## Introduction

Aerosol–cloud interaction (ACI) is thought to exert a significant cooling effect on the Earth’s climate, which may offset a substantial fraction of the warming effects of greenhouse gases1. However, estimates of the magnitude of this cooling are still uncertain, despite enormous research efforts over the past few decades. In particular, estimation of aerosol-induced modulation of cloudiness, called the lifetime effect2, still has large uncertainties1. In some global climate models (GCMs), this uncertainty has originated from uncertain cloud parameters3, which tend to be optimised to adjust the magnitude of the aerosol indirect effect so that the models reproduce historical climate changes4. Such model tuning is currently being evaluated using recent satellite observations, which provide a constraint on cloud parameters. However, satellite-based model constraints have been found to be inconsistent with the model representations of historical temperature trends as reported in previous studies4,5. These studies investigated how climate simulations are sensitive to a particular tunable parameter, the threshold cloud particle radius (rcrit) for the conversion from cloud to rain, which largely controls the magnitude of the ACI. When a GCM is driven by a value of rcrit optimised to reproduce the historical temperature trend, with a tuned magnitude of ACI, the model cannot represent the vertical microphysical structures observed by satellites, and vice versa. This suggests that conventional GCMs contain flawed representations of the aerosol indirect effect, even though they reproduce the historical temperature trend.

A growing body of evidence also suggests that cooling due to the indirect effect may be less than has been estimated by conventional GCMs6. One possible cause of this is the lack of climate model representations of the buffered system inherent in the real atmosphere7, which acts to reduce the cloud response to aerosol perturbations. The buffered system hypothesis is supported by a recent case study of a volcanic eruption8, which reported a muted response of the liquid water path (LWP) to aerosol perturbations in moderate-resolution imaging spectroradiometer (MODIS) satellite observations, in contrast to GCMs that indicated coherent positive responses of the LWP. This result implies that the lifetime effect can be buffered due to the variation in cloud air mixing, which originates from the aerosol-induced reduction in cloud particle size9. These recent findings motivated us to re-investigate the response of cloud microphysical properties to aerosol perturbations at the global scale.

For the lifetime effect, the cloud response is typically quantified by the aerosol-induced modulation of the cloud LWP, which is given by λc = d[LC]/d[CC]10. The notation of each symbol is summarised in Table 1. As in previous studies10, we targeted only warm-topped clouds, whose cloud top temperatures exceed 273.15 K due to their large contributions to the Earth’s energy budget11. The traditional theory of the lifetime effect produces positive values of λc because LWP increases with increasing aerosol loading through inhibition of rain formation due to reduced cloud particle sizes. This is also the major assumption adopted by conventional GCMs, which predict global-mean positive values of λc10,12,13, with the exception of a few that predict negative values14,15. By contrast, λc estimated from satellite observations can have either positive or negative values depending on the atmospheric stability and precipitation strength16, with a negative global-mean value16 (Fig. 1a, d). This discrepancy between model results and satellite observations suggests that conventional GCMs inherently overestimate the magnitude of the lifetime effect.

A recent study reported that this overestimation can be mitigated by using a sophisticated parameterisation of rain17. Via a series of the recently developed GCMs, a sophisticated two-moment bulk scheme has been implemented into a GCM18, and detailed analysis of the overestimation based on the cloud microphysical properties has become possible. However, even using such state-of-the-art GCMs, the issue has not been overcome completely, at least in part because GCMs still rely on horizontal grid resolutions that are too coarse to resolve individual clouds. This resolution issue can be addressed using large-eddy simulation (LES) models that reproduce both negative and positive values of λc depending on cloud regimes19. Another study using an LES model also indicated that the response of LWP to aerosol perturbations can be either positive or negative depending on the relative humidity (RH) above the cloud20. These studies using LES models have enabled the uncertainty of the estimation of the lifetime effect to be reduced, but such simulations have been limited to small domains. As a result, there is still a fundamental gap in the understanding of the cloud response to aerosol perturbations between process models and GCMs.

