Properties of mid-latitude cirrus cloud from surface Ka-band radar observations during 2014-2017

The physical properties and radiative role of cirrus clouds remain one of the uncertainties in the Earth–atmosphere system. In this study, we present a detailed analysis of cirrus properties based on four years of surface millimetre wavelength radar measurements in Beijing, China, where summer monsoon from the ocean and winter monsoon from the continent prevails alternately, resulting in various cirrus clouds. More than 6600 cirrus clusters were studied to quantify the properties of cirrus clouds, such as the height, optical depth and horizontal extent, which can serve as a reference for parameterization and 10 characterization in global climate models. In addition, comparison between cirrus clusters formed under summer monsoon and winter monsoon indicates the different formation and evolution mechanisms of cirrus. Statistically, the temperature of more than 90% of cirrus bins are below −15oC. The dependence of the radar reflectivity of cirrus particles on the height and temperature was also observed in this study, indicating that the reflectivity of cirrus bins increases (decreases) as the temperature (height) increases. In addition, it was found that there is a strong linear relationship between the mean reflectivity 15 and the cirrus cloud depth. Due to various synoptic circumstances, the cirrus clouds in summer are warmer, higher, and thicker, with larger reflectivity than that in winter; in particular, the mean cloud-top height of cirrus clouds in summer is 2.5 km higher than that in winter. It was found that most cirrus clusters in winter are likely to be the in situ origin type cirrus but some cirrus clusters in summer are the in situ origin cirrus and others are the liquid origin type cirrus.

cloud cluster into nine types: Cs, Cc, Ac, As, St, Sc, Ns, Cu and Cb clouds. Clouds identified as Cs and Cc are the objects of this study. Further, in order to ensure all cirrus clouds are determined exactly, two criteria have been added after the classification algorithm; namely, the cloud-top temperature should be less than −30°C and the cloud-base temperature should be less than 0°C. In some studies Luebke et al. 2016;Heymsfield et al. 2017;Wolf et al. 2018), cirrus clouds are defined as ice clouds with lower temperature < -38℃. In this study, according to the Glossary of the American 95 Meteorological Society (AMS, 2019), the cirrus clouds are referred to all types of cirriform clouds (Ci, Cc and Cs clouds), which is determined by the reflectivity, temperature, height and depth.

Other datasets
In this study, we also used some other datasets to complement our investigation of the properties of cirrus cloud, such as the temperature profile, water vapor, wind velocity, cloud optical thickness, etc. The research datasets of cloud optical thickness 100 (produced from Himawari-8) used in this paper were supplied by the P-Tree System, 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).

Cirrus cloud samples under summer and winter monsoon
Cirrus clouds can be vertically and horizontally extensive, with their various appearances dependent on the diverse range of associated atmospheric movements and processes. KPDR is located in the north of the North China Plain, where to the west and north are mountains and to the south and east is the Bohai Sea. In the region's hot summers, monsoon from the sea brings large quantities of water vapor, whereas dry and cold monsoon from the northern continent dominates this region in winter. 110 These different monsoon types support various atmospheric conditions, such as increasing relative humidity, cooling, updrafts, etc., required for the formation of cirrus clouds, ultimately resulting in distinct cirrus distributions. Figure 1 presents a typical example of a cirrus cloud distribution collected by KPDR in one month of winter (January 2016) and one month of summer (August 2015). https://doi.org/10.5194/acp-2020-74 Preprint. Discussion started: 2 March 2020 c Author(s) 2020. CC BY 4.0 License. Figure 1. Cirrus clouds occurring in (a) January 2016 (winter) and (b) August 2015 (summer). The mean cloud-top height, mean base height and lifetime of each cirrus cluster forms a cirrus "rectangle". Its mean radar reflectivity is illustrated with different colours. Dark red rectangles on the horizontal axis indicate periods without vertically pointing radar measurements.
The surface temperature (T, left-hand y-axis) and total water vapor (TWV, right-hand y-axis) in the two months are presented in (c). 120 There are more cirrus clusters in August than in January, and the mean radar reflectivity of cirrus in August is higher than that in January. Cirrus 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 cirrus clouds (Fig. 1c). Thus, to better understand the physical or optical properties of cirrus clouds, statistical analyses were 125 carried out in this study for different seasons. Such comparisons of the cirrus clouds among the four seasons benefit our understanding of the dominant formation origins of cirrus clouds when a region is governed alternately by different monsoon types. In this study, four years of radar observations presented more than 6600 cirrus clusters for our analysis.

