nearly neutral, largely due to compensating effects from natural variability—such as volcanic eruptions—and the growing influence of anthropogenic aerosols, which exerted a cooling effect by reflecting sunlight at specific wavelengths of the solar spectrum [20,21].

Throughout the 20th century, particularly after 1950, EEI began to increase more noticeably as GHGs emissions intensified. Nevertheless, this trend was partially masked by elevated levels of aerosol pollution, especially in the Northern Hemisphere, which continued to offset some of the warming by enhancing Earth's reflectivity.

Since the early 1980s—during the satellite era—space-based observations have shown that EEI has become persistently positive, indicating that Earth is accumulating energy. Combined satellite and OHC data reveal an average EEI of approximately +0.5 Wm⁻² between 1971 and 2020, rising to around +0.74 Wm⁻² during the 2006–2020 period [5]. Recent satellite data indicate that the EEI is rising at a rate much faster than climate models have projected, reaching approximately +1.8 Wm⁻² in 2023 [22]—nearly twice the best estimate presented in the IPCC AR6 [16]. This increase has more than doubled over the past two decades, challenging the ability of state-of-the-art climate models to fully reproduce the observed acceleration [23]. Several factors contribute to this rapid increase in EEI. First, Loeb et al. (2021) [24] attribute it to a reduction in Earth's reflectivity caused by decreased cloud cover and sea ice extent. At the same time, a reduction in OLR is driven by increased concentrations of trace GHGs and water vapor. Radiative forcing from GHGs has grown substantially, with Kramer et al. (2021) [25] reporting an increase in instantaneous radiative forcing from +0.42 to +0.64 Wm⁻² between 2003 and 2018. Meanwhile, the cooling effect of anthropogenic aerosols—caused by their reflection of sunlight and interactions with clouds—has diminished. This trend is reinforced by international regulations such as the International Maritime Organization (IMO)'s MARPOL Annex VI, which mandates reduced sulfur content in marine fuels. The global sulfur cap was lowered from 3.5% to 0.5% on 1 January 2020 (IMO 2020), following stricter limits already applied in Sulfur Emission Control Areas (SECAs) since 2015. As a result, marine sulfur dioxide ($SO_2$) emissions and consequently sulfate aerosol concentrations have significantly decreased—particularly impacting stratocumulus cloud formation in regions like the Peruvian coast. With fewer aerosols acting as cloud condensation nuclei, the frequency and optical thickness of marine stratiform clouds may decrease, allowing more solar radiation to reach the surface and thereby altering local atmospheric dynamics. These aerosol-related changes are supported by studies from Subba et al. (2020) [26] and Quaas et al. (2022) [27], which noted an increase in TOA forcing by +0.17 Wm⁻² per decade from 2000 to 2017. The reduction in aerosols likely contributed to increased solar absorption, compounding the warming effects of GHGs. Additional indirect effects on clouds may also be involved. Moreover, recent Sea Surface Temperature (SST) patterns, such as reduced low-level cloud cover in the subtropical Pacific, appear to be amplifying solar absorption to levels exceeding model predictions [28]. Beyond these anthropogenic influences, natural factors also play a role. The notable temperature peak in 2023 coincides with the transition from La Niña to El Niño conditions, which increased global surface temperatures but paradoxically reduced the net
EEI due to enhanced outgoing radiation, as we will show in this study. Additionally, the in-
jection of water vapor into the stratosphere following the Hunga Tonga volcanic eruption
may have contributed a transient warming effect of approximately +0.16 Wm⁻² [29,30],
although some studies suggest compensatory cooling effects in the upper atmosphere [31].
Another contributing factor is the solar cycle. Solar activity follows an approximately 11-
year cycle that modulates TSI by about 0.1%. Solar Cycle 25, which began at the end of 2019,
is showing a gradual increase in solar activity compared to the previous minimum. While
the contribution of this cycle to global warming is real, its impact on Earth's global mean
surface temperature remains minor—estimated at no more than 0.1 °C. The recent warming
and record temperatures in 2023–2024 were primarily driven by anthropogenic forcing (e.g.,
CO₂ and CH₄), with solar variability playing only a secondary role. Events such as the
2023–2024 El Niño further amplified surface temperatures but do not explain the long-term
trend. Other influences include regional changes such as a reduction in Saharan dust
affecting North Atlantic warming, the radiative effects of wildfires (e.g., a −0.18 Wm⁻²
effective radiative forcing between 2014 and 2022 [32]), and potential modulation of local
energy fluxes due to ocean circulation changes (e.g., Atlantic Meridional Overturning Circ-
culation, AMOC) and the so-called Cold Ocean–Warm Land (COWL) effect [33]. Overall,
the observed acceleration in EEI reflects a complex interplay of anthropogenic forcing,
feedback mechanisms, and natural variability. Understanding how reductions in aerosols
contribute to warming via cloud changes remains a key challenge. The temperature peak
of 2023 likely results from a combination of factors—GHGs, aerosols, volcanic activity,
solar variability, El Niño–Southern Oscillation (ENSO) dynamics, and transient ocean–land
interactions. Whether the net EEI is directly linked to this temperature peak remains an
open question that requires further investigation.

Monitoring EEI is therefore essential for quantifying the rate of global warming and
tracking heat accumulation in the climate system [3]. It is a key metric for validating climate
models and improving projections of future scenarios. Moreover, EEI helps disentangle the
contributions of different forcing agents, such as GHGs, aerosols, and natural variability,
and serves to guide mitigation and adaptation policies by directly measuring changes
in Earth's energy state [34]. EEI leads to heat accumulation in the atmosphere, oceans,
and land, thereby accelerating cryospheric melt [5]. As a result, this energy surplus drives
global temperature increases, sea-level rise, and the growing intensity and frequency of
extreme weather events (IPCC, 2021). Despite the fundamental role of EEI in governing
the climate system, the ERB observational capacity is rapidly declining as essential satel-
lite missions are decommissioned [35]. To avoid potential gaps and setbacks, since the
2010s, we have actively pursued alternative observation strategies based on the use of
small satellites (Uvsq-Sat constellation) to complement measurements made by CERES.
We now look forward to the timely implementation of the Libera mission (named after the
Roman goddess Libera, who is sometimes associated with fertility and, on rare occasions,
identified with Proserpina), which is scheduled for launch in late 2027 aboard NOAA's Joint
Polar Satellite System-3. This mission will be able to conduct observations in parallel with
the Uvsq-Sat NG demonstrator, which was launched into orbit in March 2025. The data
provided by these satellites over short time periods are also highly valuable. In addition
to these efforts, the Earth Radiation Measurement (ERM) instruments flown aboard the
Fengyun-3 (FY-3) series of Chinese satellites since 2008 [36,37] have provided continuous
broadband and spectral measurements, contributing to long-term monitoring of the Earth's
radiation budget. Furthermore, the Moon-based Earth Radiation Budget (MERB) instru-
ment aboard Chang'e-7 [38] will enable complementary observations of Earth's radiation
budget from the Moon starting in 2026–2027.
These insights underscore the critical importance of maintaining and enhancing high-precision satellite observations to disentangle the intricate drivers of Earth's radiative energy balance and improve projections of future climate change. Indeed, continuing existing missions and proposing new ones reduce the likelihood of data gaps. This continuity is also essential for supporting the validation of datasets such as ERA5, the fifth-generation global reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). While ERA5 does not assimilate ERB measurements, these observations are widely used by the ECMWF and other major climate modeling and reanalysis centers to independently evaluate and improve the accuracy of atmospheric, land, and oceanic variables estimated at high temporal and spatial resolution.

