1 Introduction

How to monitor and identify clouds and precipitation system is the basis for improving the accuracy of high-resolution weather forecasts and for the operation of weather modification (Yao 2006). At present, clouds and precipitation are observed mainly by aircraft sounding (Brown and Swann 1997; Jorgensen 1984; King et al. 2004), ground-based (Deshpande and Raj 2009; Ecklund et al. 1995; Gage et al. 1996; Orr and Martner 1996; Nissen et al. 2005; Germann et al. 2006) and space-based remote sensing (Tokuno and Tsuchiya 1994; Richards and Arkin 1981; Spencer et al. 1983; Janowiak and Xie 1999; Rosenfeld and Lensky 1998; Iguchi et al. 2000). These are, of course, of great importance for recognizing the microphysical structures and the developing characteristics of clouds and precipitation systems.

Stratiform cloud precipitation, which is usually associated with large-scale weather system with complex meso-scale structures in clouds, tends to appear in spring and autumn in the northern part of China. The microphysical process and precipitation mechanism of the stratiform clouds are very complicated (Lei et al. 2008; Hou et al. 2011). It is generally believed that the precipitation of temperate stratiform cloud mainly develops through the ice crystal process. The formation of such precipitation particles usually goes through three levels, namely, the ice crystal layer, the ice crystal and supercooled water droplet layer, and the water droplet layer with the temperature higher than 0 °C (Yang et al. 2011). The ice crystal layer is the layer consisting of ice crystals, which serve as the ice embryo to develop low clouds precipitation. Then the ice crystals descend into the supercooled water droplet layer, where the desublimation growth and the collision-coalescence process start. The ice crystals can grow bigger either by rapid desublimation of Bergeron process, or snowflakes can form by collision-coalescence between ice crystals. The desublimation growth process is of vital importance for ice crystal growth. At last, the ice crystals gradually melt into water droplets below 0 °C level, grow by colliding and coalesce with the small cloud droplets and fall (Sheng et al. 2003).

Since 1970s, many field observation experiments and study focusing on stratiform cloud precipitation systems and frontal cloud system have been conducted in China and abroad (Choi and Bindschadler 2004; Radke and Hobbs 1969; Yang et al. 2005). The larger-scale field observation tests include the observation on winter stratiform clouds by the former Soviet Union, the detection of extrotropical cyclone cloud systems and orographic clouds by United States, and the experiment on artificial precipitation enhancement in the stratiform clouds in northern China. Of these experiments, the most representative one is the Study on Middle Latitude Cyclones (also named CYCLES Program) which was implemented by Hobbs et al. (Hobbs et al. 1980; Hobbs 1978; Hobbs and Persson 1982; Herzegh and Hobbs 1980; Rutledge and Hobbs 1983). Based on these research results, a series of conceptual models for cloud systems have been constructed, such as the Conceptual Model of Frontal Cloud System that was put forward by Hobbs et al. and the Conceptual Model of the Precipitation Cloud Systems in the North of China which was constructed by Chinese scientists (Gu 1980; You et al. 2002; Hong and Zhou 2005; Hu et al. 2007). These achievements have laid a good foundation for the study of the potential of artificial precipitation enhancement. In China, systematic research on stratiform cloud precipitation began in 1980s. Through the Artificial Precipitation Experiment on Stratiform clouds in North China, scientists established a system for understanding stratiform cloud precipitation. They built a conceptual model of the cloud physics for rainfall systems and brought forward some catalytic conditions, chances and methods of artificial precipitation enhancement (You et al. 2002; Li 2002).

