The Non-Monotonic Response of Cumulus Congestus to the Concentration of Cloud Condensation Nuclei

Abstract

This study uses idealized simulations to investigate the impact of cloud condensation nuclei (CCN) on a cumulus congestus. Thirteen cases with the initial CCN_C, which is the CCN concentration at 1% supersaturation with respect to water, from 10 to 10,000 cm⁻³ are simulated. The analysis focuses on the liquid phase due to the negligible ice phase in this study. A non-monotonic response of cloud properties and precipitation to CCN concentration is observed. When CCN_C is increased from 10 to 50 cm⁻³, the enhanced condensation due to the more numerous droplets invigorates the cumulus congestus. The delayed precipitation formation due to the smaller droplets also facilitates the cloud development. The two processes together lead to a higher liquid water path (LWP), higher cloud top, and heavier precipitation. The cumulus congestus has the highest cloud top, the strongest updraft, and the most accumulated precipitation and at CCN_C = 50 cm⁻³. When CCN_C is increased from 50 to 500 cm⁻³, the condensation near the cloud base is further enhanced and the precipitation is further delayed, both of which lead to more liquid water remaining in the cloud, and thus an even higher LWP and heavier precipitation rate in the later stage. However, the significantly enhanced evaporation near the cloud top limits the vertical development of the cumulus congestus, leading to a lower cloud top. When CCN_C is further increased to be higher than 1000 cm⁻³, the cumulus congestus is strongly suppressed, and no precipitation forms. The ratio of the precipitation production rate to vertical cloud water flux in the updraft is not a constant, as is generally assumed in cumulus parameterization schemes, but decreases significantly with increasing CCN concentration. It is also found that the CCN effect on the cumulus congestus relies on which parameters are used to describe the cloud strength. In this study, as CCN_C increases, the LWP and the maximum precipitation rate peak at CCN_C = 500 cm⁻³, while the cloud top height, maximum updraft, and accumulated precipitation amount peak at CCN_C = 50 cm⁻³.

1. Introduction

Cumulus congestus is the intermediate mode between shallow cumulus and cumulonimbus, with the cloud top generally between 3 and 9.5 km [1,2,3,4]. It has been recognized that cumulus congestus is as frequent and important as shallow cumulus and cumulonimbus in the tropical regions. Cumulus congestus contributes to nearly 30% of the total convective rainfall in tropical regions, although their precipitation is generally not as strong as that of cumulonimbus [1,5]. Cumulus congestus plays an essential role in moistening and cooling the mid-troposphere through cloud top detrainment, which create a favorable environment for subsequent cloud development. As a result, cumulus congestus has the potential in promoting the subsequent development of deep convection and is important in the transition from shallow convection to deep convection [1,6,7,8,9,10,11]. Although cumulus congestus is of significant importance, most global models cannot reproduce cumulus congestus with high fidelity, as indicated by the underestimation of mid-level clouds [12,13]. To improve the parameterization in global models, we need to better understand the evolution of cumulus congestus.

Aerosols can serve as cloud condensation nuclei (CCN) to affect clouds and precipitation. The effect of CCN on convective clouds and precipitation depends on the convection types [14,15]. Increasing CCN concentration produces more but smaller droplets, e.g., [16,17,18], leading to lower collision–coalescence efficiency. This suppresses or delays the warm-rain precipitation and, hence, increases the cloud liquid water, cloud fraction, and cloud thickness of warm clouds, e.g., [15,19,20,21,22,23,24]. Xue et al. [25] simulated a shallow cumulus field, where the cloud tops are below 2000 m. They found that the cloud water and cloud fraction increase with CCN only when CCN aerosol concentration is lower than 100 mg⁻¹ and precipitation exists. When CCN aerosol concentration is higher than 100 mg⁻¹ and nearly no precipitation exists, further increasing CCN concentration reduces the cloud fraction, cloud size, and cloud thickness due to the faster evaporation of the smaller droplets [25,26]. Therefore, there is a non-monotonic response of shallow cumulus clouds as CCN is increased [25,27].

