Identifying Supercooled Liquid Water in Cloud Based on Airborne Observations:Correlation of Cloud Particle Number Concentration with Icing Probability and Proportion of Spherical Particles

Yuquan ZHOU, Can SONG, Miao CAI, Siyao LIU, Yang GAO, and Rong ZHANG

1 CMA Cloud–Precipitation Physics and Weather Modification Key Laboratory (CPML), Beijing 100081 2 Weather Modification Center of Henan Province, Zhengzhou 450000 3 College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875

ABSTRACT Identifying supercooled liquid water (SLW) in clouds is critical for weather modification, aviation safety, and atmospheric radiation calculations.Currently, aircraft identification in the SLW area mostly depends on empirical estimation of cloud particle number concentration (Nc) in China, and scientific verification and quantitative identification criteria are urgently needed.In this study, the observations are from the Fast Cloud Droplets Probe, Rosemount ice detector (RICE), and Cloud Particle Imager (CPI) onboard a King Air aircraft during seven flights in 2018 and 2019 over central and eastern China.Based on this, the correlation among Nc, the proportion of spherical particles(Ps), and the probability of icing (Pi) in supercooled stratiform and cumulus-stratus clouds is statistically analyzed.Subsequently, this study proposes a method to identify SLW areas using Nc in combination with ambient temperature.The reliability of this method is evaluated through the true skill statistics (TSS) and threat score (TS) methods.Numerous airborne observations during the seven flights reveal a strong correlation among Nc, Ps, and Pi at the temperature from 0 to −18°C.When Nc is greater than a certain threshold of 5 cm−3, there is always the SLW, i.e., Pi and Ps are high.Evaluation results demonstrate that the TSS and TS values for Nc =5 cm−3 are higher than those for Nc < 5 cm−3, and a larger Nc threshold (> 5 cm−3) corresponds to a higher SLW identification hit rate and a higher SLW content.Therefore, Nc = 5 cm−3 can be used as the minimum criterion for identifying the SLW in clouds at temperature lower than 0°C.The SLW identification method proposed in this study is especially helpful in common situations where aircraft are equipped with only Nc probes and without the CPI and RICE.

Key words: supercooled liquid water (SLW), icing probability, cloud particle shape, cloud particle number concentration

1.Introduction

In nature, there are still droplets in clouds that are not frozen but exist as the supercooled liquid drops when the temperature is below 0°C, which are called supercooled liquid water (SLW).Numerous studies have shown that the SLW still exists in clouds at temperature from 0 to−20°C or even lower (Sassen et al., 1985; Heymsfield and Miloshevich, 1989; Rosenfeld and Woodley, 2000;Gu, 2017).The SLW is of great significance to many aspects of research.For instance, accurately determining the location of SLW areas is the key to the success of cold cloud catalysis for weather modification.The SLW is a core factor in developing and utilizing mixed-phase cloud water resources (Zhou et al., 2020).For the global climate, the SLW in clouds can greatly affect the global radiation balance (Sassen et al., 1985).Additionally, the airworthiness certification of aircraft icing highly relies on identifying the SLW.The SLW distribution and its characteristics can severely impact aviation flight safety(Politovich and Bernstein, 2002), and the lack of understanding of the SLW also restricts the development of the aviation industry in China.

Many researchers have tried to identify and analyze the SLW using different observation methods.There are differences in the absorption properties of liquid droplets and ice crystals at different wavelengths.Based on the brightness temperature difference between different infrared bands (Platnick et al., 2003; Baum et al., 2012),the thermodynamic phase of cloud top can be identified.The brightness temperature at 11.2 μm and its difference of several infrared bands pairs, combined with the 0.64-and 0.16-μm channel reflectivity are used to judge the phase of cloud particles forHimawari-8(Mouri et al.,2016).Hu et al.(2010) distinguished the phase of cloud particles based on the depolarization ratio from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPOSO) data.Wu et al.(2015) utilized lidar backscatter coefficients combined with the velocity spectrum widths from cloud radars to identify the SLW in stratiform clouds.Combined with aircraft observations, Gu (2017) proposed a method to identify the SLW based on echo-top temperature, echo intensity and its variation gradient.However, these results obtained by remote sensing methods still need to be verified by insitu observations.

