Effects of a Vertical Cloud Condensation Nuclei Concentration Explosion in an Idealized Hailstorm Simulation

Determination of the key vertical level for cloud condensation nuclei concentration (CCNC) explosions has been a long‐term issue in CCN‐cloud interaction studies. An idealized hailstorm is simulated with 37 sensitivity runs, including an initial CCNC grouping vertically from the ground to the cloud top, increasing from 100 to 3,000 mg−1. The results reveal a key zone from 750 to 800 hPa near the median boundary layer, where an explosion of CCNC plays a dominant role in the nonmonotonic response of the hail precipitation rate. The explosion of CCNC in this zone could initially result in the condensation of more water vapor into the clouds, which could be transported to a greater vertical extent to significantly affect the riming collection efficiency. However, the dominant zone for the total precipitation rate is wider at heights of 700–800 hPa due to the lower sensitivity of the riming collection efficiency.


Introduction
Hail is a product of a typical severe convective storm that threatens urban traffic, electricity, industry, personal safety, and so on worldwide (Brown et al., 2015;X. Li, Zhang, et al., 2018); hail is very sensitive to aerosols under specific conditions (Andreae & Rosenfeld, 2008;Rosenfeld & Woodley, 2000).From the perspective of cloud microphysics, understanding the sensitivity of hail formation to future aerosol changes and studying its corresponding response pose significant challenges.
As part of aerosols with strong hygroscopicity, cloud condensation nuclei (CCN) enable water vapor to condense into cloud droplets, which consequently affects larger hydrometeors, such as raindrops, ice crystals, graupels, and hailstones (Fan et al., 2016;Rosenfeld et al., 2014).The effect of CCN on hail has received much attention in recent scientific research, including the CCN-induced bias on hail predictability (e.g., X. Li et al., 2021) and longterm hail trends considering increased atmospheric pollution with more CCN (e.g., Fu & Dan, 2014).
The ability of CCN to alter the microphysics, dynamics, and precipitation characteristics of deep convective clouds has led to a growing interest in the effects of CCN on hailstorms (Q.Chen et al., 2019;Fan et al., 2016).An increase in CCN from atmospheric pollution seems to cause extreme weather, such as hail, to occur more frequently in parts of China (Fu & Dan, 2014).However, this approach is not certain due to the challenges in distinguishing aerosol-cloud interactions from meteorological covariates and uncertainties in observations (M.Li et al., 2016;Nishant et al., 2019).More mechanistic research, especially modeling, should be conducted (Fu & Dan, 2014) since the effect of CCN on hail predictability is significant and stronger than that of initial meteorological conditions (X.Li et al., 2021).As the cloud condensation nuclei concentration (CCNC) increases, hail may increase (e.g., Chen et al., 2019, considered 56% of the number of aerosols to be CCN), decrease (e.g., Barrett & Hoose, 2023, the CCNC was decreasing exponentially from the 4 km height), or increase and then decrease (e.g., X. Li et al., 2017, the CCNC was decreasing exponentially from the 2 km height).These studies did not use the same parameterization settings, and the vertical distribution of CCN may explain these differences.In the real atmosphere, the vertical distribution of CCN can be influenced by atmospheric pollution and meteorological conditions (Huang et al., 2014;Zang et al., 2023).High emissions of anthropogenic pollutants result in high CCNC below the atmospheric mixing layer (Z.Chen et al., 2020;K. Li, Zhang, et al., 2018), and the abundance of water vapor at low altitudes makes this region likely to have the most significant effect on CCNcloud interactions.The transport of air pollutants from other regions by strong winds leads to high CCNC explosions at higher altitudes (Bai et al., 2022;Kang et al., 2019), and the abundance of supercooled water makes this region likely to have a significant effect on hail precipitation.The vertical distribution of the CCNC is complex and variable; considering the significant differences in convective cloud processes in different vertical zones, there is likely a key vertical interval in which the CCN influences hail storms.Therefore, reducing the errors induced by the vertical distribution of the CCNC and identifying its critical vertical interval could be helpful in hail forecasting.