For deep convective clouds, the mixed-phase processes are involved because of the inclusion of the ice phase. The aerosol–cloud interactions in deep convective clouds are, therefore, more complicated. Observations found that a higher aerosol loading is associated with stronger convection, as indicated by a higher cloud top, stronger mixed-phase processes, and heavier precipitation, e.g., [28,29,30,31]. Rosenfeld et al. [32] proposed that the invigoration of deep convective clouds and the additional precipitation in polluted conditions are mainly caused by more droplets ascending to above the 0 °C level, freezing into ice phase, and releasing more latent heat. This invigoration effect of CCN is also supported by several numerical simulation studies, e.g., [31,33,34,35,36,37]. Tao et al. [34] found that if the stronger cold pool due to the enhanced precipitation couples well with the surface wind shear, the low-level convergence will be stronger. This facilitates the secondary cloud formation and, therefore, increases precipitation. Fan et al. [38] suggested that the dramatically increased cloud cover and cloud height with the increased CCN is mainly caused by the more but smaller ice crystals in the anvil regions, which leads to larger and more persistent anvil clouds. However, similar to shallow convections, the CCN effect on the strength of deep convection, such as cloud top height, updrafts, and cloud coverage, is also non-monotonic. When CCN concentration is extremely high, a further increase in CCN concentration leads to an insignificant or even opposite effect on the strength of deep convection [33,39,40]. One of the possible reasons is the enhanced evaporation of smaller droplets in the polluted conditions [39], which is similar to that in shallow cumulus [25]. Precipitation can also decrease with increasing CCN because of the stronger sublimation of ice particles (including ice, snow, and graupel) and the stronger evaporation of raindrops as they fall in the dry air [41].

For cumulus congestus, although the cloud top is generally near or even above the 0 °C level, warm cloud processes are more important than the mixed-phase processes. This is because many of the cumulus congestus may not glaciate until the temperature is colder than −15 °C [42]. Ice water content in the cumulus congestus is generally one or more orders of magnitude less than the liquid water content, e.g., [1,4]. Cumulus congestus can also be invigorated by the increased CCN, similar to the deep convective cloud. In the more polluted conditions, Li et al. [43] revealed the potential that more cumulus congestus strengthens into deep convective clouds, which produce heavy precipitation. Sheffield et al. [4] found that the increased CCN concentration leads to larger liquid and ice water content, stronger updrafts, and higher cloud top. However, the enhanced latent heat release through vapor condensation rather than droplet freezing contributes most to the invigoration of cumulus congestus by aerosols because nearly no ice phase process is involved [4,43]. The non-monotonic CCN effect is also found for cumulus congestus cases. The extremely high CCN concentration leads to a weaker cumulus congestus due to the enhanced evaporation near the cloud edges [27], which is in good agreement with the results for shallow convection and deep convection.

Although the effects of CCN on convective clouds and its precipitation have been examined by many observational and modeling studies, they are rarely considered in cumulus parameterizations used in large-scale models. Many cumulus parameterizations, e.g., [44,45,46], assume that the precipitation production is proportional to the vertical flux of cloud water in the updraft and simplify the proportion to be a constant of 0.002 m⁻¹, e.g., [44,45]. Previous studies suggest that the CCN effect can change the precipitation production efficiency, so the constant assumption may be unrealistic. This study will quantitatively analyze how CCN affects the precipitation production efficiency.

The purpose of this study is to investigate the response of the cumulus congestus and its precipitation to CCN concentration. We study the dominant processes in the development of cumulus congestus under different aerosol conditions. We also study how CCN concentration affects the relationship between the precipitation production rate and the vertical flux of cloud water. Section 2 introduces the model and case used in this study. Section 3 shows the non-monotonic response of cumulus congestus to CCN concentration and analyzes the dominant microphysical and thermodynamical processes in the development of the cumulus congestus under different CCN concentrations. Section 3 also investigates the impacts of CCN concentration on precipitation production efficiency. The conclusion and discussion are given in Section 4.

2. Model and Case

This study uses the Weather Research and Forecasting (WRF) Model version 3.6.1 to perform a series of idealized simulations of a cumulus congestus case. An ellipsoid bubble (potential temperature perturbation) is released at the center of the domain and at the height of 0.5 km at the beginning of the simulation. The horizontal and vertical radii of the ellipsoid bubble are 3 km and 0.5 km, respectively. The potential temperature is 1.5 K higher at the bubble center than the surrounding environment and gradually decreases to the potential temperature of the environment. The warm bubble perturbation is widely used to trigger convective clouds in idealized simulations [27,47,48].

