Introduction

Surface Albedo (SA), defined as the ratio of reflected short-wave radiation to downward short-wave radiation at the surface, ranges from 0 – 1, with higher values indicating greater reflectivity1. The SA is highly variable, particularly over land, with spatio-temporal distribution being influenced by natural processes and human activities, such as land use changes, rain, snow, drought, and so on2. Changes in SA alter the radiative flux reaching the Earth’s surface, thus affecting the climate3. Due to its important role in Earth’s energy balance, SA is widely recognized and used in both weather forecast and climate prediction1.

Atmospheric aerosols are suspended solid and liquid particles in the atmosphere. They significantly affect environmental quality, climate and health4,5. Aerosols impact Earth’s energy budget by scattering and reflecting solar radiation back into space, thus decreasing incoming energy and cooling the surface, or by absorbing solar radiation, thereby warming the atmosphere6,7. They also act as cloud condensation and/or ice nuclei, modifying cloud properties such as water path, droplet size, cloud amount, and life cycle8,9,10,11. These changes in cloud macro- and micro-physical characteristics affect the radiative fluxes reaching the Earth, thereby influencing the climate.

The term Aerosol Direct Radiative Effect (ADRE) describes radiative flux changes due to direct absorption and scattering by anthropogenic or natural aerosols12. This phenomenon intricately influences the Earth-atmosphere system’s energy balance, primarily through modifications to the planetary albedo, which can lead to either cooling or warming effects6,13. In the clear-sky, the planetary albedo is dominated by the aerosol optical properties like Aerosol Optical Depth (AOD), Single Scattering Albedo (SSA), Asymmetry Factor (ASY), along with environmental factors like SA14. Changes in aerosol optical properties and SA result in corresponding shifts in regional planetary albedo, thereby causing variations in the ADRE, where an increase or decrease in regional planetary albedo leads to a corresponding increase or decrease in ADRE15. The Critical SA is identified as the juncture at which ADRE transitions from negative to positive value, marking a shift in its impact from cooling to warming effects on the regional Earth-atmosphere system. In the pioneering work on Critical SA, Atwater16 developed an equation that detailed how aerosols affect planetary albedo, indicating a shift from cooling to warming due to the evolving nature of aerosol absorption and backscattering in urbanized areas16. Further computations using radiative transfer models revealed that the aerosol short-wave radiative warming effect (AWE) depends on AOD, SSA, backscattering ratio, and SA, with the magnitude of AWE increasing with AOD17,18,19. Recent ground-based aerosol observations, particularly from the Aerosol Robotic Network (AERONET), have advanced research on the Critical SA. These studies suggest that Critical SA values are typically above 0.3, though they vary by region and are influenced by the type of aerosols or their SSA20,21,22,23.

To sum up, the interaction between SA and aerosol is important in balancing Earth’s energy. However, the alteration of surface types and their corresponding SA in recent years presents a significant and yet unresolved question: How do these changes in SA affect the ADRE and corresponding AWE? This investigation explores the intricate interaction between modifications in SA and their resulting impact on ADRE and AWE. More specifically, this study contributes by analyzing the global spatial and temporal distribution of ADRE and AWE, quantifying the contribution of SA to ADRE, and evaluating its potential influence on AWE. We first analyze the ADRE and AWE distributions using satellite data from Clouds and the Earth’s Radiant Energy System (CERES) and ground observations from AERONET. Then, using AERONET, we calculate Critical SA for different AOD and SSA conditions and map Critical SA with CERES data. Finally, we merge CERES data with aerosol reanalysis data from Aerosol Climatology in its second version form Max Planck institute (MACv2), enabling us to quantify recent changes in ADRE attributable to monthly and annual SA fluctuations between March 2000 and February 2020. This study enhances our understanding of how SA interactions with ADRE influence the Earth’s radiative balance.

