Freezing Nucleus Spectra for Hailstone Samples in China From Droplet Freezing Experiments

Ice nucleating particles (INPs) can be important for deep convective storms through affecting microphysical, thermodynamical, and radiative properties and precipitation. Since the mass of a hailstone is predominantly contributed by supercooled cloud droplets, INPs in supercooled cloud droplets during deep convective storms can be indicated from INPs in hailstones. In this study, hailstones are collected from eight deep convective cases in three regions of China, and immersion freezing INPs in hailstones are measured using droplet freezing experiments over a wide temperature range from −27.5°C to −4.0°C. INP concentrations can vary by 2–3 orders of magnitude, which is consistent with the result in a previous study on hailstones for the same eight cases that insoluble aerosol number concentrations in hailstones also have a variability of 2–3 orders of magnitude. Using the fitting method, three INP modes are suggested to be included for most hailstone samples, while one to two INP modes can be good enough for a couple of hailstone samples. Furthermore, the INPs for warmer mode are more heat‐sensitive, indicating possible existence of proteinaceous biological species.


Introduction
Ice nucleating particles (INPs) are required for primary ice formation at temperatures between 38°C and 0°C in the atmosphere.Observations have revealed that the existence of effective INPs, such as biological aerosol, dust, pollution, and smoke, can enhance the frequency of ice-containing clouds (Creamean et al., 2013;Kanitz et al., 2011;Tan et al., 2014;Rosenfeld et al., 2011;Yin et al., 2021).Numerical simulations have also suggested that the properties of INPs, such as their ice nucleating abilities and number concentrations, can largely impact cloud and climate (Burrows et al., 2022;DeMott et al., 2010).In mixed-phase stratocumulus clouds, INPs with a better ice nucleating ability can produce primary ice at higher temperatures, leading to faster cloud dissipation (Fu & Xue, 2017).Increasing INP concentrations in mixed-phase stratocumulus clouds can produce more ice and consume more supercooled liquid water, which can also lead to cloud dissipation (Eirund et al., 2019;Fu & Xue, 2017;Lee et al., 2021;Ovchinnikov et al., 2014;Xie et al., 2013).In deep convective storms, INPs with steeper temperature dependence can lead to less freezing at lower mixed-phase altitudes, promoting the transport of supercooled liquid water to upper cloud levels, and lead to more freezing at upper mixed-phase altitudes, resulting in a higher outgoing radiation (Hawker et al., 2021).Increasing INP concentrations in deep convective storms can produce more ice and enhance depositional growth and riming processes, leading to greater updrafts, deeper anvils, and more precipitation (Q.Chen et al., 2019;Connolly et al., 2006;Fan et al., 2017;Van den Heever et al., 2006;Y. D. Zhang et al., 2021).
Airborne INPs have been widely investigated directly from air samples in the recent decades.It has been found that the main species of airborne INPs include bacteria, pollen, mineral dust, and soot (Hoose & Mohler, 2012;Kanji et al., 2017;Murray et al., 2012).The dominant species of immersion freezing INPs changes with temperature.Under most circumstances, the dominant species of immersion freezing INPs is biological aerosols at temperatures above 15°C (or even above 20°C), and is mineral dust particles at temperatures between 30°C and 20°C (J.C. Chen et al., 2021;Hartmann et al., 2020;Ladino et al., 2019;O'Sullivan et al., 2018;Santl-Temkiv et al., 2019;Si et al., 2019;Suski et al., 2018).Under some specific conditions, such as in wildfire plumes, organic compositions of soot can be the dominant species of immersion freezing INPs at temperatures between 30°C and 20°C (Barry et al., 2021).For the suburban environment in Beijing, anthropogenic organic compositions can be the dominant species of immersion freezing INPs at 30°C (Tian et al., 2022).Under most conditions, air samples are a mixture of these main species that generally have different ice nucleating abilities, resulting in several individual "modes" with different temperature dependences in the INP spectrum over a wide temperature range (Creamean et al., 2019).For example, for air samples consisting of both primary biological aerosol particles (PBAPs) and mineral dust particles or other less efficient INP species, as the temperature decreases, the INP concentration shows a sharp increase at high temperatures where PBAPs are dominant, and shows a less sharp increase at low temperatures where mineral dust particles or other less efficient INP species are dominant (e.g., J. C. Chen et al., 2021;Suski et al., 2018).