To better understand hail climatology in a future climate with variable aerosols, we need to find this critical zone to evaluate the effects of CCN on hail.In this paper, the sensitivities of different CCNCs and their vertical distributions during typical hailstorm weather are investigated via numerical modeling.A clean case is used as a control member, and six groups with six vertical zones are established.The simulation results accurately reveal the key CCN zones that affect hail and precipitation, providing a reference for hail forecasting.

Experimental Designs
In this study, an idealized hailstorm simulation via the Weather Research and Forecasting (WRF) model version 4.0.1 (Skamarock et al., 2019) was utilized.The initial weather sounding data for this typical hailstorm simulation were obtained from Li et al. (2017Li et al. ( , 2018Li et al. ( , 2021) ) and included the temperature, water vapor mixing ratio, and horizontal winds at different pressure heights.The model configuration (Text.S1 in Supporting Information S1) follows the methodology of Li et al. (2017).The formation of giant cloud droplets under special meteorological conditions is not considered in the model.The default parameterization scheme is used for ice forming nuclei concentrations.A total of 37 aerosol scenarios were set up.The surface CCNC concentration was set to 100 mg 1 in the control member, and the value decreased exponentially with altitude.The remaining 36 members were divided into six groups (Figure 1a-1f).Considering the key heights that can affect the participation of the CCNC in the hail formation process during an actual weather process, 800 hPa was used to represent the median boundary layer (Text.S1 in Supporting Information S1) in the heat bubble region (Figure 1, red dashed line); 750 hPa was used to represent an atmospheric boundary layer (Figure 1, green dashed line); 700 hPa was used to represent the cloud bottom height (Figure 1, blue dashed line); 500 hPa was used to represent a layer height of the 0°C layer (Figure 1, pink dashed line); and 200 hPa was used to represent the maximum height of the cloud top (Figure 1, cyan dashed line); these values are taken as vertical demarcation criteria.As a result, these six groups are set up with CCNC explosions occurring at 200-500 hPa (group A), 500-700 hPa (group B), 700-750 hPa (group C), 750-800 hPa (group D), 800 hPa-ground (group E), and all vertical layers (group F).Each group had six members, named 1-6, corresponding to CCNC values of 100, 300, 500, 700, 1,000, and 3,000 (mg 1 ).

Responses of Hail Precipitation and Total Precipitation
The effect of CCNC explosion at the initial moment in different vertical zones on hail precipitation (Figure 2) is extremely significant (Text.S2).The hail precipitation rate ranged from 0 to 0.22 mm/min (Figure 2 con and F2) with changes in the CCNC.Compared with other sensitive vertical zones, the nonmonotonic response of the hail precipitation rate to varied CCNC occurred only in group D (750-800 hPa), which was consistent with group F (all vertical layers), with peaks at CCN700 and CCN300 (Figure 2).However, they all increased monotonically in the remaining four groups.Moreover, the peak value of the hail precipitation rate in this group member reached 1.8 mm/min, which was more than twice that in the other groups.The degree of criticality (Text.S1) was constructed to determine the critical vertical zones, and zones with a criticality greater than 1 were considered to be critical vertical zones.The degree of criticality from 750 to 800 hPa for hail precipitation is approximately 6.9, whereas that of all other zones is less than 1.Therefore, the critical vertical region for determining the effect of CCN on the hail precipitation rate occurs at 750-800 hPa.This height is slightly lower than the height of the cloud base and 700-750 hPa where the center of the heat bubble is located.
The effect of CCNC explosions on the total precipitation rate in different vertical zones is not as significant as that of hail, ranging from 0.7 mm/min to 3.3 mm/min.The criticality degrees of 2.3 and three in group C and group D, respectively, are the critical zones for total precipitation.The critical zones for hail precipitation are narrower and more critical than those for total precipitation (Text.S3 in Supporting Information S1).This finding indicates that the impact of CCN explosions is more concentrated in the critical vertical region and that the uncertainty in the forecast of hail precipitation is greater than that in the total precipitation.In other words, the operational zone over which CCN explosions can artificially affect hail may be narrower than that of rain precipitation.

