Advances in Meteorology

Volume 2017, Article ID 8621239, 8 pages

https://doi.org/10.1155/2017/8621239

## Regional Attenuation Correction of Weather Radar Using a Distributed Microwave-Links Network

College of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing, Jiangsu, China

Correspondence should be addressed to Xi-chuan Liu; moc.liamg@58cxuil

Received 28 January 2017; Revised 11 April 2017; Accepted 27 April 2017; Published 22 May 2017

Academic Editor: Hongkai Gao

Copyright © 2017 Yang Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The complex temporal-spatial variation of raindrop size distribution will affect the precision of precipitation quantitative estimates (QPE) produced from radar data, making it difficult to correct echo attenuation. Given the fact that microwave links can obtain the total path attenuation accurately, we introduce the concept of regional attenuation correction using a multiple-microwave-links network based on the tomographic reconstruction of attenuation coefficients. Derived from the radar-based equation, the effect of rainfall distribution on the propagation of radar and microwave link signals was analyzed. This article focuses on modeling of the tomographic reconstruction of attenuation coefficients and regional attenuation correction algorithms. Finally, a numerical simulation of regional attenuation correction was performed to verify the algorithms employed here. The results demonstrate that the correction coefficient (0.9175) falls between the corrected and initial field of radar reflectivity factor (root mean square error, 2.3476 dBz; average deviation, 0.0113 dBz). Compared with uncorrected data, the accuracy of the corrected radar reflectivity factor was improved by 26.12%, and the corrected rainfall intensity distribution was improved by 51.85% validating the region attenuation correction algorithm. This method can correct the regional attenuation of weather radar echo effectively and efficiently; it can be widely used for the radar attenuation correction and the promotion of quantitative precipitation estimation by weather radar.

#### 1. Introduction

The attenuation of precipitation on the propagation of electromagnetic waves is one of the main factors that affect the quantitative precipitation estimation (QPE) by weather radar [1, 2]. The attenuation effect will cause a decrease in radar echo intensity and detection area. In particular, at relatively far distances, radar reflectivity factors are lower than actual values and cannot reflect the actual distribution of rainfall. For short-wavelength radar, such as X-band radar, this type of attenuation is particularly serious. The development of correction techniques that address the attenuation of radar echoes has been extensively analyzed.

The most important aspect of attenuation correction is to obtain the characteristic of microwave attenuation. In some weather radar applications, researchers desire to measure attenuation along the propagation path to improve the effect of attenuation correction. Lin and Lv [3] proposed the use of a microwave radiometer to measure the total path attenuation. Serrar et al. [4] suggested the estimation of total attenuation of the echoes via the echo difference between sunny and rainy days. However, variations in terrain and fluctuations in the refraction in the path limit the usefulness of this method. Perez [5] introduced a method that can be used to obtain the attenuation of X-band radar by using dual-wavelength radar (S, X) based on the assumption that the S-band radar is with no attenuation. However, during relatively intense rainfall events, the attenuation difference between two bands is notably small and does not provide additional effective X-band attenuation information. The surface reference technique (SRT) is commonly used with space-borne precipitation radar to calculate the path attenuation by comparing the measured echo differences between areas of rainfall and nonrainfall. This method provides the advantage that the relative error decreases with an increase in integral path, but the reflection and attenuation of the electromagnetic waves are different because of the apparent fluctuation of the ground surface and humidity, which causes the SRT to have some limitations [6].

A new approach for rainfall measurement was recently presented using the attenuation caused by rainfall that affects the microwave signals for wireless data exchange [7, 8]. Microwave propagation attenuation can be obtained by detecting the signal level of both the transmitter and receiver of a microwave link. During a rainfall event, the microwave is attenuated by falling raindrops when passing through the rain area. The degree of microwave attenuation can be obtained by measuring the difference between clear and rainy days, and these data can be used to retrieve rainfall intensity and its spatial distribution [9, 10] and correct the radar reflectivity factor as a constraint. Krämer et al. [11, 12] described forward and backward iterative algorithms that can be used to correct the X-band radar reflectivity factor using a 10.5/17.5 GHz dual-frequency microwave link. Krämer and Verworn [13] used a dual-frequency microwave link to correct the C-band radar reflectivity factor. Cummings et al. [14] explored the use of two single-frequency microwave links in weather radar correction. However, these studies only enable corrections of the radar signal along the ray under the link path with a narrow range of a radial beam. Therefore, expanding the correction range using microwave links is worth exploring.

