The properties of the cloud field are calculated from the Moderate Resolution Imaging Spectroradiometer (MODIS) cloud retrieval onboard both the Aqua and Terra satellites over the 10-year period 2007–2017 (inclusive). The Terra and Aqua satellites provide information about cloud properties 3 h apart from the two daytime overpasses. The cloud Nd and LWP is derived from the values of re and the cloud optical depth τ from the 2.1 µm retrievals . The cloud Nd is calculated following the sampling criteria in , and sampling strategy G18 in . Only single-layered, liquid-phase clouds are considered. This strategy also excludes pixels with solar zenith > 65° and satellite zenith angle > 55° to account for uncertainties at high viewing angles. An adiabatic cloud is assumed for all the selected pixels. The LWP is calculated using all available liquid pixels. These data are then aggregated to a 1° × 1° latitude-longitude grid.

Following , boundary layer winds are used to account for advection between the observation times of the different instruments, restricting analysis to grid boxes where Nd and LWP are available for both instruments. The cloud field is advected using ERA5 reanalysis wind fields at 1000 hPa. The advection is calculated on a 0.25° × 0.25° resolution grid (as the movement of the cloud fields over 3h is expected to be less than 1°). Each grid box on the fine resolution grid is treated as a parcel trajectory and advected using the wind fields. The Aqua data are then sampled at the end points of these trajectories, and aggregated to a 1° × 1° grid.

Surface wind speeds are obtained from ERA5, reanalysis product (on a 1° × 1° grid) that offer an estimate of global atmospheric conditions that are collocated with the MODIS observations . Precipitating and not-precipitating cases are differentiated using the probability of precipitation (PoP) at each MODIS grid point, based on the proportion of liquid re retrievals greater than 15 µm . This is calculated from the MODIS level 3 daily gridded product (MOD08_D3) using the re histogram counts. The PoP is the ratio of small drops (sum of all histogram bins less than 15 µm) to all drops in the distribution/histogram (sum of all bins). If PoP > 70 %, then the gridbox is considered to be precipitating. The results in Sect.  and are from a region within the southeastern Atlantic stratocumulus deck between 40° S to 10° N and 30° W to 10° E.

The temporal evolution of the Nd and LWP (dNd/dt and dLWP/dt respectively), is obtained by calculating the difference in properties between the two daytime satellite overpasses, which are approximately 3 h apart – at 10:30 and 13:30 local solar time for Terra and Aqua respectively. Joint histograms in the Nd–LWP space are then generated by binning the cloud data as a function of their initial Nd and LWP . These are then converted to relative rates of changes by dividing the differences first with the bin widths (Nd bins for dNd, and the LWP bins for dLWP), and then with the time step of 3 h (time difference between Aqua and Terra observations). The final result is expressed as a percentage with units of (% per hour) by multiplying with 100.

By strictly controlling the initial state of the cloud, we account for the confounding impact of existing meteorological variables which can change the properties of aerosol and the cloud simultaneously, and could introduce spurious correlations on the development of Nd-LWP relationships. If the clouds are advected across regions with a large gradient in meteorological properties, this would result in a large change in the cloud properties owing to how correlated the cloud is to a strong climatological change. Clouds with a high (low) initial value of LWP or Nd is likely to show a decrease (increase) in LWP or Nd, which is consistent with a “regression to the mean” effect. This can happen as a statistical effect, where even when the cloud is remaining stationary, a positively biased first measurement (of re) is followed by a smaller second measurement. Since re is positively correlated with LWP and negatively correlated with Nd, this shows up as a highly negative dLWP and a large positive dNd. Previous studies accounted for this by looking at anomalous changes across Lagrangian trajectories by removing seasonal means for day and night separately. On the other hand, it was shown by (where dLWP and dNd were calculated in a similar way from MODIS Terra and Aqua) that the “flowfields” (the rate of change of Nd and LWP) do not look the same when dLWP and dNd are binned by the final LWP and Nd. If there was indeed a regression to the mean effect, the flowfields should have looked the same when calculated from either direction. As stated in , while this does not completely rule out the impact of retrieval biases and the regression to the mean effect, it does rule out the possiblity of the results being a statistical artefact caused by random biases.

Here, the difference-of-rates (DoR) method is introduced which accounts for these effects. The relative rates of change (in % per hour) are calculated by separating or stratifying the cloud population based on a cloud/meteorological variable (such as surface (10 m) wind speeds, ws), and calculating the differences with respect to a reference data set. For example, in Fig. , the DoR (presented herewith with a symbol Δ) with respect to ws is calculated as 1ΔwsdNd=Δ(ws+)dNd-Δ(ws-)dNd where ws+=ws > 4 m s⁻¹ and ws-=ws < 4 m s⁻¹. Here, the cloud population with ws- is the reference data set. Multiple DoRs can be calculated by splitting ws+ into smaller bins/data ranges (different columns in Fig. ).

