A CR-WRF model (Skamarock, 2004) is used in the study to simulate cumulus clouds. A two-moment bulk microphysical scheme developed by Li et al. (2008a) is utilized to account for the aerosol–cloud interactions in the simulations. The mass mixing ratio and number concentration of five hydrometeors are predicted in the bulk microphysical scheme, including cloud water, rain water, ice crystal, snow flake, and graupel. The gamma function is used to represent the size distribution of the five hydrometeors. Detailed information is provided in Li et al. (2008a).

In order to consider the aerosol activation to CCN and IN, the Community Multiscale Air Quality (CMAQ)/Model-3 aerosol module (Binkowski and Roselle, 2003) is implemented into the CR-WRF model. Aerosols are simulated in the CMAQ using a modal approach assuming that particles are represented by three superimposed lognormal size distributions. The aerosol species – including sulfate, nitrate, ammonium, organic and black carbon, and other unidentified species (dust-like) – are predicted in the module.

For the CCN nucleation, the critical radius of dry aerosols is calculated from the k-Köhler theory developed by Petters and Kreidenweis (2007, 2008, 2013) using water supersaturation predicted by the CR-WRF model (Rogers and Yau, 1989; Pruppacher and Klett, 1997). If the activated CCN radius is less than 0.03 µm, the mass of water condensation on CCN is calculated under the equilibrium assumption; otherwise, the mass of water condensing on CCN is calculated by mw = K43πra3ρw at zero supersaturation, where 3 < K < 8 (Khain, 2000). Additionally, a novel, flexible approach proposed by Philips et al. (2008, 2013) has been used to parameterize the ice heterogeneous nucleation within clouds. The method has empirically derived dependencies on the chemistry and surface area of multiple species of IN aerosols, mainly including dust and black and organic carbon aerosols. Three kinds of ice nucleation mechanisms are considered in the method: contact, immersion, and condensation freezing.

The spatial resolution used in the cloud simulations is 1 km in the horizontal direction and about 250 m in the vertical direction. The model domain of 200 × 200 × 80 grid boxes along the x, y, and z directions, respectively, has been used to provide 200 km × 200 km horizontal and 20 km vertical coverage in this study. The initial and boundary conditions of water vapor are from the sounding data. The simulations use the open boundary conditions under which variables of all horizontal gradients are zero at the lateral boundary.

Two types of cumulus clouds are simulated using the CR-WRF model. The cumulus cloud over the TP (hereafter referred to as Cu-TP) is initialized using the sounding data (87.08∘ E, 28.63∘ N, 4302 m a.s.l.) at 08:00 UTC on 24 August 2014 (Fig. 1a). The cumulus cloud over the NCP (hereafter referred to as Cu-NCP) is initialized using the sounding data (114.35∘ E, 37.17∘ N, 181 m a.s.l.) at 08:00 UTC on 12 August 2014 (Fig. 1b). The selected sounding profiles over the TP and NCP reveal a moderate instability in the atmosphere, with similar convective available potential energy (CAPE) for comparison, i.e., 675 J kg-1 for Cu-TP and 651 J kg-1 for Cu-NCP. Although Cu-TP and Cu-NCP have a similar CAPE, the remarkable difference of the initialization elevation between Cu-TP and Cu-NCP causes their distinct development processes. The 0 ∘C isotherm is generally at a level of around 5 km a.s.l. in the summer. Therefore, when an air parcel perturbed in the boundary layer ascends to form a cloud, the rising distance to the 0 ∘C isotherm is around 1 km over the TP and about 4 km over the NCP. Therefore, the occurrence of the efficient mixed-phase process is much earlier for the cumulus cloud over the TP than the NCP, which substantially advances the development of the cloud over the TP.

The cumulus development is triggered by a warm bubble 15 km wide and a maximum temperature anomaly of 4 ∘C at the height of 1.5 km a.g.l. (Li et al., 2008a), and the integration time is 2 h. Observed aerosol concentrations over the TP exhibit a large variation during the monsoon season; i.e., the observed sulfate concentrations range from 0.1 µg m-3 to several micrograms per square meter (Decesari et al., 2010). Therefore, a set of 28 initial aerosol size distributions with the aerosol number concentration ranging from 20 to 9000 cm-3 and the sulfate mass concentration ranging from 0.02 to 9.0 µg cm-3 at the surface level is used. Other aerosol species are scaled using the measurement at the Nepal Climate Observatory – Pyramid (NCO-P) (Decesari et al., 2010). These aerosol distributions are designated for environments ranging from very clean background air mass to polluted urban plumes over the TP and NCP. Although the observed organic aerosol dominates the aerosol composition at NCO-P (Decesari et al., 2010), considering the large uncertainties in the hygroscopicity of organic aerosols, the hygroscopicity parameter for the secondary organic aerosol is set to 0.05 in the study (Petters and Kreidenweis, 2007, 2008). Hence, sulfate aerosols (or inorganic aerosols) still play a dominant role in the CCN activation. The aerosol concentration is assumed to decrease exponentially with height in the model simulations (Li et al., 2008a).

