Compared with global models, regional climate models offer higher spatial resolution and a greater capability to capture small-scale climatic features (Denis et al., 2002). Here, we employ the regional climate and chemistry coupled model (RegCM-Chem), developed by the Abdus Salam International Centre for Theoretical Physics (ICTP), to assess the climate effects of BC over East Asia. In recent years, RegCM-Chem has been widely applied in studies of the regional aerosol–climate interactions (Ghosh et al., 2023; Ma et al., 2023; Hu et al., 2024; Cao et al., 2026). To better address trace gases, inorganic and secondary organic aerosols, a gas phase chemistry module with a Carbon-Bond Mechanism version Z (Shalaby et al., 2012), a thermodynamic equilibrium model ISORROPIA (Fountoukis and Nenes, 2007) and a volatility basis set model (Yin et al., 2015) have been coupled into the model. Additionally, the current version of RegCM-Chem also involves new physical parameterization schemes, such as those for land surface, planetary boundary layer and air–sea flux (Giorgi et al., 2012). The radiative transfer package from the National Center for Atmospheric Research Community Climate Model, version 3 is adopted to investigate the direct radiative forcing of aerosols (Kiehl et al., 1996).

The aerosol module in RegCM-Chem incorporates hydrophobic and hydrophilic BC and primary organic carbon (OC), as well as a sulfate aerosol scheme described in Qian et al. (2001). The mass concentrations of these species are tracked independently, and they are assumed to be externally mixed. For a given tracer i, the rate of change in its mass mixing ratio is governed by the following tracer transport equation (Solmon et al., 2006): 1∂mi∂t=-V‾⋅∇mi+FHi+FVi+TCi+Ei-RWlsi-RWci-Ddi+∑Qpi-Qli, where the first four terms represent advection, horizontal and vertical turbulent diffusion, and convective transport, respectively. The surface emission term Ei will be detailed in the subsequent section. RWlsi and RWci are the wet removal rates associated with large-scale and convective rain, respectively, and Ddi denotes the dry deposition. The final term ∑Qpi-Qli for BC represents production and loss due to the aging process, which is simplified in the current scheme as a transformation from a hydrophobic to a hydrophilic state with a fixed e-folding timescale of τ0=1.15 d (27.6 h) (Cooke et al., 1999). The atmospheric lifetime of aerosols is primarily determined by dry and wet deposition processes. In RegCM-Chem, the dry deposition flux is computed from the tracer concentration in the model's lowest layer and the dry deposition velocity depending on particle physical properties and aerodynamic transport mechanisms (Giorgi, 1986; Zakey et al., 2008). Wet deposition in the model is divided into in-cloud and below-cloud scavenging. The in-cloud scavenging process occurs in large-scale clouds when the liquid water in the model layers with a nonzero cloud fraction exceeds a prescribed threshold, and it is parameterized as a function of the fractional removal rate of the liquid water and aerosol solubility (Ghosh et al., 2023). Different aerosol solubilities are assigned to hydrophobic and hydrophilic particles, thereby distinguishing their in-cloud scavenging rates (Table 1). The below-cloud scavenging is determined by the precipitation rate and particle collection efficiency, the latter of which is calculated from the aerosol effective diameter and density (Giorgi, 1989; Nair et al., 2012).

Based on the work of Fierce et al. (2017) and Ghosh et al. (2021), we replace the currently adopted 1.15 d fixed aging timescale in RegCM-Chem with a dynamic BC aging parameterization. Fierce et al. (2017) used a high-detail particle-resolved model to simulate the aging evolution of aerosols through condensation and coagulation processes. Through parameter regression, the required timescale for the transition to achieve internal mixing is expressed as a function of the condensation rate (Icond) and the overall aerosol number concentration (N): 2τmix=1Icond⋅kcond+N⋅kcoag, where the parameters kcond=0.1 nm⁻¹ and kcoag=6×10-6 cm³ h⁻¹ are obtained by least-squares regression using the outputs from hundreds of particle-resolved simulations that include effects of condensation and coagulation individually. The benchmark ensemble varied 28 inputs across 100 scenarios generated using Latin hypercube sampling, covering a wide range of aging conditions from polluted urban to pristine background. Simulations involving the combined processes are used to validate the parameterization, as described in detail by Fierce et al. (2017). Following Ghosh et al. (2021), the total aerosol number concentration (N) is calculated using the following equation: 3N=ΣMD3⋅ρ⋅π6, where M, D and ρ represent the mass concentration, characteristic effective diameter, and density of a specific tracer, respectively (Table 1). The condensation growth term (Icond) in Eq. (2) is determined as follows: 4Icond=∂mSO4∂tcondρSO4⋅Saer, where ∂mSO4∂tcond and ρSO4 are the condensation mass flux and density of sulfate aerosols, respectively. Saer is the surface area concentration of aerosols. The condensation mass flux is represented as the local mass production rate of secondary sulfate aerosols, which is mainly driven by the oxidation of SO₂ (Qian et al., 2001). Detailed information of the aging scheme can be found in Fierce et al. (2017) and Ghosh et al. (2021).

