A Bayesian Hydrometeor Classiﬁcation Algorithm for C-Band Polarimetric Radar

: A hydrometeor classiﬁcation algorithm is developed by applying Bayes’ theorem to C-band polarimetric weather radar measurements. The Bayesian hydrometeor classiﬁcation algorithm (BHCA) includes eight hydrometeor types: hail, rain, graupel, dry snow, wet snow, crystal, biological scatterers (BS) and ground clutter (GC). The conditional likelihood probability distribution functions (PDFs) for each hydrometeor type are constructed with training data from radar observations. The prior PDFs include not only temperature information but also background information about occurrence frequency of hydrometeor types at each altitude, which is incorporated by a hydrometeor classiﬁcation algorithm for the ﬁrst time. The BHCA is evaluated by comparing with the Marzano-Bayesian hydrometeor classiﬁcation algorithm (MBHC) and NCAR fuzzy logic classiﬁer (NFLC). Results show that wet snow is largely missed in MBHC, while crystals are not adequately identiﬁed by NFLC. This may be due to the inappropriate conditional likelihood PDFs or membership functions. The prior PDFs in the MBHC may cause unexpected hail due to unreasonable variation above 0 ◦ C. In addition, the prior PDFs of graupel and dry snow in the MBHC appear below − 52 ◦ C, which is not realistic. The BHCA proposed in this study overcomes these shortcomings in the prior PDFs and produces an overall reasonable classiﬁcation product over the Yangtze-Huaihe River Basin (YHRB), Eastern China.


Introduction
Dual-polarization weather radar can offer various variables including horizontal reflectivity (Z H ), differential reflectivity (Z DR ), the cross-correlation coefficient (ρ hv ), and specific differential phase (K DP ), providing indicative information about hydrometeor size, shape, orientation, concentration and phase [1]. Based on this information, hydrometeor classification (HC) can be achieved [2,3], which leads to various important applications. For example, it can be used to resolve cloud microphysical processes [4,5], perform severe weather surveillance and nowcast involving different precipitation phases [6,7], and remove nonweather echoes (e.g., biological scatterers and ground clutter) for data quality control [8]. Furthermore, according to the identified hydrometeor types, appropriate rain rate relations can be derived to improve quantitative precipitation estimation [9]. completed within seven minutes followed by a vertically-pointing Z DR calibration scan. Range-height indicator (RHI) scans are performed manually if there is intense convection. The azimuthal and radial resolutions are 1.2 • and 75 m, respectively. The maximum range is 144 km. For RHI scans, the maximum elevation is 30 • . More details about the system characteristics of NJU C-POL are listed in [28]. A sphere calibration experiment was conducted to ensure low system biases of Z H and Z DR . The dataset for validation is processed by the MBHC and NCAR fuzzy logic classifier (NFLC) which use K DP as input. The K DP is estimated from differential propagation phase shift by piecewise linear regression using a least square fit following Wang and Chandrasekar [30]. Attenuation is corrected with the linear relation with KDP [31].

The Bayesian Hydrometeor Classification Method
In the BHCA, five radar variables-Z H , Z H -Z DR , ρ hv , SD(Z H ), and SD(Φ DP )-are chosen as inputs. Z H and Z DR are used as joint probability since they are not independent in rain. SD(Z H ) and SD(Φ DP ) are calculated along the radial direction over five gates centered on the current gate. Eight hydrometeor classes are defined in the BHCA, namely, hail (HA), rain (RN), graupel (GR), dry snow (DS), wet snow (WS), crystals (CR), biological scatterers (BS) and ground clutter (GC). The training dataset for the CLPDFs and prior PDFs are based on the data collected during 13:04-15:06 LST (LST = UTC + 8) on June 1, 09:05-11:08 LST on July 15, 06:05-06:59 and 15:24-16:27 LST on 24 July, 2014, including both RHI and PPI data.

Bayesian Classification Concept
Bayes' theorem was applied in the Bayesian classifier, with the assumption that five variables were mutually independent for eight classes. The formula was given as follows: where C i represents a hydrometeor class; V 1 , . . . , V 5 denote variables Z H , Z H -Z DR , ρ hv , SD(Z H ) and SD(Φ DP ), respectively; P(C i ) is the prior PDF; and P(V m |C i ) is the CLPDF. Each V m is assumed to be conditionally independent on any other V n (n m). P(V 1 , V 2 , V 3 , V 4 , V 5 ) is assumed to be a constant. Thus, Equation (1) is transformed into where SF represents scaling factor for normalizing the CLPDFs. According to the above equation, the conditional probability P(C i |V 1 , . . . , V 5 ) of each hydrometeor class at each range volume can be calculated. Essentially, the class with the largest conditional posterior probability P(C i |V 1 , . . . , V 5 ) will be assigned to the range volume by the classifier.

