Rain Attenuation Correction of Reflectivity for X-Band Dual-Polarization Radar

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.


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][2][3][4][5][6][7][8][9][10].Previous studies on the application of dual-polarization radars are mostly designed for S, C-band radars [11][12][13][14][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 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 Z H and rainfall intensity R(Z H = aR b ; a, b are empirical constants).This method retrieves Z ret using the measured rainfall intensity R and then calculates horizontal specific attenuation coefficient A H (A H = Z ret −Z H ) [18].However, the relationship between Z H 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 (φ DP ) and specific differential phases (K DP ).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 φ DP and K DP .Bringi et al. [19] found that there was almost a linear relationship (A H = α H K DP ) between the attenuation (A H ) and specific differential phase (K DP ) by scattering simulation.Zrnic and Ryzhkov [20] pointed out that K DP 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 φ DP and Z H or differential reflectivity (Z DR ) 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 φ DP , then obtained the relation coefficient α' H between A H and φ DP , 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 K DP with the convectional correction method and found that the correction by K DP was better than by Z H .However, the K DP correction method would cause errors since the K DP may contain errors when rainfall intensity is small.Thus he proposed a comprehensive Z H -K DP correction method to overcome shortcomings of the correction by Z H or by K DP .However, Z H -K DP correction method still uses a fixed coefficient to correct rain attenuation.
Smyth and Illingworth [25] introduced a constraint to correct the differential reflectivity (Z DR ) for S-band dual-polarization radars.In this method, the coefficient (α H ) of the relationship between K DP and A DP is not fixed, but determined by the constraint that Z DR 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 Z DR as 0 dB at the farther edge of a rain zone.It is necessary to create a new Z DR 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 A H 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 α H of the relationship between A H and K DP .
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 Z H correction and the method of Smyth and Illingworth [25] for Z DR correction.One of the advantages of the algorithm is that the coefficient α H of the relationship between A H and K DP 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 α H by scattering simulation using drop size distributions.Kim et al. [29] corrected Z DR by the horizontal reflectivity Z H and the vertical reflectivity Z V 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 K DP 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 K DP can reach 10 • /km or more in convective cores.Such a resolution may result in errors when correcting convective cloud.In addition, φ DP would be used to correct Z H and Z V 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.

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.

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 Z h (mm 6 m −3 ) in linear scale and Z H (dBZ) in logarithm scale have the following relationship: The corrected reflectivity Z H A (dBZ) at a range r is related to the attenuated (measured) reflectivity Z H as follows: where A H is specific attenuation in decibels per kilometer.The change in differential propagation phase is as follows: where r 0 and r 1 are the beginning and ending range gate, respectively.In Bringi et al. [3], specific attenuation A H is determined with a constraint that the cumulative attenuation from range r 0 to r 1 should be consistent with the total change in differential propagation phase ∆φ DP .Under the assumption that there is a linear relationship between A H and K DP , the final formula of A H is given by where, I(r, r 1 ) = 0.46b 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 A H and Z h and a linear relationship between specific attenuation A H and specific differential phase K DP at frequencies from 2.8 to 9.3 GHz; that is, the exponent c in Equation ( 8) is close to 1.
where K DP is in • •km −1 and c is set as a constant 1.Therefore, if A H (r) is calculated by Equation ( 4) and substituted into Equation (2), the corrected reflectivity Z HA (r) at a range r is obtained.However, α and b need to be set to a fixed value before calculating A H (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 A H (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 (α min , α max ), 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 φ cal DP (r; α) is calculated as follows: The optimal α is the value that leads Equation (10) to the minimum.
where i denotes the range gate from r 0 to r 1 .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 r 0 and r 1 as 1.0 km with an overlap of 0.5 km (ultimately, α has a resolution of 0.5 km), referring to Figure 1a.In the paper, the SSCC method employs a slide window processing shown in Figure 1b by setting the distance between r 0 and r 1 as 1.5 km (10 gates), thus α has a high-resolution of 0.15 km, improving the resolution of α estimation.After developing the method of Bringi et al. [3], Equations ( 3) and (10) become as follows: In addition, the new method does not seek the initial and terminal phase of each radial as the method of Bringi et al. [3] does, which would finally cause correction errors.
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 0.5 km (ultimately, α has a resolution of 0.5 km), referring to Figure 1a.In the paper, the SSCC method employs a slide window processing shown in Figure 1b by setting the distance between r0 and r1 as 1.5 km (10 gates), thus α has a high-resolution of 0.15 km, improving the resolution of α estimation.After developing the method of Bringi et al. [3], Equations ( 3) and (10) become as follows: In addition, the new method does not seek the initial and terminal phase of each radial as the method of Bringi et al. [3] does, which would finally cause correction errors.

