Characteristics of summer and winter precipitation over northern China

Accepted Manuscript Characteristics of summer and winter precipitation over northern China

Guang Wen, Hui Xiao, Huiling Yang, Yongheng Bi, Wenjing Xu PII: DOI: Reference:

S0169-8095(17)30407-6 doi: 10.1016/j.atmosres.2017.07.023 ATMOS 4018

To appear in:

Atmospheric Research

Received date: Revised date: Accepted date:

11 April 2017 1 July 2017 26 July 2017

Please cite this article as: Guang Wen, Hui Xiao, Huiling Yang, Yongheng Bi, Wenjing Xu , Characteristics of summer and winter precipitation over northern China, Atmospheric Research (2017), doi: 10.1016/j.atmosres.2017.07.023

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Characteristics of summer and winter precipitation over northern China

Guang Wen Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029， China

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Hui Xiao1

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Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029， China, and University of Chinese Academy of Sciences (UCAS), Beijing 100049,

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China

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Huiling Yang

Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,

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China

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Yongheng Bi

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Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029，

Wenjing Xu

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China

Institute of Urban Meteorology, China Meteorological Administration, Beijing

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100089, China

1

Corresponding author address: Key Laboratory of Cloud-Precipitation and Severe

Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Huayanli 40, Chaoyang District, Beijing 100029, China. E-mail: [email protected]

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Abstract In this paper, the statistical properties of summer and winter precipitation over the northern China plain are investigated by using a two-dimensional video disdrometer (2DVD) and a micro-rain radar (MRR). The properties of summer precipitation

presented

herein

are

bulk

properties

(radar

reflectivity,

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reflectivity-weighted fall velocity, liquid water content, and rainfall rate), raindrop fall velocity, axis ratio, and particle size distribution. Well correlations can be found

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among the diurnal cycles of radar reflectivity, liquid water content, and rainfall rate, whereas reflectivity-weighted fall velocity is poorly related to other bulk properties.

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The vertical profiles exhibit that radar reflectivity for stratiform rain is increasing with the altitude decreasing, in contrast, liquid water content and rainfall rate are reducing

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during the falling. These facts are useful for the radar-based rainfall rate retrieval algorithm. Axis ratio measurements are, for the first time, obtained and analyzed in

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northern China, which are particularly important for improving microphysical scheme in the climate models. In the constraint gamma model, the    relation is adapted

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to the particle size distribution of stratiform rain, while the normalized gamma

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distributions for convective rain are separated to maritime-like and continental categories following the orientations and mechanisms of the storms. A new

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bulk-property-based algorithm is developed for the classification of convective and stratiform precipitation. For winter precipitation, radar reflectivity and snowfall rate

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for aggregates are calculated from the disdrometer data. The relationship of radar reflectivity and snowfall rate is obtained and validated with MRR data. The characteristics of summer and winter precipitation will be used to improve the microphysical scheme and evaluate the representation of precipitation in the climate models.

Keywords: Bulk properties; raindrop fall velocity; axis ratio, particle size distribution; radar reflectivity-snowfall rate relation

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1. Introduction Precipitation is important for the evolution of weather and climate in the Earth system, as it significantly contributes to the global hydrologic cycle. Over the past few years, large-scale climate models show some improvements on the spatial and temporal distributions of precipitation (Beate and Michael, 2012; Flato et al., 2013),

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however, the representation of the precipitation as well as the related microphysical processes within the models are still less confident, since the properties of

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precipitation vary at a scale very smaller than the model resolution (Boucher et al., 2013). Remote sensing observations (e.g., radars) and in-situ measurements on the

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ground (e.g., disdrometers) give a great opportunity to address this issue by characterizing the temporal and spatial variability of precipitation in a high resolution

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(Protat et al., 2010; Penide et al., 2013; Giangrande et al., 2014). The long-term observational data can be used to improve microphysical scheme (Jakob, 2010) and to

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evaluate the global climate models (Stephens et al., 2010). The characteristics of summer precipitation have been widely studied across a

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variety of climatic regimes based on the observations of disdrometers and radars (e.g.,

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Bringi et al., 2003; Cao et al., 2008; Moumouni et al., 2008; Bringi et al., 2009; Marzano et al., 2010; Thurai et al., 2010; Thompson et al., 2015; Friedrich et al., 2016). During the past few years, this research attracts more attention in China, where

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increasing number of field experiments have been conducted. Niu et al. (2010) investigated the joint distribution of raindrop size and fall velocity as well as the drop

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size distribution of stratiform and convective rain at a semiarid hill-gully location in central China. Chen et al. (2013a) and Wen et al. (2016) documented the rain characteristics during the Meiyu season in eastern China with a one-dimensional optical disdrometer and a two-dimensional video disdrometer, respectively. Their studies showed that the raindrop size distribution in Meiyu are distinct from that in Baiu in Japan (Bringi et al., 2006; Oue et al., 2010), although the precipitation is brought by the same rainband, called Meiyu-Baiu front. Tang et al. (2014) compared the characteristics of raindrop size distributions of stratiform and convective rain in different climatic regions, including northern China, southern China, and a transition

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zone of Loess Plateau and Mongolian Plateau. Chen et al. (2015) used a network of micro-rain radars (MRR) and rain gauges to measure the small-scale variability of summer precipitation in Xilin River catchment in Inner Mongolia region of northern China. Similarly, Chen et al. (2016) analyzed the spatial variability of raindrop size distribution in a midlatitude continental squall line event using four Thies

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disdrometers in eastern China. For winter precipitation, it is difficult to obtain quantitative measurements of the

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snow intensity, and further derive the relationship between radar reflectivity and snowfall rate, due to the variability of the particle density, shape, and fall velocity

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(Matrosov, 1998). The two-dimensional video disdrometer (2DVD) is able to measure the fall velocity and shape of a snowflake by using snow matching algorithm

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(Hanesch, 1999). To characterize the snow density, Brandes et al. (2007) studied the particle size distribution of snow and aggregates, and then derived a relation between

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bulk density and particle median volume diameter using 2DVD data. Huang et al. (2010) established the relations between equivalent radar reflectivity and snow rate

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based on the power-law fit of the diameter-density relations. Huang et al. (2015)

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expanded this work and evaluated radar-based snow intensity with ground observations. Zhang et al. (2011) also considered mixed-phase precipitation and proposed a method of snow density adjustment. In addition, Szyrmer and Zawadzki

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(2010) derived the reflectivity-snow rate function by using the average relationship of snow mass and fall velocity.

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This work aims to contribute to the representation of summer and winter precipitation in a semi-humid and semi-arid continental monsoon climatic regime over northern China by using the simultaneous measurements of 2DVD and MRR. On one hand, to improve the microphysical scheme of precipitation, the raindrop axis ratio and fall velocity as a function of drop diameter are derived based on the unique observations of raindrop shapes in northern China with a 2DVD, and the gamma model, normalized gamma model, and constraint gamma model of particle size distributions are also investigated. On the other hand, to evaluate the representation of precipitation in the numerical models, the temporal and vertical variabilities of bulk

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properties of rainfalls and snowfalls are documented, providing an insight into the statistical properties of summer and winter precipitation over the northern China region. The present paper is organized as follows. Section 2 describes the dataset used in this study, as well as the methods for processing the disdrometer and micro-rain radar data. Section 3 presents the diurnal cycles and vertical structures of bulk

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properties, the statistics of raindrop fall velocity and axis ratio as a function of diameter, and the characteristics of particle size distribution of summer precipitation

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in terms of convective and stratiform. Section 4 shows the observations of two snowfall events in time-series, and derives the relationship between radar reflectivity

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and snowfall rate. Finally, section 5 summaries and concludes this paper.

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2. Data and methods a. Dataset

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This study analyzed the precipitation measurements collected simultaneously by a two-dimensional video disdrometer (2DVD), a micro-rain radar (MRR) and rain

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gauges (RGs) in 2015 and 2016. The devices were deployed at the Shunyi national

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meteorological observation station (40o07’37‖N, 116o36’55‖E), Beijing, China. Shunyi is located at the marginal zone of Asian summer monsoon in the midlatitude, with an altitude of 28.6 m above sea level. The monsoon variation has a significant

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influence on heavy rainfalls, causing a large inter-annual variability of precipitation. The annual average precipitation amount is approximately 571.6 mm, while 70% of

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the precipitation occurs between June and August, according to the records of the last three decades (1981-2010, Shunyi meteorological observation station, personal communications).

