Observational estimation of in-cloud supersaturation

We carried out observations at two different locations in Japan: Tokyo, which is dominated by fresh urban pollution25 in which BC-containing aerosols have higher SS c (i.e., they are more hydrophobic), and Okinawa, which is frequently influenced by aged Asian continent pollution26 in which BC-containing aerosols have lower SS c (i.e., more hydrophilic) (Supplementary Table 1).

For each rainfall event, we estimated the SS lsd value experienced by the removed aerosols from the results of a detailed comparison between the BC-containing aerosols in the surface air before the rainfall and the BC particles in the rainwater, under the assumption that the former had been transformed to the latter through localized moist convection (BC tracer method: Fig. 1). The BC tracer method utilizes the experimental finding that the mass-equivalent diameter of each water-insoluble BC particle core, denoted here as D tr , is invariant during the rainout process.8 The assumption of localized moist convection by the method is plausible for convective-type precipitation but would be invalid for stratiform-type precipitation.27 We introduce the Convective Precipitation Index (CPI) as a measure of the relative contribution of lower tropospheric water vapor to vertically integrated condensed-water production near each observation site (see Methods). The assumption of localized moist convection is more plausible for rainfall events with higher CPI (Supplementary Table 1). Therefore, we pay particular attention to events with CPI > 0.5 (N = 23) among the observed rainfall events (N = 37) in the following analysis and discussion.

For each rainfall event, we calculated the ratio of the size-resolved tracer number concentration, dN/dlogD tr , in rainwater (i.e., the removed tracer) to dN/dlogD tr in the surface air before precipitation (i.e., the initial tracer) from in situ measurements (Fig. 2a, b). This rain-to-air number concentration ratio, the scavenged number fraction (SNF), is a function of D tr and is denoted here as SNF(D tr ). Further, we define Relative SNF(D tr ) as SNF(D tr ) normalized by the SNF value at a particular D tr = D std . In this study, D std was set to 900 ± 100 nm (Fig. 2a, b). We used Relative SNF in our analysis so that the results would be unaffected by the absolute tracer concentration in rainwater. We used κ-Köhler theory28 with measured input parameters (e.g., coating volume on BC core; Supplementary Fig. 1) to derive SS c -resolved number concentrations of the initial tracer-containing aerosols at each of four small-tracer D tr values (D = 200 ± 10 nm, 220 ± 10 nm, 263 ± 15 nm, or 302 ± 20 nm) and at one large-tracer D tr value (=D std , 900 ± 100 nm) (see Methods) (Fig. 2c–f).

Fig. 2 Observational results of tracer particles used for estimating the SS lsd experienced by the removed tracers during each of the rainfall events (thin curves). Thick curves show averaged results over all rainfall events in each observation site. a Normalized size-resolved number concentrations (dN/dlogD tr ) of the initial and removed tracer particles and the resulting D tr -resolved relative scavenged number fraction (Relative SNF) in Tokyo. b Same as panel (a) but for Okinawa. c Normalized SS c -revolved number concentration (dN/dSS c ) of the initial tracer evaluated at D tr = 200 nm and at D tr = D std (900 ± 100 nm) in Tokyo, where the SS c of tracer (BC)-containing particles was predicted by using κ-Köhler theory. d Same as panel (c) but for Okinawa. e, f Same as panels (c, d) but for D tr = 302 nm instead of D tr = 200 nm Full size image

Under our observational conditions, we estimated that the fractional contribution of nucleation scavenging to total scavenging is always greater than 0.8 for aerosols containing tracer particles in the size range 200 nm ≤ D tr ≤ 1000 nm (see Methods). Thus, the following data analysis assumes that nucleation scavenging predominates over in-cloud and below-cloud impaction scavenging.

