Introduction

Africa accounts for more than half of the global biomass burning aerosol (BBA) emissions1,2. In Southern Africa, the peak fire season is from July to September due to agricultural practices that necessitate extensive burning of savannas, woodlands, and forests3. The overall BBA radiative effect depends primarily on its vertical distribution4 and the optical properties (partition, mixing, coating, and ageing)5,6,7,8,9 of its coexisting scattering (e.g., organic carbon, inorganic species such as nitrate, ammonium, sulfate) and light-absorbing aerosols (e.g., black carbon, brown carbon)3,10,11. While scattering aerosols increase the top of the atmosphere (TOA) reflected shortwave radiation, absorbing aerosols generally warm the troposphere by storing energy, especially when above clouds and reduce the outgoing shortwave radiation12. Absorbing aerosols near clouds may also alter the thermodynamic processes governing cloud formation by heating the ambient atmosphere13. Therefore, BBA can have a significant regional radiative impact through the direct, semi-direct, and indirect effects of aerosols14,15,16,17,18. This study focuses on the shortwave direct radiative effect of BBA (DARE) at TOA over the South-Eastern Atlantic (SEA) ocean region. Waquet et al.19 show that the global maximum positive values occur over the SEA ocean due to the presence of large amounts of absorbing aerosols transported from central Southern Africa and semi-permanent stratocumulus in the marine boundary layer. It has been demonstrated that the TOA forcing caused by BBA is negative in clear-sky conditions but positive with the presence of stratocumulus over SEA12,20. Several studies have attempted to estimate the BBA DARE both over cloud-free oceans or above SEA stratocumulus and by combining satellite data with radiative transfer models21,22,23,24,25,26,27,28,29,30. However, results show significant diversity that can be attributed to different recovery methods, satellite sensors, space coverage, and time periods.

Most of these previous studies have looked at the instantaneous or average aerosol radiative effects. We expand on this by addressing long-term changes in DARE over the SEA ocean during extended fire seasons to see whether the complex interactions between BBA, cloud, and SW radiation still hold and how they evolve. Retrievals from passive satellite sensors are used to examine changes in aerosol optical depth (AOD), TOA shortwave radiation, and clouds between 2002 and 2021 at regional scales. The analysis is supplemented by chemical transport model simulations to consolidate the satellite changes in DAREall, in all-sky conditions derived from the CERES and MODIS datasets.

Results

Observational trends in aerosol amount

By comparing temporal trends derived from various satellite aerosol products, Wei et al.31 demonstrated that MODerate Resolution Imaging Spectroradiometer (MODIS32) performs best compared to other instruments, with minimal estimation uncertainties in most regions but overall overestimates the aerosol optical depth (AOD). Figure 1 shows the mean and linear trend of AOD at 550 nm (2002–2021 period) during the fire seasons (July-September) from MODIS (Aqua and Terra) products centered on the SEA region.

Fig. 1: Spatial distribution of the seasonal mean and trend of AOD.
figure 1

Seasonal (JAS) mean (unitless) (a) and trends (unitless per year) (b) of AODs at 550 nm over the period 2002–2021 from MODIS (Terra+Aqua) satellites. Dots indicate geographical cells for which the AOD trends are statistically significant (at a 5% significance level). Bounded area coordinates are 2–20°S, 10°W –10°E. Regions experiencing over 8% monthly data missing are excluded from mean and trend calculations.

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The spatial distribution and magnitude of the seasonal mean of AOD reported in Fig. 1a are consistent with recent previous studies33,34 and show maximum values above the BBA continental source of central Africa and over the ocean along the Angolan coast. Downwind of BBA continental sources, statistically significant positives seasonal AOD trends (Fig. 1b) are clearly observed over central Africa and its adjoining SEA ocean region. Particularly within the red bounded area with coordinates of 2–20°S, 10°W–10°E where stratocumulus dominates, as described by Keil and Haywood12 and Diamond et al.34, and as shown in Supplementary Fig. 1 with the seasonal average cloud cover fraction over the period 2002–2021 from MODIS datasets. The seasonal AOD trend, when averaged over the bounded area, shows an increase of ~+0.06 ± 0.08 (geographical standard deviation) (with a relative trend of +19.9 ± 17.2% - Supplementary Fig. 2a) over the 20-year period. Note that all subsequent averaging calculations and analyses will be concentrated exclusively within this defined bounded area. Hereafter, all mentions of mean trend value are listed in Supplementary Table 1 and given with its associated geographical standard deviation.

