By acting as cloud condensation nuclei (CCN), aerosol can alter cloud properties and precipitation1,2, thereby influencing the Earth’s radiation budget and hence climate change. An increase in CCN number concentration will generate a cloud with more droplets. The consequence is scattering more solar radiation back to space, thus exerting a negative climate forcing. This is known as the cloud albedo effect or the Twomey effect1. Although extensive investigations have been made to quantify the radiative forcing by aerosol–cloud interaction (RFaci), significant uncertainties remain on its magnitude3,4.

The satellite-based RFaci using retrievals of column aerosol and cloud properties, typically in the range of −0.2 to −0.7 W m−2 (see refs. 5,6,7,8,9), is much weaker than the modeled values of −0.3 to −1.8 W m−2 (see ref. 3). Though observational estimates based on metrics like aerosol mass, that are derived including additional model information, tend to generate higher RFaci (−0.97 ± 0.23 W m−2)10,11, they are still generally lower than modeled values. Studies constraining numerical models with satellite observations reported smaller RFaci values than that from models alone12,13. It is also noteworthy that, by putting a larger weight to satellite-based studies, the best estimate of RFaci by IPCC decreased from −0.7 W m−2 (see ref. 3) to −0.45 W m−2 (see ref. 4). Therefore, it is essential to reconcile significant differences between satellite- and model-based RFaci, in particular, to improve the estimates from an observational perspective.

In addition to the uncertainties of model simulations, this discrepancy may also be partly due to satellite-related issues. The most unavoidable limitation is retrieval biases in both aerosol and cloud properties, such as overestimated aerosol optical depth (AOD) due to either cloud contaminations14 or cloud adjacency effects15, as well as misestimated cloud effective radius (CER) thus cloud droplet number concentration (Nd) owing to inadequate retrievals applied to broken and/or inhomogeneous clouds16. Further investigations suggested that the covariation of retrieval biases in aerosol and cloud properties could incur a false correlation between them, thereby underestimating the cloud albedo effect17. By utilizing satellite simulators, Ma et al.18 found that low-aerosol loading conditions are not well detected by satellites, but modeled clouds are sensitive to aerosol perturbations in these conditions, which contributes a large part to the difference of cloud susceptibilities derived from model and satellite. Also, whether the Nd–AOD relationship under present-day (PD) can be used to determine the preindustrial (PI) Nd19,20, and whether the AOD in cloud-free regions is an adequate proxy for CCN at cloud base21, are still under debate. If aerosol information is available at cloud base altitude, an even stronger aerosol–cloud relationship would be expected22. All of these tend to underestimate the RFaci19,23.

Our focus here is on another potential contributor to the underestimates of satellite-based RFaci, i.e., sampling biases, which were not explored in detail previously. Passive remote sensing only allows us to retrieve aerosol properties in clear pixels. In order to collect adjacent aerosol and cloud retrievals for statistical analysis, many studies used AOD on a coarse-resolved grid (such as 1° × 1° on a latitude–longitude grid) to match cloud pixels, assuming that aerosols properties in adjacent clear areas are representative of those under cloudy conditions5,7,24. Nevertheless, in the case that the clouds fully cover this larger grid box, hampering any AOD retrievals, these clouds were not sampled for the analysis on a daily basis. It is thus expected that stratiform clouds with high cloud fraction (f) at the aggregate scale would be artificially and systematically excluded in current satellite-based investigations that link daily aerosol and cloud properties. This is problematic especially because stratiform clouds have been reported to exert much stronger aerosol indirect effects (AIE) than cumulus clouds25,26.

Typically, the sampling biases can affect derived RFaci values through two pathways. First, it changes the regressions between cloud quantities and AOD (i.e., \(\frac{{d{\rm{ln}}N}_{d}}{d{\rm{ln}}{\rm{AOD}}}\)). All satellite-related estimates would suffer from this, including the studies that utilize pure satellite measurements5,27,28, that involve satellite measurements but with a radiative transfer model29, as well as that constrain models with satellite observations12,13. The second pathway is by altering f directly, key parameters in the calculation of RFaci (see Eq. (3) in “Methods”). This pathway is only relevant to the abovementioned pure satellite-based investigations that require the coexistence of retrievals of cloud and aerosol when computing RFaci value.

In this study, we employ the satellite-based approach proposed by Quaas et al.5 to reassess RFaci by accounting for the impacts of sampling biases. The key idea is to make use of an aerosol reanalysis product that is tied to the satellite-retrieved AOD wherever it is available and also makes use of model information and thus allows for a consistent AOD estimate everywhere in space and time, including in regions that are cloud-covered. The RFaci is also estimated by adopting fine-mode AOD (AODf) in addition to AOD that was commonly used in previous satellite-based investigations, as well as different anthropogenic fractions, to assess the sensitivity of the results to choices of CCN proxy and anthropogenic fraction. We find that after fixing the sampling biases the RFaci is substantially more negative (particularly over land), along with a surprisingly similar spatial distribution to the modeled result. Also, the magnitude of RFaci almost doubles when switching AOD to AODf which is a better proxy for CCN.