Aircraft detection is the most direct means of observing the SLW in clouds.Due to the urgent need for weather modification, the area with a cloud particle number concentration (Nc) greater than 20 cm−3detected by the Forward Scattering Spectrometer Probes (FSSP) is empirically regarded as a suitable seeding area in China,which is considered to have the SLW in clouds (Hu,2001; Tao et al., 2001; Li et al., 2003; Cai et al., 2013).This threshold ofNcis obtained empirically and still needs to be validated scientifically.

Under natural conditions, there are sufficient cloud condensation nuclei but few ice nuclei.The concentration of ice crystals in clouds generally does not exceed 10 cm−3due to the self-inhibiting process of ice nucleation (Tao et al., 2001).Numerous previous studies have investigated the relationship betweenNcand SLW.Heymsfield and Miloshevich (1989) showed that there was no ice accretion at 99% of the moment whenNcfrom the FSSP was less than 1.5 cm−3at all levels.Cober et al.(2001b) suggested that in ice clouds, the median volume diameter from the FSSP data is usually larger than 30 μm, and the particle concentration is less than 15 cm−3, while this phenomenon occurs less than 4% of the time in pure liquid clouds.Wang et al.(2013) compared the liquid water content observed by the FSSP and a King probe, and they found that particles with diameters of 3.5-18.5 μm are mostly liquid.Gu (2017) indicated that the effective diameter of cloud particles is basically less than 20 μm whenNcis higher than 20 cm−3.In addition, the spectral distribution showed a large number of small particles.Thus, Gu (2017) concluded that there is a high possibility of liquid water droplets in the region withNc> 20 cm−3.In summary, there is a theoretical basis for the SLW identification based onNcobserved by the FSSP.However, the FSSP cannot distinguish the phase of particles, and this method still lacks verification based on observations.Therefore, usingNcfrom the FSSP to identify the SLW is questioned.

The main airborne instruments currently used for SLW detection include the Rosemount ice detector(RICE), King probe, Nevzorov probe, and cloud particle image probe.At present, there are several image probes from three kinds of airborne particle detection systems,i.e., two-dimensional cloud (2DC) optical array probe and two-dimensional precipitation (2DP) optical array probe from the Particle Measuring System (PMS), Cloud Imaging Probe (CIP) and Precipitation Imaging Probe(PIP) from the Droplet Measurement Technologies(DMT) detection system, and the Cloud Particle Imager(CPI) from the Stratton Park Engineering Company(SPEC) detection system developed in recent years.

The RICE has been chosen to detect the SLW in many integrated observation projects (Hill, 1991; Heymsfield and Miloshevich, 1993; Claffey et al., 1995).Cober et al.(2001a) found no obvious response of the RICE to ice clouds in any of the 38 flights conducted in winter storms, implying that this instrument can be used to distinguish ice and mixed-phase clouds.Although several scholars used the RICE to obtain the SLW content in clouds (Mazin et al., 2001), the RICE is mainly used to identify the existence of the SLW due to the difficulties in calibration and post-processing of its data.The King and Nevzorov probes are another means of detecting the SLW in clouds (Guan et al., 2001; Cober et al., 2005).The minimum liquid water content detected by the King probe is 0.02 g m−3(Heymsfield and Miloshevich, 1989).Cober et al.(2005) investigated the environmental characteristics of the SLW area using the liquid water content observed by the King probe.Unfortunately, no reliable liquid water content observations are obtained from the Nevzorov probe during flight time in this study.

Two-dimensional cloud particle images are the main method widely used to detect and identify the SLW.Holroyd III (1987) proposed a recognition method of cloud particle shape and divided the observed cloud particles into nine types, i.e., tiny, linear, aggregates, graupel,spheres, hexagonal, oriented, dendrite, and irregular.However, the accuracy of the method is affected by shattered pseudo-particles (Wang et al., 2014).Huang and Lei (2020) further improved the Holroyd method by pre-classifying the particles, removing the influence of shattered pseudo-particles and performing shape recognition separately for intact and non-intact particles to improve the shape recognition accuracy.

Besides, studies on particle shape by using PMS and DMT instruments (i.e., 2DC, 2DP, CIP, and PIP) have been conducted (Cober et al., 2001b; Hou et al., 2011,2014, 2021; Zhu and Guo, 2014; Dong et al., 2021).However, these probes cannot detect cloud particles smaller than 25 μm.Moreover, three pixel points are required to discriminate the particle shape at least, which means that image analysis can only be performed for particles above 75 μm.These probes of PMS and DMT instruments are only adapted for image analysis of large particles (Liu et al., 2021).However, most of the supercooled liquid droplets are small-sized particles.Therefore, there is large uncertainty in studying the SLW with the two-dimensional optical array probes of the PMS and DMT.The CPI of the SPEC detection system with a resolution of 2.3 μm can distinguish the shape and size of small cloud particles, which has been widely used in cloud particle image analysis in recent years (Qi et al.,2019; Xiao et al., 2019; Dong et al., 2020; Liu et al.,2020).CPI largely compensates for the deficiencies of the cloud and precipitation particle images from the PMS and DMT that cannot accurately identify the shape of small cloud particles.

