Freezing precipitation (i.e., freezing rain or freezing drizzle) is an extremely hazardous weather that can cause severe socioeconomic loss and compromise human safety. To better document and understand the microphysics of this type of precipitation, drop size spectra were collected with an optical disdrometer during a freezing precipitation event on 27 January 2008 in southern China. The drop size distribution (DSD) characteristics, the correlations between the shape (μ), slope (Λ), and intercept (N0) of the gamma distribution, and the relations between the reflectivity (Z) and rainfall rate (R) have been investigated. It was found that the DSDs of freezing precipitation were characterized by weak stratiform rain with a small mass-weighted diameter (Dm, 0.63 mm) and a large normalized intercept (Nw, 4.25 log10 mm−1 m−3). This indicated that freezing precipitation was not formed by the melting of larger, dry snowflakes but by the melting of smaller, rimed ice particles. Furthermore, the derived μ-Λ, N0-μ, and Z-R relations are distinctly different from the convective rains or tropical stratiform rains reported in the literature.
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 Freezing precipitation (i.e., freezing rain or freezing drizzle) is an extremely hazardous weather that can lead to catastrophic icing events and cause severe socioeconomic loss and compromise human safety. One such example is the 2008 Freezing Rain and Snowstorm in southern China, the most catastrophic winter weather event in Chinese history, which caused 129 fatalities and over $21 billion U.S. dollars in damages.
 Freezing precipitation is liquid precipitation that falls in liquid form but freezes upon impact to form a coating of glaze on the ground and exposed objects. Freezing precipitation forms through the collision and coalescence of droplets, referred to as the warm rain process, or the classical melting process [Bocchieri, 1980; Huffman and Norman, 1988; Rauber et al., 2000]. The classical melting process occurs when ice particles fall into a layer of above-freezing air, melt to form rain or drizzle, then fall into a layer of subfreezing air to become supercooled rain or drizzle. It generally has been accepted that most freezing precipitation forms via the melting process. The warm rain process typically occurs in clouds composed primarily of liquid water and with cloud top temperatures greater than about −10°C. This is the primary process for the formation of freezing drizzle [Bernstein, 2000; Rauber et al., 2000].
 Despite such studies were thorough, no published studies have focused on the measurements of freezing precipitation spectra. Information about drop size distribution (DSD) is essential for understanding precipitation physics, estimating rainfall, and improving microphysics parameterizations in numerical weather prediction models. DSD also affects icing characteristics. When supercooled raindrops and ice particles coexist within the refreezing layer, the raindrops may come into contact with ice particles. As a result, the collisions not only alter the amounts and sizes of supercooled rain and ice particles, but also may form a new category of particle. For instance, ice pellets, an important type of winter precipitation, may be formed through the interaction between supercooled raindrops with ice crystals in the refreezing layer [Thériault and Stewart, 2010]. However, the interactions between liquid drops and ice particles are highly dependent on the drop sizes [Pruppacher and Klett, 1997]. Consequently, the DSD can affect the formation of winter precipitation at the surface.
 Given the importance of freezing precipitation and the lack of previous study, we report the characteristics of drop size spectra for freezing precipitation based on disdrometer data at a 1 min time resolution observed in southern China. The primary goals are to better understand the microphysics of freezing precipitation, and to investigate what freezing precipitation differs in the DSD characteristics from other rain types.
2. Data and Methodology
2.1. Instrumentation and Data
 The particle size spectra data analyzed in this study were collected with an OTT PARSIVEL disdrometer manufactured by the company OTT Messtechnik, Germany. Battaglia et al.  provided a detailed description of this instrument. Briefly, the instrument is a ground-based optical disdrometer that is designed to count and measure simultaneously the fall speed and size of precipitation particles. The core element of the instrument is an optical sensor that produces a horizontal sheet of light (180 mm long, 30 mm wide, and 1 mm high). PARSIVEL can measure sizes up to about 26 mm and uses 32 size bins of different widths, ranging from 0.125 to 3 mm. The lowest two size bins are not used at all, because of their low signal-to-noise ratio. Exclusive of the first two bins, the range of particle sizes that can be measured spans from 0.3 to 26 mm in diameter. The smallest and largest detectable fall velocity is about 0.05 m s−1 and 21 m s−1, respectively. The velocity is also subdivided into 32 bins with different widths, ranging from 0.1 to 3.2 m s−1. PARSIVEL detects and identifies eight different precipitation types as drizzle, mixed drizzle/rain, rain, mixed rain/snow, snow, snow grains, ice pellets (also known as sleet in the United States) and hail, according to the WMO, SYNOP, METAR and NWS weather codes. Yuter et al.  confirmed that PARSIVEL can be exploited as a present weather sensor because of its capability to distinguish rain, snow, and wet snow.