Results

The spatio-temporal distributions of ADRE and AWE

Satellite observations reveal that, over multiple years from March 2000 to February 2020, the average ADRE is predominantly negative across most regions, suggesting that aerosols generally have a cooling effect on the Earth-atmosphere system (as shown in Fig. 1a). The magnitude of aerosol cooling effect is closely associated with AOD values. Particularly, in areas such as Eastern China and Northern India (depicted in Fig. S1a), high AOD values are aligned with most pronounced cooling effects, exceeding 15 W/m2. Adjacent marine areas, the Western Pacific, and the Indian Ocean also exhibit strong cooling effects due to transported aerosol24. The AWE is primarily concentrated in mid-to-high latitude regions, characterized by long-term ice and snow coverage like the polar regions, or locally prevalent absorbing aerosols such as in the Arctic, Northern Africa’s desert areas, Siberia, Northeast Asia, and Central North America (Fig. 1b). The occurrence of AWE is significantly more frequent in the polar regions than lower latitude regions. Specifically, the highest occurrence of AWE has been observed in Greenland within the Arctic, as well as in the Weddell Sea and southwestern parts of Antarctica, as illustrated in Fig. 1c. This spatial pattern underscores that the regions with high surface albedo, such as the ice-covered polar areas, are with markedly increase of ADRE. In terms of hemispherical distribution, AWE is more pronounced in the Northern Hemisphere than in the Southern Hemisphere, and more so in the Arctic than in Antarctica, due to higher anthropogenic aerosol emissions in the Northern Hemisphere. Ground-based observations reveal that the geographical distribution of AWE mirrors that observed by satellites. Nevertheless, due to the higher temporal resolution of AERONET data compared to the CERES data utilized in this study, it becomes evident that AWE is more broadly found by AERONET across land areas (Fig. 1d). For example, frequent AWE events occur over the southwest US and Chile, which may be due to the declining SSA trend in these regions25.

Fig. 1: The spatio-temporal distributions of the Aerosol Direct Radiative Effect (ADRE) and aerosol short-wave radiative warming effect (AWE).
figure 1

(a) the spatial distribution of the multi-year average ADRE from March 2000 – February 2020; (b) similar to (a), but for the AWE; (c) similar to (b), but depicting the frequency of AWE; (d) the spatial distribution of multi-year average AWE and occurrence frequency at AERONET sites, where the size of the circles represents the frequency of AWE at each site, and the color indicates the average value of AWE. Note that both the ADRE and AWE are in the clear-sky condition.

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The AWE exhibits significant monthly variations. As shown in Fig. 2, during the Northern Hemisphere winter months, such as from December to January, the ADRE and AWE in the Arctic are nearly zero due to the absence of sunlight. Similarly, during the Southern Hemisphere winter from June to August, the AWE over Antarctica is also nearly zero. Spanning from November through October of the following year, the Arctic observes a rise and then a decline in the AWE, with a notable peak exceeding 5 W/m2 occurring in May and June. In the Northern Hemisphere, the spatial coverage of AWE reaches its maximum roughly between January and March, stretching into the mid-latitudes of the Eurasian and North American continents. This expansion can be attributed to the progressively decreasing solar zenith angle during these months, coupled with heightened emissions of absorbing aerosols, along with the persistence of snow and ice coverage over the land. In the North African region, AWE is found every month due to abundant solar irradiance throughout the year. However, a slight decrease in AWE values during the Northern Hemisphere winter can be observed, possibly because the turbulence and convection are weaker in the winter, making it more difficult for dust aerosols to enter the atmosphere26. Besides, the AWE in the all-sky appears in marine regions, such as the South Atlantic, North Pacific and East Pacific (Fig. S2b) due to the impact of high reflecting low-level clouds (Fig. S2d)15,27, but the distribution of ADRE in the all-sky is similar to that in the clear-sky, and the AWE in the all-sky is also more frequent in the high latitude regions than other regions (Fig. S2 a and c).

Fig. 2: The spatial distributions of monthly average aerosol short-wave radiative warming effect (AWE) in the clear-sky condition for period from March 2000 to February 2020.
figure 2

a–l respectively represent the month from March to next February.

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Combining the information from Fig. 1 and Fig. 2, it becomes evident that while aerosols predominantly exert a cooling influence on the Earth-atmosphere system across most global regions, the AWE is also present on every continent. This is particularly noticeable in snow- and ice-covered mid-to-high latitudes, where the SA is comparatively higher than on other types of surfaces28. Additionally, the AWE is distinctly observable in regions characterized by a dominance of absorbing aerosols. AWE is easier to detect with higher temporal resolution measurements, such as 15 min AERONET data, than CERES monthly data. AWE shows clear monthly variations, closely linked to local snow and ice cover, aerosol emissions, and the monthly variation of solar irradiance. This study, by integrating both satellite and ground-based data, reveals that the AWE is a ubiquitous phenomenon, occurring across various times and locations. Significantly, SA plays a vital role in determining the magnitude of AWE.

