Reflections on cloud effects How much impact does the abundance of cloud condensation nuclei (CCN) aerosols above the oceans have on global temperatures? Rosenfeld et al. analyzed how CCN affect the properties of marine stratocumulus clouds, which reflect much of the solar radiation received by Earth back to space (see the Perspective by Sato and Suzuki). The CCN abundance explained most of the variability in the radiative cooling. Thus, the magnitude of radiative forcing provided by these clouds is much more sensitive to the presence of CCN than current models indicate, which suggests the existence of other compensating warming effects. Science, this issue p. eaav0566; see also p. 580

Structured Abstract INTRODUCTION Human-made emissions of particulate air pollution can offset part of the warming induced by emissions of greenhouse gases, by enhancing low-level clouds that reflect more solar radiation back to space. The aerosol particles have this effect because cloud droplets must condense on preexisting tiny particles in the same way as dew forms on cold objects; more aerosol particles from human-made emissions lead to larger numbers of smaller cloud droplets. One major pathway for low-level cloud enhancement is through the suppression of rain by reducing cloud droplet sizes. This leaves more water in the cloud for a longer time, thus increasing the cloud cover and water content and thereby reflecting more solar heat to space. This effect is strongest over the oceans, where moisture for sustaining low-level clouds over vast areas is abundant. Predicting global warming requires a quantitative understanding of how cloud cover and water content are affected by human-made aerosols. RATIONALE Quantifying the aerosol cloud–mediated radiative effects has been a major challenge and has driven the uncertainty in climate predictions. It has been difficult to measure cloud-active aerosols from satellites and to isolate their effects on clouds from meteorological data. The development of novel methodologies to retrieve cloud droplet concentrations and vertical winds from satellites represents a breakthrough that made this quantification possible. The methodologies were applied to the world’s oceans between the equator and 40°S. Aerosol and meteorological variables explained 95% of the variability in the cloud radiative effects. RESULTS The measured aerosol cloud–mediated cooling effect was much larger than the present estimates, especially via the effect of aerosols on the suppression of precipitation, which makes the clouds retain more water, persist longer, and have a larger fractional coverage. This goes against most previous observations and simulations, which reported that vertically integrated cloud water may even decrease with additional aerosols, especially in precipitating clouds. The major reason for this apparent discrepancy is because deeper clouds have more water and produce rainfall more easily, thus scavenging the aerosols more efficiently. The outcome is that clouds with fewer aerosols have more water, but it has nothing to do with aerosol effects on clouds. This fallacy is overcome when assessing the effects for clouds with a given fixed geometrical thickness. The large aerosol sensitivity of the water content and coverage of shallow marine clouds dispels another belief that the effects of added aerosols are mostly buffered by adjustment of the cloud properties, which counteracts the initial aerosol effect. For example, adding aerosols suppresses rain, so the clouds respond by deepening just enough to restore the rain amount that was suppressed. But the time scale required for the completion of this adjustment process is substantially longer than the life cycle of the cloud systems, which is mostly under 12 hours. Therefore, most of the marine shallow clouds are not buffered for the aerosol effects, which are inducing cooling to a much greater extent than previously believed. CONCLUSION Aerosols explain three-fourths of the variability in the cooling effects of low-level marine clouds for a given geometrical thickness. Doubling the cloud droplet concentration nearly doubles the cooling. This reveals a much greater sensitivity to aerosols than previously reported, meaning too much cooling if incorporated into present climate models. This argument has been used to dismiss such large sensitivities. To avoid that, the aerosol effects in some of the models were tuned down. Accepting the large sensitivity revealed in this study implies that aerosols have another large positive forcing, possibly through the deep clouds, which is not accounted for in current models. This reveals additional uncertainty that must be accounted for and requires a major revision in calculating Earth’s energy budget and climate predictions. Paradoxically, this advancement in our knowledge increases the uncertainty in aerosol cloud–mediated radiative forcing. But it paves the way to eventual substantial reduction of this uncertainty. Coverage and droplet concentrations (N d ) of shallow marine clouds over the northeast Pacific. Smoke particles emitted from ship smokestacks form cloud droplets and elevate N d . The smoke-free clouds (N d < ~30 cm−3) precipitate and break up. The fraction of cloud cover increases with more N d that suppresses precipitation. The solid cloud cover is maintained by smoke that was spread from old ship tracks, crossed by newer ones.