Cloud Characteristics
The difference between the hail and total precipitation rates is due to the evolution of the characterization within the cloud.Similar to the hail precipitation rate, 750-800 hPa is the key zone in which CCNC explosions affect hail mixing ratios and hail number concentrations (Fig. S1 in Supporting Information S1), with a rapid increase in the peak hail mixing ratio from 0.25 to 1.5 (mg kg 1 ) and a maximum hail number concentration from 5 to 65 (10 3 kg 1 , Fig. S1 in Supporting Information S1, 750-800 hPa).The higher hail mixing ratio and hail number concentration produced in the clouds make 750-800 hPa a critical zone for CCNC explosions in terms of affecting hail precipitation.Unlike the hail precipitation rate, the hail mixing ratio and the hail number concentration increased monotonically with increasing CCNC in group D (Fig. S1 in Supporting Information S1, 750-800 hPa), while the peak was delayed from CCN300 to CCN700, although with a nonmonotonic response.In group F (Fig. S1 ALL in Supporting Information S1), the hail number concentration and the hail mixing ratio increased simultaneously with increasing CCNC, which was essentially a positive correlation.However, in groups D and F, after the hail precipitation rate peaked (CCN700 and CCN300; Fig. S1 D4 and F2 in Supporting Information S1), the hail mixing ratio increased slowly or decreased, but the hail number concentration increased substantially.Overall, as the amount of CCNC increased, the peak concentrations appeared in the order of the hail precipitation rate, hail mixing ratio, and hail number concentration from front to back.A more detailed analysis of in-cloud features is needed to determine why these peaks do not occur simultaneously.
Hail generation took approximately 30 min.Some members had two peaks in the hail mixing ratio over time.The two peaks were most pronounced for members of group F. Members F2 and F4 (Fig. S1 F2 and F4 in Supporting Information S1) had pre-peaks and post-peaks in hail mixing ratios and hail number concentrations, respectively (the same characteristics were found in D4 and D6 in group D).This finding suggests that hail forms by two different processes.The process through which hail is first produced is the main source of hail precipitation, and the hail precipitation rate peaks in the lower CCNC members.The critical zone at which 750-800 hPa CCNC explosions affect the hail precipitation rate is because this process is more intense.The process that produces hail afterward has a higher hail number concentration at the same hail mixing ratio, which shows that it produces smaller hail and peaks in higher CCNC members.This process results in the peak hail mixing ratio and hail number concentration lagging behind the hail precipitation rate.Hail production was significantly delayed after the hail precipitation rate peaked (F2 and D4), likely because the previous hail-forming process weakened.The hail mixing ratio and hail number concentration appeared between 1 and 10 km; however, the high-value area was always concentrated between 4 and 6 km, which proved that this interval was the area of hail formation (Fig. S1 in Supporting Information S1).The front peak is slightly greater than the back peak, which proves that there is some difference between the two processes in the vertical interval of hail formation.Additional cloud characterization ), for the members in Figure 1 and the control members.The seven colors correspond to the control members (black line) and the six CCNC include 100 mg 1 (purple line, 1), 300 mg 1 (blue line, 2), 500 mg 1 (blue-green line, 3), 700 mg 1 (yellow line, 4), 1000 mg 1 (red line, 5) and 3000 mg 1 (deep red line, 6).Cr represents the degree of criticality for each zone.
of the water condensate (Text.S4 in Supporting Information S1), and analyses of hail formation processes are needed to determine the specific mechanisms involved in hail formation.