The Conditional Likelihood PDFs of Radar Variables
The conditional PDFs and the prior PDFs are crucial components in the Bayesian classifier. One of the advantages of the simple Bayesian classifier is that a relatively small amount of training data is required for the construction of the PDFs. The training and evaluation datasets are strictly separated from each other. Homogeneous areas and "true" hydrometeor types are chosen to construct PDFs by human experts through subjectively checking every polarimetric radar variables. Then, all the PDFs for each variable need to be modeled before applying them to the BHCA. The PDFs show different shapes, and the best fitting function is chosen for negative skewness (Equation (3)), positive skewness (Equation (4)), and Gaussian shape (Equation (5)): where V stands for input variables; a, b, c and d are the fitting parameters of PDFs given in Table 1, and the modeling functions are showed in Figure 1; and V and σ 2 denote the mean and variance listed in Table 2. A nonlinear least squares curve fitting method is used to derive these parameters. Finally, the bivariate Gaussian function is used to fit joint PDFs of Z H -Z DR : where V 1 and V 2 represent Z H and Z DR , respectively; V i and σ i stand for the mean and variance presented in Table 3. The PDF fitting parameter ρ is the correlation coefficient between Z H and Z DR . Note that Z DR has large fluctuations for GC. Therefore, this study uses the PDF of Z H instead of the joint probability of Z H -Z DR for GC. The identification for GC is not affected by this change because it mainly depends on SD(Z H ) ( Figure 1g) and SD(Φ DP ) (Figure 1i). Figure 1g and j show the big difference between GC and the other types. These two variables were also used by fuzzy logic methods for identification of GC [8,11,[32][33][34]. The y-scale (Z DR ) in Figure 1d has a break and repeats to prevent overlap.
where and represent ZH and ZDR, respectively; ⟨ ⟩ and stand for the mean and variance presented in Table 3. The PDF fitting parameter is the correlation coefficient between ZH and ZDR. Note that ZDR has large fluctuations for GC. Therefore, this study uses the PDF of ZH instead of the joint probability of ZH-ZDR for GC. The identification for GC is not affected by this change because it mainly depends on SD(ZH) (Figure 1g) and SD(ΦDP) (Figure 1i). Figure 1g and j show the big difference between GC and the other types. These two variables were also used by fuzzy logic methods for identification of GC [8,11,[32][33][34]. The y-scale (ZDR) in Figure 1d has a break and repeats to prevent overlap.    Table 3. Mean value V 1 ( V 2 ) and standard deviation σ 1 (σ 2 ) for variable Z H (Z DR ) and correlation coefficient ρ in Equation (6).

The Prior PDFs of Hydrometeor Types
The prior PDFs are usually constructed as a function of temperature [24] because the hydrometeors only exist within certain temperature ranges. In addition to the temperature, occurrence frequency of hydrometeor types at each altitude is also included in the prior PDFs. Considering the weather and non-weather echoes, the prior PDFs of hydrometeor types are designed to be functions of altitude as a compromise for simplification, where the altitude is computed based on the elevation and range gate detected by radar. The prior PDFs of GC and BS are functions of altitude relative to mean sea level, while the others are relative to freezing level.
In this study, for the independence between the training and testing datasets, the C-band hydrometeor identification algorithm (RCHIA) developed by [12] is used to determine the training data along with the subjective selection in order to confirm the HC's reliability. The RCHIA is well tuned and shows a reasonable classification in Eastern China [5]. The fitted PDFs are presented in Table 4 and Figure 2, with the fitting functions based on Equations (3)-(5), and a combination of them for bimodal PDFs.
The BS, GC, WS and DS (Table 4a) show a single peak. CR (RN) almost monotonically increases (decreases) with altitude (Table 4b). The prior PDFs of GR and HA are bimodal (Table 4b). The primary peaks are due to the high altitude, where the stratiform precipitation cannot reach. Therefore, only strong convection could be detected with fewer total points at the high levels than at the low levels.
The secondary peak is due to the most suitable region where GR (HA) develops, causing the largest absolute quantity in the vertical dimension.   Below the freezing level (blue circle in Figure 3), BB can be obviously seen from Figure 2a-d as indicated by increased ZH and ZDR and decreased ρhv in the stratiform precipitation near the freezing level. Most of these signatures are identified by the BHCA and the NFLC, while the MBHC only detects several pixels of WS and much GR and RN in the BB. The evaluation of [24] showed that the classification accuracy (hits) of WS is also low (55%), indicating the CLPDF of WS in the MBHC may not be robust. The pool performance of WS identification may be related to large uncertainty in