In addition to acting as a sink for the cloud Nd through the sedimentation of droplets, precipitation plays a key role in the scavenging of CCN (wet or below-cloud scavenging), which in turn can reduce Nd. The effects of precipitation are usually seen primarily in the (upper) left quadrant (LWP > 50 g m⁻², Nd<50 cm⁻³), i.e., for clouds with a high initial LWP and a low Nd. An overall positive change is seen in the dNd field in this region for both precipitating and non-precipitating clouds (red region in Fig. a, b), which is possibly a regression to the mean effect (discussed in the next paragraph). In addition to precipitation, other processes such as the primary production of CCN from sea spray, and entrainment of aerosols from the free troposphere (especially closer to the coast) can possibly act as significant sources of Nd for clouds with an initially low Nd. However, precipitation rates as low as 1 mm d⁻¹ have been shown to be effective in reducing Nd by a factor of three over the SE Pacific . The DoRs between precipitating and not-precipitating clouds (Fig. c) reveal that precipitation acts as a sink for the cloud Nd, with a reduction of Nd observed in more strongly precipitating cases. Precipitation results in a smaller overall net increase in dNd (i.e., the change in Nd over 3 h) with Fig. a showing lighter reds and darker greens. There is a smaller decrease (larger increase) in dNd for not-precipitating clouds in Fig. b (darker reds and lighter greens). Consequently, the corresponding DoR, ΔPoPdNd (difference between Fig. a and b, i.e., a - b), is negative (Fig. c).

The few positive values (red) in the DoR field in Fig. c are possibly not-precipitating clouds which were not filtered out using the re threshold. The positive and negative regions in Fig. a and b may be partly driven by the regression to the mean effect by using a filter in re, which is also used to calculate Nd and LWP. Similar patterns were obtained as in the Fig. a–c when an independent data source for precipitation was used Appendix ). The MODIS filters were subsequently chosen to identify precipitating clouds for the rest of the analysis. Using re as a measure of precipitation allows the precipitation data at the start of the time step to be included, such that the impact of precipitation on the cloud evolution is identified (rather than the impact of cloud evolution on precipitation, as is obtained using precipitation from the later overpass at the end of the timestep).

Droplet sedimentation at the cloud-top entrainment interfacial layer (EIL) depletes liquid water from this zone, leading to reduced entrainment and thicker clouds (high LWP) . In precipitating clouds the re is generally higher leading to droplets sedimenting out of the EIL. Conversely, in not-precipitating clouds, the re is smaller, and there are more, smaller cloud droplets in the entrainment interfacial layer at the cloud top. This leads to evaporative enhancement of entrainment of free tropospheric air, leading to a thinner cloud layer or a higher decrease (or a smaller increase) in LWP in not-precipitating clouds compared to precipitating ones. Consequently, the DoR for LWP is positive in Fig. f everywhere except in the region corresponding to the strongly negative region in Fig. c for Nd. Here, strongly precipitating clouds lose more liquid water (as rain) resulting in a more negative (less positive) change in LWP.

With the new framework effectively extracting the precipitation fingerprint, we apply this technique to identify the different processes that modify the re. To investigate the simultaneous effects of FSS and CMA in altering re through changes in Nd, the DoRs are calculated by stratifying the data by surface wind speeds. Horizontal low-level (10 m) winds have been shown to be strongly correlated with sea salt production . In contrast to Fig. , all the plots in Fig.  are DoRs, ΔwsdNd and ΔwsdLWP, calculated for different wind speed ranges and with respect to a reference dataset with ws < 4 m s⁻¹ (as detailed in the methods section). Additionally, we treat initially precipitating and not-precipitating clouds separately as the impact of aerosol-induced precipitation suppression works differently for these two categories.

For initially precipitating clouds, precipitation suppression is expected to increase at higher ws with the introduction of additional FSS. Therefore, dNd would tend to be less (more) negative (positive) as ws increases (due to reduced in-cloud scavenging). Consequently, ΔwsdNd would be negative (blue) as seen in the left quadrant in Fig. a to d.

A positive fingerprint, consistent with FSS acting as CCN, strengthens with wind speed and dominates the precipitation effect at wind speeds greater than 12 m s⁻¹ in Fig. d. In addition to the increased aerosol burden, high ws leads to stronger updrafts at the cloud base increasing the activation of FSS and the formation of new droplets.

The effect of CMA is seen in not-precipitating clouds with a high initial Nd (> 100 cm⁻³) in Fig. e–h, with a negative trend in ΔwsdNd consistent with the results from . The CMA are usually the first to activate and form droplets at the cloud base. This depletes the supersaturation here, thereby inhibiting the activation of FSS into smaller droplets. This skews the droplet size distribution to larger sizes, enhancing the collision-coalescence rate . Both processes lead to a higher re which is a key precursor to precipitation initiation.

A negative ΔwsdNd region is consistent with a giant CCN-induced reduction in dNd. In addition to fewer new activated droplets, the smaller dNd could also be due to giant CCN-induced precipitation (in initially not-precipitating clouds). Once giant CCNs are activated, condensational growth and collision-coalescence to raindrop sizes are expedited within this time scale (of 3 h). Increasing ws leads to the formation of more CMA which shows up as a stronger signal in the DoR. As expected, there is no perceptible impact of CMA on already raining clouds as drizzle is already active.

