4.1.1. Comparison With Observations
 First, we evaluate the simulated clouds using available observations from the AMF site at Shouxian. For comparison with the measurements from the single point at Shouxian, the model results are averaged over a volume of 3 × 3 grid cells (i.e., 7.2 × 7.2 km2) near that point. Figure 3 presents the comparisons of liquid water content (LWC) (sum of cloud droplet water and rainwater content), LWP, cloud base and top heights among P_sbm, C_sbm and observations. Since comparisons of the bulk simulations with observations are worse than the SBM runs and do not provide additional information, the bulk simulations are not included in the figure, but will be discussed below. As shown in Figure 3a, the Microwave Radiometer Profiler (MWRP) did not work because of the storm and heavy rain at 18:00–20:00 LST. LWC should peak sometime during this period when the storm cloud occurred. In P_SBM, LWC peaks around 19:00 LST (Figure 3b), meaning the timing of the storm is close to the observations, although the modeled cloud at SX starts a couple of hours earlier. After 20:00 LST, the modeled LWC from P_sbm has a similar magnitude as the observations. However, in C_sbm, LWC peaks at 17:00 LST, about 2-h earlier (Figure 3c) and much higher than P_sbm. The cloud at 5 h in P_sbm was not detected by MWRP, which could be because MWRP only sees clouds directly above the instrument, but the results from the simulations are averaged over a volume of 9 grid cells, of which only 4 grids have clouds at that time. LWC drops off much more quickly relative to P_sbm afterwards and becomes 5–10 times lower than observations after 20:00 LST. The LWC and IWC in P_sbm (Figures 3b and 3c) are lower because the convection cell is much weaker relative to C_sbm at that location. Although we see that the increase in CCN weakens the storm at this location, storms in other places could become stronger (results over a larger region are discussed later). Clearly, the increase in CCN delays the storm by about 2 h. Note that uncertainty of LWC from MWRP is about 30% for these fairly thick clouds. For the SC case where cloud is thinner, the uncertainty can be as high as 60%.
Figure 3. Time series of LWC (g cm−3) profile retrieved from (a) MWRP at SX, (b) P_sbm and (c) C_sbm. The comparison of the times series of (d) LWP (mm) and (e) cloud base height (km) retrieved from MWRP and (f) cloud top height (km) from FY-2 satellite with the modeled values from P_sbm and C_sbm for July 17 (LST). The black line in Figures 3b and 3c is the IWC from the corresponding simulation. The model results are averages over a cloud volume of 3 × 3 grid cells.
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 The liquid water path (LWP) in P_sbm agrees with the observations in magnitude very well after 20:00 LST (the values are not shown for 18–20:00 LST) (Figure 3d). The uncertainty of LWP from the MWRP is about 30 g m−2 (about 0.03 mm), which is small relative to the high LWP in this case. Obviously, C_sbm predicts a few times larger LWP and the timing is much earlier. The modeled cloud base heights from P_sbm are generally larger than the observed values from MWRP, which has an uncertainty of about 0.5 km (Figure 3e), and the simulated cloud top height of about 15 km is in good agreement with the Chinese Feng-Yun-2 (FY-2) geostationary meteorological satellite measurements (Figure 3f). The model, however, does not capture the decrease of cloud top height after 21:00 LST, suggesting a slower dissipation of cloud anvils in the model, which could be related to the enhanced anvil formation due to the uniform vertical distribution of CCN. Generally, somewhat higher cloud base and lower cloud top are seen in C_sbm relative to P_sbm, implying the invigoration effect of CCN on the DCC. Note that the cloud top height is retrieved with the method of SB2 DART 2 (Santa Barbara DISORT Atmospheric Radiative Transfer) [Zhou et al., 2008] from FY-2 and the uncertainty is very difficult to estimate, although it is known that the uncertainty could be very large above 10 km.