Our instruments collected 96 rainfall events between 30th July and 30th September in 2015 and between 9th June and 26th September in 2016, with the rain accumulations of 664 mm and the data samples of 15267 minutes. For snowfall, two events were observed on 20th and 22nd November 2015, while the liquid-equivalent snow accumulations (durations) were 1.5 mm (1025 minutes) and 11.4 mm (820 minutes), respectively.

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b. Methods 1) Two-dimensional video disdrometer (2DVD) The two-dimensional video disdrometer measures the shadows of a precipitation particle at two orthogonal views to reconstruct the particle shape, size, fall velocity,

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etc (Kruger and Krajewski, 2002). The performance of the 2DVD has been assessed and improved since it was invented (Schönhuber et al., 2007), and many other studies

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have been conducted with this device (e.g., Thompson et al., 2015; Thurai et al., 2016;

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Wen et al., 2016).

(i) Particle size distribution (PSD)

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The number density of particles per unit volume per unit size interval at the

period. It is formulated as

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discrete time is calculated with the counts passing the sensing area within a certain

Ni  

(1),

D

j

106 60  Sij Vij  T  Di

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where i is the index of a size bin, j is the index of a particle, Ni is the discrete size distribution for the ith size bin in m-3 mm-1, Sij is the sensing area in mm2, Vij is the fall

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velocity in m s-1, T is the time interval in minutes, and Di is the bin interval in millimetres, respectively. Note a uniform diameter bin interval is used, which differs

2013a).

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from that of the conventional one-dimensional optical disdrometer (Chen et al.,

(ii) Bulk properties The discrete PSD can be integrated to compute a number of nth order PSD moments

D n , which is defined as (Tokay and Short, 1996) 

Dn   Dn N ( D)dD

(2).

0

The rainfall bulk properties are then derived via the PSD moments,

Dn ,

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including liquid water content (LWC), total number concentration (NT), and radar reflectivity (z). They are formulated as LWC  5.236 104 D3 NT  D0

(3)

(m-3), and

(4)

(mm6 m-3), respectively.

The radar reflectivity is often defined in a logarithm form as

(6)

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Z  10 log10 ( z ) (dBZ).

(5)

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z  D6

(g m-3),

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The mass-weighted mean diameter (Dm) and generalized intercept (Nw) are calculated as (Bringi et al., 2003)

D4

D3

(mm), and

(m-3 mm-1), respectively.

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N w  10.667

D3

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Dm 

4 m

D

(7)

(8)

The median volume diameter ( D0 ) is calculated in terms of the third PSD moment, as

D



D0

1 3 0 D N ( D)dD  2 0 D N ( D)dD , where D0 in millimeters.

(9)

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3

The rainfall rate is produced by the interaction of the particle fall velocity and PSD.

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For convenience, we define the velocity-weighted PSD moment, VD n , as 

VDn   VDn N ( D)dD .

(10)

0

Hence, the rainfall rate (R) can be written as R  6 104 VD3

(mm h-1).

(11)

The first moment of Doppler spectrum is equivalent to the sixth order of the velocity-weighted PSD moment, which is also known as reflectivity-weighted velocity, VD  VD6

(m s-1).

The liquid-equivalent snow rate (SR) is defined as (Huang et al., 2010)

(12)

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SR 

s ( D j )Vol 60 (mm/h),  T j Sj

(13)

where the snow density as a function of diameter,  s ( D j ) , follows the empirical fit of Brandes et al. (2007), and Vol is the apparent volume (Schönhuber et al., 2000).

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(iii) Gamma models

N ( D )  N 0 D  exp(D ) .

(14)

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The gamma function is defined as

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where N0 is an intercept parameter,  is a shape parameter, and  is a slope parameter. It is widely accepted as the model of the continuous PSD (Ulbrich, 1983;

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Willis, 1984), and the parameterization scheme can be implemented in the most numerical weather prediction models with a limited amount of computations. The

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fitting of a measured PSD to a gamma distribution is achieved by means of matching moments, as defined in Eq. (2). In the gamma model, the nth moment is 

  Dn N ( D)dD 

D

D

n

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0

(n    1) N0 , n  1

(15)

where ( ) is a standard gamma function. The parameters within the gamma fit can

i3

D n1

i1

,

Dn2

i2

, and

, if they satisfy the relation as

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D n3

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be obtained by combining at least three PSD moments,

In this study, we use assuming F 

D4 D2

n2i2  n1i1  n3i3 . D2 ,

D4

and

D6

(16) to retrieve  ,  and N 0 . By

2

D6

, the parameters are calculated as

(11F  7)  1  14F  F 2 ,  2(1  F )   (4   )(3   )

D2 D4

, and

(17)

(18)

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N0 

 5  D4 . (5   )

(19)

The combination of the third-fourth-sixth moments was used in other studies (Kozu and Nakamura, 1991). Cao and Zhang (2009) showed that the second-fourth-sixth moment estimator and the third-fourth-sixth moment estimator do

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not significantly differ from each other. An alternative approach to estimation of the PSD parameters is using the truncated moment method (Vivekanandan et al., 2004),

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which involved in the incomplete gamma function.

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(iv) Error analyses

Strong wind may affect the raindrop measurements by the 2DVD (Nešpor et al.,

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2000). Disturbances caused by wind shear near ground or airflow around the instrument can occasionally distort the raindrop shapes, and under-count the number

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of drops through the sensing area. Therefore, our study is restricted to the data with horizontal wind speeds of less than 20 m s-1, and axis ratio of less than 2. A terminal

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velocity filter similar to Bringi et al. (2002) was applied to the data, but following the

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diameter-terminal velocity relation of Brandes et al. (2002). The wind influences were not very significant for the snow measurements in our dataset, since the snowfall events occurred under less windy conditions.

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Another issue is the sampling errors that arise from the partition of drop diameter to a specific size category. Poor sampling of large drop size may affect the

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calculations of PSD moments, especially for higher-order moments. To quantify the sampling errors, it is reasonable to assume that the number of drops in each size category follows a Poisson distribution (Smith et al., 1993). Therefore, the contribution of number concentration to the PSD moments is also Poisson distribution (Schuur et al., 2001). For example, the variance of radar reflectivity calculated from disdrometer data is then expressed as var(Z )   D6 E ( N )dD

(20)

where E(N) is the expected values of number concentration for a specific size

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category. Furthermore, the stratiform rain can be assumed as a stationary process, and expected values for each size category is estimated by using all the available data (Cao et al., 2008), hence, the statistical errors for radar reflectivity is equal to 4.6% of the expected values for our dataset.

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2). Micro-rain radar (MRR) The micro-rain radar is a continuous wave frequency modulated vertical-pointing

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Doppler radar with high sensitivity. The transmit power is nominally 50 mW to avoid separated transmitting and receiving antennas. The micro-rain radar provides the

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Doppler spectra to derive the PSD based on the assumption of the diameter-fall velocity relation in Atlas et al. (1973). It can calculate the profiles of bulk properties,

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such as the rainfall rate, liquid water content, fall velocity, and radar reflectivity, by integrating the PSD over a size range of low uncertainty (Peters et al., 2005). As the

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device is operating at a wavelength of 1.24 cm, the attenuation correction is required,

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especially for moderate and heavy rain intensities (Peters et al., 2010).

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(i) Error analyses

Several factors contaminate the MRR measurements of power spectrum, and consequently affect the PSD estimates. Firstly, the standard process of MRR assumes

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that the precipitation falls in still air, but vertical wind may present in the atmosphere. Thus, the measured power spectrum reflects a combination of the precipitation fall

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speed and air motion. The noise estimation process is used to reduce the effect of the ambient air velocity in stratiform precipitation, since typical vertical air velocities are much smaller than that of the hydrometeors (Houze, 1994). However, the presence of undetected updrafts, downdrafts and turbulence can significantly bias the retrievals of number concentration. Furthermore, as the Nyquist velocity is 0 to 12 m s-1, strong vertical airflows may cause Doppler aliasing in the MRR data by folding the spectra of higher values to that of lower ones, and subsequently produce unrealistic PSD and bulk properties (Tridon et al., 2011). In this study, we removed the data due to this effect, to provide consistent results with the 2DVD data. For snow measurements, the

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method of Maahn and Kollias (2012) was applied to estimate the noise level and de-aliase the spectra. Secondly, the spectral power of a power spectrum contains a large stochastic component due to the uncorrelated phases of the randomly distributed targets within the radar illumination volume (Peters et al., 2005). The standard deviation of the

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power is equal to the expected value. To reduce the stochastic component, it is desirable to average ensembles of power spectra, hence, the standard deviation can be

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reduced by 1/ n , if n power spectral samples are used for averaging. For 1-min

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measurement period, the corresponding spectral samples are about 560 by assuming that MRR takes 10 samples per second and requires 4 seconds for transmission. In

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this way, the statistical errors are reduced to about 4.23% of the expected values. Additionally, ground clutter with near-zero velocities at the lowest sampling

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heights may increase the number concentration of very small drops, thus, this study excludes the first two radar range gates to reduce the clutter effect.