Since INPs come from certain species of aerosols, the INP concentration usually varies with the concentration of those aerosols.For example, in the Arctic, the INP concentration at 10°C has a significant positive correlation with the concentration of bacterial-marker-genes (Santl-Temkiv et al., 2019).In a forest ecosystem in the United States, the INP concentration increases as the number concentration of PBAPs increases, and the positive correlation is stronger at higher temperatures (Huffman et al., 2013;Tobo et al., 2013).In the Canadian High Arctic, the INP concentration at 25°C has a good correlation with mineral dust tracers.In the dusty tropical Atlantic, the INP concentration is largely determined by dust loading (Price et al., 2018).In Israel and China, higher INP concentrations are observed during dust events than non-dust events (Ardon-Dryer & Levin, 2014; J. C. Chen et al., 2021).In these studies, the INP concentration can have a large variability when INPs are from the same source and the species of aerosols that dominates INPs does not change.When INPs are from different sources and the species of aerosols that dominates INPs may change, the variability of INP concentrations can be much larger (e.g., J. C. Chen et al., 2021;Reicher et al., 2019).
INPs in cloud hydrometeor samples can be more representative of in-cloud immersion freezing INPs than those from air samples.Measurements have found that the cloud hydrometeor (including cloud water, cloud rime, rain, and snow) has higher INP concentrations than the cloud-level air (Creamean et al., 2019;Gong et al., 2020;Pereira et al., 2021).This is likely because cloud-level airborne INPs are largely activated to cloud droplets or ice crystals, and only a small fraction remains in the air (Gong et al., 2020;Pereira et al., 2021).The dominant species of immersion freezing INPs in cloud hydrometeor samples are similar to those in air samples, that is, generally biological aerosols at temperatures above 15°C (or above 20°C) and mineral dust particles at temperatures between 30 and 20°C (e.g., J. Chen et al., 2021;Christner et al., 2008;Hill et al., 2014;Joly et al., 2014;Joyce et al., 2019;Vepuri et al., 2021;Yadav et al., 2019;S. J. Zhang et al., 2020).The INP concentration in cloud hydrometeor samples can depend on the concentration of aerosols of certain species that dominate INPs and the scavenging efficiency of the aerosols into cloud droplets (Petters & Wright, 2015).At a particular temperature, the variability of INP concentrations can be as large as five orders of magnitude (Petters & Wright, 2015).
The in-cloud immersion freezing INPs during deep convective storms can also be investigated from hailstone samples.Using hailstone samples from five deep convective storm cases in Alberta, Canada, INP spectra at temperatures from 19 to 6°C were provided, and INP concentrations showed a variability of up to two orders of magnitude at a particular temperature (Vali, 1966(Vali, , 1971a)).With the application of bacterial community analysis, bacteria were detected in hailstone samples from one deep convective storm case in Ljubljana, Slovenia (Temkiv et al., 2012), and also detected in a hailstone sample in Wyoming, where an INP spectrum from 13 to 5°C was provided (Hill et al., 2014).From eight-teen deep convective storm cases in the Texas Panhandle, many types of bacteria were detected in hailstone samples, and INP spectra at temperatures from 25 to 4°C were provided, with a variability of 2-3 orders of magnitude in INP concentrations at a particular temperature (Vepuri et al., 2021).Besides biological particles, mineral dust particles were detected to be abundant in hailstones from three Rocky Mountain storm cases (Michaud et al., 2014) and from eight deep convective storm cases in three different regions of China (H.F. Zhang et al., 2023).
A hailstone forms through the riming of supercooled cloud droplets onto a hailstone embryo (either a graupel or a frozen drop), and the mass of a hailstone generally has a dominant contribution from supercooled cloud droplets (Lamb & Verlinde, 2011)