In China, the demand for weather modification operations is great, and the SLW identification in clouds is a critical step for weather modification.A large number of detections and cloud seeding operations by aircraft with particle detection systems have been conducted in various regions of China, and numerous aircraft measurements of theNchave been accumulated in the past decade (Huang et al., 2005; Hou et al., 2011; Zhang et al.,2011; Sun et al., 2014; Peng et al., 2016; Yang et al.,2021).However, these aircraft have long been equipped with onlyNcprobes and do not carry both the CPI and RICE.

To investigate the possibility of objectively identifying the SLW in clouds and to better utilize the aboveNcmeasurements, we explore the correlation amongNc, proportion of spherical particles, and icing probability by analyzing simultaneous observations from the Fast Cloud Droplets Probe (FCDP), RICE, and CPI probes onboard the King Air B-10GD aircraft during its multiple flights in 2018 and 2019 organized by the Weather Modification Center of the China Meteorological Administration(CMA).Based on the multi-flight integrated airborne observations, we propose, demonstrate, and verify the feasibility of the SLW identification method based onNcand ambient temperature.This method allows the SLW objective identification by usingNcobservations, which is especially valuable for the application of aircraft measurements with onlyNcprobes but without the CPI and RICE.Meanwhile, this research can also provide a more reliable dataset for validation of SLW areas identified by remote sensing methods such as satellite (Wang et al.,2019) and radar (Wu et al., 2015; Gu, 2017) data.Thus,this study has important scientific significance and application value for the SLW identification in China.

2.Instruments and data

2.1 Airborne instruments onboard the King Air B-10GD aircraft

Through the first regional weather modification project of China—the Northeast China Weather Modification Project, the Weather Modification Center of the CMA possesses a fleet of high-performance aircraft for cloud physics detections and operations.Among them,the King Air B-10GD aircraft has a detection height reaching 10 km, with a flight endurance of more than 5 h.This aircraft is equipped with a variety of cloud physics probes, including 26 kinds of detection instruments such as the FCDP, RICE, CPI, two-dimensional stereo probe(2DS), high-volume precipitation spectrometer (HVPS-3), Aircraft-Integrated Meteorological Measurement System (AIMMS-20), cloud condensation nucleus counter(CCN-100), and Total Temperature Sensor (TTS).The data used in this study include the FCDP, RICE, CPI, and TTS measurements.

The FCDP is a forward scattering spectrometer probe that calculates particle diameter and concentration by measuring the forward scattering of particles as they pass through the laser beam.The instrument detects particles in the diameter range of 1-50 μm, with a total of 21 channels, and is capable of sizing particles in the velocity range of 10-200 m s−1.The first 20 channels have a resolution of 1.5-4 μm, and the last channel is an oversize bin.The FCDP is designed with knife-edge tips to reduce artifacts caused by large ice particles shattering.Moreover, the FCDP has a powerful information acquisition system that records the arrival time, transit time, and pulse amplitude of each particle signal in detail, which can help us eliminate the influence of shattered particles and ensure the reliability of particle concentration observations.Compared with the cloud droplet probe (CDP)and FSSP, the FCDP has a higher sampling frequency and negligible pulse vacancy time, thus reducing the loss of counts during the dead time and making the measurement more accurate.

The CPI is an atmospheric detector that captures highresolution images of particles passing through the instrument, sampling and photographing cloud particles with the velocity up to 200 m s−1.The pixel resolution of the CPI is 2.3 μm, and its photographing frame rate is as high as 400 frames per second, allowing more than 25 particles to be imaged per frame.This instrument can obtain numerous images of cloud particles passing through sampling areas, while collecting information of the length, width, circumference, and area of each particle.Based on the above information on these particle properties, the cloud particles are classified into sphere, plate,column, and other types, which provides a possibility to study the cloud particle shape at the scale range of 7-2300 μm (the scale refers to the maximum length of particles).In this study, spherical particles are considered as liquid water droplets, and the effects of graupel particles and tiny ice balls are ignored.Other types of particles are uniformly classified as non-spherical types, and they are considered to be ice crystals.More descriptions of the CPI are available at http://www.specinc.com.