 The spatially distributed hourly precipitation data (measured by rain gauges) obtained from China Meteorological Administration (CMA) allow us to compare the modeled and observed system more closely. Figure 4 shows the spatial distribution of hourly rain rates from observations, P_sbm and C_sbm at 18:00 (Figure 4a) and 20:00 LST (Figure 4b). Note that most of the blank area in the panels for observations indicates no rain or very light rain (<0.1 mm hr−1) rather than lack of data as the spatial distribution of the meteorological stations is dense. Overall, the model tends to predict a strong convective system and overestimate rain rates. Since the distribution of rain gauges is coarser in the area west of 116 E, the observations may not capture the entire rain system indicated by P_sbm. The rain pattern from P_sbm resembles the observations both spatially and temporally. For example, the precipitation around Shouxian (SX for short) is very strong at 18:00 LST in both P_sbm and observations (Figure 4a), and becomes much weaker two hours later (Figure 4b). However, in the clean case, strong convection/precipitation is not found around SX at 18:00 LST. In fact, what we see is the dissipating stage of precipitation because the storm occurs about 2 h earlier in C_sbm. In addition, the spatial distribution of rain pattern in C_sbm is quite different from P_sbm and observations: strong precipitation is found around the region of 114.5–116E in C_sbm, which is not seen in P_sbm and observations. Therefore, CCN change the spatial distribution of precipitation quite significantly. When comparing the rain rates at SX from the ARM surface meteorological measurement, CMA, P_sbm, and C_sbm (Figure 5), we see a better agreement between P_sbm and the observations. But the rain rate peaks about 2 h earlier in C_sbm, consistent with the LWC shown in Figure 3. Unfortunately, the single-point measurements at the ARM site for such a short time (24 h) and the much coarser CMA precipitation data prevent us from making meaningful statistical comparison (such as scatter or frequency distribution plots) between model results and observations.
Figure 4. Spatial distribution of hourly rain rates (mm hr−1) from observations, P_sbm and C_sbm at (a) 18:00 and (b) 20:00 LST, which are 10:00 and 12:00 UTC, respectively. Note LST = UTC + 8:00. The red box shows the study region and the gray one denotes the large region for the statistical data in Table 2.
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Figure 5. Comparisons of the time series of rain rates (mm hr−1) at Shouxian from the ARM surface meteorological measurement, CMA, P_sbm and C_sbm for July 17 (LST).
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 Although the simulation with Bulk in the polluted environment (P_bulk) is also able to simulate the convective system around SX, it predicts stronger convection/precipitation and higher cloud top height (up to 2 km higher), compared to P_sbm and observations (not shown). The timing of the storm around SX in P_bulk does not differ from P_sbm significantly, although rain duration is shorter in P-bulk. Therefore, we do not see significant impact of microphysical parameterizations on the timing of the storm. Under the clean condition, neither Bulk (C_bulk) nor SBM (C_sbm) captures the general spatial distribution of precipitation.
4.1.2. Effects on Convection/Precipitation
 To further investigate the differences of the effects between SBM and Bulk and aerosol effects on the convective system over the SX region, a subdomain covering 31.1–33.3 N and 115.5–117.5 E (about 245 × 187 km2) where the convective system occurred is selected for further study (the red box in Figure 4a; referred to as “the study region”). Here, to examine the time evolution of the convection system, we confine our analysis to a relatively isolated storm with local dynamics-microphysics feedbacks rather than multiple convective systems with potential large-scale feedbacks for easier interpretation of the modeled results. This way our analysis focuses on the effects of aerosols at the cloud scale rather than large-scale features, which is consistent with our experimental design in which the same boundary conditions from the coarse domain are used in all of the simulations in the fine domain. Nevertheless, we also perform a statistical analysis over a larger area (about 375 × 365 km2) where multiple convection systems are included (the gray box in Figure 4a; referred to as “the large region”) and the results will be discussed.