Result
The SSCC method is evaluated using the data collected by the X-band dual-polarization radar (IAP-714XDP-A), which is located in Shunyi District of Beijing City (BJ) from June to September 2015.The data contain observations of convective cloud, stratiform cloud and the stratiform cloud with embedded convection.The corrected reflectivity is compared with the intrinsic reflectivity at Xband calculated from the reflectivity at S-band, which is obtained by the CINRAD/SA S-band single-polarization weather radar located in Daxing District of Beijing City. Figure 2 shows the locations of the two radars.The X-band radar (at ShunyiSY, 116.68°E, 40.19°N) is located at the northeast of the S-band radar (at DaxingDX, 116.47°E, 39.81° N).The straight-line distance between the two radars is about 46 km.

Result
The SSCC method is evaluated using the data collected by the X-band dual-polarization radar (IAP-714XDP-A), which is located in Shunyi District of Beijing City (BJ) from June to September 2015.The data contain observations of convective cloud, stratiform cloud and the stratiform cloud with embedded convection.The corrected reflectivity is compared with the intrinsic reflectivity at X-band calculated from the reflectivity at S-band, which is obtained by the CINRAD/SA S-band single-polarization weather radar located in Daxing District of Beijing City.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 0.5 km (ultimately, α has a resolution of 0.5 km), referring to Figure 1a.In the paper, the SSCC method employs a slide window processing shown in Figure 1b by setting the distance between r0 and r1 as 1.5 km (10 gates), thus α has a high-resolution of 0.15 km, improving the resolution of α estimation.After developing the method of Bringi et al. [3], Equations ( 3) and ( 10) become as follows: In addition, the new method does not seek the initial and terminal phase of each radial as the method of Bringi et al. [3] does, which would finally cause correction errors.