The direct radiative effect of aerosols is highly dependent on aerosol optical depth (AOD). The BC AOD Φiλ at different wavelengths λ in RegCM-Chem is calculated according to the following formula (Kasten, 1969; Kiehl and Briegleb, 1993; Kiehl et al., 2000): 5Φiλ=Miβλi(1-RH)-α, where Mi is the mass concentration of a specific tracer i (including hydrophobic/fresh and hydrophilic/aged BC). βλi denotes the wavelength-dependent mass extinction coefficient, which is derived from the refractive index and lognormal size distribution based on a Mie code (Matzler, 2002). The effect of relative humidity (RH) on AOD is also included. α represents the hygroscopic growth factor and differs among aerosol species. The physical and optical parameters used in this study are listed in Table 1. To account for coating growth and absorption enhancement due to aging, hydrophilic BC is implicitly assigned a larger characteristic diameter and extinction coefficient. Specifically, in the shortwave spectral range, the extinction coefficient of hydrophilic BC is approximately 1.3 times that of hydrophobic BC (Solmon et al., 2006). Further descriptions of BC direct effect treatments (e.g. single-scattering albedo and asymmetry factor) are provided in Solmon et al. (2006) and Huang et al. (2007).

To address the aerosol first indirect effect, the cloud droplet activation parameterization of Abdul-Razzak and Ghan (2000, 2002) is further developed, in which the cloud droplet number concentration (Nd) is expressed as follows: 6Nd=∑iNi×121-erfui,7ui=2×ln⁡SmiSmax⁡32×ln⁡σi, where Ni, Smi and σi denote the number concentration, critical supersaturation and geometric standard deviation of tracer i, respectively. Smi is determined by the coefficient of the curvature effect and hygroscopicity. Previous studies generally assumed a uniform hygroscopicity value of 5.0×10-7 for BC (Ghan et al., 2001; Takemura et al., 2005). Here, the hygroscopicity of hydrophilic BC is set to 0.22 to reflect the enhanced activation capacity of BC particles due to the aging process, following the bulk hygroscopicity range (0.11–0.34) recommended by Wu et al. (2019) based on observations. Smax⁡ denotes the maximum supersaturation, which is related to Smi, updraft velocity, heat diffusion, particle moisture and other factors. The vertical velocity w is composed of the grid mean value (w‾) and the subgrid-scale vertical velocity (σw), shown as Jiang and Cotton (2005): 8w=w‾+c×σw, where the coefficient c is derived from Wang and Penner (2009). The subgrid-scale variability of cloud-base updraft velocity, represented by σw, is parameterized from turbulent kinetic energy (TKE) which is calculated online in RegCM-Chem (Lohmann et al., 1999; Virtanen et al., 2025). The effective radius of the cloud droplets (Reff) can be obtained via the following scheme (Martin et al., 1994): 9Reff=k3q4πρwNd13,10k=1+2ϵ2231+ϵ213,11ϵ=-12.3Dvc-2.20+0.41, where q and ρw are the cloud liquid water content and water density, respectively. k is the ratio of Reff to the mean volume radius, which is related to the relative dispersion of the cloud size distribution ϵ (Liu and Daum, 2002). As defined in Eq. (11), a double-parameter scheme for ϵ proposed by Zou et al. (2022) is employed here, in which the volume-mean diameter of cloud droplets Dvc is expressed as a function of q and Nd.

The autoconversion rate of cloud liquid water to rainwater (P) is further introduced in the model to account for the aerosol second indirect effect, as described below (Liou and Ou, 1989; Boucher and Lohmann, 1995): 12P=Cl,autq2ρaρwqNdρaρw13Hre-rec, where Cl,aut, ρa and Hre-rec are the Stokes constant, air density and Heaviside function, respectively. re is the mean volume cloud droplet radius and rec denotes its critical value. Details can also be found in Wang et al. (2015) and Zhuang et al. (2025). Background cloud droplets are employed here because this model does not include background aerosols. Wang and Penner (2009) suggested that it is reasonable to set a background Nd to prevent situations in which the simulated aerosol loadings are too low. The background Nd is prescribed as 400 cm⁻³ over land (decreasing with height) and 150 cm⁻³ over ocean, as recommended by Kristjánsson (2002).

As shown in Fig. 1, the simulated domain is centered at (106° E, 30° N) and covers most regions of East Asia, South Asia and Southeast Asia, with a horizontal resolution of 60 km and grid number of 117×137. There are 18 σ-coordinate layers in the vertical direction from the surface to 5 hPa. The 6 h European Centre for Medium-Range Weather Forecasts Re-Analysis-Interim data with a spatial resolution of 1.5° (EIN15) and the weekly mean product of the National Oceanic and Atmospheric Administration's Optimum Interpolated sea surface temperature with a spatial resolution of 1° (OISST) are used to drive RegCM-Chem. The chemical data from the Model for Ozone and Related Chemical Tracers, version 4 (MOZART-4) are applied for the initial and boundary conditions of aerosols (Emmons et al., 2010). Anthropogenic emissions in China are provided by the Multi-resolution Emission Inventory for China (MEIC), a bottom-up emission inventory model developed by Tsinghua University (Li et al., 2017a; Zheng et al., 2018). The spatial resolution of the MEIC inventory is 0.25°, which includes monthly and interannual variations across the simulation period. The 2008 MIX Asian inventory provides the anthropogenic emission for the domain outside China (Li et al., 2017b), with the same monthly emissions repeated annually.