**3. Instrument Description, Calibration, and Relevance to ERB Measurement Challenges**

Uvsq-Sat [10] is a CubeSat developed by LATMOS and launched in January 2021 into an SSO orbit at approximately 540 km altitude. Its primary objective was to demonstrate the feasibility of using miniaturized instrumentation to monitor ERB, focusing on OSR and OLR. The satellite carries ERS sensors, thermopile-based detectors designed for broadband radiative flux measurements. Each of the six satellite faces is equipped with two ERS units—one coated with bonded Vantablack S-IR carbon nanotubes (Surrey NanoSystems Ltd., UK) for near-unity absorptivity across the UV-to-far-infrared range, and one with an optical solar reflector (Excelitas Technologies (as Qioptiq), UK) for spectral selectivity. These sensors capture radiative flux via thermoelectric conversion, without the need for scanning mechanisms, and offer a WFOV for instantaneous flux detection. A second Cube-Sat, Inspire-Sat [11], was launched in April 2023 into a similar SSO orbit at 508 km. Also developed by LATMOS, it carries the same ERS instruments. The mission goal is to extend ERB monitoring by providing temporal coverage at a different local solar time (10:30 a.m. for Inspire-Sat vs. 9:30 a.m. for Uvsq-Sat), thus improving sampling of the diurnal cycle in TOA fluxes when used in constellation. The ERS sensors underwent extensive pre-launch calibration. For characterizing the shortwave response (OSR), a radiometric calibration setup comprising a Xenon lamp coupled with a LATMOS Newtonian telescope was used to simulate solar illumination (30 Wm⁻²). For the longwave response (OLR), the LATMOS BX-500 blackbody—operated at controlled temperature set points between 323 K and 343 K—was used to test the instrument's ability to measure thermal radiative fluxes. Direct solar calibration was performed by integrating the CubeSats into the LATMOS/OVSQ INTRA Solar Tracker system, allowing exposure to solar irradiance (1000 Wm⁻²). This calibration was independently validated using ground-based pyranometers—specifically the Kimo SAM30 and Kipp & Zonen SMP6-V—to ensure consistency of the measurements. Additionally, the absolute calibration of the ERS was conducted on a dedicated test bench using a National Institute of Standards and Technology (NIST)-traceable 1000 W quartz halogen lamp (F-546) precisely aligned along the optical axis of Uvsq-Sat or Inspire-Sat using laser guidance. This lamp, calibrated by NIST and traceable to the International Temperature Scale of 1990 (ITS-90), provided a well-characterized spectral irradiance in the solar bands (approximately 1362 Wm⁻²). During calibration, the satellite instrument was positioned 50 cm from the lamp, and measurements were corrected for dark current. This procedure enabled the determination of the ERS's absolute response and transfer function, ensuring that the measurements were accurate. Finally, thermal vacuum chamber tests (LATMOS/OVSQ) were performed to evaluate sensor performance under space-like environmental conditions, with the chamber walls simulating the cold background of space and infrared radiation fields used to reproduce the thermal loads experienced in orbit. Together, these calibration and testing efforts yielded a pre-flight absolute uncertainty of
approximately ±5 Wm⁻² (1σ) for outgoing shortwave and longwave radiation measurements, supporting the reliability of ERS data throughout the mission [39]. In orbit, Uvsq-Sat and Inspire-Sat lack active onboard calibration systems (e.g., calibration lamps, reference gallium source [40], etc.), limiting direct tracking of instrument degradation. However, the choice of materials—bonded Vantablack S-IR and optical solar reflector—was made to mitigate this, as these coatings have demonstrated extremely low degradation in low Earth orbit environments. Wong et al. (2018) [8] provide a comprehensive review of the limitations inherent to non-scanner, WFOV instruments, such as those used on Uvsq-Sat and Inspire-Sat. Their analysis highlights several critical challenges affecting the accuracy and long-term reliability of TOA radiative flux measurements. One major concern is the degradation of optical coatings in orbit—particularly in the shortwave spectral region—which leads to on-orbit gain variations that require empirical and often uncertain correction strategies. In addition, thermal fluctuations can induce drifts in instrument offsets, complicating the separation of instrumental noise from the true radiative signal. Wong et al. (2018) [8] also emphasize the difficulties in achieving consistent inter-satellite calibration, especially when there are differences in sensor footprint sizes or limited opportunities for overlapping observations. The process of inverting radiance measurements to TOA fluxes introduces further complexity, particularly for shortwave radiation where angular anisotropy and scene-dependent geometry contribute substantial uncertainty. Moreover, edge effects within the instrument footprint and partial illumination—especially in limb or terminator regions—complicate radiative flux retrievals due to non-uniform scene brightness. Finally, changes in satellite altitude can bias flux measurements by altering footprint geometry and viewing angle, further affecting retrieval accuracy and comparability over time. These findings underscore the need for careful instrument design, calibration strategies, and data processing techniques when interpreting measurements from non-scanner CubeSat platforms.

In light of these challenges, the Uvsq-Sat and Inspire-Sat instruments were designed to minimize thermal gradients (use of thermal insulation material), electrical noise (use of high-stability resistors), and optical degradation (use of thermo-optical coatings with low aging in space conditions). While onboard correction mechanisms are not available, the ERS architecture and the use of inert, space-proven materials provide robust radiative flux measurements within the mission's targeted uncertainty envelope.

# 4. Methodology for Reconstructing TOA Radiative Flux Maps from Uvsq-Sat and Inspire-Sat Time-Series Data

We use time-series data from Uvsq-Sat [10] and Inspire-Sat [11] to reconstruct specific-date maps of OSR and OLR at TOA with 1° × 1° resolution. Then, by combining these maps with incoming solar radiation data from the Spectral And Total Irradiance REconstruction in the satellite era (SATIRE-S) model (Figure 2, Top), we can analyze the Earth's radiation budget and its energy imbalance over time.

## 4.1. *Times Series Used for the Flux Maps Reconstruction*

Time-series data from Uvsq-Sat and Inspire-Sat provide observations of the OSR and OLR at the TOA. The overlapping operational periods of these two CubeSats missions provide an opportunity to observe Earth's radiative fluxes at different solar local times and to analyze their diurnal and seasonal variability. Figure 2 shows the temporal evolution of radiative fluxes from Uvsq-Sat used in this study, including the TSI from the SATIRE-S reconstruction model. The Naval Research Laboratory Total Solar Irradiance (NRLTSI2) model [41,42] is not shown here, but it represents an alternative source, providing results similar to those of the SATIRE-S model. Both models can be used interchangeably.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (Top) Daily TSI from SATIRE-S and its monthly mean. (Middle) Uvsq-Sat OSR at TOA, shown with 30-second resolution data and monthly mean. The OSR exhibits a semi-annual modulation, reflecting the solar declination cycle and hemispheric alternation in insolation and albedo. (Bottom) Uvsq-Sat OLR at TOA, also shown with 30-second resolution data and monthly mean. The OLR shows a dominant annual cycle linked to the seasonal variation of global surface temperature.</figcaption></figure>