The impact of surface albedo on the AWE and ADRE

A key aspect of this study is to investigate the intricate relationship between SA and AWE, as well as ADRE. We examine the specific SA value termed the ‘Critical SA’, marking the point where ADRE transitions from a negative to a positive value. By using the AERONET data, we divided the samples into four intervals of AOD and SSA based on equal sample size to investigate the impact of SA on the ADRE as well as AWE under different AOD and SSA conditions. We conducted linear fittings of ADRE against SA within each of intervals (illustrated as red lines in Fig. 3a–d), which allows us to elucidate the relationship between SA and ADRE clearly. All linear fits in each subplot of Fig. 3 have P < 0.01, passing the significance test with a confidence level of 99%. The Critical SA for each AOD and SSA interval is identified at the point of SA where ADRE is equal to zero (black lines in the Fig. 3). As depicted in Fig. 3a–d, an increase in SA leads to a rise in the ADRE value, indicating that an increase in SA amplifies the absorption within the aerosol layer, thereby weakening the aerosol cooling effect and consequently increasing the possibility of AWE occurrence. When SSA and AOD are low, aerosols are more likely to exert AWE, and the corresponding Critical SA is smaller (Fig. 3a1), indicating that thinner and/or more absorbing aerosols more easily heat the Earth-atmosphere system statistically, although the variations of absorbing and scattering aerosols Critical SA with AOD may be slightly different. Figure 4a shows the values of Critical SA across different SSA and AOD intervals, ranging from 0.18 to 0.96. As AOD and SSA increase, Critical SA also increases. When AOD > 0.26 and SSA > 0.97, AWE does not occur (Fig. 3d4), with unrealistic theoretical Critical SA values of 1.09 and 2.42, respectively. Besides, the variations of Critical SA are more sensitive to SSA than AOD according to Figs. 3 and 4a. It should be noted that all data containing all solar zenith angle (SZA) samples in the Version 3 Level 1.5 product are separated into different AOD and SSA intervals by the same sample numbers, and to estimate the Critical SA by linear regression. The variations of Critical SA with SSA and AOD at different SZA calculated using linear regression are shown in Fig. S3a–c. The results are similar to those presented in Fig. 4a, where Critical SA increases with the increase of SSA and AOD. The comparison with Critical SA calculated by linear regression and Santa Barbara DISORT Atmospheric Radiative Transfer Model (SBDART)29 is shown in Fig. S3d. Considering that AERONET is distributed globally, the atmospheric environment at each site and the solar altitude throughout the year are not the same. The majority of Critical SA points are located near the 1:1 line, which indicates that the simulated Critical SA is relatively consistent with the Critical SA calculated by linear regression. Early satellite remote sensing studies suggested that for conditions with a SA value near Critical SA, the radiative flux is independent of AOD and sensitive to SSA, enabling satellite retrieval of SSA17,30, while recent studies have noted a slight increase in Critical SA with increasing AOD31,32,33, which is confirmed by our study. These results emphasize that thinner and/or more strongly absorbing aerosols exert less cooling effect at the top of atmosphere (TOA) and more easily cause AWE with a smaller Critical SA.

Fig. 3: The variations of Aerosol Direct Radiative Effect (ADRE) with Surface albedo (SA) in the clear-sky condition.
figure 3

a–d illustrate the variation of ADRE with SA under different Aerosol Optical Depths (AOD) and Single Scattering Albedo (SSA) conditions. AOD and SSA are divided into four intervals with an equal sample number. Sub-figures numbered 1–4 correspond to different SSA intervals: (0, 0.89], (0.89, 0.93], (0.93, 0.97], (0.97, 1], while Sub-figures labeled (a–d) correspond to different AOD intervals: (0, 0.07], (0.07, 0.13], (0.13, 0.26], (0.26, 1.5]. Due to the few extremely high values of AOD (AOD > 5), the final AOD interval is chosen as (0.26, 1.5]. The color represents the probability of sample occurrence, black lines indicate the ADRE equal to zero, and red lines represent linear fittings of ADRE with SA. All red lines in the Sub-figures are with P < 0.01.

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Fig. 4: The variations of Critical surface albedo (Critical SA) with Aerosol Optical Depths (AOD) and Single Scattering Albedos (SSA), as well as the distribution of Critical SA in the 60-90oN regions.
figure 4

(a) the values of Critical SA across different SSA and AOD intervals, represented by the intersections of the red and black lines in Fig. 3a–d, with colors indicating the numerical values of Critical SA. (b) the geographical distribution of Critical SA in the Arctic region calculated using the CERES data, specifically retaining those grids where the significance level (P-value) is <0.05 and where the AWE is observed. The calculations are based on the clear-sky condition.