To investigate the impact of dynamic aging scheme on the BC climate effect, eight experiments are carried out in this study (Table 2). Experiment 1 serves as a control run with the fixed aging timescale of 1.15 d and excludes any BC effects. Experiments 2–4 are sensitivity experiments under the same configuration in Table 1 but incorporate BC–radiation interactions, BC–cloud interactions and BC–radiation–cloud interactions, respectively. Therefore, Exps. 2–4 minus Exp. 1 represent the direct (Def_Dir), indirect (Def_Ind) and total (Def_Tot) climate effects of BC under default aging settings, respectively. Experiments 5–8 follow the same design as Exps. 1–4 but only replace τ0 with the dynamic aging scheme to simulate the BC direct (Dyn_Dir), indirect (Dyn_Ind) and total (Dyn_Tot) effects. All simulations are integrated from November 2007 to November 2021, with a spin-up period of one month. Only the outputs in summer (June–August) are analyzed in the following sections. A two-sided paired Student's t-test is performed on the seasonal summer means of each year (n=14) to evaluate the statistical significance of the difference between the experiment results (Zwiers and von Storch, 1995), with the effective sample size (neff=n1-r11+r1) adjusted to account for the lag-1 autocorrelation coefficient (r1).

The RegCM-Chem model has been demonstrated to effectively capture the climatic and pollutant characteristics over East Asia (Sun et al., 2012; Zhou et al., 2014; Zhuang et al., 2018; Gao et al., 2022; Ma et al., 2023; Chen et al., 2024). In this study, we further evaluate the summer output from the Exp. 8 against multiple reference datasets. Specifically, the simulated seasonal mean thermodynamic fields and humidity at 850 and 500 hPa are compared with ERA5 reanalysis data, and surface precipitation is compared with satellite observations from GPM, as shown in Fig. 1. The results indicate that RegCM-Chem successfully reproduces the regional climatic features of East Asia in summer, with values decreasing from south to north. Additionally, the model's performance in simulating cloud fraction, cloud optical depth and net longwave and shortwave radiative fluxes has been validated in previous studies (Ma et al., 2023; Hu et al., 2024).

The simulated BC surface concentration in the Exps. 4 and 8 is further evaluated against observations at 33 sites from the China BC Observational Network (CBNET) during 2012–2018 (Table S1 in the Supplement). Figure S1 shows the observed and simulated annual mean BC surface concentrations and their decreasing trends, and the corresponding statistical metrics are summarized in Table S2. The model reasonably reproduces the distribution of BC surface concentration, with correlation coefficients of 0.97 and 0.70 in the temporal and spatial dimensions, respectively. Nevertheless, the model still substantially underestimates BC surface concentration. Such a discrepancy is comparable to or smaller than the findings from most current climate modeling studies, which have typically reported underestimations of 30 %–60 % in simulated BC surface concentrations across China (Li et al., 2016; Yang et al., 2017; Fang et al., 2020; Liu et al., 2022). Compared with Exp. 4, Exp. 8 slightly reduces the temporal RMSE and NMB and better captures the declining trend under the context of emission reductions, whereas the influence on the spatial distribution is not significant (Fig. S1 and Table S2). These results indicate that although the dynamic aging treatment modestly reduces the overall negative bias in simulated BC concentration to some extent, this improvement remains limited, in agreement with the findings of Ghosh et al. (2021) and Shen et al. (2023). This bias may stem from other processes in the climate model, such as grid resolution, dry and wet deposition, and aerosol transport (Wang et al., 2013; Liu et al., 2016). Beyond the systematic comparison, the model-simulated BC loadings also show reasonable agreement with observations at several intensive monitoring sites (Zhou et al., 2024; Tiwari et al., 2025). In addition, a reanalysis-based evaluation of the simulated BC AOD is conducted using MERRA-2 AOD as the reference. Compared with the relatively modest improvement in BC concentration, Exp. 8 more substantially reduces the low bias of BC AOD, although the low bias still remains (Fig. 1 and Table S2). This performance reflects the physically consistent response of BC optical properties to dynamic aging, as discussed in Sect. 3.4.

Figure 2a presents the spatial distribution of aerosol precursor (SO₂ + BC + OC) emissions across East Asia from 2008 to 2021. In summer, high emissions are predominantly concentrated in northern India, central to northern and southeastern China, the Pearl River Delta and the Yangtze River Delta. These hotspots, driven primarily by power plants and industrial activities (Li et al., 2017b; Zhuang et al., 2019), exhibit peak emission flux of 4.54 µg m⁻² s⁻¹. Moreover, except for the Qinghai-Tibet region and northeastern China, the simulated BC aging timescale for the Exp. 8 in most of the eastern China and Indian landmass is generally shorter than the default value used in the model (27.6 h), which indicates that the fast aging exists widely in summer (Fig. 2b). Even shorter timescales (<10 h) are observed over the North China Plain and the Sichuan Basin, with the minimum monthly mean reaching 2.84 h. Under the new dynamic aging scheme, the BC aging timescale exhibits a clear inverse relationship with local pollutant emissions in its spatial distribution, which is attributable to the fact that the abundant condensable species and hygroscopic particles in highly polluted environment accelerate the conversion of fresh BC by enhancing the condensation and coagulation processes. Conversely, in remote regions such as the Qinghai-Tibet region or over the oceanic areas, where anthropogenic emissions are weak and condensable material is limited, BC aging typically requires more than one day and may even extend to several days.

