Rain Attenuation Correction of Reflectivity for X ... - Semantic Scholar

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Rain Attenuation Correction of Reflectivity for X-Band Dual-Polarization Radar Liang Feng 1,2 , Hui Xiao 1,2, *, Guang Wen 1 , Zongfei Li 3 , Yue Sun 1,2 , Qi Tang 1 and Yanan Liu 4 1

2 3 4

*

Key Laboratory of Cloud-Precipitation and Severe Storms, Center of Disaster Reduction, Institute of Atmospheric Physics, Chinese Academy of Sciences, Huayanli No.40, Qijiahuozi, Deshengmenwai Avenue, Beijing 100029, China; [email protected] (L.F.); [email protected] (G.W.); [email protected] (Y.S.); [email protected] (Q.T.) University of Chinese Academy of Sciences, Beijing 100049, China Tianjin Meteorological Information Center, Tianjin 300074, China; [email protected] Dalian Meteorological Equipment Support Center, Dalian 116001, China; [email protected] Correspondence: [email protected]; Tel.: +86-10-8299-5319

Academic Editor: Guifu Zhang Received: 19 September 2016; Accepted: 8 December 2016; Published: 17 December 2016

Abstract: In order to improve the performance of X-band dual-polarization radars, it is necessary to conduct attenuation correction before using the X-band radar data. This study analyzes a variety of attenuation correction methods for the X-band radar reflectivity, and proposes a high-resolution slide self-consistency correction (SSCC) method, which is an improvement of Kim et al.’s method based on Bringi et al.’s original method. The new method is comprehensively evaluated with the observational data of convective cloud, stratiform cloud, and the stratiform cloud with embedded convection. Comparing with the intrinsic reflectivity at X-band calculated from the reflectivity at S-band, it is found that the new method can effectively reduce the correction errors when calculating differential propagation shift increments using the conventional self-consistency attenuation correction method. This method can efficiently correct the X-band dual-polarization radar reflectivity, in particular, for the echoes with reflectivity greater than 35 dBZ. Keywords: high-resolution slide self-consistency correction method; reflectivity attenuation correction for rain; X-band dual-polarization radar

1. Introduction Comparing with the conventional Doppler weather radar, dual-polarization radars can measure more valuable polarized information precipitation systems. The polarized information allows to improve the accuracy of radar-based quantitative precipitation estimation, raindrop size distribution (DSD) retrieval and precipitation particle identification [1–10]. Previous studies on the application of dual-polarization radars are mostly designed for S, C-band radars [11–15]. Research on X-band dual-polarization radars is limited, since X-band radars experience severe attenuation compared to S, C-band radars. However, due to their low cost, small antennas, easy mobility and high temporal and spatial resolution, X-band dual-polarization radars have become an important detection equipment in the areas of cloud and precipitation physics and weather modification. In order to improve the performance of X-band dual-polarization radars, the attenuation needs to be corrected before application. Atlas and Banks [16] showed there were two main factors resulting in attenuation. One is detection range, whereby the echo power received by the radar will decrease with increasing range, and this applies to all radar wavelengths; the other is rain attenuation. With the exception of intense storms, rain attenuation for electromagnetic waves with a wavelength greater than approximately 7 cm is

Atmosphere 2016, 7, 164; doi:10.3390/atmos7120164

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Atmosphere 2016, 7, 164

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negligible. Zhang et al. [17] noted that the first attenuation factor is mainly because gas molecules absorb electromagnetic waves and the influence of scattering can be neglected. The absorption attenuation of electromagnetic waves with a wavelength greater than 2 cm is generally small, but when the wavelength is approximately 1 cm or the detection range is large, the attenuation caused by the first factor still needs to be considered. Therefore, the attenuation at X-band (about 3 cm in wavelength) is mainly due to the second factor. The conventional method of attenuation correction for single-polarization radars is mostly based on the empirical relationship between horizontal reflectivity factor ZH and rainfall intensity R(ZH = aRb ; a, b are empirical constants). This method retrieves Zret using the measured rainfall intensity R and then calculates horizontal specific attenuation coefficient AH (AH = Zret −ZH ) [18]. However, the relationship between ZH and R is not stable, depending on not only different locations, seasons and precipitation patterns, but also precipitation process and time. It is mainly because of the variability of drop size distributions (DSDs). Meanwhile, the empirical relationship is also affected by radar calibration and beam blockage. Therefore, it is not accurate to correct rain attenuation by using this method. Dual-polarization radars can avoid the shortcomings of the single-polarization radar attenuation correction method, because they can provide differential propagation phases (φDP ) and specific differential phases (KDP ). The two parameters are independent of radar calibration, rain attenuation and partial beam blockage. Therefore, dual-polarization radars can provide a stable rain attenuation correction relationship using φDP and KDP . Bringi et al. [19] found that there was almost a linear relationship (AH = αH KDP ) between the attenuation (AH ) and specific differential phase (KDP ) by scattering simulation. Zrnic and Ryzhkov [20] pointed out that KDP was unaffected by attenuation and relatively immune to the beam blockage. Based on this fact, Ryzhkov and Zrnic [21] proposed an empirical correction method, where the coefficients were determined as a mean slope between φDP and ZH or differential reflectivity (ZDR ) in a sampling area. Their method was evaluated with the S-band dual-polarization radar data and improved for the C-band dual-polarization radar data by Carey et al. [22]. He et al. [23] adopted this correction method and introduced Kalman filter for filtering the measured φDP , then obtained the relation coefficient α’H between AH and φDP , finally corrected the stratiform case, which was detected by an X-band dual-polarization radar. Although Carey et al. [22] and He et al. [23] have greatly improved the method of Ryzhkov and Zrnic [21], the method is only applied to stratiform precipitation. Hu et al. [24] compared the correction method by KDP with the convectional correction method and found that the correction by KDP was better than by ZH . However, the KDP correction method would cause errors since the KDP may contain errors when rainfall intensity is small. Thus he proposed a comprehensive ZH -KDP correction method to overcome shortcomings of the correction by ZH or by KDP . However, ZH -KDP correction method still uses a fixed coefficient to correct rain attenuation. Smyth and Illingworth [25] introduced a constraint to correct the differential reflectivity (ZDR ) for S-band dual-polarization radars. In this method, the coefficient (αH ) of the relationship between KDP and ADP is not fixed, but determined by the constraint that ZDR at the edge of a rain cell should be 0 dB (assuming that edge of the rain cell is drizzle). However, this is not applicable in some cases, particularly for the shorter wavelengths, high-resolution X-band dual-polarization radar observations. Due to rain attenuation, the rain edge of the radar display is not necessarily the actual edge of the rain cell. The rain edge may be drizzle, moderate or even heavy rain. Thus, it is inappropriate to set ZDR as 0 dB at the farther edge of a rain zone. It is necessary to create a new ZDR constraint according to the actual situation. Testud et al. [26] proposed an attenuation correction method, called ZPHI method. The core idea assumes that the differential propagation phase calculated by AH should be equal to the increments of the measured radial differential propagation phase. This method achieves a better performance, but still needs to set the coefficient αH of the relationship between AH and KDP . Bringi et al. [3] proposed an algorithm referred to as “the self-consistent method with constraints”, which can resolve the limitations of Smyth and Illingworth [25] and Testud et al. [26]. The algorithm improved the method of Testud et al. [26] for ZH correction and the method of Smyth and