To bridge this gap, we conducted a global simulation using a model that incorporates an explicit representation of cloud microphysical processes21. Henceforth, we refer to this simulation as a global cloud system resolving model (GCRM) simulation. Through comparative analyses of the results of the GCRM and GCM, we attempted to understand the reason for the key discrepancy in λc between GCM results and satellite observations. The analyses elucidated that the GCRM accurately reproduced the negative λc. The negative λc was originated from the response of the evaporation and condensation processes to the aerosol loading.

## Results

### The GCRM successfully simulated the negative λ c

Figure 1 shows the λc values estimated from the A-Train satellite and another index of cloud modulation in response to aerosol perturbations, λ = d[LC]/d[AC], as a proxy for λc, simulated by the models. Although the absolute value of λ is different from that of λc, the signs of λ and λc are similar. The results from our GCRM simulations (Fig. 1b, e) reproduce the regional variability in λ, including both positive and negative values. The correspondence of λ with satellite observations (Fig. 1a, d) was greatly improved with the correct sign of the response being simulated. This is in stark contrast to traditional GCMs that cannot reproduce negative values of λ (Fig. 1c, f).

A successful simulation of λ by the GCRM that is consistent with observations would offer an unprecedented opportunity to explore the possible mechanisms through which LWP increases or decreases with increasing aerosol loading at the global scale. We investigated the vertical profiles of λ, denoted as λlwc = d[L]/d[A], targeting clouds over the ocean between 60° S and 60° N. The GCRM predicted positive and negative values of λlwc in the lower (up to 500 m from the cloud base) and upper (above 500 m from the cloud base) layers of clouds, respectively (Fig. 2a). The vertical switch in the sign of λlwc from positive to negative with height suggests that key mechanisms in the liquid water content (LWC) response to aerosol perturbations vary with height. We demonstrate that the responses of two different processes leading to aerosol perturbations, the condensation and evaporation processes, are responsible for the positive and negative LWC responses, respectively.

Aerosol-induced reduction in cloud particle size makes the condensation and evaporation processes efficient22 when ambient air is saturated and sub-saturated, respectively. In the lower layer of clouds, condensation becomes more active with increasing aerosol loading (Fig. 2b) because of the moist ambient air (Fig. 2d). On the other hand, evaporation becomes more active with increasing aerosol loading (Fig. 2c) because of the dry ambient air (Fig. 2d). The increase in condensation leads to a positive λlwc value in the lower part of the cloud, while the negative λlwc value in the upper part is due to the increase in evaporation. This dependency of λlwc on surrounding environmental conditions supports a previous satellite observation, where LWP was found to decrease with an increase in the aerosol index under low RH conditions and vice versa23.

The relative contributions of the two competing processes responsible for the positive and negative responses of cloud water to aerosol perturbations vary with altitude. In the lower parts of clouds, the increase in LWC through the response of the condensation process is larger than the decrease in LWC through the evaporation process, and vice versa in the upper parts of clouds. This vertical switch in the predominant process results in the vertical variability in λlwc values.

These findings can be summarised as follows. Under unstable conditions, characterised by low values of lower tropospheric stability (LTS)24 with strong precipitation, the cloud thickness exceeds 1000 m (Fig. 2d) and RH is low due to the weak temperature inversion, while λlwc is negative (Fig. 2a). Because the positive value of λlwc in the lower layer is outweighed by the negative value of λlwc in the upper layer, λ, the value of λlwc for whole layer, becomes negative. By contrast, over the stable region, characterised by high values of LTS with weak precipitation, the cloud thickness is mostly below 500–1000 m (Fig. 2d) due to the strong temperature inversion24. In this region, λ becomes positive or close to zero, because the contribution of the positive value of λlwc in the lower layer to the column value (λ) is larger or equal to that of the negative value of λlwc in the upper layer.