Figure 2 (Top) illustrates the upward trend in TSI flux, reflecting the increasing solar activity of Solar Cycle 25, which initiated in December 2019. The OSR flux (Figure 2, Middle) shows the day-night alternation, along with variability in the mean flux that highlights seasonal effects. In contrast, the OLR flux (Figure 2, Bottom) exhibits a less pronounced day-night cycle, while the seasonal variability is more evident. To reconstruct Earth's radiation flux maps, data were selected over specific time periods and under defined conditions (e.g., daytime, nighttime, both day and night, all-sky). Figure 3 presents an example of the spatial distribution of Uvsq-Sat observations in a global map, based on a selection covering the period from 1 March 2021 to 1 October 2024. A noticeably lower density of data points appears over France and Western Europe. This reduction in data availability is caused by radio frequency interference during satellite data downlinks to the LATMOS ground station located in Guyancourt (Yvelines, France), which affects the quality of measurements and results in fewer valid observations in this region. Additionally, no data samples are present over the poles due to the characteristics of the SSO Orbit. The orbital path does not pass directly over the extreme polar regions, and the satellite's viewing geometry further limits observations near the poles, leading to gaps in coverage in these areas.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Spatial distribution of observations from Uvsq-Sat between March 2021 and October 2024.</figcaption></figure>

It is important to note that the duration of the observation period significantly impacts data quality. The more data points are accumulated, the higher the accuracy of radiative flux estimates at each latitude and longitude. Generating global coverage maps from time series of OSR and OLR typically requires aggregating observations over a period of about 30 days. Due to their orbital characteristics and narrow swath widths, satellites like Uvsq-Sat and Inspire-Sat have limited instantaneous spatial coverage. By accumulating data over a month, it becomes possible to sample a wide range of latitudes and longitudes, effectively filling spatial gaps and enabling comprehensive global map. Using a satellite constellation provides a major advantage for maximizing observational coverage. Unlike a single satellite, a constellation comprises multiple satellites operating simultaneously in coordinated orbits, which increases both the frequency and spatial density of observations. This approach enables more complete and timely data collection across different latitudes and longitudes, thereby reducing spatial and temporal gaps in the datasets.

## 4.2. Map Reconstruction Method from Satellites Time Series

Based on the time-series data, we reconstructed monthly mean maps—or maps at specific dates—of radiative fluxes at the TOA over the entire Earth's surface. These maps have a spatial resolution of 1° by 1° in latitude and longitude, and they represent the spatial distribution of reflected shortwave (SW) fluxes and emitted longwave (LW) fluxes. Analyzing the temporal evolution of these maps enables the assessment of spatial and temporal variations in OSR and OLR. By also accounting for the variability of incoming solar radiation over time, we can estimate how energy accumulates within the Earth's climate system. The incoming solar radiation is derived from TSI estimates provided by the SATIRE-S model [43], which reconstructs solar irradiance based on variations in solar surface magnetism.

The method used to generate OSR and OLR maps from Uvsq-Sat data relies on a physically informed modeling of the satellite's observation geometry and radiative transfer conditions [39]. Each measurement represents an integral over the Earth's surface of the quantity of interest (OSR or OLR) and depends on a wide range of factors, including the Bidirectional Reflectance Distribution Function (BRDF) of the surface, the optical thickness
of the atmosphere (influenced by clouds, aerosols, temperature, and pressure), and the spectral and angular response of the satellite instruments—particularly their FOV.

The Earth is modeled as a regular grid in latitude and longitude. Each grid cell (i, j) has coordinates ($\lambda_i, \varphi_j$) and an area, as defined in Equation (1).

$$S_{ij} = R^2 \times \cos(\varphi_j) \times \Delta\lambda_i \times \Delta\varphi_j \quad (1)$$

The satellite position is described by its coordinates ($\lambda_{sat}, \varphi_{sat}$) and its altitude ($z_{sat}$). The angle $\theta_{ij}$ between the satellite and a surface pixel (i, j), measured from the Earth's center, is computed using spherical trigonometry while accounting for the Earth's shape as an oblate spheroid to improve accuracy. From $\theta_{ij}$, we derive the off-nadir angle $\alpha_{ij}$ and the elevation angle $\beta_{ij}$ of the satellite as seen from the surface. The solid angle $\Omega_{ij}$ under which the satellite views pixel (i, j) is calculated as shown in Equation (2).

$$\Omega_{ij} = \begin{cases} \frac{S_{ij}}{z^2} \times \cos(\alpha_{ij}) \times \sin(\beta_{ij}) & \text{if } \beta_{ij} \ge 0 \\ 0 & \text{if } \beta_{ij} < 0 \end{cases} \quad (2)$$

Each pixel's contribution is weighted by a Gaussian distribution (Equation (3)), which represents the angular response of the satellite's ERS sensors. The ERS exhibits maximum sensitivity at nadir, with a gradual decrease toward the edges of the field of view.

$$G(\theta_{ij}) = \exp\left(-\frac{\alpha_{ij}^2}{2\sigma^2}\right) \quad (3)$$

where $\sigma$ is related to the sensor's Field-Of-View (FOV), as given in Equation (4).

$$\sigma = \frac{\text{FOV}}{2} \quad (4)$$

For Uvsq-Sat, with an altitude around 540 km and a FOV of 135°, the footprint on the ground spans approximately 2600 km in diameter. At a given satellite position, the flux observed by Uvsq-Sat is determined by a normalized and weighted summation (Equation (5)).

$$F_{\text{sat}}(\lambda_{\text{sat}}, \varphi_{\text{sat}}) = \frac{\sum_{i,j} \Omega_{ij} G_{ij} F_{ij}}{\sum_{i,j} \Omega_{ij} G_{ij}} \quad (5)$$

where $F_{ij}$ represents the radiative flux (either OSR or OLR) at pixel (i, j). This formulation accounts for the observation geometry and the ERS sensor's angular sensitivity, enabling reconstruction of spatial flux distributions along the satellite track.

### 4.3. Uvsq-Sat Map Reconstruction Examples

Figures 4 and 5 show maps derived from data collected by a single Uvsq-Sat satellite operating in an SSO orbit. This satellite observed each location at a fixed local solar time, so the data represent cumulative measurements taken consistently at the same solar observation hour rather than instantaneous snapshots or full diurnal averages. Figure 4 presents the TOA all-sky SW flux (reflected solar radiation), and Figure 5 displays the TOA all-sky LW flux (thermal emission). No diurnal modeling or combination of data from multiple satellites was applied, allowing for consistent comparison of spatial and temporal variability at the satellite overpass times.
<figure><img src="image_6.png" /><figcaption>Figure 4. TOA all-sky shortwave (SW) flux from Uvsq-Sat: March 2021–October 2024.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5. TOA all-sky longwave (LW) flux from Uvsq-Sat: March 2021–October 2024.</figcaption></figure>

Observations from Uvsq-Sat reveal that the OSR (Figure 4) displays marked spatial variability, largely influenced by surface albedo, cloud cover, atmospheric aerosol concentrations, and variations in the solar zenith angle. High-albedo surfaces—such as snow, ice, deserts, and bright clouds—reflect a significant portion of incoming solar radiation, contributing to elevated OSR values. This effect is typically observed in polar regions, where persistent snow and ice cover—especially during local summers—enhance reflectivity. However, accurately observing these regions by satellite is challenging, as low solar elevation angles and highly oblique viewing geometries reduce measurement precision—or even render observations impossible in areas with limited or no satellite coverage. In other regions, large desert areas like the Sahara and Arabian Peninsula maintain high OSR throughout the year due to their consistently bright, dry surfaces. In contrast, darker landscapes such as vegetated regions, urban areas, and soils with low albedo absorb more
sunlight, resulting in lower OSR values. Over the oceans, the OSR is relatively low under clear skies, as the dark water surface reflects only about 5–10% of incoming radiation. However, cloud cover, as a dominant modulator of OSR, can significantly enhance OSR in these regions. Thick and widespread cloud systems—particularly those associated with tropical convection, the InterTropical Convergence Zone (ITCZ), monsoonal flows, and midlatitude storms—reflect substantial amounts of solar radiation back to space. In many cases, their impact on the OSR exceeds that of surface albedo, especially over low-reflectivity regions such as oceans. Marine stratocumulus clouds in subtropical high-pressure zones, such as the eastern Pacific and Atlantic, also act as effective reflectors, producing OSR values comparable to bright continental surfaces. In contrast, clearer subtropical gyres or regions affected by ENSO-related subsidence display lower OSRs, reflecting the ocean's inherently absorptive nature. Additionally, atmospheric aerosols—including dust, smoke, and industrial pollutants—modulate the OSR by scattering sunlight. Moreover, the solar zenith angle, which varies with latitude, time of day, and season, influences both the intensity of incoming solar radiation and surface reflectivity. These combined factors contribute to the spatial and temporal variability of OSRs, underscoring the importance of satellite observations at different solar local times.