The simulations are initialized homogenously in the horizontal direction. The initial profile is based on the sounding at 00 UTC, 22 July 2022, at Shaowu station (117.47° E, 27.33° N). Figure 1 is the skew-T diagram of the initial profile. The lifting condensation level (LCL) is at about 1.4 km, which can be considered as the theoretical cloud base of the convective cloud. The simulated cloud base height is about 1.5 km and is almost constant with time during the whole life time of the convective cloud. The convective available potential energy (CAPE) is 1324 J kg⁻¹, and the convective inhibition (CIN) is negligible. The strongest simulated cloud has a cloud top up to 7–8 km (about −15 °C). Wind shear is not considered for simplification. Some sensitivity studies with a different sounding (e.g., the idealized sounding used by Weisman and Klemp [49]) and with different warm bubble sizes (e.g., horizontal radii of 0.5–10.0 km and vertical radii of 0.5–2.0 km) have been carried out. It is found that the CCN effects on the cumulus congestus are qualitatively the same.

The domain size is 20 × 20 × 15 km³ with a horizontal resolution of 100 m. In the vertical direction, 150 vertical layers are used, and the vertical resolution varies from 63 to 143 m. A smaller region of 6 km × 6 km, which covers the whole cloud in all simulations, is used to calculate the horizontal mean quantities. All simulations last for 2 h, which is long enough to cover the whole lifetime of the cumulus congestus in this study. The simulation results are output every 1 min.

The microphysical processes are parameterized with the NSSL scheme, e.g., [50,51]. It is a two-moment bulk microphysics scheme developed by the National Severe Storms Laboratory (NSSL) of the National Oceanic and Atmospheric Administration (NOAA). The NSSL scheme is widely used by previous studies to investigate the microphysical processes and/or the aerosol effects on convective clouds, e.g., [51,52,53]. The NSSL scheme can predict both the mass and number mixing ratios of five hydrometeors (cloud water, rain, cloud ice, snow, and graupel). In addition, the NSSL scheme predicts the number mixing ratios of two types of aerosols: one represents CCN and the other represents ice nuclei (IN). The aerosol scavenging is treated by removing the aerosol particles that are converted to droplets or ice crystals at each time step and each grid cell. The aerosols are transported by the flows and can be transported into the domain from the boundaries. No surface emission of aerosols is considered. The parameterizations of radiation, surface layer, boundary layer, and cumulus are not considered.

In the NSSL scheme, cloud droplet activation is parameterized based on the relationship $N_{CCN}=CCN\_C·S^k$ [54], where the parameter CCN_C is the number concentration of active CCN at 1% supersaturation with respect to water. It is a variable that can be measured in the field. CCN_C is the prognostic variable for describing the total amount of CCN in the NSSL scheme. S is the supersaturation with respect to water and is diagnosed by the NSSL scheme at the cloud base and within the cloud, as described by Mansell et al. [50]. The parameter k is the CCN activity property of aerosol. Ice nucleation can occur through homogenous freezing, deposition–nucleation/condensation–freezing, immersion freezing, and contact freezing. However, in our simulations, the overall ice formation rate is very low. As a result, ice water content (including ice, snow, and graupel) is several orders of magnitude lower than liquid water content (including cloud water and rainwater), which is consistent with previous studies, e.g., [4]. Therefore, the analysis in this study focuses on the liquid phase only.

CCN_C and IN number concentration are initialized homogenously in the horizontal direction in the whole domain. Aerosols are usually observed to be well mixed in the boundary layer near the surface, where the concentration is close to a constant. Above the boundary layer, the aerosol concentration generally decreases exponentially with altitude, e.g., [55]. In this study, the number concentrations are constant from the surface to 850 hPa and decrease exponentially with height with a scale height of 3 km above 850 hPa [51]. The parameter CCN_C is observed to vary from 10 to 10⁴ cm⁻³ [56,57,58,59,60,61]. Accordingly, thirteen cases with initial CCN_C as 10, 25, 50, 75, 100, 250, 500, 750, 1000, 2500, 5000, 7500, and 10,000 cm⁻³ are simulated to represent the extremely clean to extremely polluted conditions. k varies from 0.3 to 2.0 in observations [57,58,59]. For all simulations in this study, k is fixed as 0.65, which is observed in the urban regions in South China [58], and similar values (0.6–0.7) are also observed in some relatively clean environments, e.g., [57]. Increasing CCN_C can significantly increase the number concentration of cloud droplets. For example, in this study, at 12 min (when the cloud just forms) and 2 km height (about 500 m above the cloud base), the cloud-averaged number concentration of cloud droplets (averaged over all grid cells with cloud mixing ratio higher than 0.01 g kg⁻¹ at 2 km height) is about 6.1, 32.7, 221.1, and 657.6 cm⁻³ when CCN_C is 10, 50, 500, and 5000 cm⁻³, respectively. The concentration of IN aerosols is initially set as 1 L⁻¹ near the surface in all simulations.