Result
The SSCC method is evaluated using the data collected by the X-band dual-polarization radar (IAP-714XDP-A), which is located in Shunyi District of Beijing City (BJ) from June to September 2015.The data contain observations of convective cloud, stratiform cloud and the stratiform cloud with embedded convection.The corrected reflectivity is compared with the intrinsic reflectivity at Xband calculated from the reflectivity at S-band, which is obtained by the CINRAD/SA S-band single-polarization weather radar located in Daxing District of Beijing City. Figure 2 shows the locations of the two radars.The X-band radar (at ShunyiSY, 116.68°E, 40.19°N) is located at the northeast of the S-band radar (at DaxingDX, 116.47°E, 39.81° N).The straight-line distance between the two radars is about 46 km.Hubbert and Bringi [31] pointed out that the measured differential propagation phase Ψ C consists of true differential propagation phase φ DP and backward scattering differential phase shift δ.Since δ could result in errors of K DP estimation, δ needs to be eliminated before using Ψ C .In this paper, the method of Hubbet and Bringi [31] is applied to filter δ out.
A strong convective weather event swept Beijing City from north to south on 19 June 2015.Hubbert and Bringi [31] pointed out that the measured differential propagation phase ΨC consists of true differential propagation phase φDP and backward scattering differential phase shift δ.Since δ could result in errors of KDP estimation, δ needs to be eliminated before using ΨC.In this paper, the method of Hubbet and Bringi [31] is applied to filter δ out.
A strong convective weather event swept Beijing City from north to south on 19 June 2015.Figure 3 shows the plane position indicator (PPI) of the X-band radar at elevation 3° at 14:45 Beijing Time (BJT), 19 June 2015.Three strong echo cores of convective cloud are situated between the two radars and the largest reflectivity observed by the S-band radar is about 60 dBZ.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 data and the empirical conversion method is used in the paper.Figure 4 shows a plot of the 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 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 radar measurements at S-band.Note that the reflectivity at S-band is assumed to be non-attenuated.
In order to analyze the accuracy of the SSCC method, the corrected X-band radar reflectivity is compared with the intrinsic reflectivity at X-band, which is calculated from the reflectivity at S-band.The S-band radar reflectivity from the volume scan data is interpolated into the coordinate of the X-band radar.The X-band radar PPI is shown in Figure 5a. Figure 5b is the intrinsic reflectivity at X-band.As shown in Figure 5a, there is a strong convective cloud band with three strong echo cores in the southwest of the X-band radar.Due to severe attenuation, the X-band radar 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.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 data and the empirical conversion method is used in the paper.Figure 4 shows a plot of the 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 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 radar measurements at S-band.Note that the reflectivity at S-band is assumed to be non-attenuated.
In order to analyze the accuracy of the SSCC method, the corrected X-band radar reflectivity is compared with the intrinsic reflectivity at X-band, which is calculated from the reflectivity at S-band.The S-band radar reflectivity from the volume scan data is interpolated into the coordinate of the X-band radar.The X-band radar PPI is shown in Figure 5a. Figure 5b is the intrinsic reflectivity at X-band.As shown in Figure 5a, there is a strong convective cloud band with three strong echo cores in the southwest of the X-band radar.Due to severe attenuation, the X-band radar 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.The shapes of the two radar echoes are similar to each other, but the X-band radar reflectivity is seriously attenuated.The maximum reflectivity of convective cores at X-band is about 50 dBZ, while the corresponding intrinsic reflectivity is about 60 dBZ, indicating that the X-band radar echo has a serious distortion due to rain attenuation.
The reflectivity at X-band is corrected by the SSCC method, which is shown in Figure 6.Compared with the uncorrected X-band radar reflectivity in Figure 5a, the corrected reflectivity is effectively compensated and the scope of strong echois extended.For further analysis, the reflectivity is mapped into a 1000 × 1000 matrix grids with a resolution of 150 m.
Figure 7 shows the scatter diagrams of the uncorrected and corrected X-band radar reflectivity 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 uncorrected reflectivity and the intrinsic reflectivity (the green line) is y = 0.5824x + 9.2234, while the fitting line between the corrected reflectivity and the intrinsic reflectivity becomes y = 0.8036x+ 3.8382, referring to Figure 7b.After attenuation correction, the slope of fitting line turns 0.5824 into 0.8036, indicating that the corrected reflectivity is much closer to the intrinsic reflectivity.The shapes of the two radar echoes are similar to each other, but the X-band radar reflectivity is seriously attenuated.The maximum reflectivity of convective cores at X-band is about 50 dBZ, while the corresponding intrinsic reflectivity is about 60 dBZ, indicating that the X-band radar echo has a serious distortion due to rain attenuation.
The reflectivity at X-band is corrected by the SSCC method, which is shown in Figure 6.Compared with the uncorrected X-band radar reflectivity in Figure 5a, the corrected reflectivity is effectively compensated and the scope of strong echois extended.For further analysis, the reflectivity is mapped into a 1000 × 1000 matrix grids with a resolution of 150 m.
Figure 7 shows the scatter diagrams of the uncorrected and corrected X-band radar reflectivity 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 uncorrected reflectivity and the intrinsic reflectivity (the green line) is y = 0.5824x + 9.2234, while the fitting line between the corrected reflectivity and the intrinsic reflectivity becomes y = 0.8036x+ 3.8382, referring to Figure 7b.After attenuation correction, the slope of fitting line turns 0.5824 into 0.8036, indicating that the corrected reflectivity is much closer to the intrinsic reflectivity.The shapes of the two radar echoes are similar to each other, but the X-band radar reflectivity is seriously attenuated.The maximum reflectivity of convective cores at X-band is about 50 dBZ, while the corresponding intrinsic reflectivity is about 60 dBZ, indicating that the X-band radar echo has a serious distortion due to rain attenuation.
The reflectivity at X-band is corrected by the SSCC method, which is shown in Figure 6.Compared with the uncorrected X-band radar reflectivity in Figure 5a, the corrected reflectivity is effectively compensated and the scope of strong echois extended.For further analysis, the reflectivity is mapped into a 1000 × 1000 matrix grids with a resolution of 150 m.