Abstract A lack of reliable estimates of cloud condensation nuclei (CCN) aerosols over oceans has severely limited our ability to quantify their effects on cloud properties and extent of cooling by reflecting solar radiation—a key uncertainty in anthropogenic climate forcing. We introduce a methodology for ascribing cloud properties to CCN and isolating the aerosol effects from meteorological effects. Its application showed that for a given meteorology, CCN explains three-fourths of the variability in the radiative cooling effect of clouds, mainly through affecting shallow cloud cover and water path. This reveals a much greater sensitivity of cloud radiative forcing to CCN than previously reported, which means too much cooling if incorporated into present climate models. This suggests the existence of compensating aerosol warming effects yet to be discovered, possibly through deep clouds.

Marine stratocumulus clouds (MSCs) are responsible for reflecting much of the solar radiation received by Earth back to space. Therefore, understanding the causes for the variability in their radiative effects is necessary for understanding the natural and anthropogenic controls of Earth’s energy budget and the resultant climatic implications. The effects of MSCs on the albedo of a given ocean area are determined by cloud fraction (Cf), droplet concentration (N d ), and liquid water path (LWP). Cloud droplets must form on cloud condensation nuclei (CCN) aerosols, and N d is determined by the CCN activation spectrum as a function of vapor supersaturation (S), which in turn is driven by cloud base updraft velocity (W b ) (1). The overall properties of the cloud system are determined by the meteorological setting, which includes vertical thermodynamic and wind profiles. However, radiation emitted by the clouds and precipitation from them may modify their state. Because such feedbacks can depend on the aerosol effects on cloud microstructure and precipitation, it is very difficult to isolate the effects of aerosols on the cloud properties (2). Here, we addressed this challenge by calculating, for a given meteorological condition, the amount of variability in Cf, LWP, and cloud radiative effect (CRE) that can be explained by variability in CCN. The meteorology is encapsulated by the satellite-retrieved W b , the cloud geometrical thickness (CGT), and the thermodynamic structure of the lower troposphere.

Known effects of aerosols on shallow water clouds This study is limited to cumulus and MSC clouds with geometrical thickness of up to 800 m. Most cloud droplets in shallow convective clouds form at their base. In adiabatic cloud parcels, the cloud drop mass grows nearly linearly with height above cloud base while the N d mixing ratio remains constant. This leads to a nearly linear increase in cloud liquid water content (LWC) with height above base. Therefore, integration of LWC with height results in LWP ∝ CGT2. Aircraft observations have shown that the cores of actual shallow convective clouds and MSCs do not deviate substantially from this ideal behavior (3). The cloud drop coalescence rate is proportional to LWC2r e 5, where r e is the cloud drop effective radius (4). When r e exceeds 14 μm, the clouds start precipitating through the quick formation of drizzle (5–10). The drizzle leads to accretion that forms raindrops from the full column of the clouds (10). The CGT for reaching that value of r e depends linearly on N d (4, 11, 12). Overcast decks of MSCs usually break up when they begin to produce substantial amounts of precipitation (rain rate > ~2 mm day−1) in response to the thermodynamic effects. The clouds break up mainly because rain-driven downdrafts form miniature gust fronts at the sea surface, which trigger convective cloud formation when they collide with each other (13–15). This leads to a large decrease in Cf from near unity to ~0.6 (16). The precipitation scavenging of the CCN leads to a decrease of N d at the convective cores from an average of 55 cm−3 to 15 cm−3 from just before to after the transition from closed to open cells of MSCs, whereas LWC does not change significantly during the transition (16, 17). Aerosol optical depth (AOD) and aerosol index (AI) have been used as proxies for CCN (18–20). However, direct comparisons of satellite-observed relationships of AOD and cloud properties disagree with model simulations, as the models have a much larger sensitivity to aerosols than observations indicate (21). This is caused by issues that decorrelate the aerosol properties retrieved by satellite from boundary layer CCN concentrations, such as aerosol swelling due to higher relative humidity in the vicinity of clouds [see review in (22)]. Furthermore, aerosols cannot be retrieved in cloudy conditions, where they are most needed. Even under simulated ideal conditions, AOD can explain only a small fraction of the variability of CCN in the boundary layer (23). This might explain the findings of Gryspeerdt et al. (24), who showed that ~80% of the indicated positive relationship between AOD and Cf is explained by factors that cannot readily be interpreted as a causal effect of AOD variability on Cf. Much of this problem is caused by the poor relationship between AOD and CCN, especially in areas with small CCN concentrations, where a small absolute change in the concentration is a large fractional change. Because the effects of aerosols on cloud properties are logarithmic (25), the largest aerosol effects on clouds are poorly detected. The situation is worst over the Southern Oceans, where the clouds prevent retrieval of AOD most of the time. Furthermore, when AOD is retrieved, its value is often within the detection limit of 0.06 over ocean [figure 11 of (26), which translates to >100 to 200 CCN cm−3 at S = 0.4% (27)]. Moreover, according to figure 14 of (26), the median satellite-indicated AOD over ocean is only 0.05, which is within the range of measurement error. This situation requires an approach that does not depend on AOD. In response, we use N d and W b as proxies for CCN at cloud base (28). This has become possible as a result of recently developed methodologies for retrieving N d (29) and W b (30, 31) of the convective cores of clouds, which best reflect CCN concentrations ingested into cloud bases.