Recently, a significant increasing annual AOD trend (0.1 AOD decade−1) in SEA and central Southern Africa regions has been documented by Gupta et al.35 from MODIS and MERRA-2 datasets. Using CALIOP datasets, Mehta et al.36 also reported significant positive trends in AOD and aerosol extinction (within 1–4 km above mean sea level) due to smoke over central Africa.

Trends in estimated aerosol abundance are reflected in observations of aerosol emissions. In areas dominated by biomass burning, Che et al.37 shows an increase in black and organic carbon emissions derived from the Peking University emissions inventory, including the open fires source category38.

Observational trends in clear and all skies’ DARE

The Clouds and the Earth’s Radiant Energy System (CERES) datasets are used to estimate the variability of the shortwave outgoing radiation at the top of the atmosphere39. For simplicity, the TOA shortwave outgoing radiation in clear-sky and all-sky conditions is denoted, respectively, by SWRclr and SWRall. All variability in TOA shortwave outgoing radiation in clear-sky conditions is assumed to be the result of changes in aerosols. Then, the TOA clear-sky shortwave outgoing radiation (SWRclr) is referred to as the DARE, and the subscript clr is used to denote the clear-sky conditions component of DAREclr.

Figure 2 shows the seasonal trend (2002–2021 period) of the DAREclr (a) and SWRall (b). The observed large increase in AOD has caused a mean DAREclr change of −0.09 ± 0.06 W m−2 yr−1 over the bounded area (Fig. 2a). The integral decline over the 20-year period is −1.74 ± 1.16 W m−2. While in the presence of clouds, the mean changes in the bounded area show an increase in SWRall by +0.36 ± 0.21 W m−2 yr−1 and +7.22 ± 4.26 W m−2 over the full period (Fig. 2b). On a global scale, previous studies have uncovered consistent patterns in clear-sky TOA shortwave radiation from CERES that correspond with changes in aerosol distribution over time and space40,41,42.

Fig. 2: Spatial distribution of the seasonal trends of shortwave outgoing radiation.
figure 2

a, b Seasonal (JAS) trends (2002–2021) of the top of the atmosphere shortwave outgoing radiation (watt per square meter per year) for clear-sky (DAREclr) and all-sky (SWRall) regions as retrieved from CERES satellite. Dots indicate geographical cells for which the trends are statistically significant (at a 5% significance level).

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For all-sky broadband radiation, variabilities, and trend values are significantly influenced by clouds. Figure 3 shows the seasonal trend (2002–2021 period) in retrievals of cloud properties from MODIS datasets43. Overall, there is a significant negative trend in liquid cloud retrieval fraction (CF) (Fig. 3d) and a negative trend in liquid cloud optical thickness (COT, Fig. 3a), associated with the negative trend in liquid cloud water path (LWP, Fig. 3b) and with a slightly positive trend in liquid cloud effective radius (Reff, Fig. 3c). The associated relative trends are represented in Supplementary Fig. 2, and their average in the red bounded area are listed in Supplementary Table 1. Thereby, the increase in SWRall (Fig. 2b) can be partly explained by the decline in CF and COT.

Fig. 3: Spatial distribution of seasonal trends in cloud properties.
figure 3

a–d Seasonal (JAS) trends (2002–2021) of liquid cloud optical thickness (COT in unitless per year), liquid cloud water path (LWP in gram per square meter per year), liquid cloud effective radius (Reff in micrometer per year), and liquid cloud fraction (CF in unitless per year) retrieved from MODIS (Terra+Aqua) satellite. Dots indicate geographical cells for which the trends are statistically significant (at a 5% significance level). Regions experiencing over 8% monthly data missing are excluded from trend calculations.