Figure 7 shows the scatter diagrams of the uncorrected and corrected X-band radar reflectivity 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 uncorrected reflectivity and the intrinsic reflectivity (the green line) is y = 0.5824x + 9.2234, while the fitting line between the corrected reflectivity and the intrinsic reflectivity becomes y = 0.8036x + 3.8382, referring to Figure 7b.After attenuation correction, the slope of fitting line turns 0.5824 into 0.8036, indicating that the corrected reflectivity is much closer to the intrinsic reflectivity.In order to show the validity of the correction for any path, the reflectivity at X-band with an azimuth angle of 228° is analyzed herein.As shown in Figure 3, the electromagnetic wave successively passes from A to D. Due to the impact of distance, antenna elevation and earth curvature, there are not echoes of the S-band radar in the area A, referring to Figure 8a.Compared with the intrinsic reflectivity (Intrinsic), the uncorrected reflectivity (UnC) nearly has no attenuation in areas A, B and C while with serious attenuation in area D. Figure 8b also illustrates this phenomenon, the φDP increases by nearly 50°, corresponding to intensive rain region, while no increase in areas A, B and C.After attenuation correction using the SSCC method, the corrected X-band radar reflectivity at 33 km has compensated about 10 dBZ (SSCC).The corrected reflectivity at X-band is consistent with the intrinsic reflectivity.However, the corrected reflectivity using the method of Kim et al. [4] (Kim) is lower than the intrinsic 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 reflectivity.This results from the rapid development and fast moving speed of the convective cloud.Because the intrinsic reflectivity shown in Figure 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 influence is significant at the edge of convective cloud but negligible for the stratiform cloud and the 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 (b) (a)  In order to show the validity of the correction for any path, the reflectivity at X-band with an azimuth angle of 228° is analyzed herein.As shown in Figure 3, the electromagnetic wave successively passes from A to D. Due to the impact of distance, antenna elevation and earth curvature, there are not echoes of the S-band radar in the area A, referring to Figure 8a.Compared with the intrinsic reflectivity (Intrinsic), the uncorrected reflectivity (UnC) nearly has no attenuation in areas A, B and C while with serious attenuation in area D. Figure 8b also illustrates this phenomenon, the φDP increases by nearly 50°, corresponding to intensive rain region, while no increase in areas A, B and C.After attenuation correction using the SSCC method, the corrected X-band radar reflectivity at 33 km has compensated about 10 dBZ (SSCC).The corrected reflectivity at X-band is consistent with the intrinsic reflectivity.However, the corrected reflectivity using the method of Kim et al. [4] (Kim) is lower than the intrinsic 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 reflectivity.This results from the rapid development and fast moving speed of the convective cloud.Because the intrinsic reflectivity shown in Figure 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 influence is significant at the edge of convective cloud but negligible for the stratiform cloud and the 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 (b) (a) In order to show the validity of the correction for any path, the reflectivity at X-band with an azimuth angle of 228 • is analyzed herein.As shown in Figure 3, the electromagnetic wave successively passes from A to D. Due to the impact of distance, antenna elevation and earth curvature, there are not echoes of the S-band radar in the area A, referring to Figure 8a.Compared with the intrinsic reflectivity (Intrinsic), the uncorrected reflectivity (UnC) nearly has no attenuation in areas A, B and C while with serious attenuation in area D. Figure 8b also illustrates this phenomenon, the φ DP increases by nearly 50 • , corresponding to intensive rain region, while no increase in areas A, B and C.After attenuation correction using the SSCC method, the corrected X-band radar reflectivity at 33 km has compensated about 10 dBZ (SSCC).The corrected reflectivity at X-band is consistent with the intrinsic reflectivity.However, the corrected reflectivity using the method of Kim et al. [4] (Kim) is lower than the intrinsic 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 reflectivity.This results from the rapid development and fast moving speed of the convective cloud.Because the intrinsic reflectivity shown in Figure 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 influence is significant at the edge of convective cloud but negligible for the stratiform cloud and the 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 has an advantage over Kim et al. [4] in correcting the reflectivity of the convective cloud.In order to analyze the two methods comprehensively, all the radials are used.
Atmosphere 2016, 7, 164 9 of 17 has an advantage over Kim et al. [4] in correcting the reflectivity of the convective cloud.In order to analyze the two methods comprehensively, all the radials are used.The average bias (AB) shown in Figure 10 is defined as below: where  *  x is average value above parameter x, R is the reflectivity at X-band and RS is the intrinsic reflectivity.As shown in Figure 10a, the AB between the uncorrected reflectivity and the intrinsic reflectivity (line UnC) is decreasing with increasing reflectivity.The AB of the UnC is greater than 10 dB, indicating that the attenuation is significantin the rain area.The AB of the Kim and SSCC significantly reduces the difference from the intrinsic reflectivity.To accurately retrieve meteorological products, a resolution of 1 dB for the reflectivity is necessary.Figure 10b shows that there are more than 1 dB differences between the Kim and SSCC from 35 dBZ, illustrating that the SSCC method has a better performance than Kim et al.'s method at correcting convective cloud, especially with reflectivity greater than 35 dBZ.In order to analyze the impact of different sampling resolutions for the SSCC method, the range resolution is set at 0.45 km (SSCC_450) and 0.75 km (SSCC_750) as shown in Figure 11, respectively.The SSCC_750 is further away from the Intrinsic than the SSCC_450, which is closer to the method by Kim et al. [4] (the range resolution is 0.5 km). Figure 11 shows that the decreasing range resolution would lead to reduced correction effect and the SSCC method performs better than the method by Kim et al. [4] for convective cloud.The average bias (AB) shown in Figure 10 is defined as below: where * | x is average value above parameter x, R is the reflectivity at X-band and R S is the intrinsic reflectivity.As shown in Figure 10a, the AB between the uncorrected reflectivity and the intrinsic reflectivity (line UnC) is decreasing with increasing reflectivity.The AB of the UnC is greater than 10 dB, indicating that the attenuation is significantin the rain area.The AB of the Kim and SSCC significantly reduces the difference from the intrinsic reflectivity.To accurately retrieve meteorological products, a resolution of 1 dB for the reflectivity is necessary.Figure 10b shows that there are more than 1 dB differences between the Kim and SSCC from 35 dBZ, illustrating that the SSCC method has a better performance than Kim et al.'s method at correcting convective cloud, especially with reflectivity greater than 35 dBZ.