 The particle diameter as measured by the PARSIVEL disdrometer is calculated from the maximum reduction of the voltage. A spheroid model is used to estimate the size of the particles as a function of voltage reduction. So, the particle sizes directly derived by the instrument, defined as the PARSIVEL size, are equivalent sphere diameter. However, the particle sizes frequently overestimate the large raindrop diameter [Löffler-Mang and Joss, 2000; Löffler-Mang and Blahak, 2001; Battaglia et al., 2010]. To minimize the potential instrument error, the observed data herein are corrected following the method of Battaglia et al. . In this scheme, particles below 1 mm equivalent sphere diameter DeqPAR are assumed to be spheres, where the superscript PAR stands for PARSIVEL. In the range from 1 to 5 mm, all raindrops are assumed to be horizontally oriented oblate spheroids with axial ratio arPAR (defined as the ratio between height and width) linearly varying from 1 to 0.7, that is,
For particles with diameters above 5 mm, the axial ratio is kept constant at a value of 0.7.
 The PARSIVEL disdrometer was installed on a flat roof of a low building on the Qianshan Meteorological Bureau (about 10 m from surface level), Anhui Province, China. Continuous measurements were taken from 26 to 28 January 2008 to cover the main winter storms. Studies herein focus on the 27 January freezing precipitation event. The site of the measurement is located in the middle and lower reaches of the Yangtze River, with latitude and longitude of 30.63°N and 116.58°E, and the altitude of about 35 m above mean sea level, which is a severely affected area during the freezing precipitation event. Figure 1 shows the location of the observational site and topographic features. The Anqing station, the nearest upper air observation station to the disdrometer site, about 50 km southeast of Qianshan, is also indicated in Figure 1. Radiosonde data from the Anqing sounding, including pressure, temperature, dew point temperature and wind data are available at both standard and significant levels, available twice daily at 0000 and 1200 UTC, were utilized to examine the thermodynamic stratification of freezing precipitation events. Owing to the lack of observations of hourly precipitation type and amount for icing season at weather station, hourly surface meteorological data taken at Qianshan (1.5 m temperature, hereafter referred to as the surface temperature, relative humidity and wind) were utilized to determine occurrence of freezing precipitation.
2.2. Partitioning of Precipitation Types
 Generally, freezing precipitation episodes are typically characterized by an above-freezing layer, an upper level inversion, and overlaying a lower level subfreezing layer [Stewart, 1985; Stewart and King, 1987]. Moreover, freezing precipitation is usually associated with fronts which can bring widespread stratiform precipitation. Under such environment, the melting process occurs when snow falls into a layer of above-freezing air, melts to form rain or drizzle, and then falls into a layer of subfreezing air to become supercooled rain or drizzle. Recent studies have shown that the freezing precipitation event in January 2008 in southern China was directly linked to the activity of quasi-stationary front located at southern China [Qian and Fu, 2010; Sun and Zhao, 2010]. Figure 2 shows vertical profiles of temperature from the Anqing sounding on 27 January at 0000 and 1200 UTC. One can see that a melting layer and lower subfreezing layer are evident in 1200 UTC profiles. At that time, the maximum temperature in the melting layer and the minimum temperature in the subfreezing layer were 2.7°C and −7.1°C, respectively. The depths were about 600 m for the melting layer and 2500 m for the lower refreezing layer. The maximum temperature and the depth of the melting layer herein are consistent with those found by Roberts and Stewart  favorable for freezing rain over the eastern Canadian Arctic. But the later posses a smaller depth of the lower subfreezing layer owing to in the higher latitude. Actually, as documented by, the precipitation types reported at the surface are more sensitive to the melting characteristics than the lower subfreezing characteristics [Zerr, 1997; Rauber et al., 2001; Roberts and Stewart, 2008]. Although the temperature of the entire air column was less than 0°C in the 0000 UTC vertical profiles, it is undoubtedly that a melting layer exists during the following 12 h according to the trend of temperature profiles. Therefore, the thermodynamic structure is favorable for the occurrence of freezing rain.