As shown in Figure 5, the OLR displays notable spatial variability worldwide, largely governed by surface temperature, the composition of the atmosphere, and cloud dynamics. Since thermal radiation increases with temperature, warmer regions emit more longwave radiation. Consequently, the highest OLR values are typically found in hot, arid areas such as the Sahara Desert, the Arabian Peninsula, and parts of southern California, where clear skies and elevated surface temperatures facilitate efficient infrared emission to space. In contrast, polar regions exhibit much lower OLRs due to consistently cold surface temperatures and reduced thermal emissions. Tropical regions, despite their warmth, often show suppressed OLR levels because of persistent cloud cover and deep convective activity, especially within the ITCZ. Thick cumulonimbus clouds in these areas reflect incoming solar radiation and trap outgoing infrared radiation, reducing the net energy emitted at TOA. Over the oceans, OLR patterns are governed by SST, atmospheric moisture, and cloudiness. Warm oceanic regions such as the western Pacific Warm Pool, tropical Indian Ocean, and parts of the Atlantic emit relatively high OLRs under clear skies. However, intense convection and persistent cloud cover in these zones, particularly deep convective cloud systems with cold, high-altitude tops, significantly lower the OLR by emitting less infrared radiation than the warm ocean surface below. This results in the characteristic “cold patch” signature on OLR maps along the ITCZ. Subtropical ocean regions, typically dominated by descending air in the Hadley circulation, are more cloud-free and thus display higher OLR values due to clearer skies and relatively warm waters. These include areas like the eastern Pacific and Atlantic subtropics. The spatial and temporal variability of OLRs is a critical indicator of surface heating and atmospheric dynamics, including phenomena such as ENSO, monsoonal cycles, and tropical cyclone formation. Continuous satellite monitoring of OLRs provides essential data for understanding Earth's energy balance and improving climate and weather forecasting models.

# 5. Results

## 5.1. Evolution of Earth's TOA Radiative Fluxes and EEI Since 2013

To analyze the evolution of Earth's TOA radiative fluxes, we used monthly global maps of OSRs and OLRs, primarily from the CERES-EBAF dataset at a 1° × 1° latitude-longitude resolution. The CERES-EBAF product provides monthly mean fluxes corrected for diurnal cycle sampling and constrained by energy balance based on observations from multiple satellite platforms (Terra, Aqua, and NOAA-20). Although CERES-EBAF fluxes represent
monthly averages, they are compared here with monthly means from Uvsq-Sat data, which are based on measurements taken at fixed solar local times (e.g., Uvsq-Sat at 9:30 a.m.) and averaged monthly as well as over multiple-month periods (Figures A1 and A2).

To achieve a more consistent comparison, we relied on the SSF1deg Level 3 CERES data products (https://ceres.larc.nasa.gov/data/, accessed on 14 July 2025). Terra Edition 4.1 was employed for the period March 2000 to July 2024, while Edition 4.2 was used for the more recent interval, from August 2023 to October 2024. These datasets provide instantaneous TOA fluxes at the Terra satellite overpass time (10:30 a.m. local solar time). These snapshot measurements are comparable to those obtained by Inspire-Sat (10:30 a.m.) and Uvsq-Sat.

In future work, we plan to implement a systematic spatiotemporal colocation methodology to compare CubeSat measurements from Uvsq-Sat and Inspire-Sat with CERES data. Specifically, we will use the CERES SSF1deg-Hour Terra Edition4A dataset (https://asdc.larc.nasa.gov/project/CERES/CER_SSF1deg-Hour_Terra-MODIS_Edition4A, accessed on 28 June 2025) [44], which provides instantaneous TOA radiative fluxes.

For the current study, for each month, global mean fluxes were calculated by applying area weighting using the cosine of latitude, ensuring that each grid cell contributes proportionally to its actual surface area on Earth. The periods of interest are from January 2013 to October 2024 for CERES and from February 2021 to October 2024 for Uvsq-Sat. A CERES anomaly was defined as the difference between observed radiative fluxes and a reference climatological mean for the same calendar month. Anomalies for Uvsq-Sat were computed in the same way, using its own baseline period (e.g., 2021–2024), to ensure consistency and comparability with CERES. In the case of Uvsq-Sat, the solar flux was derived from SATIRE-S data, while the NET flux was calculated as the difference between the incoming solar flux and the outgoing OSR and OLR fluxes. The uncertainty in the NET flux was estimated by combining individual error sources in quadrature. To smooth out seasonal cycles and short-term variability in TOA radiative flux anomalies, a 12-month running mean was applied to the monthly anomaly time series from both CERES and Uvsq-Sat. Finally, to ensure a consistent comparison between Uvsq-Sat and CERES measurements, constant offset corrections were applied to the Uvsq-Sat data for the incoming solar flux, OSR, and OLR. These offsets account for small but systematic calibration differences between the satellite instruments. The absolute flux levels measured by Uvsq-Sat over the study period were $105.52 \pm 5 \text{ Wm}^{-2}$ for OSR and $236.18 \pm 5 \text{ Wm}^{-2}$ for OLR ($1\sigma$ uncertainty). To focus on temporal variability rather than absolute values, the Uvsq-Sat time-series data were normalized relative to their respective means and adjusted using the following constant offsets derived from the average differences with CERES: $+0.17 \text{ Wm}^{-2}$ for the solar flux (TSI/4), $-1.10 \text{ Wm}^{-2}$ for OSR, and $+0.40 \text{ Wm}^{-2}$ for OLR. 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*).

$$ \text{NET}^* = \left( \frac{\text{TSI}}{4} - \left\langle \frac{\text{TSI}}{4} \right\rangle + 0.17 \right) - (\text{OSR} - \langle \text{OSR} \rangle - 1.10) - (\text{OLR} - \langle \text{OLR} \rangle + 0.40) \quad (6) $$

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 SSF1deg).
<figure><img src="image_8.png" /><figcaption>**Figure 6.** 12-month running means of global relative anomalies in ERB from Uvsq-Sat and CERES data (EBAF and SSF1deg products). The grey area represents the uncertainty range of the Uvsq-Sat data. The overall patterns of the EBAF and SSF1deg time series are broadly consistent. However, beginning in mid-2021, notable discrepancies emerge in both OSR and OLR.</figcaption></figure>

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 Niño event. This pattern mirrors the post-El Niño response observed after the 2009/2010 event, although the decline was less pronounced following the 2015/2016 El Niño. 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. Forster et al. (2024) [45]
reported a rise of +0.96 Wm⁻² over the 2011–2023 period, while Hodnebrog 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. The PDO influences surface temperatures and can modulate OLR through changes in ocean-atmosphere heat exchange. However, the relationship between PDO and OLR may be evolving, potentially due to more complex ocean dynamics, increasing climate variability (including ENSO behavior), and external forcings such as volcanic activity or solar fluctuations. Together, these findings underscore the interplay between human-induced changes and natural variability in shaping Earth’s energy budget, emphasizing the critical importance of continued monitoring of EEI. Indeed, Forster et al. (2025) [47] highlight that human-induced climate warming continues to increase at an unprecedented rate, with the observed global average temperature in 2024 significantly exceeding pre-industrial levels, while GHG emissions remain at historically high levels.