Atmosphere 2016, 7, 164 10 of 17 The average bias (AB) shown in Figure 10 is defined as below: where  *  x is average value above parameter x, R is the reflectivity at X-band and RS is the intrinsic reflectivity.As shown in Figure 10a, the AB between the uncorrected reflectivity and the intrinsic reflectivity (line UnC) is decreasing with increasing reflectivity.The AB of the UnC is greater than 10 dB, indicating that the attenuation is significantin the rain area.The AB of the Kim and SSCC significantly reduces the difference from the intrinsic reflectivity.To accurately retrieve meteorological products, a resolution of 1 dB for the reflectivity is necessary.Figure 10b shows that there are more than 1 dB differences between the Kim and SSCC from 35 dBZ, illustrating that the SSCC method has a better performance than Kim et al.'s method at correcting convective cloud, especially with reflectivity greater than 35 dBZ.In order to analyze the impact of different sampling resolutions for the SSCC method, the range resolution is set at 0.45 km (SSCC_450) and 0.75 km (SSCC_750) as shown in Figure 11, respectively.The SSCC_750 is further away from the Intrinsic than the SSCC_450, which is closer to the method by Kim et al. [4] (the range resolution is 0.5 km). Figure 11 shows that the decreasing range resolution would lead to reduced correction effect and the SSCC method performs better than the method by Kim et al. [4] for convective cloud.In order to analyze the impact of different sampling resolutions for the SSCC method, the range resolution is set at 0.45 km (SSCC_450) and 0.75 km (SSCC_750) as shown in Figure 11, respectively.The SSCC_750 is further away from the Intrinsic than the SSCC_450, which is closer to the method by Kim et al. [4] (the range resolution is 0.5 km). Figure 11 shows that the decreasing range resolution would lead to reduced correction effect and the SSCC method performs better than the method by Kim et al. [4] for convective cloud.Compared with the method by Bringi et al. [3], the SSCC method does not require an initial and a terminal differential propagation phase of each radial, which could avoid correction errors.To illustrate this problem, we assume the terminal phase is true and examine the errors due to the wrong initial phase.Figure 12 shows correction errors with various initial phases using the method by Bringi et al. [3], whereby 275° (Bringi_275) is the actual radar initial phase and 255° (Bringi_255) and 265° (Bringi_265) are not.The SSCC is consistent with the Bringi_275.In contrast, the Bringi_255 and the Bringi_265 are far away from the Bringi_275, indicating the SSCC method does not require seeking the initial phase and terminal phase but the cumulative distribution is also consistent with that of the true correction results.To verify the applicability of the SSCC method under various precipitation conditions, the stratiform cloud with embedded convection on 26 June 2015 (Figures 13 and 14), and the stratiform 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 of the intrinsic reflectivity.Figures 19 and 20 show that the SSCC method is consistent with the method by Kim et al. [4].The change of the resolution does not lead to correction biases, because the KDP of the stratiform cloud with embedded convection and the stratiform cloud is lower than that of the convective cloud.Figures 21 and 22 illustrate that the corrected cumulative distribution using 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 is also applicable for the stratiform cloud and the stratiform cloud with embedded convection.Note that Compared with the method by Bringi et al. [3], the SSCC method does not require an initial and a terminal differential propagation phase of each radial, which could avoid correction errors.To illustrate this problem, we assume the terminal phase is true and examine the errors due to the wrong initial phase.Figure 12 shows correction errors with various initial phases using the method by Bringi et al. [3], whereby 275 • (Bringi_275) is the actual radar initial phase and 255 • (Bringi_255) and 265 • (Bringi_265) are not.The SSCC is consistent with the Bringi_275.In contrast, the Bringi_255 and the Bringi_265 are far away from the Bringi_275, indicating the SSCC method does not require seeking the initial phase and terminal phase but the cumulative distribution is also consistent with that of the true correction results.Compared with the method by Bringi et al. [3], the SSCC method does not require an initial and a terminal differential propagation phase of each radial, which could avoid correction errors.To illustrate this problem, we assume the terminal phase is true and examine the errors due to the wrong initial phase.Figure 12 shows correction errors with various initial phases using the method by Bringi et al. [3], whereby 275° (Bringi_275) is the actual radar initial phase and 255° (Bringi_255) and 265° (Bringi_265) are not.The SSCC is consistent with the Bringi_275.In contrast, the Bringi_255 and the Bringi_265 are far away from the Bringi_275, indicating the SSCC method does not require seeking the initial phase and terminal phase but the cumulative distribution is also consistent with that of the true correction results.To verify the applicability of the SSCC method under various precipitation conditions, the stratiform cloud with embedded convection on 26 June 2015 (Figures 13 and 14), and the stratiform 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 of the intrinsic reflectivity.Figures 19 and 20 show that the SSCC method is consistent with the method by Kim et al. [4].The change of the resolution does not lead to correction biases, because the KDP of the stratiform cloud with embedded convection and the stratiform cloud is lower than that of the convective cloud.Figures 21 and 22 illustrate that the corrected cumulative distribution using 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 is also applicable for the stratiform cloud and the stratiform cloud with embedded convection.Note that To verify the applicability of the SSCC method under various precipitation conditions, the stratiform cloud with embedded convection on 26 June 2015 (Figures 13 and 14), and the stratiform 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 of the intrinsic reflectivity.Figures 19 and 20 show that the SSCC method is consistent with the method by Kim et al. [4].The change of the resolution does not lead to correction biases, because the K DP of the stratiform cloud with embedded convection and the stratiform cloud is lower than that of the convective cloud.Figures 21 and 22 illustrate that the corrected cumulative distribution using 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 is also applicable for the stratiform cloud and the stratiform cloud with embedded convection.Note that both the SSCC method and the method by Kim et al. [4] may have no significant effect or lead to slightly worse attenuation correction due to the error of the integration resolution when correcting stratiform rain if the rainfall is very small.both the SSCC method and the method by Kim et al. [4] may have no significant effect or lead to slightly worse attenuation correction due to the error of the integration resolution when correcting stratiform rain if the rainfall is very small.both the SSCC method and the method by Kim et al. [4] may have no significant effect or lead to slightly worse attenuation correction due to the error of the integration resolution when correcting stratiform rain if the rainfall is very small.both the SSCC method and the method by Kim et al. [4] may have no significant effect or lead to slightly worse attenuation correction due to the error of the integration resolution when correcting stratiform rain if the rainfall is very small.