The RICE is a magnetostrictive vibration probe that oscillates at an intrinsic frequency of approximately 40 kHz.Its sensing probe is a cylinder with a length of 2.54 cm and a diameter of 0.635 cm exposed to air.SLW droplets collide and accumulate on the instrument surface, while solid ice particles bounce off the instrument surface and are blown away by the airflow.When the SLW in clouds freezes on the probe, the vibration frequency of the RICE decreases as the mass of attached ice increases.When the icing thickness reaches the preset value (about 0.5 mm), the icing instrument removes the ice by the internal heating element.Due to the adiabatic heating associated with aircraft speed, sublimation occurs in vapor saturation environment, and the detection threshold of the RICE at the flight speed of 100 m s−1is approximately 0.002 g m−3(Heymsfield and Miloshevich, 1989, 1993; Mazin et al., 2001).

2.2 Data and processing

The data used in this research are the observations from seven flight detections (about 18 h) by the King Air B-10GD aircraft in 2018 and 2019.According to the flight order, seven flights are numbered as Flights 1-7 in turn (see as Table 1).Figure 1 shows seven flight tracks(denoted by different colors).Detection regions(30.89°-33.63°N, 111.14°-120.94°E) are located in Hubei, Anhui, and Jiangsu provinces in eastern and central China.

According to Fengyun-4 satellite observations and weather radar echoes, all detection data of seven flights are observations of stratiform and cumulus-stratus mixed cloud systems.Observations in 2018 are mainly from eastern China.The average cloud top height in the detection area is 2.8-5.6 km, and the average optical thickness is greater than 20.In 2019, cloud systems detected in central China developed deeper than that in 2018, with the average cloud top height of 5.7-9.4 km in the detection area and obvious precipitation on the ground.

In this study, the aircraft detection data per second is taken as one observation sample.We select the samples with simultaneous observations from four instruments(FCDP, CPI, RICE, and TTS).Thus, a sample mentioned in this research contains the observation results from four instruments.Table 1 presents the flight time,detection temperature range, and sample number below 0 and −2°C for the seven flight detections.The temperature used in this case is observed from −18.1 to 27.5°C,and 43,578 samples are obtained below 0°C.

Table 1.Data list from the King Air aircraft

The time resolution of the FCDP and RICE data is 1 s.In processing the FCDP data, closely spaced particles that may be caused by particles shattered on the probe inlet are rejected based on arrival time.The CPI photographs at 400 frames per second to obtain a large number of particle images.The observations at each second are counted to obtain the percentage of spherical particles in the total and match with the results of the FCDP and others in time.

The following is a brief introduction to the main physical quantities mentioned in this study and their calculation methods.The variablePsindicates the proportion of spherical particles observed by the CPI.Based on the CPI observations per second,Psis calculated by dividing the number of spherical particles by the number of total particles.The variablePirepresents the probability of icing.According to the vibration frequency of the RICE, it can be judged whether there is icing on the RICE probe at a certain moment.Piis obtained by the ratio of samples with icing to the total samples.

Fig.1.Flight tracks (colored lines) of seven flights over eastern and central China in 2018 and 2019.

2.3 Observations on 11 October 2019

We take the flight detection on 11 October 2019(Flight 5) as an example to analyze the measurement results of each instrument.Figure 2 shows the temporal variations in the vibration frequency of the RICE probe(Hz), ambient temperature (°C),Psobserved by the CPI,andNc(cm−3) observed by the FCDP.In addition, the particle images observed by the CPI at typical moments(T1 and T2) are also presented in Fig.2.

The results suggest that the observations from the several instruments are in good consistency.The observation period can be divided into four stages, i.e., L1-L4.

Specifically, from 0319 to 0325 UTC (L1), the averageNcvalue is 75.2 cm−3.The CPI image at 0321 UTC(T1) indicates that the cloud particles are basically smallscale spherical particles, andPsexceeds 0.8 at most moments.There is no icing on the RICE probe due to the temperature higher than 0°C at this stage.

During 0330-0335 UTC (L2), the averageNcvalue is 37.7 cm−3, and the detected temperature ranges from−5°C to −9°C.The CPI observation image shows a large number of spherical particles, andPsis greater than 0.5 at most moments.A decrease in the vibration frequency of the RICE during this time indicates the generation of icing.