## 5.2. Role of Cloud Cover in Modulating OSR

A key aspect is examining how OSR varies with cloud cover. Figure 7 highlights the temporal relationship between Cloud Area Fraction (CAF) derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) and OSR as observed by Uvsq-Sat and CERES.

<figure><img src="image_9.png" /><figcaption>**Figure 7.** 12-month running means of OSR anomalies from Uvsq-Sat and CERES (EBAF and SSF1deg products), alongside CAF data derived from MODIS.</figcaption></figure>

As highlighted by Loeb et al. (2024) [35], cloud variability is one of the dominant factors driving changes in OSR. This relationship is reflected in recent trends, with similar patterns observed between CAF (2013–2024) and OSR as measured by CERES (2013–2024) and Uvsq-Sat (2021–2024). Cloud cover is influenced by a complex interplay of atmospheric,
oceanic, and surface factors. Key drivers include atmospheric moisture and humidity, which provide the water vapor necessary for cloud formation, and temperature profiles that affect cloud altitude and type. Large-scale atmospheric circulation patterns, such as the Hadley cell and jet streams, modulate regional cloud distribution, while ocean–atmosphere interactions—particularly ENSO phases—alter SST and convection, impacting cloud dynamics. Aerosols act as cloud condensation nuclei, influencing cloud microphysics and coverage. Additionally, surface characteristics, including land–ocean contrasts, vegetation, and urbanization, affect local cloud formation through modifications of heat flux and surface roughness. Orographic effects from topography further induce localized cloud formation. Human activities, such as pollution and land-use changes, also play a significant role in altering cloud properties and spatial patterns. Understanding these factors is crucial for interpreting observed cloud cover variability and its effects on Earth’s radiation budget. This integrated approach offers valuable insights into how cloud dynamics modulate radiative fluxes, improves the interpretation of satellite-based observations, and supports the evaluation and enhancement of climate model performance. The Uvsq-Sat NG mission aims to demonstrate the technical feasibility of combining visible cloud imagery with Earth’s radiation budget measurements aboard a small satellite. Future developments will focus on enhancing spatial and temporal resolution, integrating multi-spectral observations, and improving retrieval algorithms to better quantify cloud radiative effects and their role in the climate system.

### 5.3. 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 El Niño events. It is physically more meaningful to compare the rate of change of ocean heat content, $\partial\text{OHC}/\partial t$, 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 $\partial\text{OHC}/\partial t$ and EEI: Bagnell and DeVries (2021) [48] demonstrated near one-to-one tracking of these quantities through 2019; Hakuba et al. (2021) [49] estimated average ocean heat uptake at $0.62 \pm 0.10 \text{ Wm}^{-2}$ compared to CERES EEI of $0.77 \pm 0.10 \text{ Wm}^{-2}$ over 2005–2019; Marti et al. (2022) [50] used satellite altimetry and gravimetry to derive OHC changes and confirmed strong agreement with CERES EEI over 2002–2016. Furthermore, Loeb 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. Meyssignac et al. (2019) [52] provide a comprehensive review of multiple methods to estimate OHC and EEI, emphasizing $\partial\text{OHC}/\partial t$ as the primary physical linkage between ocean and TOA energy measurements.
Figure 8 presents the temporal evolution of $\partial\text{OHC}/\partial t$ 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 ± 0.2 Wm$^{-2}$. In contrast, during the most recent decade (January 2013 to December 2022), it increased to +1.0 ± 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 ± 0.23 Wm$^{-2}$, closely aligning with the recent CERES trend with clear responses to El Niño and La Niña 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, $\partial\text{OHC}/\partial t$ data over the same period exhibit partially divergent behavior, both in the timing and magnitude of heat uptake. These discrepancies may reflect differences in the response timescales of the ocean compared to the atmosphere, where satellite-based EEI observations display enhanced short-term variability (on monthly to annual timescales), driven by fluctuations in cloud cover, volcanic aerosol loading, ENSO phases, and other radiative feedback processes, as well as potential errors inherent in instrumental measurements.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** 12-month running means of EEI anomalies from Uvsq-Sat and CERES (EBAF and SSF1deg products), alongside $\partial\text{OHC}/\partial t$ (data series spanning from 2013 to May 2024).</figcaption></figure>

Together, OHC measurements from the Argo float network and EEI estimates from satellite observations provide complementary insights into ERB, enhancing our ability to monitor, understand, and predict changes in the climate system. A comparison of their temporal evolutions highlights how these datasets offer consistent, yet distinct, information
on Earth's energy dynamics. Maintaining the continuity of both observation systems is essential for accurately tracking the progression of ongoing climate change.

5.4. *Advancing Climate Monitoring with Small Satellite Constellations*

An initial test was conducted using two satellites (Uvsq-Sat and Inspire-Sat) orbiting simultaneously but with different LTAN. Figure 9 illustrates an example of the results (for OSR and OLR) obtained from these two satellites, highlighting differences that are particularly visible in the OSR maps.

<figure><img src="image_11.png" /><figcaption>**Figure 9.** (Top) TOA all-sky SW flux from Uvsq-Sat (LTDN of 9:30 a.m.), covering the period from 15 July 2023 to 15 July 2024. (Bottom) TOA all-sky SW flux from Inspire-Sat (LTAN of 10:30 a.m.), covering the period from 15 July 2023 to 15 July 2024.</figcaption></figure>
While a constellation of small satellites equipped with WFOV instruments offers significant potential for improving temporal coverage of Earth's radiative fluxes, current absolute uncertainties of individual instruments (on the order of few Wm⁻²) exceed the requirement of being less than 0.5 Wm⁻² for climate-quality data. Achieving the necessary accuracy and stability will require advanced cross-calibration techniques—such as coordinated observations of common Earth scenes—as well as the development and integration of onboard reference standards. One promising approach for achieving absolute calibration in orbit involves the use of onboard reference sources, such as gallium fixed-point blackbody radiators. Exploiting the well-defined melting/freezing point of gallium (29.7646 °C), these radiators provide a stable radiometric reference. Recent studies [40] have demonstrated their feasibility for space applications, offering a means to establish and maintain absolute calibration of WFOV instruments throughout the mission lifetime. Nevertheless, the constellation's vulnerability to sudden loss or degradation of individual satellites remains a challenge. Such events could introduce discontinuities into the radiative flux record, potentially mimicking or obscuring real climate signals. This underscores the need for resilient data processing methods, robust anomaly detection, and inter-calibration algorithms to ensure the continuity and reliability of the Earth's radiation budget record. Due to OSR's sensitivity to short-term phenomena like cloud dynamics and solar angle, high-frequency observations are essential. Single satellites, particularly those in polar orbits, have limited temporal coverage, resulting in data gaps, while geostationary satellites cannot observe the entire Earth's surface. In contrast, satellite constellations dramatically increase revisit frequency and spatial coverage, enabling near-continuous global monitoring. This multi-satellite approach enhances data reliability through cross-calibration, increases measurement accuracy, and reduces costs compared to large, complex missions. It also provides redundancy, improving resilience in the event of satellite failure.