Conclusions and Discussion
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 Kim et al.'s method.The proposed method improved the correction resolution and effect, adapting a slide window consisting of 10 gates.
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 results from the methods by Bringi et al. [3] and Kim et al. [4], as well as the intrinsic reflectivity at X-band calculated from the reflectivity at the S-band.It is found that the reflectivity at X-band 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 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 precipitation cloud is much less than that of the convective cloud.For this reason, the SSCC 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 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.
In summary, the SSCC method has three advantages as follows: 1. Improving the correction resolution; 2. Having no need for seeking the initial and terminal 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 SSCC method by the length (1.5 km) of the sliding window and this is a more significant effect than the resolution.

Conclusions and Discussion
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 Kim et al.'s method.The proposed method improved the correction resolution and effect, adapting a slide window consisting of 10 gates.
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 results from the methods by Bringi et al. [3] and Kim et al. [4], as well as the intrinsic reflectivity at X-band calculated from the reflectivity at the S-band.It is found that the reflectivity at X-band 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 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 K DP of the two kinds of precipitation cloud is much less than that of the convective cloud.For this reason, the SSCC 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 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.
In summary, the SSCC method has three advantages as follows: 1. Improving the correction resolution; 2.
Having no need for seeking the initial and terminal 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 SSCC method by the length (1.5 km) of the sliding window and this is a more significant effect than the resolution.

