EM waves and its propagation 雷達氣象學講義-台大周仲島 • Electromagnetic or radio waves are electric E and magnetic H force fields that propagate through space at the speed of light and interact with matter along their paths. • These interactions cause the scattering, diffraction, and refraction also common to visible light. 散射、繞射、折射
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EM waves and its propagation 雷達氣象學講義-台大周仲島jou-p3.as.ntu.edu.tw/P3/file/teaching/c1386322959.pdf · EM Waves and Propagation Wave propagation speed, wavelength,
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EM waves and its propagation 雷達氣象學講義-台大周仲島
• Electromagnetic or radio waves are electric E and magnetic H force fields that propagate through space at the speed of light and interact with matter along their paths. • These interactions cause the scattering, diffraction, and refraction also common to visible light. 散射、繞射、折射
Electric field E (r, θ, φ, t) = A (θ, φ)/r cos[2πf(t-r/c)+ ψ] = A(θ, φ)/r exp[j2πf (t-r/c) + jψ] V m-1, A(θ, φ)/r is the amplitude and 2πf(t-r/c)+ψ is the phase of the periodic electric field, r is the wave propagating distance, and ψ is the transmitter phase angle.
何謂極化 (Polarization)
If we place a dielectric in an electric field, induced surface charges appear which tend to weaken the original field within the dielectric.
水平與垂直極化,線性極化 (linear polarization)
二次(橢圓)極化(elliptical polarization)
Polarization
Circular-polarized electric field
Electric field E (r, θ, φ, t) = A (θ, φ)/r exp[j2πf(t-r/c)+ jψ]
The time rate of change of β [=2πf(t-r/c)+ψ] is frequency, and it can be seen that frequency is composed of two items: ω = 2πƒ is the transmitted or carrier frequency ( radians s-1 ), and (2πƒ/c) dr/dt is a Doppler shift that would be experienced by an observer at r moving at velocity dr/dt. The time dependence of the phase is important in understanding the principles of Doppler radar.
(magnitude of the complex Poynting vector S = E x H*/2 波印亭向量顯示電磁能流的方向)
S (r, θ, φ) = ½ E • E* / η0
= ½ A2 (θ, φ) / [η0 r2] W m-2 η0 is the wave impedance電磁波傳播時的阻抗,是電場振幅和磁場振幅比值,在地球大氣為常數 = 377 ohms.
Time averages are averages of power over a cycle or period ƒ-1 of the wave;but if power is pulsed, then A and S are functions of time and, moreover, the average of power over a cycle of ƒ can change during the pulse.
Products of S with areas represent the power that is received, absorbed, scattered, and so on.
Time-averaged power(energy flow)density 電場強度S
The angular resolution is well approximated by (Bean and Duton 1968) : ∆θ ≅ 104 λ / D deg , where D is the diameter of the antenna system. 雷達的天線大小與所發射電磁波長決定該雷達系統可解析之最小角度。
考慮一個均質大氣, 若波束所走路徑為一直線之相當地球半徑為ae= kea=a/[1+ a(dn/dh)]. 在此一相當地球上, 直線波束離地表之高度和原地球彎曲波束路徑離地表高度相同。研究人員發現在近地面一至二公里高度-dn/dh ≈ -1/4 a (n隨高度變化為線性關係) ,且dh/ds<<1(低仰角) 狀況時,有效地球半徑為 ae= a /{1+ a[dn/dh]} = 4/3a, 在此模型下
h = [r2 + (kea)2 +2rke a sinθe ] ½ - kea , s = ke a sin-1 [r cosθe / (ke a+h)]
利用正弦定律, 彎曲之雷達波束離地表高度可以下式表示 h = rc[sinψr / sin ψ] – a
若是 – (dn/dh)-1 = rc= a, 則 h =0, 表示雷達波束仰角 θe = 0 的路徑將留在地表亦即所謂陷波狀態.
Ray paths for an ae = 4a/3 model (dn/dh = -1/4a, linear dependent, -40 N km-1) and reference standard atmosphere with exponentially dependent refractive index {N(h) = Ns exp (-0.1439h)}, Ns=313.
Note there is large difference of N between these two models above 2 km height. That is because of the assumption of dh/ds<<1. However, the differences of ray paths are not large at all. So, use of effective radius ae=4a/3 model predicts beam height with sufficient accuracy.
大氣導管與反射高度 Atmospheric ducts and
reflection height
考慮較極端的例子, 折射指數在近地面為dN/dh= -300km-1 之後為dN/dh=-40km-1的情形.當h<<a (set h1=.1km), 線性化後的路徑方程可寫成s(h)=[(cosθe) / (1+β0a)] {[a2sin2θe + 2a(1+β0a)/h] 1/2 -a sinθe}, 其中 β0 = -300 km-1 is the gradient of n at the surface. 注意s(h)會變成複數, 當[a2sin2θe + 2a(1+β0a)/h]<0時, 定義侵入角(penetration angle) θp = sin-1[-2h1(1+β0a)/a]1/2 , (此個案之θp=0.310),當仰角小於侵入角時雷達波將被陷住。此時
hr = (-a sin2θe)/2(β0a+1),
s(hr) = (-a cosθe sinθe)/(β0a+1).
Anomalous Propagation(AP) caused by strong ground-based temperature inversion