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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.
Figure 1. 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 Table 1. 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.
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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. -
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.
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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 Table 2. The ZDR biases estimated by the light rain method in three precipitation processes.
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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: -
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 Table 3. Melting layer data observed by Shunyi X-POL.
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.
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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.
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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.
Figure 12. 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 − − Table 4. 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.
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.
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 |