## 6. Conclusions

This study demonstrates the value of small satellite constellations, including Uvsq-Sat (2021–2024) and Inspire-Sat (2023–2024), for advancing continuous monitoring of the Earth's radiation budget and Energy Imbalance at different solar local times. This approach helps capture the complex feedbacks—linked to greenhouse gases, clouds, aerosols, and solar variability—that govern Earth's energy balance.

It is worth noting that the current absolute accuracy of Uvsq-Sat and Inspire-Sat, on the order of a few Wm⁻², exceeds the <0.5 Wm⁻² threshold typically required for quantitative climate research on Earth's radiative fluxes. However, this level of accuracy is well suited to the demonstrator nature of these missions, which focus on relative measurements and broad radiative flux variations rather than absolute climate-grade precision—a requirement that becomes particularly important when multiple satellites are conducting absolute measurements simultaneously.

With more resources and time, ground calibration procedures for satellites like Uvsq-Sat could be refined to further reduce uncertainty. Looking ahead, calibration improvements—including onboard degradation monitoring and cross-calibration between satellites—are planned to enhance data quality. Although such measures are complex, they will be essential for future small satellite constellations designed to meet the absolute stringent requirements.

By measuring both reflected solar radiation and outgoing longwave radiation, Uvsq-Sat and Inspire-Sat provide data that complement CERES observations. While Wide Field-Of-View measurements do not replace Narrow Field-Of-View observations, they extend angular coverage and offer a broader radiative perspective. The integration of Wide Field-Of-View Earth's radiation budget instruments within a constellation frame-
work enables improved monitoring frequency, enhanced data reliability, and increased resilience. This approach offers a transformative path for tracking Earth's radiative energy budget—essential for improving climate model validation, deepening the understanding of climate feedbacks, and informing policy decisions to address climate change.

Our analysis reveals a generally good agreement between Uvsq-Sat and CERES data for Earth's energy imbalance from 2021 to 2024. Over this period, EEI derived from Uvsq-Sat averaged +0.87 ± 0.23 Wm⁻², closely matching the recent CERES trend. Both datasets indicate a peak in EEI around mid-2023, followed by a decline throughout 2024, likely reflecting stabilizing feedbacks triggered by the 2023 El Niño event.

**Author Contributions:** All authors formulated and directed the methodology and results analysis. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work received funding from Agence Nationale de la Recherche (ANR, France), Académie de Versailles (78, France), Communauté d'Agglomération de Saint-Quentin-en-Yvelines (SQY, France), and Centre Paris-Saclay des Sciences Spatiales (CPS3, France). This work was also supported by State funding, managed by the French National Research Agency under the 'Académie Spatiale IdF' initiative, as part of France 2030, with the reference ANR-23-CMAS-0001.

**Data Availability Statement:** The Uvsq-Sat data derived in this work are available at http://bdap.ipsl.fr/uvsqsat/ and http://nahla.projet.latmos.ipsl.fr—accessed on 14 July 2025.

**Acknowledgments:** We thank the International Satellite Program in Research and Education (IN-SPIRE) team for their continued collaboration in advancing space research and the deployment of small satellites dedicated to science. We also wish to express our gratitude to the team at the Plateforme d'Intégration et de Tests (PIT) of the Observatoire de Versailles Saint-Quentin-en-Yvelines (France) for their support and technical assistance during the Uvsq-Sat and Inspire-Sat satellites Assembly, Integration, and Testing (AIT) phase. We thank our student Nahla Ben Naghrouzi (Master's in Arctic Studies) for her contribution to the development of the Uvsq-Sat ERB data access website, alongside Jean-Luc Engler (LATMOS). We gratefully acknowledge support from the following institutions and organizations: Université de Versailles Saint-Quentin-en-Yvelines (UVSQ, France), Sorbonne Université (SU, France), Université Paris-Saclay (France), Centre National de la Recherche Scientifique (CNRS, France), Centre National d'Études Spatiales (CNES, France), Office National d'Études et de Recherches Aérospatiales (ONERA, France), Royal Belgian Institute for Space Astronomy (BIRA-IASB, Belgium), Laboratory for Atmospheric and Space Physics (LASP, USA), National Central University (NCU, Taiwan), Nanyang Technological University (NTU, Singapore) and French small and medium enterprises ADRELYS and ACRI-ST. The CERES data were obtained from the CERES EBAF website (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAFTOA421Selection.jsp, accessed on 14 July 2025) and from https://ceres.larc.nasa.gov/data/, accessed on 14 July 2025. The SATIRE-S data were accessed from the Max Planck Institute for Solar System Research website (https://www2.mps.mpg.de/projects/sun-climate/data.html, accessed on 14 July 2025). Finally, we thank the anonymous reviewers for their constructive comments and valuable suggestions, which greatly contributed to improving the quality and clarity of this manuscript.

**Conflicts of Interest:** The authors declare no conflicts of interest.
<figure><img src="image_12.png" /><figcaption>Appendix A. Uvsq-Sat—Regional OSR Plots (MAM 2021–2024)</figcaption></figure>

**Figure A1.** TOA all-sky shortwave flux from Uvsq-Sat during the March–April–May (MAM) seasons from 2021 to 2024.
<figure><img src="image_13.png" /><figcaption>**Figure A2.** TOA all-sky longwave flux from Uvsq-Sat during the March–April–May (MAM) seasons from 2021 to 2024.</figcaption></figure>
## References

1. Kiehl, J.T.; Trenberth, K.E. Earth's annual global mean energy budget. *Bull. Am. Meteorol. Soc.* **1997**, *78*, 197-208. [CrossRef]

2. Stephens, G.L.; Li, J.; Wild, M.; Clayson, C.A.; Loeb, N.; Kato, S.; L'Ecuyer, T.; Stackhouse, P.W.; Lebsock, M.; Andrews, T. An update on Earth's energy balance in light of the latest global observations. *Nat. Geosci.* **2012**, *5*, 691-696. [CrossRef]

3. Hansen, J.; Sato, M.; Kharecha, P.; von Schuckmann, K. Earth's energy imbalance and implications. *Atmos. Chem. Phys.* **2011**, *11*, 13421-13449. [CrossRef]

4. von Schuckmann, K.; Palmer, M.D.; Trenberth, K.E.; Cazenave, A.; Chambers, D.; Champollion, N.; Hansen, J.; Josey, S.A.; Loeb, N.; Mathieu, P.P.; et al. An imperative to monitor Earth's energy imbalance. *Nat. Clim. Chang.* **2016**, *6*, 138-144. [CrossRef]

5. Von Schuckmann, K.; Minière, A.; Gues, F.; Cuesta-Valero, F.J.; Kirchengast, G.; Adusumilli, S.; Straneo, F.; Ablain, M.; Allan, R.P.; Barker, P.M.; et al. Heat stored in the Earth system 1960-2020: Where does the energy go? *Earth Syst. Sci. Data* **2023**, *15*, 1675-1709. [CrossRef]

6. Johnson, G.C.; Lyman, J.M.; Loeb, N.G. Improving estimates of Earth's energy imbalance. *Nat. Clim. Chang.* **2016**, *6*, 639-640. [CrossRef]

7. Gristey, J.J.; Chiu, J.C.; Gurney, R.J.; Han, S.C.; Morcrette, C.J. Determination of global Earth outgoing radiation at high temporal resolution using a theoretical constellation of satellites. *J. Geophys. Res. Atmos.* **2017**, *122*, 1114-1131. [CrossRef]