## Discussion

The GCRM results described above indicate that condensation and evaporation efficiencies play a critical role in determining the sign of the LWP response to changes in aerosol loading. In particular, vertical variations in these processes and their responses to aerosol perturbations appear to be key to accurate representation of the lifetime effect. A comparison of the vertical structure simulated by the GCRM (Fig. 2) with that simulated by the GCM indicates the reason for the overestimation of λ in GCMs. Here, we investigated the vertical structure (Fig. 3). GCMs cannot reproduce the vertical inhomogeneity in the response of evaporation and condensation processes to aerosol perturbations (Fig. 3b, c). The responses of these processes to aerosol perturbations were much smaller than in the GCRM. Due to this weak response of the evaporation and condensation processes, the negative λlwc in the upper part of the cloud was unclear in the GCM (Fig. 3a). This is because the cloud parameterisation in conventional GCMs does not explicitly include the interaction between the cloud microphysics and dynamics. As a result, conventional GCMs cannot reproduce the negative global-mean value of λ.

The positive λ in the GCM mainly originated from the positive λlwc around the cloud bottom because the cloud thickness simulated by the GCM was mostly smaller than 1000 m (Fig. 3d). The positive λlwc around the cloud bottom originated from the pronounced inhibition of the collision process due to the aerosol-induced reduction of cloud particle sizes, whereas the responses of the evaporation process were not large enough to buffer the cloud water enhancement due to the inhibition of the collision process. The evaporation responses should be appropriately represented in the GCM to reproduce the negative λ.

The responses of the condensation and evaporation efficiencies to aerosol perturbations buffer the cloud responses to aerosol loadings7. Our GCRM simulations, with explicit representations of cloud microphysical processes, enabled us to incorporate this buffering effect at the global scale, and thus to represent the lifetime effect better than has been parameterised previously by GCMs. The GCRM results provide a useful insight into improvement of parameterisations in current GCMs, particularly when the results are analysed in the context of key cloud processes as described above. Such ‘process-oriented’ analyses, with combined use of a GCRM and satellite observations, are required to make substantial advances in climate modelling by providing more accurate and reliable climate predictions.

The negative global-mean value of λ implies that the radiative forcing due to the lifetime effect, which is usually estimated as negative by GCMs10, can be tuned into slightly positive. This suggests that estimates of the net negative radiative forcing due to the total ACI1 can also be significantly reduced and its uncertainty range could even include positive values. This strongly encourages us to estimate radiative forcing based on the GCRM and compare it with GCM values as the next step in this work. In addition, the analyses should also be extended to ice clouds in future studies for a more complete understanding of cloud system responses.

## Methods

### Numerical models

Global-scale simulations were conducted using a GCRM, the Non-hydrostatic Icosahedral Atmospheric Model (NICAM)25,26, and a GCM, the Model for Interdisciplinary Research on Climate (MIROC)27 coupled with an aerosol module, the Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS)28. Details of the models and model parameters have been described previously16,21,29. The horizontal resolution of GCRM used in this study was 14 km. A one-moment bulk microphysical scheme30 was adopted, but the cumulus parameterisation was not applied31 in the GCRM. The vapor mixing ratio (qv), and mixing ratios of cloud (qc), rain (qr), ice (qi), snow (qs), and graupel (qg) were predicted. The condensation/evaporation/sublimation, autoconversion, accretion, gravitational settling, freezing, and melting processes were considered in the microphysical scheme. Large scale condensation27 and cumulus parameterisation32 were applied in the GCM. In the schemes, qv, qc, qi, the cloud droplet number concentration (Nc), and the number concentration of ice (Ni) were predicted.

In the GRCM, saturation adjustment was applied, and the impacts of the aerosol on cloud microphysical properties were represented by reducing the autoconversion rate with increasing aerosol number concentration as follows. The equation of the autoconversion rate (Pauto) of the Berry-type scheme33, which was adopted in both models, incorporates Nc as:

$$P_{{\mathrm{auto}}} = \frac{1}{\rho }\left[ {a\left( {\rho q_{\mathrm{c}}} \right)^2\left( {b + \frac{{cN_{\mathrm{c}}}}{{D_{\mathrm{d}}\rho q_{\mathrm{c}}}}} \right)^{ - 1}} \right]$$
(1)

where ρ is total density, and Dd = 0.146–5.964 × 10–2 × ln(dNc), a = 16.7, b = 5.0, c = 3.6 × 10−5, d = 5 × 10−4, respectively. The unit of Nc is cm−3. The number concentration of cloud condensation nuclei predicted by SPRINTARS was used as Nc in Eq. (1) in GCRM. In the GCM, Nc was predicted by itself and it was used as Nc in Eq. (1).