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To obtain the geographical distribution of Critical SA, we further used data of radiation and SA from CERES to perform linear fits of ADRE against SA for each grid, specifically retaining those grids where the significance level (P-value) is <0.05 and where the AWE is observed. These results show that these grids are mainly concentrated in the high latitudes of the Northern Hemisphere. Consequently, Fig. 4b exclusively showcases the geographical distribution of Critical SA within the 60–90°N latitude range. It should be noted that current satellite sensors are challenging to obtain long-term and reliable SSA products15, and the MACv2 data only provide multi-year averages of annual or monthly SSA. Due to the lack of long-term, high-quality satellite data and reanalysis data of SSA, we have to use the linear regression to calculate Critical SA without considering the variation of SSA. Actually, in the Arctic region where the multi-year average of ADRE exceeds zero, the multi-year average SSA is 0.96 with a standard deviation of 0.002, based on MACv2 data. As depicted in Fig. S4, the cumulative distribution function (CDF) shows that the probability of SSA reaching 0.93 is 0.86, whereas for SSA at 0.91, it drops to 0.01. The SSA average is 0.92, with the standard deviation being 0.0088. These indicate that the majority of SSA samples are concentrated between 0.91 and 0.93. Considering that SSA values from 0.89 to 0.93 are categorized within the same interval for deriving the Critical SA in Figs. 3 and 4a and the slight variation of SSA, it could be reasonable to overlook the variations in SSA in Fig. 4b. The Critical SA is mainly concentrated around the Arctic Ocean and the southern part of Greenland, with values all above 0.4 and slightly higher in southern Greenland island than in the Arctic Ocean.

Figure 5a presents the spatial distribution of decadal trend in SA from 2000 to 2020. The global annual mean of SA change (including all regions) is 5.58 * 10-3/decade (P < 0.05), resulting ΔADRE -0.134 W/m2/decade. However, in the regions where the SA trend is significant, SA has decreased at a more significant average rate of -0.012/decade, with the greatest decline observed in the Arctic at -0.039/decade. Based on the global reanalysis dataset, Yu & Huang34 decomposed the trend of clear-sky ADRE into components such as AOD, SA, and insolation, among others. There is a variance in the magnitude of ADRE trends between this study and that of Yu & Huang34, which is likely attributed to differences in the spatial-temporal range and resolution of the data used, as well as the analytical methods employed. Nonetheless, both studies underscore that changes in SA, driven by sea ice melting, have a significant impact on ADRE trends, particularly in the Arctic34. Besides the Arctic, regions showing a significant decrease in SA include India, Central and Northern Africa and Southeast Asia. In contrast, regions like Eastern China and Eastern South America, have shown significant increase in SA, likely influenced by changes in precipitation patterns35, agricultural production36, urbanization37, and snow cover38. Figure 5b illustrates the spatial distribution of ΔADRE, with a global average of -0.2 ± 0.17 W/m2/decade; that is, the average of ΔADRE in these grids with significant SA trend is -0.2 ± 0.17 W/m2/decade. In regions where SA significantly increases (or decreases), the value of ADRE shows a corresponding increase (or decrease). In the 60–90°N regions, where the SA decline is the greatest globally, the decrease in ΔADRE exceeds the global average by more than double (-0.46 W/m2/decade). In snow-covered areas such as polar regions and high-altitude areas, there exists positive ice-albedo feedback39, where melting snow/ice leads to decreased SA, causing more solar short-wave absorption at the surface and further snow melt. When snow melt leads to a reduction in SA, the cooling effect of aerosols on the Earth-atmosphere system intensifies, acting to counterbalance the ice-albedo feedback. This implies that aerosols, particularly in the short-wave spectrum, have the potential to mitigate warming in the Arctic or high-altitude regions, although the extent of this moderating influence might be limited. Besides, the magnitude of ΔADRE is also closely related to the local aerosols. For example, the magnitude of the ΔADRE is about 1 W/m2/decade in India, where aerosols are more absorbing (lower SSA) and the SA has a slower decreasing rate (-0.005 /decade).