The BC aging timescale simulated in this study is broadly comparable to observations and other modeling studies. Using an environmental chamber approach, Peng et al. (2016) derived a BC aging timescale of 4.6 h during August–October in Beijing, one of the most polluted areas over East Asia. Similarly, this short timescale was also reported in Shen et al. (2023) (3.8 h) and Chen et al. (2017) (<2 h). By comparison, the summertime timescale in our study is found to be 6.94 h. This overestimation may stem from a sampling bias toward daytime or afternoon periods in these studies, whereas BC aging typically exhibits significant diurnal variation and tends to be slower at night (Riemer et al., 2004; Jacobson, 2010; Chen et al., 2017). Based on constraints from the HIAPER Pole-to-Pole Observations (HIPPO) observations, the e-folding timescale of BC emissions from East Asia or near source regions was estimated to be on the order of a few hours (Shen et al., 2014; Zhang et al., 2015; He et al., 2016), consistent with our simulated results (Fig. 2b). By coupling a parameterization scheme of BC aging into the model, Ghosh et al. (2021) and Shen et al. (2023) both indicated that BC aging in western China and the Qinghai-Tibet region occurs on timescales of several days, which are substantially longer than those in eastern China. Overall, the results in this study can be considered to be reasonable in representing BC aging under different atmospheric conditions.

The summertime spatial distributions of BC surface concentration and column burden under the dynamic aging scheme are presented in Fig. 3a and b. Driven by anthropogenic emissions, high BC levels are mainly found over northern India and eastern China, where the maximum concentration and burden reach 8.82 µg m⁻³ and 2.73 mg m⁻², respectively. This spatial pattern is consistent with previous studies (Li et al., 2017b; Zhuang et al., 2019). Northeastern India and the Sichuan Basin exhibit a higher column burden, and this slight discrepancy from the emission distribution may be attributed to topography, atmospheric transport and circulation background (Ji et al., 2015; Yang et al., 2021; Gao et al., 2024). The response of BC loadings to accelerated aging is also shown in Fig. 3, derived from the differences between Exps. 8 and 4. BC concentrations increase over the southeastern coast of China and the North China Plain, with the maximum exceeding 0.2 µg m⁻³ when the dynamic aging timescale is used (Fig. 3c). Negative changes are found over central to southern China. Meanwhile, the BC column burden exhibits a spatially coherent decrease across East Asia by a regional mean of 0.12 mg m⁻² (Fig. 3d). These findings indicate that introducing the dynamic aging timescale can substantially alter the spatial distribution of BC mass.

These results can be explained as follows. Generally, rapid BC aging in an area facilitates the conversion of hydrophobic BC to hydrophilic BC (Fig. S2), and vice versa. By altering the partitioning between hydrophobic and hydrophilic particles, changes in the aging rate further alter the removal efficiency and atmospheric lifetime of BC by modulating dry and wet deposition. In regions such as eastern China which undergo faster aging, a larger fraction of hydrophilic BC is involved in both dry and wet deposition, whereas the contribution of hydrophobic particles to deposition is reduced because of their lower abundance (Fig. 4). It is worth noting that, hydrophilic BC is more readily removed by wet deposition but is less susceptible to dry deposition compared with hydrophobic BC. This is attributed to the larger characteristic diameter and higher solubility assigned to hydrophilic tracers, which in turn reduces their dry deposition velocity, consistent with the fundamental principles of aerosol dynamics (Solmon et al., 2006; Ghosh et al., 2021). Therefore, as illustrated in Fig. 4c and f, total BC dry deposition decreases while wet deposition increases, in agreement with the respective changes in hydrophobic and hydrophilic BC. The two processes act in a compensatory manner to co-regulate the overall BC sink. For example, the reduction in dry deposition dominates the increase in surface concentration in the North China Plain, where precipitation and wet deposition are relatively limited in summer (Fig. 3c). A similar phenomenon observed along the southeastern coastal regions may also be associated with the decreased dry deposition of hydrophobic BC. In terms of vertical distribution, wet deposition, which is dominated by in-cloud scavenging, is the primary mechanism for the removal of BC particles from the atmosphere (Park et al., 2003; Cozic et al., 2007; Ohata et al., 2016). Compared to surface layer, the wet removal efficiency of BC at higher altitudes is more sensitive to the aging rate (Wang et al., 2013; Shen et al., 2023). In the lower troposphere near source regions in eastern China, the high abundance of pollutants still induces rapid aging of BC (Fig. S3). As a result, BC mass is efficiently removed by wet scavenging, leading to an observed decline in the BC column burden (Fig. 3d).

