澳门班雷达气象学雷达探测

1、多普勒雷达测速原理和相关问题From Josh WurmanNCAR S-POL DOPPLER RADAR黄兴友2015-10-14南京信息工程大学大气物理学院 Doppler 频移: A frequency shift that occurs in electromagnetic waves due to the motion of scatterers toward or away from the observer.Doppler 雷达: A radar that can determine the frequency shift through measurement of the

2、phase change that occurs in electromagnetic waves during a series of pulses.Analogy: The Doppler shift for sound waves is the frequency shift that occurs as race cars approach and then recede from a stationary observer入射电磁波的电场散射回波的电场发射波和回波的时间差为将时间差带入得到回波信号的频率可以由括号中变量对时间求导数、再除以2p得到：多普勒信息的提取多普勒频率雷达目标多

3、普勒雷达工作原理fd的提取回波的幅度:回波的相位:径向速度多普勒雷达功率谱和速度谱宽多普勒雷达谱宽信息的提取其中R(Ts)是一个延迟脉冲的自相关函数，S是零延迟的自相关函数。其中R(1）即为R(Ts). M是取样总数(32以上)；V是包含噪声的样本信号（I + iQ），N是噪声功率一次龙卷回波的信号谱多普勒频率和移动方向如果背向运动（远离雷达），则Doppler频移为负 回波频率降低（红移），用红色/暖色表示如果朝向移动，则Doppler频移为正，回波频率变高，用蓝色/冷色表示在多普勒速度图像上，大多采用冷暖颜色区分目标朝向或远离雷达蓝色:朝向雷达红色: 离开雷达径向速度图像 （反映出中尺度气

4、旋）径向速度图像 （反映出中尺度气旋）VAD图像-反映风向的变化VWP图像-反映不同高度的水平风向多普勒频移(fd=2V/)与频率、径向速度的关系雷达工作频率X 波段 C 波段S 波段9.37 GHz 5.62 GHz 3.0 GHz径向速度1 m/s10 m/s50 m/s62.5 Hz 37.5 Hz 20.0 Hz625 Hz 375 Hz 200 Hz3125 Hz 1876 Hz 1000 Hz相对雷达风工作频率来说，多普勒频移非常小: 因此, 多普勒雷达系统的发射机和接收机的频率必须非常稳定，否则，难以检测出由相对移动产生的多普勒频移问题： 哪个波段的多普勒雷达更好 ？多普勒雷达测

5、量的最大径向速度采样定理：Nyquist指出，采样频率必须达到信号频率的两倍以上。 雷达系统的采样频率是 PRF 信号频率是 fd = 2V/PRF = 2 fd = 4V/ V 0) RED SHIFTThe Doppler frequency is positive (higher frequency, blue shift) for objects approaching the radar (vr0) VIOLET SHIFTIn VPR the radial velocity accounts for hydrometeor terminal velocity and vertica

6、l windNB: there is no consensus on the convention on velocity signsMagnitude of the Doppler ShiftTransmitted FrequencyW band X band C band S band 94 GHz 9.37 GHz5.62 GHz 3.0 GHzRadial velocity1 m/s10 m/s50 m/s625 Hz 62.5 Hz 37.5 Hz 20.0 Hz6.25 KHz 625 Hz 375 Hz 200 Hz31.25 KHz 3125 Hz 1876 Hz 1000 H

7、zThese frequency shifts are very small (compared to the radar-frequency 6 order of magnitude lower): for this reason, Doppler radars must employ very stable transmitters and receivers (klystron or magnetron systems)Mapping velocities into particle size: rationaleDifferent particles have different ve

8、locities with larger particles typically falling faster. This is the key feature for using Doppler spectra in microphysical retrievals. Unambiguous (hydrometeor-type dependent) relationships between particle fall speeds and diameters mirror into an unambiguous relationship between Doppler frequency

9、shifts and diameters profile of Doppler spectra can provide range-resolved information about the size distribution of the particles contained in the radar backscattering volume.Raindrops terminal velocitiesSaturation of terminal velocities 71Velocity-size relationship for other hydrometeorsThere is

10、a larger dynamics in terminal velocities for rain than for graupel and snow snow is particularly challenging. On the other hand the difference between different hydrometeors immediately helps in hydrometeor classification.Spectral reflectivity factorParticle size distribution in 1/(m3mm)2-way attenu

11、ationRadar equation for distributed targetsPSDFrom Mie/scattering theoryWhen considering the return power at different frequencies we can define the spectral powerApplying the same reasoning to the reflectivity factor we can define a spectral reflectivity factor Jacobian for mapping D into vWe tend

12、to refer this to the Doppler spectrumRadar volume at range r73Broadening of an ideal Doppler spectra for distributed targetVelocity of individual targets in contributing volume vary due to:3) Wind shear2) Vertical wind speed and turbulenceDifferential fall velocity of targets (particularly at high e