Fig. 5: The spatio-temporal distributions of Aerosol Direct Radiative Effect (ADRE) change (ΔADRE) due to surface albedo change (ΔSA) in the clear-sky condition.
figure 5

a the spatial distribution of the decadal trend in Surface Albedo from 2000 to 2020, with grids having P < 0.05 shown with the percentage to the total data points being 30.41%; (b) similar to (a) but for ΔADRE; (c) the variation of ΔADRE with ΔSA globally and in each hemisphere, with error bars representing standard deviations; (d1) the monthly average of ΔADRE at global (black line) and at hemispheric scales, where red and blue lines represent that at the Southern Hemisphere (SH) and Northern Hemisphere (NH), respectively; (d2) the monthly variations of ΔSA globally and in each hemisphere, with bar graphs showing the trends of SA; the red line indicates the monthly average of Aerosol Optical Depths (AOD), where triangles represent the global average of AOD, and squares and circles represent that at the NH and SH, respectively. Noted that the average values of ΔADRE, ΔSA and AOD in Fig. 5c, d are derived from regions where the SA trend is significant.

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Figure 5c shows the variation of ΔADRE with ΔSA globally and in each hemisphere. As SA increases (decreases), the change of ADRE due to SA also increases (decreases), with the most pronounced changes in the Northern Hemisphere (NH), where every 0.1 change in SA results in >1 W/m2 change in ADRE averagely, higher than that in the global average and in the Southern Hemisphere (SH). In Fig. 5d1, the monthly average of ΔADRE at global and hemispheric grids with significant SA changes is presented. Both globally and in the Northern Hemisphere, the average ΔSA shows a gradual decrease from June to September. The most significant reductions in the ADRE are found in June and July, with values reaching -0.37 (globally) and -1.31 W/m2/decade (NH). These periods with the largest magnitudes of ΔADRE correspond with the peak in monthly average AOD, which are ~0.16 (globally) and 0.26 (NH) during June to July. From October to the February, the ΔADRE in the NH has a trend toward 0. Instead, both the average change in ΔSA and AOD reach their peaks at 0.003/decade and 0.11 in the SH, respectively, and the ΔADRE in the SH attains its minimum value, dropping to -0.16 W/m2/decade.

In summary, from 2000 to 2020, most global regions experienced a declining trend in SA. This decline led to more negative values of ADRE at the TOA, indicating an enhanced aerosol cooling capacity of the Earth-atmosphere system, particularly pronounced in the Northern Hemisphere during summer.

Discussion

Aerosols and SA are key factors influencing the Earth’s radiative energy balance. In general, aerosols increase through reflection the outgoing solar radiation at TOA, producing thus a planetary cooling. However, aerosols can produce a warming effect under high SA condition due to more reflected radiation from the surface, which enhances the aerosols’ absorption. Recent shifts in surface types and their corresponding SA, driven by both human activities and natural processes, raise a pivotal and yet unresolved question: How do these alterations impact the ADRE and the radiation budget of the Earth? This study analyzes the spatio-temporal distribution of the AWE globally, as well as the impact of SA on the ADRE by combining satellite data from CERES, ground observations from AERONET and aerosol reanalysis data from MACv2.

We found that except for the polar regions, aerosols generally have a short-wave radiative cooling effect on the Earth-atmosphere system, which indicates that under the global warming, the cooling effect of aerosols may partially offset the temperature rise caused by greenhouse gases. However, when SA is larger than the value of Critical SA, the ADRE probably shifts from negative to positive for certain SSA and AOD, therefore aerosols generate the warming effect at the TOA. The Critical SA ranges from 0.18–0.96 and increases with SSA and AOD, meaning that thick and highly scattering aerosols hardly exert AWE even with SA close to 1. Therefore, the AWE is widespread in snow- and ice-covered mid-to-high latitude regions with higher SA, and regions dominated by absorbing aerosols. In polar regions during polar nights, AWE and ADRE are close to zero, and the peak of AWE occurs around May-June in the Arctic, while the AWE over Antarctica is also zero from June to August. Our study suggests that in the regions where the SA trend is significant, the average declining rate of SA is -0.012/decade, leading to a -0.2 ± 0.17 W/m2/decade change in ADRE. As SA increases (decreases), the change of ADRE due to SA also increases (decreases), with the most pronounced changes in the Northern Hemisphere, where every 0.1 change in SA leads to over 1 W/m2 ADRE change, higher than the global and Southern Hemisphere averages. This result underscores the significant influence of SA on both the ADRE and AWE, demonstrating that changes in SA significantly influence the aerosol short-wave radiative cooling and warming effects. Predominantly, in the regions exhibiting a decline in SA, we observe an amplification in the aerosol short-wave radiative cooling effect at the TOA, and a diminished AWE. Such a mechanism could act to partially counterbalance the warming effects associated with reductions in SA, which are worth quantifying in the future studies. For example, in the Arctic, with the substantial SA changes (-0.039/decade, more than three times the global average) and the ΔADRE being more sensitive to ΔSA (Fig. S5), the average ΔADRE reaches about -0.46 (standard deviation: 0.36) W/m2/decade, more than twice the global average. This observation intimates that enhanced aerosol-induced cooling could attenuate the rate of snow and ice melting, albeit the extent of this regulatory impact remains circumscribed. The quantification of this deceleration, particularly within climatically sensitive zones such as polar regions, presents a compelling subject for further inquiry.