The distributions of the seasonal mean BC aerosol optical depth (AOD) and instantaneous direct radiative forcing (IDRF) for summer are presented in Fig. 5a–c. Consistent with the spatial pattern of BC loadings, high AOD appears in southwestern and central to northern China, with a maximum exceeding 0.05. Owing to the strong absorption of solar radiation, BC can exert a positive IDRF at the top of the atmosphere (TOA) and a negative radiative forcing at the surface. Here, IDRF is defined as the change in net radiative flux under clear-sky conditions caused only by aerosol–radiation interactions, without considering the influences of cloud cover or climate feedbacks. In the IDRF calculation, the radiative transfer model is called twice that with and without BC at each time step. The radiative forcing calculated in this study is relative to zero BC effect. Therefore, the distribution of BC IDRF is closely related to AOD. Generally, the IDRF at the surface exhibits a spatial pattern similar to that at the TOA but a greater magnitude over East Asia, with regional mean values of +0.82 and -3.00 W m⁻², respectively. In northwestern and northeastern China where the AOD is low, BC still induces a stronger IDRF at the TOA (Fig. 5b). This is likely because the higher surface albedo in these regions reflects more incoming solar radiation back into the atmosphere, thereby enhancing BC absorption and leading to a stronger TOA IDRF but weaker surface values (Ocko et al., 2012; Zhuang et al., 2014; Gao et al., 2024).

The response of BC AOD to dynamic aging does not remain consistent with the change in column burden, but instead shows a significant increase over eastern China (Fig. 5d). Although AOD represents the vertical integral of total extinction in the atmospheric column, the increase in near-surface BC concentration plays a dominant role in enhanced BC AOD, as BC is primarily concentrated in the lower troposphere. In addition, rapid aging accelerates the production of hydrophilic BC, whose extinction coefficient is larger than that of hydrophobic particles (Solmon et al., 2006), therefore making an additional positive contribution to AOD. This also helps explain why the magnitude of the AOD increase exceeds that of the surface concentration (Figs. 3c and 5d). As a result, in regions where AOD increases, the attenuation of solar radiation by BC is correspondingly strengthened, leading to stronger IDRF at both the TOA and surface (Fig. 5e and f). The sensitivity of surface IDRF in response to AOD is more pronounced, especially in summer when the solar altitude angle is higher (Zhuang et al., 2014).

Radiative perturbations caused by BC can significantly trigger dynamical adjustments. Figure 6 illustrates the changes in horizontal and vertical atmospheric circulation directions driven by the BC direct effects. Adjustments in the low-tropospheric wind field subsequently modulate moisture transport and cloud formation. A comparison between the Dyn_Dir and Def_Dir experiments reveals that the introduction of the dynamic aging scheme dominates this response over eastern China. As shown in Fig. 6c, pronounced southerly wind anomalies originating from the ocean are observed along the southeastern coast of China. A similar feature was also reported by Zhuang et al. (2019), who suggested that the southerly anomaly could become more substantial in southern China if there were considerable BC loadings in East Asia. This anomaly promotes a cyclonic anomaly near 850 hPa over southern China and effectively transports warm and moist air from the South China Sea inland (Fig. 6a). Meanwhile, the increase in BC-induced heating due to the dynamic aging scheme further strengthens the anomalous ascending motion and meridional circulation, with the shortwave heating rate exceeding 1.4×10-6 K s⁻¹ (∼0.12 K d⁻¹) (Fig. 6b and d). These processes collectively promote moisture convergence and a 1 %–2 % increase in cloud fraction (CF) over the southern region. Similarly, moist oceanic airflow and cyclonic updraft are conducive to the increased cloud cover over eastern India and the Indochina Peninsula (Fig. 6a). The responses of the wind field near 850 hPa to the BC direct effects can be advantageous to the development of the East Asian summer monsoon, consistent with previous studies (Wang et al., 2015; Zhuang et al., 2018; Chen et al., 2020). Over northern China, the BC heating center is located near 35° N, which likewise induces upward motion with the moist accumulation in the middle troposphere. Conversely, compensating subsidence develops in the lower troposphere on both sides of this ascending center, accompanied by decreased specific humidity (Fig. 6b and d). Horizontally, the southwesterly anomalies formed over the North China Plain under the dynamic aging scheme favor the eastward transport of local moisture, while the compensating northerly flow brings colder and drier air southward from higher latitudes (Fig. 6c), leading to a reduction in CF of 2 %–3 %. Additionally, the stronger semi-direct effect by high BC loadings in northern China also contributes to the suppression of cloud formation to a certain extent (Zhuang et al., 2013).

