The ice clouds analyzed in this study are from observations of a Ka-band polarization Doppler radar (KPDR) situated at the Institute of Atmospheric Physics (IAP; 39.967∘ N, 116.367∘ E), Beijing, China. The KPDR was set up in 2010 and works at a frequency of 35.075 GHz (wavelength of 8.55 mm; Huo et al., 2019), measuring the equivalent reflectivity factor (Ze, hereinafter simply “reflectivity”; units mm6 m-3; dBZ =10log⁡(Ze)), Doppler velocity, spectral width and linear depolarization ratio of cloud. It is equipped with a magnetron-type transmitter with a minimum sensitivity of -45 dBZ for cloud determination. For comparison, the 94 GHz cloud profiling radar (CPR) on CloudSat has a sensitivity of approximately -30 dBZ. Calculations or measurements of radar reflectivity in previous studies reveal that the reflectivity of ice clouds over midlatitude regions are mostly larger than -30 dBZ (Deng et al., 2010; Pokharel and Vali, 2011; Matrosov and Heymsfield, 2017). Therefore, the KPDR is capable of detecting most ice clouds over Beijing. However, the Ka-band radar is more sensitive to larger particles in a cloud target since the reflectivity is proportional to the D6 (D is particle size). For the CPR, thin ice clouds with ice water content (IWC) lower than approximately 0.4 mg m-3 are invisible (Wu et al., 2009). It is possible that the KPDR misses some thin ice clouds when they consist of small ice crystals (i.e., D less than 20 µm) or the IWC is smaller than 0.4 mg m-3. The pulse width of the KPDR is 0.2 µs, and the beamwidth is 0.4∘. Its repetition frequency is 3.5 kHz, and its vertical resolution is 30 m. The KPDR has operated daily since 2012, mostly in the vertically pointing mode. During special events – for example, short-term collaborative observations with other instruments – the scanning mode changes to the plane position indicator or radar height indicator mode. In 2013 and 2018, the KPDR was nonoperational during almost the whole of the summer period. The radar data used in this paper were observed from 1 January 2014 to 31 December 2017. During these 4 years, the valid operational time of the radar in the vertically pointing mode occupied more than 80 % of the total time. Namely, there are more than 28 000 h of radar measurements in the vertically pointing mode during the period 2014–2017.

Ice clouds are composed of various types of ice crystals and are usually thin. Cirrus clouds also consist of ice crystals. Definitions of cirrus clouds in previous publications provide us with references for ice cloud identification with the KPDR. For example, in the cloud classification algorithm developed for the CPR on the CloudSat satellite, the average temperature at the largest Ze, the average height of the maximum Ze, the cloud-base height (CBH), etc. are combined to determine cirrus cloud (Wang and Sassen, 2001b). Sassen et al. (2008) classified cloud layers as cirrus via defining two criteria: namely, the visible optical depth should be less than 3.0 and the cloud-top temperature should be lower than -40 ∘C, categorizing cirrus clouds via cloud physical and optical parameters. Deng et al. (2010) identified cirrus layers by cloud-top and cloud-base temperature (Ttop < -40 ∘C and Tbase < -10 ∘C). In some recent studies, cirrus clouds are defined as ice clouds with temperatures < -38∘ (Krämer et al., 2016; Luebke et al., 2016; Heymsfield et al., 2017). Ge et al. (2019) used two temperature criteria to identify cirrus cloud: the temperature of the cloud top should be less than -30 ∘C, and the temperature at the maximum Ze layer and at the cloud base should be less than 0 ∘C. The KPDR has a cloud clustering and classification algorithm, a detailed description of which has been presented by Huo et al. (2019). Here, we briefly describe it as follows. Firstly, the KPDR cloud profiles are grouped as clusters based on a combination of a time–height clustering method and a k-means clustering method. After each cloud cluster is determined, a fuzzy-logic method is applied using multiple cloud properties, such as CBH, cloud depth (CD) and radar reflectivity, to classify the cloud cluster into nine types: Cs, Cc, Ac, As, St, Sc, Ns, Cu and Cb clouds. According to the definitions and identification approaches in previous studies, we use two criteria to identify ice clouds from KPDR data after the clustering and classification algorithm is performed. Namely, a cloud cluster for which the mean cloud-top temperature is less than -40 ∘C and the maximum cloud-base temperature is less than -10 ∘C is determined as ice cloud. Ice cloud with a cloud-base temperature below -38 ∘C is regarded as cirrus cloud in this paper. It should be noted that supercooled water might exist in ice clouds with a temperature above -38 ∘C, and thus what the radar measures should indicate different physical properties from that of ice particles. In this paper, the supercooled water is not distinguished, and its proportion and properties will be investigated in the future.