Monthly and hourly occurrence frequency of cirrus clouds
Radar data collected in vertically viewing mode were used to calculate the occurrence frequency of all clouds (O all ), which is 130 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 cirrus clouds (O ci ), which is the ratio of profiles containing cirrus to all radar profiles: where N all is the number of cloudy profiles, N r is the number of all radar profiles, and N ci is the number of cirrus clouds profiles. 135 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 are lower than the cloud coverage calculated from data with a broad FOV. KPDR operates continuously and thus allows the diurnal variation of Oci to be studied, which illustrates the potential relationship with local thermal convection caused by solar heating. As shown in Fig. 2a, the three highest Oci values in spring, summer, autumn and winter occur at 22:00/12:00/20:00, 16:00/22:00/23:00, 22:00/23:00/00:00 and 20:00/14:00/00:00, respectively, indicating larger Oci values appear both at night and during daytime. The hourly variations of Oci in the four seasons are different; however, there is no apparent difference between day and night in each season. The diurnal variation of Oci seems to be insensitive to solar heating, which drives the development of regional thermal convection. Here, the presence of cirrus clouds over KPDR is not closely related with local air-updraft activities, indicating that these cirrus clouds may not be generated locally by thermal convections. 155

Height, depth and extent of cirrus clouds
The top height of cirrus clouds indicates the highest condensation level in the troposphere, above which clouds cannot form because of the non-conducive condensation conditions. The base height of cirrus clouds indicates the lowest level required for cirrus formation. In this study, the cloud-top height (CTH) and cloud-base height (CBH) were calculated for each cirrus cloud cluster; specifically, the CTH and CBH are the mean values of all cloudy profiles in a cirrus cluster. The distributions of the 160 mean CTH and CBH of all cirrus 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 cirrus clouds varies in the range of 5.09-13.35 km (Fig. 3a). The difference between the maximum CTH and the minimum CTH is about 7 km in each season, indicating the ranges of the condensation level and various formation mechanisms of cirrus clouds. Besides, differences in the CTH between the four seasons are also apparent. 165 Both the maximum CTH (13.35 km) and the highest mean CTH (10.16 km) are found in summer, whereas winter has the minimum CTH (11.25 km) and lowest mean CTH (7.66 km). In summer, 98% of cirrus clouds have a CTH greater than 8 km and 57% are greater than 10 km. In winter, only 37% of cirrus clouds have a CTH larger than 8 km, and those with a CTH higher than 6 km account for 94%. The mean CTH in summer is 2.5 km higher than that in winter, which means the average condensation level in summer is also 2.5 km higher. Spring and autumn are two transition seasons and their CTHs are 8.95 km 170 and 9.09 km, respectively, which are between those of summer and winter.   to each other, ranging between 5.0 and 5.5 km. However, the mean CBH in summer is the highest (9.39 km) among the four seasons, while the lowest (7.1 km) is in winter. The difference in CBH between summer and winter is 2.2 km. The CBHs in spring and autumn are 8.30 km and 8.39 km, respectively. In summer, the percentage of cirrus clouds with a CBH larger than 8 km is 87%, while it is only 21% in winter. In winter, 86% of cirrus clouds have a CBH greater than 6 km. The CBH of cirrus clouds in Beijing, especially in winter, is somewhat lower than that reported by Heymsfield et al. (2017), who stated cirrus 180 clouds were generally above 8 km.
It is shown that the mean cloud depths (CDs) of cirrus 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, 57% of clusters have a CD of less than 0.5 km, 80% less than 1 km, 90% less than 1.5 km, and 95% less than 2km. It is found that the maximum CD is 7.4 km, which occurs in the summer. However, the maximum CD in winter is 3.6 km, which is almost half of that in the summer. It should be noted that the 185 CTH, CBH and CD here are the mean values of a cirrus 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 cirrus clouds indicates its lifetime and the formation mechanism type. For the KPDR, the EXT of a cirrus cluster is computed as follows: where V hw is the mean velocity of horizontal wind calculated from the ECMWF-ERA5 dataset and T ci is the continuous time during which a cirrus cluster moves over the KPDR. It is found that the maximum EXT of cirrus clouds reaches 3100 km, which is in October 2017, and the maximum T ci is 21 hours, which is in March 2016. The EXT ranges through orders of magnitude from low values of less than 0.1 km to over 3000 km. Summer has the minimum mean, median and trimmed mean EXT, while cirrus clouds in autumn have the maximum mean, median and trimmed mean EXT. Statistically, about 75% 195 of cirrus clouds have an EXT less than 50 km and 87% less than 100 km. The statistically quantified structural properties of cirrus clouds in the four seasons are presented in Table 1.