Figure 7 presents the changes in the cloud droplet number concentration (Nd) resulting from the BC indirect effects (Dyn_Ind), as well as the changes attributable to the dynamic aging scheme (calculated as Dyn_Ind minus Def_Ind) and the BC direct effects (calculated as Dyn_Tot minus Dyn_Ind). As other aerosols (sulfate and OC) are not considered in the Nd calculation, the results here only represent the idealized BC-only activation conditions against the background Nd (Method). There is a substantial increase (more than 150 cm⁻³) in the region with high BC loadings since Nd highly depends on the aerosol number concentration (Fig. 7a). The mean Nd in the lower troposphere is increased by approximately 36.98 cm⁻³ in East Asia for BC. Marked Nd responses are also found over some low-to-mid latitude oceans and remote clean regions, such as the South China Sea and eastern Kazakhstan. This phenomenon may be due to the abundant water vapor and strong upward convective motions in these regions, which are more favorable for offering higher maximum supersaturation. Moreover, the lower background aerosol concentration weakens the competition for water vapor among particles, thereby increasing the sensitivity of Nd to aerosol perturbations (Reutter et al., 2009; Sullivan et al., 2016; Gryspeerdt et al., 2023). Compared to the default aging scheme, the introduction of the dynamic aging timescale accelerates the production of hydrophilic BC, whose larger hygroscopicity lowers the critical supersaturation and thus increases the potential to be activated as cloud droplets (McFiggans et al., 2006; Petters and Kreidenweis, 2007). Consequently, the rapid aging process increases the mean Nd over East Asia by 9.37 cm⁻³. In the Dyn_Tot experiment, Nd also increases over southern China and Shaanxi Province (Fig. 7c), likely because the upward motion caused by the BC direct heating promotes particle activation (Reutter et al., 2009). This is reflected in the distribution of turbulent kinetic energy (TKE) shown in Fig. 7d, given that the updraft velocity at the cloud base is not explicitly resolved in climate models but instead parameterized from TKE (Virtanen et al., 2025).

Aerosol particles can reduce the effective radius of cloud droplets by increasing Nd, thereby enhancing both the cloud optical depth (COD) and cloud albedo (Twomey, 1977). In summer, the BC indirect effects lead to a decrease in cloud effective radius (up to -0.9 µm) in the lower troposphere (not shown), accompanied by an overall increase in COD over East Asia (Fig. 8a). However, in addition to the influence of aerosol–cloud interactions on microphysical processes, thermodynamic adjustments induced by the BC indirect effects can also substantially affect cloud formation. In contrast to the BC direct heating, the COD enhancement caused by BC indirect effects reduces the solar radiation reaching the surface, thereby inducing radiative cooling. This cooling may weaken the development of the East and South Asian Summer Monsoons by diminishing the land-sea thermal gradient (Wang et al., 2015), which in turn suppresses the moisture transport from the oceans, as illustrated in Fig. 8d. Furthermore, the anticyclonic anomaly over southern China contributes to a localized reduction in CF. Consistent but stronger divergence anomalies appear over northeastern China, and their influence exceeds that of the aerosol indirect effects themselves on COD because of the lower Nd there, resulting instead in a decrease in CF and COD. Overall, the thermodynamic responses to BC–cloud interactions are unfavorable for cloud formation over East Asia. A similar pattern is observed in the comparison between the Dyn_Ind and Def_Ind experiments. Although the introduction of the new aging scheme generally leads to a nearly linear increase in Nd over East Asia (Fig. 7b), the response of the atmospheric circulation dominates the differences in cloud cover and COD between the two experiments, even though the increased Nd still makes a positive contribution to COD to some extent (Fig. 8b and e). Figure 8f reveals the changes in the wind field driven by the BC direct effects similar to those in the Dyn_Dir experiment (Fig. 6a). However, due to the consideration of feedbacks from the BC–cloud interactions, cloud cover in northern or southern China exhibits a stronger response (ranging from -4.13 to 3.71 %), which is likely related to BC-induced changes in cloud microphysical processes there. For example, the cyclonic updraft over southern China favors an increase in Nd and cloud formation.

To further assess the sensitivity of the modeled BC–cloud interactions to the hygroscopicity parameter, additional sensitivity experiments are performed based on Exp. 7, in which the hygroscopicity value of hydrophilic BC (0.22) is replaced by 0.11 and 0.34, respectively. The formation of Nd induced by BC exhibits limited sensitivity to variations in the assumed hygroscopicity. Specifically, as the value increases from 0.11 to 0.34 (about a threefold increase), the BC-induced Nd ranges from -13.1 % to 8.1 % relative to the results in Exp. 7. Similar results have also been reported in the observational study by Wu et al. (2019), who found the BC activation fraction was 33±16 % at a critical supersaturation of 0.1 % within the aforementioned hygroscopicity range. In contrast, the sensitivity of the BC-induced cloud radiative forcing and regional climate response to the assumed hygroscopicity is stronger. For example, the surface ERF over East Asia varied from -0.25 to -0.93 W m⁻² across the tested hygroscopicity values. This indicates that, although the changes in Nd are relatively weak, subsequent cloud radiative and dynamical adjustments can amplify the regional radiative forcing and climate response to BC hygroscopicity, which is also reflected in the sensitivity of the BC indirect effect to dynamic aging (Figs. 7 and 8). Previous studies have reported a wide range of BC indirect radiative forcing in liquid clouds from -0.64 to +0.23 W m⁻² (Kristjánsson, 2002; Chen et al., 2010; Koch et al., 2011; Spracklen et al., 2011; Storelvmo, 2012), with considerable uncertainty largely attributed to challenges in accurately assessing the hygroscopicity of BC-containing particles (Zhang et al., 2025). Therefore, it should be clarified that the absolute climate responses here depend on the single parameterization scheme selected in this study.