We have adopted several assumptions and simplifications for the processes associated with aerosols. In the simulations, only the accumulation mode of aerosols is used for the CCN and IN activation, and the aerosol spatial distributions are determined by the initial and boundary conditions, without consideration of chemistry, emissions, and release from cloud droplet evaporation or ice crystal sublimation. The sulfate, nitrate, ammonium, organic and black carbon, and dust-like aerosols in the accumulation mode are included to consider the aerosol CCN and IN effects. Therefore, the surface-level aerosol number concentration ([Na]) is used to represent all types of aerosols, and the CCN concentration at a certain supersaturation (SS) is not used in the study. It is worth noting that the simple aerosol assumption is liable to cause rather large uncertainties in the aerosol activation to CCN and IN. Aerosol chemistry in clouds plays a considerable role in the aerosol nucleation and growth. Direct emissions from anthropogenic sources contribute substantially to the CCN and IN, even over the TP with increasing human activities. Furthermore, mineral dust from the natural source frequently dominates the TP throughout the year. Therefore, future studies need to be conducted to include all the aerosol modes, chemistry, and emissions.

In order to evaluate the overall response of simulated cumulus clouds to changes in aerosol concentrations, the population mean (p mean) of a given variable over all qualified grid points and for a given integration interval is used in the study (Wang, 2005), defined as C‾p=1∑t=T1T2N(t)∑t=T1T2∑n>nminq>qminc(x,y,t), where c represents a given quantity. The calculation only applies to the grid points where both the mass concentration q and number concentration n of a hydrometeor or the summation of several hydrometeors exceed the given minima. The total number of the grid points at a given output time step t is represented by N(t). T1 and T2 are the start and end output time steps, respectively.

Figure 2a depicts the dependence of the p mean of the cloud droplet number concentration (CDNC) on the [Na]. Increasing [Na] provides more CCN to activate, and, although more activated droplets compete for the available water vapor, the water vapor condensation efficiency is enhanced due to the increased bulk droplet surface area, accelerating the latent heat release and the updraft to provide more supersaturated water vapor. Therefore, the increasing CDNC is very consistent with increasing [Na] in Cu-TP and Cu-NCP, in good agreement with previous studies (e.g., Fan et al., 2007a, b; Li et al., 2008a). When the [Na] increases from about 20 to 9000 cm-3, the p mean of the CDNC increases from 0.56 to 218 cm-3 for Cu-NCP. However, more aerosols are activated in Cu-TP compared to Cu-NCP, and the p mean of the CDNC increases from 0.80 to 415 cm-3 for Cu-TP. Although the CAPE is similar for Cu-TP and Cu-NCP, the p mean of CDNC in Cu-TP is higher than that in Cu-NCP with the same [Na].

With the [Na] increasing from 20 to 9000 cm-3, the effective radius of cloud droplet (Reff) in Cu-TP is reduced from about 18.5 to 4.1 µm, and the Reff in Cu-NCP is also consistently reduced from 14.3 to 6.6 µm (Fig. 2b). Interestingly, when the [Na] is less than about 240 cm-3, the Reff in Cu-TP is larger than that in Cu-NCP with the same [Na], although the CDNC in Cu-TP is higher than that in Cu-NCP, showing more cloud water condensed in Cu-TP. Figure 3a presents the dependence of the cloud water content (CWC) on the [Na] in Cu-TP and Cu-NCP, showing that the CWC increases with increasing [Na]. This positive relationship is caused by the combined effects of the increase in CDNC and the decrease in Reff, which inhibit the collision/coalescence of cloud droplets and also enhance the water vapor condensation efficiency and the updraft to generate more available condensable water vapor. The CWC in Cu-TP is higher than that in Cu-NCP for the same [Na], due to higher CDNC and likely stronger updrafts in Cu-TP. The Cu-TP is triggered at an elevation of more than 4000 m a.s.l. Therefore, considering that the 0 ∘C isotherm is at a level of around 5000 m a.s.l., the cloud water formed in the cumulus tends to be transported above the 0 ∘C isotherm to become supercooled, initiating the efficient mixed-phase process to release more latent heat and enhance the updraft. Therefore, there exists more supercooled cloud water in Cu-TP than Cu-NCP when [Na] is the same (Fig. 3b).

