Discrete Dynamics in Nature and Society

Volume 2015 (2015), Article ID 479804, 6 pages

http://dx.doi.org/10.1155/2015/479804

## Wind Shear Target Echo Modeling and Simulation

^{1}School of Computer Science and Engineering, Chongqing University of Technology, Chongqing 400054, China^{2}Postdoctoral Research Station of Information and Communication Engineering, Chongqing University, Chongqing 400030, China

Received 3 December 2014; Revised 19 March 2015; Accepted 23 March 2015

Academic Editor: Filippo Cacace

Copyright © 2015 Xiaoyang Liu 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

Wind shear is a dangerous atmospheric phenomenon in aviation. Wind shear is defined as a sudden change of speed or direction of the wind. In order to analyze the influence of wind shear on the efficiency of the airplane, this paper proposes a mathematical model of point target rain echo and weather target signal echo based on Doppler effect. The wind field model is developed in this paper, and the antenna model is also studied by using Bessel function. The spectrum distribution of symmetric and asymmetric wind fields is researched by using the mathematical model proposed in this paper. The simulation results are in accordance with radial velocity component, and the simulation results also confirm the correctness of the established model of antenna.

#### 1. Introduction

As for airborne weather radar, wind shear is a unique atmosphere phenomenon. Microburst is a main form in wind shear. Wind shear often refers to the wind speed or size changing suddenly. Wind shear especially low-level wind shear can cause the maximum damage to airplane. In the aeronautical meteorology, according to the structure of the wind field, wind shear can mainly consist of three kinds of basic situation: vertical wind shear of horizontal wind, horizontal wind shear of horizontal wind, and wind shear of vertical wind. In the actual atmosphere, these three kinds of wind shear can affect flight. According to the airplane relative to the wind vector, the wind shear can be divided into the following: wind shear, cross wind shear, partial wind shear, and head wind shear four forms [1–5].

The scale and strength of low-level wind shear are closely related to wind shear weather system and environmental conditions. Because the phenomenon of wind shear belongs to a small probability event, the existence time of this unique atmosphere phenomenon is only a few minutes [6–9]. It is not repeated. If we rely on the actual test method, not only the cost is very high, but also the risk is quite large, so it is necessary for us to study real wind shear weather change rule of the simulation method [10].

When people realize the serious harm of wind shear, people have invented many equipment which can detect wind field and wind shear, including ground anemometer theodolite, radiosonde wind profile, line radar laser radar, Doppler weather radar, Doppler sound radar, and airborne sensors. The malignant plane crash accident is mainly caused by wind shear [11]. Therefore, it is the most effective method for detecting low-level wind shear in time, so that the airplane has enough time and space to avoid it [12].

The testing technology of low-level wind shear is mainly by means of signal processing algorithm, analyzing radar echo signal of wind shear [13]. The echo power, wind speed of Doppler, and spectrum width parameters can be extracted by using signal processing algorithm. The wind speed of Doppler is the most important parameter among all the parameters, because it reflects the wind field characteristics of the movement [14–16].

The paper is organized as follows. Section 2 contains mathematical model of point target echo, and the signal model of target echo is established in Section 3. Wind field and antenna model are proposed in Section 4, followed by the analysis of simulation results in Section 5. Finally, Section 6 contains the conclusions.

#### 2. The Proposed Mathematical Model of Point Target Echo

There is a relative motion between airborne weather radar and the meteorological scattering target. So the Doppler frequency shift consists of two parts: the speed of an airplane and meteorological scattering target. For airborne pulsed Doppler radar detecting meteorological target of wind shear, we assume that the speed of airplane is , the average radial velocity among meteorological scattering target is , the initial distance between the airplane and the meteorological scattering target is , and the distance of airplane away from meteorological scattering unit is . The relationship between and time is as follows:

The time rate of the phase iswhere is the Doppler frequency shift caused by the airplane and is the Doppler frequency shift caused by the meteorological scattering target. Equation (2) indicates that the Doppler frequency shift can be extracted which is caused by the target movement of wind shear rain echo.

The average power of wind shear target rain echo can be expressed aswhere is the transmit power, is the antenna gain, is the wavelength of airborne weather radar, the scattering rate of meteorological target is , system loss is , and the distance between target and meteorological target is .

We assume that the body reflectivity of meteorological target is ; represents the target volume unit.

As for airborne weather radar, we assume that the target is the ideal point target; the effective scattering cross section of the target is . Sowhere the body reflectivity of meteorological target can be expressed aswhere is the wavelength of airborne weather radar. represents the diameter of the target sphere, is the dielectric constant of scattering particle, and denotes the reflection factor.

We assume that the radar transmitted signal is a narrow signal. It can be expressed aswhere

The is carrier frequency. So, echo signal can be regarded as a signal delay form of transmitted signal. Its amplitude is multiplied by a scale factor .

We assume that the complex reflection constant is . We also defined the scale factor :

The echo signal of the mathematical formula can be expressed aswhere time delay can be expressed as

Putting (2) into (10), we can get

Then by putting (11) into (9), we can getwhere is time delay of target echo.

So, for a single wind shear meteorological target scattering body, echo signal of radar target can be expressed aswhere is the total path length and is the random phase caused by the scatter body. is the amplitude of echo signal. can be expressed aswhere denotes the average power of the wind shear rain echo.

#### 3. Signal Model of Target Echo

We assume that denotes the speed component of target scatter body; represents the speed component of airplane along the radial. is constant. We defined

The in-phase component and quadrature component of the target echo signal can be expressed, respectively, aswhere is the random phase of the scatter target and represents the transmitted phase error. is the receiver noise. expresses the number of pulses. is the pulse time interval.

Signal amplitude can be obtained by radar equation and reflectivity factor. can be expressed as wherewhere is the constant of radar equation and represents the receiver loss. indicates the volume of the scatter body. shows the multipath fading factor. is the antenna gain. is wind shear wind field reflectivity.

Signal phase is mainly decided by the Doppler frequency shift. Doppler frequency shift consists of two parts, and .

The total rain echo signal phase can be expressed as

The principle diagram of wind shear target echo simulation is shown in Figure 1.