1.Institute of Urban Meteorology, China Meteorological Administration, Beijing 100089, China 2.State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China Manuscript received: 2019-01-22 Manuscript revised: 2019-08-23 Manuscript accepted: 2019-09-06 Abstract:Using melting layer (ML) and non-melting layer (NML) data observed with the X-band dual linear polarization Doppler weather radar (X-POL) in Shunyi, Beijing, the reflectivity (ZH), differential reflectivity (ZDR), and correlation coefficient (CC) in the ML and NML are obtained in several stable precipitation processes. The prior probability density distributions (PDDs) of the ZH, ZDR and CC are calculated first, and then the probabilities of ZH, ZDR and CC at each radar gate are determined (PBB in the ML and PNB in the NML) by the Bayesian method. When PBB > PNB the gate belongs to the ML, and when PBB < PNB the gate belongs to the NML. The ML identification results with the Bayesian method are contrasted under the conditions of the independent PDDs and joint PDDs of the ZH, ZDR and CC. The results suggest that MLs can be identified effectively, although there are slight differences between the two methods. Because the values of the polarization parameters are similar in light rain and dry snow, it is difficult for the polarization radar to distinguish them. After using the Bayesian method to identify the ML, light rain and dry snow can be effectively separated with the X-POL observed data. Keywords: X-band polarimetric radar, Bayesian method, melting layer identification, hydrometeor classification 摘要:利用北京顺义X波段双线偏振多普勒天气雷达观测的多次稳定性降水过程资料,获取了融化层和非融化层反射率(ZH) 、差分反射率(ZDR) 和相关系数(CC) 数据,利用获取的数据首先计算融化层和非融化层ZH、 ZDR和CC先验概率密度分布,利用先验概率密度分布,采用贝叶斯方法,计算雷达所有距离库(ZH, ZDR, CC)在融化层概率PBB和非融化层概率PNB ,当PBB > PNB时,该距离库属于融化层,否则属于非融化层。文中比较分析了ZH、ZDR和CC独立概率密度分布和联合概率密度分布条件下,采用贝叶斯方法识别融化层效果,分析表明,两种方式有细微差别,但是都能有效识别出雷达观测的融化层。由于小雨和干雪偏振参量值范围相近,导致偏振雷达区分小雨和干雪困难,采用贝叶斯方法识别出融化层后,X波段偏振雷达可以有效区分出小雨和干雪。 关键词:X波段偏振雷达, 贝叶斯方法, 融化层识别, 降水粒子分类
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2. Illustration of the X-POL network To strengthen the monitoring of disastrous weather and compensate for the deficiency of CINRAD/SA Doppler weather radars in low-altitude detection, five new X-POLs were built in the Beijing area in 2016 for the monitoring and early warning of disastrous weather. The spatial distribution of the five radars is shown in Fig. 1, in which the solid circles represent the detection ranges (60 km) of the X-POLs. The basic radar performance parameters are shown in Table 1. The volume scans are composed of nine elevation angle scans ranging from 0.5° to approximately 19.5° according to a standard WSR-88D scanning strategy (VCP21 mode), but the volume scan period is three minutes. The detection parameters include ZH, radial velocity (Vr), velocity spectrum width (Sw), ZDR, CC, and propagation phase shift (ФDP). The data for the bright band analysis are from X-POL in 2018 in Shunyi, Beijing. Figure1. The distribution of Beijing X-POLs, where the circles indicate the radar detection ranges of the X-POLs (60 km).
Specification
Parameter (s)
Transmitter
Klystron
Frequency
9.3–9.5 GHz
Wavelength
3.2 cm
Peak power
≥ 70 kW
Average power
112 W
Max. duty ratio
0.16%
Antenna diameter
2.4 m
Beam width
0.94°
Polarization mode
Linear horizontal and vertical; simultaneous transmission and reception
Detection range
150–230 km
Gate width
75 m
Max. pulse width
0.5 μs
Detection parameters
ZH, Vr, Sw, ZDR, CC, ΦDP, and SNR
Table1. The main performance parameters of X-POL.