Optical depth of cirrus clouds
Cloud optical depths (COD) are 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 (AMS, 2019). Therefore, the CODs of cirrus clouds depend directly on the CD, the ice water content, and the size distribution of the ice crystals, 205 indicating a cooling effect or warming effect in the energy budget.
The Advanced Himawari Imager (AHI), onboard the geostationary meteorological Himawari-8 satellite operated by the Japanese 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) (Kawamoto et al. 2001;Nakajima and 210 Nakajma 1995). Quantified uncertainties of the AHI-CODs have not been reported, so we use them here directly. The data nearest to KPDR that both AHI and KPDR determine as cirrus type are selected and their CODs are investigated. Those  In the four seasons, CODs show an increasing tendency with increasing CD. The mean reflectivity shows a similar 220 tendency, meaning thicker cirrus clouds generally contain larger particles and a greater number density of ice particles. The probability density distributions of COD in the four seasons show a higher probability occurring at lower COD. The mean COD in spring, summer, autumn and winter is 4.43, 6.17, 4.65, and 4.62, respectively. The proportions of CODs lower than 3 in spring, summer, autumn and winter are 44%, 35%, 47% and 52%, respectively. The proportions of CODs lower than 10 in spring, summer, autumn and winter are 90%, 78%, 87% and 90%, respectively. 225

Microphysical properties of cirrus clouds
The most important microphysical quantities of cirrus clouds are the ice particle size distribution, the ice water content (IWC), and their shapes . It is known that the radar equivalent (or effective) reflectivity factor (Z e ) can be expressed as where , , ∅ is the backscattering cross section with maximum dimension D and an axial direction , ∅ with respect to the radar beam, , , ∅ is the number density, λ is the wavelength, and m is the complex index of refraction of the scattering target. To date, numerous empirical relationships between Z e and cloud properties (P)-e.g., IWC, snow precipitation rate-have been developed, usually in the power-law form of