From 0335 to 0338 UTC (L3), there is no change in the frequency of the RICE probe, which suggests that no SLW was frozen on the probe.The FCDP does not observe any particles at this stage, andPsis basically below 0.3, indicating the lack of the SLW in clouds during this stage.At 0336 UTC (T2), the CPI particle image shows that most particles are needle-shaped, columnshaped, and dendrite-shaped ice crystals, while there are smaller-scale irregular ice crystals.

Between 0338 and 0342 UTC (L4), the detected temperature is between 0 and −2°C, and the averageNcvalue observed by the FCDP is 38.9 cm−3.In addition, there is a highPsvalue observed by the CPI, but the vibration frequency of the RICE does not change during this period.

Fig.2.Temporal variations of (a) the vibration frequency of the RICE probe, (b) temperature (T), (c) proportion of spherical particles(Ps) observed by the CPI, and (d) number concentration of cloud particles (Nc) observed by the FCDP on 11 October 2019.The blue solid line in Fig.2b represents 0°C, and T1 and T2 denote two typical moments when cloud particle images were observed by the CPI.

Table 2 summarizes the characteristics of physical quantities at different stages (L1-L4).Although this case has the shortest observation time, it covers four different stages of physical quantity variations, which is the reason that it was selected to present the observation results.

3.Correlation between Pi and Ps

The icing and spherical particles in clouds are considered as a criterion for the presence of the SLW.Using the detection data from the above seven flights in Table 1,we statistically calculatePiwith differentPsto study the correlation betweenPsandPiat different temperature.

Table 2.Main characteristics of physical quantities at different stages observed on 11 October 2019

Among all the samples, there are 17486 particle samples observed by the CPI below 0°C.The variablePsobserved by the CPI can be divided into five intervals:0.0-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, and 0.8-1.0.Based on this, we statistically analyzePiin the different intervals ofPsat different temperature, as shown in Fig.3.The results indicate thatPiincreases with decreasing temperature whenPsis greater than 0.4.The difference inPiat different temperature increases asPsincreases.When the temperature is below −2°C,Pibasically no longer varies with the temperature.The variablePivalue is less than 10% whenPsis less than 0.4.AsPsincreases,Pialso increases.WhenPsis greater than 0.6,Pican reach 60%-70%.

At the temperature below −2°C, there are still several moments when the RICE probe detects no icing andPsis greater than 0.8.Among the samples withPslarger than 0.8 and no icing observed by the RICE, about 67% of the samples have a liquid water content calculated by the FCDP less than the minimum detectable threshold of the RICE.Therefore, althoughPsis high, the liquid water content is small, which may be a reason for the no icing detected by the RICE.In summary, there is a close positive correlation between the RICE and CPI observations.

Fig.3.Relationship between Pi and Ps at different temperature.The red numbers represent the numbers of samples in different intervals of Ps at the temperature below 0°C.

4.Correlation of Nc with Pi and Ps

4.1 Nc and Pi

The variableNcdetected by the FCDP is classified into 11 bins, i.e., 0-0.1, 0.1-0.25, 0.25-0.5, 0.5-1, 1-5, 5-10,10-20, 20-30, 30-40, 40-50, and > 50 μm.At different temperature thresholds,Pifor the RICE detections is calculated with differentNcvalues, as shown in Fig.4.

Figure 4 indicates thatPiincreases with decreasing temperature threshold, but when the temperature is below −2°C, the change inPiwith temperature is no longer obvious.The variablePiis 3%-12% greater at temperature below −2°C than that at temperature below 0°C for differentNc.WhenNcis less than 1 cm−3, the samples without icing account for the majority, andPiis less than 10%.The numbers 98% of these samples without icing have a liquid water content less than the minimum detectable threshold (0.002 g m−3) of the RICE.However,the statistics of samples with a liquid water content more than the minimum detectable threshold are generally consistent with the total sample statistics (Fig.4b).The correlation betweenNcandPiis high, andPiincreases continuously with increasingNc.The statistical results of samples with temperatures below −2°C suggest thatPiis greater than 50% whenNcis greater than 5 cm−3.ForNcof 10-40 cm−3, icing moments account for 50%-60% of all moments with temperature below −2°C.The variablePiis up to 80% at theNcgreater than 40 cm−3(Fig.4b).