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Therefore, to analyze longer-term changes in DARE in all-sky conditions (DAREall), one approach is to subtract the cloud radiative effect contributions (SWRcld, and the subscript cld is used to denote the cloudy-sky conditions) from the SWRall seasonal trend.

$${d{\rm{DARE}}}_{{\rm{all}}}={d{\rm{SWR}}}_{{\rm{all}}}-{d{\rm{SWR}}}_{{\rm{cld}}}$$
(1)

There is a strong correlation between SWRall and the cloud fraction and cloud optical thickness (Fig. 4aR2 = 0.97). However, we notice that this relationship is slightly influenced by AOD, as seen in Supplementary Fig. 3. Following the approach described in the Methods-Statistics-linear regression model subsections, we incorporate the influence of aerosols and derived the following linear regression equation:

$$\frac{dy}{{dt}}=76.320\frac{d{x}_{1}}{{dt}}+4.291\frac{d{x}_{2}}{{dt}}$$
(2)
Fig. 4: Relationship between shortwave outgoing radiation and cloud properties.
figure 4

Multiple linear regression model (a) where the SWRall (\(y\) in W m−2) is shown as the response variable as a function of two predictor variables: CF (\({x}_{1}\) in unit) and COT (\({x}_{2}\) in unit). Seasonal (JAS) trends (2002–2021) of the predicted SWRcld (b) for each combination of CF (Fig. 3d) and COT (Fig. 3a) through the equation \(\frac{{dy}}{{dt}}=76.320\,\frac{d{x}_{1}}{{dt}}+4.291\frac{d{x}_{2}}{{dt}}\) (derived from the multiple linear regression equations and the weighted average of the regression coefficients in Supplementary Fig. 3 and the residual DAREall (c) as the difference between the observed SWRall (Fig. 2a) and the predicted SWRcld trends. Regions experiencing over 8% monthly data missing are excluded from trend calculations.

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The predicted SWRcld seasonal trend (Fig. 4b) can be, therefore, estimated based on the relationship between collocated SWRall (\(y\)) from CERES with CF (\({x}_{1}\)) and COT (\({x}_{2}\)) retrievals by MODIS.

Notably, the long-term evolution in cloud properties (\(d{{\rm{SWR}}}_{{\rm{cld}}}\)) includes potential local indirect and semi-direct effects induced by BBA44. However, it is very interesting to see that long term trend in MODIS observations shows an increasing trend in AOD but decreasing trend in CF, COT. The trend in CF and COT may be influenced by indirect and semi-direct aerosol effects but the \(d{{\rm{SWR}}}_{{\rm{cld}}}\) responds to many other factors such as global warming, climate feedback and natural variability.

The residual TOA shortwave radiation seasonal trend in Fig. 4c is the difference between the observed SWRall (Fig. 2a) and the predicted SWRcld (Fig. 4b) and corresponds to DAREall according to the definition in Eq. 1. The mean changes in the bounded area show increases of +0.32 ± 0.21 W m−2 yr−1 and +0.04 ± 0.15 W m−2 yr−1 in predicted SWRcld and residual DAREall, respectively. The high geographical standard deviation of the residual DAREall mean is caused by the spatial variation that includes regions with decreasing CF northwards from 7°S (Fig. 3d). There have been several measurement campaigns in this area that showed that BBA is mostly located above the clouds4,45,46,47. The positive mean seasonal trend of DAREall could thus be potentially linked to the positive forcing by BBA above Sc.

Another interesting result is that the seasonal trend in DAREall shows a dipole pattern (Fig. 4c) over the SEA with a negative trend south of 7°S and a positive trend further north. This pattern is determined by the larger decrease in CF trend northwards from 7°S (Fig. 3d). Thus, increasing absorbing aerosols located south (north) of 7°S may have induced a more positive (more negative) DAREall while the cloudiness trend is almost zero (is negative). This dipole pattern has been recently documented and simulated in Mallet et al.34.

Since the cloud and aerosol satellite retrievals cannot strictly collocate, it is difficult to establish a clear link between the seasonal trend in satellite-derived AOD and in DAREall. This is why this satellite-based analysis is complemented by modeling simulations.

