The MODIS Collection 6.1 cloud product is derived from the observations acquired from the Aqua satellite, which follows a polar orbit crossing the equator at approximately 01:30 p.m. local time. This product includes retrievals of cloud optical properties such as effective droplet radius (Re) and optical thickness (τc) at multiple wavelengths (1.6, 2.1, and 3.7 µm) and cloud thermodynamic phase, as well as infrared retrievals of the cloud top temperature (CTT), pressure (CTP), and height (CTH) . These products are retrieved at a nominal spatial resolution of 1 km at the surface at nadir. Due to oblique viewing angles and projection effects onto Earth's curved surface, MODIS pixel size increases from 1 km at nadir to nearly 4 km at the swath edges. MODIS data are provided as 1354 × 2030-pixel granules. This dataset includes three filters applied to the MODIS retrievals for liquid warm clouds:

All. Includes retrieved cloud properties where phase =2 (liquid) and CTT >268 K.

MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) is a reanalysis product developed by GMAO. It provides meteorological data spanning from 1980 to the present, assimilating observations from various satellites and ground-based stations. MERRA-2 offers a spatial resolution of approximately 0.625° (about 50 km) and includes 72 vertical levels spanning the atmosphere. The temporal resolution is 1 h for all surface meteorological variables and 3 h for 3D fields. We utilize vertical profiles of temperature and specific humidity to compute estimated inversion strength and humidity above the boundary layer, near-surface meteorological variables to compute the near surface temperature advection and various other cloud controlling factors based on the 3D winds. MERRA-2 computes planetary boundary layer height (PBLH) as the the lowest level at which the heat diffusivity drops below a threshold value for more details see. These meteorological quantities have been shown to strongly influence ACI relationships . The MERRA-2 products are temporally interpolated to match the instantaneous time of the MODIS satellite overpass and spatially resampled using a KDTree approach and bilinear interpolation to match the MERRA-2 products to the pixel-scale resolution of the MODIS instrument for each individual L2 granule.

European Centre for Medium-Range Weather Forecasting (ECMWF) Reanalysis v5 (ERA5) is a reanalysis dataset that provides global meteorological data from 1950 to the present with ∼31 km spatial and hourly temporal resolution . It assimilates satellite and ground-based observations, including atmospheric motion vectors from cloud tops, offering strong wind constraints. We also match this reanalysis product to the instantaneous footprint from MODIS and use it to train our ML model.

MODIS cloud retrievals at 1 km spatial resolution are gridded globally into daily files from 2007–2011 by 10, 5, 1, 0.5, 0.1, and 0.05° regions. MODIS data is aggregated within each grid-box (at these different resolutions yielding, on average, 1E6, 2.5E5, 1E4, 2.5E3, 1E3, and 25 number of daily samples over the grid-box for each grid-resolution, respectively). All products are aggregated in the grid resolutions down to 0.5°. At 0.1 and 0.05° resolutions the data products at coarser spatial resolutions than the grid (i.e. AMSR-E of 13 km, CERES of 25 km) are bilinearly interpolated in space between the locations of the level-2 satellite footprints to the grid box of the gridded product in question. All of the cloud product averages are composed of warm liquid clouds only and if any ice clouds are detected within a grid-cell it is not used in the analysis.

A random forest model is an ensemble learning technique that combines multiple decision trees to improve predictive accuracy and robustness. It works by aggregating predictions from each tree, trained on random subsets of the data with replacement, and is effective in handling complex relationships and high-dimensional datasets . employs a random forest algorithm to investigate the impacts of volcanic aerosols and meteorology on clouds surrounding Iceland. This approach enables the comparison of cloud responses of volcanic aerosol perturbations, isolating ACI signals. We adopt a similar approach by constructing a regression forest consisting of 100 trees independently trained to predict LWP, N_d, and CTH based on the following 13 predictor variables: PBLH, isentropic lifted condensation level based on the surface air temperature, pressure, and dew point (LCL), relative humidity above the height level of the PBLH (rhAbovePBL), estimated inversion strength (EIS), horizontal temperature advection at the surface (Tadv), surface latent heat flux (LH), total column water vapor (tqv), 10 m surface wind speed (ws10), surface precipitation (AMSRE-E), CTH (MODIS), CF (MODIS), cloud albedo (Acld; CERES), and Nd (MODIS). A comprehensive list of predictors and their respective data sources is provided in Table S1.