Hailstone Sampling
Hailstones were collected from the same eight deep convective storms as the cases in H. F. Zhang et al. (2023).As shown in Figure 1, the sampling locations of the eight cases are in different regions of China.Four cases, Fushun (FS), Beijing1(BJ1), Beijing2 (BJ2), Yantai (YT), are located in the plain in the north region of China; two cases, Guyuan1 (GY1) and Guyuan2 (GY2), are located in the plateau in the northwest region of China; two cases, Guiyang (GYA) and Baise (BS), are located in the plateau in the southwest region of China.The sampling dates of the eight cases are from 2016 to 2021, and the local times are from afternoon to early evening.Details of coordinates and dates and times are summarized in Table 1.During or just after the storms, volunteers collected these hailstones and stored them in clean containers, such as plastic bags, glass containers and tinfoil, at temperatures between 18 and 4°C.After the hailstones were transported to the laboratory in Beijing, they were stored in vacuum-sealed plastic pockets at temperatures between 29 and 23°C.The surface of each hailstone was pretreated to remove possible contamination before being melted for experiments, because surface contamination may happen during collection or storage processes, or can come from the collection of aerosols in the subcloud layer by hailstones.For the pretreatment, each hailstone was contained in a polypropylene tube and exposed to room temperature (about 20°C) until liquid water was produced on the surface.Then, the hailstone was placed on a polypropylene plate and rinsed with ultrapure water to remove surface contamination.Finally, the hailstone was melted at room temperature to obtain a melted hailstone sample.Each water sample would be used for experiments within 48 hr after melting.The volumes of the melted hailstone samples in this study are listed in Table 1.For the BJ1, BJ2, and YT cases, hailstones are big, so that three individual hailstones from each case are melted into three water samples.For the FS, GY1, GY2, and GYA cases, hailstones are small, so that multiple hailstones in a case are melted into one water sample to make a sufficiently big volume (>2 ml) for experiments.The hailstones used for experiments in this study are chosen based on their size distribution in a case.For the FS, BJ1, BJ2, GY1, GY2, and GYA cases, hailstones have a narrow size distribution, and therefore hailstones used in the experiments are of similar sizes.For the YT case, hailstones have a broad size distribution, and therefore the three hailstones with quite different sizes are chosen.For the BS case, there are only a few hailstones, and therefore only one hailstone close to the median size is melted into one water sample.A total of 14 water samples are prepared for the droplet freezing experiments.

Droplet Freezing Experiments and Freezing Nucleus Spectra
Droplet freezing experiments are conducted with the Freezing Ice Nucleation Detector Array (FINDA) (Figure 2a) (Bi et al., 2021).The sample array is a 96-well polypropylene plate (Figure 2b) sitting on an aluminum alloy cold stage (Figure 2c), which is immersed in the silicone-based refrigerant (JULABO Thermal H5) in the commercially available cooling stage system (FP-50 HL, Julabo, Germany).Four platinum resistance thermometers (Pt-100) are fixed to the inner bottom of the four corner wells of the 96-well plate, and the four wells are fixed to the cold stage.Ninety-two individual droplet samples are pipetted into the wells with a volume of 10 μL (2.67 mm in diameter).The droplet samples are illuminated with light-emitting diodes (LEDs), and photographed every 0.2 s with a charge-coupled device (CCD) camera.
The refrigerant first cools the sample array from room temperature (about 20°C) to 0°C, and maintains at 0°C for 10 min to minimize the temperature difference between the bottom of a well of the sample array and the air above it (Beall et al., 2017).Then the temperature of the sample array decreases from 0°C to 38°C at a controlled cooling rate of 1°C min 1 .This is the cooling rate experienced by an updraft assuming a wet-adiabatic lapse rate of 7°C km 1 with a vertical velocity of 2.4 m s 1 .During the cooling process, the temperature uncertainty becomes larger, likely due to the increased temperature difference between the bottom of a well and the air above it, and is ±0.75°C at 25°C (Bi et al., 2021).The uncertainty value is comparable to that for other recently developed droplet freezing arrays, which show the uncertainty of ±0.9°C at 25°C (David et al., 2019;Harrison et al., 2018).Using photographs from the CCD camera, the phase state of each droplet can be monitored.The sudden luminance change of a droplet is considered as a freezing event, and the number of frozen droplets N f (T ) at temperature T can be counted every 0.5°C from 0°C to 38°C.
The fraction of frozen droplets f(T ) is calculated as where N d is the number of total droplets, which is 92 for all experiments.Following Vali (1971b), the cumulative INP concentration, which is the concentration of INPs that are active at all temperatures higher than T, can be derived as where V d is the volume of droplets with a value of 10 μL, and DF is the dilution factor of the melted hailstone sample.The C INP (T ) also has a temperature resolution of 0.5°C in this study.The differential INP concentration, which is the density of INPs active at each temperature, is defined as Vali (1971bVali ( , 2019) The differential freezing nucleus spectrum is identified as an effective description of the temperature dependence of INP concentrations, and can demonstrate INP modes in a direct fashion (Creamean et al., 2019;de Almeida Ribeiro et al., 2023).
Two sets of droplet freezing experiments are conducted.In one set, the melted liquid is directly used in the experiments.In the other set, the melted liquid is heated in a water bath at 100°C for 10 min before the droplet freezing experiments in order to study the heat sensitivity of the INPs.For both sets of experiments, the undiluted liquid is used to study the INP concentrations at relatively high temperatures.To measure the INPs activated at lower temperatures, where concentrations are higher, the melted liquid is diluted with a dilution factor of 100.For the GY1 and GY2 cases, because the freezing temperature of the last frozen droplets is still high in the diluted experiments, an additional experiment with a larger dilution factor of 1,000 is added in order to measure INPs at lower temperatures.Eventually, an INP spectrum covering a wide temperature range can be obtained from the two sets of experiments.
The ultrapure water used for dilution is produced from filtered distilled water.We filter the distilled water (Watsons®) twice with 0.1 μm filter (Whatman Anotop Syringe Filter) and then twice with 0.02 μm filter (Whatman Anotop Syringe Filter).The freezing curves of the ultrapure water from 13 experiments as blank measurements and hailstone samples from 60 experiments (14 unheated and undiluted, 16 unheated and diluted, 14 heated and undiluted, and 16 heated and diluted) are shown in Figure S1 in Supporting Information S1.Over the experiment temperature range, the frozen fractions of droplets from hailstone samples are much higher than those of ultrapure water droplets.