Since the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, effective radiative forcing (ERF) has gained more attention because the climate response to aerosols can also influence the energy balance of the Earth–atmosphere system (IPCC, 2013). Unlike IDRF, ERF is defined as the changes in net radiative flux at the TOA and surface after a perturbation is imposed, allowing for the rapid adjustments of meteorological factors in the troposphere and stratosphere. In this study, the summer ERFs induced by BC–radiation interactions (ERF_bri), BC–cloud interactions (ERF_bci) and BC–radiation–cloud interactions (total ERF) under the new aging scheme are calculated as the differences between the corresponding sensitivity experiments and the control experiment, as described in the Method section (Fig. 9). Similar to the spatial patterns of BC IDRF, the ERF_bri over most of the study domain is positive at the TOA and negative at the surface due to the strong absorption of solar radiation, with regional mean values of +3.60 and -0.31 W m⁻² over East Asia in summer, respectively (Fig. 9a and d). However, significant discrepancies exist between IDRF and ERF_bri because the latter accounts for meteorological adjustments, primarily driven by cloud responses (Gao et al., 2024). For instance, reduced CF over northern China and the North China Plain allows more solar radiation to be absorbed and to reach the surface (Fig. 6a), thereby enhancing radiative income at both the TOA and surface. Such positive adjustments can offset or even exceed the initial negative IDRF, leading to a net positive ERF_bri at the surface (Fig. 9d). Opposite trends are observed in regions such as India. The significance of climate feedbacks for the ERF_bri has also been demonstrated in previous studies, which suggest that approximately 30 %–50 % of the BC IDRF can be affected by adjustments in clouds and the temperature lapse rate (Stjern et al., 2017; Smith et al., 2018; Zhao and Suzuki, 2019). In contrast, the ERF_bci exhibits a more consistent spatial distribution at the TOA and at the surface in East Asia (Fig. 9b and e), as the BC indirect effects are primarily mediated through cloud-driven radiative changes. The increase in low-level COD associated with BC-induced Nd enhances the radiative cooling effect of clouds. As a result, the BC indirect effects produce predominantly negative ERF_bci at both the TOA and surface over East Asia, with maximum values reaching -7.46 and -5.94 W m⁻², respectively. Nevertheless, strong circulation and cloud responses also modulate the spatial distribution of ERF_bci in a similar way to some extent. As shown in Figs. 8d and 9, decreased cloud cover in the middle and lower reaches of the Yangtze River and the upper Yellow River results in localized positive ERF_bci. Although the sign of the total ERF remains consistent with that of ERF_bri, the inclusion of cooling effects from BC–cloud interactions results in a more negative surface ERF of -2.68 W m⁻² over East Asia, whereas the total ERF at the TOA is reduced to 0.90 W m⁻². In addition, the total ERF is not simply equal to the linear sum of the ERF_bri and ERF_bci, which may be closely related to climate feedbacks (Zhuang et al., 2019; Chen et al., 2020; Gao et al., 2024). This nonlinear behavior is also evident in the regional differences before and after the introduction of the dynamic aging scheme, as shown in Table 3.

Figure 10a–c illustrate the responses of surface air temperature at 2 m (T2m) to different BC climate effects over East Asia during summer with the new aging scheme. The spatial distribution of the air temperature anomalies aligns closely with the ERF patterns but exhibits an inverse relationship with cloud cover. In the Dyn_Dir experiment, the reduction in surface radiation directly induces surface cooling over the Sichuan Basin and southern China (Figs. 9d and 10a), with a maximum temperature decrease of -0.54 K. In contrast, surface warming occurs over the North China Plain and northeastern China, where low-level CF decreases and ERF_bri becomes positive. A similar relationship is also evident in the temperature changes induced by BC–cloud interactions, with a regional mean anomaly of -0.01 K over eastern China (20–40° N, 100–120° E), ranging from -0.27 to 0.35 K (Fig. 10b). Simulation in the Dyn_Tot experiment shows an average warming of 0.044 K in northern China and a cooling of -0.042 K in the south due to the BC total effect. Notably, the temperature changes here further highlight the nonlinearity of regional climate responses (Zhuang et al., 2019). For example, while the increased air temperature is found over northeastern China in both Dyn_Dir and Dyn_Ind experiments, an opposite cooling trend appears in the Dyn_Tot experiment. Feedbacks from wind fields and cloud cover play a critical role in this nonlinearity, further triggering the complex and heterogeneous response of precipitation.