The random forest is constructed from 100 trees with a minimal leaf size of 7 and no leaf merging. The full dataset was randomly partitioned into three independent subsets: 65 % for training, 25 % for testing, and 10 % for validation. Randomized sampling partitions, as opposed to sequential (e.g., yearly) splits, did not have a significant impact on the model’s outcomes. Within the training set, each decision tree in the random forest is trained on approximately 60 % of the training data (sampled with replacement), while the remaining 40 % serves as out-of-bag data for internal performance evaluation. The validation set was used for tuning model hyperparameters described in Table S2. After hyperparameter tuning, the model was retrained using both the training and validation data (75 % total) to optimize performance, ensuring that the test set remained unseen and provided an unbiased assessment of model accuracy. Cloud controlling variables were primarily chosen from the selection used in the studies of and . Model performance is further evaluated using different hyperparameter values, such as the number of trees and the minimum number of samples per leaf, which are discussed below. Choosing predictors that have significant influence on cloud properties helps in effectively capturing their variability to best ensure that the model can discern meaningful patterns and relationships crucial for understanding complex atmospheric processes.

Twelve oceanic regions are used in this study (Fig. a), encompassing the subtropics California; CAL, Peruvian; PER, Namibian; NAM, and Australian; AUS, similar to, tropics (Central East Pacific; CEP, Central Atlantic; CEA, and Western Indian; WEI), mid-latitudes (Central North Pacific; CNP, Eastern South Atlantic; ESA, and Eastern South Indian; ESI), and mixed regions (Eastern North Atlantic; ENA and Western North Pacific; WNP), with tropical and mid-latitude regions selected to ensure representation in both hemispheres and alignment within similar latitude belts. The subtropical locations contain a large abundance (greater than 60 %) of warm low-level (below 3 km) marine stratocumulus cloud (Fig. S1). Tropical and Mid-latitude locations also contain substantial amounts of warm boundary layer clouds, but these regions have significant differences in sea surface temperature (Fig. b) with much higher amounts of mid and high-level clouds (Fig. c). On average, planetary boundary layer depths are significantly lower in the mid-latitude regions but have the heaviest precipitation rates (Fig. e) where a long tail (positive skewness) is apparent indicating a higher propensity for heavier rainfall by frequent large-scale storm-track systems. Precipitation rates are also large in the tropics (compared to the subtropics). The diversity in meteorological conditions across regions provides essential test-beds to isolate and study the impact of different cloud states and environmental controls on ACI.

Six spatial resolutions with grid spacing from 10 to 0.05° are used to examine how the shape of the Nd–LWP relationship changes within each region. The total number of grid-cells over the 5 year period in the region increase roughly an order of magnitude for each grid resolution (numbers used in each grid-resolution 7.3×103, 2.9×104, 6.9×105, 2.6×106, 5.2×107, 1.9×108, respectively). Using the All warm-cloud filter at 1° grid resolution reveals a pronounced inverted-V distribution with distinct ascending and descending branches for the California region (Fig. c). This result agrees with . As the spatial resolution increases and becomes finer, the inverted-V shape morphs into multiple modes more closely resembling an “M” shape (Fig. e and f). The inverted-V shape of the Nd–LWP relationship can be modeled using a piecewise linear function in log–log space, following a similar approach to . The function is defined with a single turning point corresponding to the median in the probability distribution function (PDF) of LWP as a function of Nd: 1ln⁡L=ln⁡Lp+m1(ln⁡Nd-ln⁡Nd,p), if Nd<Nd,pln⁡Lp+m2(ln⁡Nd-ln⁡Nd,p), if Nd,p≥Nd,p Here, Nd,p denotes the turning point – defined as the mode in LWP for a given Nd – with slope coefficients m1 and m2 representing the log–log gradients to the left and right of Nd,p, respectively, and Lp the corresponding LWP value at the turning point. At 1° resolution, the Nd–LWP distributions exhibit a well-defined inverted-V structure. However, as spatial resolution increases (e.g., 0.1 and 0.05°), the median of the PDF deviates from this structure and reveals a more prominent “M” shape relative to the piecewise linear fit, reflecting increased subgrid variability. We focus on results at 0.1° resolution in the main analysis to balance computational cost with spatial fidelity, unless otherwise noted.