The data are preprocessed by attenuation correction and de-noised by wavelet analysis (Hu et al., 2010; Hu and Liu, 2014), and the processing methods are briefly described in the following subsections.
2 2.1. Attenuation correction
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2.1. Attenuation correction
The attenuation effect on radar ZH and ZDR at the X-band is substantial and cannot be ignored. The path-integral attenuations are compensated for by adding the attenuation to the measured ZH and ZDR as follows: where $Z_{\rm{H}}^{(m)}(R)$ and$Z_{{\rm{DR}}}^{(m)}(R)$ are the raw measurements in the range R; m represents the measured ZH and ZDR values; and AH and ADP (in dB km?1) are the specific attenuation and specific differential attenuation, respectively, which are estimated using a composite method from either the specific differential phase (KDP) or ZH, expressed (Hu and Liu, 2010; Hu et al., 2014) as follows: where Zh = $10^{Z_{{\rm H}/10}} $, and the parameters in the formulas are set as: α = 1.37 × 10?4 dB km?1 (mm6 m?3)?1; β = 0.779; d = 1.13; γ = 0.14; σ1 = 0.2 deg km?1 and σ2 = 4.0 deg km?1; and ${a_1}$ = 0.22 dB deg?1 and ${a_2}$ = 0.033 dB deg?1.
2 2.2. Wavelet de-noising -->
2.2. Wavelet de-noising
The random fluctuation is reduced using wavelet de-noising with the following steps: (1) Deconstruction: each radial data is deconstructed into five levels with a db5 wavelet function. (2) De-noising: the detail coefficients in each level are suppressed with a ФDP penalty strategy. (3) Reconstruction: the data are reconstructed by means of an approximation and the processed detail coefficients with a soft function scheme. Once the data have been processed with the aforementioned attenuation correction and denoising, they are analyzed for BBML identification, as described in the following sections.
2 2.3. Data reliability -->
2.3. Data reliability
According to the physical meaning of ZDR, the ZDR value in light rain should be approximately equal to zero. In order to verify the reliability of ZDR, some light rain data are selected in three precipitation processes. The criteria for light rain echoes are: signal to noise ratio (SNR) > 20 dB; slant range between 10 km and 20 km away from the radar; ZH < 15 dBZ; and CC > 0.98. After finding the gates that meet the light rain criteria, and averaging these gates of ZDR, SNR and CC, the maximum average value of ZDR is 0.12 dB and the minimum is 0.06 dB, as shown in Table 2. All the average values of ZDR are close to zero, which indicates there is almost no systematic deviation in the ZDR value.
Date
Gates
ZDR (dB)
SNR (dB)
CC
12 August 2017
135 990
0.06
21.4
0.993
11 July 2018
124 738
0.12
20.5
0.996
15 October 2018
152 678
0.08
21.5
0.995
Table2. The ZDR biases estimated by the light rain method in three precipitation processes.