Cloud Process
The source of hail can be determined from the differences in each water condensate within the cloud; however, the exact influence process needs to be analyzed by cloud microphysical processes.The CCN microphysical effects on all other hydrometeor fields are essential for the generation and growth of hail (Figure 3).The two most important hail-increasing processes are the collection of rainwater by hail and the collection of cloud droplets by hail, followed by the conversion of graupel to hail (Figure 3).This finding shows that CCN affects hail mainly through two pathways; CCN-cloud-hail (the collection of cloud droplets by hail) and CCN-cloud-rain-hail (the collection of rainwater by hail), and these two processes correspond to the two peaks that occur before and after the hail mixing ratio, respectively.Based on the characteristics of the variations in the cloud and rain mixing ratios with the number concentration, the front peak corresponds to rainwater collection by the hail process, and the back peak corresponds to cloud droplets collection by the hail process.This finding is evidenced by the time-height variation plots for the cloud droplets collection by hail (Fig. S2 in Supporting Information S1) and the rainwater collection by hail (Fig. S3 in Supporting Information S1).For these two main hail formation processes, the contribution of group D is approximately 80% at CCN100 (Fig. S4 in Supporting Information S1).As CCNC increases to 3,000 mg 1 for the cloud droplet and rainwater collection by hail processes, the contributions of group D decrease to approximately 50% and approximately 30%, respectively (Fig. S4 in Supporting Information S1).The contribution of group D to the hail precipitation rate (Figure 2) was essentially the same as that to rainwater collection by the hail process (Fig. S5 in Supporting Information S1), but less than that to the droplet collection by the hail process (Text.S3 in Supporting Information S1).These results demonstrate that hail precipitation originates from the collection of rainwater via the hail process (Figure 3), known as the CCN-cloudrain-hail pathway.The conversion of graupel to hail, although at a lower rate than the collection of cloud droplets and rainwater by hail processes, produces hail embryos that may be larger (Barrett & Hoose, 2023) and thus may also play a certain role in the hail precipitation rate.The domain-averaged mixing ratio of graupel to snow shows that graupel forms before snow, proving that the graupel formation process originates mainly from frozen droplets.The path of hail formation at this time is either CCN-cloud-rain-graupel-hail or CCN-cloud-graupelhail.
The CCN condenses water vapor into clouds that collide with rain, setting the basis for the formation of hail.A higher CCNC would lead to more numerous cloud droplets and therefore small sizes.The rate of coalescence of cloud droplets into raindrops (autoconversion) slows so that more water can reach heights below the 0°C level, promoting hail production (Rosenfeld et al., 2008).This change was expressed as a decrease in low-altitude rainfall and an increase in high-altitude rainfall (Fig. S6 in Supporting Information S1).This result explains the hail precipitation rates in Group F (Figure 2) but not the differences in the critical vertical zones or latent heat of condensation (Fig. S7 in Supporting Information S1) for CCNC explosions.The latent heat of condensation increases with increasing CCNC, demonstrating the existence of a mechanism that causes additional condensation (Fig. S7 in Supporting Information S1).The vertical distribution of the CCNC has almost no effect on the minimum cloud bottom height or the maximum cloud bottom temperature, so the volume and strength of the updraft are key to the involvement of low-level CCNs in condensation.The convection triggered by the initial heat bubble is determined, and if the CCNC explosion is too low, it becomes challenging to initiate the condensation process (group E).To assess the intensity of the convection, we consider the updraft volume of the region exhibiting radar reflectivity exceeding 35 dBZ and a updraft velocity greater than 10 m s 1 .As the CCNC concentration increases, the maximum updraft volume exhibits a similar trend in Fig. S8 in Supporting Information S1 to that showed in the hail precipitation rate in Figure 2. Latent heat from condensation and freezing (Figs.S7 and S9 in Supporting Information S1) causes updrafts (Mansell & Ziegler, 2013).These updrafts and initial heat bubbles generated by condensation near the base of the cloud play similar roles.once again causing low-level CCN and water vapor to rise to the height of the cloud base and condense.A sufficient CCN below the cloud base altitude allows this process to occur repeatedly, creating a cycle (groups C and D).The condensation of CCN caused by this cycling process is more important than the condensation of CCN in regions above the altitude of the cloud base.The cyclic process of updrafts carries CCN along with water vapor to the cloud base altitude at low altitudes, thus bringing more water vapor condensation.The 750-800 hPa zone is a critical vertical zone for CCN to influence hail because of the abundance of water vapor and its ability to be moved by updrafts to cloudbottom heights to produce condensation.After the peak of the hail precipitation rate (Figure 2), the maximum updraft slowly decreased as the hail precipitation rate decreased (Fig. S8 in Supporting Information S1).The excessively high CCNC causes the freezing latent heat generation height to rise above 8 km (Fig. S9 in Supporting Information S1), which prevents updrafts from being generated (X.Li et al., 2017).The hail precipitation rate also begins to decrease at this time, but the decrease occurs much faster.Therefore, there are other reasons for the decrease in the hail precipitation rate.