Fitting of Freezing Nucleus Spectra and INP Modes
To directly demonstrate INP modes, the differential freezing nucleus spectrum is suggested to be calculated (Creamean et al., 2019;de Almeida Ribeiro et al., 2023).However, when calculated using the finite differentiation method according to Equation 3, the differential freezing nucleus spectrum is sensitive to the choice of the temperature interval, and usually suffers a significant noise (de Almeida Ribeiro et al., 2023;Vali, 2019).Therefore, in this study, the differential freezing nucleus spectrum is recovered using fitting method.According to de Almeida Ribeiro et al. ( 2023), the differential freezing nucleus spectrum of each INP mode can be represented by a Gaussian (i.e., normal) distribution, where the subscript i represents the i th mode, N i is the total INP concentration of the mode, T i is the most likely freezing temperature of the mode, and σ i is the spread of distribution of freezing temperatures.The cumulative freezing nucleus spectrum for the i th mode is calculated as and the cumulative freezing nucleus spectrum for all INP modes is calculated as where T 0 = 0°C, and k is the number of modes.
In this study, the fitting procedure is performed as follows.At the beginning, the freezing nucleus spectrum is assumed to have one mode, that is, k = 1.We calculate the cumulative freezing nucleus spectrum according to Equations 4-6, and then find out the best-fit parameters (i.e., N 1 , T 1 , and σ 1 ) through performing log-linear leastsquares fitting to the measured cumulative INP concentrations.Next, the freezing nucleus spectrum is assumed to have two modes, that is, k = 2. Through performing the same fitting steps, the best-fit parameters (i.e., N 1 , T 1 , σ 1 , N 2 , T 2 , and σ 2 ) can be found.Logically, the number of modes k can be systematically increased, and these steps can be repeated to obtain the best-fit parameters for any number of modes (i.e., N 1 , T 1 , σ 1 ,…, N k , T k , and σ k ).As the number of modes increases, the number of parameters increases, and the sum of squared residuals (SSR) decreases.
The best number of modes is determined using F-test (Makridakis et al., 2008).For example, when the number of modes is increased from one to two, we define the F statistic to be the relative reduction of SSR, and can be calculated as where dof k is the degree of freedom calculated as where n is the number of data points of measured cumulative INP concentrations C INP (T ).F-test is used to determine if the relative reduction of SSR from one mode to two modes is statistically significant.Through looking up the table of F-test critical values, we can get the probability for the relative reduction of SSR not being statistically significant.If this probability is larger than 0.05, then the best number of modes is one.If this probability is smaller than 0.05, then the better number of modes is two rather than one, and we will continue to determine if the reduction of SSR from two modes to three modes is statistically significant.The steps are repeated until the best number of modes is obtained.For each C INP (T ) derived from a hailstone sample, the best number of modes with the best-fit parameters is eventually provided.