Most satellite-based studies on RFaci estimates and/or aerosol–cloud correlations require the coincidence of aerosol and cloud retrievals and thus miss cloud samples in grid boxes in which no aerosol is successfully retrieved. To explore the influences of sampling biases quantitatively, analyses under different scenarios are conducted by combining cloud retrievals from the Clouds and the Earth’s Radiant Energy System (CERES)30 with the MODerate Resolution Imaging Spectroradiometer (MODIS) aerosol retrievals31 and the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) aerosol reanalysis32. The coarse-resolution aerosol data (1°  × 1° resolution for MODIS retrieval and 0.5° × 0.625° resolution for MERRA-2 reanalysis) are projected to the higher resolution of pixel-scale cloud observations, generating 20 × 20 km2 resolution aerosol–cloud data pairs for analysis. The key idea is that the reanalysis is tied to the satellite retrievals of AOD wherever they are available (in cloud-free conditions) but also provides AOD in cloud-covered regions. Figure 1 illustrates four basic scenarios. Aero_Cld includes the samples for which both aerosol (according to the satellite sampling) and cloud retrievals are available, while Cld includes ones that only cloud retrievals are available (filling in AOD from the model information in the reanalysis). All_Cld employs the combined datasets in Aero_Cld and Cld, i.e., all available ambient clouds. Aero_Cld_Modis is the same as Aero_Cld but using MODIS AOD, which is the most common configuration in satellite-based investigations. Aero_Cld should be largely consistent with Aero_Cld_Modis as MERRA-2 assimilates MODIS AOD, but avoids retrieval artifacts at least to some extent. On the basis of Aero_Cld and All_Cld, two additional scenarios (Aero_Cld_R and Aero_Cld_C) are designed to quantify the individual contributions of changed f and regression slopes (\(\frac{{d{\rm{ln}}N}_{d}}{d{\rm{ln}}{\rm{AOD}}}\)) to RFaci estimate (see the section “RFaci estimates”).

Fig. 1: Schematic diagram of four basic scenarios in this study.
figure 1

The schematic shows the combinations of clouds and its associated aerosol retrieval (green; MODIS aerosol optical depth (AOD))/reanalysis (yellow; MERRA-2 AOD) within 1° × 1° atmospheric column (cuboid) for different scenarios. Aero_Cld_Modis represents the combination of the clouds not fully covering 1° × 1° area and its adjacent MODIS aerosol retrieval. Aero_Cld includes the same cloud samples as Aero_Cld_Modis but utilizing MERRA-2 AOD. Cld scenario involves the clouds fully covering 1° × 1° area, i.e., no successful AOD retrieval so that one has to fill with re-analyzed AOD. All_Cld employs the combined datasets in Aero_Cld and Cld, including all available ambient clouds.

Missed cloud samples

Although the sampling biases have been initially noticed6,33,34, it remains unclear what amount of data could be missed and its potential consequences, which is essential to correct the results from previous satellite-based studies. Table 1 summarizes the number of samples (N; i.e., daily 20 × 20 km2 resolution aerosol–cloud data pairs) and averaged f for Aero_Cld and Cld for fourteen different oceanic and continental regions (see Supplementary Fig. 1 for the geographical distribution), respectively, over the period 2002–2018. It is noteworthy that N for Cld is comparable to that for Aero_Cld, and even doubled in some regions over land (e.g., NAM, EUR, ASI, and SAM), indicating that more than half of the cloud samples were artificially discarded in previous satellite-based researches. Meanwhile, f for Cld in each region is substantially larger than that for Aero_Cld, implying those missed clouds also have a stronger radiative effect. After including all cloud samples, globally averaged f increases relatively by 13%, compared to Aero_Cld. Spatially, significant increases of f occur over land (Fig. 2), especially for the regions with strong anthropogenic emissions (e.g., NAM, ERU, ASI, and SAM). According to Eq. (3) in “Methods”, such a spatial pattern would further amplify the effect of sampling biases on RFaci.

Table 1 The total number of samples in All_Cld (Ntotal), and the number of samples (N), averaged cloud fraction (f) in Aero_Cld and Cld, respectively, for the fourteen regions over the period 2002–2018.
Fig. 2: Geographical distribution of relative changes (%) in cloud fraction (f).
figure 2

Changes in f from the scenario only including the cloud samples with successful aerosol retrievals (Aero_Cld) to the scenario including all ambient clouds (All_Cld), which are computed for each 10° × 10° grid box over the period 2002–2018.