Heymsfield and Miloshevich (1989) demonstrated that when FSSP concentrations in any size bin is greater than 1.5 cm−3,Piobserved by the RICE is 68% at temperature between −35 and −20°C.Additionally, the liquid water content in most of the 32% samples without icing is less than the minimum detectable threshold of the RICE.The findings in this study and Heymsfield and Miloshevich(1989) both indicate thatNcis in good agreement withPiobserved by the RICE.

Overall,Piis obviously higher at temperature below−2°C than at temperature lower than 0°C.From the observations in Flight 5, it can be seen that there was no icing on the RICE probe when the temperature was slightly below 0°C at stage L4 (Fig.2).Cober et al.(2001a) also found that the RICE did not detect icing when the liquid water content was 0.2-0.3 g m−3at the temperature of -4°C.When the liquid water content in clouds reaches a certain upper limit, latent heat release causes the surface temperature to 0°C, which prevents the SLW from freezing, thus making the vibration frequency of the probe unchanged (Ludlam, 1951; Cober et al., 2001a), leading to the above phenomenon.Mazin et al.(2001) reported that the upper limit of liquid water content increases with the decrease of temperature and wind speed.In a word, the observational limitation of the RICE probe near 0°C needs to be considered.

Fig.4.Relationships between Pi and Nc at temperature below 0, −1, −2, −3, and −4°C for (a) all samples and (b) the samples with a cloud water content calculated by the FCDP greater than 0.002 g m−3.The red numbers represent the numbers of samples with different Nc at temperature below 0°C.

4.2 Nc and Ps

Particle shape is often used as another criterion to identify the SLW.In this section, the relationship betweenNcandPsis investigated based on combined observations of the FCDP and CPI below 0°C.The variablePsfrom the CPI observations is also divided into five ranges, i.e., 0-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, and 0.8-1.0.The frequency distribution ofPsis discussed in differentNcranges (same as those in Section 4.1).

From Fig.5, it can be found that when temperature below 0°C andNc< 1 cm−3, the number of samples withPsof 0-0.2 is the largest, accounting for about 55% of the total samples.The samples withPsdetected by CPI less than 0.4 account for more than 75% of the total samples.Overall,Psincreases obviously with increasingNc.WhenNc> 1 cm−3, the frequency distribution ofPsvaries dramatically.Samples withPslarger than 0.8 become account for the majority, while the weight of samples withPsless than 0.2 continuously decreases asNcgradually increases.The frequency ofPslarger than 0.4 is more than 85% atNclarger than 5 cm−3.The number of samples withPslarger than 0.4 accounts for about 95%of the total samples whenNc> 50 cm−3.The meanPsis less than 0.3 atNcof 0-1 cm−3.The meanPsrapidly increases from 0.3 to 0.7 whenNcincreases from 0.5 to 10 cm−3.The increase rate of the meanPsdecreases whenNcis larger than 10 cm−3.The variation trend of the medianPsis similar to that of the meanPs.ForNcless than 1 cm−3, the medianPs(around 0.16) is less than the meanPs.However, the medianPsis greater than the meanPswhenNcis greater than 1 cm−3.

Fig.5.The stacked frequency of Ps with different Nc at temperature below 0°C.The black solid line with diamond markers and the black dashed line show the mean Ps and median Ps at each Nc range, respectively.

The above results reveal that bothPsandPiare low whenNcis low.Nchas a strong positive correlation withPsandPi.The concentration of ice nuclei in nature is relatively low, generally from 0.1 to dozens per liter, depending on the temperature (You et al., 2002; Yang et al., 2013; Che et al., 2021).Consequently, the concentration of ice crystals formed under natural conditions is low.Cloud physical processes such as fragmentation can also result in the generation of secondary ice crystals,making the concentration of ice crystals in clouds higher than the concentration of ice nuclei.However, previous studies have suggested that the concentration of the actually observed ice crystals generally does not exceed 1 cm−3(Mossop et al., 1972; Huang and Lei, 2020; Yang et al., 2021).Since there are numerous cloud condensation nuclei, the concentration of liquid water droplets generated in clouds is quite large, reaching 102-103cm−3.Therefore, when the temperature is lower than 0°C, andNcis low, the cloud particles are more likely to be dominated by ice crystals.Under the influence of the Bergeron process, the size of ice crystals increases by consuming liquid water droplets, but the concentration of particles is still low.Simultaneously, bothPsandPiare low.AsNcincreases, the probability of liquid water droplets in clouds increases.