Known effects of meteorology on shallow water clouds Marine stratocumulus clouds form by radiative cooling of the cloud-topped marine boundary layer. This is promoted by the moist marine boundary layer that is capped by a pronounced inversion with dry air above it, which allows a strong radiative cooling of the cloud tops. The dryness of the free troposphere air is often a result of subsidence in anticyclones. Klein et al. (32) showed that lower tropospheric stability (LTS, the difference between potential temperature at 700 hPa and at the surface) explains most of the variability in the seasonally averaged amount of MSCs at five oceanic regions, with a 6% increase of Cf for each 1 K increase of LTS within the LTS range of 14 to 22 K. They also showed that the cloud top radiative cooling rate (CTRC) explains similarly most of the variability in Cf with the same data. This can be the case because the LTS and CTRC are not independent. A recent similar analysis using an artificial neuron network (33) reconfirmed the major role of LTS in the determination of Cf. Andersen et al. (33) also showed that LWP is dominated by boundary layer height. This makes physical sense because a deeper boundary layer allows a proportionally larger CGT, whereas adiabatic LWP is proportional to CGT2. We isolated the effects of aerosols and meteorology on the components of CRE—N d , Cf, and LWP—of boundary layer marine water clouds by testing their dependence on meteorological factors (LTS, CGT, CTRC) and on aerosols, as approximated by N d and W b . The value of N d is determined by CCN and by W b ; in turn, W b is determined by cloud base height (30) and CTRC (31). A surrogate for the CCN is calculated by accounting for the effect of W b on N d and obtaining N d /W b 0.5, as described in the methodology. Whereas previous analyses were done on large areas at monthly to seasonal scales, N d varies at much smaller scales in time and space. The fraction of variability in CRE and its components that is explained by each of these meteorological and aerosol properties is quantified.

Data and methodology MODIS data were analyzed over the Southern Oceans between the equator and 40°S. The data were collected for the southern summers, for the months of November and December 2014, January and February 2015, November and December 2015, January and February 2016, November and December 2016, and January and February 2017. A total of 4620 MODIS granules were analyzed. Each granule was divided into 306 scenes of 110 km × 110 km (about 1° × 1° near the equator). The two external scenes on each edge were truncated for data quality (Fig. 1A). A scene was selected for analysis if it included only liquid water–phase clouds that were not obscured by higher cloud layers in any part of the scene. We analyzed 664,128 (Fig. 2) out of 1,413,868 scenes (47% of total scenes viewed by the satellites). Fig. 1 The MODIS Terra overpass on 7 December 2017, 18:25 UT. (A) MODIS natural projection, divided into 110 km × 110 km scenes. The red areas were excluded from the analysis. (B) A geographically rectified image. The contours show the LTS from the reanalysis data. Fig. 2 Distribution of N d and LTS for the analyzed scenes. The color represents the 1° × 1° averaged N d (A) and LTS (B). The following cloud properties were calculated for each 110 km × 110 km scene: 1) Cloud drop concentrations (N d ) in units of cm−3. To obtain N d that is most relevant to CCN below cloud base, we used the methodology of Zhu et al. (29) that was developed specifically for application to this study. The input is obtained from MODIS collection 6 level-2 cloud products of r e and cloud optical depth (τ). The