In addition to altering average cloud properties, the sampling bias is also likely to influence the regressions between cloud quantities and AOD. As shown in Fig. 3a, b, the slopes of ln Nd versus ln AOD are overall larger for Cld and All_Cld than that for Aero_Cld, with the exception of EUR and three regions over the Southern Ocean (SPO, SAO, and SIO). Note that the Southern Oceans only has a limited impact on the global-averaged RFaci due to its low anthropogenic fraction35. In situ observations have demonstrated that the response of Nd to aerosols is more sensitive for stratiform clouds than cumuliform clouds26. Also, stratiform ones have smaller retrieval biases for the Nd retrieval than cumulus ones16, thus suffer less AIE underestimation caused by partly cloudy retrievals17,25. Thus, the larger slopes for Cld and All_Cld may be due to the inclusion of more samples with large f, which corresponds predominantly to stratiform clouds. Furthermore, to check if using different CCN proxies can change the above conclusion, we conduct the regression analyses based on re-analyzed aerosol index (AI) containing the information of aerosol size, and sulfate mass concentration (SO4) that eliminate the influence of aerosol swelling, which have been reported to greatly modulate the correlations between AOD and cloud quantities (Nd36, f37, and CER38) via relative humidity. Supplementary Fig. 2 shows that the results are rather similar with the AOD-based analysis, i.e., generally larger slopes for Cld and All_Cld than Aero_Cld.

Fig. 3: Annual averaged slopes of the linear regressions between the logarithm of cloud droplet number concentration (Nd) and those of aerosol optical depth (AOD) and fine-mode AOD, i.e., ln Nd versus ln AOD (AODf), for different scenarios.
figure 3

a, b The slopes calculated from retrieved AOD-Nd data pairs (Aero_Cld_Modis), and from MERRA-2 re-analyzed AOD and CERES-retrieved Nd data pairs for the scenario that aerosol and cloud retrievals are simultaneously successful (Aero_Cld), the scenario that only cloud retrievals are successful (Cld), and the scenario including all ambient clouds (All_Cld). The slopes calculated by POLDER-3 AOD, POLDER-3 fine-mode AOD (AODf), MERRA-2 AOD (same as All_Cld), and MERRA-2 AODf are also shown (c, d). The annual averaged slope here is the average of the monthly slopes. The standard deviation of the inter-monthly variability of the regression slopes is shown as an error bar. A total of 12 × 14 × 7 = 1176 linear regressions (for twelve months, fourteen regions and seven scenarios) were conducted, among which the slopes for 95% cases are at a statistically significant level (according to a Student’s t test, α = 0.01).

For a better comparison with previous satellite-based results, it is critical to know the change of slopes induced by utilizing different AOD products (e.g., satellite versus reanalysis data). As shown in Fig. 3a, b, the slopes for Aero_Cld are ~65% higher than those for Aero_Cld_Modis over land on average, whereas no systematic difference is found over the ocean. The difference between the two tests is likely due to the retrieval biases of AOD in Aero_Cld_Modis, which have been reported to result in a serious underestimation of AIE due to the covariation of retrieval biases in AOD and CER17. When retrieving aerosol in cloudy pixels, AOD can be artificially overestimated due to either cloud contaminations14 or cloud adjacency effects15, and the overestimation has been found to increase with f14. However, MERRA-2 AOD implements an online aerosol chemistry, radiation, and transport model and restricts the assimilation of MODIS to the pixels of f <70% to ensure a less biased source32, so that it can provide more physically reasonable aerosol distributions to avoid the spuriously high AOD near clouds, thereby largely reducing the retrieval artifacts as seen in MODIS AOD. As expected, MODIS AOD agrees well with MERRA-2 for the clear sky, but the former is indeed systematically higher than the later in the presence of clouds (Supplementary Fig. 3), along with an increasing difference as f increases (Supplementary Fig. 4). Also, the response of the difference to f over land is overall more sensitive than that over the ocean, implying that more serious retrieval artifacts occur over land, which might explain the larger discrepancy of slopes between Aero_Cld and Aero_Cld_Modis over land (Fig. 3a, b). Given all that, the re-analyzed AOD may be a better option for correlating with cloud quantities.

For Aero_Cld_Modis, the slopes of ln Nd versus ln AOD over land (0.08–0.33) are significantly lower than those over the ocean (0.14–0.51), which is consistent with previous satellite observations analyses5,7. The other three tests using MERRA-2 AOD, however, show weaker land–sea contrast. Also, the modeled land–sea contrast was reported to be much weaker than the satellite-observed one39,40. It is thus likely that the land–sea contrast of slopes might have been overestimated by previous studies relying purely on satellite observations.