Xinjiang is situated in the northwest of China, accounting for 17% of the total area of China. It belongs to a typical arid climate zone where the annual surface runoff within Xinjiang is only 3% of the total runoffs in the whole country. Therefore, the shortage of water resources is the key bottle-neck problems that restrict the sustainable socio-economic development of Xinjiang. In Xinjiang lie the Tianshan Mountains, which is a famous mountain chain in central Asia. The economic belts in the two sides of the Tianshan Mountains are the first priority on the socio-economic development of Xinjiang, where there are 9 prefectural cities including 46 counties and the population is over 10 million. Therefore, the problem of water shortage needs solving first of all to develop the economy and environment sustainably in this region. For a long time, the Tianshan Mountains is an ideal target area for the operation of artificial rainfall (snowfall) enhancement in Xinjiang. Now, supported by the Chinese government, the meteorological integrated observation networks in the Tianshan Mountains have gained improved significance and monitoring bases for clouds and precipitation have been established. In 2012, the Urumqi Institute of Desert Meteorology, which is attached to the China Meteorological Administration (CMA), started the project “Research and application of key technologies for artificial rain and snow enhancement in the Tianshan Mountains”. This project is a part of the supported science and technology program of the “12th Five-Year Plan” in China, whose purpose is to study the physical mechanisms of clouds and precipitation system in the Tianshan Mountains. Theoretically, it is very meaningful for operating artificial precipitation enhancement, increasing rainfall amount in mountains and alleviating the shortage of water resources effectively. Thus, for at this project, the Urumqi Institute of Desert Meteorology, CMA, adopted a wind-profiling radar and a Doppler weather radar and conducted the detection experiment in Bayanbulak in the central part of the Tianshan Mountains from 1 to 31 August 2012. Based on the observation data from the wind-profiling radar and Doppler weather radar, this paper thoroughly analyzes the dynamic, thermodynamic, radar echo intensity and macro-micro structure characteristics of the precipitation process that occurred in 2–3 August 2012. This study aims to deepen the understanding on the physical structure of the stratiform clouds precipitation over the Tianshan Mountains in summer, and to provide scientific basis for cloud seeding operation over this area.

2 Data and Method

2.1 Equipment and Data

The equipment used in this study includes the CFL-03 boundary wind-profiling radar and 724XD pulse Doppler weather radar (Fig. 1). The CFL-03 boundary wind-profiling radar adopts a detection mode of five fixed beams, i.e. one vertical beam and four tilt beams at a zenith angle of 15°. These tilt beams are evenly and orthogonally distributed in azimuth. To balance the detection height and resolution in case of low-level operation, CFL-03 boundary wind-profiling radar runs in two modes: low and high. The former uses a narrow pulse with a height resolution of 50 m, while the latter uses a wide pulse with a height resolution of 100 m. The two modes function alternately to ensure a high low-level resolution and a high detection height at the same time. The data from CFL-03 boundary wind-profiling radar include velocity PSD (power spectral density) in high or low mode, horizontal wind, vertical velocity, signal to noise ratio, turbulence refractive index structure constant (\( {C}_n^2 \)), spectral width, etc.. Tables 1 and 2 respectively list the main technical parameters of CFL-03 boundary wind-profiling radar and 724XD pulse Doppler weather radar.

Fig. 1
figure 1

CFL-03 wind-profiling radar and 724XD pulse Doppler radar used in the detection over Bayanbulak, the central part of the Tianshan Mountains

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Table 1 Technical parameters of the CFL-03 wind-profiling radar
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Table 2 Technical parameters of the 724XD pulse doppler weather radar
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The data used in this paper include the wind-profiling radar data, Doppler weather radar data, ground rainfall, FY-2 infrared satellite images and the U.S. National Centers for Environmental Prediction (NCEP) 1° × 1° reanalysis data of the precipitation process in Bayanbulak (43°02’N, 84°09′E; altitude: 2459.0 m) of the Tianshan Mountains in 1–3 August 2012. The data from the Doppler weather radar are mainly composite reflectivity factor (echo intensity) and echo tops during precipitation. The Doppler weather radar will be impacted be some highly reflective objects on the ground, so FFT is applied to ground clutter filter and suppression in this study. To be specific, transform the radar pulse on the time domain signal to frequency domain data; filter the clutter components at or near zero Doppler frequency; then convert the frequency domain data to the radar pulse data on the time domain again. Via this practice, ground clutter suppression is achieved. The data from the wind-profiling radar mainly include velocity PSD (power spectral density) from vertical beam in high mode, which is utilized to calculate the echo intensity and to retrieve the raindrop size distribution. In addition, the horizontal wind profile data could be used to analyze wind field and to retrieve temperature advection. Beijing Time (BT) is applied in this paper.