Validation Concept
Validation is difficult for all HC methods because in-situ measurements of hydrometeors are difficult to obtain. Therefore, alternative approaches are typically adopted for validation [12,15,21,24,[35][36][37][38]. For example, observations on the ground were used to verify HCs in winter [35][36][37]. Automated Surface Observation System and voluntary observations of precipitation types provided by the public can be used as "truth". If HA falls on the ground in summer, results of HC at low levels can be verified as well. However, for most cases in the YHRB, there is only RN on the ground, with other solid hydrometeor types at higher altitudes. Liu and Chandrasekar [13] and [17] compared results of a HC against in-situ observations collected by High-Volume Particle Spectrometer image probe installed under a T-28 aircraft. This approach is very expensive, and only data on the aircraft trajectory can be verified, but it is the most objective way for validation. A testing dataset was constructed based on simulation [24] or subjective identification [21] for quantitative evaluation of a HC method. According to the uniqueness of certain HC types, other methods can be developed for validation as well. One example was from Snyder and Ryzhkov [15], who developed a fuzzy logic method for detecting tornadic debris signature (TDS) and compared it with tornado tracks for qualitative validation. Comparisons between different HC methods [20] were also performed to evaluate a new HC approach. It is probably not a real evaluation, because HC products from other HC method are not the "truth", but this is an effective way to see how well the new HC method performs compared to other well-established approaches. Subjective validation was conducted as well, where the microphysics derived from a HC algorithm were compared with human knowledge or conceptual models [3,8,11,12].
Due to the lack of in-situ microphysical measurements in this study, comparisons between the BHCA and MBHC [24] as well as conceptual models seem to be a realistic way for evaluation. There are 10 hydrometeor types in the MBHC but only eight types in the BHCA. It is necessary to combine several hydrometeor types in the MBHC for comparison. In particular, large drops, light rain, medium rain and heavy rain are combined to RN; hail and rain/hail mixture are merged to HA. The other types in MBHC are the same with those in the BHCA. However, it should be noted that the combined types are not exactly the same as the types in the BHCA. In addition, the NFLC is a well-established fuzzy logic method which has been widely used. Comparison with the NFLC [16] (C-band version available at https://ral.ucar.edu/projects/titan/docs/radial_formats/pid_thresholds.cband.shv.txt) is also conducted to evaluate the performance of BHCA. Note that the NFLC is developed with the dataset under a North American climate; it may not perform well over YHRB. In addition, it should be mentioned that any method in this study is not considered as the reference or benchmark. The results from HC methods are mainly discussed with relevant polarimetric radar signatures and microphysical processes. Otherwise, comparison with the NFLC could evaluate the identification of GC and BS which are not included in MBHC. Similarly, drizzle, light rain, moderate rain and heavy rain are combined into RN; hail and rain hail mixture are merged into HA; GR/small HA and GR/RN are combined into GR; ice crystals and irregular ice crystals are combined into CR; supercooled liquid droplets and second trip are combined into other types which are not included in the BHCA.

