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

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## Abstract

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## 1. Introduction

_{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.

_{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.

_{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}.

_{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.

## 2. Radar Feature

## 3. The Slide Self-Consistency Correction Method

_{h}(mm

^{6}m

^{−3}) in linear scale and Z

_{H}(dBZ) in logarithm scale have the following relationship:

_{H}is specific attenuation in decibels per kilometer. The change in differential propagation phase is as follows:

_{0}and r

_{1}are the beginning and ending range gate, respectively.

_{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 $\Delta {\mathsf{\varphi}}_{DP}$. Under the assumption that there is a linear relationship between A

_{H}and K

_{DP}, the final formula of A

_{H}is given by

_{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.

_{DP}is in °·km

^{−1}and c is set as a constant 1.

_{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.

_{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.

_{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.

_{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:

## 4. Result

_{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.

_{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.

_{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.

_{DP}of the stratiform cloud with embedded convection and the stratiform cloud is lower than that of the convective cloud. Figure 21 and Figure 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.

## 5. Conclusions and Discussion

_{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.

- Improving the correction resolution;
- Having no need for seeking the initial and terminal differential phases;
- Good performance in correcting convective cloud.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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

**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.**(

**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.**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.**(

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

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

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

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

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

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

Item | IAP-714XDP-A Radar |
---|---|

Frequency | 9.370 GHz |

Antenna type | 2.4 m diameter parabolic antenna |

Antenna gain | 44.78 dB |

Beam width | 1° |

Pulse width | 0.5/1/2 μs |

Pulse repetition frequency | 500~2000 Hz |

Polarization | Horizontal/Vertical |

Observation range | 75/150/300 km |

Observation parameters | Z_{H}, Z_{DR}, φ_{DP}, K_{DP}, ρ_{HV}, V, W |

Doppler processing | PPP/FFT |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Feng, L.; Xiao, H.; Wen, G.; Li, Z.; Sun, Y.; Tang, Q.; Liu, Y.
Rain Attenuation Correction of Reflectivity for X-Band Dual-Polarization Radar. *Atmosphere* **2016**, *7*, 164.
https://doi.org/10.3390/atmos7120164

**AMA Style**

Feng L, Xiao H, Wen G, Li Z, Sun Y, Tang Q, Liu Y.
Rain Attenuation Correction of Reflectivity for X-Band Dual-Polarization Radar. *Atmosphere*. 2016; 7(12):164.
https://doi.org/10.3390/atmos7120164

**Chicago/Turabian Style**

Feng, Liang, Hui Xiao, Guang Wen, Zongfei Li, Yue Sun, Qi Tang, and Yanan Liu.
2016. "Rain Attenuation Correction of Reflectivity for X-Band Dual-Polarization Radar" *Atmosphere* 7, no. 12: 164.
https://doi.org/10.3390/atmos7120164