pixels with highest 10% of τ within the scene are used for retrieving N d (29) because the brightest clouds are the convective cores which are closest to adiabatic. Its high value (median τ = 21) further reduces the retrieval bias of N d due to upwelling radiation from below cloud tops (34). This methodology minimizes the retrieval bias of N d in broken clouds relative to full cloud cover to less than 5% (29). The geographical distribution of average N d is shown in Fig. 2A. 2) Liquid water path at cloud cores (LWP core ) in units of g m−2. It was averaged over the highest 10% of τ within the scene from pixel values obtained from MODIS cloud products. 3) Geometrical thickness of the cloudy layer (CGT). Both cloud top and base heights are uniquely defined for any combination of LWP, cloud top temperature (CTT), and sea surface temperature (SST) when assuming dry adiabatic lapse rate from SST to cloud base, and moist adiabatic from cloud base to cloud top. We solve for CGT and cloud base height (CBH) under these assumptions. This is done for the convective cores by averaging CTT and LWP core over the highest 10% of τ for the scene. The daily mean SST data at a spatial resolution of 0.25° × 0.25° were provided by the National Oceanic and Atmospheric Administration (NOAA). Clouds with CGT > 800 m were excluded to restrict the analysis for shallow clouds. This excluded only 2% of the total number of scenes with single–boundary layer water clouds. 4) Cloud fraction (Cf), defined as the fraction of pixels of the scene that have 0.64 μm reflectance greater than the reflectance that is matched to the minimum detectable τ. This allows counting pixels as cloudy even when τ is not calculable in the MODIS products, as shown in fig. S12. 5) Cloud top radiative cooling rate (CTRC) in units of K day−1. CTRC was calculated by a radiative transfer model, SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer), with input as CTT and the vertical profile of temperature and relative humidity above cloud tops, as obtained from the National Centers for Environmental Prediction (NCEP) reanalysis data (31). A full description of the methodology is provided in the supplementary materials. 6) Lower tropospheric stability (LTS) in units of K. The LTS was calculated according to the difference of the geopotential temperature between the sea surface and 700 hPa. Both calculations rely on atmospheric profiles from the NCEP reanalysis data. The geographical distribution of average LTS is shown in Fig. 2B. 7) The strength of the inversion at the cloud tops (Δθ), calculated from the reanalysis data as the difference in the potential temperature (θ) above and below the inversion. 8) Neutralized N d for W b (N d /W b 0.5), which is determined primarily by CCN. Twomey (1) showed that for a given CCN(S) = N 0 Sk, N d depends on W b according to N d‐Twomey = 0.88 N 0 2 / ( k + 2 ) ( 0.07 W b 1.5 ) k / ( k + 2 ) (1)where N 0 is CCN concentration at supersaturation S = 1.01, and k is the coefficient of the power law. We estimated W b for convective clouds according to Zheng and Rosenfeld (30), who approximated W b = 0.9 CBH, where W b is in ms−1 and CBH is in km. Clouds were considered as convective for LTS ≤ 16 K. For MSCs (LTS > 16 K), we used the relationships of Zheng et al. (31), who showed that W b of MSCs is driven by CTRC and is approximated as W b = [–0.37(CTRC) + 26.1]/100 ms−1. Clouds in scenes with CBH > 1 km were considered decoupled and used W b = [–0.38(CTRC) + 8.4]/100 ms−1 (35). The N d sensitivity to W b was calculated according to Eq. 1, while assuming k = 1, as W b 0.5. Thus, N d-Twomey neutralized to the effect of W b was calculated as N d /W b 0.5.