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Illingworth [25] for ZDR correction. One of the advantages of the algorithm is that the coefficient αH of the relationship between AH and KDP is estimated from the radar data rather than scattering simulation. Park et al. [27,28] extended the algorithm to the X-band dual polarization radar, and calculated the range of αH by scattering simulation using drop size distributions. Kim et al. [29] corrected ZDR by the horizontal reflectivity ZH and the vertical reflectivity ZV using the method of Bringi et al. [3]. The method turned the range resolution into 1.5 km. Later, Kim et al. [4] improved the resolution to 0.5 km further. For stratiform cloud and the stratiform cloud with embedded convection, a resolution of 0.5 km may be appropriate, because the KDP is not large in the two kinds of cloud for X-band dual polarization radars. However, it is large for convective cloud, for example, the KDP can reach 10◦ /km or more in convective cores. Such a resolution may result in errors when correcting convective cloud. In addition, φDP would be used to correct ZH and ZV in the method of Bringi et al. [3]. This method needs to seek an initial phase and a terminal phase for every radial in the corrected process. This may result in phase errors due to radar system noise and finally result in correction errors. In this paper, we propose a high-resolution slide self-consistency correction method to improve the method of Bringi et al. [3]. The new algorithm applies a slide window to avoid seeking the initial and terminal phases. The accuracy of the correction results is evaluated with convective cloud, stratiform cloud and the stratiform cloud with embedded convection by comparing with the intrinsic reflectivity at X-band, which is calculated from the reflectivity at S-band. 2. Radar Feature The IAP-714XDP-A mobile dual-polarization weather radar has been operated since 2006 by the Key Laboratory of Cloud-Precipitation Physics and Severe storms (LACS), Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (CAS). The signal processor of the radar is RVP8. The scanning strategy includes plane position indicator (PPI), radar height indicator (RHI) and volume coverage pattern (VCP). The main specifications of the IAP-714XDP-A mobile radar system are listed in Table 1. Table 1. System Characteristics of the IAP-714XDP-A radar. Item

IAP-714XDP-A Radar

Frequency Antenna type Antenna gain Beam width Pulse width Pulse repetition frequency Polarization Observation range Observation parameters Doppler processing

9.370 GHz 2.4 m diameter parabolic antenna 44.78 dB 1◦ 0.5/1/2 µs 500~2000 Hz Horizontal/Vertical 75/150/300 km ZH , ZDR , φDP , KDP , ρHV , V, W PPP/FFT

3. The Slide Self-Consistency Correction Method The Slide Self-Consistency Correction (SSCC) method is mainly based on the self-consistent method with constraints proposed by Bringi et al. [3]. The radar reflectivity factor Zh (mm6 m−3 ) in linear scale and ZH (dBZ) in logarithm scale have the following relationship: ZH = 10lgZh

(1)

The corrected reflectivity ZH A (dBZ) at a range r is related to the attenuated (measured) reflectivity ZH as follows: Z r

Z H A (r ) = Z H (r ) + 2

0

A H (s)ds

(2)


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where AH is specific attenuation in decibels per kilometer. The change in differential propagation phase is as follows: ∆φDP = φDP (r1 ) − φDP (r0 ) (3) where r0 and r1 are the beginning and ending range gate, respectively. In Bringi et al. [3], specific attenuation AH is determined with a constraint that the cumulative attenuation from range r0 to r1 should be consistent with the total change in differential propagation phase ∆φDP . Under the assumption that there is a linear relationship between AH and KDP , the final formula of AH is given by h i [ Zh (r )]b × 100.1(bα)∆φDP − 1 A H (r ) = I (r0 , r1 ) + 100.1(bα)∆φDP − 1 × I (r, r1 ) where, I (r0 , r1 ) = 0.46b I (r, r1 ) = 0.46b

Z r 1 r0

Z r 1 r

(4)

[ Zh (s)]b ds

(5)

[ Zh (s)]b ds

(6)

In the above equations, α and b are the empirical parameters of the following Equations (8) and (7) that can be obtained by scattering simulation by raindrop size distribution. Bringi et al. [3,19] found an exponent relationship between AH and Zh and a linear relationship between specific attenuation AH and specific differential phase KDP at frequencies from 2.8 to 9.3 GHz; that is, the exponent c in Equation (8) is close to 1. A H = aZhb (7) c A H = αK DP

(8)

where KDP is in ◦ ·km−1 and c is set as a constant 1. Therefore, if AH (r) is calculated by Equation (4) and substituted into Equation (2), the corrected reflectivity ZHA (r) at a range r is obtained. However, α and b need to be set to a fixed value before calculating AH (r). Carey et al. [22] noted that the coefficient α can vary widely with temperature and drop shape. Park et al. [27] found that it changes from 0.139 to 0.335 dB(◦ )−1 at X-band. Comparing with α, the exponent b is less influenced. Delriu et al. [30] found that b varies from 0.76 to 0.84 at X-band. Thus, in this paper, b is set as a constant 0.8. When calculating AH (r) using a fixed α value, the correction errors are introduced in the process of attenuation correction. To eliminate the impact of the α variability, Bringi et al. [3] proposed a self-consistent method with constraints. This method does not set α as a fixed constant, but seek an optimal α within a predetermined scope (αmin , αmax ), which is obtained from scattering simulation under various temperatures and raindrop size distributions. For each α, A H (r; α) at each range is calculated by Equation (4), and then φcal DP (r; α) is calculated as follows: Z r 1 A ( s; α) H φcal ( r; α ) = 2 ds (9) DP α r0 The optimal α is the value that leads Equation (10) to the minimum. φerror DP (α) =

N

∑ φcal DP (ri ; α) − φ DP (ri )

(10)

i =1

where i denotes the range gate from r0 to r1 . The main advantage of the self-consistent method with constraints is estimating an optimal α rather than setting a fixed value. According to the scattering simulation results at X-band by Park et al. [27], α is set between 0.1 and 0.5, in a step of 0.03. Kim et al. [4] sets the distance between r0 and r1 as 1.0 km with an overlap of