INP Concentrations
The INP concentrations calculated from Equation 2 Over the experiment temperature range, the cumulative INP concentrations have a variability of 2-3 orders of magnitude.For example, at 10.0°C, the variability of INP concentrations is about three orders of magnitude, with the GYA and BS cases having the lowest INP concentrations of about 10 0 cm 3 water and the GY1 case having the highest INP concentrations of about 10 3 cm 3 water.At 20.0°C, the variability of INP concentrations is about two orders of magnitude, with the GY2 case having the highest INP concentrations of about 10 5 cm 3 water.According to the measurement on insoluble aerosols in hailstones using scanning electron microscopy and energy-dispersive X-ray spectrometry in H. F. Zhang et al. (2023), the total number concentrations of insoluble aerosols in hailstones for the eight cases have a variability of 2-3 orders of magnitude, with the GY1 and GY2 cases having the highest number concentrations of insoluble aerosols, which is quite consistent with the variability of INP concentrations in this study.
The range of cumulative INP concentrations for precipitation samples in Petters and Wright (2015) is shown in Figure 3. Petters and Wright (2015) have reviewed a variety of hydrometer samples, including cloud water, rain, sleet, snow, and hailstones, from various precipitation systems around the world.By contrast, most samples in this study have INP concentrations within the range in Petters and Wright (2015), but hailstone samples for GY1 and GY2 cases in the northwest region of China have about one order of magnitude higher INP concentrations than samples in Petters and Wright (2015).The range of cumulative INP concentrations for storm precipitation samples in Vepuri et al. (2021) is also shown in Figure 3. Vepuri et al. (2021) have measured INP concentrations for storm precipitation samples from a fixed site in the Texas Panhandle.In comparison, the range of INP concentrations in this study is similar to that in Vepuri et al. (2021).

INP Modes
Using fitting method described in Section 2.3 (see Table S1 for details of the fitting procedure), freezing nucleus spectra for the 14 hailstone samples are obtained as shown in Figure 4. Within the experiment temperature range in this study, the best number of INP modes for fitting is one for BJ1-2 sample, two for BJ1-3 and BS samples, and  As indicated in Figure 4, the relative contribution of each INP mode to the cumulative freezing nucleus spectrum changes with temperature.We consider the INP mode that contributes most to the cumulative INP concentration at a given temperature as the dominant INP mode, and the temperature ranges where each INP mode is dominant are shown in Figure 5.It can be seen that the temperature range for each INP mode varies with the hailstone sample.Specifically, the temperature range where the 1st INP mode is dominant can be from 27.5°C to 6.0°C; the temperature range where the 2nd INP mode is dominant can be from 23.0°C to 6.5°C; the temperature range where the 3rd INP mode is dominant can be from 17.0°C to 4.0°C.These results may be useful for the simplification of the INP parameterization in models.For example, if all the cloud is at levels with temperatures below 23.0°C,only using the 1st INP mode to describe INPs is practical.In previous studies, the dominant species of INPs is mineral dust particles at temperatures between 30°C and 20°C, and is biological aerosols at temperatures above 15°C (or even above 20°C) (J.C. Chen et al., 2021;Hartmann et al., 2020;Ladino et al., 2019;O'Sullivan et al., 2018;Santl-Temkiv et al., 2019;Si et al., 2019;Suski et al., 2018).Moreover, according to the detection of insoluble aerosol species in hailstones from the same eight cases by H. F. Zhang et al. (2023), mineral dust particles and biological aerosols are the main species.We therefore infer that the 1st INP mode may contain mineral dust particles, and the 3rd INP mode may contain biological aerosols, but further studies are required to prove this.