AI and AODf are believed as better proxies for the CCN than total AOD, as they are representative of fine-mode aerosol particles, which contribute the most to CCN number concentration19. However, the analysis based on MODIS AI or AODf is not conducted in this study due to the poor skill in retrieving aerosol size parameters over land31. As an alternative, the sparser but more reliable POLarization and Directionality of Earth’s Reflectance-3 (POLDER-3) AODf41 is used here, which has been extensively validated with ground-based observations over land42,43. Since the sparseness of POLDER-3 AODf would result in a serious lack of data, we also employ MERRA-2 AODf with full spatial and temporal coverage, which is calculated as the sum of AODs of sulfate, black carbon, organic aerosols, and 30% sea salt aerosols6. Figure 3c, d compares the slopes of ln Nd -ln AOD and ln Nd -ln AODf based on both POLDER-3 retrievals and MERRA-2 reanalysis, respectively. The results show that there is no systematic difference between AOD- and AODf-based slopes over lands. An exception is the dust source region (AFR), where the slope of ln Nd -ln AODf is higher presumably due to eliminating the influence of dust events. Over most ocean regions, in turn, the slopes with respect to AODf are systematically larger than the ones with respect to AOD with only a few exceptions. This can be found in both MERRA-2- and POLDER-3-based results. It is noted that POLDER-3-based slopes are generally smaller than MERRA-2-based ones, possibly due to the serious sampling bias in the former. Therefore, to account for both sampling biases and contribution of fine-mode aerosols, RFaci based on MERRA-2 AODf (i.e., same as All_Cld but using AODf) will be estimated in the next section.

RFaci estimates

To compute RFaci, a change of AOD (AODf) from PI to PD is necessary, which is obtained from GEOS-Chem-APM44 simulations basically (see “Methods”). Figure 4a–d shows the spatial distributions of RFaci for Aero_Cld_Modis, Aero_Cld, Cld, and All_Cld, respectively. The corresponding values for different regions are summarized in Supplementary Table 1. For ease of comparison, the modeled one from Yu et al.45 is shown here as a reference (Fig. 4e). For Aero_Cld_Modis (Fig. 4a), which derives RFaci in the same manner as previous satellite-based studies5,7 but with the updated dataset, the global annual average RFaci is estimated as −0.36 W m−2 (−0.24 W m−2 over land and −0.4 W m−2 over ocean). The slightly higher value than earlier estimates, −0.2 W m−2 by Quaas et al.5 and −0.34 W m−2 by Ma et al.7, is likely caused by the improvement of retrieval algorithms in the updated dataset. Despite a slight increase, RFaci is still considerably lower than that from models (the best estimate of −0.7 W m−2 (see ref. 3)), and shows a different spatial pattern compared to models (Fig. 4e, and also see Boucher and Pham46; Chen et al.47; Déandreis et al.48), i.e., much smaller RFaci over land with strong anthropogenic emissions (e.g., NAM, EUR, and ASI; Fig. 4a). By instead using MERRA-2 AOD (Aero_Cld), which enhances the slopes of ln Nd versus ln AOD over land compared to Aero_Cld_Modis (Fig. 3), the estimated global RFaci correspondingly increases to −0.38 W m−2 (−0.33 W m−2 over land and −0.4 W m−2 over ocean).

Fig. 4: Annual mean first indirect forcing (RFaci) at a global scale (60°S to 60°N) for different scenarios.
figure 4

The RFaci calculated from a MODIS-retrieved aerosol optical depth (AOD) and CERES-retrieved cloud droplet number concentration (Nd) data pairs (Aero_Cld_Modis), and from MERRA-2 re-analyzed AOD and CERES-retrieved Nd data pairs for b the scenario that aerosol and cloud retrievals are simultaneously successful (Aero_Cld, including same cloud samples with Aero_Cld_Modis), c the scenario that only cloud retrievals are successful (Cld), and d the scenario including all ambient clouds (All_Cld). e Modeled RFaci from Yu et al.44. The respective RFaci values for different regions are also listed in Supplementary Table 1.

As discussed in the last section, the sampling biases can induce remarkable impacts on both cloud properties and susceptibility of Nd to AOD, which are the key terms to calculate RFaci (Eq. (3) in “Methods”). Figure 4c illustrates that the clouds missed by the satellite-based method have a much stronger RFaci than those that actually have been analyzed (−0.75 W m−2 versus −0.38 W m−2), particularly over land (−1.22 W m−2 versus −0.33 W m−2), which is attributable to the joint impact of the increased f (Fig. 2) and slopes of ln Nd versus ln AOD (Fig. 3a, b). After including all cloud samples into the calculation, which is consistent with what models do, the estimated RFaci increases to −0.59 W m−2 (−0.77 W m−2 over land and −0.53 W m−2 over ocean), along with a surprisingly similar spatial distribution to the modeled result (Fig. 4d, e), i.e., the maximum values over major continents and followed by immediate outflow regions. There also exists a significant contrast in RFaci between hemispheres, i.e., much stronger in the Northern (−0.98 W m−2) than in the Southern hemisphere (−0.19 W m−2), where anthropogenic emissions are weaker.