Simulated trends in clear and all skies’ DARE

It has been demonstrated that the simulated radiative impact of BBA over the SEA region from the global three-dimensional chemical transport model OsloCTM compares well to measurements20. Additionally, the simulated optical properties of aerosols above clouds from OsloCTM compare favorably to observations4. Brown et al.8, reveal that, in general, most climate models tend to overestimate the absorptivity of BBA, but OsloCTM exhibits better agreement with observational data on single scattering albedo (SSA), particularly over South Africa.

Aerosols from OsloCTM3 simulations in Lund et al.48 have been adopted, but two modifications have been made to achieve better agreement with aerosol observations. The BBA has been doubled to better agree with MODIS AOD, and the single scattering albedo has been fixed to 0.83 at 550 nm (but with same spectral variation as in the original OsloCTM3 simulations). The simulated column SSA at 550 nm reports an average value (2010–2017) including all aerosol types of 0.87 ± 0.02, which is representative of recent measurement campaign-based studies. It has been demonstrated that the free-tropospheric SSA at 550 nm ranges from 0.85 to 0.88 for BBA within the Southern African Regional Science Initiative (SAFARI 2000) and ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) measurement campaigns from late August-September45,47,49. The CLARIFY (Clouds and Aerosol Radiative Impacts and Forcing) observations were made further west (Ascension Island) than the ORACLES region (off the coast of Namibia) and had undergone additional days of ageing. The average SSA of BBA at the free troposphere observed during CLARIFY was 0.83 ± 0.03 at 550 nm, falling within the lowest level of the above-reported range50,51.

Two simulations have been performed, including a control one with anthropogenic and biomass-burning emissions set to ON (CTL) and a second one with all emissions set to OFF (NOAERO) over a period of 8 years (2010–2017). The simulated TOA SW in all sky from CTL experiment (Supplementary Fig. 4) compares well to CERES satellite data. Defined as the difference between the outgoing shortwave radiation from CTL and NOAERO experiments, a normalized (divided by the AODCTL) aerosol radiative efficiency (W m−2 AOD−1) at TOA has been calculated and averaged over 8 years (2010–2017) as represented in Fig. 5a under clear-sky conditions and in Fig. 5b under all-sky conditions. By multiplying these terms by the MODIS AOD trends (in unit yr−1, as shown in Fig. 1), we should be able to retrieve the direct aerosol radiative effect from BBA in clear-sky conditions (DAREclr,OsloCTM3+MODIS – Fig. 5c) and from BBA in all-sky conditions (DAREall,OsloCTM3+MODIS – Fig. 5d). DAREclr,OsloCTM3+MODIS shows a negative mean trend of an order of magnitude of -0.09 ± 0.08 W m−2 yr−1 very close to the DAREclr trend derived from CERES dataset (−0.09 ± 0.06 W m−2 yr−1). This confirms the ability of the OsloCTM3 to well reproduce the clear-sky radiative impact of BBA over the SEA region. While DAREall,OsloCTM3+MODIS shows a positive mean trend of an order of magnitude of +0.04 ± 0.07 W m−2 yr−1, which is very close to the DAREall trend retrieved from CERES and MODIS (+0.04 ± 0.15 W m−2 yr−1).

Fig. 5: Spatial distribution of seasonal trends in simulated shortwave outgoing radiation.
figure 5

a, b Seasonal (JAS) means (2010–2017) of simulated aerosol radiative efficiency (watt per square meter per AOD) at the TOA, defined by the difference in the outgoing shortwave radiation from CTL and NOAERO experiments divided by the AODCTL from OsloCTM3 in clear-sky conditions and in all-sky conditions. c, d Seasonal (JAS) linear trends (2002–2021) of DAREclr,OsloCTM3+MODIS and DAREall,OsloCTM3+MODIS as retrieved by multiplying (a) and (b) respectively by the AOD trend from MODIS in Fig. 1a.

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By multiplying the simulated aerosol radiative efficiency at TOA from OsloCTM3 with the AOD trend from MODIS, we retrieve linear trends of DAREclr and DAREall close to the CERES observations. These results confirm that under the clear-sky conditions, the SEA Ocean region depicts a significant increasing trend of cooling at the TOA induced by BBA by −0.09 W m−2 yr−1, while under the all-sky conditions, BBA induces a significant increasing trend of warming of the TOA by +0.04 W m−2 yr−1. However, we note that the DAREall has a large spatial variation, mainly because of variation in the stratocumulus cloud cover influencing the radiative efficiency of BBA, as shown in Fig. 5.