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According to to the the scattering scattering simulation simulation results results at at X-band X-band by by Park Park et et al. al. [27], [27], α α is is set set between between 0.1 0.1 According and 0.5, in a step of 0.03. Kim et al. [4] sets the distance between r 0 and r1 as 1.0 km with an overlap and 0.5,(ultimately, in a step ofα0.03. et al. [4] the distance and 1 as 1.0 km with an overlap 0.5 km has aKim resolution of sets 0.5 km), referringbetween to Figurer01a. Inrthe paper, the SSCC method of 0.5 0.5 km km (ultimately, (ultimately, α α has has aa resolution resolution of of 0.5 0.5 km), km), referring referring to to Figure Figure 1a. 1a. In In the the paper, paper, the SSCC SSCC of employs a slide window processing shown in Figure 1b by setting the distance between r0the and r1 as method employs a slide window processing shown in Figure 1b by setting the distance between method employs slide processing shown Figure 1b by setting the distance between rr00 1.5 km (10 gates), athus α window has a high-resolution of 0.15inkm, improving the resolution of α estimation. and r 1 as 1.5 km (10 gates), thus α has a high-resolution of 0.15 km, improving the resolution of α and as 1.5 km (10 α haseta al. high-resolution resolution of α Afterr1developing the gates), methodthus of Bringi [3], Equationsof (3)0.15 andkm, (10)improving become as the follows: estimation. After developing the method of Bringi et al. [3], Equations (3) and (10) become as follows: follows: estimation. After developing the method of Bringi et al. [3], Equations (3) and (10) become as ∆φDP_10gates ((G Gi+10) )− − Δφ DP _ 10 gates===φφφDP φ φ(DP G () Gi ) Δφ DP (G i + 10 ) − φ DP (G i ) DP _ 10 gates DP i + 10 DP i

(11) (11) (11)

999 error cal α= (rrri ;;i α φerror (α(()α ;αα)) )−−− φ((DP  φφφcalcal φφerror )) ==∑ φφDP rri ))(ri ) DP _ 10 gates DP (( DP DP_10gates

(12) (12) (12)

DP _ 10 gates



i =ii==000

DP

i

DP

i

In addition, addition, the the new new method method does does not not seek seek the the initial initial and and terminal terminal phase phase of of each each radial radial as as the the In method of of Bringi Bringi et et al. al. [3] [3] does, would finally finally cause cause correction correction errors. errors. method does, which which would would finally cause correction errors.

(a) (a)

(b) (b)

Figure 1. 1. (a) (a) The The Kim Kim et et al.’s al.’s method; method; (b) (b) the the SSCC SSCC method, method, assuming assuming α αiii = = 00 (i (i === 0, 0, 4; 995,999). Figure 0, 4; 4; 995,999). 995,999). method, assuming α

4. Result Result 4.

The SSCC SSCC method method is is evaluated evaluated using using the the data data collected collected by by the the X-band X-band dual-polarization dual-polarization radar radar The (IAP-714XDP-A), which is located in Shunyi District of Beijing City (BJ) from June to September 2015. (IAP-714XDP-A), Shunyi District of Beijing CityCity (BJ) from June June to September 2015. (IAP-714XDP-A), which whichisislocated locatedinin Shunyi District of Beijing (BJ) from to September The data contain observations of convective cloud, stratiform cloud and the stratiform cloud with The observations of convective cloud,cloud, stratiform cloud cloud and the stratiform cloudcloud with 2015.data Thecontain data contain observations of convective stratiform and the stratiform embedded convection. The corrected corrected reflectivity is compared compared withwith the the intrinsic reflectivity at XXembedded convection. The reflectivity is with the intrinsic reflectivity at with embedded convection. The corrected reflectivity is compared intrinsic reflectivity at band calculated from the reflectivity at S-band, which is obtained by the CINRAD/SA S-band band calculated CINRAD/SA S-band X-band calculatedfrom fromthe thereflectivity reflectivityatatS-band, S-band, which which is is obtained obtained by the CINRAD/SA single-polarization weather weather radar radar located located in in Daxing Daxing District District of of Beijing Beijing City. City. Figure Figure 22 shows shows the the single-polarization City. locations of of the the two two radars. radars. The The X-band radar (at ShunyiSY, 116.68°◦ E, E, 40.19°◦ N) N) is located located at at the the locations locations The X-band X-band radar radar (at (at ShunyiSY, ShunyiSY, 116.68° 116.68 E, 40.19° 40.19 N) is northeast of the S-band radar (at DaxingDX, 116.47° E, 39.81° N). The straight-line distance between ◦ ◦ northeast of the S-band radar (at DaxingDX, 116.47 116.47° E, 39.81° 39.81 N). The straight-line distance between the two two radars radars is is about about 46 46 km. km. the

Figure 2. 2. The The locations of the X-band radar and the S-band radar,the X-band radar is at Shunyi (SY, The locations locations of of the the X-band X-band radar radar and and the the S-band S-band radar,the radar,the X-band X-band radar radaris is at at Shunyi Shunyi(SY, (SY, Figure ◦ ◦ ◦ ◦ 116.68° E, 40.19° N), the S-band radar is at Daxing (DX, 116.47° E, 39.81° N). The symbols BJ, HB and 116.68 E, 40.19° 40.19 N), N), the the S-band radar is at Daxing (DX, 116.47° 116.47 E, 39.81° 39.81 N). N). The The symbols BJ, HB and 116.68° TJ in in the the Figure Figure are are the the abbreviation abbreviation of of Beijing Beijing City, City,Hebei HebeiProvince Provinceand andTianjin TianjinCity, City,respectively. respectively. TJ abbreviation of Beijing City, Hebei Province and Tianjin City, respectively.

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Hubbert [31] pointed out out that that the measured differential propagation phase Ψphase C consists Hubbert and andBringi Bringi [31] pointed the measured differential propagation ΨC of true differential propagation phase φ and backward scattering differential phase shift δ. Since δ consists of true differential propagationDP phase φDP and backward scattering differential phase shift δ. could in result errors in of errors KDP estimation, δ needs toδ be eliminated before using ΨC . using In thisΨ paper, the Since result δ could of KDP estimation, needs to be eliminated before C. In this method of Hubbet and Bringi [31] is applied to filter δ out. paper, the method of Hubbet and Bringi [31] is applied to filter δ out. A event swept Beijing City City from from north north to south 19 June Figure 3 A strong strongconvective convectiveweather weather event swept Beijing to on south on 2015. 19 June 2015. ◦ shows plane the position of the(PPI) X-band radar at elevation at 14:45 Beijing TimeBeijing (BJT), Figurethe 3 shows planeindicator position (PPI) indicator of the X-band radar at3 elevation 3° at 14:45 19 June 2015. Three strong echo cores of convective cloud are situated between the two radars and the Time (BJT), 19 June 2015. Three strong echo cores of convective cloud are situated between the two largest reflectivity observed by theobserved S-band radar is S-band about 60radar dBZ.is about 60 dBZ. radars and the largest reflectivity by the

◦ ; range: Figure 3. 3. The The reflectivity reflectivity at at X-band X-band (elevation (elevation angle: angle: 33°; range: 75 14:45 BJT, BJT, 19 19 June June 2015. 2015. Figure 75 km) km) at at 14:45