Heat Sensitivity of INPs
The cumulative INP concentrations measured from the set of experiments where melted hailstone samples are heated as a pretreatment are shown in Figure 6 (the cumulative INP concentrations for the hailstone samples plus background INP concentrations of ultrapure water are shown in Figure S3 in Supporting Information S1), as well as the cumulative INP concentrations for the unheated samples for comparison.Proteinaceous biological species as INPs are known to be heat-sensitive, whereas mineral dust species as INPs are not (Daily et al., 2022).The difference in temperature for a particular INP concentration between unheated and heated experiments can show how heat sensitive the INPs are.
Within the temperature range where one mode dominates INP concentrations as shown in Figure 5, we calculate the temperature drop for the mode as the difference of the temperature for a given INP concentration between unheated and heated experiments.For the 1st mode, the temperature drop after heat treatment is about 0-2°C, indicating that INPs of the 1st mode are not heat-sensitive or only slightly heat-sensitive.An exception is the warm part of the 1st mode for BJ1-2 sample, where the temperature drop after heat treatment can be as large as about 5°C, indicating that INPs of this part are highly heat-sensitive, and are likely to be the proteinaceous biological species.As discussed in Section 3.2, there may be another INP mode overshadowed by the 1st mode, although one mode is enough to describe the cumulative INP concentrations for BJ1-2 sample.For the 2nd mode, the temperature drop after heat treatment is mostly about 2-4°C, and the largest temperature drop is about 6°C for YT-3 sample, indicating that INPs of this mode are heat-sensitive.One exception is BJ2-3 sample with a temperature drop of nearly 0°C.For the 3rd mode, the temperature drop after heat treatment can be mostly larger than 4°C, indicating that INPs of this mode are highly heat-sensitive, and are expected to be the proteinaceous biological species.One exception is GYA sample with a temperature drop of about 2°C.

Discussion and Atmospheric Implication
Based on the limited samples in this study, it seems that a potential pattern may exist in INP concentrations.As shown in Figure 3, the region-to-region variability of INP concentrations for hailstone samples from different regions is larger than the case-to-case variability for hailstone samples from the same region.INP concentrations generally decrease for hailstone samples from the northwest region to the north region and to the southwest region.This pattern also exists in number concentrations of insoluble aerosols in H. F. Zhang et al. (2023), where hailstone samples from the northwest region have the highest number concentrations of insoluble aerosols, and hailstone samples from the southwest region have the lowest number concentrations of insoluble aerosols.More cases may be required to investigate the dependence of INPs on regions, and how regional sources of aerosols affect INPs is expected for further studies.Besides, radar observations and cloud-resolving simulations are suggested to assess how the variation of INP concentrations may affect deep convective storms.The variability of INP concentrations can be 2-3 orders of magnitude among these hailstone samples, and the GY1 and GY2 cases have the highest INP concentrations.These results are consistent with those in H. F. Zhang et al. (2023) that the insoluble aerosol number concentrations in hailstones have a variability of 2-3 orders of magnitude, with GY1 and GY2 having the highest insoluble aerosol number concentrations.Besides, hailstone samples for most cases in this study have INP concentrations similar to global precipitation samples in Petters and Wright (2015), but the GY1 and GY2 cases have much higher INP concentrations than those in Petters and Wright (2015).The range of INP concentrations in this study is comparable to that in Vepuri et al. (2021) who have measured storm precipitation samples from a fixed site.

Conclusions
Using the fitting method, the best number of INP modes is one for BJ1-2 sample, two for BJ1-3 and BS samples, and three for other hailstone samples.This implies that three INP modes are expected to be commonly included for the best description of INP concentrations for hailstones within the experiment temperature range.The temperature range where each INP mode is dominant varies with hailstone samples.The 1st INP mode can be dominant at temperatures of 27.5°C to 6.0°C; the 2nd INP mode can be dominant at temperatures of 23.0°C to 6.5°C; the 3rd INP mode can be dominant at temperatures of 17.0°C to 4.0°C.
The heat sensitivity is different for different INP modes.For the 1st INP mode, INPs are not heat-sensitive or only slightly heat-sensitive, and are inferred to be mineral dust species as detected in H. F. Zhang et al. (2023).For the 2nd INP mode, INPs are heat-sensitive for most hailstone samples, and are likely to be the proteinaceous biological species.For the 3rd INP mode, INPs are highly heat-sensitive, and are indicated to be the proteinaceous biological species as detected in H. F. Zhang et al. (2023).
In this study, we use hailstone samples from the same eight deep convective storm cases in three different regions of China as the cases in H. F. Zhang et al. (2023) to investigate the hailstone INPs.Droplet freezing experiments have been conducted on 14 hailstone samples to obtain INP concentrations within a wide temperature range.INP modes in freezing nucleus spectra are then derived.Heat sensitivity of hailstone INPs is also investigated.

Figure 1 .
Figure 1.The topography of China.The locations where hailstone samples were collected from the eight deep convective cases are marked with red dots.