Squall Line
On 30 July, 2014, a few isolated thunderstorms initiated north of Hefei, Anhui Province in the afternoon. A few hours later, these isolated cells merged, and more convection occurred, eventually became a squall line with trailing stratiform region in the evening. Below the freezing level (blue circle in Figure 3), BB can be obviously seen from Figure 3a-d as indicated by increased Z H and Z DR and decreased ρ hv in the stratiform precipitation near the freezing level. Most of these signatures are identified by the BHCA and the NFLC, while the MBHC only detects several pixels of WS and much GR and RN in the BB. The evaluation of [24] showed that the classification accuracy (hits) of WS is also low (55%), indicating the CLPDF of WS in the MBHC may not be robust. The pool performance of WS identification may be related to large uncertainty in modelling the melting hydrometeor [39]. The NFLC also identifies several areas of GR (black rectangles in Figure 3g), which seem not realistic. Above the freezing level, the BHCA, MBHC and NFLC identify similar areas of DS, which agrees well with the polarimetric radar signatures with moderate Z H (20-30 dBZ), small Z DR (< 1 dB), and high ρ hv (> 0.97). The DS and RN identified by the MBHC (Figure 3f) are strictly separated by the freezing level, indicating that these two hydrometeor types strongly depend on temperature. The DS and RN identified by the BHCA (Figure 3e) seem more realistic near the freezing level than those identified by the MBHC (Figure 3f).
The polarimetric radar signatures within convection show high Z H (40-50 dBZ), low Z DR (< 1 dB), and high ρ hv (> 0.94), indicating GR or small HA. These signatures are reasonably identified as GR by the BHCA, MBHC and NFLC. In the convection core, there are some pixels that show higher Z H (~55 dBZ), low Z DR (< 1dB), high K DP (> 4 • ) (not shown) and low ρ hv (< 0.9), which are all indicators of HA. The classification results from the three methods are roughly consistent (Figure 3e-g) in this area. Figure 4 shows the RHI scan for the squall line along the black dash line in Figure 3. The output classifications identified by the three methods show some differences. Within the strong convection at range~90 km, polarimetric radar variables show increased Z DR (> 0.75 dB) and large Z H (> 45 dBZ) extended above 6 km, indicating supercooled liquid water is lifted by strong updrafts [40], resulting in riming of GR and the growth of small HA. Therefore, a large area of GR is expected, but discontinuous GR, and HA mixed with DS in the area are identified by the MBHC. The DS type in the MBHC is only related to the Z H and temperature. Furthermore, the CLPDF may not include appropriate measurement biases and random fluctuations, which may introduce a noisy output. On the contrary, the BHCA and NFLC provide much more reasonable output classifications of GR in this area. In addition, a small area of WS is identified by the NFLC within the weak convection. The microphysical process of the weak convection by polarimetric radar signature is riming rather than melting, and similar to the strong one at~90 km range, indicating that the WS within the weak convection identified by the NFLC may not be reasonable.
Below the freezing level, more HA is identified by the MBHC relative to the BHCA. It is hard to tell which is closer to the truth without in-situ measurements. However, we want to note that HA is a rare weather phenomenon over the YHRB. As a result, the CLPDF and prior PDF for HA may not be sufficient. Improvements should be made by incorporating more HA observations in the future. Another obviously different output classification is the WS. As the DS particles fall below the melting layer, they begin to melt at different rates, resulting in water coated on their exterior or sucked inward to the vertices, causing increases in Z H , Z DR and a decrease in ρ hv . The polarimetric radar signatures show a clear BB within the stratiform region, most of which are identified by the BHCA and NFLC. The MBHC detects much GR and several pixels of WS in this area. Although rimed aggregates left over from collapsing deep convection or produced by Kelvin-Helmholtz instability, which are difficult to distinguish using polarimetric radar, could exist within stratiform regions [41], the main BB signature is missed by the MBHC. Within the BB at range <20 km, the radar signatures present strong Z H (> 50 dBZ) and low ρ hv (< 0.85), which are nearly beyond the membership function in the fuzzy logic method or CLPDF in the Bayesian approach. This is likely due to snow melting and strong rimming of aggregates. Both the BHCA and NFLC identify GR in most of this area.    Above the freezing level, the dominant polarimetric radar signatures present moderate Z H (20-30 dBZ), small Z DR (< 1 dB), and high ρ hv (> 0.98), which indicate DS. In this area, the BHCA identifies predominant DS and a small area of CR on the edge of the convection and a few pixels of CR within the stratiform region. The MBHC detects dominant DS and large area of CR on the edge of the convective and stratiform region. The NFLC also identifies a large area of CR within the stratiform region, but nearly no CR identified within the convection. This is because the same membership function for temperature is used for DS and CR in the NFLC, resulting in some vagueness in the boundary between them. While the prior PDFs of CR in the BHCA and MBHC show obvious differences from that of DS, it is difficult to quantify which is closer to the truth without in-situ measurements. Nevertheless, this difference reflects the different prior PDF and CLPDF or membership functions used in the three methods.