Figure 4 provides the vertical profiles of the hydrometeors mass concentrations (summed over the horizontal domain and then averaged during the simulation period) under three aerosol scenarios: a very low [Na] of 90 cm-3, a low [Na] of 900 cm-3, and a high [Na] of 9000 cm-3, corresponding to the background, clean, and polluted atmosphere, respectively. In Cu-TP and Cu-NCP, the CWC achieves the highest level under the high [Na] case and the lowest under the very low [Na] case (Fig. 4a and b). A higher [Na] enhances CDNC and reduces Reff, suppressing the conversion from cloud water to rain water and sustaining more CWC in the cloud. In Table 1, the initial formation time of rain water is delayed with the [Na] increase in Cu-TP and Cu-NCP. The height of the maximum CWC slightly increases from the very low to high-[Na] conditions in Cu-TP and Cu-NCP, but the maximum CWC occurs at 6–8 km a.s.l. in Cu-TP and 2–4 km a.s.l. in Cu-NCP. Therefore, for Cu-TP, most of cloud droplets are above the 0 ∘C isotherm (about 5 km a.s.l.) and supercooled.

The ice particles (ice + snow) generally reach the highest level in the high [Na] and lowest in the very low [Na], which is consistent with those of the CWC in Cu-TP and Cu-NCP (Fig. 4e and f). In the present study, the homogeneous freezing and rime-splintering mechanisms (DeMott et al., 1994; Hallett and Mossop, 1974) are included for the ice nucleation. In addition, the heterogeneous ice nucleation – including the contact, immersion, and condensation freezing – is all parameterized using the method proposed by Philips et al. (2008, 2013) and considering the IN effect, depending not only on temperature and ice supersaturation but also on the chemistry and surface area of multiple species of IN aerosols. The [Na] enhancement generally suppresses the warm-rain process to reduce the rain water but provides more IN and supercooled CWC to accelerate the ice nucleation process. In addition, the rime-splintering mechanism also affects the ice particle profiles at the height with temperature ranging from -8 to -3 ∘C (Hallet and Mosssop, 1974). At the height of 6–8 km a.s.l. in Cu-TP and 4–6 km a.s.l. in Cu-NCP, the ice particle profiles are similar in the very low and low [Na] cases, which is caused by the rime-splintering mechanism. The ice crystal production from the rime-splintering mechanism is related to the graupel particles and the cloud droplets with radii exceeding 24 µm. Large cloud droplets in the very low [Na] facilitate the ice crystal productions from the rime-splintering mechanism, increasing the ice particle mass concentrations at the height of 6–8 km a.s.l. in Cu-TP and 4–6 km a.s.l. in Cu-NCP. Furthermore, there are more ice particles in Cu-TP than Cu-NCP with the same [Na] conditions. The initial formation time of ice crystals is advanced by at least 12 min in Cu-TP compared to Cu-NCP (Table 1). The 0 ∘C isotherm is at a level of around 5 km a.s.l. for the Cu-TP and Cu-NCP. However, the occurrence heights for the Cu-TP and Cu-NCP are more than 4 km and about 0.2 km a.s.l., respectively; when an air parcel perturbed in the boundary layer ascends to form a cloud, the rising distance to the 0 ∘C isotherm is about 1 km over the TP and around 4 km over the NCP. Therefore, the ice crystal formation time is significantly shortened in the Cu-TP compared to the Cu-NCP. The early formation of ice crystals not only facilitates their growth but also advances the glaciation process to intensify convections, further enhancing the growth process.