2.2 Raindrop Size Distribution Inversion Method

  • Step 1: Using velocity PSD (power spectral density) data from the wind-profiling radar with vertical beam in high mode, echo intensity Z is calculated (He 2006; Ming et al. 2014).

  • Step 2: Ulbrich and Chilson (1994) discovered that when vertical motion of the atmosphere is relatively stable, return signal intensity of the precipitation particles can be utilized to estimate the vertical velocity of the atmosphere wi, which is shown in Formula (1) below:

$$ {\mathrm{w}}_{\mathrm{i}}\left(\mathrm{h}\right)=3.5\ \mathrm{Z}{\left(\mathrm{h}\right)}^{0.084}{\left({\uprho}_0/\uprho \left(\mathrm{h}\right)\right)}^{0.4} $$
(1)

where Z(h) represents echo intensity at the height of h, (ρ0/ρ(h))0.4 is the calibration factor. ρ(h) stands for the atmospheric density at the height of h, while ρ0 represents the atmospheric density at the sea level. According to terminal velocity of the gravitational precipitation particles calculated by Foote and Toit (1969): ρ0/ρ(h) ≈ eh/9.58.

  • Step 3: During raining process, vi (vertical velocity) detected by the wind-profiling radar consists of v0i (terminal velocity of the gravitational precipitation particles) and wi (vertical velocity of the atmosphere). In terms of envelope, S(v0i) (terminal velocity PSD distribution of the gravitational precipitation particles) and S(vi) (return signal velocity PSD distribution received by the radar) are the same, so:

$$ \mathrm{S}\left({\mathrm{v}}_{0\mathrm{i}}\right)=\mathrm{S}\left({\mathrm{v}}_{\mathrm{i}}-{\mathrm{w}}_{\mathrm{i}}\right) $$
(2)

Using return signal velocity PSD and echo intensity data from the wind-profiling radar, the terminal velocity PSD distribution S(v0i) of the gravitational precipitation particles can be obtained via Formula (1) and Formula (2).

  • Step 4: The formula between V (terminal velocity of the gravitational precipitation particles) and D (diameter of the precipitation particles) was brought forward by Gunn and Kinzer (1949):

$$ \mathrm{V}\left({\mathrm{D}}_{\mathrm{i}}\right)=9.65-10.3{\mathrm{e}}^{-0.6\mathrm{D}}{\left[\frac{\uprho \left(\mathrm{h}\right)}{\uprho_0}\right]}^{-0.4} $$
(3)

Using S(v0i) (terminal velocity PSD distribution of the gravitational precipitation particles), the corresponding S(Di) (diameter PSD distribution of the precipitation particles) can be calculated.

  • Step 5: According to the radar weather equation, the Pri (echo power of the single precipitation particle with the diameter of Di) is derived as follows (Zhang et al. 2001).

$$ {\mathrm{P}}_{\mathrm{ri}}=\frac{\uppi^3}{1024\ln 2}\frac{{\uptau \mathrm{cP}}_{\mathrm{t}}{\mathrm{G}}^2\uptheta \upvarphi}{2{\uplambda}^2{\mathrm{R}}^2\mathrm{L}}{\left|\frac{{\mathrm{m}}^2-1}{{\mathrm{m}}^2+1}\right|}^2{\mathrm{D}}_{\mathrm{i}}^6 $$
(4)

where π is constant, τ is pulse width, c is light velocity, Pt is transmitting peak power, G is antenna gain, φ is horizontal beam width, θ is vertical beam width, λ is radar wavelength, L is feeder loss, and \( {\left|\frac{{\mathrm{m}}^2-1}{{\mathrm{m}}^2+1}\right|}^2 \) is square modulus of complex refractive index, whose value is 0.93.