Figure 2 .
Figure 2. The locations of the X-band radar and the S-band radar,the X-band radar is at Shunyi (SY, 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 TJ in the Figure are the abbreviation of Beijing City, Hebei Province and Tianjin City, respectively.

Figure 2
shows the locations of the two radars.The X-band radar (at ShunyiSY, 116.68 • E, 40.19 • N) is located at the northeast of the S-band radar (at DaxingDX, 116.47 • E, 39.81 • N).The straight-line distance between the two radars is about 46 km.Atmosphere 2016, 7, 164 5 of 17

Figure 2 .
Figure 2. The locations of the X-band radar and the S-band radar,the X-band radar is at Shunyi (SY, 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 TJ in the Figure are the abbreviation of Beijing City, Hebei Province and Tianjin City, respectively.

Figure 2 .
Figure 2. The locations of the X-band radar and the S-band radar,the X-band radar is at Shunyi (SY, 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 TJ in the Figure are the abbreviation of Beijing City, Hebei Province and Tianjin City, respectively.
Figure 3 shows the plane position indicator (PPI) of the X-band radar at elevation 3 • at 14:45 Beijing Time (BJT), 19 June 2015.Three strong echo cores of convective cloud are situated between the two radars and the largest reflectivity observed by the S-band radar is about 60 dBZ.Atmosphere 2016, 7, 164 6 of 17

Figure 4 .
Figure 4. Scattering simulation of intrinsic reflectivity at X and S bands.The blue line stands for the intrinsic reflectivity at X-band is equal to the reflectivity at S-band.The red curve is obtained by scattering simulation.