The rain water in Cu-TP achieves the highest level in the very low [Na] and lowest in the high [Na], and vice versa in Cu-NCP (Fig. 4c and d). Not considering the contribution of graupel melting to the rain water, enhancement of [Na] suppresses the warm-rain process to reduce the rain water but enhances the raindrop size, which conversely accelerates the raindrop falling (Table 1). In Cu-TP, due to relatively low temperature below the freezing level and short falling distance (about 1 km), graupel dominates the precipitating particles, melting less to rain water. So early occurrence of the warm-rain process in the very low [Na] case causes the most rain water formation (Fig. 4c). However, in Cu-NCP, graupel falling below the freezing level tends to melt due to high temperature and long falling distance (about 4–5 km), enhancing the rain water formation. More ice particles and supercooled CWC in the high [Na] case are favorable for the ice growth through deposition, aggregation among ice crystals, and riming of supercooled droplets (Wang and Change, 1993a, b; Lou et al., 2003), and heavily rimed ice crystals are transferred to graupel, enhancing the graupel formation. Therefore, in Cu-NCP, the high [Na] corresponds to the maximum graupel content and also rain water content (Fig. 4d and h). However, in Cu-TP, below 12 km, the low [Na] corresponds to the largest amounts of graupel. Early occurrence of the glaciation process in Cu-TP causes most raindrops to be frozen to form graupel. The freezing rate of raindrops depends on the temperature, the raindrop size and number, and their corresponding variations with time (Lou et al., 2003). Generally, the raindrops with the larger size are easier to be frozen under the lower temperature. The [Na] enhancement decreases the raindrop number but increases its size and updraft to lower the temperature, causing the maximum raindrop freezing efficiency under the low-[Na] conditions. In addition, increasing the [Na] invigorates the convection and produce larger graupel, and then the melting of the graupel causes the formation of larger raindrops (Table 1).

It is worth noting that ice particles and graupel are transported above 12 km a.s.l. or even exceeding 16 km a.s.l. (near tropopause) in Cu-TP, showing intensified convection and also contributing to moistening the upper troposphere.

The p mean of the updraft and downdraft in a core area is used to measure the convective strength of the simulated cumulus clouds, which is defined by the absolute vertical wind speed exceeding 1 m s-1 and total condensed water mixing ratio being more than 10-2 g kg-1 (Wang, 2005). When the [Na] increases from 20 to 9000 cm-3, the p mean of the core updraft increases from 2.0 to 4.3 m s-1 in Cu-TP and from 1.5 to 2.7 m s-1 in Cu-NCP (Fig. 5a). The enhancement of the core updraft with increasing [Na] is caused by the suppression of the warm-rain process to induce the more efficient mixed-phase process, releasing more latent heat to intensify the convection. With the same [Na], the p mean of the core updraft is larger in Cu-TP than in Cu-NCP, showing the significant impact of the early occurrence of the glaciation process on the cloud development.

In Cu-TP, with the [Na] increase, the p mean of the downdraft increases when the [Na] is less than 90 cm-3, but it becomes insensitive to the changes in [Na] when the [Na] is between 90 and 1800 cm-3, and it commences to decrease when the [Na] exceeds 1800 cm-3 (Fig. 5b). The complex nonlinear variation of the p mean of the downdraft with the [Na] reflects the change in the vertical distribution of ice particles and graupel caused by the enhancement of [Na] in Cu-TP. The enhancement of the convective strength with increasing [Na] not only intensifies the convection to facilitate precipitation, producing more precipitable particles, but also transports more ice particles and graupel to the upper troposphere due to the specific topography and further suppresses the occurrence of the downdraft. However, the p mean of the downdraft in Cu-NCP increases steadily with [Na]. Such an increase in the core downdraft with [Na] might be caused by the formation of a large mass loading of precipitable particles to reduce buoyancy and increase downdrafts. Interestingly, when the [Na] is less than about 450 cm-3, the p mean of downdraft in Cu-TP is greater than that in Cu-NCP, but opposite when [Na] exceeding 450 cm-3, indicating the influence of the early occurrence of the glaciation process due to the specific topography in Cu-TP.

The maximum updraft, representing the largest local latent heat release, generally increases with [Na] in Cu-TP and Cu-NCP (Fig. 6a). The maximum updraft in Cu-TP is much higher than that in Cu-NCP with the same [Na]. In Cu-TP, when the [Na] exceeds 750 cm-3, the maximum updraft becomes insensitive to changes in the [Na]. In Cu-NCP, the maximum updraft is not very sensitive to changes in the [Na] when the [Na] exceeds 2400 cm-3. The maximum downdraft, or the largest drag speed, indicating the largest strength to inhibit the development of the convection, also increases generally with the [Na] in Cu-TP and Cu-NCP (Fig. 6b), but Cu-TP produces a more intensive maximum downdraft than Cu-NCP.