This study also used some other datasets to complement the investigation of the properties of ice and cirrus cloud, such as the temperature profile, water vapor, wind velocity and cloud optical thickness. The research datasets of cloud optical thickness (produced from Himawari-8) used in this paper were supplied by the P-Tree System of the Japan Aerospace Exploration Agency (https://www.eorc.jaxa.jp/ptree/index.html, last access: 6 January 2020). Other meteorological reanalysis data employed were from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 datasets (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5, last access: 6 January 2020).

Ice clouds can be vertically and horizontally extensive, with their various appearances dependent on the diverse range of associated atmospheric movements and processes. The KPDR is located in the north of the North China Plain, where to the west and north there are mountains and to the south and east is the Bohai Sea. In the region's hot summers, the monsoon from the sea brings large quantities of water vapor, whereas the dry and cold monsoon from the northern continent dominates this region in winter. These different monsoon types support various atmospheric conditions, such as increasing relative humidity, cooling and updrafts, required for the formation of ice clouds, ultimately resulting in distinct cirrus distributions. Figure 1 presents a typical example of an ice cloud distribution collected by the KPDR in 1 month of winter (January 2016) and 1 month of summer (August 2015).

There are more ice clouds in August than in January, and the mean radar reflectivity of ice cloud in August is higher than that in January. Ice clouds in August also show larger vertical dimensions than in January. The temperature and amount of water vapor are two key parameters in the formation of clouds, especially in plain areas where orographic uplift is negligible. The strong contrast in the climatic circumstances between a month in summer and a month in winter generates a diverse range of ice clouds (Fig. 1c). Thus, to better understand the physical or optical properties of ice clouds, statistical analyses were carried out in this study for different seasons. Such comparisons of the ice clouds among the four seasons benefit our understanding of the dominant formation origins of ice clouds when a region is governed alternately by different monsoon types. In this study, 4 years of radar observations presented more than 6300 ice cloud clusters for our analysis.

Radar data collected in vertically viewing mode were used to calculate the occurrence frequency of all clouds (Oall), which is the ratio of cloudy profiles to all profiles in a certain time range (i.e., an hour or a month), as well as the occurrence frequency of ice clouds (Oic), which is the ratio of profiles determined as ice clouds to all radar profiles: 1Oall=Nall/Nr,2Oic=Nic/Nr, where Nall is the number of cloudy profiles, Nr is the number of all radar profiles and Nic is the number of ice cloud profiles. Figure 2 shows the monthly occurrence frequency of all clouds and ice clouds in 4 years. In addition, the occurrence frequency of cirrus clouds is also presented for contrast. September has the maximum Oall among all months, and summer/winter has the maximum/minimum Oall among the four seasons. Relative to Oall, Oic decreases to 33 %–50 %, and in winter Oic is about 33 % of Oall. The average Oic in April and June is about 20 %, whereas in winter (December–February) it is no more than 10 %. The average Oic in the 4 years is 14 %, which is lower than the ice cloud coverage of 24 % reported by Hahn and Warren (2007) based on satellite measurements over North China. This might be associated with the observation location and the field of view (FOV) of the KPDR. Large quantities of water vapor over the sea areas and orographic-lift movements over mountain areas provide advantageous conditions for the formation of clouds, meaning more clouds occur over these areas relative to plain areas. Therefore, the occurrence frequency calculated from the KPDR data with a small FOV is lower than the cloud coverage calculated from data with a broad FOV. For cirrus clouds, the largest occurrence frequency (4 %) occurs in April. Spring, but not summer, has the most cirrus clouds.

The KPDR operates continuously and thus allows the diurnal variation in Oic to be studied, which illustrates the potential relationship with local thermal convection caused by solar heating. As shown in Fig. 2a, the three highest Oic values in spring, summer, autumn and winter occur at 20:00/22:00/19:00, 21:00/23:00/22:00, 00:00/22:00/21:00 and 14:00/13:00/17:00 LT (UTC+8), respectively. The hourly variations in Oic in the four seasons are different; in spring, summer and autumn, larger Oic values appear at night, whereas larger Oic values in winter appear during the daytime. The diurnal variation in Oic seems to be insensitive to solar heating, which drives the development of regional thermal convection. Here, the presence of ice clouds over the KPDR is not closely related to local air-updraft activities, indicating that these ice clouds may mostly not be generated locally by thermal convections. It is interesting that Oic decreases from 00:00 to 02:00 LT and then increases after that in the four seasons. Is there a decay process in ice clouds during this period? Is the decrease caused by wind, vertical movement or turbulence? Further analysis is required in the future to answer these questions.