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(ii) Calibration

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The measurements of the MRR often show a difference from that of 2DVD due to variations of PSD and distinct sampling volumes. To achieve better agreement

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between the two devices, we calibrated the MRR data at 90 m height against the 2DVD data during two stratiform rainfall events at the beginning of each year. The

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calibration follows the procedures described in the user manual and in Chen et al. (2015). Figure 1 illustrates the original and calibrated MRR rain accumulations and radar reflectivity comparing to 2DVD. A relatively large difference of the rain accumulations (Figure 1.a) is found between the 2DVD and original MRR data, whereas the radar reflectivity (Figure 1.b) presents a smaller bias since it is in a logarithm scale. The calibration increases the rain accumulations by a few tenth millimeters and produces better consistency than the original one. Furthermore, the mean error (ME) and root square mean error (RMSE) are calculated to allow quantitative comparisons. The ME is improved from 0.18 to -0.03 mm for the 1-hr

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rain accumulations, and from 70.03 to 4.56 mm6 m-3 for radar reflectivity. The root mean square error also gives positive results by improving the 1-hr rain accumulations and radar reflectivity by 0.15 mm and 31.24 mm6 m-3, respectively.

3). Classification of convective and stratiform rain

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The variations of the parameters in the continuous PSDs are closely related to the riming and aggregation of ice crystals, and coalescence and breakup of raindrops. It is

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necessary to identify the rainfall types before the analyses of the PSD data (Tokay and Short, 1996; Testud et al., 2001). The rainfall types are normally classified as

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stratiform and convective, and many methods have been proposed in the literature. One class of these methods use the profiles of the fall velocity of raindrops and

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vertical air motion to separate the two rain types. In the stratiform rain, the air motion is usually smaller than the raindrop fall velocity, whereas they are very close to each

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other in the convective rain. Gamache and Houze (1982) and Churchill and Houze (1984) proposed to use the horizontal homogeneity of clouds to distinguish the

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convective and stratiform rain in a mesoscale system. Rosenfeld et al. (1995)

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considered the vertical profiles of radar reflectivity by interpolating the scanning data to a Cartesian grid, while Steiner et al. (1995) separated convective from stratiform with the local peaks and the associated area in the Cartesian gridded radar echoes.

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Furthermore, the classification can be done with the thresholds of the PSD parameters and rainfall rate. Johnson and Hamilton (1988) identified the convective rain as that

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with the accumulation of 0.5 mm in 5 minutes. Tokay and Short (1996) classified the convective and stratiform with the empirical relation of N0 and rainfall rate based on the disdrometer data. Testud et al. (2001) used the threshold of rainfall rate less than 10 mm h-1 within 10 minutes for the stratiform rain, while Moumouni et al. (2008) extended the time interval to 20 minutes. In addition, the relationship between Nw and D0 is used for such a classification (Bringi et al., 2009; Thurai et al., 2016). The advantage of this method is that it can also identify a transition period from convective to stratiform. In this study, we adopted a disdrometer-based method similar to that of Bringi et

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al. (2003) and Tang et al. (2014). The rain at time T is marked as convective when the value of the rainfall rate at T exceeds 5 mm/h and the standard deviation in a fraction of L minutes centered at T is larger than 1.5 mm/h. The time interval L is set to 10 minutes by comparing to the radar echoes passing the study area. The stratiform rain is considered as the data with rainfall rate larger than 0.1 mm/h and the fractional

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standard deviation smaller than 1.5 mm/h. As shown in Table 1, the classified data consists of 1458 samples (15%) of convective rain and 8444 samples (85%) of

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stratiform rain. Although the convective samples take a smaller portion of the entire dataset, they contribute approximately 81% to the total rain accumulation. The radar

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reflectivity of convective rain ranges from 26.0 to 53.4 dBZ. The upper boundary is consistent with the reflectivity threshold for eliminating hail contamination (Austin,

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1987; Baeck and Smith, 1998). On the other hand, the upper limit of stratiform rain (40.9 dBZ) is close to the absolute value used for identifying convective centers in

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Steiner et al. (1995).

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3. Summer precipitation

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In this section, we present the statistical characteristics of the bulk properties and PSD parameters for summer precipitation derived using the moment methods. First, the general features of the stratiform (ST) and convective (CV) rain over northern

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China are discussed in terms of probability density function (PDF), diurnal cycle, and vertical structure. Next, the distributions of raindrop axis ratio and fall velocity are

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analyzed, and the polynomial fits for the axis ratio and fall velocity as a function of the diameter are given. Finally, the characteristics of the PSDs and their parameters, including  ,  , Nw, and Dm for CV and ST are presented.

a. Overview of bulk properties 1) Probability density functions The microphysical properties of total dataset (TL), stratiform rain (ST), and convective rain (CV) are first compared with each other in terms of probability

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density function (PDF). Figure 2 illustrates the PDFs of radar reflectivity (Z), reflectivity-weighted fall velocity (VD), liquid water content (LWC) and rainfall rate (R) of CV and ST measured by 2DVD and MRR. In Figure 2a, it is noteworthy that although the reflectivity PDF for TL measured by 2DVD is highly correlated with that for ST, the PDF for TL is skewed towards to larger values, and exhibits a significant

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difference above 30 dBZ, which corresponds to a high frequency distribution for CV. The mean and standard deviation of CV are 41.4 dBZ and 43.8 dBZ, respectively,

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comparing to the values of 25.9 dBZ and 29.3 dBZ for ST. If the logarithm scale of radar reflectivity is considered, the full width at half maximum (FWHM) of CV is 9

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dB, whereas that of ST reaches 15 dB. The student’s t-test and Kolmogorov-Smirnov test (Wilks, 2011) both reject the null hypothesis that the CV and ST samples come

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from the same probability distribution at the 5% significance level, indicating the PDF for CV is significantly different from that for ST. Referring to Eq. (5), it indicates that

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the raindrop diameter and number concentration of CV are both superior to that of ST due to combined effects of coalescence and breakup processes, updrafts, and melting

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of rimed ice in CV.

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The reflectivity-weighted fall velocity (VD) measured by 2DVD also shows a notable difference between CV and ST (Figure 2b). The mean values are 5.0 m s-1 for ST and 6.8 m s-1 for CV owing to strong weights on larger raindrop diameters, while

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the PDF of ST fall velocity is 0.3 m s-1 broader than that of CV. The liquid water content (LWC; Figure 2c) and rainfall rate (R; Figure 2d) are both transferred to

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logarithmic scale to show a symmetric shape. The skewness of the two sets of PDFs reduced by a factor of 1-2 comparing to the ones in linear scale. In addition, the PDFs of CV LWC and R are both one order higher than that of ST. The mean values of rainfall rate are 1.2 mm h-1 for ST and 17.6 mm h-1 for CV, which are very similar to the ones observed by an optical disdrometer in the same climatic regime (Tang et al., 2014). By comparing between the 2DVD and MRR, the PDFs are generally consistent with each other for ST, however, the PDFs of CV for VD, LWC, and R measured by MRR are shifted towards smaller values comparing to that measured by 2DVD. The

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standard process of MRR assumes the relation between terminal fall velocity and drop size as that in Atlas et al. (1973), whereas the actual drop fall velocity is relative to the ambient air flows in real atmosphere. Updrafts can decrease the fall velocity of raindrops, resulting in an underestimation of the drop size. Since the radar cross section under Rayleigh approximation depends on the sixth order of the drop diameter

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and the drop size distribution is proportional to the radar power spectrum by a factor of radar cross section, the increasing fall velocity also leads to an overestimation of

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the number concentration. Furthermore, the liquid water content and rainfall rate are proportional to the third PSD moment in Eq. (3) and the third velocity-weighted PSD

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moments in Eq. (11), respectively. Therefore, these two bulk properties are also underestimated in case of updrafts. This effect may also be due to enhanced collision

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process aloft or strong attenuation along the path in the convective rainfall.