The findings not only contribute to our understanding of the climate impacts of aerosol and surface albedo, but also emphasize the importance of integrating these factors into climate models and strategies aimed at mitigating climate change.

Methods

Data

The CERES, part of the National Aeronautics and Space Administration (NASA) Earth Observing System (EOS), provides satellite-based observations of Earth’s radiative energy data globally with temporal resolution from hourly to monthly40. Utilizing the CERES instruments on the Terra and Aqua satellites, it directly measures radiative fluxes at the TOA. This paper utilizes the Level 3 product of the CERES Synoptic TOA and Surface Fluxes and Clouds (SYN1deg Level 3) dataset. This dataset includes short-wave radiative fluxes in the clear-sky and the pristine sky (aerosol and cloud free sky), and surface albedo. SA retrieval varies between land and ocean and depends on sky conditions. For land, it’s derived from clear-sky TOA albedo by CERES measurements and the Fu-Liou radiative transfer model. For ocean, using a validated coupled ocean-atmosphere radiative transfer model to create an ocean albedo look up table considers factors like SZA, wind speed, cloud and aerosol optical depth and chlorophyll concentration. The integration of land and ocean SA measurements by CERES SYN1deg provides a quality global monthly SA dataset under both clear-sky and cloudy conditions. The SZA in CERES data is considered the midpoint of the hour, for example, 0–1 Greenwich Mean Time (GMT) is defined as the first hour in a day, the corresponding midpoint is 0.5 GMT, so the cosine of the SZA in 0.5 GMT is treated as the cosine of the SZA between 0 to 1 GMT41. We use CERES data spanning from March 2001–February 2020 with monthly temporal resolution and a spatial resolution of 1o× 1o to calculate the spatial distribution of ADRE and AWE, and monthly variation of the AWE globally.

AERONET inversion uses radiative transfer model combined with optimal statistical methods to obtain aerosol optical characteristics such as AOD, SSA, phase function and microphysical characteristics. The radiometer of AERONET conducts two fundamental measurements: direct sun and sky, through structured programs. It measures in eight spectral bands: 340, 380, 440, 500, 670, 870, 940 and 1020 nm, taking about 10 s each. Measurements begin and end at air masses of 7, spanning from morning to evening. AOD is derived via the Beer-Bouguer Law, adjusting for Rayleigh scattering, ozone absorption, and gaseous pollutants. Measurements are taken in triplets 30 s apart to enable cloud screening, with intervals of 15 min under smaller air masses for cloud contamination checks. The AERONET provides global observations and inversion products of aerosol optical properties, including AOD, SSA, short-wave radiative fluxes, ADRE, and SA. It should be noted that with the AOD decreasing, the retrieval of SSA uncertainty is increasing from AERONET. AERONET products provides Level 1.5 and Level 2 data, with the samples of AOD < 0.4 are included in Level 1.5 while Level 2 does not42. Thus, the SSA uncertainty in the Level 2 are smaller than that in the Level 1.5. Although we would prefer to use Level 2 products ideally with more accurate SSA, the SSA of Level 2 has a limitation of AOD > 0.4, excluding samples from most observation sites. Considering that there are no other more suitable products, we use Level 1.5 products here. The Version 3 Level 1.5 data product, based on automatic data quality control algorithms, includes improved cloud screening and quality control methods43. This study employs data from the Version 3 Level 1.5 product of the AERONET, which provides high temporal resolution (15 min) measurements at 1403 sites globally and the time span of each site is from the date when the site started operating to the date when the site stopped working or to the date when the data was downloaded in this research (18 September 2023). The data include AOD, SSA, ADRE, and other key aerosol optical and radiative parameters in the mid-visible spectral range. Utilizing the comprehensive AERONET dataset, this study calculates the Critical SA and examines how Critical SA varies with different aerosol optical properties. Specifically, all data in the Version 3 Level 1.5 product are separated into different AOD and SSA intervals by the same sample numbers and then used to estimate the Critical SA by the linear regression shown in Fig. 3 and Fig. 4a in the manuscript and Fig. S3 in the supplementary Material.