The top height of ice cloud, especially cirrus cloud, indicates the highest condensation level in the troposphere, above which clouds cannot form because of the nonconducive condensation conditions. The base height of ice clouds indicates the lowest level required for ice formation. In this study, the CTH and CBH were calculated for each ice cloud cluster; specifically, the CTH and CBH are the mean values of all cloudy profiles in an ice cloud cluster. The distributions of the mean CTH and CBH of all ice clouds in the four seasons are presented in Fig. 3, and Table 1 presents the quantified statistical results.

It is shown that the CTH of ice clouds varies in the range of 5.5–12.9 km (Fig. 3a). The difference between the maximum and the minimum is about 6 km in each season, indicating the ranges of the condensation level and various formation mechanisms of ice clouds. Besides, differences in the CTH between the four seasons are also apparent. Both the maximum (12.9 km) and the highest mean (9.27 km) CTH are found in summer, whereas winter has the minimum CTH (9.94 km) and lowest mean CTH (7.02 km). In summer, 85 % of ice clouds have a CTH greater than 8 km and 29 % are greater than 10 km. In winter, 71 % of ice clouds have a CTH larger than 8 km and those with a CTH higher than 6 km account for 97 %. The mean CTH in summer is 2.2 km higher than that in winter, which means the average condensation level in summer is also 2.2 km higher. Spring and autumn are two transition seasons and their CTHs are 8.16 and 8.23 km, respectively, which are between those of summer and winter.

Figure 3b shows that the CBH changes within a range of 5.3–12.4 km, and the minimum CBHs in the four seasons are close to each other, ranging between 5.3 and 5.7 km. However, the mean CBH in summer is the highest (8.7 km) among the four seasons, while the lowest (6.6 km) is in winter. The difference in CBH between summer and winter is 2.1 km. The mean CBHs in spring and autumn are both 7.7 km. In summer, the percentage of ice clouds with a CBH larger than 8 km is 72 %, while it is only 65 % in winter. In summer and winter, 95 % of ice clouds have a CBH greater than 6 km.

It is shown that the mean CDs of ice clouds in the four seasons are close, with the depths of most clusters being less than 1 km (Fig. 3c). Statistically, in the four seasons, 68 % of clusters have a CD of less than 0.5 km, 90 % have a CD of less than 1 km and 96 % have a CD of less than 1.5 km. It should be noted that the CTH, CBH and CD here are the mean values of an ice cloud cluster. It is therefore possible that there are some instances of CTH, CBH and CD that are greater than their corresponding mean values.

The horizontal extent (EXT) of ice clouds indicates the clouds' lifetimes and their formation mechanism type. For the KPDR, the EXT of an ice cloud cluster is computed as follows: 3EXT=Vhw×Tci, where Vhw is the mean velocity of horizontal wind calculated from the ECMWF-ERA5 dataset and Tci is the continuous time during which an ice cluster moves over the KPDR. It is found that the maximum EXT of ice clouds reaches 2800 km, in April 2017, and the maximum Tci is 21 h, in March 2016. The EXT ranges through orders of magnitude from low values of less than 0.1 km to over 2800 km. Summer has the minimum mean, median and trimmed mean EXT, while ice clouds in autumn have the maximum mean, median and trimmed mean EXT. Statistically, about 75 % of ice clouds have an EXT of less than 50 km and 87 % have an EXT of less than 100 km. The statistically quantified structural properties of ice clouds in the four seasons are presented in Table 1.

Cloud optical depth (COD) is relatively independent of wavelength throughout the visible spectrum. In the visible portion of the spectrum, the COD is almost entirely due to scattering by droplets or crystals of clouds (American Meteorological Society, 2019). Therefore, the CODs of ice clouds depend directly on the CD, the IWC and the size distribution of the ice crystals, indicating a cooling effect or warming effect in the energy budget.

The Advanced Himawari Imager (AHI), on board the geostationary meteorological Himawari-8 satellite operated by the Japan Meteorological Agency, observes the Beijing area every 10 min and began releasing COD and cloud-type products in July 2015 with a spatial resolution of 5 km. The CODs are retrieved by using nonabsorbing visible wavelengths (i.e., 0.51 or 0.64 µm) and water-absorbing, near-infrared wavelengths (i.e., 1.6 or 2.3 µm; Nakajima and Nakajma, 1995; Kawamoto et al., 2001). Quantified uncertainties in the AHI CODs have not been reported, so we use them here directly. The data nearest to the KPDR that the AHI determines as cirrus cloud and the KPDR determines as ice cloud are selected, and their CODs are investigated. Those collocated CODs (collected from the year 2016 to 2017) combined with the mean CDs and mean reflectivity, which are calculated from all cloudy KPDR bins observed within 10 min of the AHI observing time, are presented in Fig. 4.