 Figure 6a shows the rain occurrence frequency for different rain rate categories in the study region. Following the World Meteorological Organization (WMO) definition of rain category, light rain is defined as rain rate less than 0.1 mm hr−1 and heavy rain is for rain rate larger than 5 mm hr−1. Between 0.1–5 mm hr−1, we divide the rain rate into two intermediate rain categories between 0.1–1 and 1–5 mm hr−1. Both SBM and Bulk consistently show that the increase of CCN reduces the rain occurrence frequency and amount (Figures 6a and 6b) for light and intermediate rain. However, for heavy rain, SBM simulates an increase in rain frequency and amount by over 20% from the clean to polluted condition, but no significant change (i.e., only a few percent decrease) is simulated by Bulk. To determine if the results are robust since the simulation of DCC could be sensitive to initial conditions, we performed 5 ensemble runs for the bulk simulations under each CCN condition by adding random perturbations to the initial temperature over the entire 3D fine domain. The random perturbation is represented by a normal distribution with mean 0 and a standard deviation varying from 0.2 to 0.5 K for different runs. As shown in Figure 6(blue color), the averaged results from the ensemble runs tell the same story: with bulk, increasing CCN decreases the frequency and amount for light and intermediate rain but no significant change for heavy rain. Although we did not perform similar ensemble runs with SBM because of computational cost, it should be noted that the reduced frequency and amount for light rain and vice versa for heavy rain in the polluted case simulated by SBM are also found in analyses of long-term observational data [Qian et al., 2009; Yao et al., 2008]. Furthermore, invigoration of convection/precipitation by CCN for this case is supported by the finding of Fan et al. [2009b], since the observed wind shears are weak with a maximum value less than 8 m s−1 within 0–10 km (Figure 2c).
Figure 6. (a) Percentage of rain occurrence for each rain category in the study region for July 17 (0–23:00 LST), (b) relative change of rain amount from clean to polluted condition simulated by SBM and Bulk for each rain category, and (c) accumulated precipitation on the surface averaged over the study region. The rain occurrence frequency is calculated by the number of grid points falling in a certain rain category divided by the total grid points during the entire day of July 17. “Ensemb” in the legends represents the ensemble runs shown in blue colors.
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 The significant increase in the frequency and amount of heavy rain in the polluted case with SBM suggests the invigoration effect of CCN on deep convection. By examining the profiles of updraft velocity over the study region (Figure 7), the convective strength is indeed stronger in P_sbm compared to C_sbm between 15 and 20:00 LST when the convective system around SX is active. The average w with w > 2 m s−1 over the study region during 12–23:00 LST is 4.1 m s−1, about 5% larger relative to C_sbm. The stronger convection in P_sbm results in ∼18% increase in the accumulated surface precipitation relative to C_sbm (Figure 6c). However, with Bulk, the clean case (C_bulk) predicts stronger convection than the polluted case (P_bulk) with an increase of maximum updraft velocity from 36.2 m s−1 in P_bulk to 43.6 in C_bulk over the study region. Overall, convection is suppressed, rain rate is decreased, and the accumulated surface precipitation is reduced by increasing CCN with the bulk scheme. From Figure 6c, suppression of precipitation by CCN in the beginning of the storm and then invigoration of precipitation later is clearly simulated by SBM. With Bulk, precipitation is reduced by CCN in the afternoon, corresponding to the suppressed convection. Note that P_bulk appears to give stronger convection between 2 and 9 LST than C_bulk, under the conditions of much less activated CCN relative to the afternoon. The ensemble runs with Bulk give similar results in precipitation (Figure 6c, blue line) and convection with the average w of 4.4 in P_bulk over the study region from 12:00–23:00 LST but 4.6 in C_bulk. Although the ensemble average results show a smaller change in the total precipitation and convection from increasing CCN compared to the single simulation results, they are qualitatively consistent.
Figure 7. Profiles of updraft velocity (w) (m s−1) from (a) P_sbm, (b) C_sbm, (c) P_bulk, (d) C_bulk, (e) P_bulkP and (f) C_bulkP for July 17 (LST), calculated by averaging over the grids with w > 2 m s−1.
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 From Figure 7, we can also see that Bulk generally predicts stronger convection than SBM, a typical feature of many bulk schemes indicated in many past studies [e.g., Khain and Lynn, 2009; Tao et al., 2007; Li et al., 2009], explaining the higher cloud top heights in P_bulk than P_sbm as shown in Figure 3. The maximum vertical velocity in C_bulk is 43.6 m s−1, while it is only 30 m s−1 in C_sbm. The reasons for the stronger convection predicted by bulk schemes with saturation adjustment have been detailed by Khain and Lynn . They suggested that the saturation adjustment method in those bulk schemes cannot accurately account for the decrease of supersaturation due to droplet growth during a single time step and supersaturation is removed by condensation growth at each time step, leading to overestimation of latent heat release by condensation [Khain et al., 2000, 2008]. Although Bulk predicts stronger convection than SBM, it estimates less accumulated rain, especially in the polluted case, as a result of very different microphysical properties that will be discussed in the next section. Therefore, the differences in convection and accumulated precipitation simulated by Bulk versus SBM are even larger than the aerosol effects on them (Figures 6c and 7). To improve estimates of aerosol indirect effects, it is crucial to further constrain cloud microphysical schemes to reduce model uncertainties.