The MACv2 offers aerosol climatological data, including micro-physical properties like AOD, SSA, and Asymmetry Factor (ASY) in every 20 years from 1865 to 208544. The aerosol optical properties, based on trusted ground-based observations sampled over the last two decades, are in the mid-visible spectral range at 550 nm. As observations are sparsely distributed, spatial context from global ‘bottom-up’ modeling is added to yield spatially and temporally complete fields45. It has a monthly temporal resolution, global spatial coverage, and a spatial resolution of 1° × 1° that coincides with the CERES data. In this study, the climatological values of aerosol optical properties from MACv2 (Fig. S1), combined with SA data from CERES, are used to quantify the recent shifts in the ADRE and AWE attributable to variations in SA.

General approaches

The Aerosol Direct Radiative Effect (ADRE), measured in watts per square meter (W/m2), is defined as the difference in net radiative flux between with and without aerosols. In this study, unless otherwise specified, all ADRE and corresponding AWE are in the clear-sky condition. We also provide the multi-year distribution of ADRE and AWE in the all-sky condition in Fig. S2. The ADRE quantifies the change in radiative flux at the surface, in the atmosphere, and at the TOA due to the presence of natural and anthropogenic aerosols. This comparison helps to isolate the impact of aerosols on the Earth’s radiative balance24. This study focuses primarily on the ADRE at the TOA, as it represents the impact of aerosols on the radiative energy of the Earth-atmosphere system. Hence, The ADRE in this paper refers to the ADRE at the TOA. The aerosol short-wave warming radiative effect (AWE) represents the positive value of the ADRE. The calculation of ADRE is shown in Eq. (1).

$${ADRE}=\,{F}_{C}^{\uparrow }-{F}_{A}^{\uparrow }$$
(1)

where \({F}_{C}^{\uparrow }\) is the upward flux in the aerosol free sky at the TOA and \({F}_{A}^{\uparrow }\) is the upward flux in the presence of aerosol at the TOA. \({F}_{C}^{\uparrow }\) and \({F}_{A}^{\uparrow }\) are both obtained from CERES data. Considering the clear sky scattering and absorption by molecules and trace gases are compensated in Eq. (1), which are mostly independent of aerosol scattering and absorption, thus leading to the conclusion that Eq. (1) is reliable for the calculation of ADRE. Therefore, Eq. (1) is widely used to evaluate ADRE in the previous studies21,23.

The Theil-Sen Median method, also known as the median slope estimator, is a robust statistical method for linear regression that determines the slope of a linear model by computing the median of the slopes calculated between all possible pairs of sample points. This approach minimizes the impact of outliers, thereby enhancing the estimator’s robustness against non-normal error distributions. It has been widely used in the trend analysis of aerosol46. The Mann-Kendall test operates on the principle of assessing the rank correlations between pairs of observations in a time series to detect any monotonic trends. It evaluates the signs of differences between all pairs of observed data points, thereby determining whether there is a statistically significant upward or downward trend without requiring the data to follow a specific distribution. It is also resilient to missing and outlier values, making it extensively applicable in trend testing of data with long time series. In this study, we employ the Theil-Sen Median approach to calculate trend values, complementing with the Mann-Kendall method to assess the significance of these trends.

Donohoe and Battisti47 proposed an assumption that the atmosphere can be approximated as a single uniform layer with given reflectivity and transmissivity, distinguishing the contributions of the surface and the atmosphere to the TOA albedo47. Stephens et al.48 further developed this concept by providing functional relationships between TOA albedo and atmospheric transmissivity with respect to Surface Albedo48. Loeb et al.49 expanded upon these ideas and developed a diagnostic tool for determining the contributions of the surface and the atmosphere to inter-annual variations in reflected short-wave radiation at the TOA and the net downward short-wave radiative flux at the surface49. These approaches simplify the complex interactions between surface and atmospheric properties, allowing for a more straightforward analysis of their individual effects on TOA albedo, thereby providing insights into the drivers of radiation balance changes over time49,50,51. This study adopts a similar methodology to quantify the impact of SA on ADRE at the TOA. Assuming the aerosol as a single, uniform layer with given reflectance and transmittance, we consider the atmosphere to be mostly transparent to short-wave radiation in the aerosol-free conditions, so the TOA albedo is approximately equal to SA and the atmospheric transmittance of short-wave radiation is equal to 1 in the aerosol-free condition, which is a reasonable approximation48,52,53. Under aerosol conditions, aerosol primarily governs the extinction of short-wave radiation. The TOA albedo (\({R}_{{toa}}\)) depends on the reflectivity and the transmissivity of aerosol layer and SA. The relationship between \({R}_{{toa}}\) and SA, as well as the aerosol layer features, can be formulated as Eq. (2)54

$${R}_{{toa}}={r}_{{aer}}+\frac{{SA}*{{t}_{{aer}}}^{2}}{1-{SA}*{r}_{{aer}}}$$
(2)

where \({r}_{{aer}}\) and \({t}_{{aer}}\) are the reflectivity and transmissivity of aerosol layer, which are parameterized by the AOD, SSA and ASY54. Consequently, in every grid, the relationship between ADRE and SA can be established by Eq. (3) derived from Eq. (1).