Under the assumption that both small (D tr = D) and large (D tr = D std ) tracer particles in a collected rainwater sample are activated to droplets at environmental supersaturation SS lsd , we estimated SS lsd by numerically solving the following equation with respect to SS lsd :

$${\mathrm{Relative}\,\mathrm{SNF}}\left( D \right) = \frac{{\mathop {\int }

olimits_0^{\mathrm{SS}_{{\mathrm{lsd}}}} \left( {\left. {\frac{{\mathrm{d}N}}{{\mathrm{dSS}_{\mathrm{c}}}}} \right|_{D_{{\mathrm{tr}}} = D}} \right)\mathrm{dSS}_{\mathrm{c}}}}{{\mathop {\int }

olimits_0^{\mathrm{SS}_{{\mathrm{lsd}}}} \left( {\left. {\frac{{\mathrm{d}N}}{{\mathrm{dSS}_{\mathrm{c}}}}} \right|_{D_{{\mathrm{tr}}} = D_{{\mathrm{std}}}}} \right)\mathrm{dSS}_{\mathrm{c}}}},$$ (1)

where dN/dSS c denotes the probability density function of the observational SS c -resolved number concentration of tracer-containing aerosols at the indicated D tr value normalized by

$$\mathop {\int }

olimits_0^\infty \left( {\left. {\frac{{\mathrm{d}N}}{{\mathrm{dSS}_{\mathrm{c}}}}} \right|_{D_{{\mathrm{tr}}}}} \right)\mathrm{dSS}_{\mathrm{c}} = 1.$$ (2)

We estimated the systematic relative error of the derived SS lsd value resulting from the measurement uncertainties, and neglecting other scavenging mechanisms, to range between −10 and +20% (see Methods).

For each rainfall event, the SS lsd value determined by this procedure can be physically interpreted as the average of SS lsd k (k = 1,…, n) weighted by the number of measured tracer particles in rainwater that have been scavenged in LSDk (k = 1,…, n). For each rainfall event, the time duration of rainwater sampling ranged mostly from 5 to 30 min (Supplementary Table 1). For a cloud system moving horizontally with a constant speed of ~10 ms–1, which is a typical wind speed in the lower troposphere, the moving distance during the sampling time would thus be ~100−101 km. In this case, we can interpret the derived SS lsd value as the average over the LSDs distributed within a horizontal scale of ~100−101 km (Fig. 1). In the case of a cloud system that does not appreciably move during the sampling time, we can interpret the derived SS lsd value as the average over the LSDs above the observation site within a period of ~100−101 min. On the basis of these considerations, we interpret the derived SS lsd as the tracer-weighted average of SS lsd k (k = 1,…, n) in a particular space-and-time (4D) domain with a horizontal scale of ~100−101 km and a timescale of ~100−101 min.

The absolute scavenged number fraction of tracer particles at D tr = D is defined here as

$${\mathrm{Absolute}\,\mathrm{SNF}}\left( D \right) = \mathop {\int }

olimits_0^{\mathrm{SS}_{{\mathrm{lsd}}}} \left( {\left. {\frac{{\mathrm{d}N}}{{\mathrm{d}\mathrm{SS}_{\mathrm{c}}}}} \right|_{D_{{\mathrm{tr}}} = D}} \right)\mathrm{d}\mathrm{SS}_{\mathrm{c}},$$ (3)

where SS lsd is determined by solving Eq. (1). Absolute SNF can be physically interpreted as the expected scavenged number fraction of initial tracer-containing aerosol particles with D tr = D that have experienced environmental supersaturation SS lsd .

We compared scatter plots of Absolute SNF versus SS lsd for each of the four small-tracer D tr values for all observed events (Fig. 3a) and for events with CPI > 0.5 (Fig. 3b). For the reason mentioned above, we assume the results for CPI > 0.5 events to be more reliable than those for all events. Consistent with our expectation, for CPI > 0.5 events, SS lsd did not depend on D tr (Fig. 3b). For all events, we interpret the systematic dependence of SS lsd on D tr (Fig. 3a) as an artifact resulting from the inclusion of low-CPI events that violate the assumption of localized moist convection.