The 750-800 hPa CCNC explosion produced a stronger updraft, which brought more condensation and freezing through the circulation process and therefore produced higher marginalization rates (the highest riming rates were found in the D4 member, Fig. S8 D4 in Supporting Information S1).The 700-750 hPa CCNC explosion produced a relatively low rate of riming (Fig. S8 C6 in Supporting Information S1).The hail precipitation rate is extremely sensitive to changes in riming collection, whereas the total precipitation rate is not sensitive.Thus, the critical vertical zone for CCNs on the hail precipitation rate is narrower than that on the total precipitation rate (Figure 2).As CCNC increases, the rate of riming shows a nonmonotonic response of low-high-low.At a CCNC that is too low, there is a lack of high-altitude clouds (Fig. S10 in Supporting Information S1) and rain (Fig. S6 in Supporting Information S1) due to updraft limitations (Fig. S8 in Supporting Information S1), and the rate of riming is slow.As the CCNC increases, sufficient updrafts bring adequate clouds (Fig. S10 in Supporting Information S1) and rain (Fig. S6 in Supporting Information S1), and both the collection of cloud droplets and rainwater by hail (Figure 3) processes increase.Since raindrops are larger than cloud drops, hail embryos absorb raindrops with a high rate of riming.Therefore, hail precipitation is dominated by the collection of rainwater by hail, at which time the rate of hail precipitation reaches its peak (Figure 2).When the CCNC is excessive, too much CCN diverts the limited water vapor, forming clouds with smaller droplet sizes and making collisions with rain difficult.Airborne rain is substantially reduced (Fig. S6 in Supporting Information S1), but excess clouds (Fig. S10 in Supporting Information S1) cause the cloud droplet collection by hail to be the dominant process for hail production (Figure 3).The collection of cloud droplets by the hail process generates smaller hail embryos, so the hail number concentration peaks (Fig. S1 in Supporting Information S1).Moreover, smaller cloud droplets reduce the riming collection rate, resulting in a lower rate of hail precipitation (Figure 2).Therefore, changes in the rate of riming are directly responsible for the influence of CCN over the hail precipitation rate.

Conclusions
In this study, 37 different members, divided into member controls and 36 members in six different vertical zones and six CCNC explosions were established via a 3D idealized hail simulation.The effect of the CCNC and vertical intervals of the explosion at the initial moment on the hail properties is investigated considering cloud characteristics and cloud processes.The conclusions are described as follows.
1.The 750-800 hPa interval is a key zone for the CCN to influence hail, with a criticality of 6.9.This zone is located in the lower part of the heat bubble between 500 and 1,000 m from the cloud bottom and the center of the heat bubble (approximately 700 hPa).There is a nonmonotonic response of the hail rate to CCNC in this zone, and the hail precipitation rate peaks at 1.8 mm/min at member CCN700, which is more than twice as high as that in the other zones.The cycling process of hail impacts from CCNC explosions at low altitudes is key to bringing about more hail, where condensation (freezing) processes and updrafts reinforce each other.The 750-800 hPa altitude zone can initiate cycling and drive sufficient water vapor and is therefore a key vertical region for hail impacts from CCNC explosions.2. The dominant zone of CCN that affects hail precipitation is narrower than that of total precipitation and is more critical in the dominant zone for hail precipitation.The critical zone of CCN influence on total precipitation is 700-800 hPa (groups C and D), with criticality levels of 2.3 and 3. Hail precipitation is more sensitive to changes in riming collection efficiency than total precipitation is.An explosion of CCN at 750-800 hPa results in a high riming collection, leading to a significant effects on both hail and total precipitation rates.The 700-750 hPa CCN explosion leads to a slightly lower riming collection, which leads to a significant reduction in the hail precipitation rate, whereas the total precipitation rate is not sensitive to this difference.3. Hail precipitation rates, hail mixing ratios, and hail number concentrations exhibited varying responses to CCN explosions.Three peaks were observed successively with increasing CCNC.Hail precipitation rates ranged from 0 to 0.22 mm/min with changes in CCN explosion.Moreover, the hail mixing ratio range and hail number concentration were 0-1.5 (mg kg 1 ) and 75 (10 3 kg 1 ), respectively.The main path through which CCNs influence hail precipitation is the CCN-cloud-rain-hail path, which corresponds to the collection of rainwater by the hail process, followed by the CCN-cloud-hail path, which corresponds to cloud droplets collection by the hail process.In addition, the conversion of graupel to hail also has an important influence on the path.