In the four seasons, CODs show an increasing tendency with increasing CD. The mean reflectivity shows a similar tendency, meaning thicker ice clouds generally contain larger particles and a greater number density of ice particles. The probability density distributions of CODs in the four seasons show a higher probability occurring at lower CODs. The mean COD in spring, summer, autumn and winter is 4.27, 6.07, 4.62 and 4.52, respectively. The proportions of CODs lower than 3 in spring, summer, autumn and winter are 46 %, 36 %, 49 % and 52 %, respectively. The proportions of CODs lower than 10 in the four seasons are 91 %, 79 %, 87 % and 90 %, respectively. In Fig. 4, KPDR cirrus clouds are shown with purple circles. The proportions of CODs for cirrus clouds lower than 3 in spring, summer, autumn and winter are 70 %, 55 %, 77 % and 79 %, respectively. The proportions of CODs lower than 6 in the four seasons are 93 %, 77 %, 94 % and 98 %, respectively. As shown in previous studies, the primary cirrus optical depth is below 3 (Kienast-Sjögren et al., 2016; Sassen et al., 2008). Here, our analysis shows larger CODs, indicating possible mixed-phase clouds. Also, it might be related to the uncertainty in CODs, as the uncertainties in AHI CODs and the different FOV between the KPDR and the AHI may cause the employed CODs to differ from the real CODs. The results here present statistical features of the CODs of ice clouds over Beijing based on a COD dataset of limited accessibility. For cirrus clouds, lidar should provide accurate COD measurements.

The KPDR detects clouds at a 30 m vertical resolution. All ice radar bins collected from 2014 to 2017 were counted according to their reflectivity and height, and the relative frequencies (counts; calculated at 0.25 dBZ and 30 m intervals within 15 km) are shown separately in Fig. 5. As presented, ice clouds exist below the height of 13 km. In summer, the reflectivity mostly varies between -35 and -10 dBZ, while most of the reflectivity falls within the range of -40 to -20 dBZ in winter. In spring and autumn, the reflectivity primarily ranges between -35 and -15 dBZ. The range of variation in reflectivity in summer is the biggest among the four seasons, while it is the smallest in winter. Statistically, at the same height where ice clouds exist in the four seasons, the mean reflectivity of winter is 5 dBZ less than that of spring or autumn and it is 10 dBZ less than that of summer. In the four seasons, the mean reflectivity declines as the height increases below 11 km, with a similar slope. At the height above 11 km, the relationship between reflectivity and the height varies greatly among the four seasons, which might be due to the small sample counts. It can also be seen that the ice bins in summer are located at higher heights than in winter.

Temperature plays a key role in the formation, evolution and lifetime of ice clouds. Activation of liquid water drops does not happen below -38 ∘C because the relative humidity where the ice forms is below water saturation. At temperatures higher than -38 ∘C, primary ice clouds form only when aided by ice-nucleating particles (Kanji et al., 2017). The summer monsoon and winter monsoon in Beijing support distinct temperatures, water vapor, etc., i.e., the conditions necessary for the formation of ice clouds, resulting in distributions of reflectivity with different features corresponding to temperature. The frequencies (counts; calculated at 0.25 dBZ and 1 ∘C intervals) are shown separately in Fig. 6.

In spring, summer and autumn, ice clouds occur mostly at temperatures within the range of -10 to -55 ∘C, relative to which ice clouds in winter occur at lower temperatures. Statistically, the percent of ice bins with temperatures less than -15 ∘C is 99 %, 95 %, 95 % and 99 % in spring, summer, autumn and winter, respectively; the percent of ice bins with temperatures less than -25 ∘C is 85 %, 71 %, 72 % and 92 % in spring, summer, autumn and winter, respectively; and the percent of ice bins with temperatures less than -35 ∘C is 52 %, 36 %, 35 % and 60 % in spring, summer, autumn and winter, respectively. The reflectivity shows a dependence on the temperature, increasing when temperature increases. Statistically, the mean temperature of ice clouds in winter is lower than that in other seasons, even though these ice clouds appear at lower heights. As the temperature decreases, the difference in reflectivity between winter and summer declines. At the same temperature, the mean reflectivity in summer is higher than that in winter. The slopes among the four seasons are close to each other when temperature is above -50 ∘C, demonstrating a determinative effect of the temperature on the cloud particle properties. The slopes in the four seasons disperse at temperatures lower than -50 ∘C, which might be because the small sample counts influence the representativeness of statistical results.

Based on all the ice clusters in the 4 years, we calculated the mean reflectivity and the mean depth of each cluster (Fig. 7), and it was interesting to find that there is a strong linear relationship between the mean reflectivity and the CD. Specifically, the mean reflectivity increases as the CD increases. The linear equation shown in Fig. 7 represents a method that can be used to estimate the mean reflectivity (or CD) if the CD (or reflectivity) is known, which should be useful for cloud parameterization in GCMs.