To explain why the “M” shape emerges at the 0.1 and 0.05° resolutions, a detailed analysis of τc and Re is conducted. Since LWP is proportional to the product of τc and Re (i.e., LWP=2/3ρwτcRe, where ρw is the density of water), the localized decrease in LWP in the bottom of the “M” trough (Fig. e and f), which does not appear in the classic inverted-V shape (Fig. c), occurs due to a higher occurrence of clouds with smaller τc (Fig. b). This change in LWP is primarily driven by variations in τc, as the changes in Re between grid resolutions are similar (Fig. c). The statistical differences between these datasets indicate that finer resolutions capture more variability in cloud optical properties, leading to a wider spread in LWP values. This results in a lower median LWP at finer scales due to the increased detection of smaller optical depth clouds.

The Nd–LWP relationship varies significantly across subtropical, tropical, and midlatitude regions (Fig. ). In subtropical regions, a distinct inverted-V distribution with clear ascending and descending branches is evident at a 1° grid resolution (Fig. S2). At higher resolutions, this pattern transitions to an “M” shape, that is robust across all dominant subtropical stratocumulus locations (Figs. d and S3). Consistent with , the linear-fit slope of Nd-LWP (over the whole range in Nd) is negative in the subtropics at 1° grid resolution. It is also negative at 0.1° grid resolution albeit the slope is significantly less negative at higher spatial resolution. In the tropics, the shapes of these distributions are less pronounced, and LWP exhibits a more neutral/positive trend with Nd. In midlatitudes, the relationship sometimes resembles an inverted-V, but with a significant increase in LWP at high Nd. Linear-fit slopes in midlatitudes tend to be more positive than in the subtropics and tropical regions especially at higher spatial resolution. While the relationships remain broadly consistent within subtropical, tropical, and midlatitude regions, variations in dominant cloud types which respond differently to aerosols, e.g. see,, as well as differences in large-scale meteorology and zonal gradients across these domains, can also play a role in shaping the Nd–LWP relationship, a topic we will further explore using ML.

The accuracy of τc and Re retrievals, which are used to compute LWP and Nd, is generally improved by removing thin and/or broken cloud fields. Thicker overcast cloud fields have less noise from shortwave radiation scattering off a homogenous cloud-scene and more closely adhere to the scattering assumptions inherent in the plane-parallel approximation . A common approach to reduce these errors is to require τc to be greater than 4. This more stringent filtering is applied in the Q06 and G18 composites. However, thinner clouds, which are removed in these composites, are generally more sensitive to aerosol perturbations .

Figure  illustrates the impact of removing thin cloud retrievals from the calculation of the slope in Δln⁡LWP/Δln⁡Nd across the globe using the 1° gridded product. When All clouds are included (Fig. a), the slope is predominantly positive, except in the subtropics. However, using 0.1° data results in less negative slopes in these regions (Fig. S4), consistent with the observed differences between 1 and 0.1° resolutions in Fig. . When thin clouds are removed using the Q06 and G18 composites (Fig. b–c), the global distribution of slopes becomes predominantly negative, except in the Southern Hemisphere mid-latitude storm track, Polynesia, and various continental regions. Negative slopes are reported in the literature when applying similar τc thresholds e.g., Fig. 2 inwhich used the thicker cloud composite of G18. Removing thin clouds reduces the number of cloud retrieval samples by 54 % (Fig. d), highlighting the trade-off between reducing retrieval uncertainties and altering the sign of the LWP adjustment.