By accounting for the effect of sampling biases, the estimated RFaci has increased by 55% (from Aero_Cld to All_Cld) on a global average (133% over land and 33% over ocean). The most evident enhancements are over the land areas with strong anthropogenic aerosol emissions, e.g., NAM (−0.91 W m−2), EUR (−0.41 W m−2), and ASI (−0.72 W m−2). As mentioned in the last section, both changes of f (Fig. 2) and regression slopes (Fig. 3a, b) contribute to the increase of RFaci. To gain insight into their individual effects, we conduct two additional tests on the basis of Aero_Cld. One is referred to as Aero_Cld_R that uses the regression coefficients acquired from All_Cld but keeps other quantities the same as Aero_Cld, in order to evaluate the effect of changed regression coefficients, and the other is denoted as Aero_Cld_C that is the same as Aero_Cld but uses cloud quantities from All_Cld, for the purpose of quantifying the impact of changed f. As demonstrated in Supplementary Fig. 5, the increased slopes lead to a relative change of +21% in the magnitude of RFaci (from −0.38 W m−2 in Aero_Cld to −0.46 W m−2 in Aero_Cld_R). The increased f, in turn, amplify RFaci by 34% (from −0.38 W m−2 in Aero_Cld to −0.51 W m−2 in Aero_Cld_C) with the largest increases over NAM (−0.55 W m−2), EUR (−0.66 W m-2), and ASI (−0.42 W m−2), where high anthropogenic fractions of AOD (0.57, 0.59, and 0.59, respectively) and significant enhancements of f (86%, 83%, and 70%, respectively) occur simultaneously.

A recent study relying on the combinations of ln Nd-AODf relationship and radiative transfer modeling reported the best estimate of RFaci near −0.7 W m−2 with the associated uncertainty range between −0.5 to −1.2 W m−2 (see ref. 9), which is more negative than previous satellite analyses as well as our optimized AOD-based estimate (−0.59 W m−2 in All_Cld). Here, RFaci for the All_Cld scenario but replacing AOD by fine-mode AOD is thus computed for comparison with the original All_Cld result (Fig. 5c). Anthropogenic fraction is correspondingly defined via the modeled fine-mode AOD with the same definition as MERRA-2 AODf (see “Methods”). Since the fine-mode aerosols dominate the anthropogenic contributions, with almost the same absolute increases of AOD and AODf from PI to PD (Supplementary Fig. 6c, d), one obtains a much larger anthropogenic fraction if AODf rather than total AOD is applied. Figure 5a, b shows the maps of anthropogenic fractions of AOD (fant) and AODf (fant-fine). It is clear that the most significant difference between fant and fant-fine occurs over dust source regions and oceans in the northern hemisphere, where coarse particles (sea salt and dust aerosols) account for a large part of total extinction so that using total AOD rather than AODf will underestimate the anthropogenic contributions from PI to PD. When switching AOD to AODf, the estimated RFaci increases by 85% (from −0.59 to −1.09 W m−2; Figs. 4d and  5c), in which the increased slope and anthropogenic fraction contribute 17% and 68%, respectively. Since a part of sea salt and dust aerosols can also serve as CCN, the actual RFaci should be between −0.59 W m−2 and −1.09 W m−2.

Fig. 5: Annual (2010) averaged anthropogenic fractions and first indirect forcing (RFaci).
figure 5

Anthropogenic fractions of a aerosol optical depth (AOD) and b fine-mode AOD (AODf) from the GEOS-Chem-APM simulations. c RFaci based on MERRA-2 daily AODf for the scenario including all ambient clouds (All_Cld). d RFaci based on monthly POLDER-3 AODf.

In addition to relying on the reanalysis product, another potential way to sidestep the sampling biases would be the use of monthly aerosol/cloud statistics from satellite observations. Figure 5d shows the RFaci estimated by employing monthly POLDER-3 AODf and monthly cloud properties. The global-averaged RFaci (−1.02 W m−2) is close to the MERRA-2 daily-based one (−1.09 W m−2; Fig. 5c) but with different spatial distributions, i.e., much smaller RFaci over land, which is also in contrast to models (Fig. 4e). A comparison of the slopes of ln Nd versus ln AODf between the two cases shows that POLDER monthly-based slopes are significantly lower than MERRA-2 daily-based ones over land (Supplementary Fig. 7). One reason would be covariation of retrieval biases in aerosol and cloud properties, tending to underestimate aerosol–cloud correlations17. It should also be noted that the use of monthly statistics can only avoid the sampling bias of clouds, while aerosol information associated with the clouds that fully cover 1° × 1° grid box are impossible to be sampled. That is, this monthly AODf would be not well representative of the number of aerosols actually linking with monthly Nd. Our analysis demonstrates that even though all clouds have been sampled, missing the collocated aerosols in monthly statistics can still lead to an underestimation of aerosol–cloud correlations (Supplementary Fig. 8). Comparing monthly (Supplementary Fig. 8) and daily (Fig. 3) slopes for All_Cld case, it is interesting that the former are generally larger than the latter, which might be partly due to the inclusion of short-term feedbacks or delayed responses of clouds in monthly aerosol–cloud associations.