3. Results

In this section, we first present the CCN effects on the liquid water path (LWP), cloud top height, updraft velocity, precipitation rate, and accumulated precipitation amount. These parameters are widely used by previous studies to describe the strength of convective clouds (Section 3.1). We then analyze in detail how the varying CCN concentration affects these parameters by analyzing the temporal evolutions of the vertical cross sections of hydrometeor mixing ratio (Section 3.2), as well as the temporal evolutions of the condensation rate, evaporation rate, and conversion rate from cloud droplets to raindrops (Section 3.3). At the end of this section, we analyze how CCN affects the precipitation efficiency (Section 3.4).

3.1. The Response of Cumulus Congestus and Precipitation to CCN Concentration

For all the simulated cumulus congestus, the properties of cumulus congestus (e.g., the LWP, cloud top height, updraft velocity, and precipitation rate if nonzero) all increase with time in the developing stage, peak at the mature stage, then decrease with time when the cloud begins to weaken, and finally dissipate. Accumulated precipitation during the whole lifetime is also an important factor for convective precipitation. Therefore, we choose the maximum horizontally averaged (6 km × 6 km) LWP, the maximum cloud top height, the maximum updraft velocity, horizontally averaged accumulated precipitation amount, and the maximum horizontally averaged precipitation rate to describe the strength of cumulus congestus and its precipitation. The cloudy columns, which are defined as columns with the LWP greater than 100 g m⁻², cover about one third of the 6 × 6 km² domain in all cases when the cloud area is largest. The variation of those factors at different CCN concentrations are shown in Figure 2. The cloud top is defined as the highest grid point with hydrometeor mixing ratio greater than 0.01 g kg⁻¹.

The LWP of the cumulus congestus changes non-monotonically with increasing CCN concentrations (Figure 2a). The horizontally averaged LWP increases from 0.25 kg m⁻² to 0.42 kg m⁻² when CCN_C is increased from 10 to 50 cm⁻³, further increases to 0.62 kg m⁻² when CCN_C is increased to 500 cm⁻³, and decreases and then fluctuates between 0.51 and 0.55 kg m⁻² when CCN_C is further increased to 10,000 cm⁻³.

The variation of the cloud top height with CCN concentration is shown in Figure 2b. The cloud top height peaks at 7.8 km when CCN_C is 50 cm⁻³ and is lower for the other cases (e.g., when CCN_C is 10 and 75 cm⁻³, the cloud top height is about 7.2 km). When CCN_C is higher than 1000 cm⁻³, the cloud top is lower than 4.3 km (thus the cloud depth is lower than 3 km). It indicates that the extremely high CCN concentration can substantially limit the development of cumulus congestus, and the resulting cloud is actually a shallow cumulus. We note that the peak of the LWP is at CCN_C of 500 cm⁻³, while the peak of cloud top height is at CCN_C of 50 cm⁻³. This suggests that increasing CCN_C from 50 to 500 cm⁻³ leads to more hydrometeor concentrating in a thinner cloud.

The response of the maximum updraft velocity to increasing CCN concentration is shown in Figure 2c. Maximum updraft velocity increases from 11.3 to 14.1 m s⁻¹ with increasing CCN_C from 10 to 50 cm⁻³, then decreases with further increased CCN_C, and finally fluctuates when CCN_C is larger than 100 cm⁻³. The CCN effect on maximum updraft velocity is generally similar to that on the cloud top height.

Precipitation also varies non-monotonically with increasing CCN_C (Figure 2d,e). When CCN_C is increased from 10 to 50 cm⁻³ (relatively clean conditions), the accumulated precipitation amount increases from 0.23 to 0.44 mm, and the maximum precipitation rate increases from 0.72 to 1.56 mm h⁻¹. When CCN_C is further increased from 50 to 500 cm⁻³ (relatively polluted conditions), the accumulated precipitation amount decreases from 0.44 to 0.30 mm, while the maximum precipitation rate further increases from 1.56 to 4.86 mm h⁻¹. When CCN_C is increased from 500 to 1000 cm⁻³, both the maximum precipitation rate and the accumulated precipitation amount decrease to near 0. When CCN_C is even higher (very polluted conditions), surface precipitation is completely inhibited.