Discussion

During the peak fire season, the South-Eastern Atlantic region is characterized by the presence of stratocumulus, which alters the DARE of BBA, leading to a positive forcing at the TOA due to absorbing aerosols that reduce the outgoing shortwave radiation. While the majority of previous studies focus on the quantification of the magnitude of DARE, in this study, we aim to provide additional information on the trend over the past 20 years. Highly advanced passive satellite sensors for measuring radiative fluxes at the TOA (CERES) and AOD and cloud properties (MODIS) were used to address long-term changes (2002–2021) in DARE over the SEA ocean. Observational trends of direct aerosol radiative effect in clear skies (DAREclr) and all skies (DAREall) have been retrieved separately, and their values have been reproduced by the equivalent simulated variables from the chemical transport model OsloCTM3.

At TOA, results show lines of evidence that DAREclr has become more negative (-0.09 ± 0.06 W m−2 yr−1) due to the positive trend in the amount of BBA in the SEA region. On the other hand, DAREall has become more positive ( + 0.04 ± 0.15 W m−2 yr−1) due to aerosols in cloudy sky regions. The trend in DAREall represents a radiative forcing of ~0.8 W m−2 over the 20-year period.

Although the OsloCTM3 simulations were conducted over only 8 years (2010–2017), the primary approach was to accurately quantify the simulated AOD radiative efficiency, closely aligning it with observations, to facilitate the derivation of the trend of simulated DAREOsloCTM3+MODIS by multiplying it with the MODIS AOD trend. Subsequently, a comparison with observations was made to validate the order of magnitude of the observed (CERES + MODIS) DARE trends both in clear and all-skies. OsloCTM3 has demonstrated its capability, in previous studies, to simulate the radiative impact of BBA over SEA region accurately. Notably, while many climate models tend to overestimate the absorptivity of BBA, OsloCTM3 shows better agreement with observational data on SSA over South Africa. Adjustment of the single scattering albedo to match observations, along with the utilization of cloud fields from climatology, has been implemented in osloCTM3. This approach helps reduce uncertainties associated with these parameters and/or with the representation of meteorology.

Furthermore, we demonstrate that the simulated TOA SW radiation in both clear and all-sky conditions from the CTL experiment aligns well with CERES satellite data. Additionally, the simulated AOD from the CTL experiment exhibits a similar scale to MODIS observations.

Collectively, these factors support the conclusion that the agreement between the linear trends of simulated and observed DAREclr and DAREall, can be attributed to the increased presence of aerosols in the SEA region.

As for the quantitative values of DARE, some uncertainties may be associated with the simulated DAREOsloCTM3+MODIS as the value of SSA of BBA is fixed in the model and do not account its long-term changes in this parameter. However, this simplification may be mitigated by the fact that we utilize the AOD trend from MODIS to derive the simulated DAREOsloCTM3+MODIS.

Additionally, the observed DARE depends on \(d{{\rm{SWR}}}_{{\rm{cld}}}\), predicted from \(d{{\rm{SWR}}}_{{\rm{all}}}\), which includes signals not only from cloud radiative effect contribution and global warming but also from DARE (above the cloud top) (Supplementary Fig. 3 supports this point). Although the contribution may be small compared to cloud radiative effect, it cannot be neglected and likely has an impact on the quantification of the observed DAREall value.

However, the most substantial uncertainty that can impact the outcome is associated with the calculation of the trends themselves. The ‘95% CI’ column in Supplementary Table 1 represents the 95% confidence intervals calculated based on the Theil-Sen slope of the observations after their geographic aggregation over the bounded area. The broader interval indicates increased uncertainty in the values, compounded by the inherent uncertainty in the observations, further complicating the quantification of DARE.