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2) Diurnal cycle

The diurnal cycle of the precipitation microphysical property is characterized by

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a two-dimensional probability density function constructed by time and bulk

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properties, called time-dependent probability density function (TPDF, Protat et al., 2010). It shows the temporal variability of bulk properties, which can be useful for studying the weather and climatological properties over northern China. Figure 3

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compares the diurnal cycles of Z, VD, LWC and R of CV and ST during the summer seasons of 2015 and 2016. The bulk properties all remain steady in the region of high

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occurrences of CV and ST. During the late night (0000-0500 LST), the radar reflectivity of ST (Figure 3a) slumps before a large rise between 0100-0300 LST, and decreases slightly until early morning (0600-0700 LST). In the morning, the ST reflectivity reaches a peak at around 0800 LST, following a dramatically fall and then fluctuating until the midday (1200 LST). There is an upward trend after a sudden increase in the afternoon, peaking at about 1600 LST. In the nighttime, the TPDF for ST reaches a third plateau at around 2000 LST. On the contrary, the mean values of CV reflectivity (Figure 3b) are significantly higher than the ones of ST, with a much larger variability in the diurnal cycle. The CV reflectivity generally follows a similar

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trend as the ST, whereas the CV peaks appearing about two hours later than ST. This is because the CV clouds are likely initialized over the west mountains in afternoon due to peaked surface heating, and then the associated thunderstorms propagate eastward to the plain regions (Zhang and Zhai, 2011; Chen et al., 2013b; Li et al., 2017). In addition, the CV reflectivity shows a large uncertainty due to very low

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frequency (less than 1%) at the time of 0100, 0500, 0800, 2000, 2100 and 2300 LST. The diurnal cycles of LWC (Figure 3e and f) and R (Figure 3.g and h) are

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correlated with radar reflectivity, with peaks of average values at 0500-0600, 1400-1600, and 2000-2100 of local time, respectively. Comparing between the ST and

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CV, not only the mean values of CV are significantly higher than ST, but the variability of the CV means also tends to 1-2 dB higher. In contrast, the distributions

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of ST are much broader than CV due to the transformation to logarithm. Although the average values of fall velocity along time has a similar trend to radar reflectivity, the

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TPDF of fall velocity is very different from that of radar reflectivity. Overall, the diurnal cycles of the bulk properties remain stable, with three peaks occurring at 0800,

3) Vertical profiles

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1600, and 2000 LST for ST, and at 1000, 1800, and 2200 LST for CV.

The vertical profiles of Z, VD, LWC, and R need to be analyzed in terms of

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microphysical processes. Figure 4 shows the Contoured Frequency by Altitude Diagrams (CFADs) proposed by Yuter and Houze (1995). The left and middle

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columns in Figure 4 are the CFADs for ST and CV, respectively, together with the mean profiles as black curves. The right column is the difference between CV and ST (i.e., CV-ST) corresponding to the four bulk properties. Figure 4.a and b exhibit a common feature relative to the stratiform and convective precipitation presented in time-series data of Yuter and Houze (1995). The melting layer of northern China is normally between 4 km and 6 km along the altitude in the summer season, hence, the vertical profiles between 0.3 km and 2.8 km as shown in Figure 4 are generally in liquid phase toward the surface. For radar reflectivity, the profiles of ST (Figure 4a) from the MRR observations

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illustrate very slow increase with a decreasing altitude. This increasing trend can be interpreted as the combination of the coalescence and breakup of raindrops, accretion with cloud droplets, and evaporation. It is consistent with the theoretical results in the earlier work (e.g., Mason and Ramanadham, 1954; Hardy, 1963), but different from the decreasing trend over the tropics (Figure 6 in Penide et al., 2013), where the

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breakup and evaporation processes dominate below the melting layer. The frequency distribution of Z concentrates on around 20 dBZ with a probability of no more than

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30%. The distribution below 1 km is considerably narrower than that above 1.5 km, which may be due to coalescence and evaporation of small raindrops during the

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falling. In contrast, the reflectivity profiles of CV (Figure 4b) exhibit a relatively different feature along the height. Notably, there is a dramatic increase of average

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values, from 27.2 dBZ to 39.5 dBZ (see the solid black line in Figure 4b), implying significantly changes of drop number and diameter due to the cloud microphysical

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processes which are differing from ST. The convective clouds have intensive updrafts and downdrafts than the stratiform, resulting in distinct cloud microphysics that is

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dominated mainly by riming process above the melting layer (Houze, 1994), and

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enhanced coalescence and accretion below the melting layer (Hu and Srivastava, 1995). Therefore, the large raindrop size and concentration grow rapidly while falling to the ground, which explains the large slope of CV reflectivity comparing to the ST

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at the same level. The distribution of CV reflectivity at upper level is narrower than ST, since the collisional processes are more active in the convective clouds. The

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reflectivity CFAD difference (Figure 4c) shows a clear separation between ST and CV, where the CV reflectivity distributes between 30 and 50 dBZ, but the ST reflectivity concentrates on 10-30 dBZ. In addition, the maximal probability at 1 km height is about 20% higher than that at 2.8 km height, which indicates that the difference between ST and CV is large at the lower level. The features of velocity CFADs (Figure 4d, e, and f) are similar to that of Z, where the vertical profiles of ST (Figure 4d) exhibit a quasi-uniform distribution between 0.3 and 2.8 km along the height. The profiles of CV (Figure 4e) slightly differ from the radar reflectivity. The mean velocity of CV gradually goes up from 5.5

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m s-1 at 2.8 km to 6.5 m s-1 at 0.7 km, and then stays constant at a terminal velocity towards the surface. The distinction between ST and CV is also clear from the CFAD difference, whereas the mean profile of total dataset is around 5 m s-1 with a steady increase along the height. The vertical profiles of LWC and R for ST present a small decline, which is very

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different from the radar reflectivity and reflectivity-weighted fall velocity. It can be interpreted as that raindrops are merged to form larger-size drops via coalescence,

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causing an increase of the drop diameter. Meanwhile, drops are consumed due to evaporation (Kumjian and Ryzhkov, 2010), and the evaporation rate is inversely

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proportional to the drop diameter, implying that the diameters of smaller drops reduce more rapidly than larger drops under a sub-saturated environment. The evaporation

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process also results in a decrease of number concentration of smaller drops, as they can be totally evaporated. The LWC and R are more sensitive than Z and VD to the

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lower side of the drop size distribution, therefore, the evaporation effects on LWC and R are more significant than that on Z and VD. The combination of the coalescence and

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evaporation processes produces an increasing Z and VD profiles, but a reduction of

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LWC and R profiles along the height. In contrast, the LWC and R profile for CV is characterized by a positive shift (0.6 in logarithm of g m-3 for LWC and 0.8 in logarithm of mm h-1 for R) towards to larger values, with a high frequency occurring

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below 1 km for LWC and between 1 and 2 km along the height for R. The differences between CV and ST for the two quantities exhibit a well-defined boundary, which is

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consistent with Z.

b. Raindrop fall velocity and axis ratio 1) Raindrop fall velocity Raindrop fall velocity is closely related to the dynamic conditions in the atmosphere, including gravity force, air buoyancy, and drag force. If air is in under-saturated condition, a cloud droplet or raindrop is gradually reducing its size due to evaporation while falling. Normally, we consider 0.1 mm as a threshold for discrimination between cloud droplet and raindrop. Tokay et al. (2001) pointed out a

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diameter larger than 0.2 mm is a reliable criterion for a raindrop measurement by 2DVD. However, we calibrated the device by using metal spheres with a range from 0.5 to 10 mm in diameter, therefore, the data with a diameter larger than 0.5 mm is used to obtain an unbiased fit of the diameter and fall velocity relation in this study. Figure 5 illustrates the logarithmic probability distribution as a function of

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raindrop diameter (D) and fall velocity (V) together with the fit curve and the laboratory measurements (Atlas et al., 1973; Brandes et al., 2002) for ST, CV and TL.