 Considering surface meteorology, the rain can be regarded as freezing rain when the surface temperature is below 0°C. According to the weather reports made by the meteorological observers, the precipitation type during the observation period was light liquid precipitation in the form of drizzle and light rain, snow or ice pellets were not found at surface. While the surface temperature varied from −1.2°C to −2.0°C and relative humidity from 85% to 95% (Figure 3). The average wind speed was about 2.8 m s−1 with a standard deviation of 0.5 m s−1 (not shown). On the basis of the above analysis for upper air and surface observations, the occurrence of freezing precipitation was accordingly determined.
 The disdrometer database used in this work consists of an about 7.5 h time series of 1 min drop size and fall speed distributions, collected with the PARSIVEL during the time period from 0500 to 1400 UTC, 27 January 2008. The precipitation types reported by the PARSIVEL include drizzle (WMO-4680 codes 51–53, drizzle not freezing slight, moderate and heavy, respectively), mixed drizzle/rain (codes 57–58, drizzle and rain slight or moderate/heavy) and rain (codes 61–62, rain not freezing slight or moderate). It is found that the PARSIVEL is in good agreement with the human observations. However, we noted that the original database included several snow samples which occurred occasionally within a continuous rain period. These samples have been removed from the data set. Overall, the sample partitioning in the whole data set is roughly 58% for drizzle, 8% for rain, and 34% for mixed drizzle/rain. In further analysis, these three types of liquid precipitation are collectively classified as rain.
 The measured drop size and velocity distributions for the entire event are shown in Figure 4. Different color shades indicate drop numbers were recorded within a particular size and velocity category. Average fall velocities for each size bin and the corresponding fitted power law relations with a form V = cDγ are also shown. In addition, for reference we also present the measurements from Gunn and Kinzer  for raindrops, empirical fall velocity relations for ice pellets [Milbrandt and Yau, 2005], and lump graupel [Locatelli and Hobbs, 1974]. One can see that the maximum drop size was less than 2 mm in diameter and high concentrations of small drops dominated the entire precipitation event, where the maximum concentration occurred at a diameter of 0.44 mm. The small drops with diameter less than 1 mm contributed more than 98% of the total particles. Overall, the distribution of observed fall velocities as a function of diameter closely around Gunn and Kinzer's  measurements, but significantly departs from ice pellets and graupel. However, the PARSIVEL also reports high number of smaller drops, especially between 0.2 and 0.5 mm, owing to the so-called margin effect [Yuter et al., 2006]. While the fall velocities of midsized drops are slightly underestimated.
 The good agreement between the observed fall speeds by the disdrometer and Gunn and Kinzer's  measurements illustrated in Figure 4 confirms the rain types categorized by the PARSIVEL for the 27 January 2008 precipitation event.
 Drop size distributions were fit with the well-known gamma function [Ulbrich, 1983] given by
where D (mm) is the drop diameter, N(D) (mm−1 m−3) is the number of drops per unit volume per unit size interval, N0 (mm−1−μ m−3) is the number concentration parameter, μ is the shape parameter, and Λ (mm−1) is the slope parameter. The governing parameters in equation (2) were estimated from the second, fourth, and sixth moments of the observed distributions, respectively, described by Ulbrich and Atlas  and Zhang et al. . Specifically, for the gamma model, the nth-order moment of the drop size distributions is expressed as
The N(D) (mm−1 m−3) at the discrete instant has been calculated from the PARSIVEL disdrometer counts using
where nij is the number of drops reckoned in the size bin i and velocity bin j, A (m−2) and Δt (s) is the sampling area and time, Di (mm) is the drop diameter for the size bin i and ΔDi is the corresponding diameter interval (mm), and Vj (m s−1) is the fall speed for the velocity bin j. Similarly, we can obtain the drop velocity distribution N(V) (s m−4) when equation (4) is summed over all of the size bins:
where ΔVj is the fall speed interval (m s−1) corresponding to the velocity bin j.