Step 6: According to the relationship between S(Di) (diameter PSD distribution of the precipitation particles), Pri (echo power of the single precipitation particle with the diameter of Di) and N(Di) (the raindrop size distribution), the following Formula (5) is obtained.

$$ \mathrm{N}\left({\mathrm{D}}_{\mathrm{i}}\right)=\mathrm{S}\left({\mathrm{D}}_{\mathrm{i}}\right)/{\mathrm{P}}_{\mathrm{ri}} $$
(5)

3 Result and Analysis

3.1 Description of Precipitation Process

Affected by the eastward movement of the trough which results from the weakening of the Central Asia vortex (Fig. 2b), from 1 to 3 August most parts of Xinjiang from west to east successively experienced the rainfall weather. Among these areas, moderate to torrential rains occurred over Yili River Valley, Bortala of Mongolian Autonomous Prefecture, the Tianshan Mountains and its two sides, the west part of South Xinjiang, Bayingolin of Mongolian Autonomous Prefecture and Hami. From 20:00 BT 2 August to 15:00 BT 3 August, Bayanbulak of the Tianshan Mountains saw light to moderate rains, having an amount of 6.4 mm (Fig. 3). However, the rainfall mainly concentrated in the period of 20:00–23:00 BT 2 August.

Fig. 2
figure 2

Upper-level charts at 100 hPa at 08:00 BT 01 August and at 500 hPa at 20:00 BT 02 August 2012 respectively

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Fig. 3
figure 3

Ground rainfall at Bayanbulak from 2 to 3 August 2012

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The upper-level chart at 100 hPa at 08:00 BT 1 August before the rainfall began shows that the upper-air circulation is in the pattern of two ridges and one trough over Eurasia. One long-wave ridge is over the northern part of the Mediterranean Sea and the Caspian Sea and another is over the Lake Baikal while the long-wave trough is located in the Ural Mountains. The South Asian High has its center over the southern part of Tibetan Plateau (Fig. 2a). By 20:00 BT 2 August, the South Asian High gradually develops into a dual type and the high pressure centers are over the Iranian Plateau and the Tibetan Plateau separately. The western section of the high is more intense than its eastern section. The dual-type distribution of the South Asian High is conductive to the deepening of the long-wave trough.

From the upper-level chart at 500 hPa (Fig. 2b), it is seen that at 20:00 BT 2 August, the northern part of Mediterranean Sea and the Caspian Sea are controlled by high ridges and the trough is over the West Siberia. The Bayanbulak region of the Tianshan Mountains is in the southwest airflows in front of the trough. With the continuous eastward development of the high ridge over the Caspian Sea and the Aral Sea, the low trough in the front of the high ridge is brought into Xinjiang, triggering the occurrence of the precipitation.

3.2 Variation of Cloud Structures

Figure 4 presents the FY-2 infrared satellite cloud images and cloud top brightness temperature (TBB) during the process of precipitation 2–3 August. It is seen that at 18:00 BT 2 August one loose cloud system with uneven brightness in the direction of northeast-southwest moves eastward into Xinjiang within the range 40–60°N and 80–90°E. Inside the cloud system there are meso-scale cloud clusters between which the structure of the cloud system is not well-proportioned. In addition, these cloud clusters have different brightnesses, indicating the different thickness of the clouds. At 21:00 BT 2 August, the cloud clusters develop and merge together, moving toward the northeast and gradually becoming a compact banded cloud system with uniform colors. This cloud system covers the western part of North Xinjiang and parts of the Tianshan Mountains. The boundary behind the cloud system looks smoother but in front of this boundary it is not consistent. At 10:00 BT 3 August, the main body of the cloud system gradually moves out of Xinjiang. The cloud top brightness temperature is the radiance of the cloud top and the ground surface of the cloudless area, which is collected by the infrared detection of the meteorological satellite. The cloud top brightness temperature is indicated by Black-Body Temperature (TBB) with equivalent radiance. TBB could reveal the existence of the clouds and demonstrate some typical characteristics during the clouds development. In clouds, TBB represents the black-body radiance temperature of the cloud top. The lower TBB temperature indicates the higher cloud top and the thicker cloud; and vice versa (Meng et al. 2002). Figure 4d presents the cloud top brightness temperature (TBB) at 22:15 BT 2 August. It can be clearly seen that the TBB distribution is uniform relatively, changing in the range of −12 °C~ − 42 °C; and the TBB over Bayanbulak of Tianshan Mountains varies from −12 °C to −30 °C. These indicate that the cloud top height is low and no obvious convective systems appear. This analysis suggests that the rainfall in the mountainous region of Bayanbulak results from this cloud system and its evolution is closely related to the motion of the low trough.