Figure  illustrates the effect of increasing the τc threshold on the slope of the Nd-LWP relationship. Beyond an optical thickness of approximately 1.25, the inclusion of thicker clouds with lower susceptibility results in a progressively more negative slope, converging with other composites around an optical thickness of 10. The reliability of cloud property retrievals for thin clouds depends on several factors, including sea state roughness, CF, satellite viewing and zenith angles, and particle size. highlight the challenges of retrieving accurate optical thickness values below 0.1, as subvisible cirrus (optical depth >0.03) can impact the retrieval when they exist as determined by spaceborne lidar;. However, they demonstrate that retrievals are generally reliable for optical depths greater than 1.0, particularly over the ocean, where surface reflectance is well constrained. Given the strong influence of cloud filtering on slope estimates and the significant uncertainties in LWP adjustments, improved constraints on thin clouds are essential for refining radiative forcing estimates. The Q06 and G18 datasets may thus be too conservative and result in overly strong negative slopes. Therefore, to maximize sample size in Nd-LWP relationship, while recognizing the retrieval uncertainties that are intrinsic to thin and broken clouds, we will use the All dataset to assess meteorological impacts in our ML analysis.

Precipitation is identified by the ML model as the most influential cloud-controlling factor in predicting LWP. It significantly impacts the Nd-LWP relationship, generally leading to increasingly positive slopes of dln⁡LWPdln⁡Nd as precipitation rates increase. The average slope is estimated using both an ordinary least squares (OLS) fit in log–log space and a numerical differentiation approach based on finite differences that computes the mean of local slopes between adjacent points along the random forest predictions as a function of Nd. While the OLS fit captures the overall trend, the finite-difference approach reflects the average instantaneous rate of change, which can differ in shape-sensitive cases such as inverted-V functions. The OLS fitted slope is consistent across all regions (Fig. S9). Furthermore, the random forest ML model accurately captures the shape of LWP as a function of Nd with increasing slopes using finite-differences as precipitation increases across composites (Fig. S10).

Precipitation (probability and intensity) and Nd are closely associated with LWP, typically increasing as LWP increases in warm clouds. While LWP and precipitation generally increase together as clouds deepen, in more developed or heavily drizzling systems, efficient rainout processes can deplete cloud liquid water, leading to a reduction in LWP and a bidirectional response in dln⁡LWPdln⁡Nd e.g., in CloudSat observations of. The ML model supports this effect, showing little variation in LWP with respect to Nd for non-precipitating clouds, likely because increased aerosol concentrations cannot further suppress drizzle in clouds that are already non-raining – yielding a flat or slightly negative response consistent with A-Train observations . In precipitating clouds, by contrast, higher Nd tends to suppress precipitation by reducing droplet size and limiting collision–coalescence. As shown in Fig. S10c, LWP rises sharply with Nd before increasing more gradually beyond about 20 cm⁻³. The random forest model performs consistently well across all 12 regions, exhibiting a similar pattern of small slightly positive or negative dln⁡LWPdln⁡Nd sensitivities for non-precipitating clouds and larger positive sensitivities for raining clouds (Table S3).

Cloud albedo plays the next most significant role in modulating the Nd-LWP relationship. Under all-sky conditions, we observe an “M” pattern (Fig. ), but when stratifying the data into low cloud albedo (0<Acld<0.25), average cloud albedo (0.25<Acld<0.4), and high cloud albedo (0.4<Acld<1), the relationship shifts to solely an inverted-V shape (Fig. S11), even at the highest 0.05° grid-resolution. For dimmer clouds, the peak of the inverted-V occurs at a relatively lower Nd (around 10 cm⁻³), while for brighter clouds, the peak is broader and spans a wider range of concentrations (20–80 cm⁻³), with the LWP shifted to larger values. The linear least squares fit is negative in each composite, while the finite-difference method applied to the random forest predictions yields a weaker average slope due to the pronounced positive increase at low Nd, which is not well captured by the OLS fit. Nevertheless, the consistency of slopes across composites suggests that the influence of precipitation – which tends to steepen the slope – is similar across Acld groupings.