 Given the DSD, the integral rainfall parameters of interest in this work can be computed, including the radar reflectivity factor Z (mm6 m−3) and rain rate R (mm h−1) given by
 Other two parameters of interest are the mass-weighted mean diameter Dm (mm) computed as the ratio of the fourth to third moment of the size distribution,
where ρw (1.0 g m−3) represents the density of water and W (g m−3) represents the liquid water content for the corresponding size distribution.
3. Drop Size Distribution Characteristics
Figures 5 and 6 present the time series of the drop size distribution N(D) and fall speed distribution N(V), and the corresponding integral rainfall parameters. One can see that the precipitation event can be divided into three different segments. The first segment lasted over 2.5 h and exhibited the event's smallest concentration, about 120 drops m−3 in average and 500 m−3 in maximum, minimum rain intensity with mean values of ∼0.06 mm h−1 and lowest liquid water content of ∼0.007 g m−3. Significant features for the first segment were the relatively low concentration and high variability of drop size spectra where the maximum drop diameter was 1.55 mm. The second segment lasted over 3 h and was totally dominated by a large number of small drops in the form of freezing drizzle and lack of large drops. Although maximum drop in this segment was 1.2 mm in diameter, only two large drops with D > 1 mm were observed. The mean maximum diameter was 0.76 mm versus 0.89 mm in the first segment. Compared with the first segment, the second segment had relatively higher concentrations, liquid water contents and rain rates but smaller drop sizes. The number concentrations in this period were about 670 m−3 in average and 1480 m−3 in maximum, the rain rate 0.26 mm h−1, and the liquid water content 0.037 g m−3. The peak concentration was around 0.44 mm in diameter and 1.5 m s−1 in fall speed. Low variability in the spectra was a significant feature for this segment. The coefficient of drop variation, herein defined as 100% times the standard deviation of drop diameter divided by the mean diameter to measure the fluctuating magnitude, was approximately 14% versus 32% for the first segment, showing a weak intraphase variation and steady rainfall feature. The last segment exhibited the event's largest concentration, 1500 drops m−3, highest liquid water content, 0.212 g m−3, and maximum rain intensity, 2.55 mm h−1, owing to the high concentration of midsize drops and the presence of large drops (1.95 mm in diameter and 7 m s−1 in fall speed). Within the 2 h observation period, over 43% of samples were detected with the appearance of midsize drops with D > 1 mm. While the coefficient of drop variation of ∼32% indicated that the last segment also had a high variability of drop size spectra.
 To investigate the overall DSD characteristics, Figure 7 presented the composite drop size distribution obtained by averaging all the instant size spectra for the whole data set and the corresponding gamma functional distribution. One can see that the composite size spectra was characterized by a single peak distribution in which the high concentration of drops occurred at 0.44 mm, but the size distribution was very narrow where the maximum drop diameter was less than 2 mm in diameter, showing a typical drop size distribution of stratiform rain. The relatively high concentrations of small drops in the presence of narrow drop spectra resulted in large values of the intercept parameter N0 and the slope parameter Λ. In fact, the intercept parameter together with the characteristic diameter, for example, the generalized intercept parameter Nw and the mass-weighted mean diameter Dm, can reflect the microphysical formation mechanisms of stratiform rain [Bringi et al., 2003]. Here the Nw and Dm derived from the composite size spectra were 17886 m−3 mm−1 (4.25 in logarithmic scale) and 0.63 mm, respectively. This Nw-Dm pair was located in the stratiform rain region suggested by Bringi et al. . For further information, Figure 8 presents the Nw-Dm pairs based on all disdrometer data. Meanwhile, for clarity we also superimposed Bringi et al.'s  result of stratiform rain (shown as a dashed line in Figure 8) and contours of liquid water content. One can see that all Nw-Dm points fall in the stratiform rain area by Bringi et al. , which indicated that the DSDs of the freezing precipitation were characterized by typical stratiform rains. Additionally, the small concentration of drops 540 m−3, weak rain intensity 0.3 mm h−1 and low rainwater content 0.035 g m−3 for the whole event averaged also indicated stratiform precipitation. For constant rainwater content, there was an inverse relationship between logarithmic Nw and Dm; in fact, it was quite remarkable that a straight line fit (shown as a solid line in Figure 8) results. However, different from Bringi et al.'s  data, nearly all Nw points herein were below Dm = 1 mm and centered around 0.5 mm with the values of logarithmic Nw ∼ 4–5. Considering microphysical perspective, stratiform rain results via the melting of snowflakes and/or tiny graupel or rimed particles. The variation in the Nw-Dm values, suggested by Bringi et al. , reflects the different microphysical formation mechanisms of stratiform rain due to melting of large dry snowflakes (larger Dm and smaller Nw) versus melting of tiny graupel or smaller rimed ice particles (smaller Dm and larger Nw). Thus, so large Nw and small Dm in the present work indicated that the freezing precipitation was formed by the melting of tiny, compact graupel or rimed ice particles but not the melting of large, low-density snowflakes.