The temporal evolutions of precipitation rate are further analyzed in Figure 3. It is evident that when CCN concentration is relatively low (e.g., CCN_C < 100 cm⁻³), the precipitation has two peaks. As CCN_C becomes larger, the first peak is promoted but delayed gradually. However, when CCN_C is relatively high (e.g., 500–1000 cm⁻³), only one peak of precipitation exists. In the 500 cm⁻³ case, the maximum precipitation rate is strongest but only lasts for a very short period. We further define the beginning and ending of the surface precipitation with a threshold of 0.05 mm h⁻¹. When CCN concentration is increased, the precipitation starts later and ceases earlier (Figure 3b), leading to a shorter precipitation duration. For example, when CCN_C is 50 cm⁻³, surface precipitation begins at 26 min and ends at 64 min, lasting for 38 min; when CCN_C is 500 cm⁻³, surface precipitation begins at 9 min later but ends at 11 min earlier, thus the precipitation duration decreases by more than half. The significantly decreased precipitation duration leads to the decreased accumulated precipitation when CCN_C is increased from 50 to 500 cm⁻³, even if the maximum precipitation rate is increased.

3.2. The Evolutions of Cumulus Congestus under Different CCN Concentrations

Figure 4 shows the vertical cross sections at the center of the cumulus congestus in the four simulations with CCN_C of 10, 50, 500, and 5000 cm⁻³. Snapshots at 12, 24, 36, 48, and 60 min are chosen to examine the different stages of the cumulus congestus. The case with CCN_C of 10 cm⁻³ is chosen as an example to explain the typical evolution of a cumulus congestus under clean conditions (first row in Figure 4). At 12 min, the cumulus congestus just forms, the cloud top is at 2.3 km, and precipitation at the cloud base has not formed. As the cumulus congestus continues to develop, the hydrometeor mixing ratio gradually increases, and the cloud top increases to about 3 km at 24 min. Raindrops form and fall down to the surface, but the surface precipitation rate is still very small at this time. At 36 min, the cumulus congestus becomes mature, with a maximum hydrometeor mixing ratio of 2.7 g kg⁻¹. The surface precipitation is relatively strong, and the cloud top ascends to 4.8 km. At 48 min, the cloud top is even higher (about 7.2 km). The surface precipitation rate is still large, but the hydrometeors remaining in the cloud begin to decrease due to the depletion by precipitation. Another 12 min later, the cumulus congestus weakens, as is evident from the reduced hydrometeor content, smaller surface precipitation, and a slightly lower cloud top. When CCN_C is increased to 50 cm⁻³ (the second row in Figure 4), the evolution of the cumulus congestus is generally the same, but the maximum hydrometeor mixing ratio and the maximum surface precipitation rate are both larger (e.g., maximum hydrometeor mixing ratio is about 3.3 g kg⁻¹ at 36 min).

The evolution of the cumulus congestus when CCN_C is 500 cm⁻³ is shown with the third row in Figure 4. At 24 min, the cloud top is similar to those in the cases with CCN_C of 10 and 50 cm⁻³, but the hydrometeor mixing ratio is much higher (the maximum is about 2.5 times that in the case with CCN_C of 10 cm⁻³). However, nearly no precipitation occurs at the cloud base at this time. At 36 min, the cumulus congestus reaches the mature stage, with a much higher hydrometeor mixing ratio and stronger surface precipitation than that in the 10 and 50 cm⁻³, but the cloud top is slightly lower. The area of cloud and precipitation at the mature stage is also larger in this case than those in the 10 and 50 cm⁻³ cases. That is one of the reasons that both the horizontally averaged LWP and precipitation rate peak when CCN_C is 500 cm⁻³. At 48 min, the cumulus congestus significantly weakens with a much lower hydrometeor mixing ratio and surface precipitation than at the mature stage. However, the cloud top remains similar to that at 12 min earlier. This is quite different from the 10 and 50 cm⁻³ case, where the cloud tops are higher at 48 min than at 36 min. The results indicate that the cumulus congestus in the relatively polluted case dissipates earlier than in the relatively clean case. At 60 min, the cumulus congestus has dissipated completely.