BC–radiation interactions primarily affect precipitation through thermodynamic adjustments by radiative perturbations. Generally, local floods result from an increase in moisture transport or a convergence anomaly, and vice versa (Figs. 6a and 10d). For instance, moisture convergence over southern China leads to a significant increase in precipitation there. Although the BC loading is relatively low in this region, the magnitude of precipitation change exceeds that in northern China. This aligns with previous studies suggesting that circulation responses in regions where AOD is weak dominate precipitation changes (Gu et al., 2016; Chen et al., 2020; Zhuang et al., 2025). Compared with the annual mean (Gao et al., 2024), summer precipitation changes are also substantially larger because of the more vigorous background atmospheric circulation, which also supports this opinion. Similarly, stronger precipitation responses can also be observed over the ocean, where compensating airflows drive more pronounced moisture transport. A widespread reduction in precipitation over East Asia is observed in the Dyn_Ind experiment, with regional mean and maximum values of -0.11 and -1.92 mm d⁻¹, respectively (Fig. 10e). In addition to the aerosol second indirect effect, which suppresses precipitation by reducing the conversion rate of cloud water into rainwater, the influence of large-scale circulation patterns may exceed that of local cloud microphysical processes on seasonal timescales by modulating monsoon intensity and moisture transport pathways (Wang et al., 2021a, 2024; Qie et al., 2025). Consequently, precipitation shows an increase over parts of central China. With respect to the total effects, the circulation background dominated by the BC direct effects shapes the evolution of the south–wet and north–dry precipitation patterns in summer, with regional mean values of -0.09 and +0.13 mm d⁻¹ in northern and southern China, respectively (Figs. 8f and 10f). The responses in precipitation found in this study agree with some previous findings (Menon et al., 2002; Zhuang et al., 2018; Gao et al., 2024).

The above analyses demonstrate that the complexity and inconsistency of regional climate responses to BC perturbations are reflected not only in the nonlinear dependence on BC concentration or aging timescale, but also in the pronounced non-additivity among the direct, indirect and total climate responses. To explicitly quantify the nonlinear coupling between BC–radiation and BC–cloud interactions, a nonlinear interaction term is introduced for both the dynamic and default aging experiments (Table 3). For the series of dynamic aging experiments, the nonlinear interaction term (Dyn_I) is calculated as Dyn_Tot - Dyn_Dir - Dyn_Ind. Similarly, the corresponding term for the default aging experiments (Def_I) is calculated as Def_Tot - Def_Dir - Def_Ind. A two-sided paired Student's t-test is performed between the total response and the sum of the isolated BC–radiation and BC–cloud interaction responses based on the summer means for each individual year. Figure 11 further presents the spatial distributions of Dyn_I in TOA and surface ERF, CF, wind field, specific humidity, T2m and precipitation. Significant nonlinear residuals in major climate variables over East Asia are generally consistent with the changes in circulation and cloud cover. In particular, this interaction enhances moisture convergence and CF over northeastern China (Fig. 11c and d), leading to substantial negative residuals in ERF (-2.12 W m⁻² at the TOA and -2.00 W m⁻² at the surface) and T2m (-0.076 K) over East Asia (Table 3). In southern China, the anomalous cyclonic flow is conducive to cloud formation. Meanwhile, the upward motion induced by BC–radiation interactions may also promote increases in Nd and strengthen the CF response (Figs. 7c and 11c). These coupled moisture and cloud adjustments subsequently contribute to increased precipitation over most areas of East Asia, resulting in the Dyn_I of 0.10 mm d⁻¹ in precipitation (Fig. 11). Similar relationships are also evident for Def_I. For example, opposite changes in CF over northern and southern China correspond to different signs in ERF and surface temperature residuals (Fig. S4). Over the low-latitude South China Sea, the reduction in water vapor associated with descending airflow weakens atmospheric absorption of solar shortwave radiation during summer (Kim et al., 2022; Harris et al., 2025), thereby increasing the radiative forcing at the sea surface and contributing to reduced precipitation there. These results indicate that the pronounced nonlinear residuals arise primarily from coupled circulation–moisture–cloud adjustments (Sadiq et al., 2015).

In the experiment considering only BC–radiation interactions, BC direct heating induces thermodynamic and semi-direct cloud responses, whereas in the experiment for only BC–cloud interactions, perturbations to cloud microphysical processes by BC trigger adjustments in cloud radiation and dynamics. When the two pathways are activated simultaneously, processes that are separated in the individual pathway experiments become dynamically coupled through complex climate and aerosol feedbacks, and their combined responses cannot be reconstructed as a linear sum. Therefore, the results diagnosed from the BC direct or indirect effects are interpreted as sensitivities of isolated pathways rather than as additive components of the combined climate responses in this study. Strongly nonlinear climate responses have also been reported in previous studies (Zhuang et al., 2019; Chen et al., 2020; Gao et al., 2024, 2025), as aerosol-induced changes in atmospheric circulation and clouds can feed back onto the initial radiative perturbation, although their experimental designs differ from that employed here. Chen et al. (2020) and Zhuang et al. (2019) both found that the combined direct effect of BC emissions from multiple source regions or sectors could not be reproduced by a simple linear summation of the effects caused by individual source region or sector. Gao et al. (2024, 2025) demonstrated that regional climate responses to future aerosol emission reductions also exhibited pronounced nonlinear behavior. Therefore, different from source-region contributions or emission changes, the nonlinearity reported here is more appropriately represented as a strong pathway-dependent interaction (coupling between BC–radiation and BC–cloud interactions) within the summertime East Asian climate system. Notably, the magnitude of this interaction can be comparable to, or even exceed, isolated pathway responses at the regional scale (Table 3).