 The sounding analysis also showed that the atmospheric conditions were unfavorable for occurrence of freezing precipitation through the warm rain process. On the basis of the observed soundings, we estimated the cloud top at about 400–500 hPa with the cloud top temperature of −20°C to −10°C; here the cloud top was defined as the first level above the low-level cloud layer where the dew point depression exceeded 3°C, provided that the dew point depression remained >3°C through a layer of at least 1 km depth [Rauber et al., 2000]. For the warm rain process to occur, the cloud top temperature generally exceeds about −10°C [Rauber et al., 2000]. Considering such conditions, we further believed that the freezing precipitation formed through the melting process.
4. The μ-Λ and Z-R Relationships
 Although the gamma distribution function has been widely used in the numerical weather prediction models to describe a variety of drop size distributions, the shape parameter μ is often assumed to be a fixed constant. In fact, the three parameters N0, μ and Λ are not independent of each other. Figure 9 provided the time series of these three parameters, clearly showing a rather similar behavior and a very strong correlation. Thus, the parameter μ can be determined from the μ-N0 or μ-Λ relationship. Ulbrich  found that the μ-N0 relation could be represented by the form N0 = αeβμ, where α = 6 × 104 and β = 3.2, while Brandes et al.  and Zhang et al.  suggested an empirical relation between Λ and μ using a polynomial of second degree given by
However, this relation was obtained from the observed disdrometer data under the condition an intense convective rainfall rate greater than 5 mm h−1, for weak or stratiform precipitation, this relation might not hold that well [Seifert, 2005]. Despite some new μ-Λ relations having been reported [e.g., Chu and Su, 2008; Chang et al., 2009], few studies focus on the freezing rain associated with winter stratiform precipitation.
 The empirical μ-N0 (shown by the log10N0) and μ-Λ relations for freezing rain are shown in Figures 10 and 11, respectively. Similar to the results of Ulbrich  and Ulbrich and Atlas , the μ-N0 relation was represented well by the exponential form N0 = αeβμ, where α = 1096 and β = 1.916. Here very small values for the coefficients α and β are not surprising in view of the high curvature in narrow size distribution for stratiform rain. Compared with the results of Brandes et al.  and Zhang et al. , the μ-Λ relationship in this work had a larger slope given by
Even though compared with the results of tropical stratiform rain [e.g., Atlas and Ulbrich, 2006; Ulbrich and Atlas, 2007], the Λ and μ values were relatively larger. This was mainly due to relatively narrow spectra with small mean diameter. For the tropical stratiform rain, the μ-Λ values were limited in the range 0.5 mm < D0 < 1.5 mm, where D0 was the median volume diameter and related to Dm for gamma distribution as D0/Dm = (3.67 + μ)/(4 + μ). However, as shown in Figure 11, nearly all Λ-μ pairs fall in the range Dm < 1 mm and about 50% in the range D0 < 0.5 mm, indicating that the μ-Λ relation was dominated by small D0 (or Dm) values for this freezing precipitation event.