8. Wong, T.; Smith, G.L.; Kato, S.; Loeb, N.G.; Kopp, G.; Shrestha, A.K. On the lessons learned from the operations of the ERBE nonscanner instrument in space and the production of the nonscanner TOA radiation budget data set. *IEEE Trans. Geosci. Remote Sens.* **2018**, *56*, 5936-5947. [CrossRef]

9. Barkstrom, B.R. The Earth Radiation Budget Experiment (ERBE). *Bull. Am. Meteorol. Soc.* **1984**, *65*, 1170-1185. [CrossRef]

10. Meftah, M.; Damé, L.; Keckhut, P.; Bekki, S.; Sarkissian, A.; Hauchecorne, A.; Bertran, E.; Carta, J.P.; Rogers, D.; Abbaki, S.; et al. UVSQ-SAT, a Pathfinder CubeSat Mission for Observing Essential Climate Variables. *Remote Sens.* **2020**, *12*, 92. [CrossRef]

11. Meftah, M.; Boust, F.; Keckhut, P.; Sarkissian, A.; Boutéraon, T.; Bekki, S.; Damé, L.; Galopeau, P.; Hauchecorne, A.; Dufour, C.; et al. INSPIRE-SAT 7, a Second CubeSat to Measure the Earth's Energy Budget and to Probe the Ionosphere. *Remote Sens.* **2022**, *14*, 186. [CrossRef]

12. Meftah, M.; Clavier, C.; Sarkissian, A.; Hauchecorne, A.; Bekki, S.; Lefèvre, F.; Galopeau, P.; Yahoo, P.R.; Pazmino, A.; Vieau, A.J.; et al. Uvsq-Sat NG, a New CubeSat Pathfinder for Monitoring Earth Outgoing Energy and Greenhouse Gases. *Remote Sens.* **2023**, *15*, 4876. [CrossRef]

13. Meftah, M.; Dufour, C.; Bolsée, D.; Van Laeken, L.; Clavier, C.; Chandran, A.; Chang, L.; Sarkissian, A.; Galopeau, P.; Hauchecorne, A.; et al. Advancing CubeSats Capabilities: Ground-Based Calibration of Uvsq-Sat NG Satellite's NIR Spectrometer and Determination of the Extraterrestrial Solar Spectrum. *Remote Sens.* **2024**, *16*, 3655. [CrossRef]

14. Clavier, C.; Meftah, M.; Sarkissian, A.; Romand, F.; Hembise Fanton d'Andon, O.; Mangin, A.; Bekki, S.; Yahoo, P.R.; Galopeau, P.; Lefèvre, F.; et al. Assessing Greenhouse Gas Monitoring Capabilities Using SolAtmos End-to-End Simulator: Application to the Uvsq-Sat NG Mission. *Remote Sens.* **2024**, *16*, 1442. [CrossRef]

15. Loeb, N.G.; Doelling, D.R.; Wang, H.; Su, W.; Nguyen, C.; Corbett, J.G.; Liang, L.; Mitrescu, C.; Rose, F.G.; Kato, S. Clouds and the earth's radiant energy system (CERES) energy balanced and filled (EBAF) top-of-atmosphere (TOA) edition-4.0 data product. *J. Clim.* **2018**, *31*, 895-918. [CrossRef]

16. Intergovernmental Panel on Climate Change (IPCC). *Climate Change 2021—The Physical Science Basis: Working Group I Contribution to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change*; Cambridge University Press: Cambridge, UK, 2023.

17. Hansen, J.; Nazarenko, L.; Ruedy, R.; Sato, M.; Willis, J.; Del Genio, A.; Koch, D.; Lacis, A.; Lo, K.; Menon, S.; et al. Earth's Energy Imbalance: Confirmation and Implications. *Science* **2005**, *308*, 1431-1435. [CrossRef]

18. Wild, M.; Folini, D.; Schär, C.; Loeb, N.; Dutton, E.G.; König-Langlo, G. The global energy balance from a surface perspective. *Clim. Dyn.* **2013**, *40*, 3107-3134. [CrossRef]

19. Otto, A.; Otto, F.E.L.; Boucher, O.; Church, J.; Hegerl, G.; Forster, P.M.; Gillett, N.P.; Gregory, J.; Johnson, G.C.; Knutti, R.; et al. Energy budget constraints on climate response. *Nat. Geosci.* **2013**, *6*, 415-416. [CrossRef]

20. Meftah, M.; Damé, L.; Bolsée, D.; Hauchecorne, A.; Pereira, N.; Sluse, D.; Cessateur, G.; Irbah, A.; Bureau, J.; Weber, M.; et al. SOLAR-ISS: A new reference spectrum based on SOLAR/SOLSPEC observations. *Astron. Astrophys.* **2018**, *611*, A1. [CrossRef]

21. Meftah, M.; Sarkissian, A.; Keckhut, P.; Hauchecorne, A. The SOLAR-HRS New High-Resolution Solar Spectra for Disk-Integrated, Disk-Center, and Intermediate Cases. *Remote Sens.* **2023**, *15*, 3560. [CrossRef]

22. Mauritsen, T.; Tsushima, Y.; Meyssignac, B.; Loeb, N.G.; Hakuba, M.; Pilewskie, P.; Cole, J.; Suzuki, K.; Ackerman, T.P.; Allan, R.P.; et al. Earth's Energy Imbalance More Than Doubled in Recent Decades. *AGU Adv.* **2025**, *6*, e2024AV001636. [CrossRef]

23. Raghuraman, S.P.; Paynter, D.; Ramaswamy, V. Anthropogenic forcing and response yield observed positive trend in Earth's energy imbalance. *Nat. Commun.* **2021**, *12*, 4577. [CrossRef]

24. Loeb, N.G.; Johnson, G.C.; Thorsen, T.J.; Lyman, J.M.; Rose, F.G.; Kato, S. Satellite and Ocean Data Reveal Marked Increase in Earth's Heating Rate. *Geophys. Res. Lett.* **2021**, *48*, e2021GL093047. [CrossRef]
25. Kramer, R.J.; He, H.; Soden, B.J.; Oreopoulos, L.; Myhre, G.; Forster, P.M.; Smith, C.J. Observational Evidence of Increasing Global Radiative Forcing. Geophys. Res. Lett. **2021**, *48*, e2020GL091585. [CrossRef]

26. Subba, T.; Gogoi, M.M.; Pathak, B.; Bhuyan, P.K.; Babu, S.S. Recent trend in the global distribution of aerosol direct radiative forcing from satellite measurements. Atmos. Sci. Lett. **2020**, *21*, e975. [CrossRef]

27. Quaas, J.; Jia, H.; Smith, C.; Albright, A.L.; Aas, W.; Bellouin, N.; Boucher, O.; Doutriaux-Boucher, M.; Forster, P.M.; Grosvenor, D.; et al. Robust evidence for reversal of the trend in aerosol effective climate forcing. Atmos. Chem. Phys. **2022**, *22*, 12221–12239. [CrossRef]

28. Loeb, N.G.; Wang, H.; Allan, R.P.; Andrews, T.; Armour, K.; Cole, J.N.S.; Dufresne, J.L.; Forster, P.; Gettelman, A.; Guo, H.; et al. New Generation of Climate Models Track Recent Unprecedented Changes in Earth's Radiation Budget Observed by CERES. Geophys. Res. Lett. **2020**, *47*, e2019GL086705. [CrossRef]