Results Figure 3 shows the dependence of Cf on N d for various intervals of LWP core and the dependence of Cf, LTS, CGT, and CTRC on N d for fixed intervals of CGT. The data were classified into four-dimensional bins of N d , LTS, CGT, and CTRC. Binning is necessary to average out variability in Cf at the scale of the scene (110 km × 110 km) that is not related to meteorology, such as self-organization of cloud clusters, as is evident in Fig. 1B. Fig. 3 Dependence of cloud properties on drop concentrations. (A) Dependence of Cf on N d for intervals of LWP core . (B to D) Dependence of Cf (B), LWP (C), and CRE (D) on N d for fixed intervals of CGT. The data are for all the scenes over the Southern Oceans between 0° and 40°S. Cloud top drop effective radius of each line (i.e., for a given LWP core ) decreases with increasing droplet concentration, reaching 14 μm at the dotted line. The values are the medians for each bin. (The equivalent fig. S1 shows the means of the bins.) The box plot distributions for each bin are shown in figs. S5 to S8. The median values of Cf for the individual scenes in each bin for N d , LWP core , and CGT are shown in Fig. 3. The box plot distributions of the cases that compose each of the points of Fig. 3 are shown in figs. S5 to S8. For a given CGT, Cf increases with both LWP core and N d until reaching nearly full cloud cover for N d > 100 cm−3 and LWP core ≥ 240 g m−2 (Fig. 3, A and B). This result is qualitatively similar to the N d -Cf relationship shown in figure 5 of Gryspeerdt et al. (24). However, they assumed that CCN correlates with AOD and concluded that the much poorer correlation of N d with AOD meant that only 20% of the observed N d -Cf relationships could be interpreted as related to CCN, whereas the remaining 80% was caused by retrieval errors and meteorological factors. We question the validity of such an interpretation, because low CCN concentrations typical of the boundary layer of the open ocean poorly correspond to AOD (23) and therefore AOD also poorly corresponds to N d . It follows that the poor correlation between AOD and CCN weakens the N d -AOD relationships. Instead, we ascribe the variability in N d directly to CCN by using N d of the convective cores and correcting it for W b , while accounting for most of the variability in meteorology as manifested by CGT, Δθ, and CTRC. Because N d and LWP core represent the cloud cores, which are the closest to adiabatic, increasing N d for a given LWP core decreases r e in a known way under an assumption of a fixed adiabatic fraction. The points where r e reaches the precipitation initiation value of 14 μm are connected by the dotted line in Fig. 3A. The clouds to the left of the dotted line have smaller N d and therefore r e > 14 μm. Because the coalescence rate is proportional to r e 5, the clouds with r e > 14 μm precipitate substantially (rain rate > ~2 mm/day), whereas precipitation in clouds to the right of the dotted line is mostly suppressed as a result of the small cloud droplet size when N d becomes large. It is noteworthy that the nearly full cloud cover for LWP core ≥ 240 g m−2 breaks up abruptly with the onset of precipitation, as indicated by r e exceeding 14 μm at N d < 100 cm−3. The abruptness of the breakup is attributed to the positive feedback of scavenging the CCN by the precipitation (13). This, along with the fact that MSC decks break up when starting to precipitate heavily, indicates that Cf is determined to a large extent by the CCN control on N d . The meteorological control of Cf is known to be related mostly to LTS at seasonal time scales and regional space scales, because the formation of MSCs depends on a strong capping inversion with dry air above it (32). Indeed, fig. S3A shows that for a given N d , Cf increases by a factor of ~3 from low to high LTS. Dry air above cloud tops allows strong CTRC, which helps to maintain the cloud cover. This is captured by the strong indicated increase of Cf with CTRC (fig. S3B), especially for the weakly precipitating clouds (large N d ). The Cf of such clouds depends strongly on meteorological factors depicted here by CGT, LTS, and CTRC. However, Cf and LWP decrease substantially when clouds start to precipitate substantially (> ∼2 mm/day), as indicated by r e > 14 μm, especially when they are deeper than ~300 m (Fig. 3, A and B). A full cloud cover requires large LTS, CTRC rate < ~ –50 W m−2, CGT > ~300 m, and sufficiently large N d to suppress precipitation (>60 to 100 cm−3, more for deeper clouds). Although aerosol effects on MSC cloud cover are relatively well documented (13, 36, 37), aerosol effects on cumulus (Cu) clouds have been more elusive. To explore the role of cloud regimes in the aerosol effects, we repeated the analysis shown in Fig. 3 for Cu (LTS < 14 K), MSC (LTS > 18 K), and a transition cloud regime for 18 K ≥ LTS ≥ 14 K (Fig. 4). The overall shape of the relationships of cloud properties with N d shown in Fig. 3 remains similar for both MSC and Cu, although the magnitude of the slopes decreases gradually to slightly more than half when transitioning from MSC to Cu. Quantification