Figure 12 shows a scatterplot of the values of the radar reflectivity factor Z and the rain rate R. We have also derived the empirical power law Z-R relationships in the form Z = ARb on the basis of a gamma distribution parameter method described by Ulbrich and Atlas , in which they used the parameters μ and N0 (m−3 cm−μ−1) to determine the coefficients A and b given by
Note that in Z-R analysis for determination the coefficients A and b, the rain rate R was approximated by a form in which the drop fall speed was assumed by a power law of the form V(D) = 17.67D0.67 [Atlas and Ulbrich, 1977], where V(D) was in m s−1 and D was in cm.
 On the basis of the parameters μ and N0 estimated from the composite drop size spectra shown in Figure 7, we obtained the coefficients A = 117 and b = 1.35. Compared with the tropical maritime stratiform rain [e.g., Tokay and Short, 1996; Atlas et al., 2000; Ulbrich and Atlas, 2002, 2007], the b values were generally consistent but the A values were considerably smaller because of the generally smaller values of D0. The D0 was only in the range of 0.31–1.33 mm with the mean values of 0.55 mm, that values were smaller than that of the reported in the literature for tropical maritime stratiform rain [Tokay and Short, 1996; Ulbrich and Atlas, 2007]. Clearly, the smaller D0 is, the narrower is the DSD, the larger is the range of μ, and the larger is the range of N0, thereby the smaller is the range of the coefficient A.
5. Summary and Conclusions
 In this study, the microphysical characteristics of drop size distributions during a severe hazardous freezing precipitation event were investigated using the PARSIVEL disdrometer data observed in southern China on 27 January 2008. During a 9 h observation period, we obtained about 7.5 h instant samples of 1 min raindrop size and fall speed distributions. It has been found that the DSDs exhibited the typical properties of stratiform rain, as shown in Table 1, characterized by weak rainfall intensity, low rainwater content, and number concentration of small-sized drops, and a low drop variability.
Table 1. Microphysical Characteristic Values of Drop Spectra for the Whole Data Set of the 27 January 2008 Freezing Precipitation Event in Southern China
Rain rate (mm h−1)
Liquid water content (g m−3)
Drop number density (m−3)
Maximum diameter (mm)
Peak diameter (mm)
Mass-weighted mean diameter (mm)
Coefficient of drop variation (%)
 The NW-Dm relationships agree with Bringi et al.'s  findings for stratiform rains but have been extended over a smaller Dm range owing to the inclusion of drizzle precipitation. The log10Nw ranges from 2.65 to 4.99 while Dm ranges from 0.37 to 1.16 mm, respectively. The average is 4.25 for log10Nw and only 0.63 mm for Dm. Following Bringi et al.'s  suggestion, we accordingly conclude that the freezing precipitation was formed by the melting of smaller, compact graupel or rimed ice particles but not the melting of larger, dry snowflakes.
 The μ-Λ relation derived here is distinctly different from the convective rains and tropical stratiform rains reported in the literature, showing a larger μ and Λ values. Compared to the values associated with stratiform rains reported in other regions, the coefficient b value in Z = ARb is generally consistent while the A value is usually much smaller because of the generally smaller values of characteristic drop sizes, like D0 or Dm. Specifically, the value is 117 for A and 1.35 for b.
 In summary, this study confirmed that the DSD characteristics of freezing rain of winter precipitation showed important differences with other rain types, for example, the convective rains or tropical stratiform rains. Although this work has advanced our understanding of the characteristics of freezing rain, much remains to be learned about this form of winter precipitation including in specific regions and/or seasons or specific rain type.
 In a future study, we propose to investigate the microphysical mechanisms of freezing precipitation for this event by high-resolution numerical model simulations with detailed microphysics.
 This work was partially supported by the National Natural Science Foundation of China (grant 40775005), the National Special Funding Project for Meteorology (GYHY200906003), the Foundation of the Key Laboratory for Cloud Physics and Weather Modification of CMA (2009007), the Foundation of Jiangsu Meteorological Bureau (200902), and the National Grand Fundamental Research 973 Program of China (973; 2009CB421502). The authors would also like to thank the reviewers for their insightful and helpful comments.