Figure 2 .
Figure 2. Setup of the Freezing Ice Nucleation Detector Array (FINDA).(a) Photograph of FINDA.(b) Top view schematic of the 8 × 12 sample array, containing 92 droplet samples and four platinum resistance thermometers (Pt-100).(c) Side view schematic of the FINDA.
is the cumulative INP concentrations for the hailstone samples plus background INP concentrations of ultrapure water (as shown in Figure S2 in Supporting Information S1).The background INP concentrations are much smaller than the cumulative INP concentrations for the hailstone samples in this study, and are subtracted from the calculated INP concentrations to get the cumulative INP concentrations for the hailstone samples.Moreover, if there is a temperature overlap of data points between liquids with different dilution factors, the cumulative INP concentration at that temperature is then calculated as a weighted logarithmic mean (the weights are given by the reciprocal of error bars so that the data point with a smaller error bar has a bigger weight than the other data point).The cumulative INP concentrations for the 14 hailstones are obtained as shown in Figure 3. Freezing events for the 14 hailstone samples occur within a wide temperature range from 27.5°C to 4.0°C.Onset temperatures of freezing events are from 11.0°C to 4.0°C, hinting at biological INPs.While YT-2 sample has the highest onset temperature of 4.0°C, GYA and BS samples have the lowest onset temperature of 9.0°C and 11.0°C.The other hailstone samples have onset temperatures from 7.0°C to 5.0°C.

Figure 3 .
Figure 3.The cumulative INP concentrations for the 14 hailstone samples.Data points for different samples are marked with different colors or symbols.Shaded areas are ranges of cumulative INP concentrations for various hydrometer samples in Petters and Wright (2015), and two black solid lines are the boundaries of cumulative INP concentrations for storm samples in Vepuri et al. (2021).

Figure 4 .
Figure 4.The freezing nucleus spectra for the 14 hailstone samples.Data points of measured cumulative INP concentrations are marked with black circles.Lines are the best-fit freezing nucleus spectra (see TableS2for details of the fitting parameters), including differential freezing nucleus spectra for each INP mode (light blue, green, and red lines), cumulative freezing nucleus spectra for each INP mode (dark blue, green, and red lines), and cumulative freezing nucleus spectra for all INP modes (black lines).

Figure 5 .
Figure 5.The dominant INP mode in cumulative freezing nucleus spectra over the experiment temperature range for the 14 hailstone samples.Colors represent temperature ranges where cumulative INP concentrations are dominated by the 1st (deep blue), the 2nd (deep green), or the 3rd (deep red) INP mode.

Figure 6 .
Figure 6.The measured cumulative INP concentrations for the 14 hailstone samples before and after heat treatment.Data points of measured cumulative INP concentrations without heat treatment are marked with black circles, and those after heat treatment are marked with black crosses.Lines are the best-fit freezing nucleus spectra for cumulative INP concentrations without heat treatment the same as those in Figure 4, including cumulative freezing nucleus spectra for each INP mode (dark blue, green, and red lines), and cumulative freezing nucleus spectra for all INP modes (black lines).
Hailstones, made of rimed supercooled cloud droplets, are good materials for obtaining the knowledge of INPs in supercooled cloud droplets during deep convective storms.To investigate INPs during deep convective storms in China, hailstones are collected from the same eight deep convective storms as the cases in H. F. Zhang et al. (2023), and immersion freezing INPs in 14 hailstone samples are measured using droplet freezing experiment over a wide temperature range from 27.5°C to 4.0°C.The INP spectra derived from hailstone samples in this study can indicate the temperature dependence of immersion freezing INP concentrations in supercooled cloud droplets, which does not mean that these INPs freeze the hailstone in the atmosphere.
. Among all available materials during deep convective storms, hailstones made of rimed supercooled cloud droplets may have INPs that are the most similar to potential INPs inducing ice formation in supercooled cloud droplets.In this way, measuring immersion freezing INPs in hailstones can provide insights into the immersion freezing INPs in supercooled cloud droplets in the mixed-phase zone of deep convective storms.This does not mean that the INPs measured using a hailstone sample are the INPs that freeze the hailstone in the atmosphere.Since the concentration of aerosols in hailstones may vary for different deep convective storm cases, especially for those in different regions where hailstone aerosols may originate from different sources, the variation of INP concentrations needs to be investigated.

Table 1
Details of the Eight Deep Convective Cases, Including Case Identification, Sampling Location, Sampling Date and Time, and Volume of the Melted Hailstone Sample