A relationship between CMA and re by altering Nd can clearly be seen. However, there is a strong positive signal in ΔdLWP across all initial Nd suggesting an alternate pathway to explain the ws–re correlation. Stronger surface winds over the ocean lead to an increase in surface fluxes through increased evaporation . This moistens the marine boundary layer and increases the moisture available at the cloud base. This can increase the cloud depth either by lowering the cloud base through condensation or increasing the cloud top height by entrainment (driven by buoyant production of kinetic energy in the updrafts; ). The current methodology does not allow us to distinguish between these two effects. In addition, higher wind speeds enhance wave formation – these waves can break and produce white caps and sea spray, which enhances the sea-to-air latent heat flux. This is an additional source to the cloud LWP leading to thicker clouds with larger droplets, and corresponding larger dLWP over the observed period (Fig. i–l).

The analysis presented thus far was restricted to the southeastern Atlantic (SEA) Sc clouds. In this section, we extend the analysis to the rest of the globe. DoR plots similar to Fig.  are generated for the stratocumulus decks over the north and south Pacific oceans (Figs.  and in Appendix ). In the north Pacific (NP) Sc deck, results are broadly consistent with those found over the SEA deck: for initially non-precipitating clouds, the influence of GCCN is evident, with a decrease in Nd at high initial Nd and LWP > 30 g m⁻² (Fig. e–h). For precipitating clouds, however, the impact of precipitation dominates the Nd response, even at very high ws (Fig. a–d). Similar to the SEA deck, LWP in the NP deck increases with ws (Fig. i–p) for both not-precipitating and precipitating clouds. In contrast, for the south Pacific (SP) Sc clouds, the signals associated with the same processes are less clear when using the DoR method – the changes in Nd appear to show similar behavior as the NP clouds for both not-precipitating and precipitating clouds (Fig. a–h), as does the change in LWP for precipitating clouds. For not-precipitating clouds (Fig. m–p), there is a strong negative and positive presence with no obvious pattern emerging.

To further investigate this behavior, global maps of the DoRs of dNd (ΔwsdNd in cm⁻³) and dLWP (ΔwsdLWP in g m⁻²) are analyzed for different ws ranges. These are plotted separately for clouds with a mid-range (30 < Nd < 100 cm⁻³) and high (Nd > 100 cm⁻³) initial Nd. Figure , showing not-precipitating clouds with an initial Nd between 30 and 100 cm⁻³, reveals ΔwsdNd transitioning from positive to negative values in the northern hemisphere and regions off the shore of the African and south American continents with increasing ws. The areas enclosed in the three boxes are the grid points used to make the joint histograms in Figs. , and for the SEA, NP and SP decks respectively.

It is possible that the negative DoRs are driven by competition for activation between sea salt and sulfates advected from the continent. Sea-salt aerosols are an important component of the so-called natural “background aerosol/CCN” population. Introduction of more sea-salt aerosols in already polluted background states (over and offshore from the continent) results in competition between CCN particles for the liquid water/supersaturation required to activate to form cloud droplets. At higher wind speeds, sea salt becomes a dominant contributor to background aerosol concentrations, especially in the coarse mode. The increased surface area enhances condensation of water vapor thereby reducing maximum supersaturation. This inhibits the activation of new sulfates or other small aerosols leading to a net reduction in Nd or a smaller increase in dNd compared to low ws conditions. This could explain the negative values (blue regions) over the northern hemisphere and along the coast of the continents in the southern hemisphere. More pristine conditions exists further away from the continental coastlines in the southern hemisphere where the competition is less prominent, leading to almost constant changes (positive) as ws increases in these regions.

The influence of GCCN in initiating precipitation is illustrated in Fig. , which shows ΔwsdNd (in cm⁻³) for different ws for initially not-precipitating clouds with Nd > 100 cm⁻³. Outside the tropics, a robust decrease in dNd is observed over the oceans in both hemispheres driven by precipitation.

Figure  shows the global distribution of DoRs of dLWP (ΔwsLWP in g m⁻²) for not-precipitating clouds with an initial droplet number concentration Nd > 30 cm⁻³. A clear increase in dLWP with increasing ws is observed. This signal is particularly pronounced over the subtropical and mid-latitude oceans in both hemispheres. Notably, a distinct increase in dLWP is evident for the SP deck, especially near the coast. This coastal signal is not clearly captured in the DoR joint histograms (Fig. m–p), likely because those include clouds farther offshore, where stratocumulus transitions to cumulus regimes. For initially precipitating clouds, even though the change in LWP appears more positive (Fig. ), no distinct signals can be observed in the maps even though the DoR histograms capture the increase in LWP. Coarsening the grid to a 5° × 5° grid also did not reveal any clear patterns (not shown) in the maps. However, a combination of the DoR method along with global maps of the DoRs can provide a strong picture of the effects of wind-driven processes over the evolution of Sc decks across the globe along with any hemispherical differences.