13、levation angles, e.g. for vertical incidence)4) Finite beamwidth Ideal quiet air Doppler spectrum RR=5 mm/hSpectral reflectivity factorIdeal quiet air Doppler spectrum: RR=5 mm/hSpectral reflectivity factorMie oscillations sizing infoRayleigh regionIce particles: more difficult to compute sback(Stef

14、ans talk)Ideal quiet air Doppler spectrum: RR=5 mm/hSpectral reflectivity factorRaindrop terminal velocityNot a good mapping between diameters and velocities: all large raindrops end up in the same velocity binSpectral reflectivity factorLinear units! The dynamic range of rain reflectivity values is

15、 strongly reduced at W-bandIdeal quiet air Doppler spectrum: RR=5 mm/hSpectral reflectivity factorLinear units! The dynamic range of rain reflectivity values is strongly reduced at W-bandIdeal quiet air Doppler spectrum: RR=5 mm/hEffectof frequencySpectral reflectivity factorRegion wheremulti-freque

16、ncyapproach can be usefulKollias et al., 2002: detection of the Mie notch at D = 1.65 mm, i.e. Vfall = 5.8 m s-1Ideal quiet air Doppler spectrum: RR=5 mm/hSpectral reflectivity factorKollias et al., 2002: detection of the Mie notch at D = 1.65 mm, i.e. Vfall = 5.8 m s-1Ideal quiet air Doppler spectr

17、um: RR=5 mm/hReflectivityMean radial velocitySpectral widthThe moments of the Doppler spectraEd will introduce additional spectral moments!Moments of rain spectra for RR=5 mm/hSpectral reflectivity factorOnly due to PSDMP distributionInversion and retrieval of PSDSpectral reflectivity factorIf the m

18、easured spectrum had this shape thenThe particle size distribution N(D) can be directly derived from the radar return power S(V)Is this inversion possible? N.B This is what is done in several algorithm, e.g. the MRR retrieval. But Atlas et al. 1973 already recognized that even when updrafts are esti

19、mated to better than about 0:25m/s errors in the concentration of raindrops for certain size ranges may exceed a factor of two.Effect of Vertical Air motion and turbulenceOne size particles Different size particles 84The presence of turbulent vertical air motion add a Gaussian distributed random com

20、ponent to the terminal velocity of the raindropsIn reality there is always turbulent air motions in our radar spectrum: some droplets will be slow down due to turbulent upward motions, some of them accelerate due to downward motions.85Effect of turbulence on W-band spectrumThere is a smearing of the

21、 no air motion Doppler spectrum, first Mie notch can disappearFirst Mie notchOne order ofmagnitudeWhat controls the magnitude of the broadening t?OConnor et al. 2005; Bouniol et al., 2003, Kollias et al., 2001Unresolved scales of turbulenceThe energy (variance) can be estimated using the variance of

22、 the mean Doppler velocityRetrieve the eddy dissipation rate 86st related to the eddy dissipation rate esmallest scale probed by the Doppler radar Kolgomorov length scale describing the scattering volume dimension includes large eddies traveling through the sampling volume within the radar dwell tim

23、eKollias et al., 2002Detailed formulas can be foundIn Frisch and Clifford, JAS, 1974Turbulence broadening t88Linear wind fields result in Doppler spectrum broadening (detailed formulas in Doviak-Zrnic). Discontinuous (step function) wind field profile results in bimodal Doppler spectrum.Wind shear b

24、roadening sh If the vertical wind is changing inside the radar backscattering volume (either moving parallel or perpendicular to the radar beam) this will add extra broadening to the spectrum89Wind shear broadening sh If the vertical wind is changing inside the radar backscattering volume (either mo

25、ving parallel or perpendicular to the radar beam) this will add extra broadening to the spectrumWind shear of 10-2-10-1 s-1 are possible close to convective core w variation of 10 m/s in 100mKollias et al., JAS, 2001The cross-beam wind velocity induces a broadening proportional to the beamwidth beca

26、use of the radial component of the cross-beam wind vector pointing in directions away from the beam axisFor a 9 degree beamwidth wind profiler (typical 915-MHz) B is 1.4 ms-1 for a 30 ms-1 cross wind velocity For a 0.5 degree beamwidth cloud radar (typical cloud radar) B is 0.08 ms-190Finite beamwid

27、th broadening B UFor a Gaussin circular antennaParticles along the green line appearto recede from the radar EarthCARE CPRFor the EarthCARE CPR, the beamwidth is 0.095 degrees but the satellite (cross beam wind) is 7,600 ms-1 and B is 3.7 ms-191Spaceborne-radars: finite beamwidth broadening B The sa

28、me reasoning applies if the radar moves. LEO satellite moves quite fast huge effect even withSmall beamwidthsApparently receding from radar/going downwardApproaching/upward Thats why Doppler spectra from air-borne andSpace-borne radars are not so usefulRadar Doppler Spectrumrising particlesfalling particlesclouddrizzlelight rainmoderaterainheavyrain*ice/snownoiseVelocity (m/s)Received Power (dB)Particle sizeincreasingParticle size decreasingupdraftsdowndraftsturbu