, (5) 235
where A is the prefactor coefficient and B is the exponent derived in terms of calculated or measured datasets (Austin et al. 2009;Delanoë and Hogan 2010;Deng et al. 2015;Heymsfield et al. 2018;Heymsfield et al. 2008;Liu and Illingworth 2000;Matrosov and Heymsfield 2017;Wang and Sassen 2001a). Hogan (2008, 2010) proposed a different method using a forward model to retrieve the IWC and the effective radius by combination with the COD. Also, the basic principles of this method are applied in the CloudSat/CALIPSO cloud microphysical retrieval algorithm. However, the utility of 240 empirical relations such as Eq. (5) is still common in many practical measurements, and the correspondence between the IWC and Z e is related with the particle size distribution (the gamma distribution is mostly used for ice clouds).
For the KPDR, the development of the IWC and particle size retrieval algorithm is in progress but has not been tested completely. In this paper, we use the measured radar reflectivity factor Z e (hereinafter just reflectivity; units: mm 6 /m 3 ; dBZ=10log(Z e )) directly, not the retrieved microphysical quantities, to study and characterize the microphysical properties of 245 cirrus clouds. It can be found from the Eq. (4) that reflectivity increases when σ and N increase; in other words, a larger reflectivity normally indicates a larger D, N and IWC.

Reflectivity of cirrus clouds and height dependence
KPDR detects clouds at a 30-m vertical resolution. All cirrus radar bins collected from 2014 to 2017 were counted according to their reflectivity and height, and the relative frequencies are shown separately in Fig. 5. In summer, the reflectivity mostly varies between −30 and −10 dBZ, while most of the reflectivity falls within the range of −35 to −25 dBZ in winter. In spring and autumn, the reflectivity primarily ranges between −30 and −20 dBZ. The range of variation in reflectivity in summer is the biggest among the four seasons, while it is smallest in winter. Statistically, at the same height where cirrus 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, with a similar slope. It can also be seen 255 that the cirrus bins in summer are located at higher heights than in winter.

Temperature dependence
Temperature plays a key role in the formation, evolution and lifetime of cirrus clouds. Activation of liquid waterdrops does not happen below −38ºC because the relative humidity where the ice forms is below water saturation. At temperatures higher than −38ºC, cirrus clouds can form heterogeneously or homogeneously (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 cirrus 265 clouds, resulting in distributions of reflectivity with different features corresponding to temperature (see Fig. 6). In spring, summer and autumn, cirrus clouds occur mostly at temperatures within the range of −15ºC to −55ºC, relative to which cirrus clouds in winter occur at lower temperatures. Statistically, the frequency of cirrus bins with temperatures less 270 than −15ºC is 96%, 94%, 95% and 95% in spring, summer, autumn and winter, respectively; the frequency of cirrus bins with temperatures less than −25ºC is 81%, 72%, 66% and 92% in spring, summer, autumn and winter, respectively; the frequency of cirrus bins with temperatures less than −35ºC is 45%, 37%, 27% and 55% in spring, summer, autumn and winter, respectively. The reflectivity shows a dependence on the temperature, increasing when temperature increases.
Statistically, the mean temperature of cirrus clouds in winter is lower than that in other seasons, even though these cirrus 275 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.

Depth dependence
Based on all the cirrus clusters in the four 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. The mean 280 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.