Fig. 4
figure 4

FY-2 infrared satellite cloud images (a) at 18:00 on 2 August 2012 (b) at 21:00 on 2 August 2012 (c) at 10:00 on 3 August 2012 (d) Cloud top brightness temperature chart (TBB) at 22:15 on 2 August 2012

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3.3 Evolution Characteristics of Doppler Radar Echoes during the Precipitation

Figure 5a-c show the composite reflectivity factor (echo intensity) detected by the Doppler weather radar during the precipitation on 2 August 2012. It is seen that the precipitation echo distribution are platelike generally. At 20:58, the large value center of the echo intensity is above the observation station, with echo intensity up to 38 dBZ. During that time, the surface precipitation is quite great, with the hourly rainfall of 3.1 mm. As time goes by, the echo intensity above the observation station weakens remarkably at 22:16, and the surface precipitation reduces as well. Figure 5d is the echo tops image captured during the rainfall process. The maximum height of precipitation echoes reaches about 5000–9000 m. The echo tops is absolute height, and the local altitude is 2459 m; therefore, it is indicated that the height of the whole precipitation cloud system is no higher than about 6500 m. It should be noted that the detection equipment is pulse Doppler radar, with extended frequency and 3.2 cm radar wavelength. Path attenuation of electromagnetic wave and atmospheric attenuation are already corrected during the radar signal processing. But the radar wave attenuation in the precipitation cloud is not taken into consideration. Thus, the detected reflectivity is a little weaker than actual reflectivity.

Fig. 5
figure 5

Doppler radar echo during the precipitation on 2 August 2012

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Bright band in radar echo is one of the most prominent features during the stratiform precipitation process. From Fig. 5e echo intensity profile of the Doppler radar, it is clearly seen that precipitation cloud system is below 6500 m. A horizontal bright band is between 1200 m and 2000 m height, with echo intensity ranging from 25 to 38 dBZ. Combining the temperature-latitude profile in Fig.6 (from NCEP analysis temperature data), 0 °C-layer isotherm is about 600 hPa and about 2000 m above the ground, which is just above the radar echo bright band. The consistency illustrates the bright band of Doppler weather radar echo intensity is 0 °C-layer bright band. Theoretically, 0 °C-layer bright band results from the melting of ice crystals or snowflakes as they fall to the elevation of melting layer. Then the rapid increase of dielectric constant strengthens the reflectivity within bright band. Besides, the collision-coalescence between melting particles of ice crystals or snowflakes makes particle size bigger, which increases the reflectivity in bright band. However, below 0 °C level bright band, ice crystals or snowflakes already transform into to raindrops. Since the shape of raindrops is almost spherical, their falling velocity is much faster than ice crystals and snowflakes, which makes the amount of precipitation particles in unit volume reduce considerably, weakens the total scattering and reduces the echo intensity below bright band (Yang et al. 2011; Sheng et al. 2003). The presence of bright band indicates that the transformation from ice to liquid is confined within a narrow layer; it also illustrates that air flow in this precipitation cloud is stable, with no apparent air convection. What’s more, combing the precipitation echo intensity profile and the atmospheric temperature vertical profile, the cloud top temperature is determined roughly, which ranges from −25 °C to −32 °C. Based on the analysis above, this precipitation process is identified as a stratiform cold cloud precipitation.