The intrinsic reflectivity at X-band is not equal to the reflectivity at S-band. Chandrasekar et al. [32] The intrinsic reflectivity at X-band is not equal to the reflectivity at S-band. Chandrasekar et al. [32] proposed three different methodologies for simulating X-band radar observations from the S-band radar proposed three different methodologies for simulating X-band radar observations from the S-band data and the empirical conversion method is used in the paper. Figure 4 shows a plot of the intrinsic radar data and the empirical conversion method is used in the paper. Figure 4 shows a plot of the reflectivity at X and S bands for a monodispersed drop size distribution using the shape mode intrinsic reflectivity at X and S bands for a monodispersed drop size distribution using the shape mode proposed by Beard and Chuang [33]. The relationship between the intrinsic reflectivity at X-band and proposed by Beard and Chuang [33]. The relationship between the intrinsic reflectivity at X-band and the reflectivity at S-band is obtained by curve fitting, which is divided into three parts as shown in the reflectivity at S-band is obtained by curve fitting, which is divided into three parts as shown in Equation (13) where subscripts X and S indicate simulated radar variables at X-band and measured Equation (13) where subscripts X and S indicate simulated radar variables at X-band and measured radar measurements at S-band. Note that the reflectivity at S-band is assumed to be non-attenuated. radar measurements at S-band. Note that the reflectivity at S-band is assumed to be non-attenuated.  0.9696ZH , S − 0.0145 ZH , S ≤ 25dBZ  ZH, S ≤ 25dBZ  0.9696ZH, S − 0.0145 ZH , X = 1.1982ZH , S − 5.7726 25dBZ < ZH , S < 45dBZ (13) ZH, X = (13) 1.1982ZH, S − 5.7726 25dBZ < ZH, S < 45dBZ   0.8206Z + ≥ 0.8206 Z 11.7934 Z 45 dBZ + 11.7934 Z ≥ 45dBZ H , S H , S H, S H, S  In In order order to to analyze analyze the the accuracy accuracy of of the the SSCC SSCC method, method, the the corrected corrected X-band X-band radar radar reflectivity reflectivity is is compared with the intrinsic reflectivity at X-band, which is calculated from the reflectivity at S-band. S-band. compared with the intrinsic reflectivity at X-band, which is calculated from the reflectivity at The The S-band S-band radar radar reflectivity reflectivity from from the the volume volume scan scan data data is is interpolated interpolated into into the the coordinate coordinate of of the the X-band radar. The X-band radar PPI is shown in Figure 5a. Figure 5b is the intrinsic reflectivity X-band radar. The X-band radar PPI is shown in Figure 5a. Figure 5b is the intrinsic reflectivity at at X-band. Figure 5a,5a, there is a is strong convective cloudcloud band with cores in X-band. As Asshown showninin Figure there a strong convective bandthree withstrong three echo strong echo the southwest of the X-band radar. Dueradar. to severe the X-band radar cannotradar observe the cores in the southwest of the X-band Dueattenuation, to severe attenuation, the X-band cannot

observe the echo after the intensive rain region, which is shown in circle A in Figure 5b. The echo of the circle B is also not be detected by the X-band radar, resulting from partial beam blockage.


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echo after the intensive rain region, which is shown in circle A in Figure 5b. The echo of the circle B is also not be detected Atmosphere 2016, 7,7,164 77of Atmosphere 2016, 164 by the X-band radar, resulting from partial beam blockage. of17 17

Figure XXX and SS bands. The blue line stands for Figure 4. 4. Scattering Scattering simulation of intrinsic reflectivity atat and The blue lineline stands for the the Figure 4. Scatteringsimulation simulationof ofintrinsic intrinsicreflectivity reflectivityat and Sbands. bands. The blue stands for intrinsic reflectivity at X-band is equal to the reflectivity at S-band. The red curve is obtained intrinsic reflectivity at X-band is is equal totothe obtained by by the intrinsic reflectivity at X-band equal thereflectivity reflectivityatatS-band. S-band.The The red red curve curve is obtained by scattering simulation. scatteringsimulation. simulation. scattering

Figure 5. June 2015; (b) the intrinsic Figure 5. 5. (a) (a) Original Original reflectivity reflectivity at at X-band X-band for for convective convective cloud cloud on on 19 19 June June 2015; 2015; (b) (b) the the intrinsic intrinsic Figure (a) Original reflectivity at X-band for convective cloud on 19 reflectivity at X-band. The color shade guide the reflectivity factor unit dBZ and the X-Y axis reflectivityat atX-band. X-band.The Thecolor colorshade shadeguide guideisisisthe thereflectivity reflectivity factor in unit of dBZ and the X-Y axis reflectivity factor inin unit ofof dBZ and the X-Y axis is is the range in unit of km in the figure and the following figures. the range in unit of km in the figure andand thethe following figures. is the range in unit of km in the figure following figures.

The but the Theshapes shapesof ofthe thetwo tworadar radarechoes echoesare aresimilar similarto to each eachother, other,but butthe theX-band X-bandradar radarreflectivity reflectivityis The shapes of the two radar echoes are similar to each other, X-band radar reflectivity isis seriously attenuated. The maximum reflectivity of convective cores at X-band isisabout 50 dBZ, while seriously attenuated. The maximum reflectivity of convective cores at X-band about 50 dBZ, while seriously attenuated. The maximum reflectivity of convective cores at X-band is about 50 dBZ, while the about 60 dBZ, indicating that the X-band radar echo has a the corresponding corresponding intrinsic intrinsic reflectivity reflectivity isis the corresponding intrinsic reflectivity is about about 60 60 dBZ, dBZ, indicating indicatingthat thatthe theX-band X-bandradar radarecho echohas hasa serious distortion due to rain attenuation. aserious seriousdistortion distortiondue duetotorain rainattenuation. attenuation. The reflectivity at X-band isis corrected by the which isis shown in Figure The reflectivity at X-band corrected the SSCC SSCC method, method, Figure 6. 6. The reflectivity at X-band is corrected by thebySSCC method, which iswhich shown in shown Figure 6.inCompared Compared with the uncorrected X-band radar reflectivity in Figure 5a, the corrected reflectivity is Compared with the uncorrected X-band radar in reflectivity Figure 5a, thereflectivity corrected is reflectivity is with the uncorrected X-band radar reflectivity Figure 5a,inthe corrected effectively effectively compensated and the scope of strong echois extended. For further analysis, the reflectivity effectively compensated and the scope of strong echois extended. For further analysis, the reflectivity compensated and the scope of strong echois extended. For further analysis, the reflectivity is mapped isis mapped into aa1000 ××1000 matrix grids with of 150 m. mapped into 1000 1000 matrix withaa resolution resolution into a 1000 × 1000 matrix grids with agrids resolution of 150 m. of 150 m. Figure 7 shows the scatter diagrams of the uncorrected and corrected X-band radar Figure 77shows shows the thescatter scatterdiagrams diagrams of ofthe theuncorrected uncorrected and and corrected corrected X-band X-band radar radar reflectivity reflectivity Figure reflectivity versus the intrinsic reflectivity. Figure 7a shows that the uncorrected reflectivity significantly deviates versus the intrinsic reflectivity. Figure 7a shows that the uncorrected reflectivity significantly deviates versus the intrinsic reflectivity. Figure 7a shows that the uncorrected reflectivity significantly deviates from the intrinsic reflectivity, especially when the echoes are strong. The fitting line between the from the the intrinsic intrinsic reflectivity, reflectivity,especially especiallywhen whenthe theechoes echoesare arestrong. strong. The Thefitting fittingline linebetween between the the from uncorrected reflectivity and the intrinsic reflectivity (the green line) is y = 0.5824x + 9.2234, while the uncorrected reflectivity and the intrinsic reflectivity (the green line) is y = 0.5824x + 9.2234, while the uncorrected reflectivity and the intrinsic reflectivity (the green line) is y = 0.5824x + 9.2234, while the fitting line between the reflectivity and the reflectivity becomes fittingline line between the corrected corrected and reflectivity the intrinsic intrinsic reflectivity fitting between the corrected reflectivityreflectivity and the intrinsic becomes y = 0.8036x becomes + 3.8382, yy == 0.8036x+ 3.8382, referring to Figure 7b. After attenuation correction, the slope of fitting line 0.8036x+ 3.8382, to Figurecorrection, 7b. After attenuation the slope of into fitting line referring to Figure 7b.referring After attenuation the slope of correction, fitting line turns 0.5824 0.8036, turns 0.5824 into 0.8036, indicating that the corrected reflectivity isismuch closer to the intrinsic reflectivity. turns 0.5824 into 0.8036, indicating that the corrected reflectivity much closer to the intrinsic reflectivity. indicating that the corrected reflectivity is much closer to the intrinsic reflectivity.