This study is only a preliminary exploration of the laws that govern the vertical interval of CCNC explosions affecting hail.The moment of CCNC explosion in this model is the initial moment before the start of the cloud process, but in the actual air pollutant, CCNC explosion can occurred at any time.Therefore, additional members are needed in the future to consider the effects of CCNC explosions on hail formation at different moments after convection generation.Simplifications of the actual process by the microphysics scheme may also have an impact on these conclusions, for example, frozen raindrops are directly considered to be graupel particles.The conclusions of the study must be verified in real cases.A series of physical parameterization schemes that are ignored here need to be discussed during migration from the ideal case to the real case.It is debatable whether the CCNC effect is under the synergistic influence of increased radiation, boundary layer processes, and surface and ground processes.
In this hail case, 750-800 hPa is the key vertical zone where CCN explosions affect hail.However, during different hail storms, the critical zone should vary relative to the different cloud-bottom heights and the location where convection occurs (where the heat bubble is released in the model); this relative location may be more important than the specific 750-800 hPa zone.To determine the effect of the cloud-bottom height and the location of convection generation on the critical vertical region, the release height of the thermal bubbles was increased to 2,000 m, and the remaining setup was consistent with the original configuration.The hail precipitation rates indicate that the elevation of the heat bubble weakens the hail in group F. The 700-750 hPa zone has the strongest effect on hail from CCN explosions, demonstrating that the critical zone where CCNs affect hail precipitation is related to the convection generation location.The position of 750-800 hPa relative to the heat bubble is similar to that of the original model's 800 hPa-ground zone; however, the CCN explosions in this region still significantly affect hail precipitation.Therefore, the region located in the lower part of the heat bubble with sufficient water vapor and close to the height of the cloud bottom is most likely to be the key vertical region in which CCN explosions affect hail, and additional studies are needed to verify this conclusion.This study was supported by the National Natural Science Foundation of China (Grant 42005005 and 42030607), the Science and Technology Department of Shaanxi Province (2024JC-YBQN-0248), the Education Department of Shaanxi Province (23JK0686), the Xi'an Science and Technology Project (22GXFW0131), and the Young Talent Fund of the University Association for Science and Technology in Shaanxi (20210706).This work was conducted on the highperformance computing platform at the College of Urban and Environmental Sciences, Northwest University, Xi'an, China.
the explosion of cloud condensation nuclei concentration in different vertical layers • The exploded cloud condensation nuclei concentration near the median boundary layer controls the sensitivity of hail precipitation • The dominant vertical zone of the cloud condensation nuclei concentration effect on hail is narrower than that on rain Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.Vertical distribution of CCNC in panels A-F with explosion intervals of 200 hPa (near maximum cloud top, cyan dashed line)-500 hPa (near average 0°C layer, pink dashed line), 500-700 hPa (near minimum cloud bottom, blue dashed line), 700-750 hPa (near average atmospheric boundary layer, green dashed line), 750-800 hPa (near median boundary layer in the heat bubble region, red dashed line), 800 hPa-ground, and all vertical layers from the initial moments of the control experiment (cloud base and cloud top from all moments).

Figure 2 .
Figure 2. Maximum values of the 95% quantile of the hail precipitation rate (a) and the total precipitation rate (b) in the effective area (hail precipitation or total precipitation >0) of the domain (in mm min 1 ), for the members in Figure1and the control members.The seven colors correspond to the control members (black line) and the six CCNC include 100 mg 1 (purple line, 1), 300 mg 1 (blue line, 2), 500 mg 1 (blue-green line, 3), 700 mg 1 (yellow line, 4), 1000 mg 1 (red line, 5) and 3000 mg 1 (deep red line, 6).Cr represents the degree of criticality for each zone.

Figure 3 .
Figure 3. Line charts showing the average rates of the individual processes in the overall hail-increasing process and the net increase, in kg kg 1 s 1 , on a natural logarithmic scale, for the members in Figure 1 and the control members.The hail-increasing process includes the following individual processes: deposition of vapor to hail (DPV), collection of cloud droplets by hail (ACC), collection of rainwater by hail (ACR), collection of ice crystals by hail (ACI), collection of snow by hail (ACS), and conversion of graupel to hail (CNG).