The positive mean seasonal trend of DAREall is linked to aerosols in cloudy sky regions. Observations indicate that most of the aerosols are situated above clouds, but in some cases, they can be found both within clouds and below clouds17,52,53. A recent study36 demonstrates that the increasing AOD trends of BBA over Central Africa find validation in the escalating extinction trends of BBA at various altitude levels. As a prospective avenue for further research, this study emphasizes the potential contributions that analyzing the evolution of the vertical structure (e.g., CALIPSO) and absorbent characteristics (e.g., AERONET) of BBAs over the last decade could provide, offering a clearer response to the hypothesis.

While the positive direct radiative effect of biomass burning aerosols primarily depends on their geographical (SEA region) and seasonal (dry season) distribution, their long-term increase may give rise to significant local or regional climate effects and could also represent an underrecognized source of global warming. Overall, this study underscores the need to better constrain uncertainties related to the direct radiative effect of biomass burning aerosols over the south-eastern Atlantic (SEA) stratocumulus region.

Methods

Satellite data

Criteria of selection

The A-Train satellite constellation facilitates simultaneous and coordinated measurements. CERES provides accurate continuous estimates of top-of-atmosphere (TOA) radiation, while MODIS complements this with detailed aerosol and cloud property information. MODIS provides higher spatial resolution imagery, while CERES has a coarser spatial resolution. Both operate with daily temporal resolution. For spatial and temporal collocation in DARE calculations, we use Level 3 Monthly Global Gridded MODIS and CERES datasets at 1-degree resolution. This coordinated approach enables effective assessment of trends and variability in the direct aerosol radiative effect at TOA over extended periods.

CERES data

The TOA shortwave outgoing radiation in clear-sky (SWRclr) and all-sky (SWRall) conditions consist of monthly mean level-3 1 × 1 degree latitude-longitude dataset from the CERES39 Energy Balanced and Filled (EBAF) Edition 4.2. In clear-sky conditions, the TOA shortwave outgoing radiation variable of cloud-free areas of the region is used (e.g., “toa_sw_clr_c_mon”). Any variability in SWRclr is assumed to be the result of changes in aerosols. Consequently, the TOA SWRclr is referred to as the DAREclr.

Raghuraman et al.54 assumes a 0.20 W m−2 decade−1 (0.02 W m−2 yr−1) observational uncertainty in shortwave radiative flux trends from CERES.

MODIS data

AOD at 550 nm and cloud products (COT, LWP, Reff, and CF) consist of monthly mean level-3 1×1 degree latitude-longitude dataset from MODIS. The MODIS AOD is derived from the mean of the Dark Target and Deep Blue Combined Aerosol Products33 from the Terra satellite (MOD08_M3 Collection 6.1) dataset, along with the equivalent dataset from the Aqua satellite (MYD08_M3 Collection 6.1). The MODIS cloud products43 come directly from the combined Aqua and Terra MODIS Cloud Properties product (MCD06COSP_M3_MODIS) dataset.

Model simulations

Criteria of selection

OsloCTM’s simulated radiative impact of biomass burning aerosols over SEA aligns well with measurements20 and exhibits better agreement with observational data on single scattering albedo, particularly over South Africa, compared to most climate models4.

Setting-up

OsloCTM3 is driven by 3-hourly meteorological forecast data from the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) model with a 2.25◦ x 2.25◦ horizontal resolution with 60 vertical layers. OsloCTM3 includes, in addition to BBA, sulfate, nitrate, black carbon from fossil fuel and biofuel, OC from fossil fuel and biofuel, secondary organic aerosols, mineral dust and sea salt. Emission injection height of BBA in OsloCTM34 is between 0 and 5 km.

Offline radiative transfer calculations are performed using a multi-stream model that employs the discrete ordinate method55 and accounts for gas absorption, Rayleigh scattering, aerosol absorption, and aerosol and cloud scattering. Thus, the model OsloCTM3 can capture the differences in clouds and aerosols optical properties in subsequent radiative transfer calculations but does not include the aerosols semi-direct and indirect effects of aerosols (aerosol-cloud interactions). In the radiative transfer calculation, 3-hour data of aerosols and meteorological data consistent with OsloCTM3 are applied. Comparison of the seasonal (JAS) mean into the red bounded area between observed and simulated and SWRall shows good agreement in magnitude for each year (Supplementary Fig. 4).