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Figure 6. Corrected Corrected reflectivity at at X-band. Figure Figure 6. 6. Corrected reflectivity reflectivity at X-band. X-band.

(a) (a)

(b) (b)

Figure 7. Scatter Scatter diagramsofofthe the uncorrected(a)(a) and corrected (b) X-band radar reflectivity versus Figure and corrected (b)(b) X-band radar reflectivity versus the Figure 7. 7. Scatter diagrams diagrams of theuncorrected uncorrected (a) and corrected X-band radar reflectivity versus the intrinsic reflectivity. The red lineideal is an ideal line, indicating that the X-band corrected X-band radar intrinsic reflectivity. The red line is an line, indicating that the corrected radar reflectivity the intrinsic reflectivity. The red line is an ideal line, indicating that the corrected X-band radar reflectivity is equal to the intrinsic reflectivity. The green line is the fitting curve. is equal to the intrinsic reflectivity. The green line the fitting reflectivity is equal to the intrinsic reflectivity. Theisgreen line iscurve. the fitting curve.

In order to show the validity of the correction for any path, the reflectivity at X-band with an correction for any path, the reflectivity at X-band with an In order to show the validity of the correction azimuth angle of 228° is analyzed herein. As shown in Figure 3, the electromagnetic wave ◦ is analyzed azimuth angle angleofof is analyzed herein. As shown 3, the electromagnetic wave azimuth 228228° herein. As shown in Figurein3, Figure the electromagnetic wave successively successively passes from A to D. Due to the impact of distance, antenna elevation and earth curvature, successively fromto Athe to D. Due to impactantenna of distance, antenna and earth curvature, passes from Apasses to D. Due impact ofthe distance, elevation andelevation earth curvature, there are not there are not echoes of the S-band radar in the area A, referring to Figure 8a. Compared with the there are notS-band echoesradar of theinS-band in the area A, referring to Figure with the echoes of the the arearadar A, referring to Figure 8a. Compared with8a. theCompared intrinsic reflectivity intrinsic reflectivity (Intrinsic), the uncorrected reflectivity (UnC) nearly has no attenuation in areas intrinsic reflectivity (Intrinsic), the uncorrected reflectivity (UnC) nearly has no in areas (Intrinsic), the uncorrected reflectivity (UnC) nearly has no attenuation in areas A,attenuation B and C while with A, B and C while with serious attenuation in area D. Figure 8b also illustrates this phenomenon, the A, B and C while with serious attenuation in area D. Figure 8b also illustrates this phenomenon, the serious attenuation in area D. Figure 8b also illustrates this phenomenon, the φDP increases by nearly φDP increases by nearly 50°, corresponding to intensive rain region, while no increase in areas A, B ◦ φDP, increases by nearly 50°, corresponding intensive rain region, while areas A, B 50 corresponding to intensive rain region, to while no increase in areas A, B no andincrease C. Afterinattenuation and C. After attenuation correction using the SSCC method, the corrected X-band radar reflectivity and C. After attenuation using the SSCC method, correctedatX-band radar reflectivity correction using the SSCCcorrection method, the corrected X-band radarthe reflectivity 33 km has compensated at 33 km has compensated about 10 dBZ (SSCC). The corrected reflectivity at X-band is consistent at 33 km has compensated about 10reflectivity dBZ (SSCC). The corrected reflectivity at X-band consistent about 10 dBZ (SSCC). The corrected at X-band is consistent with the intrinsicisreflectivity. with the intrinsic reflectivity. However, the corrected reflectivity using the method of Kim et al. [4] with the intrinsic reflectivity. However, using theismethod of Kim et al. [4] However, the corrected reflectivity using the corrected method ofreflectivity Kim et al. [4] (Kim) lower than the intrinsic (Kim) is lower than the intrinsic reflectivity, indicating the correction is not enough. (Kim) is lower than the intrinsic reflectivity, indicating the correction is not enough. reflectivity, indicating the correction is not enough. The corrected X-band radar reflectivity at 37 km in Figure 8a is 15 dBZ larger than the intrinsic than the intrinsic intrinsic The corrected X-band radar reflectivity at 37 km in Figure 8a is 15 dBZ larger than reflectivity. This results from the rapid development and fast moving speed of the convective cloud. reflectivity. This This results from the rapid development and fast moving speed of the convective cloud. reflectivity. cloud. Because the intrinsic reflectivity shown in Figure 5b is interpolated by the 6-min volume scan data of Because the intrinsic reflectivity reflectivity shown shown in Figure Figure 5b 5b is interpolated by the 6-min volume scan data of the S-band radar, the two factors causes a slight deviation from the intrinsic reflectivity. This S-bandradar, radar,thethe factors causes a slight deviation from the intrinsic reflectivity. This the S-band twotwo factors causes a slight deviation from the intrinsic reflectivity. This influence influence is significant at the edge of convective cloud but negligible for the stratiform cloud and the influence is significant edge of convective cloud but negligible for the stratiform and the is significant at the edgeatofthe convective cloud but negligible for the stratiform cloud and cloud the stratiform stratiform cloud with embedded convection. As shown in Figure 8a, the corrected X-band radar stratiform cloud with embedded convection. As shown in Figure 8a, the corrected X-band radar reflectivity both the SSCC and the Kim is close to the intrinsic reflectivity. However, the SSCC method reflectivity both the SSCC and the Kim is close to the intrinsic reflectivity. However, the SSCC method


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cloud with embedded convection. As shown in Figure 8a, the corrected X-band radar reflectivity9both Atmosphere 2016, 7, 164 of 17 the SSCC and the Kim is close to the intrinsic reflectivity. However, the SSCC method has an advantage over Kim et al. [4]over in correcting of the the reflectivity convective of cloud. In order tocloud. analyze the two has an advantage Kim et al.the [4]reflectivity in correcting the convective In order to methods comprehensively, all the radials are used. analyze the two methods comprehensively, all the radials are used.