To test whether the positive LWP response to precipitation is still observed even after compositing the data by Acld, which drives an overall negative OLS linear regression fit of the Nd-LWP relationship, the data is further composited by precipitation. Figure S12 shows negative slopes of the relationship for the non-raining composites. The slope is especially negative for low-albedo clouds. As precipitation becomes heavier in the drizzle and raining regimes the slopes become more positive and larger in both the OLS and finite differences slopes. This suggests that while the observed negative slope may be shaped by cloud albedo binning, the emergence of a more positive slope is more directly tied to the presence of precipitation. However, it is important to note that cloud albedo itself is not an independent driver of cloud microphysics but rather an outcome of variables such as LWP and Nd, among others. Therefore, interpreting slope changes as being “controlled” by cloud albedo may misrepresent causal relationships and itself serves as a means for binning clouds of varying microphysical quantities.

Free tropospheric humidity has often been proposed as a key factor driving negative LWP adjustments . However, Fig. S13 does not support this expectation, that higher relative humidity leads to a more positive LWP slope as droplet concentrations increase. Based on this first-level binned analysis, LWP appears largely unaffected by relative humidity.

To verify this, we further decompose the response using the most influential variables identified by the random forest method: first by precipitation, then by cloud albedo, and finally by relative humidity. Figure  shows that the Nd-LWP OLS slope remains negative for non-precipitating clouds under all cloud controlling factor groupings. For dimmer clouds, Ac(low), higher relative humidity (moist) is actually associated with stronger LWP decreases (not increases) with Nd. Only in drizzling, high-albedo clouds does the LWP OLS slope become positive under an increased RH. If anything, higher free-tropospheric relative humidity decreases LWP. Despite a seeming consensus in the literature , our findings suggest that relative humidity above the PBL plays a relatively minor role in ACI compared to other factors like precipitation state and cloud macroscopic properties such as albedo in subtropical stratocumulus clouds. This analysis is included to explicitly demonstrate that, contrary to prior expectations, free-tropospheric humidity exerts only a weak influence on LWP. Detailed measurements and/or modeling of cloud top entrainment or divergence may be needed to close this research gap instead of relying on inferred relationships to above PBL relative humidity.

We introduce a new method using ML random forest model predictions for computing aerosol indirect radiative forcing. This approach captures nonlinear relationships between variables, simplifies the computation of partial derivatives while holding other variables constant (e.g. LWP), and eliminates the need for data stratification methods such as binning. The ML model can therefore directly predict the Twomey, LWP, and cloud fraction radiative effects, provided it has been trained with the necessary variables. The shortwave radiative forcing due to a change in anthropogenic aerosols can be expressed as 2ΔF=-ΔαF↓‾ϕatm where the negative sign denotes that an increase in planetary albedo reduces the net downward (absorbed) shortwave flux, consistent with the convention that positive ΔF denotes a warming (increase in absorbed energy). Here, F↓‾ is the annual mean incoming solar radiative flux at the top of the atmosphere (global mean value of 340.2 W m⁻²), enabling comparison of relative changes in the outgoing flux between regions, and ϕatm is a transfer function accounting for the average atmospheric attenuation above the surface and clouds, typically taken as 0.7. The change in planetary albedo due to observed variations in Nd and aerosol index (AI) is given by: 3Δα=dαdln⁡Nddln⁡Nddln⁡AIΔln⁡AI‾, where dln⁡Nddln⁡AI represents the aerosol-cloud sensitivity, which relates changes in cloud droplet concentration to changes in AI. AI is the product of aerosol optical depth (AOD retrieved at 550 nm) and the Ångström exponent computed using the AOD at 550 and 865 nm wavelength pairs derived from MODIS, which is found to be a better proxy for column cloud condensation nuclei than AOD alone . The relationship is positive across our regions with an average value of approximately 0.31±0.16 (Fig. S14). Stronger slopes are typically retrieved in stratocumulus-dominated regions, while weaker slopes tend to occur under more unstable atmospheric conditions with lower cloud fraction. Weaker slopes under these conditions may be partially caused by larger error contributions stemming from satellite retrieval artifacts related to aerosol humidification and 3D scattering effects between clouds with lower cloud fractions . Higher precipitation rates in tropical regions is also associated with smaller Nd, complicating the causal direction of aerosols and their role on clouds or potentially in this case, the precipitation impact on aerosols as shown in .