Fig. 3 Scatterplots between the absolute scavenged number fraction (Absolute SNF) and the SS lsd value estimated for a all rainfall events (N = 37) and b rainfall events with CPI > 0.5 (N = 23). Each open circle (triangle) indicates the results for a single rainfall event in Tokyo (Okinawa). The same analysis was performed using each of the four indicated distinct small-tracer D tr values. The filled circles and error bars represent the median values and the 25th–75th percentile range Full size image

For CPI > 0.5 events, SS lsd ranged from 0.03 to 0.2% (average ± standard deviation, approximately 0.08 ± 0.03%; Supplementary Table 2), and, in contrast to the general trend predicted by a model using an aerosol activation parameterization scheme,29 SS lsd did not show a clear anti-correlation with the aerosol number concentration in the surface air before the rainfall. This result implies that the actual mechanism determining SS lsd in real precipitating clouds is complex. The SS lsd value of 0.08 ± 0.03% determined herein is substantially lower than the reported values of maximum supersaturation in non-precipitating marine stratocumulus clouds in East Asia (average ± standard deviation, 0.24 ± 0.06%).23 This systematic difference implies that for the majority of LSDs in a non-adiabatic precipitating cloud system, supersaturation is not maintained at as high a level as the maximum supersaturation realized in the updraft core of adiabatic non-precipitating clouds.

Sensitivity of the global BC distribution to in-cloud supersaturation

We performed a set of numerical experiments with the CAM5-chem/ATRAS2 global aerosol model14 to quantify changes in the simulated global aerosol fields due solely to differences in the model’s treatment of environmental supersaturation (SS) and the associated nucleation scavenging process in precipitating clouds. The base simulation was performed with the default CAM5-chem/ATRAS2 parameterization scheme, in which both the determination of the SS value and the nucleation scavenging process are treated differently between grid-scale and sub-grid-scale cloud types. In the case of grid-scale clouds, the scavenged number fraction of an aerosol is predicted from the dN/dSS c distribution for that aerosol, and the prognostic SS value is determined by using the aerosol’s activation parameterization.13 In the case of sub-grid-scale clouds, the scavenged number fractions of aerosols with SS c > 1.0, SS c > 0.5, and SS c ≤ 0.5% are assumed to be 0, 0.4, and 0.8, respectively, and the SS value is not computed. The categorization of clouds between grid-scale and sub-grid-scale types depends on the selected grid resolution of CAM5; thus, a physically meaningful categorization is not assured. In the sensitivity-test simulations, SS for both grid-scale and sub-grid-scale clouds was set to 0.05, 0.08, or 0.11%, corresponding to the average ± the standard deviation (about 0.03%) of the SS lsd values determined for CPI > 0.5 events (Supplementary Table 2). Only aerosol particles with SS c < SS were assumed to be scavenged by cloud water and removed by rainfall. We applied a single SS value globally to avoid the technical complexities of applying regional values in a global model.

The simulated global distributions of the BC column burden and wet deposition flux (Figs. 4 and 5, left panels) indicate that a substantially large portion of the total atmospheric BC mass in the northern hemisphere (NH) is deposited in the mid-latitudes, in particular around East Asia, the largest source region. Thus, our sensitivity-test simulations, in which a single SS value determined from observations around East Asia was applied globally, can provide useful insights, at least into BC fields in the NH.

Fig. 4 a, c, e Global distributions of the 5-year mean column BC mass simulated by the CAM5-chem/ATRAS2 model with the supersaturation (SS) of precipitating clouds constrained to be 0.05%, 0.08%, and 0.11%, respectively. b, d, f Global distributions of the ratio of column BC mass obtained by the sensitivity-test simulations to that obtained by the base simulation. In the sensitivity-test simulations, the SS constraint was applied to both grid-scale and sub-grid-scale clouds Full size image

Fig. 5 a, c, e Global distributions of the 5-year mean BC wet deposition flux simulated by the CAM5-chem/ATRAS2 model with the supersaturation (SS) of precipitating clouds constrained to be 0.05%, 0.08%, and 0.11%, respectively. b, d, f Global distributions of the ratio of the BC wet deposition flux obtained by the sensitivity-test simulations to that obtained by the base simulation. In the sensitivity-test simulations, the SS constraint was applied to both grid-scale and sub-grid-scale clouds Full size image

According to a recent detailed investigation of the aerosol mass deposition budget, nucleation scavenging may account for 94% of in-cloud scavenging of BC, with below-cloud scavenging contributing only 14% of total annual and global mean BC deposition.30 In our simulations, the contribution of below-cloud scavenging to total BC scavenging was negligibly small (~1% of the nucleation scavenging) on annual and global average. Thus, in the following discussion we assume that BC deposition is triggered predominantly by nucleation scavenging.