(a)

Azimuth：228°

A

B

C

D

(b)

Figure 8. (a) Range profile of different reflectivity along the azimuth of 228°, uncorrected reflectivity Figure 8. (a) Range profile of different reflectivity along the azimuth of 228◦ , uncorrected reflectivity (UnC), reflectivity corrected by Kim et al.’s method (Kim), reflectivity corrected by the SSCC method (UnC), reflectivity corrected by Kim et al.’s method (Kim), reflectivity corrected by the SSCC method (SSCC) and the intrinsic reflectivity (Intrinsic); (b) the measured ΨC and the filtered φDP. (SSCC) and the intrinsic reflectivity (Intrinsic); (b) the measured ΨC and the filtered φDP .

Figure 9 shows four cumulative distributions of the radar reflectivity. Comparing with the Figure distribution 9 shows four distributions the radar reflectivity. Comparing with and the cumulative of cumulative the uncorrected reflectivityof(UnC), the method of Kim et al. [4] (Kim), cumulative distribution of the uncorrected reflectivity (UnC), the that method Kim et al. [4] (Kim), the SSCC method (SSCC) both shift to the right, indicating the of low cumulative valueand of the SSCC method (SSCC) both shift to the right, indicating that the low cumulative value of reflectivity reflectivity decreases, while the high cumulative value increases. Both the cumulative distribution of decreases, while the cumulative value increases. Both the cumulative distribution of the (AB) Kim the Kim and SSCC arehigh closer to that of the intrinsic reflectivity than the UnC. The average biases and SSCC are closer that of the of the reflectivity are to calculated forintrinsic the two reflectivity methods. than the UnC. The average biases (AB) of the reflectivity are calculated for the two methods.


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Figure 9. Cumulative distributionofofreflectivity reflectivity for for the In the figure, line line Unc Unc is Figure 9. Cumulative distribution the convective convectivecloud. cloud. In the figure, is uncorrected reflectivity, line Kim stands for reflectivity corrected by Kim et al.’s method, line SSCC uncorrected reflectivity, line Kim stands for reflectivity corrected by Kim et al.’s method, line SSCC Figure 9. Cumulative distribution the of reflectivity for the convective cloud. Infor theintrinsic figure, reflectivity. line Unc is represents reflectivity corrected SSCC method, stands represents reflectivity corrected byby the SSCC method, and andline lineIntrinsic Intrinsic stands for intrinsic reflectivity. uncorrected reflectivity, line Kim stands for reflectivity corrected by Kim et al.’s method, line SSCC represents reflectivity corrected SSCC10 method, and line The average bias (AB) shownbyinthe Figure is defined as Intrinsic below: stands for intrinsic reflectivity.

The average bias (AB) shown in Figure 10 is defined as below: R − Rs  xas below: The average bias (AB) shown in FigureAB 10 =is defined

where ∗

(14)

AB = h R − Rs i| x

x

AB x, = RR is −R  is average value above parameter the (14) s xreflectivity at X-band and RS is the intrinsic

(14)

reflectivity. As shown in Figure 10a, the AB between thereflectivity uncorrected reflectivity andRSthe intrinsic wherewhere is average value above parameter the X-band is intrinsic the intrinsic h∗i| x∗ is average value above parameterx, x, R R is is the reflectivity atat X-band andand RS is the x(line UnC) is decreasing with increasing reflectivity. The AB of the UnC is greater than 10 dB, reflectivity reflectivity. As shown in Figure 10a, the AB between the uncorrected reflectivity and the intrinsic reflectivity. Asthe shown in Figure 10a, the ABthe between the The uncorrected and significantly the intrinsic indicating that attenuation is significantin rain area. AB of thereflectivity Kim and SSCC reflectivity (line UnC) is decreasing with increasing reflectivity. The AB of the UnC is greater than reflectivity (line UnC) is decreasing with increasing reflectivity. The AB of the UnC is greater 10 dB, reduces the difference from the intrinsic reflectivity. To accurately retrieve meteorologicalthan products, 10 dB, indicating that the attenuation is significantin theThe rain area. The AB of the significantly Kim and SSCC indicating that the attenuation is significantin the rain area. AB of the Kim and SSCC a resolution of 1 dB for the reflectivity is necessary. Figure 10b shows that there are more than 1 dB significantly reduces thethe difference from intrinsic accurately retrievehas meteorological reduces the between difference from intrinsic reflectivity. To accuratelyTo retrieve meteorological products, differences Kimthe and SSCCthe from 35 dBZ,reflectivity. illustrating that the SSCC method a better products, a resolution of dB for the reflectivity is necessary. Figure 10b shows that there are aperformance resolution ofthan 1 dBKim for1 the reflectivity is necessary. Figure 10b shows that there are more than 1 dBmore et al.’s method at correcting convective cloud, especially with reflectivity between the Kim and SSCC from 35 dBZ, illustrating that the SSCC method has a better than differences 1 dB differences between the Kim and SSCC from 35 dBZ, illustrating that the SSCC method greater than 35 dBZ. performance than Kim et al.’s method at correcting convective cloud, especially with reflectivity has a better performance than Kim et al.’s method at correcting convective cloud, especially with greatergreater than 35 than dBZ. 35 dBZ. reflectivity

(a)

(b)

(a)

(b)

Figure 10. Average biases of the reflectivity for the convective cloud. (a) The AB of the uncorrected reflectivity, the reflectivity corrected by Kim et al.’s method and the reflectivity corrected by the Figure 10. the Average of the reflectivity for the convective cloud. The ABAB of the uncorrected SSCC; (b) AB ofbiases theofdifference between the Kim and the SSCC. Figure 10. Average biases the reflectivity for the convective cloud.(a)(a) The of the uncorrected reflectivity, the reflectivity corrected by Kim et al.’s method and the reflectivity corrected by the reflectivity, the reflectivity corrected by Kim et al.’s method and the reflectivity corrected by the SSCC; SSCC; (b)to the AB of the Kim andresolutions the SSCC. for the SSCC method, the range In order analyze thedifference impact ofbetween differentthe sampling

(b) the AB of the difference between the Kim and the SSCC. resolution is set at 0.45 km (SSCC_450) and 0.75 km (SSCC_750) as shown in Figure 11, respectively. In order toisanalyze impact different sampling resolutions the SSCC method, range The SSCC_750 furtherthe away fromofthe Intrinsic than the SSCC_450,for which is closer to thethe method resolution isanalyze set at 0.45 km (SSCC_450) 0.75 km (SSCC_750) shown in Figure 11, respectively. In the impact of different sampling fordecreasing the SSCCrange method, the range byorder Kim etto al. [4] (the range resolution is and 0.5 km). Figure 11 resolutions shows as that the resolution The SSCC_750 is further away from the Intrinsic than the SSCC_450, which is to 11, the method resolution islead set to at reduced 0.45 kmcorrection (SSCC_450) and 0.75 (SSCC_750) as shown incloser Figure respectively. would effect and thekm SSCC method performs better than the method by by Kim et al. range 0.5 km). Figure 11 SSCC_450, shows that the decreasing range resolution Kim et al. [4] for(the convective cloud.theisIntrinsic The SSCC_750 is [4] further awayresolution from than the which is closer to the method by would lead to range reduced correctioniseffect and the SSCC11 method than the method by Kim et al. [4] (the resolution 0.5 km). Figure showsperforms that thebetter decreasing range resolution Kim et al. [4] for convective cloud.

would lead to reduced correction effect and the SSCC method performs better than the method by Kim et al. [4] for convective cloud.