 Averaged over the large region (again, the gray box in Figure 4a), the results in Figure 6 are qualitatively similar to the results averaged over the study region. The relative differences between SBM and Bulk become smaller, which is expected for a larger domain more affected by the same boundary conditions. The aerosol effects on precipitation and updraft velocity for the large region as shown in Table 3a also agree with what we see for the smaller study region, but with much smaller magnitude because they are mainly forced by the domain average convergence from the boundary conditions that are the same in all simulations. Precipitation and updraft velocity listed in Table 3a from the ensemble runs indicate that the results discussed above are robust qualitatively.
Table 3a. Quantities Averaged Over the Large Region (30.5°N–33.8°N and 113.5°E–117.5°E), i.e., 3-D Domain Average, for DCC in July 17 (LST)
| ||P_sbm||C_sbm||P_bulk||C_bulk||P_bulk_ensemb||C_bulk_ensemb||Changes With SBMa (%)||Changes With Bulk (%)||Changes With Bulk Ensemble (%)|
|Qc (g kg−1)||0.012||0.01||0.008||0.007||0.008||0.00755||20.0||14.3||5.96|
|Qr (g kg−1)||0.044||0.045||0.038||0.041||0.04||0.042||−2.22||−7.32||−4.76|
|Qi (g kg−1)||0.069||0.058||0.043||0.044||0.037||0.045||19.0||−2.27||−17.8|
|Qg (g kg−1)||0.012||0.021||0.0335||0.0331||0.031||0.036||−42.86||1.2||−13.9|
|wb (>2 m s−1)||3.93||3.81||4.22||4.33||5.31||5.40||3.15||−1.9||−1.11|
4.1.3. Effects on Cloud Microphysical Properties
 The different behaviors between SBM and Bulk in the CCN effects on convection and precipitation should stem from very different cloud microphysical properties. Figure 8 shows the averaged hydrometeor number and mass concentrations over the study region. The most striking difference between SBM and Bulk is found in the simulated droplet and raindrop number concentrations. In the polluted case, Bulk (P_bulk) predicts over two times higher droplet concentrations (Nc) and up to 100% higher raindrop concentrations (Nr) relative to SBM during the active convection period, although the differences are small at other times, indicating that the stronger convection predicted by Bulk is one of the factors leading to the stronger droplet nucleation. Another important factor lies in the fixed CCN prescribed everywhere at each time step with Bulk. To figure out how much the fixed CCN contributes to the much higher Nc, we conducted sensitivity tests by fixing CCN size distribution during the simulations with SBM, although an advantage of SBM is in its ability to simulate time-varying CCN size distribution. In these sensitivity runs,Nc is even higher than that simulated by Bulk when CCN is fixed in SBM under both polluted and clean conditions, indicating that the fixed CCN is the major contributor to the high droplet concentration in Bulk. The lower Ncwith Bulk than SBM when CCN is fixed is because strong in-cloud scavenging is taken into account indirectly in Bulk (i.e., the total droplet number concentrations in the previous time step is deducted from the newly formed activated droplets).
Figure 8. Time series of domain-averaged (a) number and (b) mass concentrations for cloud droplet, raindrop, ice/snow, and graupel/hail over the study region.