To improve the correction of radar attenuation by using microwave links, based on a microwave link for single-beam correction, this paper proposes extending the region of radar attenuation correction using a multiple-microwave links network. In a radar detection area with simultaneously multiple communication links, several microwave links form a network that satisfies a certain topology. Deriving the attenuation coefficient of the grids based on the attenuation information of the microwave links network is the key to obtaining the total attenuation of each radial path of the radar as a reference. Therefore, in view of the above analysis, this paper presents a new method that is similar to that used in medical computerized tomography (CT) imaging technology. The area of radar and microwave link monitoring is addressed using discrete grids.

Section 2 of this paper analyzes the effects of rainfall distribution on the propagation of radar signals and microwave link signals. Section 3 analyzes and establishes the models of tomographic reconstruction of the attenuation coefficients while Section 4 proposes the regional attenuation correction algorithm, where a numerical simulation experiment spanning 20 × 20 km was performed to verify the algorithm. Section 5 provides a summary and concluding remarks.

#### 2. Theory of Radar Echo Attenuation Correction

When electromagnetic waves propagate in the atmosphere, the physical effects of weather target scattering, absorption, and reflection cause the energy of the propagation path to become attenuated. Suppose that is the average echo power without considering the attenuation of the meteorological target and is the average echo power after the attenuation is considered. The attenuation characteristic can be described by the attenuation factor ; then

Suppose is the attenuation value of the received power, which is affected by rainfall and other factors between radar and the target; this attenuation value can be expressed as

Next, the integral from 0 to is calculated, where is the distance between the radar and the target, and the average echo power is

Therefore, the dimension of is 1/km. Because the attenuation of the received power is usually expressed in decibels (dB), the attenuation coefficient is converted into in dB/km. According to , (3) can be written as

Further derivation shows that

If we use the radar reflectivity observation (mm^{6}/m^{3}) and the real radar reflectivity (mm^{6}/m^{3}) of the target instead of the echo power in the previous derivation process, thenwhere is the distance between the radar and the detection target, is the attenuation factor, and is the attenuation coefficient in dB/km. The logarithm of (7) is expressed as

In the process, we use the radar reflectivity factor. The conversion formula between radar reflectivity (mm^{6}/m^{3}) and radar reflectivity factor* z* (dBz) is

Further derivation shows thatwhere is the attenuation coefficient in dB/km; is the total attenuation value of the radar path after integration in units of dB; is the corrected radar reflectivity factor, and is the radar-measured reflectivity factor. The accurate determination of the radar path integral attenuation is the key to attenuation correction. Therefore, using the attenuation of microwave link along the path , the attenuation correction process can be expressed as

#### 3. Tomographic Model of the Attenuation Coefficient

##### 3.1. Reconstruction of the Grid Attenuation Using Microwave Links

CT (computerized tomography) imaging technology is mainly based on ray scanning, where the attenuation of a ray power pass is obtained through the wave field. Tomographic techniques include techniques aimed toward reconstructing the cross-sectional distribution of a parameter from a set of one-dimensional transmission or reflection data, measured and collected along many different paths crossing the spatial domain where the object field has to be reconstructed. The theoretical basis of a CT image reconstruction algorithm is based on a Radon transform and Fourier slicing theorem [15]. This is characterized as follows: the projection data contain the characteristic information of the original image, which can be reconstructed with the information; in order to realize the reconstruction of the image, theoretically, an infinite number of continuous projection data is needed.

Radon transform is a linear integral projection transformation, and assumes the distribution function of a two-dimensional target is ; then Radon transform* p* for the function is integral along the straight line* z*:

Therefore, the problem of tomographic image reconstruction involves the calculation of the image function by the projection data . The meanings of the other quantities in (12) are shown in Figure 1. Meanwhile, the Radon inverse transform satisfies