Atmosphere 2016, 7, 164 Atmosphere 2016, 7, 164 Atmosphere 2016, 7, 164

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Figure for the the convective convective cloud. Cumulative distribution different resolutions resolutions for Figure 11. 11. Cumulative Cumulative distribution of of reflectivity reflectivity with with different convective cloud. cloud.

Compared the method by Bringi et al. [3], the SSCC method does not require an and Compared with with [3],[3], thethe SSCC method does not not require an initial initial and Compared with the themethod methodby byBringi Bringietetal.al. SSCC method does require an initial aa terminal differential propagation phase of each radial, which could avoid correction errors. To terminal differential propagation phase of each radial, which could avoid correction errors. To and a terminal differential propagation phase of each radial, which could avoid correction errors. illustrate this problem, we assume the terminal phase is true and examine the errors due to the wrong illustrate this problem, we assume the terminal phase is true and examine the errors due to the wrong To illustrate this problem, we assume the terminal phase is true and examine the errors due to the initial Figure correction errors various initial using method by initial phase. phase. Figure 12 12 shows shows errors with with initial phases phases using the the method by Bringi Bringi wrong initial phase. Figure 12 correction shows correction errorsvarious with various initial phases using the method by et al. [3], whereby 275° (Bringi_275) is the actual radar initial phase and 255° (Bringi_255) and et al. [3], whereby 275° (Bringi_275) is the is actual radar radar initialinitial phasephase and 255° and 265° 265° Bringi et al. [3], whereby 275◦ (Bringi_275) the actual and (Bringi_255) 255◦ (Bringi_255) and (Bringi_265) are The SSCC is with the In the and the ◦ (Bringi_265) (Bringi_265) are not. not. is consistent consistent withwith the Bringi_275. Bringi_275. In contrast, contrast, the Bringi_255 Bringi_255 andand the 265 are The not. SSCC The SSCC is consistent the Bringi_275. In contrast, the Bringi_255 Bringi_265 are far away from the Bringi_275, indicating the SSCC method does not require seeking Bringi_265 are are far far away from thethe Bringi_275, indicating the Bringi_265 away from Bringi_275, indicatingthe theSSCC SSCCmethod methoddoes doesnot not require require seeking seeking the initial phase and terminal phase but the cumulative distribution is also consistent with that of the initial phase and terminal phase but the cumulative distribution is also consistent with that of the the the initial phase and terminal phase but the cumulative distribution is also consistent with that of the true correction results. true correction results. true correction results.

Figure 12. Cumulative distribution of reflectivity with initial phases for convective cloud. Figure with different different initial initial phases phases for for convective convective cloud. cloud. Figure 12. 12. Cumulative Cumulative distribution distribution of of reflectivity reflectivity with different

To To verify verify the the applicability applicability of of the the SSCC SSCC method method under under various various precipitation precipitation conditions, conditions, the the To verify the applicability of the SSCConmethod under various 13 precipitation conditions, the stratiform cloud with embedded convection 26 June 2015 (Figures and 14), and stratiform cloud with embedded convection on 26 June 2015 (Figures 13 and 14), and the the stratiform stratiform stratiform cloud with embedded 15 convection on 26analyzed. June 2015 (Figures 13 and 14), andshow the stratiform cloud cloud on on 16 16 June June 2015 2015 (Figures (Figures 15 and and 16) 16) are are analyzed. Both Both Figures Figures 17 17 and and 18 18 show that that the the cloud on 16 June 2015 (Figures 15 and 16) are analyzed. Both Figures 17 and 18 show that the reflectivity at X-band is corrected effectively and the corrected cumulative distribution closer to that reflectivity at X-band is corrected effectively and the corrected cumulative distribution closer to that reflectivity at X-band is corrected effectively and show the corrected cumulative distribution closer to thatthe of of of the the intrinsic intrinsic reflectivity. reflectivity. Figures Figures 19 19 and and 20 20 show that that the the SSCC SSCC method method is is consistent consistent with with the the intrinsic reflectivity. Figures 19 and 20 show that the SSCC method is consistent with the method method method by by Kim Kim et et al. al. [4]. [4]. The The change change of of the the resolution resolution does does not not lead lead to to correction correction biases, biases, because because the the by Kim et al. [4]. The change of the resolution does not lead to correction biases, because KDP K of the stratiform cloud with embedded convection and the stratiform cloud is lower thanthe that of KDP DP of the stratiform cloud with embedded convection and the stratiform cloud is lower than that of of the stratiform cloud with 21 embedded convection and the stratiform cloud distribution is lower than thatthe of the convective cloud. Figures and 22 illustrate that the corrected cumulative using the convective cloud. Figures 21 and 22 illustrate that the corrected cumulative distribution using the the convective cloud. Figureswith 21 and 22 illustrate that theiscorrected cumulative distribution using SSCC SSCC method method are are consistent consistent with that that of of the the 275°, 275°, which which is the the true true initial initial phase phase of of the the radar. radar. The The correction correction verification verification of of the the three three different different precipitation precipitation cases cases indicates indicates that that the the SSCC SSCC method method is is also also applicable applicable for for the the stratiform stratiform cloud cloud and and the the stratiform stratiform cloud cloud with with embedded embedded convection. convection. Note Note that that


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the SSCC method are consistent with that of the 275◦ , which is the true initial phase of the radar. The correction verification of the three different precipitation cases indicates that the SSCC method Atmosphere 2016, 7, 164 12 of 17 is also applicable for Atmosphere 2016, 7, 164the stratiform cloud and the stratiform cloud with embedded convection. 12 of 17 Note Atmosphere 2016, 7, 164 12 of 17 that both the SSCC method and the method by Kim et al. [4] may have no significant effect or to lead to both the SSCC method and the method by Kim et al. [4] may have no significant effect or lead bothworse the SSCC method and the method by Kim et al. of [4] the mayintegration have no significant effect or lead to slightly attenuation correction due to the error resolution when correcting slightly duebytoKim the error integration resolution effect when correcting both theworse SSCC attenuation method andcorrection the method et al. of [4]the may have no significant lead to slightly worse attenuation correction due to the error of the integration resolution when or correcting stratiform rain if the rainfall is verysmall. small. stratiform rain if the rainfall iscorrection very slightly worse attenuation due to the error of the integration resolution when correcting stratiform rain if the rainfall is very small. stratiform rain if the rainfall is very small.

Figure 13. Original reflectivity at X-band for the stratiform cloud with embedded convection on 26 Figure 13. 13. Original reflectivity forthe thestratiform stratiform cloud embedded convection Figure Original reflectivityat at X-band X-band for cloud withwith embedded convection on 26 on June 2015. Figure 13. Original reflectivity at X-band for the stratiform cloud with embedded convection on 26 26 June 2015. June 2015. June 2015.

(a) (a) (a)

(b) (b) (b)

Figure 14. (a) Corrected reflectivity at X-band; (b) the intrinsic reflectivity at X-band.

Figure 14. (a) Corrected reflectivity at X-band; (b) the intrinsic reflectivity at X-band. Figure 14. 14. (a)(a) Corrected X-band;(b) (b)the theintrinsic intrinsic reflectivity at X-band. Figure Correctedreflectivity reflectivity at at X-band; reflectivity at X-band.