Fig. 6
figure 6

A temperature profile along 43°N at 20:00, August 2nd, 2012

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3.4 Wind-Profiling Radar Echo Intensity and Radial Velocity during the Precipitation

Using the detection data from the wind-profiling radar with vertical beam in high mode, the echo intensity of the precipitation from 19:00 to 22:00 on 2 August 2012 is calculated and shown in Fig. 7a. This figure indicates that the height of the precipitation cloud system is below 6500 m, whose echo intensity ranges from 5 to 38 dBZ. A big value zone of precipitation echo intensity is present at 1200–2000 m height layer, and the big value zone is the 0 °C-layer bright band as well. The finding is consistent with the detection result via Doppler weather radar, which could further prove the conclusion of stratiform precipitation. It is worthy to be mentioned that the average elevation in Bayanbulak of the Tianshan Mountains is about 2500 m, and 0 °C level height in summer is relative low over the ground. The 0 °C level bright band in radar echo intensity profile is shown below the height of 2000 m, which is the remarkable feature of stratiform precipitation in this area. From the Time-height profile of radial velocity in Fig. 7b, it is revealed that the radial velocity below 0 °C-layer bright band is very fast, about 4.0–9.0 m/s. It is indicated that the falling speed increases rapidly after solid particles (ice crystals, snowflakes, etc.) are melted into liquid particles when passing through the bright band. Based on the analysis above, during precipitation the liquid precipitation particle zone is below the height of 1200 m above the observation station, the melting layer (ice crystals transform into water droplets) is between 1200 m and 2000 m height, and the solid particles (mainly including ice crystals, snowflakes, etc.) layer is above 2000 m.

Fig. 7
figure 7

Time-height profiles of echo intensity and radial velocity during precipitation on 2 August 2012 detected by wind-profiling radar

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3.5 Variation Characteristics of Horizontal Wind Profile and Temperature Advection during the Precipitation

Figure 8 illustrates the variation of wind profile before and after the precipitation. The figure shows that before the rain starts, the wind-profiling radar misses the horizontal wind data of 3000–5000 m height to some extent. With precipitation system entering the area, the wind field observed by the wind-profiling radar grows higher, and a distinct multi-layer structure appears. Because the precipitation clouds exist at the height about 6500 m, the wind profiler data can be used to explore more wind speed conditions in clouds during the precipitation. Here in Fig. 8c, the atmosphere can be divided into three layers vertically. Under the height of 1000 m, which is divided as the first layer, the northwest wind and west wind gradually turn into west wind, southwest wind and southeast wind, with speeds varying within the range of 3.0–8.0 m/s. The air at the height between 1000 m and 2500 m is the second layer which is mainly dominated by southern airflows with speeds similar to the wind in the first layer. The air beyond the height of 2500 m is the third layer where the airflows blow toward the east, northeast and north. Combining these with Fig. 7, shows that the precipitation cloud system is mainly controlled by southerly airflow, easterly airflow and southeasterly airflow, and the motion of atmosphere in the clouds is characterized by multi-layer structure with speeds of 3.0–8.0 m/s.

Fig. 8
figure 8

Variation of horizontal wind speed and direction during the rainfall process in 2–3 August 2012

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According to the principle of thermal wind, the property and size of temperature advection can be judged from the wind direction variation with height. In a certain layer of the atmosphere, if the wind direction deflects clockwise with the increase of height, it indicates the existence of warm advection; if the wind direction deflects anticlockwise with the increase of height, cold advection is present in this layer (Zhu et al. 1984). Thus the wind profile data during this precipitation is utilized to calculate the temperature advection variation with time and height changes above the observation station (Zhang et al. 2007). It is clearly shown in Fig. 9 the temperature advection in the atmosphere is presented with the vertical structure distribution of “cold-warm-cold”. Below 1200 m height it is mainly cold advection, which may reflect the cold pool by the evaporation of liquid precipitation particles and cooling. Warm advection is present between 1200 m and 2000 m height, which corresponds to 0 °C level bright band of the radar echo. Above 2000 m height, it is mainly cold advection. The vertical structure of temperature advection illustrates the relative stability of the atmospheric stratification.