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4.1. BBML identification principle based on the Bayesian method
The Bayesian method can be used to identify the ML if the distributions of the probability densities of the ZH, ZDR and CC in the ML region are known in advance. The steps of BBML identification are described as follows (Zhang, 2016): The radar echoes are divided into two categories, C = (BB, NB), in which the ML echo is represented by BB and the non-melting layer (NML) echo is represented by NB. The identification vector, ${\bf{y}}$ = (ZH, ZDR, CC), is determined by combining the polarimetric parameters of ZH, ZDR and CC. The variable ${{y}}$ belongs to BB only when p(BB|${{y}}$) is larger than p(NB|${{y}}$), where p represents the probability density. According to Bayesian theory (Papoulis, 1991), where Ci = (BB, NB), and p(${{y}}$) = K represents the probability of observing the discriminant factor, assuming that it is the same as the classification probabilities for BB and NB (i.e., p(BB) = p(NB) = 1/2). Thus, p(Ci |${{y}}$) is proportional to p(${{y}}$|Ci)p(Ci), and Eq. (5) is transformed into: Based on the assumption that the classification is independent in a simple Bayesian identification, the conditional probability density can be decomposed into: If it is assumed that the distribution of parameters in the observed discriminant vector ${{y}}$= (ZH, ZDR, CC) is not independent, the joint probability is used to determine whether ${{y}}$ belongs to the ML. Then, the conditional probability density can be decomposed into:
2 4.2. Obtaining the prior probability distribution -->
4.2. Obtaining the prior probability distribution
To obtain the probability density distributions (PDDs) of the ZH, ZDR, and CC in the BBML, the ML data observed by Shunyi X-POL shown in Table 3 are analyzed, and their prior PDDs are acquired according to the characteristic values of the X-POL in the ML. There are 634 volume scan data that include the BBML in eight days, observed by the VCP21 model, which scans one volume every three minutes. The ML region is manually selected from the 9.9° PPI, and the data influenced by lightning rods are excluded. A total of 6?705?261 sets of data are identified as ML points, and 85?368?196 sets of data are identified as NML points in the PPI. Based on these data, the IPDDs of the ZH, ZDR and CC are shown in Fig. 4, where BB represents the ML and NB represents the NML. Figure 4 shows that the IPDDs of the ZH, ZDR and CC for BB are greater than zero for approximately ZH ∈ (5, 46) dBZ, ZDR ∈ (?0.30, 3.5) dB, and CC ∈ (0.75, 0.96). It can be seen from the diagram that the PDDs of ZH and CC in the ML and NML are quite different, which is very beneficial for distinguishing the BB from the NB.
Date
Time (UTC)
Number of volume scan data
22 May 2017
0112–0730
121
25 July 2017
2130–2357
50
26 July 2017
0000–0400
81
12 August 2017
0206–0548
75
29 August 2018
2221–2357
32
30 August 2018
0000–0348
77
11 September 2018
0951–1233
54
15 October 2018
0518–1227
144
Table3. Melting layer data observed by Shunyi X-POL.
Figure4. The IPDDs of the ZH, ZDR and CC in the ML and NML.
The peak value of p(CC|BB) is located at CC = 0.93, which is obviously smaller than that of p(CC|NB) (approximately 0.98). The PDDs of the ZH and ZDR in the ML and NML partially overlap, but the ZH and ZDR values of the BBML are larger than those of the NML. Therefore, the PDD, combined with the ZH, ZDR and CC, can provide more information to distinguish the BB from the NB. Figure 5 shows the JPDDs of the ZH, ZDR and CC in the ML and NML, in which the differences in the JPDDs between the ML and NML are obvious and benefit distinguishing the BB from the NB. Figure5. The JPDD three-dimensional surface data map of (a1) ZH–ZDR, (a2) ZH–CC and (a3) ZDR–CC for BB. (b1–b3) As in (a1–a3) but for NB.
2 4.3. Singular point elimination -->
4.3. Singular point elimination
Because of the influence of ground clutter, some singularity points that are obviously non-melting points are often identified in the near surface by the above method, and these singularities need to be eliminated. The consistency check of the BBML identified by the Bayesian method is carried out to remove the singularity points that deviate from the center of the bright band thickness. The method of singularity elimination using the probability distribution is described as follows: The point value of (ZH, ZDR, CC) is substituted into Eq. (7) or Eq. (8), and the probabilities of BB and NB are obtained to determine whether the point is in the ML or NML by contrast with the PDDs in Figs. 4 and 5. The upward float is 20% towards the height of the temporary bottom and the downward float is 20% towards the height of the temporary top according to all of the BBML points identified by step (1) in a certain PPI of the polarization radar, and the temporary thickness of each azimuth is obtained from the temporary bottom and top heights. The median value, h, is calculated by sorting the results of the temporary thickness at each azimuth. Let σ = 2h; then, reidentify the BBML points in step (1) in the area determined by where x is the height corresponding to each gate and f is the probability of a normal distribution.