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As shown in Figure 5a, the fall velocity of ST concentrates between 1.0 and 5.1 m s-1 with a cumulative distribution of 90%, which is consistent with the Parsivel

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observations in the same climatic regime (Tang et al., 2014). In contrast, the CV distribution has a cumulative probability of 90% at a range between 1.0 and 6.4 m s -1

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(Figure 5b). In addition, the high probability region of the TL distribution (Figure 5c) is between 1.0 and 5.7 m s-1. Figure 5d, e and f give the corresponding polynomial fit

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associated with error bars of the mean values with an uncertainty of 1 , where  is the standard deviation. The fitting equation between raindrop diameter versus fall

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velocity from the average values are as follows: (21),

V ( D)  1.337  6.974D  1.916D 2 +0.2423D3  0.0113D 4

(CV)

(22),

V ( D)  0.9711  6.499D  1.697D 2 +0.2032D3  0.008978D 4 (TL)

(23),

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V ( D)  0.8114  6.296 D  1.654 D 2  0.2267 D3  0.01266 D 4 (ST)

where D is in millimeters and V is in m s-1. The root mean squared errors of fitting fall

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velocity are 0.041, 0.056, and 0.042 m s-1 for ST, CV, and TL, respectively, indicating a good fit for the averaged data. It can be found that the ST, CV and TL curves all pass through the mean values when D falls between 0.5 and 5.5 mm, but a large bias is found when D is smaller than 0.5 mm. For small raindrops, the mismatch problem is rather significant due to finite instrument resolution, and high concentration and spherical shape of drops. Huang et al. (2010) showed that the mismatch can cause positive skewness in the fall velocity, which is consistent with our observations for drops with diameter less than 0.5 mm. Furthermore, the ST relation is consistent with the radar and laboratorial measurements (Atlas et al., 1973, hereafter AT73; Brandes

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et al., 2002, hereafter BR02) when the diameter is between 0.5 and 2 mm. However, at larger diameters (D>2 mm), the ST relation suppresses the two theoretical curves. In contrast, the CV and TL relations are well consistent with the laboratory measurements between 0.5 and 3 mm, while the curves are lower than AT73 and BR02 between 3 and 6 mm. Thurai et al. (2013) presented a negative skewness in the

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fall velocity for drops with diameter larger than 3 mm during a period of high rain intensity. The negative skewness of fall speed may result from increased drag caused

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by asymmetric horizontal-mode oscillations of large raindrops. This is also consistent with our observations of drops with diameter larger than 3 mm, whose mean values

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are smaller than the theoretical relations. In addition, updrafts may reduce the drop fall velocity, whereas downdrafts can increase the fall velocity. Therefore, the

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variation of fall velocity may increase for every size bin.

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2) Axis ratio

The shape of raindrops has been studies under various conditions, such as

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artificial rain (e.g., Thurai and Bringi, 2005; Thurai et al., 2007, hereafter TH07),

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wind-tunnel (e.g., Pruppacher and Beard, 1970, hereafter PB70; Szakáll et al., 2009), and field experiment (e.g., Chandrasekar et al., 1988; Tokay et al., 2000). Theoretically, the shape of raindrops falling at terminal velocity in still air can be

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computed by applying the perturbation theory on the force balance model (Pruppacher and Pitter, 1971). As indicated by Szakáll et al. (2010), this model includes a

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second-order hydrostatic term, and hence, overestimates the axis ratio of distorted raindrops. Another model approximates the raindrop shape as oblate spherical, and the axis ratio is calculated based on the balance of surface and gravity forces at the equator (Green, 1975). In literature, the widely accepted model is the numerical modeling of equilibrium drop shapes (Beard and Chuang, 1987, hereafter BC87), where the actual shape is calculated from Laplace’s equation by using an internal hydrostatic pressure with an external aerodynamic pressure adjusted from sphere. The measurements of raindrop shapes in the natural atmospheric environment are very rare in China, while the axis ratio is often assumed based on the wind-tunnel data

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in the literature. With the help of 2DVD, this study is the first time to report an investigation of raindrop axis ratio in northern China. Figure 6 illustrates the normalized PDFs as a function of raindrop diameter and axis ratio for CV and ST, respectively. The two PDFs both have a Gaussian shape, which is consistent with Thurai and Bringi (2005). However, there is a clear difference between CV and ST

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peaks. The mean values are 0.94 for CV and 0.97 for ST, while the CV PDF also has a larger spread than ST, indicating that the axis ratio has a large variability in CV. The

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student’s t test and Kolmogorov-Smirnov test show that the two sets of data samples come from independent probability distributions.

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Figure 7 shows the normalized two-dimensional PDFs and the fitting curves for ST, CV and TL, respectively. Falling raindrops can be considered as rigid spheres if

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their diameters are smaller than 1 mm (Szakáll et al., 2010). In contrast, the lower bound for fitting is 1.5 mm in TH07, since the 2DVD measurements have large

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uncertainty when the diameter is less than 1.5 mm, resulting from residual mismatch and limited vertical resolution. For our data, the accumulated probability is

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approximately 1% for the region with diameter between 1 and 1.5 mm and axis ratio

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below 0.8, comparing to 21% for the one with diameter between the 1 and 1.5 mm, therefore, the data between 1 and 1.5 mm is reliable for this study. Furthermore, the

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maximal raindrop diameter with probability larger than 1105.5 is approximately 3.2 mm for ST (Figure 7.a) and 4.8 mm for CV (Figure 7b) and TL (Figure 7c).

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Consequently, the fitting ranges in this study are 1-3.2 mm for ST, and 1-4.8 mm for CV and TL, with a bin size of 0.2 mm. As shown in Figure 7d, e and f, the fitted curves are fairly consistent with BC87 and TH07 for ST, and CV and TL when the diameter is between 1 and 2.4 mm. When the diameter is above 2.4 mm for CV and TL, our data is more spherical than BC87, PB70, and TH07. It implies that these drops may not be dominated by the fundamental (2,0) oscillation mode, but the first harmonic (2,1) mode with an increased axis ratio (Beard and Kubesh, 1991). The (2,1) mode can result from collisional processes (coalescence and breakup), as indicated by the wind tunnel

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experiments (Szakáll et al., 2014). This observation is similar to the 2DVD measurements under a natural environment (Marzuki et al., 2013), but is different from that under an experimental condition (TH07). To formulate the relation between diameter and axis ratio in an analytic form, we also fit the data to a fourth-order polynomial function (Figure 7d, e, and f). The

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polynomial fits are as follows: b / a  1.116  0.1807D  0.07603D2  0.01883D3  0.001434D4

(ST)

(24), (25),

b / a  1.024  0.02478D  0.01941D2 +0.004774D3  0.0004215D4

(TL)

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b / a  0.9791  0.02403D  0.03703D2 +0.007102D3  0.0004921D4 (CV)

(26),

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where b/a is a ratio of the minimum axis (b) and the maximum axis (a) of a raindrop and D is the equivalent diameter in millimeters. The root mean square errors of

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raindrop axis ratios are 0.0054, 0.0049 and 0.0051 for ST, CV, and TL, respectively, showing a good fit. The fitting curve is approximately 0.2 higher than PB70 and

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BC87 when the diameter reaches 3 mm. As mentioned already, this is reasonable

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since the shapes of raindrops can be affected by resonance with vortex shedding, change in drag force (Tokay and Beard, 1996), increase of surface tension by

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inorganic solutes (Tuckermann, 2007), and collisional processes (Szakáll et al., 2014).

c. Distributions of PSD parameters

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1) Averaged particle size distribution To characterize the overall features of the PSDs for TL, ST, and CV, Figure 8 shows the averaged PSDs measured by 2DVD, while Table 2 illustrates the bulk microphysical properties associated with the averaged PSDs for different rain types. The averaged PSD is fitted to a gamma distribution by using the moment method, and the fitted relations are given as follows: N ( D)  4716 D0.74 exp(3.79 D) (ST)

(27),

N ( D)  8827 D0.44 exp(2.49 D) (CV)

(28),

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N ( D)  2248D 0.02 exp(2.47 D) (TL)

(29),

where N(D) is the size distribution in a unit of m-3 mm-1, D is the equivalent volume diameter in millimetres. The above particle size distributions for CV and ST both have positive  associated with a concave-downward shape. However, the shape parameter of TL is close to zero, thus the distribution for TL has a quasi-exponential

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shape consistent with the Marshall-Palmer model (Marshall and Palmer, 1948). By comparing the parameters in the gamma distributions between CV and ST, it

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is found that the intercept of CV is larger than ST, yielding a number concentration of

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CV superior to ST as shown in Table 2. In contrast, the shape and slope of CV are both smaller than ST, but the median diameter, D0, and mass-weighted diameter, Dm,

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of CV are a few tenth larger than ST. The maximum diameter, Dmax, is defined as the largest bin associated with the number concentration greater than 1103 m-3 mm-1.