Origination type of cirrus clouds
Various prefactor coefficients dependent on temperature have been derived and applied in the Z e -IWC power-law relationship [i.e., Eq. (5)] since the distribution of reflectivity has a dependence on temperature (Heymsfield et al. 2018;Heymsfield et al. 2013;Hogan et al. 2006;Matrosov and Heymsfield 2017). Based on the frequency statistics in section 4.2, we also investigated the distribution of reflectivity (similar to the probability density function, PDF) at several temperatures. 290 Figure 8 shows the normalized frequency of reflectivity at several temperatures (−45ºC, −40ºC, −35ºC, −30ºC, −25ºC, −20ºC), which are actually portions of Fig. 6. In Fig. 8, we use wider lines to illustrate the data in winter and summer for clearer contrast since the cirrus clouds show distinct features in the two seasons. Reflectivity's dependence on temperature is also shown in Fig. 8, and the six panels present different distributions of reflectivity at different temperature. Besides, in five of the panels (a, b, c, d, e) of Fig. 8, the frequencies of reflectivity show very close appearances between the summer and 295 winter when reflectivity is lower than −25 dBZ. However, when reflectivity is above −25 dBZ, its PDF in winter declines quickly, illustrating a different appearance with that in summer. The PDFs in winter differ somewhat with those in summer, even at the same temperatures, which may be due to the different origination mechanism of cirrus clouds in the two seasons. namely, in situ-and liquid-origin cirrus. The in situ-origin cirrus type forms directly as ice, while the liquid-origin type originates from mixed-phase clouds that are completely frozen until they are lifted to the cirrus formation temperature region. 305 They reported that the in situ-origin cirrus are mostly thin, with lower IWC, while liquid-origin cirrus tend to be thicker with higher IWC. Also, liquid-origin cirrus tend to have larger ice crystals than in situ-origin cirrus. Therefore, the reflectivity of in situ-origin cirrus should generally be less than that of liquid-origin cirrus. From the statistical results in Fig. 8, especially panels (a) to (d), it also seems that cirrus clouds in winter below the temperature of −30ºC are likely to be in situ-origin cirrus, whereas those in summer are formed from both types since the distribution in summer expands to a wider range and 310 larger reflectivity. Thus, in summer, cirrus with lower reflectivity may be the in situ-origin type, while those with higher reflectivity may be the liquid-origin type.
To further test the assumption, we divided the cirrus clusters in summer into two types based on a threshold of mean reflectivity: larger than −30 dBZ (accounting for 30% of all cirrus clusters) and less than −30 dBZ. The mean reflectivity of a cirrus cluster is the mean of the reflectivity of all cirrus bins in the cirrus cluster. We calculated the frequency of cirrus 315 clouds with a mean reflectivity larger than −30 dBZ, which is presented with dashed blue lines in Fig. 9 for comparison. The remaining frequency portions in each panel are from the cirrus clusters with mean reflectivity lower than −30 dBZ. When compared with the frequency distribution based on all summer cirrus clusters, these cirrus clusters with mean reflectivity larger than −30 dBZ contribute the absolute majority of those cirrus bins (in Fig. 8) with reflectivity larger than −25 dBZ, illustrating different PDFs with those in winter. Specifically, the differences in the PDFs between winter and summer are mostly due to the cirrus clusters with mean reflectivity higher than −30 dBZ. In particular, as shown in Fig. 9f, 325 those cirrus bins in Fig. 8 are wholly from these clusters with reflectivity larger than −30 dBZ. The strong contrast in Fig. 8f further confirms that the differences in the PDF between summer and winter are due to the different origination type.
From panels (a) to (f) in Fig. 9, as temperature increases, so too does the ratio of those clusters with reflectivity larger than −30 dBZ to all clusters. When the cloud temperature is lower than −30ºC, it can be inferred that the cirrus clouds in summer with mean reflectivity lower than −30 dBZ are likely to be of the in situ-origin type, while those with mean 330 reflectivity larger than −30 dBZ are likely to be of the liquid-origin type. When cirrus clouds occur at temperatures higher than −30ºC, most will be of the liquid-origin type. In winter, most cirrus clouds are of the in situ-origin type. Therefore, the distribution of reflectivity depends not only on the temperature but also on the origin type.

Summary and discussion 335
Cirrus clouds are an important component of the planetary radiation budget and remain an uncertainty source in GCMs. This study used four years of vertically pointing Ka-band radar measurements at Beijing to characterize the physical and optical properties of cirrus clouds and to investigate their origination type. The goal was to present the quantified properties of cirrus clouds over the subtropical monsoon zone, which can be represented in GCMs towards a better understanding of the relationships between temperature and radar reflectivity under different formation conditions in various monsoon climates. 340 Winter monsoon and summer monsoon prevail alternately over Beijing, resulting in four distinct seasons. Cirrus clouds in winter and summer show strikingly different features. The specific findings about the properties of cirrus can be summarized as follows: 1. The occurrence frequency, height, temperature and mean reflectivity of cirrus in winter are lower than in summer. The average occurrence frequency over Beijing is 16%, and it is 20% in summer but less than 10% in winter. The diurnal