5.Identification of SLW by Nc

The comprehensive analysis above indicates that whenNcobserved by the FCDP is larger than a certain value,Nccorresponds well with the highPsdetected by the CPI and the highPiobserved by the RICE below 0°C.On this basis, we propose a method to identify the SLW based onNcobserved by the FCDP.

As shown in the previous sections,Pidetected by the RICE andPsdetected by the CPI increase withNc.Actually, using this method to identify and forecast the SLW areas needs to consider both hit rate and missing alarm rate.In this section, we evaluate the reliability of the SLW identification method using differentNcthresholds based on RICE and CPI observations.

5.1 Evaluation methods

The true skill statistic (TSS) and the threat score (TS)methods are widely used to evaluate the performance of forecasting algorithms (Doswell III et al., 1990; Guan et al., 2001; Cai et al., 2015).We also use the TSS and TS methods to evaluate the reliability of the SLW identification method based onNc.

The size of cloud particles can affect the identification of the particle shape, and the potential error in shape identification of particles less than 10 pixels is relatively large.Cober et al.(2001b) pointed out that 5%-40% of the particles in ice clouds are misclassified as spherical particles.In this study, the occurrence probability ofPsgreater than 0.4 exceeds 90% in the case of icing observed by the RICE.The analysis in Section 3 shows thatPiis less than 10% atPsless than 0.4.Combining the proportion of shape misclassification in the results of Cober et al.(2001b) and that in Section 3, we suppose that there is SLW in clouds whenPsis larger than 0.4.

Icing observed by the RICE orPsdetected by the CPI exceeding 0.4 is used as the criterion for identifying the SLW, and the number of samples satisfying the cases in Table 3 are counted by using the criteria.Referring to Doswell III et al.(1990) and Cai et al.(2015), the frequency of hit (FOH), probability of detection (POD),probability of false detection (POFD), TSS, and TS for identifying the SLW based onNcare calculated as follows [Eqs.(1-5)].

The closer the score values of the TSS and TS are to 1,the better the combined method is.

As seen in the previous analysis, RICE may respond out of order at temperatures close to 0°C due to kinetic warming and latent heat release.In order to understand the limitations of RICE and improve the data reliability,we investigatePiof RICE at different temperatures.The study shows thatPiis only 4.42% at temperatures between 0 and −1°C, and it is less than 50% when the temperature is higher than −2°C.The variablePiincreases significantly as the temperature decreases, and is about 73% at temperatures below −2°C (Table 4).Therefore, to ensure the credibility of the evaluation results,the data with temperature below −2°C is selected for the evaluation using RICE.

able 3.The contingency table for calculating TSS and TS scores

5.2 Evaluation results

The icing detected by the RICE is used as the criterion for identifying the SLW.The FOH, TS score, and TSS score are analyzed at differentNt(Ncthreshold) to identify the SLW when the temperature is below −2°C(Fig.6).The analysis reveals that the hit rate usingNcto identify the icing increases withNt.Both TS and TSS scores show a trend of increasing and then decreasing withNt.The TS score is slightly larger than the TSS score.The highest values of the TS and TSS scores are obtained whenNtis taken as 5 cm−3at temperature below −2°C, i.e., 0.68 (TS) and 0.64 (TSS).T

The reliability ofNcto identify the SLW is evaluated by using the SLW observed by the CPI as true values.Similar to the steps in Section 5.1, we count the number of samples for different cases in Table 3 and calculate the FOH, TSS, and TS scores of the SLW byNcwhen the temperature is below 0°C (Fig.7).Similar to the results when RICE observations are used as true values, the hit rate of this SLW identification method increases withNt.The highest TSS score is 0.75 atNt= 5 cm−3(Fig.7).WhenNtis greater than 5 cm−3, the TSS score obviously decreases withNt, and it decreases to about 0.5 atNt= 50 cm−3.The variation trend of the TS score is similar to that of the TSS score, but the values are generally higher than the TSS score values.The highest TS score of the SLW identification method is about 0.82 atNt= 1 cm−3.The optimal threshold may vary and still needs to be verified by increasing observation samples of different cloud types.

Table 4.Number of observed samples and Pi under different temperature conditions.The data are obtained from seven flight observations with cloud water content greater than 0.002 g m−3

As analyzed in Section 4, bothPsandPiincrease withNc.When the particle concentration reaches a certain value (Nc= 5 cm−3for this study), there is a high probability (more than 50%) of liquid water droplets in clouds.AlthoughPsandPistill show increasing trends asNcincreases, the missing alarm rate increases asNccontinues to increase.Thus, there is a non-monotonic skill score.The maximum score is found at 5 cm−3in our research.