Important implications for a satellite-based estimate of RFaci

To confidently interpret past and predict future climate change, the current significant discrepancy between satellite- and model-based RFaci has to be reconciled. Among possible directions to fill this gap (detail in the following section), analyzing satellite results in an apples-to-apples way to model simulations is essential. Although many efforts have been made to do rigorous comparisons39,49, e.g., selecting model outputs at satellite equatorial crossing time, and sampling cloud-top quantities in the uppermost liquid water cloud layer, etc., sampling biases discussed in this study have been largely ignored earlier.

Previous studies that deducted either aerosol–cloud correlations or radiative forcing relied on the assumptions that the clouds collected when adjacent aerosol retrievals are available are representative of all ambient clouds. Our findings here, however, demonstrated that sampling biases introduced by the inherent satellite retrieval limitation of aerosol-only cloud-free conditions systematically exclude liquid clouds with high f, which are predominantly thick stratiform cloud decks. These clouds, on the one hand, exert a stronger cooling effect, and, on the other hand, were found to be more responsive to the perturbations of aerosols compared to cumuliform clouds26. By fixing the sampling biases, the estimated RFaci increases by 133% over land and 33% over the ocean, which is closer to models not only in global-averaged RFaci (−0.59 W m−2) but also in its spatial distribution or land–ocean contrast. More importantly, the estimated magnitude of RFaci is almost doubled (−1.09 W m−2) when replacing AOD by AODf to derive the aerosol–cloud correlations and the anthropogenic fraction. This finding implies that previous satellite-based estimates5,7,27,28 have substantially underestimated the RFaci, especially over land, and further highlights the necessity of accounting for the sampling biases as well as utilizing fine-mode AOD (or other adequate CCN proxies) instead of total AOD in future satellite investigations.

Although the use of monthly aerosol/cloud retrievals can largely sidestep the sampling bias on clouds and also include short-term feedbacks or delayed responses of clouds, the problem of missing aerosol information under cloudy sky remains. This will cause a significant underestimation of RFaci, over land where aerosols have large inter-daily variability. The result implies that the conclusion regarding spatial distribution (land–sea contrast) of RFaci, should be drawn carefully if monthly statistics are applied.

In this study, the enhanced RFaci, from AOD- to AODf-based estimates is mainly induced by the increased anthropogenic fraction. The anthropogenic fraction depends not only on the increase in the anthropogenic aerosols but also on the preindustrial background (Supplementary Fig. 6). To understand the sensitivity of RFaci to the choice of anthropogenic fraction, the RFaci, are also computed with anthropogenic fractions of AODf from the simulations of (1) AeroCom phase1 models50 with the preindustrial year 1750 as a reference and AeroCom phase2 models51 with the preindustrial year 1850 as a reference in addition to GEOS-Chem-APM modeled ones (Supplementary Table 3 and Supplementary Fig. 9). The result indicates that the RFaci strongly scales with the anthropogenic fraction of AODf, whereas there is no evident difference in global-averaged RFaci between daily- and monthly-based estimates. With the adequate CCN proxy (AODf here), and meanwhile, sidestepping the sampling biases by relying on daily re-analyzed and monthly retrieved AODf respectively, the RFaci are estimated to range from −1.02 to −1.68 W m−2 when applying different anthropogenic fractions (Supplementary Table 3), which highlights the need for more meaningfully constrained anthropogenic fraction.


This study focuses on the roles of sampling biases and choice of the CCN proxy in the satellite-based estimate of RFaci, with a clear demonstration of the potential magnitude of the impacts of both. It should, however, be noted that the exact forcing value is also affected by other potential sources of the uncertainties, which are noteworthy for future explorations.

As mentioned above, the retrievals of AOD and cloud quantities (CER/τc) exhibit large biases in scenarios involving broken clouds, and importantly, the covariation of retrieval biases in AOD and CER (thus Nd) appears to underestimate the cloud albedo effect17. Here, we made an initial attempt to assess “overcast” clouds by restricting retrievals to clouds with f > 80%. This threshold was also adopted by previous studies16. It is found that there is no systematic difference in aerosol–cloud correlations between the analyses based on all cloud samples and “overcast” clouds only (Supplementary Fig. 10). With the use of CERES data here, which does not have any pixel-level flag identifying overcast or partly cloudy conditions, we thus do not distinguish between overcast and broken clouds. But it is believed that using pixel-level cloud retrievals with the overcast flag (e.g., MODIS level-2 product) would be a useful exercise to focus on homogeneous and overcast pixels for trusted high-quality retrievals52. In addition, it has been demonstrated that co-variability of aerosol and precipitation induced by wet removal can confound the interpretation of aerosol–cloud–precipitation interactions53. However, our analysis has been restricted to low liquid clouds, with liquid water path overall lower than 100 g m−2 (Supplementary Fig. 11), thus generating very little precipitation. Also, non-precipitating cloud pixels have been found to account for ~90% of all footprints globally54. Therefore, the co-variability of aerosol and precipitation is unlikely to significantly affect the results presented here.