6. Hydrometeor classification improvements The extents of the polarization parameter values of ZH, ZDR and CC overlap for dry snow and light rain. Figure 11 shows the PDD characteristics of light rain and dry snow in the 9.9° PPI at 0500 UTC 11 July 2018. Most of their PDDs overlap; thus, it is very difficult to use the fuzzy logic algorithm to distinguish dry snow and light rain. Therefore, it is very important to recognize the BBML because dry snow cannot appear under the BBML (Rbb in Fig. 12), and light rain should not appear above the BBML (Rtt in Fig. 12). Figure 12 shows the intersection between beam broadening and the BBML. The heavy line represents the center of the radar beam at a 9.9° elevation angle, and the dashed line represents the ±0.5° beam width (3 dB beam width). Rbb, Rb, Rt and Rtt represent the slant ranges corresponding to the intersection points between the radar beam and the BBML; and Hb and Ht represent the heights of the bottom and top of the BBML, respectively. Figure11. The IPDDs of (a) ZH, (b) ZDR and (c) CC for light rain and dry snow.
Figure12. Sketch of the intersection between beam broadening and the BBML. The heavy line represents the center of the radar beam at a 9.9° elevation angle, and the dashed line represents the ±0.5° beam width (3 dB beam width). Rbb, Rb, Rt and Rtt represent the slant range corresponding to the intersection points between the radar beam and the BBML; Hb and Ht represent the heights of the bottom and top of the BBML, respectively.
The hydrometeor particles are classified according to Table 4. Based on the distribution constraint relations of hydrometeor particles (Park et al., 2009), for a weather process in the BBML, the relationship between hydrometeor particles and the ML is as follows (R represents the slant range):
Class number
1
2
3
4
Type
AP/GC
BS
DS
WS
Classification
Abnormal propagation or ground clutter
Biological scatter
Dry snow
Wet snow
Class number
5
6
7
8
Type
CR
GP
BD
LR
Classification
Ice crystals
Graupel
Big drops
Light rain
Class number
9
10
11
12
Type
MR
HR
RH
BH
Classification
Moderate rain
Heavy rain
Rain and hail
Big hail
Class number
13
14
?
?
Type
SH
CAE
?
?
Classification
Small hail
Clear air echo
?
?
Table4. Hydrometeor particle-type classification.
0 < R < Rbb: the particles should not belong to dry snow, wet snow, ice crystals, or graupel; Rbb < R < Rb: the particles should not belong to dry snow, ice crystals, light to medium rain, or heavy rain; Rb < R < Rt: the particles should not belong to ice crystals, light to medium rain, or heavy rain; Rt < R < Rtt: the particles should not belong to light to medium rain or heavy rain; R > Rtt: the particles should not belong to ground clutter or abnormal propagation (e.g., hyper-refraction), biological scatter, wet snow, big drops, light to medium rain, or heavy rain. Without the ML detection, when the slant range is R < Rbb, it is very difficult to distinguish light rain from dry snow by the fuzzy logic algorithm (Fig. 13a). Figure 13a shows the classification identification results, revealing obvious mistakes insofar as the dry snow appears below the BBML. After the BBML is identified by the Bayesian method, according to the constraint relation of the precipitation particle distribution above the BBML, there is light to moderate rain (mainly light rain) in the slant range of R < Rbb (Fig. 13b). In the BBML area, wet snow is identified as the main precipitation type, and the type distribution is reasonable, which improves the results of precipitation particle classification by the fuzzy logic method effectively. Figure13. Hydrometeor classification before (a) and after (b) BBML identification.
In order to further verify the influence of ML recognition on hydrometeors, the results of hydrometeor classification in Fig. 10 are shown in Fig. 14, which also show that the identification of BBML can improve the hydrometeor classification results of light rain and dry snow. Figure14. Hydrometeor classification results in 9.9° PPI at 0130 UTC 11 July 2018 in Fangshan, Beijing, before (a) and after (b) BBML identification.