Figure 7 shows the variation of the accumulated precipitation with [Na] in Cu-TP and Cu-NCP. Generally, the precipitation increases with [Na], which is consistent with previous modeling studies (e.g., Khain et al., 2005, 2008; Fan et al., 2007a; Li et al., 2008a, 2009). Since Cu-TP and Cu-NCP occur under humid conditions, the precipitation enhancement with [Na] is also in good agreement with measurements. Observations have shown the precipitation enhancement around heavily polluted coastal urban areas (Shepherd and Burian, 2003; Ohashi and kida, 2002) or over oceans influenced by pollution aerosols (Cerveny and Balling Jr., 1998; Li et al., 2008b; Koren et al., 2012, 2014).

When the [Na] is increased from about 20 to 9000 cm-3, the precipitation of Cu-TP increases from 0.13 to 0.23 mm; when the [Na] exceeds 300 cm-3, the precipitation becomes insensitive to the variation in [Na]. In contrast, the precipitation of Cu-NCP consistently increases from 0.03 to 0.37 mm, with [Na] ranging from 20 to 9000 cm-3. In addition, when the [Na] is less than 500 cm-3, Cu-TP produces more precipitation than Cu-NCP, which can be explained by the early occurrence of the glaciation process causing less warm rain but more efficient mixed-phase processes. However, when the [Na] exceeds 500 cm-3, the precipitation efficiency of Cu-NCP is higher than that of Cu-TP, although the convective strength is larger in Cu-TP than Cu-NCP. The increasing convective strength with [Na] not only enhances the precipitation but also transports more ice and graupel particles above 12 km to form the anvil. The ice particles and graupel in the anvil are subject to sublimation and evaporation to moisten the upper troposphere, and they decrease the precipitation efficiency in Cu-TP.

The water content and precipitation in the Cu-TP respond well monotonically to the changes in the [Na]. Numerous studies have shown the reduced liquid water path (LWP) by increasing aerosols under relatively dry conditions (e.g., Khain et al., 2005). During the summer monsoon season, the atmosphere over the TP is humid due to the water vapor transport by the monsoon (Fig. 1a). The ambient humidity in the simulations of the Cu-TP exceeds 80 % in the low-level atmosphere, causing the good monotonicity in the responses of water content and precipitation to aerosols.

Recent studies have demonstrated that convection is more active and stronger during summertime over the Tibetan Plateau due to its unique thermodynamic forcing (Hu et al., 2016). We have further performed sensitivity studies to explore the impact of the maximum perturbation temperature (MPT) in the warm bubble on the development of cumulus clouds. The MPTs of 2.0 and 0.5 ∘C are used to trigger Cu-TP and Cu-NCP, with the [Na] ranging from 20 to 9000 cm-3.

For Cu-TP, the core updraft decreases slightly when the MPT is reduced from 4.0 to 2.0 ∘C, and particularly when the [Na] exceeds 100 cm-3 the decrease of the core updraft is indiscernible (Fig. 8a). When the MPT is reduced from 2.0 to 0.5 ∘C, the core updraft decreases considerably. However, for Cu-NCP, the core updraft decreases substantially when the MPT is reduced from 4.0 to 0.5 ∘C. When the MPT is 0.5 ∘C and the [Na] is less than 80 cm-3, the updraft core area is not formed in Cu-NCP. When the MPT is the same, the core updraft is much larger in Cu-TP than Cu-NCP with the same [Na]; even the core updraft in Cu-TP with a MPT of 0.5 ∘C is larger than that in Cu-NCP with a MPT of 4.0 ∘C when the [Na] is more than 80 cm-3. Therefore, under the unstable conditions over the Tibetan Plateau, a small perturbation can induce strong convections, which is primarily caused by early occurrence of the glaciation process due to the specific topography, as discussed in Sect. 3.1.

The accumulated precipitation generally decreases with the MPT in Cu-TP and Cu-NCP with the same [Na] (Fig. 8b). When the MPT is 4.0 ∘C, Cu-NCP produces more precipitation than Cu-TP, with the [Na] exceeding 500 cm-3, but Cu-TP produces much more precipitation than Cu-NCP, with a MPT of 0.5 ∘C under all aerosol conditions. In addition, the precipitation generally increases with increasing [Na] in Cu-TP and Cu-NCP with various MPTs, and it does not exhibit a nonlinear variation with the [Na], which is not consistent with the results in Li et al. (2008a). The possible reason is that in this study the maximum p mean of CDNC is about 410 cm-3, which is much less than that in Li et al. (2008a). If the [Na] is further increased, the precipitation might be suppressed.