The evaluation of the SLW identification method(based on both RICE and CPI observations as truth)demonstrates thatNc= 5 cm−3can be used to identify the SLW, which obtained relatively high TSS and TS scores.The hit rate increases with increasingNc, and bothPiandPsare relatively larger whenNcis set to a larger value(Figs.6 and 7).Rangno and Hobbs (2005) defined the area with particle concentration ≥10 cm−3observed by the FSSP as the cloud area, and this criterion is widely used in aircraft detection research (Huang et al., 2005;Zhang et al., 2011).Some scholars selectedNcgreater than 20 cm−3as the condition for cloud seeding catalysis(Hu, 2001; Tao et al., 2001; Li et al., 2003).In this study,it is concluded thatNcgreater than 5 cm−3should be reasonable for identifying the SLW, and a higherNccan ensure a higher hit rate and a higher liquid water content.In addition, all of the observations are from stratiform and cumulus-stratus mixed clouds.Cautions should be taken when applying the results to convective clouds.

Fig.6.The frequency of hit (FOH), TS and TSS scores of the SLW identification method at different Nc thresholds when the icing detected by the RICE is used as the criterion for identifying the SLW.The data are from seven flights of the King Air aircraft at the temperature below −2°C.

Fig.7.As in Fig.6, but for Ps larger than 0.4 as the criterion for identifying the SLW.Data used here are measurements from seven flights of the King Air aircraft below 0°C.

6.Conclusions and discussion

Based on the observation data from the FCDP, RICE,and CPI onboard the King Air B-10 GD aircraft from the Weather Modification Center of the CMA during the seven flights in 2018 and 2019, we analyzed the correlation amongNc,Ps, andPiand explored the feasibility of a method to identify the SLW area by combiningNcobserved by the FCDP with the temperature.Moreover, the FOH, TS, and TSS scores for identifying SLW based onNcat differentNcthresholds were also evaluated to provide a scientific basis for more objective identification of the SLW by usingNc.The main conclusions are as follows.

(1) There is a good positive correlation betweenPsandPi.It is found from the airborne observations thatPiis lower than 10% (greater than 50%) whenPsis lower(higher) than 40%.

(2) The higher the cloud particle (1-50 μm) number concentration (Nc), the higher thePi.Piobserved by the RICE increases from 50% to 80% whenNcincreases from 5 to 50 cm−3at temperatures below −2°C.

(3) The variablePsincreases with the increase ofNcwhen temperature is lower than 0°C.The probability ofPslarger than 0.4 is higher than 85% whenNcis larger than 5 cm−3.

(4) When temperature is between 0 and −2°C, in the region with largeNcand high SLW, kinetic warming and freezing latent heat release prevent further freezing of SLW, leading to an increase inPiwith decreasing temperature.The variablePiis 3%-12% greater at temperatures below −2°C than that at temperatures below 0°C in differentNcranges.

(5) Both TS and TSS scores show a trend of increasing and then decreasing withNt.The maximum TSS and TS scores are found at 5 cm−3in our study.

(6) In general, at temperatures between 0 and −18°C,the regions withNcobserved by FCDP greater than a certain value of 5 cm−3are in good agreement with the regions of icing and of highPs, indicating that although the FCDP does not have the ability to distinguish the particle phase,Ncobserved by the FCDP can still be used to judge the existence of SLW.

Based on the statistical analysis of numerous airborne observation samples, we proposed thatNc= 5 cm−3can be used as a lowest criterion for SLW identification.Using 20 cm−3as a cloud seeding operational condition ensures a higher hit rate and a higher SLW content.Actually, in addition to the existence of SLW, the SLW content needs to be considered.In practical applications, the most suitable threshold should be selected according to specific operations and objectives (such as weather modification and aircraft icing).Note that theNcobservations in this study are obtained from the FCDP.Thus, the calibration and comparison between different instruments still need to be performed when applying the proposed criterion to the observations from the CDP and FSSP.Moreover, the minimum temperature observed in this study is −18.1°C, and thus the accuracy of identifying the SLW based onNcat lower temperature needs to be further investigated.The data in this research are from observations of stratiform or cumulus-stratus mixed clouds,and the applicability of the findings to convective clouds remains to be studied.

Acknowledgments.The authors are grateful to professor Zhijin HU for his valuable suggestions to improve this manuscript.We thank Nanjing Hurricane Translation for reviewing the English language quality of this paper.