The Δln⁡AI‾=ln⁡AIPDAIPI‾ term represents the average log-change in aerosol optical depth due to the influence of anthropogenic aerosols (i.e., based on present-day, AIPD, and pre-industrial levels, AIPI). An Earth system model is needed to estimate this quantity. The average value of Δln⁡AI‾ is estimated from 1° spatial resolution E3SM simulations of 5-year average present-day and pre-industrial aerosol emissions, the global results of which are displayed in Fig. S15, and over our regions, Δln⁡AI‾=0.41±0.27.

The derivative of planetary albedo, defined as α=(1-CF)αclr+CFαcld, where αclr is clear-sky albedo, with respect to Nd is carried out using the chain rule expansion described in : 4dαdln⁡Nd=CF∂αcld∂ln⁡Nd|LWP,CF+∂αcld∂LWPdLWPdln⁡Nd+∂αcld∂CFdCFdln⁡Nd. where the clear-sky contribution to the planetary albedo is not included because it is part of the direct radiative effect (i.e. (αcld-αclr)dCFdln⁡Nd term). All three terms in Eq. () represent radiative sensitivities, with the first and second terms restricted to cloudy regions. When combined with Eqs. () and (), these terms correspond to the Twomey radiative effect (where LWP and CF are held constant), LWP adjustment, and CF adjustments. For completeness, the full expression can be written as 5ΔF=-F↓‾ϕatmCF∂αcld∂ln⁡Nd|LWP,CF+∂αcld∂LWPdLWPdln⁡Nd+∂αcld∂CFdCFdln⁡Nddln⁡Nddln⁡AIΔln⁡AI‾. To implement this framework, three separate random forest models are trained to predict Acld, LWP, and CF based on the same set of cloud-controlling variables. However, when training the model to predict Acld, we exclude Acld as a predictor and replace it with LWP, applying a similar replacement strategy when predicting CF. This approach ensures consistency in the input variables across all models. The performance of the ML models using Acld and CF predictors (instead of LWP) is summarized in Tables S4 and S5. These models achieve r2 values that are comparable to those obtained when predicting LWP. Across most grid resolutions, CF, LWP, and Nd are identified as the most “important” terms influencing Acld. Similarly, cloud top height, Nd , and the LCL play significant roles in predicting CF.

The three terms in parentheses correspond to the Twomey, liquid water path, and cloud fraction radiative effects, respectively. These are multiplied by a radiative scaling factor defined as (-1.)⋅CF⋅F↓‾⋅dln⁡Nddln⁡AIΔln⁡AI‾ where the negative sign indicates that an increase in albedo (from higher Nd) reduces the net downward shortwave flux. The first term (Twomey effect) inside the parenthesis, ∂αcld∂ln⁡Nd|LWP,CF, is evaluated using a radiative kernel approach, similar to that described in . First, the frequency of occurrence from cloud retrievals within logarithmic bins of LWP and linear bins of CF is estimated from the full dataset (Fig. a). Second, the sensitivity of Acld to Nd is computed within each joint LWP–CF bin, where the random forest model uses fixed values based on the median for each predictor variable corresponding to the midpoints of the bin. Predictions of Acld are generated across the full range of Nd within each bin and are fit using a linear least squares method (Fig. b). To compute uncertainty, the slope within each bin is computed three times using the median values of other cloud-controlling variables and twice more using the median ±1 standard deviation. Finally, the resulting Twomey radiative kernel (Fig. c) is calculated from the product of the normalized PDF with the sensitivity summed over all LWP and CF bins (i.e., ∂αcld∂ln⁡Nd|LWP,CF=∑i=1NLWPbins∑j=1NCFbinsNpdf,i,j∂Acld∂Ndi,j). Uncertainties are propagated using the same approach. For the California region, this results in a Twomey radiative effect slope of ∂αcld∂ln⁡Nd|LWP,CF=0.067±0.0085.