Figure 5 .
Figure 5. (a) Original reflectivity at X-band for convective cloud on 19 June 2015; (b) the intrinsic reflectivity at X-band.The color shade guide is the reflectivity factor in unit of dBZ and the X-Y axis is the range in unit of km in the figure and the following figures.

Figure 4 . 17 Figure 4 .
Figure 4. Scattering simulation of intrinsic reflectivity at X and S bands.The blue line stands for the intrinsic reflectivity at X-band is equal to the reflectivity at S-band.The red curve is obtained by scattering simulation.

Figure 5 .
Figure 5. (a) Original reflectivity at X-band for convective cloud on 19 June 2015; (b) the intrinsic reflectivity at X-band.The color shade guide is the reflectivity factor in unit of dBZ and the X-Y axis is the range in unit of km in the figure and the following figures.

Figure 5 .
Figure 5. (a) Original reflectivity at X-band for convective cloud on 19 June 2015; (b) the intrinsic reflectivity at X-band.The color shade guide is the reflectivity factor in unit of dBZ and the X-Y axis is the range in unit of km in the figure and the following figures.

Figure 7 .
Figure 7. Scatter diagrams of the uncorrected (a) and corrected (b) X-band radar reflectivity versus 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.

Figure 7 .
Figure 7. Scatter diagrams of the uncorrected (a) and corrected (b) X-band radar reflectivity versus 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.

Figure 7 .
Figure 7. Scatter diagrams of the uncorrected (a) and corrected (b) X-band radar reflectivity versus 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.

Figure 8 .
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 (SSCC) and the intrinsic reflectivity (Intrinsic); (b) the measured ΨC and the filtered φDP.

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

Figure 8 .
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 (SSCC) and the intrinsic reflectivity (Intrinsic); (b) the measured Ψ C and the filtered φ DP .

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

Figure 9 .
Figure 9. Cumulative distribution of reflectivity for the convective cloud.In the figure, line Unc is uncorrected reflectivity, line Kim stands for reflectivity corrected by Kim et al.'s method, line SSCC represents reflectivity corrected by the SSCC method, and line Intrinsic stands for intrinsic reflectivity.

Figure 10 .
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 SSCC; (b) the AB of the difference between the Kim and the SSCC.

Figure 9 .
Figure 9. Cumulative distribution of reflectivity for the convective cloud.In the figure, line Unc is uncorrected reflectivity, line Kim stands for reflectivity corrected by Kim et al.'s method, line SSCC represents reflectivity corrected by the SSCC method, and line Intrinsic stands for intrinsic reflectivity.

Figure 9 .
Figure 9. Cumulative distribution of reflectivity for the convective cloud.In the figure, line Unc is uncorrected reflectivity, line Kim stands for reflectivity corrected by Kim et al.'s method, line SSCC represents reflectivity corrected by the SSCC method, and line Intrinsic stands for intrinsic reflectivity.

Figure 10 .
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 SSCC; (b) the AB of the difference between the Kim and the SSCC.

Figure 10 .
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 SSCC; (b) the AB of the difference between the Kim and the SSCC.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Figure 17 . 17 Figure 16 .
Figure 17.Cumulative distribution of reflectivity for the stratiform rain with embedded convection.

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

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

Figure 20 .
Figure 20.Average bias of reflectivity for the stratiform rain.

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

Figure 19 . 17 Figure 19 .
Figure 19.Average bias of reflectivity for the stratiform rain with embedded convection.

Figure 20 .
Figure 20.Average bias of reflectivity for the stratiform rain.

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

Figure 20 .
Figure 20.Average bias of reflectivity for the stratiform rain.

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

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

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

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

Table 1 .
System Characteristics of the IAP-714XDP-A radar.