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 To further strengthen that the fixed CCN leads to high Nc in Bulk, we have modified the bulk scheme by implementing a prognostic CCN approach in which CCN number and mass are predicted. We conducted tests with this scheme for the clean and polluted cases (referred to as “P_bulkP” and “C_bulkP,” respectively; blue color in Figure 8). Clearly, the prognostic CCN approach gives much closer Nc compared to that of SBM. However, Nr is much higher than the simulation with the fixed CCN because the autoconversion rate becomes about 2 times higher due to larger droplet size resulted from lower Nc (Nr will be discussed more in the following paragraph). This further indicates that the fixed CCN is responsible for the much higher Nc predicted by Bulk relative to SBM. Note that the results for the prognostic CCN approach in Bulk are preliminary, so we only show the results for liquid particles to support our argument that the fixed CCN leads to much higher Nc. We will present more in-depth analysis of the prognostic CCN scheme in a follow-on paper.
 We performed additional simulations with Bulk and found that the subgrid droplet nucleation considered in Bulk through subgrid vertical velocity exerts little effect on the clouds (although it probably will have more impact in simulations with much coarser resolutions).
 The higher Nr in Bulk relative to SBM is significantly contributed by the much smaller cutoff size between droplets and raindrop in Bulk (25 μm versus 100 μm in SBM). Sensitivity test based on P_sbm in which only the cutoff size is modified to be ∼25 μm shows that Nr averaged over the study region in July 17 is increased from 0.09 to 0.145 L−1, much closer to 0.13 L−1 in P_bulk. Ncdoes not change significantly by the cutoff size. Note that the actual simulations with SBM do not depend on the cut-off size since the cutoff size is only used for outputting diagnostic quantitiesQc/Qr and Nc/Nr. Nr in Bulk is also strongly affected by the assumed size for the newly formed raindrops. When the assumed radius increases from 25 to 40 μm which is used by Seifert and Beheng  and Li et al., , Nris decreased by about 6 times. In addition, parameterizations of self-collection of raindrops and rain evaporation below cloud base could also affectNr [Seifert, 2008].
 Under the polluted condition, Bulk predicts up to 4 times higher Nc and up to 2 times higher Nr than SBM (Figure 8). However, the differences in droplet mass (Qc) and raindrop mass (Qr) concentrations between P_sbm to P_bulk are not as large as their number concentrations. This implies that the mean droplet and raindrop sizes in P_sbm are larger than those of P_bulk. Indeed, the mean droplet radius in P_sbm is about 45 μm, while it is only about 5 μm in P_bulk. For raindrops, the mean radius is about 350 μm in P_sbm, only about 15% larger than that in P_bulk. Besides the much lower Nc, the much larger cutoff size to distinguish cloud droplets and raindrops in SBM also contribute substantially to the larger cloud droplet size relative to P_bulk. The mean radius is reduced to 12 and 330 μm for droplets and raindrops, respectively, when the cutoff size is assumed to be ∼40 μm.
 To explain why the strong droplet nucleation leads to the suppressed convection in the polluted case with Bulk, we examined the time series of vertical profile of IWC and Ni in both P_bulk and C_bulk. It is found that IWC is lower in P_bulk but Ni has little differences at −15 < T < −30°C over the active convection period compared with C_bulk. The reduced ice mass in P_bulk could be attributed to deposition and droplet freezing because of the much smaller droplet sizes. Since latent heat of freezing is proportional to the produced ice mass, it suggests that latent heat release is reduced in P_bulk relative to C_bulk, explaining the suppressed convection by CCN with Bulk. It should be noted that, in the modified Bulk with the prognostic CCN, the invigoration effect on convection and the enhanced heavy rain in the polluted case occurs: from C_bulkP to P_bulkP, the averaged w over grid points with w > 2 m s−1 between 12 and 23:00 LST is increased from 4.1 to 4.4 m s−1m, and the heavy rain frequency and amount is increased by 4% and 7% respectively. These results are consistent with SBM. Similarly, the CCN invigoration effect does not occur with SBM when CCN is fixed, because unrealistically strong droplet nucleation makes Nc too high and droplet freezing becomes very inefficient in the polluted case (far beyond optimal for invigoration effect). All these tests consistently indicate that unrealistically strong droplet nucleation due to the fixed CCN is primarily responsible for suppressed convection simulated by the original bulk scheme.