Normalized radiation efficiency

Aerosol fields from OsloCTM348 have been employed for the calculation of normalized radiative efficiency with two modifications to BBA abundance and single scattering albedo, as noted above. For this purpose, two simulations have been conducted with and without anthropogenic and biomass-burning emissions over the period of available input data (2010–2017). The simulations are utilized to obtain a rate calculation (W m−2 AOD−1) and not a trend; therefore, it was assumed that the length of the simulation period is not critical. We use the seasonal mean normalized radiative efficiency between 2010 and 2017. Over the 8-year period, the normalized radiative efficiency varies from 23.66 W m−2 AOD−1 in 2015 to 27.20 W m−2 AOD−1 in 2013 in clear sky conditions, and from -14.51 W m−2 AOD−1 in 2014 to -8.06 W m−2 AOD−1 in 2010 in all-sky conditions. This corresponds to a DAREclr,OsloCTM3+MODIS and DAREall,OsloCTM3+MODIS varying from -0.093 to -0.081 W m−2 yr−1 and +0.029 to +0.053 W m−2 yr−1, respectively. Using the mean AOD radiative efficiency and considering the uncertainties, we remain within the order of magnitude compared to observations, as presented in Supplementary Table 1.

Statistics

Trend

The Mann–Kendall test is used to identify significant long-term changes in observed AODs, cloud products, and shortwave radiation. The Mann-Kendall Trend Test56,57 statistically assess if there is a consistently (monotonic) increasing or decreasing trend of the variable over time, but the trend may or may not be linear. It is a non-parametric test, applicable to all distributions. We employed a critical p-value of 0.05 for trend significance. The magnitude of the Mann-Kendall trend is estimated using the Theil58 and Sen59 method. Theil-Sen estimators are calculated60 at every grid point spatially before being averaged over the bounded area (2–20°S, 10°W –10°E).

We conducted the Mann-Kendall trend analysis with the condition that each pixel had no more than 5 missing monthly data points, accounting for 8% of the total months. In our investigation area, we observed no missing monthly data, except in a few pixels in the AOD MODIS product (<8% of total pixels). Mann-Kendall trend analysis is known for its robustness, particularly when dealing with minimal and randomly distributed missing data.

Linear regression model

The ordinary least squares multiple linear regression model is built from the response variable SWRall from CERES as a linear function of the two predictor variables CF and COT from MODIS. The regressors (CF and COTL from MODIS) are correlated, but it is primarily the CF regressor that yields a regression model with an R-squared value of 0.949 (considering a simple regression model by removing COTL). The addition of COTL allows for a slightly improved regression model with an R-squared value of 0.974. Therefore, it would have been possible to use only one regressor and maintain a rigorous linear regression.

Confidence intervals

Confidence intervals of 95% are calculated based on the Theil-Sen slope of the observations after their geographic aggregation over the bounded area.

Data fusion techniques

Predicted SWRcld

The cloud radiative effect contribution (SWRcld) is determined through linear regression between CERES SWRall and MODIS CF and COTL, as presented in Fig. 4. However, upon estimating SWRcld, we observe a slight influence of AOD, as illustrated in Supplementary Fig. 3. To account for the influence of AODs, we choose to formulate distinct multiple linear regression equations based on varying AOD thresholds (between 0 and 1 with intervals of 0.1). Next, we compute the weighted average of regression coefficients from these equations, assigning weights based on the number of observations (pixels) associated with each AOD threshold and derive a final multiple linear regression Eq. (2).

Observed DAREall

The trend TOA direct aerosol radiative effect trend under all-sky conditions (DAREall) is obtained by subtracting the trend in cloud radiative effect SWRcld from the trend in SWRall.

The assuming of independence and additivity between SWRcld and DAREall is reasonable, given that SWRcld includes the semi-direct and indirect aerosol radiative effects.

Simulated DARE

The simulated TOA direct aerosol radiative effects in clear and all-sky conditions (DAREclr,OsloCTM3+MODIS, DAREall,OsloCTM3+MODIS) are calculated by multiplying the MODIS AOD trends with the corresponding simulated normalized AOD radiative efficiency, as described in the Model Simulations section.