A global distribution map of annual mean maximum SS values in grid-scale clouds, derived from the base simulation, is shown in Supplementary Fig. 2. The major qualitative features of this map, higher SS in higher latitudes and lower SS in more polluted regions, are similar to the results obtained by another model in which a globally constant updraft velocity was assumed in grid-scale clouds.29 The simulated SS value of grid-scale clouds in our base simulation around our observation sites (Tokyo and Okinawa) was ~0.12%, which is slightly larger than our estimated SS lsd of 0.08 ± 0.03% for observed rainfall events.

The sensitivity-test simulations conducted using the three SS values all predicted substantially large BC mass concentrations (Fig. 4, right panels) and wet deposition values (Fig. 5, right panels), relative to the base simulation values, almost everywhere except near the major anthropogenic source regions in East Asia, India, Europe, and the United States. The large increase in the BC column burden in remote terrestrial and oceanic regions compared to the base simulation values is attributable to increased long-range transport of aerosols from the major BC source regions in the sensitivity-test simulations. This systematic increase in long-range BC transport in the sensitivity-test simulations relative to the base simulation can be explained by modest decreases of wet deposition and compensatory modest increases of vertical transport associated with less-efficient BC rainout during moist convection in the proximity of the major BC source regions (Fig. 5, right panels). In these regions, substantial proportions of BC-containing particles remain fresh and thus have relatively high SS c values; as a result, BC rainout efficiency tends to be more sensitive to the prescribed SS value.

The model was able to reproduce the aircraft-observed vertical profile of BC mass concentrations over East Asia (Supplementary Fig. 3a) reasonably well in both the base simulation and the sensitivity-test simulation with SS = 0.08%. In marked contrast, in the Arctic and other remote regions, the simulated vertical BC profile was up to an order of magnitude larger in the sensitivity-test simulation with SS = 0.08% compared with the base simulation (Supplementary Fig. 3b–h) because of a substantial increase in the long-range transport of BC to regions that are remote from the major source regions.

We estimated the fractional contribution of the BC emitted from the Asian region (60°E−160°E, 20°N−50°N) to the BC column burdens in Arctic (66°N−90°N) and NH mid-latitude (20°N−66°N) regions (Supplementary Table 3). The Asian source contribution to the Arctic BC column burden was ~2.5 times higher in the SS = 0.08% sensitivity-test simulation (32%) than in the base simulation (13%) as a result of the greater efficiency of long-range BC transport via moist convection. By contrast, the Asian source contribution to the NH mid-latitude BC column burden (~50% in the base simulation) did not change appreciably in the SS = 0.08% sensitivity-test simulation (~51%) because the majority of the NH mid-latitude BC column burden was attributable to the highly concentrated BC near the source regions before the moist convection processing.

Comparison of simulated and observed seasonal variations of surface BC mass concentrations at two observation sites in the Arctic (Fig. 6) shows that, except in summer, the base simulation severely underestimated, by an order of magnitude, the monthly BC mass concentration (See Sinha et al.31 for the details of these observation data). At both Arctic sites, the sensitivity-test simulation with SS = 0.08% for grid-scale + sub-grid-scale clouds reproduced the observed average and seasonal variations of surface BC concentrations better than the base simulation. This difference between the sensitivity-test and base simulation results for Arctic surface BC concentrations was due mostly to the difference in the simulated BC scavenging efficiency in grid-scale clouds. However, it should be noted that the relative contributions of grid-scale and sub-grid-scale clouds depend on the selected model grid size and the default scavenging scheme adopted in the base simulation.

Fig. 6 Comparison of monthly surface BC mass concentrations between in situ observations and the CAM5-chem/ATRAS2 simulations for a Barrow, Alaska and b Ny-Ålesund, Norway. In the sensitivity-test simulations, the SS constraint was applied to both grid-scale and sub-grid-scale clouds. The black curves show base simulation results, and the light-blue dots show observation results. The period of observation data is August 2012−May 2015 for Barrow and March 2012−May 2015 for Ny-Ålesund Full size image

The essential conclusion that we deduce from the simulation results shown in Fig. 6 is that the Arctic surface BC concentration can shift by a factor of 2−3 solely as a result of a change in SS lsd within the quite narrow range of 0.05−0.11%, which is the average ± standard deviation range of our observational SS lsd value for convective-type precipitation in East Asia.