Isolated Deep Convection
At 20:19 local solar time on 11 July, 2014, isolated strong convection occurred at 128.6 • azimuth angle to the radar site. Available RHI scan ( Figure 5) data are used to evaluate the BHCA. Because GR is excluded by the prior PDF in the MBHC below −52 • C, the prior PDF for GR is not suitable for this case. In addition, almost no CR is identified by the NFLC in Figure 5 (red rectangle), which seems unrealistic.
There is a noticeable phenomenon that much more HA is identified by the MBHC (Figure 5f) at altitude near 3 km than the altitude between 4 and 5 km. The sounding data shows that temperature near 3 km is higher than 10 • C, which is not a suitable environment for riming or deposition for HA growing, but is in favor of melting for HA. The large area of HA may be contributed by the larger prior PDF between 3 and 10 • C than that between 0 and 3 • C. On the edge of the strong convection, there are echoes with strong Z H (> 50 dBZ), large Z DR (> 3dB), low ρ hv (< 0.94). These signatures suggest HA/RN mixture, most of which are not identified by the BHCA below 2 km AGL. The MBHC and NFLC identify a small part of the HA/RN mixture. As mentioned previously, the training dataset for HA may not be sufficient. More HA observations are required for adding HA/RN mixture type in the BHCA framework. The RN regions identified by the three methods generally agree well with each other.

Biological Scatterers and Ground Clutter on 24 July 2014
At 08:03 (LST) on 24 July, 2014, a large area of BS and some GC were detected by NJU C-POL before the arrival of a typhoon outer rainband. A large area of high Z DR (>4 dB) can be seen from Figure 6b with the color bar adjusted for large variation. The corresponding Z H is between 5 and 30 dBZ; ρ hv is less than 0.9 with some pixels even below 0.6; and SD (Φ DP ) is very high. These signatures suggest BS within this area. The BHCA identifies a large area of BS as expected and agrees well with that identified by the NFLC. There is a thin line extending from northwest to southwest, and further to south in Z H , Z DR , ρ hv and Φ DP (Figure 5a-d). These signatures are found to be caused by iron towers which are identified by both methods. There are a few pixels with high Z H (Figure 6a), fluctuant Z DR (Figure 6b), low ρ hv (Figure 6c), high SD(Z H ) and SD(Φ DP ) (Figure 6d) near the radar site, suggesting these echoes are GC as well. These GC identified by the two methods are consistent with each other. The NFLC identifies some scattered GC in northwest and southeast of the radar site, which is identified as BS by the BHCA (red rectangle in Figure 6). These pixels show small SD(Z H ), which is more likely to be weather echoes or BS rather than GC [11], but the SD(Z H ) is not used by the NFLC. In addition, Z DR shows high fluctuation in this area, which may largely contribute to the identification of GC by the NFLC. At 08:03 (LST) on 24 July, 2014, a large area of BS and some GC were detected by NJU C-POL before the arrival of a typhoon outer rainband. A large area of high ZDR (>4 dB) can be seen from Figure 6b with the color bar adjusted for large variation. The corresponding ZH is between 5 and 30 dBZ; ρhv is less than 0.9 with some pixels even below 0.6; and SD (ΦDP) is very high. These signatures suggest BS within this area. The BHCA identifies a large area of BS as expected and agrees well with that identified by the NFLC. There is a thin line extending from northwest to southwest, and further to south in ZH, ZDR, ρhv and ΦDP (Figure 5a-d). These signatures are found to be caused by iron towers which are identified by both methods. There are a few pixels with high ZH (Figure 6a), fluctuant ZDR (Figure 6b), low ρhv (Figure 6c), high SD(ZH) and SD(ΦDP) (Figure 6d) near the radar site, suggesting these echoes are GC as well. These GC identified by the two methods are consistent with each other. The NFLC identifies some scattered GC in northwest and southeast of the radar site, which is identified as BS by the BHCA (red rectangle in Figure 6). These pixels show small SD(ZH), which is more likely to be weather echoes or BS rather than GC [11], but the SD(ZH) is not used by the NFLC. In addition, ZDR shows high fluctuation in this area, which may largely contribute to the identification of GC by the NFLC.   Table 5 shows the quantitative difference of each hydrometeor type identified by the BHCA, MBHC (Table 5a) and NFLC (Table 5b) during 20:04-22:57 LST on July 30 and 08:03-09:04 LST on  24 July, 2014, including both RHI and PPI data. A very small proportion of undefined type in the BHCA (P(C i |V 1 , . . . , V 5 ) in Equation (2) < 1.0 × 10 −30 ) is identified, which does not affect the comparison among the three classifiers, and thus not listed in Table 5. The values in Table 5a,b) represent the points (normalized by the total number of points along each row) classified as the hydrometeor types in the columns by the MBHC (NFLC) and the rows by the BHCA. Table 5a shows that there is good agreement between the MBHC and BHCA for RN (92%) and DS (92%). There is a good consistency (percentage > 60%) between the NFLC and BHCA for RN (96%), GR (73%), WS (69%), DS (94%) and BS (93%), which is more consistent than that in Table 5a. The largest difference (13%) is found for the CR type in Table 5a, where 83% CR identified by the MBHC are classified as DS by the BHCA. This is because DS particles are not allowed to appear below −52 • C due to the restriction of the prior PDF in MBHC, resulting in predominantly CR above that altitude in strong convection, and most of the CR below −52 • C is classified as DS by the BHCA. A similar issue can be seen from Figure 5e-f. The agreement between the NFLC and BHCA for CR is also low (22%). This is due to the fact that the same membership function is used for CR and DS, resulting in much fewer CR samples produced by the NFLC. A large difference (31%) is also found for the HA type in Table 5a, while 33% HA identified by the MBHC is classified as RN by the BHCA, indicating a large difference in HA classification below the freezing level. This is partly due to the absence of RN/HA mixture type in the BHCA, while those echoes are identified as HA by the MBHC and RN by the BHCA. This is also the reason for the large difference of HA (Table 5b) identified by the BHCA and NFLC. In addition, the large prior PDF at high temperature also results in more HA identified by the MBHC within 10-20 • C than 3-10 • C. A similar issue is found in GR type, which is the main reason why 20% GR (Table 5a) identified by the MBHC is classified as RN by the BHCA. The agreement in WS type is also low (34% in Table 5a) since most of BB is missed by the MBHC, resulting in very few WS dataset relative to that identified by the BHCA. Because the terrain around the radar site is flat, the GC dataset is rare. Most of the dataset of GC (Table 5b) is similar to Figure 5a-d. Therefore, echoes with low SD(Z H ) and fluctuating Z DR are also classified as GC by the NFLC, and the agreement of GC is moderate (51%) in Table 5b. Other than this, both the BHCA and NFLC do a reasonable job for GC classification.