When CCN concentration is extremely high (≥5000 cm⁻³), there is no precipitation at all, and the cloud begins to dissipate before it is fully developed. The cloud matures at about 24 min, much earlier than those in the cleaner cases, and its cloud top is lower than 4 km. The cloud becomes broken at about 40 min, which is much earlier than in the cases with CCN_C of 10, 50, and 500 cm⁻³, indicating a shorter lifetime. However, at about 48 min, new shallow cumulus forms, which do not appear in the cleaner cases.

3.3. The Mechanisms of CCN Effect on Cumulus Congestus

Figure 5 shows the horizontally averaged condensation rate, evaporation rate, net condensation rate, and conversion rate from cloud to rain (including both the autoconversion of cloud droplets to raindrops and the accretion of cloud droplets by raindrops) when CCN_C is 10, 50, 500, and 5000 cm⁻³. The grey solid lines indicate the cloud tops and cloud bases. The cloud base is defined as the lowest grid point with cloud water content higher than 0.01 g kg⁻¹. The black dashed contours in the first column indicate the region with strong updrafts, which are defined as the levels where the vertical velocity averaged over all ascending grid cells is greater than 1 m s⁻¹. Similarly, the black dashed contours in the second column indicate the region with strong downdrafts, which are defined as the levels where the vertical velocity averaged over all descending grid cells is less than −1 m s⁻¹. As mentioned earlier, only the warm cloud processes are analyzed due to the negligible contribution of the ice phase in this study.

We first examine the case with CCN_C of 50 cm⁻³ (second row in Figure 5). In the cloud, the net condensation rate is mainly positive, i.e., condensation is stronger than evaporation (Figure 5g). At the beginning of the cloud formation, condensation occurs near the cloud base, where the warm bubble just becomes saturated. In the later stages, condensation mainly occurs in the upper part of the cloud, where the updraft is strong. Before 45 min, condensation in the upper part of the cloud always dominates the evaporation, and hence the cloud top keeps ascending. The conversion of the cloud to rain begins at about 15 min (Figure 5h). In this case, CCN_C is still relatively low, and hence cloud droplets are generally large. Some of the cloud droplets become large enough shortly after activation and then can fall down to the surface directly from near the cloud base and form the first peak of precipitation. The remaining smaller cloud droplets ascend in the updrafts and keep growing until they become large enough to fall down from the upper part of cloud (much higher than the cloud base). They collect droplets along the falling path and reach the surface to form the second peak of precipitation. These rain droplets are larger than those in the first peak of precipitation because they undergo condensational growth for a longer time and collect more droplets as they fall. When precipitation appears below the cloud base after 20 min, evaporative cooling and downdrafts also develop below the cloud base (Figure 5f). When precipitation is relatively strong (30–40 min), the updrafts below the cloud base are completely inhibited and the downdrafts below the cloud base become stronger. As a result, the water vapor supply to the cloud is reduced. This reduces condensation and finally leads to the dissipation of the cloud.

In the case with a smaller CCN_C, e.g., 10 cm⁻³ (first row in Figure 5), the condensation and the evaporation of cloud droplets are both weaker (Figure 5a,b). This is because the number concentration of cloud droplets is lower and the size of cloud droplets is larger. In the developing stage, the net condensation rate in the cloud is weaker than in the case with CCN_C of 50 cm⁻³ (Figure 5c), which leads to weaker updrafts and hence a lower LWP and lower cloud top. Meanwhile, the larger cloud droplets lead to an earlier onset of conversion from cloud to rain, and the precipitation consequently begins slightly earlier. The earlier precipitation weakens the development of the cumulus congestus, which also contributes to the slightly lower LWP and lower cloud top. The lower LWP and thinner cloud layer provide less cloud water content and a shorter falling path for the growth of raindrops, which in turn results in weaker conversion from cloud to rain and hence weaker precipitation. As shown by the black line in Figure 3a, the precipitation rate in the second peak (at about 41 min) is stronger than that in the first peak (at about 30 min), but the evaporation rate near the surface is opposite (Figure 5b). That is because, as mentioned above, the rain droplets are generally much larger in the second peak. Larger droplets evaporate more slowly than the smaller ones. In addition, the larger droplets fall faster and hence contribute to stronger precipitation (the falling flux of hydrometeors near the surface) by shorter-time evaporation and stronger fall speed near the surface. In this case, we also note that the cumulus congestus does not dissipate quickly after the precipitation but lasts until the end of the simulation, which is different from the other cases. On the one hand, the precipitation rate is so small that only a small fraction of liquid water is removed from cloud; on the other hand, the evaporation of large cloud droplets is slow, and more droplets can remain in the cloud for a long time.