$${ADRE}={F}_{{toa}}^{\downarrow }*({SA}-{R}_{{toa}})$$
(3)

where \({F}_{{toa}}^{\downarrow }\) is the downward flux at the TOA. With the planetary albedo increase (decrease), the ADRE becomes positive (negative). There is no doubt that aerosol properties such as AOD impact ADRE significantly too. To constrain the impact of variations of aerosol and other factors on the ADRE and thus determine the change of SA (ΔSA) contribution to the change of ADRE (ΔADRE), we calculate Eqs. (4) and (5) using climatological aerosol properties, SA and \({F}_{{toa}}^{\downarrow }\).

$$\Delta {ADRE}=\overline{{F}_{{toa}}^{\downarrow }}*\left(1-\frac{\partial {R}_{{toa}}}{\partial {SA}}\right)*\Delta {SA}$$
(4)
$$\frac{\partial {R}_{{toa}}}{\partial {SA}}=\frac{{(\overline{{t}_{{are}}})}^{2}}{{(1-\overline{{SA}}*\overline{{r}_{{are}}})}^{2}}$$
(5)

where \(\frac{\partial {R}_{{toa}}}{\partial {SA}}\) is the change of TOA albedo caused by the change of SA over a period of time. \(\overline{{F}_{{toa}}^{\downarrow }}\) is the climatological downward short-wave flux at the TOA. We take the climatological AOD from CERES, climatological SSA and ASY from MACv2 to calculate the climatological \({r}_{{aer}}\,(\overline{{r}_{{aer}}})\) and \({t}_{{aer}}\,(\overline{{t}_{{aer}}})\), Combining the multi-year average of SA (\(\overline{{SA}}\)) and \(\overline{{F}_{{toa}}^{\downarrow }}\), this study can determine the partial differentiation \(\frac{\partial {R}_{{toa}}}{\partial {SA}}\) in each grid as Eq. (5) shows. The term ‘climatological’ refers to either the multi-year annual average or the multi-year monthly average. For example, to assess the long-term annual changes in SA that affect the ADRE depicted in Fig. 5b, we use multi-year annual averages. Conversely, to examine the long-term monthly changes in SA influencing ADRE, as shown in Fig. 5d, we utilize multi-year monthly averages. The distributions of the multi-year annual average of SSA, ASY and aerosol reflectivity from MACv2, and AOD, SA and downward short-wave flux at the TOA from CERES are shown in Fig. S1. After determining the ΔADRE in each grid, the global averages of ΔSA and ΔADRE are calculated in these grids with significant trend in SA (P < 0.05).

Evaluation of uncertainties in the ADRE

We use Gaussian error propagation to estimate the uncertainty of ADRE (\({{{\rm{\delta }}}}{{{\rm{ADRE}}}}\)) caused by the uncertainties of SA (\({{{\rm{\delta }}}}{{{\rm{SA}}}}\)), \({r}_{{aer}}\) (\({{{\rm{\delta }}}}{r}_{{aer}}\)), \({t}_{{aer}}\) (\({{{\rm{\delta }}}}{t}_{{aer}}\)) and \({F}_{{toa}}^{\downarrow }\) (\({{{\rm{\delta }}}}{F}_{{toa}}^{\downarrow }\)). The radiative flux measurement uncertainties are ranged roughly from 1 to 10 W/m² (~O(1–10 W/m²)) per 1° x 1° monthly grid, but are significantly reduced to ~O(0.001–0.01 W/m²) when averaged on a global scale over a long time period55. In our multi-year and global study, measurement errors are tracked through the variation in global yearly averages, as listed in Table S1. The propagating uncertainties from measurement errors to ADRE are quantified by Equation (S2), suggesting that the uncertainties are 0.17 W/m² globally, 0.20 W/m² (NH) and 0.15 W/m² (SH), which would not affect our conclusions. The details of the evaluation of uncertainties in the ADRE are shown in the Supplementary Material.