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For convective rain, this parameter reaches 6.73 mm, which is approximately 2.5 mm larger than that of stratiform rain. By integrating the averaged PSD for each rain type,

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bulk properties, such as Z, R, and LWC, can be obtained. These parameters are

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consistent with the mean values calculated from the 1-min PSD data, indicating the average PSD technique is promising. Tokay et al. (2013) used side-by-side disdrometers to investigate the differences

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of PSD measurements between 2DVD and Parsivel. It was concluded that the Parsivel disdrometer generally underestimates smaller drops and overestimates midsize and

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larger drops. Their results showed that the number concentration of 2DVD is higher than Parsivel, but the mass-weighted diameter of 2DVD is smaller. However, our measurements show larger values for the two parameters when compared to the Parsivel disdrometer (Tang et al., 2014), whereas the midsize drops (2-4 mm) of the two disdrometers are consistent. This agreement can also be seen in Figure 8 of Wen et al. (2016). When compared the Figure 8 in this study with the Figure 8 of Wen et al. (2016), the averaged PSD for ST over northern China is very similar to that over eastern China. In contrast, the averaged PSD for CV over northern China is a unimodal

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spectrum with a plateau between 0.5 and 1 mm, whereas that over eastern China exhibits two peaks at 0.5-1 mm and 2-3 mm. Furthermore, the number concentration of small drops (0.5-1 mm) over northern China is approximately one-order lower than that over eastern China, implying that the mechanisms of the convective clouds are

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distinct in these two regimes.

2) Constrained-gamma model

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The particle size distribution (PSD) is often modeled as a gamma distribution, within which the three parameters are to a certain degree correlated (Ulbrich, 1983).

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The correlation can be used to simplify the retrieval of the PSD by reducing the number of radar moments in the retrieval method. Zhang et al. (2001) discovered the

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high correlation between the shape and slope parameters, and proposed a Florida relation by fitting 2DVD data to a two-order polynomial function. Later, Cao et al.

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(2008), hereafter CQ08, obtained the Oklahoma relation after applying a SATP technique for noise suppression, while Chen et al. (2013a), hereafter CB13, and Tang

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et al. (2014), hereafter TQ14, fit the Nanjing and Beijing relations, respectively, with

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Parsivel data. In this study, to minimize the sampling errors, the PSD parameters are filtered with a threshold of R>5 mm/h and Nt>1000 m-3 as proposed by Zhang et al.

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(2003), hereafter ZG03. The fitted  -  relation for our dataset is given as   0.019 2  0.795  2.033

(30).

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Figure 9 illustrates the comparison between  -  relations obtained by 2DVD and Parsivel in a variety of climatic regimes. There is good agreement between ZG03 and our relation in Eq. (29), as 85% of the  -  pairs match to each other when

  12 . In comparison with the Parsivel measurements by CB13 and TQ14, large discrepancies can be found due to concentration disparity between 2DVD and Parsivel (Tokay et al., 2013). The relation of CQ08 presents smaller  at the same  when compared to our relation and ZG03, resulting from noise reduction by the

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SATP method. It can be concluded that the variability of the  -  relation is relatively small in different climatic regimes, but it is significantly increased when different types of devices or processing techniques are used. The shape-slope relation from the filtered data is valid under a certain condition to avoid odd PSD parameters at low rainfall rate. However, it is necessary to obtain

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the relations from the entire dataset applicable to various rain types, especially for stratiform rain. Figure 10a, b, and c illustrate the probability distribution as a function

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of  and  , and Figure 10d, e, and f give the median values and standard deviation

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for each bin with a 0.5 spacing. We select a range with an accumulative probability of

  0.020 2  1.106  1.666 (ST)

(31),

  0.017  2  0.785  1.636 (CV)

(32),

  0.019 2  1.106  1.515 (TL)

(33).

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93% to obtain  -  relations, then the fitted polynomial functions are

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For stratiform rain, the new relation tends to have a relatively larger  at the

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same  comparing to the relation for filtered data when   3 , and it has a steeper slope when   3 . In contrast, the new relation for CV has a steady slope and shape

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than the ST one, which is consistent with the results of averaged PSD. The curve of the new relation is close to the previous one, indicating the relation obtained from

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filtered data may be applicable for convective storm exclusively. The new relation for TL shares similar polynomial coefficients to the ST one, as the stratiform precipitation dominates in the dataset.

3)

N w  Dm distribution

Figure 11 shows the PDFs of the parameters within the normalized PSD for ST, CV, and TL, respectively. For stratiform rain, the PDFs for log10 N w (Figure 11a) and Dm (Figure 11b) are skewed toward positive with a spread close to 0.5, suggesting a

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relatively high variability in log10 N w and Dm for ST. The mean values of log10 N w and Dm (Figure 11a) are 3.71 and 1.26, respectively. In contrast, the skewness of log10 N w for CV exhibits slightly negative, and the spreads are narrower comparing

to the PDFs for ST. Furthermore, the mean values of log10 N w and Dm for CV are

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both a few tenth higher than that for ST, consistent with the PDFs for bulk properties, such as radar reflectivity and rainfall rate.

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In comparison with the maritime-like PSD parameters measured in eastern China during the summer Meiyu season (Chen et al., 2013a; Wen et al., 2016), our mean

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values for CV show a relatively large Dm but small log10 N w . In northern China, the

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summer convective rainfall is often produced by a variety of precipitating systems, including cold front (W/NW/N/NE), Mongolian cyclone (NW), Yellow River cyclone

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(W), northeast cold vortex (NE), vortex (NW/W), slot line (N/NE) and typhoon (S/SE/E). Figure 12 gives the scatterplots of averaged Dm and Nw for summer convective and stratiform precipitating systems associated with their orientations,

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where the local convective clouds are marked as ―L‖. The mean values of Dm and Nw

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for convective rain oriented from L, N, and W are generally consistent with the continental cluster in Bringi et al. (2003) characterized by log10 N w =3-3.5, where Nw

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is in m-3mm-1, and Dm=2-2.75 mm. The orographic effects may play an important role for the precipitation formed in the local and west regions of the experimental location.

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In contrast, the typhoon-producing rainfall often belongs to the maritime-like cluster with higher number concentration and smaller mass-weighted diameter. It can be concluded that in northern China the convective PSDs are characterized as either continental or maritime-like cloud clusters depending on the orientations and mechanisms of the precipitating systems. On the other hand, it is found that the pairs of Dm and log10 N w for ST have a linearly inverse relationship as indicated by Bringi et al. (2003), which is consistent with variations in the microphysical processes of stratiform rain. The melting of low-density snow aggregates often leads to a smaller

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log10 N w and a larger Dm comparing to the riming-producing graupel.

In addition, there is a clear separation between the ST and CV on the plane of Dm and log10 N w . Bringi et al. (2009) and Thurai et al. (2010) proposed a PSD-based classification technique, identifying ST, CV and transition rain. In our study, we use a technique of linear discriminant analysis (LDA) to obtain a boundary between ST and

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log10 N w  1.029 Dm  5.095

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CV as shown in Figure 13a. The discriminant criterion is given as

and the separation index is then derived by

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i  log10 N w ( Dm )  log10 N w

(34),

(35),

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where the upper and lower bounds of the index for a transition rain are 0.1 and -0.2, respectively. This technique classifies about 17.2% of the total data as convective,

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68.7% as stratiform, and 14.1% as transition rain for our dataset, which is generally consistent with the rain-rate-based technique. However, the DSD-based technique is largely dependent on the method for calculating the parameters within the gamma

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distribution, thus some uncertainties may arise from the model and fitting errors. In

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this study, we propose a technique based on Z and VD for ST, CV and transition rain. Figure 13b shows contours and a separator for ST and CV on the plane of Z and VD.

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The separator is expressed in mathematics as VD  0.406Z  6.461

(36),

i  VD (Z )  VD

(37).

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and the index is given as

The upper and lower limits for transition rain become -1 and 0.8, respectively, yielding results consistent with the PSD-based and rain-rate-based techniques. As the radar reflectivity and fall velocity can be derived from the radar Doppler spectrum, this method is applicable to vertical-pointing radars and profilers. The rain type classification can also be achieved by using a Bayesian method based on bulk properties (Bukovčić et al., 2015).