 Under the clean condition, differences in Nc and Nr between SBM and Bulk are even larger (Figure 8). As discussed above, the reasons could be attributed to (1) the much larger cutoff size in SBM than Bulk in distinguishing droplets from raindrops and (2) the different conversion rates from droplets to raindrops between SBM and Bulk. By examining the differences of Qc and Qr between C_bulk and C_sbm, we find that the mean droplet and raindrop sizes in C_sbm are larger than those of C_bulk, but with the differences much smaller than those under the polluted condition. In any case, Bulk generally predicts much higher Nc and Nr but smaller droplet and raindrop sizes compared to SBM. These differences are related to the stronger nucleation and smaller cutoff size between droplet and raindrop discussed in the previous paragraph, explaining the lower surface precipitation rate (small drops sediment slowly and may evaporate completely before reaching ground).
 An increase in CCN significantly increases Nc and Qc but decreases Nr; SBM and Bulk qualitatively agree with each other on this point. Increasing CCN significantly increases Ni (sum of ice and snow number concentrations) with SBM, but with Bulk a decrease of Ni is seen after 14 LST in Figure 8. Averaging over the large region, there is a slight increase (3.2%) in Ni by increasing CCN (Table 3a), but the increase is much smaller than those of SBM and other studies that used bulk schemes [Wang, 2005; Li et al., 2008]. This can be explained by the suppressed convection by CCN with Bulk and a limit on the maximum cloud ice concentration of 10 cm−3 applied to the Morrison scheme. Ni often exceeds 10 cm−3 in both P_sbm and C_sbm since in SBM only a limit of supersaturation over ice no larger than 50% is used for condensational/depositional freezing. Currently it is uncertain how high the maximum ice number can be. Since convection is enhanced by increasing CCN with SBM, and the Meyer's parameterization employed in SBM tends to predict a very high ice formation rate at high supersaturation, it is not surprising that Ni is increased in the polluted case with SBM.
 Both SBM and Bulk predict a decrease of Ng (sum of graupel and hail number concentrations) in the polluted condition. However, they do not agree on the CCN effect on Qi (sum of ice and snow mass concentrations) and Qg (sum of graupel and hail mass concentrations). SBM predicts up to 35% higher Qi in the polluted case (19% on average in July 17 over the large region as shown in Table 3a), but no significant change is seen from C_bulk to P_bulk. With SBM, Qg is decreased by increasing CCN, but there is no significant change with Bulk statistically (Table 3a). The decreased Ng by the increase of CCN with SBM is because riming efficiency is reduced due to the reduced droplet and ice particle sizes. With Bulk, the reduced Ng in the polluted case is related to the decreased raindrop mass and number. Therefore, with Bulk, the much lower Ng and not much change in Qg in the polluted case suggest larger graupel/hail sizes relative to the clean case. This is likely related to the simple parameterization of the riming process in Bulk in which riming rate is determined by a constant and the constant is uncertain. In fact, riming efficiencies are not only a function of particle size but also a function of ice crystal habit [Pruppacher and Klett, 1997], and the SBM representation is also uncertain since our understanding is not sufficient to well represent ice processes. As a result, SBM and Bulk can produce even qualitatively very different results [Muhlbauer et al., 2010]. Figure 8 also shows that, with Bulk, CCN produce significant effects on the properties of liquid particles but not ice particles, while CCN produce significant effects on both liquid and ice microphysical properties with SBM. The significantly increased Qr and Qi in the polluted case with SBM explain the enhanced precipitation. However, with bulk, Qr and Qi are decreased by the increase of CCN, explaining the decreased accumulated precipitation.
 Averaged over the large region, our major results in microphysical properties such as mass and number concentrations of cloud droplet and ice are not changed, except the peaks in the time series plots are less pronounced because multiple convective systems occur at different times and evolve differently. It suffices to note that there are no qualitative changes in the differences of the cloud microphysical properties between SBM and Bulk (Table 3a). As for aerosol effects, the results from the large region agree with those from the study region: from clean to polluted, Nc and Qc are increased but Nr and Ng are decreased. SBM and Bulk agree with each other on this. Qr is decreased significantly with Bulk but not with SBM. We also see that SBM predicts much larger change in Ni and Qi by CCN than Bulk. The ensemble runs for Bulk do not change the conclusions qualitatively, except for graupel (larger CCN effects on Ng and Qg for the ensemble results; Table 3a), which could be associated with over-simplified parameterization as discussed above.