As several studies pointed out34,35,36,37, there is room for improvement on the one-moment bulk microphysical model. For example, the evaporation of rain simulated by one moment scheme is overestimated34,36, and the formation of the rain in one moment scheme is faster than that in the sophisticated scheme like two-moment bulk scheme and spectral bin microphysical scheme35,37. The global scale simulation by GCRM coupled with such sophisticated scheme should be conducted in future for more accurate and sophisticated discussion about the ACI.

### Experimental setup

Numerical integrations were conducted for 12 months and 5 years, with time steps (Δt) of 60 s and 1200 s for the GCRM and GCM after spin-up periods of 1 month and 1 year, respectively. The GCM results for each 1-year period exhibited the same trend as the 5-year simulation, but we used the result of the 5-year simulation to obtain a statistically meaningful value of λ. For both models, the same series of emission inventories were used. The Hemispheric Transport of Air Pollution Phase 2 (HTAP_v2.2)38 was used for emission inventories of black carbon, organic carbon, and sulphur dioxide (SO2) from anthropogenic sources. The Global Fire Emissions Database, version 3 (GFEDv3)39,40 was used for emissions from biomass burning, and the Global Emissions InitiAtive (GEIA)41 was used for emissions of terpene and isoprene, which are precursor gases for secondary organic aerosols. The emissions of prescribed monthly oxidants (OH radicals, ozone, and H2O2) were obtained from the results of the GCM coupled with a chemical transport model42, and the SO2 emitted from volcanoes was obtained from the emission source of a previous study28.

### Analyses

The responses of LWP (λ), LWC (λlwc), the condensation tendency (λcond), and the evaporation tendency (λevap) to aerosol perturbations were calculated by a least-square regression analysis in each 2° × 2° and 2.8° × 2.8° grid of the GCRM and GCM. Grid points with less than five samples were excluded from the analysis.

Only warm-topped clouds whose cloud top temperatures exceeded 273.15 K were analysed due to their large contributions to the Earth’s energy budget11. A warm-topped cloud was defined as a cloud satisfying the following five conditions: cloud optical thickness > 0.2, LWP > 1 g m−2, effective radius at the cloud top > 0.4 µm, cloud top temperature > 273.15 K, and vertically integrated mass of ice water (IWP) < 1 g m−2. The cloud top height was defined as the highest layer at which the mass of hydrometeor was over 10−5 kg kg−1, based on a previous study26.

There is a difference in the data collected by satellites and models that should be noted. Aerosol properties are retrieved from a cloud-free grid in the satellite observations, so cloud and aerosol properties cannot be retrieved simultaneously. By contrast, models can simulate these properties simultaneously for use in analyses. This difference in the data sampling impacts the magnitude of λ. However, the good agreement of λ values determined by the GCRM with satellite observations, particularly the sign, indicates that the microphysical processes, which contribute to the creation of the geographical distribution of λ retrieved from satellites, were successfully simulated by the GCRM, but were not simulated by the GCM. Thus, our consideration of the difference between the GCM and the GCRM provides useful information.

The difference in the horizontal axes of Fig. 1d, e, f should also be noted. The horizontal axis of Fig. 1d is the column maximum reflectivity, whereas those of Fig. 1e, f are the precipitation intensity. Given that the column maximum reflectivity is a good indicator of precipitation intensity, based on a previous observational study43, the meaning of the horizontal axes of Fig. 1d, e, f can be considered equivalent for the purpose of interpreting the cloud response to aerosol perturbations in the context of precipitation processes.

### Code availability

The code for NICAM coupled with SPRINTARS associated with this study is available from corresponding author (Y.S.), upon reasonable request. The source code of MIROC coupled with SPRINTARS, associated with this study is available to those who conduct collaborative research with the model users under license from copyright holders. For further information on how to obtain the code please contact the corresponding author (Y.S.).

### Data availability

The data that support the findings of this study are deposited in local storage at RIKEN/AICS. It is available from the corresponding author (Y.S.) upon reasonable request.