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4. Winter precipitation In this section, we analyze two snowfall events to test the 2DVD measurements and then derive the relation of Z-SR for aggregates. To verify the disdrometer measurements, we also provides the MRR and gauge data, and the reflectivity

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calculated via the method in Zhang et al. (2011), hereafter ZG11.

a. 22 November 2015 case

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Figure 14 shows the time series data of a heavy snowfall case occurred between 0700 and 2000 LST on 22nd November 2015. Aggregates were exclusively observed

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during the entire event, while large particles (>5 mm) were frequently captured at the surface by 2DVD. At the beginning of this event (0700 LST), the ambient

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temperature was slightly above 0oC. It decreased sharply from 0.3oC to -1.7oC from 0700 to 1000 LST, and then remained steady at about -2.5 oC through the rest of the

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day. The wind measurements in the automated weather station indicated a breeze during the day, with a wind speed of 1.4 m s-1 on average.

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Figure 14a shows a comparison of radar reflectivity between 2DVD (blue), ZG11

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(green), and MRR (red) as derived from the 5-min 2DVD observations, and Figure 14.b illustrates hourly precipitation amount accumulations calculated by 2DVD, together with the gauge measurements. Radar reflectivity (Figure 14.a) has

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remarkable consistency between our data and ZG11 through between 0700 and 1100 LST, whereas the measurements of MRR are a few dB higher than the previous two

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data. In contrast, the disdrometer gives higher hourly precipitation amount accumulations than the gauge during this period, and the maximum difference reaches about 1 mm at 1000 LST. It results from the over-counting of snowflakes lifted by vertical wind at the surface as recorded by the ultrasonic anemometer located near the 2DVD. The precipitation amount accumulations of 2DVD well match the gauge data between 1100 and 1300 LST, though the 2DVD and ZG11 underestimates the reflectivity comparing to MRR. After 1400 LST, the precipitation amount accumulations of 2DVD fluctuate around the values of the gauge. Radar reflectivity of 2DVD reaches a gap at about 1500 LST, whereas that of MRR remains stable. For

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both the 2DVD and MRR, large fluctuations appear between 1700 and 1800 LST, and then the reflectivity stays steady until 2000 LST. Huang et al. (2010) presented a relation of radar reflectivity and snowfall rate (Z-SR) for seven snowfall cases measured by a C-band radar in Canada, where the coefficients range from 106.2 to 305.4 for a, and from 1.11 to 1.92 for b. For K-band

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radar, our 2DVD data gives a relation as follows: Z  42SR1.22

(38),

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where the coefficient of a is much smaller than that in the Z-SR relations of C-band

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radar. Figure 15 shows a comparison of the hourly precipitation accumulation between radar and gauge, where the precipitation amounts for radar is calculated via

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Equation (38) using the MRR data. For the 22 November 2015 case, the mean bias is 0.19 mm h-1 and root mean square error of 0.4 mm h-1, indicating a fair estimation of

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snowfall rate.

b. 20 November 2015 case

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Figure 16 illustrates another case of winter precipitation observed on 20th

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November 2015. This event began with mixed-phase precipitation, and then it turned into ice pellet through about 0200 UTC. The rest of the event was primarily aggregates, except a disconnect between 0730 and 0830 LST. During this event, the

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ambient temperature changed from 1oC at the beginning to around 0.3oC for the snowfall period, consistent with the transition of particle types at the surface. The

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wind measurements were 1.3 m s-1 on average. In general, radar reflectivity (Figure 16a) calculated by the 2DVD shows fair consistency with the MRR measurements, as the peaks of time-series data are well matched. However, the difference of reflectivity between 2DVD and MRR is still obvious during the period of mixed-phase hydrometeors. The density of snowflakes changes while the particles are melting, resulting in a variation of the dielectric constant for electromagnetic waves, and thus a fluctuation of reflectivity. Zhang et al. (2011) proposed a method of density adjustment for calculating the radar reflectivity

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and other radar variables. However, this method requires the relations of diameter and fall velocity and of diameter and bulk density for snowflakes. Further investigations will be needed to derive these relations using the 2DVD measurements. For the accumulated precipitation amount, the disdrometer gives an underestimate of accumulated precipitation amount when compared to the gauge

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between 0000 and 0700 LST. This underestimation is reasonable since the particle density is valid for aggregates, but mixed-phase hydrometeors may exist as indicated

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by the surface temperature. Another factor is wind effects and measurement errors. The mass of the aggregates is rather small, thus altering the airflow can cause

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undermatching of snow (Nešpor et al., 2000). Furthermore, multiple particles aligned in the sensing area can also results in errors for the 2DVD (Thurai and Bringi, 2005).

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In addition, the accumulated precipitation amount calculated from MRR via the Z-SR relation seem to be underestimated when compared to the gauge data (Figure 17). The

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mean bias is -0.12 mm, and the mean square error of 0.24 mm for this case, which is

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slightly better than the 22nd November 2015 case.

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5. Summary and conclusions

In this paper, the observations of a two-dimensional video disdrometer (2DVD) and a micro-rain radar (MRR) have been used to study the statistical properties of

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summer and winter precipitation over northern China. For summer precipitation, the probability distributions of the bulk properties,

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such as radar reflectivity, reflectivity-weighted fall velocity, liquid water content, and rainfall rate, are documented and discussed in terms of convective (CV) and stratiform (ST) precipitation. It appears that the mean values of the CV distribution are generally higher than ST, and the CV distributions are characterized by wider spreads due to intensive microphysical processes. The diurnal cycles of the four bulk properties for ST exhibit three peaks at about 0800 LST in the morning, 1600 LST in the afternoon, and 2000 LST in the nighttime, while the plateaus for CV are often two hours later than the ST peaks. There are well correlations among the diurnal cycles of radar reflectivity, liquid water content, and rainfall rate, whereas the diurnal cycle of

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fall velocity is very distinct. This description of temporal variation of summer precipitation will be helpful for evaluation of the numerical models. Furthermore, unlike the CV precipitation with much larger vertical variabilities, the four bulk properties for ST remain steady along the altitude. It is very interesting to note that in ST, the profile of radar reflectivity is increasing with the altitude decreasing, on the

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contrary, the profiles of liquid water content and rainfall rate are reducing during the falling. It is important to consider this effect in quantitative precipitation estimation.

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The fall velocity and axis ratio have also been investigated to obtain an empirical relation as a function of the raindrop diameter for various rain types. This work is

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valuable for studying the microphysical properties of summer precipitation in northern China, since the measurements of axis ratio have not been obtained in this

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region previously.

The particle size distribution (PSD) has been calculated and analyzed in the

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present paper, providing insights into the characteristics of summer precipitation over northern China. The averaged PSDs for ST and CV have been fitted into a gamma

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function, while the distribution of CV has a larger intercept, but smaller shape and

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slope parameters when compared to ST. In contrast, the averaged PSD for the total dataset exhibits a quasi-exponential shape, consistent with the Marshall-Palmer model. Furthermore, the constraint gamma model is studied by means of the relationship

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between the shape and slope parameters. As the previous models are built based on the filtered data, their application to a numerical forecast model is limited. To tackle

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this problem, we have obtained an empirical fit in a high probability region on the plane of the shape and slope parameters. The relations are applicable to various types of rain. Moreover, the convective precipitation during the summer season is often classified as continental and maritime-like cases by analyzing the normalized intercept and mass-weighted diameter. In northern China, the two types of CV both exist, and the types depend on the orientations and mechanisms of the storms. It can be found that CVs oriented from a local region, north, and west are continental, but that from south, southeast, and east are maritime-like, produced by a typhoon system. On the other hand, the pairs of intercept and diameter for ST show a linear shape

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controlled by the microphysical processes above the melting layer. In addition, there is a clear separation between ST and CV on the plane of the normalized intercept and mass-weighted diameter, however, the classification relies on the method of fitting to a gamma distribution. A new method based on the bulk properties, radar reflectivity and reflectivity-weighted fall velocity, has been proposed for rain type classification.

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The results are consistent with the PSD-based and rain-rate-based algorithms, indicating it is promising.