In the case with CCN_C = 500 cm⁻³ (third row in Figure 5), the more but smaller cloud droplets enhance the condensation at the early stage (Figure 5i). The enhanced condensation increases the hydrometeor mixing ratio, as well as the LWP. At the early stage, the cloud droplets are too small to fall, and hence no precipitation forms. Nearly all cloud droplets ascend in the updrafts. They start to fall down only when they ascend to the higher levels and become large enough in the later stage. As they fall, they collect droplets along the falling path, so the conversion from cloud to rain only occurs at the upper cloud at the mature stage of cumulus congestus (Figure 5l), rather than near the cloud base at the early stage (as in Figure 5d,h). As a result, only one peak of precipitation forms (Figure 3a). The strong precipitation produces strong evaporation under the cloud base and, thus, cuts off the water vapor supply. Both the stronger evaporation of cloud droplets and the stronger evaporation of rain drops below the cloud base (Figure 5j) cause the earlier dissipation of the cumulus congestus and earlier ending of precipitation. It is also seen that the cloud top in the case with CCN_C = 500 cm⁻³ is lower than the cases with smaller CCN_C. This is due to the significantly enhanced evaporation near the cloud top (Figure 5k). In addition, these rain droplets at the peak of precipitation (about 38 min) are generally larger than those in the low CCN cases because they undergo condensational growth for a longer time and collect more droplets as they fall. The larger droplets evaporate slower and fall faster. Therefore, the maximum evaporation rate near the surface in this case is only slightly higher than that in the low CCN cases (compare Figure 5j with Figure 5b,f), although the maximum precipitation rate is much stronger (Figure 3a).

In the extremely polluted conditions (≥5000 cm⁻³), the cloud droplets are so small that they evaporate easily at cloud top and cloud edges. Therefore, the cumulus congestus is not able to fully develop, leading to a much lower cloud top. At the same time, the cloud droplets are too small to trigger the warm rain formation process, producing no precipitation at all. However, the quick evaporation of cloud droplets moisturizes the environment in the cloud layer (about 1.5 to 2.8 km), and the CAPE is barely consumed. This hence facilitates the formation of subsequent clouds, which is similar to previous studies [8,9,10,11]. Once there is a slight disturbance of vertical velocity near the cloud base, the new cloud will easily form.

3.4. The Parameterization of CCN Effect on Precipitation Production Efficiency

The precipitation production efficiency (C), which is the ratio between the cloud-to-rain conversion rate and the vertical cloud water flux in the updrafts, is usually assumed a constant in cumulus parameterization schemes, e.g., [44,45,46]. As mentioned in Section 1, the CCN effect substantially changes the formation of precipitation. Therefore, the precipitation production efficiency should also vary with CCN concentration. Here, the high-resolution simulation results are used to calculate the precipitation production efficiency and investigate how it is affected by CCN. We define the cloudy updraft as the region where the cloud water mixing ratio is greater than 0.01 g kg⁻¹ and the vertical velocity is greater than 0.01 m s⁻¹. The precipitation production efficiency is calculated as the ratio between the conversion rate from cloud water to rain water averaged over the cloudy updraft and the vertical cloud water flux averaged over the cloudy updraft. In every simulation, a value of precipitation production efficiency is calculated for each time and each height.

Figure 6 shows the mean values of the precipitation production efficiency, along with its 10th and 90th percentiles for all simulations. It is obvious that C is not a constant. On the one hand, the precipitation production efficiency varies substantially within each case, as revealed by the large difference between the 10th and 90th percentiles within each case, especially in the relatively clean cases. On the other hand, the precipitation production efficiency decreases as CCN_C increases. In the case with CCN_C = 10 cm⁻³, the mean precipitation production efficiency is about 0.01 m⁻¹. When CCN_C is increased to 1000 cm⁻³, the mean precipitation production efficiency decreases to 4 × 10⁻⁵ m⁻¹. The usually assumed value of 0.002 m⁻¹ [44,45] occurs when CCN_C is 500 cm⁻³. We fit the mean precipitation production efficiency in each case as a function of CCN_C (only for the cases with non-zero precipitation). The R² is 0.97. The fitted function (blue line), which may be used in future cumulus parameterization schemes, is as follows:

$$C=-0.0023\times \mathrm{l}\mathrm{n}\left(CCN\text{\_}C\right)-0.015.$$

4. Conclusions and Discussion

This study uses a series of idealized simulations to study the cumulus congestus clouds with the initial CCN_C, which describes the CCN concentration, varying from 10 to 10,000 cm⁻³. It is found that the responses of the cumulus congestus properties and its precipitation to CCN concentrations are non-monotonic. When CCN_C is increased from 10 to 50 cm⁻³, the cumulus congestus is gradually strengthened, leading to heavier precipitation, a higher LWP, and a higher cloud top. The cloud top, updraft strength, and accumulated precipitation are all highest when CCN_C is 50 cm⁻³. When CCN_C is increased from 50 to 500 cm⁻³, the LWP and maximum precipitation rate both increase further, but the cloud top height decreases. When CCN_C is further increased, the cumulus congestus is gradually weakened, leading to weaker precipitation, a lower LWP, and a lower cloud top. When CCN_C is extremely high (≥5000 cm⁻³), the cumulus congestus cannot fully develop, resulting in no precipitation and a significantly lower cloud top than the cleaner cases.

Increasing CCN concentration leads to more but smaller cloud droplets, which enhances condensation in the cloud and evaporation near the cloud top and cloud edges, and delays the onset of the warm rain process. When CCN_C is increased from 10 to 50 cm⁻³, the enhanced condensation promotes the development of the cumulus congestus by producing more hydrometeor and releasing more latent heat to strengthen the updrafts. This leads to the higher LWP and higher cloud top of the cumulus congestus. Meanwhile, the delayed precipitation gives the cumulus congestus enough time to develop, which also leads to the higher LWP and higher cloud top. The higher LWP and higher cloud top provide more hydrometeor and longer falling path for the growth of raindrops, resulting in heavier precipitation. When CCN_C is further increased from 50 to 500 cm⁻³, the further enhanced condensation and delayed precipitation make more cloud water remain in the cloud, leading to the higher LWP and stronger precipitation in the later stage. However, the significantly enhanced evaporation near the cloud top significantly limits the vertical development of the cumulus congestus. As a result, the cloud top is much lower. The strong precipitation rate at the mature stage when CCN_C is 500 cm⁻³ inhibits the subsequent water vapor supply to the cloud and accelerates the cloud dissipation. When CCN_C is increased to be higher than 5000 cm⁻³, the cloud droplets are so small that they evaporate easily and cannot produce precipitation.

The non-monotonic effect of CCN concentration on cumulus congestus discussed in this study is similar to those found for both shallow convection and deep convection [25,27,39,40]. The results in this study are also consistent with the previous cumulus congestus study using a 1.5D cloud model [27]. This study uses a 3D model simulation to confirm that the enhanced droplet condensation can invigorate the cloud when CCN concentration is relatively low, in good agreement with previous studies, e.g., [4,43]. We further found the delayed warm rain formation to be another important mechanism through which cumulus congestus can be invigorated.

It was found that the CCN effect on the cumulus congestus relies on which parameters are used to describe the strength of the cumulus congestus. As seen in Figure 2, if we use the LWP and/or maximum precipitation rate to describe the strength of the cumulus congestus, we would conclude that the cumulus congestus is strongest when CCN_C is 500 cm⁻³. However, if we use the cloud top height, maximum updraft, and/or accumulated precipitation amount to describe the strength of the cumulus congestus, we would conclude that the cumulus congestus is strongest when CCN_C is 50 cm⁻³. All these parameters are frequently used in previous studies to describe the strengths of the clouds, and different studies usually use different parameters. Thus, the selection of parameters might be an important source of ambiguity in studying the CCN effect on clouds.

We also found that the precipitation production efficiency was not a constant in contrast to the usual assumption used by cumulus parameterization schemes. It actually decreases with the CCN concentration. This can explain the overestimation of warm convective precipitation in polluted environments to a certain extent. This also suggests that if the precipitation production efficiency based on the observation in a relatively clean maritime condition is used over the relatively polluted land, the precipitation may be overestimated. A simple relation between precipitation production efficiency and CCN concentration is obtained and can be used to improve cumulus parameterization schemes.