A single slope of ln Nd versus ln AOD is clearly not representative of a variety of cloud types. In situ-26 and satellite-based25,55 investigations have revealed that both cloud microphysical properties and vertical cloud structure have distinct responses to aerosol perturbations for stratocumulus and cumulus clouds, which highlights the importance of conducting regression analysis for each individual cloud type. Recently, Unglaub et al.56 developed a new approach to classify cloud types at cloud scale by using a newly developed cloud-based height retrieval57 in conjunction with cloud-top height variability, which makes it possible to obtain a cloud-type-based estimate of RFaci globally in future studies.

Methodological biases are partially responsible for the uncertainties of RFaci estimate as well. Given the large spatial variations in aerosol loading, aerosol type, cloud type, and meteorological conditions, spurious correlations between aerosol and cloud quantities would occur when analyzing satellite datasets over large regions. Grandey and Stier58 pointed out that for regions of 60° × 60°, close to the scale used in our study, this methodological error might overestimate the RFaci by ~80% relative to that derived from temporal variability only within 1° × 1° region. They also suggested that conducting statistical analysis over regions smaller than 4° × 4° can greatly avoid this error. Unfortunately, the insufficient data samples prevent us from doing such analysis at this time. However, the attempts of combining satellite datasets from multiple platforms, or employing pixel-level retrievals (e.g., 1 × 1 km2 cloud retrievals in MODIS level-2 dataset) in future studies, might be useful to minimize this error. In addition, Patel et al.28 found that for the derivation of regression coefficients of the relationship between planetary albedo and cloud properties (see Eq. (2) in “Methods”), the nonlinear least square statistical approach can increase the correlation by 21–23% and reduces the error compared to the multilinear regression approach5, thus reducing the uncertainty of RFaci. This finding implies the need to re-estimate RFaci by employing the updated approach. For the sake of comparison with previous studies5,7, however, the multilinear regression is still used here. Finally, it has been demonstrated that more directly retrieved CCN leads to increases in the Nd–aerosol slope23. Hasekamp et al.23 found a strong increase in RFaci when using a polarimetric retrieval of column-CCN over oceans, which, in combination with the results presented here, implies a still stronger RFaci. Beyond RFaci, also rapid adjustments such as changes in cloud liquid water path and in f add to the total radiative effect of aerosol–cloud interactions, the effective radiative forcing (ERFaci). These adjustments approximately scale with RFaci10,59, and thus our result is relevant for ERFaci, too.


Satellite and reanalysis data

The satellite data used here are similar to that in previous studies using the same approach5,7 but with an updated version, including cloud and radiative products from the CERES Single Scanner Footprint (SSF) Edition-4 dataset at a 20 × 20-km2 resolution and Dark Target and Deep Blue combined aerosol products from the MODIS Collection 6.1 dataset at 1° × 1° level-3 resolution. Both instruments are on board the Terra platform with an equatorial crossing local time at ~10.30 a.m. To determine RFaci induced by fine-mode aerosols, AODf is also required. However, aerosol size information (such as Angström exponent and fine-mode fraction) retrieved from MODIS over land may be problematic31, hampering the derivation of AODf. For this reason, we also employ the daily 1° × 1° POLDER-3 AODf product retrieved by the GRASP algorithm, which was found to have good quantitative skill over land41,43.

To fill the data gap caused by satellite sampling, the re-analyzed AOD and AODf from the MERRA-2 dataset at a 0.5° × 0.625° resolution, are also utilized in this study, which has been found to compare well with other independent observations from the ground, aircraft, and shipborne instruments32,60. Our comparison also shows a good agreement between POLDER-3 and MERRA-2 AODf (Supplementary Fig. 12). Here, AODf is defined as the sum of AODs of sulfate, black carbon and organic aerosol, and 30% sea salt aerosol. MERRA-2 assimilates AOD retrieved by multiple satellite sensors (AVHRR, MODIS, MISR) and the ground-based remote sensing network (AERONET) to correct for model departures from observations32. The re-analyzed AOD thus combines the advantages of both satellites and models, providing full spatial and temporal coverage while keeping a strong connection to observed aerosols. Hourly re-analyzed AOD/AODf at the equatorial crossing local time of satellite is used to match to the satellite-observed parameters.

The MODIS, CERES, and reanalysis data span the time period January 2002 through December 2018, and POLDER-3 data are from March 2005 to October 2013, providing sufficient samples to obtain statistically significant results. Supplementary Table 2 summarizes the surface type, aerosol, cloud, radiative parameters required for the statistical analysis and/or the RFaci calculations. For the AOD/AODf, data at the resolution of 1° × 1° (MODIS and POLDER-3) and 0.5° × 0.625° (MERRA-2) are both projected to the higher resolution of 20 × 20 km2 to match the SSF products.