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For winter precipitation, we have analyzed time-series data of two snowfall events. Aggregates were observed exclusively during the case on 22nd November 2015,

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while ice pellets and mixed-phase hydrometeors were also measured on 20th November 2015. The measurements of 2DVD are compared with MRR in terms of

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radar reflectivity, and with gauge in terms of hourly precipitation accumulation. Finally, the relation between radar reflectivity and snowfall rate is derived using the

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2DVD data, and validated with MRR and gauge data. Expansion of this work is possible in a number of ways. First, we will investigate

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the regional variability of microphysical properties of summer and winter

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precipitation using the data of the radars and disdrometers over northern, eastern, southern, and western China. Sub-regional variabilities of precipitation will also be studied over northern China, especially for the region with complex terrain, in order

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to compare the variability of rainfall characteristics of the windward and leeward slopes of a mountain, as well as the variability of snowfall characteristics between a

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plain region and a mountain area. Secondly, we will incorporate our measurements into numerical forecast models to provide improved microphysical schemes. The empirical relationships between PSD parameters and governing parameters in the models will also be derived as the input to simulations of snow and aggregates as the study in Brandes et al. (2007). This work is also useful for improvement of ice scattering property simulations in the T-matrix codes. Finally, we will calculate the radar moments by using the PSD data to study quantitative precipitation estimation as described in section 4. In addition, the hydrometeor classification can also be achieved using the radar and disdrometer data (Grazioli et al., 2014; Bernauer et al.,

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2015).

Acknowledgement The authors would like to thank Prof. Guifu Zhang of the University of Oklahoma who provides the codes of the moment method, and Xiaofeng Han of Shunyi

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meteorological observation station, who gives great helps for the maintenance of the instruments. This project is partially supported by the National Natural Science

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Foundation of China (Grant Nos. 41575037, 41605019), the National Key Basic Research 973 Program of China (Grant Nos. 2014CB441403, 2013CB430105), and

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the China Postdoctoral Science Foundation (Grant No. 2015M580123). The authors

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valuable comments and suggestions.

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would like to express our sincere thanks to the anonymous reviewers for their

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50(7), 1558-1570. Zhang, G., Vivekanandan, J., Brandes, E., 2001. A method for estimating rain rate and drop size distribution from polarimetric radar measurements. IEEE Trans. Geosci. Remote Sensing. 39(4), 830-841. Zhang, G., Vivekanandan, J., Brandes, E.A., Meneghini, R., Kozu, T., 2003. The Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information? J. Atmos. Oceanic Technol. 20(8), 1106-1119. Zhang, H., Zhai, P., 2011. Temporal and spatial characteristics of extreme hourly precipitation over eastern China in the warm season. Adv. Atmos. Sci. 28(5), 1177.

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Rain types

Samples

Rt (mm)

Zmin (dBZ)

Zmax (dBZ)

(mins) CV

1458

426.8

26.0

53.4

ST

8444

166.0

3.4

40.9

Table 1. Counts of samples, rain accumulation (Rt), minimum radar reflectivity (Zmin),

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and maximum radar reflectivity (Zmax) of convective (CV) and stratiform (ST) rain.

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NT

D0

Dm

Dmax

Z

R

LWC

(m-3)

(mm)

(mm)

(mm)

(dBZ)

(mm/h)

(g/m-3)

CV 1522.2

1.65

1.78

6.73

42.1

17.57

0.86

ST

238.7

1.17

1.25

4.27

26.8

1.20

0.07

TL

430.4

1.48

1.61

5.90

34.5

3.63

0.19

PT

Table 2. Microphysical quantities derived from the averaged PSD for convective (CV), stratiform (ST) and total data (TL), respectively. NT is the total number concentration,

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D0 is the median diameter, and Dm is the mass-weighted diameter. Dmax is the maximum diameter which is defined as the largest bin associated with number

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concentration greater than 1103 m-3mm-1. Z is the radar reflectivity in a logarithm

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form. R is the rain rate and LWC is the liquid water content.

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Figures

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Figure 1. Comparisons of original (green) and calibrated (red) MRR data at 90 m height with 2DVD data (blue): (a) one-hour rain accumulations (R1h) and (b) radar

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reflectivity (Z). Note that the radar reflectivity is computed by the sixth order of the

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PSD moment.

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Figure 2. Probability distributions of (a) radar reflectivity (Z), (b) fall velocity (VD), (c) liquid water content (LWC), and (d) rainfall rate (R). The LWC and R are in

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logarithmic forms. The start points and circle points represent the 2DVD and MRR,

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respectively, while the green, blue and red curves are the total dataset (TL), stratiform

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rain (ST), and convective rain (CV), respectively.

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Figure 3 Time-dependent probability density function (TPDF) of (a), (b) radar reflectivity, (c), (d) fall velocity, (e), (f) liquid water content, and (g), (h) rainfall rate.

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The left column is stratiform rain, and the right column is convective rain.

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Figure 4 Contoured frequency-by-altitude diagrams (CFADs) of (a), (b), (c) radar

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reflectivity, (d), (e), (f) fall velocity, (g), (h), (i) liquid water content, and (j), (k), (l) rainfall rate. The first, second, and third columns are the stratiform, convective rain,

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and their differences, respectively. The solid black lines represent the average values in the diagrams.

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Figure 5 Logarithmic probability distributions as a function of raindrop diameter (D)

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and fall velocity for (a) stratiform rain (ST), (b) convective rain (CV), and (c) total data (TL), respectively, together with the fitted curves for (d) ST, (e) CV, and (f) TL,

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respectively. In the bottom row, the mean is given as ―diamonds‖, while 1 is represented by a error bar. ―Fit‖ (blue curve) is the fitted relation of diameter and fall velocity using the 2DVD data, ―AT73‖ (green curve) is calculated from the radar data

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by Atlas et al. (1973), and ―BR02‖ (red curve) is derived from the laboratory

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measurements by Brandes et al. (2002).

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Figure 6. Normalized probability distributions as a function of raindrop diameter and

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axis ratio (b/a) for stratiform rain (ST; D: 0.12-5.57 mm) and convective rain (CV; D:

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0.12-6.72 mm).

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Figure 7 Same as Figure 5, but for axis ratio. ―Fit‖ (blue) is the fitted relation of

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diameter and axis ratio in polynomial form, ―BC87‖ (green) represents the curve of Beard and Chuang (1987) and ―PB70‖ (red) follows the relation of Pruppacher and

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Beard (1970).

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Figure 8 Averaged PSD for total data (TL; green), stratiform rain (ST; blue), and

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convective rain (CV; red), respectively, measured by 2DVD.

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Figure 9 Scatterplots of  -  values obtained from the truncated-moment method. Dash lines show the fitted curve (red), the Florida relation (green; Zhang et al., 2003),

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the Nanjing relation (magenta; Chen et al., 2013a), the Beijing relation measured by

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Parsivel (black; Tang et al., 2014), and the Oklahoma relation (cyan; Cao et al., 2008).

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Figure 10 Same as Figure 5, but for the    relation. ―Fit‖ (blue) is the fitted

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relation of  and  in polynomial form, and ―Fit_data‖ (red) is the fitted relation

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in Figure 9.

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Figure 11 PDFs of (a) log10 N w and (b) Dm for stratiform (ST; blue), convective (CV;

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red), and total data (TL; green), respectively.

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Figure 12 Average values of log10 N w versus Dm from 2DVD as indicated for stratiform (ST; blue) and convective originated from local area (L; green), north (N;

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green), west (W; green), south (S; red), southeast (SE; red), and east (E; east). The two black rectangles correspond to the maritime (up) and continental (bottom)

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convective clusters in Bringi et al. (2003).

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Figure 13 Contours of (a) log10 N w versus Dm and (b) Z versus VD for stratiform (ST; blue) and convective (CV; red), respectively. The black curves are the boundaries to

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classify ST and CV by using linear discriminant analyses.

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Figure 14 Time series of (a) 5-min radar reflectivity derived from 2DVD (blue), the

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model proposed in Zhang et al. (2011) (ZG11; green), and MRR (red), and (b) hourly precipitation accumulation measured by 2DVD (blue) and gauge (red), respectively,

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between 0700 and 1959 LST on 22nd November 2015.

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Figure 15 Scatterplots of MRR-calculated hourly precipitation accumulation versus

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gauge measured one for the 22nd November 2015.

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Figure 16 Same as Figure 14, but for the case between 0000 and 1059 LST on 20th

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November 2015.

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Figure 17 Same as Figure 15, but for the 20th November 2015 case.

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Highlights



Axis ratio as a function of raindrop diameter is investigated using 2DVD data measured in northern China.

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The constraint gamma model for stratiform rain is obtained by using an empirical fit in a high probability region on the plane of the shape and slope parameters. In northern China, the types of convective rain depend on the orientations and

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mechanisms of the storms.

A bulk-property-based algorithm is proposed for classifying the convective

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The relation between radar reflectivity and snowfall rate is derived using

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2DVD data.

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

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and stratiform rain.