Fig. 9
figure 9

Time-height profiles of temperature advection 19:00–22:00 2 August 2012. (unit: 10−5 °C s−1)

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3.6 Raindrop Size Distribution in the Precipitation Clouds

The raindrop size distribution refers to the distribution of the number of raindrops per a unit volume in terms of different raindrop diameters. The microphysical process of precipitation can be obtained by analyzing the raindrop size distribution. What’s more, the parameters can also be calculated with the raindrop size distribution, such as the liquid water content and the precipitation intensity (Zhang et al. 2001). Figure 10 shows the raindrop size distributions between 600 m and 1200 m height at four moments during the precipitation, which are retrieved from velocity PSD data of the wind-profiling radar. (The color axis changes from red to blue gradually, indicating the gradual reduction of the precipitation particle concentration.) Throughout the evolution of the raindrop size distributions from early stage of the precipitation (Fig. 10a) to its peak stage (Fig. 10b), the concentration of the tiny particle zone (D ≤ 2.5 mm) changes a little, while the concentration of the medium particle zone (2.5 < D ≤ 4 mm) and the concentration of the large particle zone (D > 4 mm) increase by 101–102. After the rainfall peak stage, the precipitation begins to weaken (Fig. 10c). Seen from Fig. 10c, the concentration of the large particle zone reduces by 102, the concentration of the medium particle zone decreases by 101, while the concentration of the tiny particle zone barely changes. The precipitation furtherly weakens (Fig. 10d), and the concentration of the tiny particle zone drops by 101–102. The above analysis shows that from the early stage of precipitation to its peak stage, the concentration of the medium particles and the concentration of the large particles increase considerably; but after peak stage the concentration in the medium particles and the concentration of the large particles decline first, then the concentration in the tiny particles reduces.

Fig. 10
figure 10

Raindrop size distributions during precipitation on 2 August 2012 (color axis unit:logN(D)(m−3mm−1))

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The liquid water content refers to the mass of water contained in the unit volume of the atmosphere, which can be expressed with the raindrop size distribution in Formula (6). The precipitation intensity refers to the amount of rainfall per unit time, which can be illustrated with the raindrop size distribution in Formula (7) (Zhang et al. 2001).

$$ \mathrm{M}=\frac{1}{6}\uppi \uprho {\sum}_{\mathrm{i}=\min}^{\mathrm{i}=\max}\mathrm{N}\left({\mathrm{D}}_{\mathrm{i}}\right){\mathrm{D}}_{\mathrm{i}}^3\Delta \mathrm{D} $$
(6)
$$ \mathrm{I}={\sum}_{\mathrm{i}=\min}^{\mathrm{i}=\max}\mathrm{N}\left({\mathrm{D}}_{\mathrm{i}}\right)\mathrm{M}\left({\mathrm{D}}_{\mathrm{i}}\right)\mathrm{v}\left({\mathrm{D}}_{\mathrm{i}}\right)\Delta \mathrm{D} $$
(7)

where M is the liquid water content, ρ is the liquid water density, Di is the diameter of particle No. i, N(Di) is the raindrop size distribution, I is the precipitation intensity, and M(Di) represents the mass of the raindrop with Di diameter, and v(Di) indicates the corresponding speed of Di.

Using the raindrop size distribution data retrieved from the wind-profiling radar, the liquid water content and precipitation intensity at 600 m–1200 m height below 0 °C level bright band (Fig. 11) can be calculated according to Formula (6) and Formula (7). Seen from Fig. 11, the characteristics of spatial-temporal variations of the liquid water content and the precipitation intensity are basically the same. During the peak stage of the precipitation, the values of the liquid water content and the precipitation intensity are big, with the instantaneous precipitation intensity up to 5.0 mm/h and the liquid water content up to 0.35 g/m3.