The next two terms, the LWP and CF adjustment terms, are computed without the need for a radiative kernel since LWP and CF vary with Nd. Figure a shows a logarithmic increase in Acld as LWP increases. (Note, the small scale variability is an artifact of random forest regressors, where averaging outputs from multiple decision trees creates a piecewise constant function that appears smooth, but specific trees cause changes in output nodes as input variables vary, and predictions were made using one RF output per Nd bin with median values of the other inputs for that bin.) This relationship is expected given the analytic two-stream approximation Acld≃τcγ+τc, where γ depends on the degree of forward scattering but for water clouds is approximately 13.33, with τc=32LWPRe . Figure b shows the familiar inverted-V relationship (at 1° spatial resolution) with a strong increase at low Nd followed by a peak and decline to larger LWP. The product of ∂Acld∂LWPdLWPdln⁡Nd represents the sensitivity for the LWP adjustment which for California is -0.016±0.007–negative and about 5 times smaller than the Twomey effect. Thus, clouds lose LWP as Nd increases causing Acld to decrease. Negative LWP adjustments have been identified in natural experiments like ship and volcano tracks as well as in general for warm boundary layer stratocumulus clouds generally assumed to be caused by enhanced cloud top entrainment and dessication drying of the clouds as they become more polluted .

The CF adjustment is generally associated with much more uncertainty. Observed positive correlations are typically found between cloud cover fraction and aerosol optical thickness. However, these correlations are influenced by physical processes as well as uncertainties caused by artifacts, such as cloud contamination of satellite-retrieved Nd under low cloud fraction conditions, co-variation of cloud fraction with relative humidity/wind speed, and cloud processing of aerosols, which may bias the magnitude of the CF adjustment . Figure c shows that Acld increases as a function of CF until approximately 0.8, where a sharp increase suddenly occurs as the cloud scene becomes fully overcast. A similar conclusion, albeit replacing Acld with τc (which, using the 2-stream approximation, is a good proxy for Acld), was also found in . The rapid rise towards overcast conditions may be a retrieval artifact caused by three-dimensional radiative transfer effects. As the separation between the clouds becomes comparable to the cloud thickness, radiation escaping through the sides of clouds has a high probability of being scattered upward by nearby clouds, thereby contributing significantly to the reflected radiances . Figure d shows that CF rapidly rises with Nd to about 85 cm⁻³ then flattens out for larger values of Nd. The mechanism behind the increase in CF with Nd has been hypothesized to be due to the reduction in precipitation efficiency, leading to more persistent clouds and possibly due to concurrent increases in evaporation and cloud breakup. suggests that the observed correlation may be due to meteorological covariations and artifacts in cloud properties. The product of ∂Acld∂CF and dCFdln⁡Nd = 0.011±0.01 for the California region. It is positive, suggesting that increased aerosol levels enhance cloud fraction and cloud albedo causing further radiative cooling.

The radiative adjustments are affected by spatial resolution. Figure e–h shows that the strength of all the adjustment slopes tend to decrease when using the 0.1° gridded product compared to 1°. The shift from inverted-V to “M” shapes (comparing Fig. b with f) is associated with weaker slopes (more positive values). Additionally, the cloud albedo sensitivity to cloud fraction and liquid water path decreases at higher spatial resolutions. These results suggest that data aggregation has a profound influence on the strength of the estimated ACI relationship. Similar conclusions about the grid-scale dependence of ACI have been noted in previous studies , but those did not explicitly examine the Nd–LWP relationship, apply machine learning, decompose the radiative forcing into components, or analyze a broad range of satellite grid resolutions at the global scale – further supporting the significance of our findings.