Figure 15. Original reflectivity at X-band for the stratiform cloud on 16 June 2015. Figure 15. Original reflectivity at X-band for the stratiform cloud on 16 June 2015. Figure 15. Original reflectivity at X-band for the stratiform cloud on 16 June 2015.

Figure 15. Original reflectivity at X-band for the stratiform cloud on 16 June 2015.

Atmosphere 2016, 7, 164 Atmosphere 2016, 7, 164 Atmosphere 2016, 7, 164 Atmosphere 2016, 7, 164

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(a) (a) (a)

(b) (b) (b)

Figure at X-band. Figure16. 16.(a) (a)Corrected Correctedreflectivity reflectivity at at X-band; X-band; (b) (b) the the intrinsic intrinsic reflectivity reflectivity Figure 16. (a) Corrected reflectivity at X-band; (b) the intrinsic reflectivity at at X-band. X-band. Figure 16. (a) Corrected reflectivity at X-band; (b) the intrinsic reflectivity at X-band.

Figure 17. Cumulative distribution of reflectivity for the stratiform rain with embedded convection. Figure 17. Cumulative distribution of reflectivity for the stratiform rain with embedded embedded convection. Figure 17. 17. Cumulative Cumulative distribution distribution of of reflectivity reflectivity for for the the stratiform stratiform rain rain with with Figure embedded convection. convection.

Figure 18. Cumulative distribution of reflectivity for the stratiform rain. Figure 18. Cumulative distribution of reflectivity for the stratiform rain. Figure rain. Figure 18. 18. Cumulative Cumulative distribution distribution of of reflectivity reflectivity for for the the stratiform stratiform rain.


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Figure 19. Average bias of reflectivity for the stratiform rain with embedded convection. Figure 19. Average bias of reflectivity for the stratiform rain with embedded convection. Figure 19. Average bias of reflectivity for the stratiform rain with embedded convection.

Figure 19. Average bias of reflectivity for the stratiform rain with embedded convection.

Figure 20. Average bias of reflectivity for the stratiform rain. Figure 20. Average bias of reflectivity for the stratiform rain. Figure 20.20. Average forthe thestratiform stratiform rain. Figure Averagebias biasof of reflectivity reflectivity for rain.

Figure 21. Cumulative distribution of reflectivity with different initial phases for the stratiform rain Figure 21. Cumulative distribution of reflectivity with different initial phases for the stratiform rain with embedded convection. Figure 21. Cumulative distribution of reflectivity with different initial phases for the stratiform rain with convection. Figure 21.embedded Cumulative distribution of reflectivity with different initial phases for the stratiform rain with embedded convection.

with embedded convection.


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Figure phases for for the the stratiform stratiform rain. rain. Figure 22. 22. Cumulative Cumulative distribution distribution of of reflectivity reflectivity with with different different initial initial phases

5. Conclusions and Discussion 5. Conclusions and Discussion Based on Bringi et al. [3], the paper proposed a high-resolution slide self-consistency correction Based on Bringi et al. [3], the paper proposed a high-resolution slide self-consistency correction (SSCC) method for the X-band dual-polarization radar reflectivity, which is an improvement from (SSCC) method for the X-band dual-polarization radar reflectivity, which is an improvement from Kim et al.’s method. The proposed method improved the correction resolution and effect, adapting a Kim et al.’s method. The proposed method improved the correction resolution and effect, adapting slide window consisting of 10 gates. a slide window consisting of 10 gates. In the paper, the SSCC method is evaluated with the reflectivity of the convective cloud, the In the paper, the SSCC method is evaluated with the reflectivity of the convective cloud, the stratiform cloud with embedded convection and the stratiform cloud, comparing with the correction stratiform cloud with embedded convection and the stratiform cloud, comparing with the correction results from the methods by Bringi et al. [3] and Kim et al. [4], as well as the intrinsic reflectivity at results from the methods by Bringi et al. [3] and Kim et al. [4], as well as the intrinsic reflectivity X-band calculated from the reflectivity at the S-band. It is found that the reflectivity at X-band can at X-band calculated from the reflectivity at the S-band. It is found that the reflectivity at X-band be corrected effectively by the SSCC method. The corrected reflectivity is closer to the intrinsic can be corrected effectively by the SSCC method. The corrected reflectivity is closer to the intrinsic reflectivity and has a better performance than the method by Kim et al. [4] in correcting the convective reflectivity and has a better performance than the method by Kim et al. [4] in correcting the convective cloud. However, the correction results of the two methods are very similar for the stratiform cloud cloud. However, the correction results of the two methods are very similar for the stratiform cloud with embedded convection and the stratiform cloud. This may be because the KDP of the two kinds of with embedded convection and the stratiform cloud. This may be because the KDP of the two kinds precipitation cloud is much less than that of the convective cloud. For this reason, the SSCC method of precipitation cloud is much less than that of the convective cloud. For this reason, the SSCC and the method by Kim et al. [4] may have no significant effect or may lead to slightly worse method and the method by Kim et al. [4] may have no significant effect or may lead to slightly worse attenuation correction when correcting stratiform rain if the rainfall is very small. In addition, the attenuation correction when correcting stratiform rain if the rainfall is very small. In addition, the SSCC method has better results than Bringi et al. [3] for the three cases due to the reduced correction SSCC method has better results than Bringi et al. [3] for the three cases due to the reduced correction errors when computing differential propagation shift increments. errors when computing differential propagation shift increments. In summary, the SSCC method has three advantages as follows: In summary, the SSCC method has three advantages as follows: 1. Improving the correction resolution; 1. Improving the correction resolution; 2. Having no need for seeking the initial and terminal differential phases; 2. Good Having no need forinseeking the initial and terminal 3. performance correcting convective cloud. differential phases; 3. Good performance in correcting convective cloud. Meanwhile, it must be noted that the accuracy of the attenuation correction is restricted in the SSCCMeanwhile, method by it the length (1.5 km) of the the accuracy sliding window and this is acorrection more significant effectinthan must be noted that of the attenuation is restricted the the resolution. SSCC method by the length (1.5 km) of the sliding window and this is a more significant effect than the resolution. Acknowledgments: This work was partially supported by the National Key Basic Research 973 Program of China (Grant Nos. 2014CB441403, 2013CB430105), the National Natural Science Foundation of China (Grant Nos. Acknowledgments: This work was partially supported by the National Key Basic Research 973 Program of 41575037, 41605019), Guizhou Province Scientific Research Joint Project (Grant No. G [2013]4001), and the Special China (Grant Nos. 2014CB441403, 2013CB430105), the National Natural Science Foundation of China (Grant Nos. Scientific of Meteorological Public Welfare Profession of China No. GYHY201006031). 41575037, Research 41605019),Project Guizhou Province Scientific Research Joint Project (Grant No.(Grant G [2013]4001), and the Special ScientificContributions: Research Project Meteorological Public Welfare Profession Author Theofauthors contribute equally to this paper. of China (Grant No. GYHY201006031). Author Contributions: The authors contribute equally to this paper. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

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