29. Millán, L.; Santee, M.L.; Lambert, A.; Livesey, N.J.; Werner, F.; Schwartz, M.J.; Pumphrey, H.C.; Manney, G.L.; Wang, Y.; Su, H.; et al. The Hunga Tonga-Hunga Ha'apai Hydration of the Stratosphere. Geophys. Res. Lett. **2022**, *49*, e2022GL099381. [CrossRef]

30. Jenkins, S.; Smith, C.; Allen, M.; Grainger, R. Tonga eruption increases chance of temporary surface temperature anomaly above 1.5C. Nat. Clim. Chang. **2023**, *13*, 127–129. [CrossRef]

31. Schoeberl, M.R.; Wang, Y.; Ueyama, R.; Dessler, A.; Taha, G.; Yu, W. The Estimated Climate Impact of the Hunga Tonga-Hunga Ha'apai Eruption Plume. Geophys. Res. Lett. **2023**, *50*, e2023GL104634. [CrossRef]

32. Yu, P.; Portmann, R.W.; Peng, Y.; Liu, C.C.; Zhu, Y.; Asher, E.; Bai, Z.; Lu, Y.; Bian, J.; Mills, M.; et al. Radiative Forcing from the 2014–2022 Volcanic and Wildfire Injections. Geophys. Res. Lett. **2023**, *50*, e2023GL103791. [CrossRef]

33. Wallace, J.M.; Zhang, Y.; Renwick, J.A. Dynamic Contribution to Hemispheric Mean Temperature Trends. Science **1995**, *270*, 780–783. [CrossRef]

34. Trenberth, K.E.; Fasullo, J.T.; Balmaseda, M.A. Earth's Energy Imbalance. J. Clim. **2014**, *27*, 3129–3144. [CrossRef]

35. Loeb, N.G.; Doelling, D.R.; Kato, S.; Su, W.; Mlynczak, P.E.; Wilkins, J.C. Continuity in Top-of-Atmosphere Earth Radiation Budget Observations. J. Clim. **2024**, *37*, 609–6108. [CrossRef]

36. Zhang, P.; Yang, J.; Wang, J.; Yu, X. Preface to the special issue on Fengyun Meteorological Satellites: Data, application and assessment. Adv. Atmos. Sci. **2021**, *38*, 1265–1266. [CrossRef]

37. Xian, D.; Zhang, P.; Gao, L.; Sun, R.; Zhang, H.; Jia, X. Fengyun meteorological satellite products for earth system science applications. Adv. Atmos. Sci. **2021**, *38*, 1267–1284. [CrossRef]

38. Liu, H.; Zhu, P.; Zhu, L.; Xu, G.; Cao, T.; Li, Q. Moon-based Earth Radiation Budget Observation for Chang'e-7 Lunar Mission. In Proceedings of the EGU General Assembly 2025, Vienna, Austria, 27 April–2 May 2025. [CrossRef]

39. Meftah, M.; Boutéraon, T.; Dufour, C.; Hauchecorne, A.; Keckhut, P.; Finance, A.; Bekki, S.; Abbaki, S.; Bertran, E.; Damé, L.; et al. The UVSQ-SAT/INSPIRESat-5 CubeSat Mission: First In-Orbit Measurements of the Earth's Outgoing Radiation. Remote Sens. **2021**, *13*, 1449. [CrossRef]

40. Swartz, W.H.; Lorentz, S.R.; Papadakis, S.J.; Huang, P.M.; Smith, A.W.; Deglau, D.M.; Yu, Y.; Reilly, S.M.; Reilly, N.M.; Anderson, D.E. RAVAN: CubeSat demonstration for multi-point Earth Radiation Budget measurements. Remote Sens. **2019**, *11*, 796. [CrossRef]

41. Lean, J. Evolution of the Sun's spectral irradiance since the Maunder Minimum. Geophys. Res. Lett. **2000**, *27*, 2425–2428. [CrossRef]

42. Coddington, O.; Lean, J.; Pilewskie, P.; Snow, M.; Lindholm, D. A solar irradiance climate data record. Bull. Am. Meteorol. Soc. **2016**, *97*, 1265–1282. [CrossRef]

43. Yeo, K.L.; Krivova, N.A.; Solanki, S.K.; Glassmeier, K.H. Reconstruction of total and spectral solar irradiance from 1974 to 2013 based on KPVT, SoHO/MDI, and SDO/HMI observations. Astron. Astrophys. **2014**, *570*, A85. [CrossRef]

44. NASA/LARC/SD/ASDC. CERES Regionally Averaged TOA Fluxes, Clouds and Aerosols Hourly Terra Edition4A; NASA Langley Research Center (LaRC): Hampton, VA, USA, 2015.

45. Forster, P.M.; Smith, C.; Walsh, T.; Lamb, W.F.; Lamboll, R.; Hall, B.; Hauser, M.; Ribes, A.; Rosen, D.; Gillett, N.P.; et al. Indicators of Global Climate Change 2023: Annual update of key indicators of the state of the climate system and human influence. Earth Syst. Sci. Data **2024**, *16*, 2625–2658. [CrossRef]

46. Hodnebrog, O.; Myhre, G.; Jouan, C.; Andrews, T.; Forster, P.M.; Jia, H.; Loeb, N.G.; Olivié, D.J.; Paynter, D.; Quaas, J.; et al. Recent reductions in aerosol emissions have increased Earth's energy imbalance. Commun. Earth Environ. **2024**, *5*, 166. [CrossRef]

47. Forster, P.M.; Smith, C.; Walsh, T.; Lamb, W.F.; Lamboll, R.; Cassou, C.; Hauser, M.; Hausfather, Z.; Lee, J.Y.; Palmer, M.D.; et al. Indicators of Global Climate Change 2024: Annual update of key indicators of the state of the climate system and human influence. Earth Syst. Sci. Data **2025**, *17*, 2641–2680. [CrossRef]

48. Bagnell, A.; DeVries, T. 20th century cooling of the deep ocean contributed to delayed acceleration of Earth's energy imbalance. Nat. Commun. **2021**, *12*, 4604. [CrossRef]

49. Hakuba, M.Z.; Frederikse, T.; Landerer, F.W. Earth's energy imbalance from the ocean perspective (2005–2019). Geophys. Res. Lett. **2021**, *48*, e2021GL093624. [CrossRef]
50. Marti, F.; Blazquez, A.; Meyssignac, B.; Ablain, M.; Barnoud, A.; Fraudeau, R.; Jugier, R.; Chenal, J.; Larnicol, G.; Pfeffer, J.; et al. Monitoring the ocean heat content change and the Earth energy imbalance from space altimetry and space gravimetry. *Earth Syst. Sci. Data* **2022**, *14*, 229–249. [CrossRef]

51. Marti, F.; Meyssignac, B.; Rousseau, V.; Ablain, M.; Fraudeau, R.; Blazquez, A.; Fourest, S. Monitoring global ocean heat content from space geodetic observations to estimate the Earth Energy Imbalance. In *Copernicus Ocean State Report (OSR8)*, 8th ed.; Copernicus Publications, State Planet: Göttingen, Germany, 2024.

52. Meyssignac, B.; Boyer, T.; Zhao, Z.; Hakuba, M.Z.; Landerer, F.W.; Stammer, D.; Köhl, A.; Kato, S.; L'ecuyer, T.; Ablain, M.; et al. Measuring global ocean heat content to estimate the earth energy imbalance. *Front. Mar. Sci.* **2019**, *6*, 432. [CrossRef]

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