Methodology for calculating RFaci in the context of liquid water clouds

For the calculation of RFaci, a critical procedure is to determine the change in Nd due to anthropogenic aerosols based on the relationship between Nd and AOD (AODf). However, Nd is not routinely retrieved in current satellite product, and needs to be empirically computed from cloud effective radius (re) and cloud optical depth (τc) for liquid water clouds assuming adiabaticity13 as follows:

$${N}_{{\rm{d}}}=\gamma {\tau }_{{\rm{c}}}^{1/2}{r}_{{\rm{e}}}^{-5/2}$$

where γ is an empirical constant with the value of 1.37 × 10−5 m−0.5 (see ref. 13). It was suggested that the Nd retrieval performs better for relatively homogeneous, optically thick and unobscured stratiform clouds under a high solar zenith angle condition16,61,62,63,64.

Quaas et al.5 have extended Loeb’s65 approach by accounting for the contribution of the clear part of a scene to estimate planetary albedo (α), where α can be described by a sigmoidal fit as

$$\alpha \approx \left(1-f\right)\left[{a}_{1}+{a}_{2}{\rm{ln}}\tau \right]+f{\left[{a}_{3}+{a}_{4}{\left(f{\tau }_{c}\right)}^{{a}_{5}}\right]}^{{a}_{6}}$$

where τ is AOD (AODf), and fitting parameters (a1a6) are obtained by a multilinear regression (a5 is set as 17). The performance of the multilinear regression fitting has been verified by previous studies. Their results showed that the fitted albedo overall agrees very well with both CERES-retrieved albedo5 and the albedo simulated by a radiative transfer model28. Quaas et al.5 suggested that the RFaci for anthropogenic aerosols can be expressed as

$${{\rm{RF}}}_{{\rm{aci}}}={f}_{{\rm{liq}}}A(f,{\tau }_{c})\frac{1}{3}\frac{d\,{\mathrm{ln}}\,{N}_{d}}{d\,{\mathrm{ln}}\,\tau }[{\mathrm{ln}}\,\tau -\,{\mathrm{ln}}(\tau -{\tau }^{ant})]S$$

with f the cloud fraction, fliq the fraction of liquid water clouds, τant the anthropogenic AOD (AODf), and S the daily mean incoming solar radiation, respectively. Here, \(A\left(f{,\tau }_{c}\right)={a}_{4}{a}_{5}{a}_{6}{\left[{a}_{3}+{a}_{4}{\left(f{\tau }_{{\rm{c}}}\right)}^{{a}_{5}}\right]}^{{a}_{6}-1}{\left(f{\tau }_{{\rm{c}}}\right)}^{{a}_{5}}\).

Since the fitting parameters (a1a6) and the slope of the linear regression fit between ln Nd and ln τ can vary both temporally and spatially, we conduct the regression analysis separately for fourteen regions (Supplementary Fig. 1) on a monthly basis. To obtain more reliable fitting parameters, only a subset of the data with smaller retrieval biases are used for statistical regressions, excluding the retrievals involving bright surfaces, high solar zenith angle (>65°), thin clouds (liquid water path, L < 20 g m−2), multilayered clouds. In addition, the lowest 15% of data for AOD (AODf) are also excluded, since the slopes of ln Nd versus ln AOD (AODf) are quite sensitive to small AOD (AODf) changes, which are not well-characterized by satellites18. As for the calculation of RFaci, these data are re-included in order to obtain an estimate in a more consistent manner with the model, i.e., minimizing the sampling biases.

As a key parameter in estimating RFaci, τant can be derived either from column-integrated aerosol properties involving size and absorption information from satellite observations28,33,66,67 and/or reanalysis data6, or from model simulations7. Total (fine-mode) τant in our study is obtained by multiplying AOD (AODf) from MODIS/MERRA-2/POLDER-3 and anthropogenic AOD (AODf) fraction (fant; fant-fine) simulated by Ma et al.7. AODf in the model is also defined in consistent with the definition for MERRA-2 AODf. To derive fant (fant-fine), two simulations were conducted with one for PD and the other for PI (with the preindustrial year 1750 as reference) aerosol particle and aerosol precursor gas emissions by employing GEOS-Chem-APM model44, in which an advanced multitype, multicomponent, size-resolved microphysics model was coupled to a global 3-D model of atmospheric chemical model GEOS-Chem. More detail of the model description can be found in Ma et al.7. Using the same approach and fant as Ma et al.7 allows us to qualify the impact of satellite product updates. The RFaci in this study is calculated for the year 2010 in order to be consistent with the latest Intergovernmental Panel on Climate Change (IPCC) report4 that used the reference year 2010 for PD conditions. In addition to the “standard” simulation mentioned above, the fant-fine from the simulations of AeroCom phase1 and phase2 models (obtained from the MACv2 aerosol climatology product68), as well as GEOS-Chem-APM model but with AODf defined as the sum of AODs of sulfate, black carbon and organic aerosol, are also adopted to understand the sensitivity of RFaci, to the choice of the anthropogenic fraction.