Conclusions
A new hydrometeor classification algorithm is developed based on Bayes' theorem. The CLPDFs of radar variables and prior PDFs of each hydrometeor types are constructed with training data, which are manually selected by experts and the classification results from RCHIA [12]. The prior PDFs in this method include not only temperature information but also background information about the occurrence frequency of different hydrometeor types at each altitude.
The performance of this BHCA approach is compared with the MBHC [24] and the widely used NFLC [16] using NJU C-POL observations from the OPACC field campaign in 2014. The testing data include a squall line with trailing stratiform precipitation, isolated strong convection, and GC and BS observations from both PPI and RHI scans. The results show that the BHCA produces a more reasonable classification output than the MBHC and NFLC over the Yangtze-Huaihe River Basin, Eastern China. CR within strong isolated convection are largely missed by the NFLC, which may be related to an inappropriate membership function. WS are almost missed by the MBHC due to large uncertainty in modelling the melting hydrometeor. The prior PDFs in the MBHC have two limitations when the algorithm is applied to the strong convection over YHRB, Eastern China. One is that the prior PDFs for GR and DS below −52 • C seem not realistic in this study. The other is that the prior PDFs for HA and GR are larger within 10-20 • C than 3-10 • C, which may result in unexpected HA and GR within area of 10-20 • C even though it is a favorable temperature range for melting rather than riming and deposition. The BHCA overcomes the two shortcomings in the prior PDFs and produces an overall reasonable classification.
To avoid the circular reasoning in this paper, the radar data used for training and testing are separated out. The training and testing datasets are also processed by different methods. Nevertheless, subjective information still exists in the training dataset and validation procedure. We hope to have the chance to do an objective validation with in-situ observations in the future. In addition, future work will include more observations to build a robust CLPDF for HA and possibly additional hydrometeor types in the BHCA.