All three terms are now combined using Eq. () to estimate the total radiative forcing. Table  lists radiative forcing estimates for the combined subtropical regions. Aside from the coarsest resolution, the Twomey effect remains relatively unchanged as a function of grid resolution, with values of approximately -1±0.2 W m⁻². The LWP adjustment contributes very little to the net radiative forcing. At 1° resolution, the CF adjustment makes up over a half of the response, but at finer resolutions, the adjustment terms become negligible. While CF increases on average as a function of grid-resolution (from 0.6 to 0.75), this contribution leads to a slightly larger radiative scaling (since the forcing is proportional to the cloud fraction). However, the primary reason for the reduction in the adjustment terms is the weakened LWP and CF sensitivities to Nd at higher spatial resolutions. While the sensitivities are slightly different between regions (radiative forcing being largest in the mid-latitudes and weakest in the tropics; Tables S6 and S7), these ACI relationships to spatial resolution are similar across regions despite having different meteorological and cloud regimes.

The structure of the Nd–LWP relationship changes significantly with increasing grid resolution. At coarser resolutions, the relationships found within the subtropics exhibits a classic inverted-V shape. As the resolution becomes finer, the relationship becomes more detailed, revealing multiple modes, including an “M” shape at scales approaching 0.1°. This increase in resolution captures more variability and impact of optically thinner clouds, resulting in a wider spread of LWP values when stratifying by primary cloud controlling variables (like precipitation and cloud albedo) identified using a random forest ML model.

The Nd–LWP relationship varies significantly between tropical, subtropical, and midlatitude regions. In subtropical regions, the relationship typically exhibits an inverted-V or “M” shape, with negative linear slopes, which become less negative at increasing spatial resolution. In tropical regions, the relationship does not show these distinct shapes and the linear sensitivity is roughly flat. In midlatitude regions, the relationship is generally positive with less coherent inverted-V or “M” structures, indicating that regional meteorological conditions significantly influence the Nd–LWP relationship.

Satellite filtering and sampling of clouds with different properties have a substantial impact on the Nd–LWP relationship. Including All retrieved warm clouds, which importantly include thin clouds, results in a predominantly positive slope, while more stringent filtering (e.g., removing thinner clouds) leads to mostly negative slopes. Thicker, opaque clouds improve the accuracy of cloud property retrievals but are less sensitive to aerosol perturbations. This indicates that the choice of cloud sampling and filtering criteria can significantly alter the interpretation of the Nd–LWP relationship and its associated radiative effects.

A random forest model identified precipitation and cloud albedo as critical factors shaping the relationship. Precipitation strongly influences the Nd-LWP relationship, with steeper positive slopes as precipitation rate increases. In non-precipitating clouds, LWP remains flat due to the absence of drizzle suppression, while in precipitating clouds, increasing Nd suppresses rainfall, which increases LWP before leveling off. Binning the relationship by cloud albedo leads to negative slopes of the inverted-V distribution, while precipitation controls the positive slopes. Relative humidity above the PBL has a minor influence on ACI compared to precipitation state and cloud macroscopic properties like albedo.

The Twomey radiative effect is the dominant term, with LWP adjustments being small by comparison; this is consistent with a breadth of observed natural laboratory results by . The radiative forcing is robust across all grid resolutions. On the other hand, the LWP and CF radiative adjustments are strongly affected by spatial grid resolution, wherein the CF adjustment makes up a 1/2 of the response at 1° resolution. Part of the sensitivity decrease is due to shifting from an inverted-V to “M” in subtropical regions, but a larger part of the response is due to a weaker Acld relationship with LWP and CF as spatial resolution increases.

Estimates of ACI relationships are sensitive to spatial resolution, regional variations, and satellite sampling methods. Associated radiative forcing is impacted by these factors, which underscores the need to evaluate high-resolution, region-specific Earth system model representations of these processes. ML models can enhance our understanding by capturing non-linear effects, identifying key predictors like precipitation and cloud albedo, and offering new capabilities for quantifying aerosol radiative forcing. As Earth system models increase spatial resolution, these data and analyses will be useful for evaluating ACI in warm clouds, which is necessary for identifying model deficiencies and will be addressed in a follow on companion paper.