of the slopes tells the same story. According to Table 1, the susceptibility of Cu properties to N d is similar to the susceptibility of MSC, although somewhat weaker. A salient feature is that Cf of MSC reaches unity at large N d and CGT (Fig. 4D), whereas Cf of Cu cannot exceed 0.7 at any N d and CGT. The transitions from MSC to Cu is gradual and depends on LTS, whereas the dependence of the average LWP, Cf, and CRE is scaled down with smaller LTS. This situation calls for a quantitative formulation of this dependence. Fig. 4 Dependence of cloud properties on drop concentrations as a function of LTS. (A, D, G, and J) LTS > 18 K; (B, E, H, and K) 18 K ≤ LTS ≤ 14 K; (C, F, I, and L) LTS < 14 K. (The equivalent fig. S2 shows the means of the bins.) Table 1 The susceptibility of Cf, LWP, and CRE to N d , based on the slopes of the lines of figs. S1 and S2. The numbers are based on the means and standard deviations of the slopes of the lines for the different CGTs in each panel. View this table: Expanding Figs. 3 and 4 to the four-dimensional dependence of CF on N d , CGT, LTS, and CTRC requires a multiple regression procedure, which allows a polynomial fit of second order. Because CGT, LTS, and CTRC are not completely independent, the regression procedure computes only the independent component that each variable contributes. The procedure was applied to the binned data. The central values of the individual bins are shown by the dots on the curves and classifier intervals in Fig. 3 and fig. S3. To average out the effect of cloud self-organization on Cf, we incorporated into the regression only bins that contained at least 10 scenes (see Fig. 1B). Replacing LTS with Δθ yielded larger R2 values, probably because Δθ is much more focused on the cloud tops than is LTS. The results with either LTS or Δθ are shown in Table 2. Table 2 Multiple regression of Cf, LWP, and CRE with log 10 (N d ) or log 10 (N d /W b 0.5), CGT, LTS or Δθ, and CTRC. The regression is applied to the means of the bins, with direct N d or with the updraft normalized N d /W b 0.5, which serves as a proxy to CCN concentrations. The contribution to R2 for each of the independent variables is the decrease in total R2 with that variable omitted. The sums of individual contributions of R2 are adjusted to equal the total R2. View this table: Table 2 shows that four parameters explain up to 95% of the variability in CRE. When using Δθ, N d alone explains 46% of the variability in CRE. Its importance is higher than that of CGT (36%), despite thicker clouds having larger Cf, when everything else is held constant. Δθ and CTRC, whose high values support the formation of MSC decks, explain 7% and 6% in the variability of CRE, respectively. Less than 6% of CRE remains unexplained by the combination of N d , CGT, CTRC, and Δθ or LTS. Can meteorology explain some of the variability in N d , thus serving as an alternative explanation to the implied high contribution of CCN to R2 of Cf? That can happen by meteorology incurring stronger W b for greater Cf, which then increases N d for the same CCN. This question can be addressed by accounting for the effect of W b on N d . The possible W b -induced enhancement of N d may be neutralized by dividing N d by the updraft enhancement factor of N d . The outcome is N d /W b 0.5, which serves as a proxy for the CCN concentrations. The results of the application of the regression to N d /W b 0.5 are shown in the lower half of Table 2. The overall R2 values of Cf, LWP, or CRE with N d /W b 0.5 are practically equal to the R2 with N d . This shows that the meteorological factors that affect W b (CBH and CTRC) cannot provide an alternative explanation to the large implied aerosol effects on cloud properties. The polynomial regressions described in Table 2 are in fact an observationally based simplified formulation of parameterization of the properties of marine boundary layer clouds. The coefficients of the equations are given in table S2. Because CGT reflects almost three-fourths of the variability in CRE due to meteorology, the analysis was extended to classes of CGT, as shown in Table 3. About 73% of the variability in CRE for clouds with a given CGT is explained by the CCN surrogate N d /W b 0.5, and up to 82% for the shallowest clouds. The total explained variability in CRE when also considering Δθ and CTRC can be as much as 95%. Using N d instead of N d /W b 0.5 (table S1) yields systematically lower R2 by a few percent. This underscores the larger relevance of the retrieved proxy to CCN relative to the retrieved N d . Table 3 Multiple regression with polynomial fit of the second order for Cf with log 10 (N d /W b 0.5), Δθ, and CTRC for different intervals of CGT. The values in columns 4 to 6 are the partial R2 (or fraction of explained variability of Cf) attributed to N d /W b 0.5, Δθ, and CTRC. The sums of individual contributions of R2 are adjusted to equal the total R2. View this table:

Supplementary Materials www.sciencemag.org/content/363/6427/eaav0566/suppl/DC1 Supplementary Text Figs. S1 to S13 Tables S1 to S3

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