Fig. 11
figure 11

Time-height chart of the liquid water content and the precipitation intensity during precipitation on 2 August 2012

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In radar meteorology, the relationship between the echo intensity Z and the precipitation intensity I during stratiform cloud precipitation is shown in Formula (8). With the echo intensity detected by the wind-profiling radar, the precipitation intensity can be calculated according to Formula (8) (Zhang et al. 2001; Ming et al. 2014).

$$ \mathrm{Z}=76.5{\mathrm{I}}^{1.6} $$
(8)

Since the ground rainfall data just record the precipitation intensity per hour. However, the precipitation intensity (Ii) calculated from the raindrop size distribution and the echo intensity are the instantaneous precipitation intensity values. In order to obtain the accurate precipitation intensity per hour (I0), one hour should be divided into 12 equal intervals, namely \( \Delta \mathrm{T}=\frac{1}{12}\mathrm{h} \) (the wind-profiling radar update the data at 5 min’ intervals). Then according to Formula (9), the precipitation intensity per hour can be obtained by means of progressive average.

$$ {\mathrm{I}}_0={\sum}_{\mathrm{I}=1}^{12}{\mathrm{I}}_{\mathrm{i}}.\Delta \mathrm{T}=\frac{1}{12}{\sum}_{\mathrm{i}=1}^{12}{\mathrm{I}}_{\mathrm{i}} $$
(9)

Figure 12 is the comparison curves of the precipitation intensity from ground observation and the precipitation intensity retrieved from the raindrop size distribution (RSD) and the echo intensity data at 700 m height. Figure 12 indicates that the precipitation intensity obtained from three sources are nearly the same in terms of curve trend and value. At 21:00, the maximum precipitation intensity from three sources are about 2.5–3.3 mm/h. The alignment proves the accuracy and feasibility of the retrieved raindrop size distribution.

Fig. 12
figure 12

The comparison curves the precipitation intensity from ground observation and the precipitation intensity retrieved from the raindrop size distribution and the echo intensity data from 19:00 to 23:00 on 2 August 2012

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4 Conclusions

This paper uses the wind-profiling radar and the Doppler weather radar data during precipitation from 2nd to 3rd August 2012 over Bayanbulak of the Tianshan Mountains, and analyzes the dynamic, thermodynamic, radar echo intensity and macro-micro structure of the 2–3 August precipitation process. The following conclusions are obtained:

  1. (1)

    The radar echo intensity during this precipitation varies in the range of 5–38 dBZ. The precipitation cloud system is under the height of 6500 m, and an obvious 0 °C level bright band exists at 1200–2000 m height. NCEP analysis data shows the cloud top temperature ranges from −25 °C to −32 °C. Thus, the rainfall is identified as stratiform cold cloud precipitation. During precipitation, the liquid precipitation particle zone is below the height of 1200 m above the observation station, the melting layer (ice crystals transform into water droplets) is between 1200 m and 2000 m height, and the solid particles (mainly including ice crystals, snowflakes, etc.) layer is above 2000 m.

  2. (2)

    Atmospheric motion during this precipitation presents multi-layer structure with wind velocity varying within the range of 3.0–8.0 m/s. The temperature advection is presented with the vertical structure distribution of “cold-warm-cold”, which indicates relative stability of the atmospheric stratification.

  3. (3)

    By retrieving and analyzing the raindrop size distributions below 0 °C level bright band within 600–1200 m height, when the rainfall cloud evolves from early stage of precipitation to its peak stage, the concentration of the tiny particle zone (D ≤ 2.5 mm) changes a little while the concentration of the medium particle zone (2.5 < D ≤ 4 mm) and the concentration of the large particle zone (D > 4 mm) increase considerably; but from peak stage to dissipating stage, the concentration of the medium particle zone and the concentration of the large particle zone decline first, then the concentration of the tiny particle zone reduces remarkably.

  4. (4)

    The spatial-temporal variation characteristics of the liquid water content and the precipitation intensity, both of which are retrieved from the raindrop size distribution, are basically the same. During peak stage of precipitation, the instantaneous precipitation intensity reaches 5.0 mm/h, and the liquid water content reaches 0.35 g/m3. What’s more, the precipitation intensity retrieved from the raindrop size distribution and radar echo intensity at the height of 700 m is consistent with the precipitation intensity via ground observation. This alignment proves the accuracy and the feasibility of the retrieved raindrop size distribution in this study.