1. Chap IV. Fundamentals of Radar Beam propagation
EM wave spectrum
Refraction of radar beam
Height of radar beam under standard refraction
Conditions of refractive propagation
Attenuation of microwaves

2. 1. EM wave spectrum f = frequency c = speed of EM wave in free space
= wavelength of EM wave
Freaquency
30Hz Hz kHz kHz kHz 3MHz 30MHz MHz 3GHz GHz GHz 3THz
10km km m m m cm cm mm mm
Wavelength
VLF LF MF HF
VHF
UHF
SHF
EHF
Band designations : L S C X Ku Ka W
Broadcast
band
Microwave region

3. (1) Change of band width

4. (2) Range-height diagram

5. 4. Conditions of refractive propagation
Refractive condition
Subrefraction
Standard refraction
(4/3 earth radius)
Super refraction
Trapping (or ducting)

6. Path of radar waves and dN/dh
Assumption:
Refractivity is only stratified in the vertical along the spherical Earth.
Snell’s law : N1 sin θ1 = N2 sin θ2
If N 1> N 2 , θ1 < θ2
ducting condition
dN/dh < -157 θ1 θ2
Normal condition
-79< dN/dh < 0
Since The gradient of refractivity is much larger in the vertical than in the horizontal, atmosphere is often assumed to be stratified in the vertical along the spherical Earth.
Under this assumption, When the radar wave propagates through the level of air that has different refractivity, the ray bends toward or away from the ground. normally since refractivity decrease with height, so we can think the case low-level N is larger than above level. Then when the ray enters the layer of smaller N then below, according to the snell’s law the zenith angle of the ray becomes larger than the incident angle at the level below, so this ray bends toward the ground. Yet the curvature of bent ray is smaller than the curvature of the Earth, this propagation condition is known as normal condition and often given as the vertical gradient between 0 and -79.
On the other hand, if the curvature is following the curvature of the Earth, which is -157 ppm/km or even larger than that, then the ray is
Trapped near the ground which called ducting. In this case, some object that was hidden in the radar horizon can be detected by the curved ray.
This tells that the propagation conditions can bring some errors in the radar observation and its applications.
Anomalous propagation 6

7. Radar ray height errors due to dN/dh
(Doviak and Zrnić 1993)
sub-refraction (dN/dh = 10 km-1.)
Normal
(dN/dh = -40 km-1)
Since a scanning radar provides data in range and azimuth at different elevation angles, if we want to know the actual height of what this radar measures, we need to compute the ray height along the trajectory that varies with propagation conditions. According to Doviak and Zrnic, this height can be computed geometrically considering the bent ray as a straight ray by enlarging the radius of the earth regarding to the propagation conditions As described here as effective earth’s radius
This graph shows an example of how the beam height varies with different conditions of the vertical refractivity gradient.
As we saw in the previous slide, for large negative gradient, beam bends toward the ground more. SO The height difference from the
Normal condition become larger with range, and it become as large as 2 km at 200km away from the radar.
This height variation are already well known, however, when it comes to compute the ray height for most radar application, we still use
the standard conditions rather than to use different conditions of propagation that’s because its simplicity.
Then how significant the height error can be if we only consider the normal condition rather than the actual condition from the sounding ?
Super-refraction (dN/dh = -140 km-1) 7

8. 2. Refraction of radar beam
Standard refraction
refractive index :
refractivity : p: air pressure, T : air temperature,e : water vapor pressure
If n=1.0003, N = 300 (N-units)
gradient of N : usually ,
standard refraction :

9. Gradient : N units per km
Summary of Refractive Propagation Conditions
Refractive Condition
Gradient : N units per km
Subrefraction
Positive gradient
No refraction
(uniform atmosphere)
Standard refraction
(4/3rd earth radius)
-39
Normal refraction
0 to -79
Superrefraction
-79 to -157
Trapping, or ducting
-157 to -∞

10. (1) Relationship between , and refractive conditions

11. (2) Condition of ducting
trapping of radion waves
Curvature of earth : KE
If the curvature of the radar beam is greater than KE ,
i.e , the radar beam is trapped in atmosphere

12. 비강수에코 사례분석
이상굴절에 의한 에코
DRY
AIR
MOIST
- 빔갇힘현상(Ducting)
INVERSION LAYER

14. 비강수에코 사례분석
이상굴절에 의한 에코
DRY
AIR
MOIST
- 빔갇힘현상(Ducting)
INVERSION LAYER

15. 서해상 이상에코 출현(5월1일)

16. 백령도 대기선도 분석(5월1일)

17. 비강수에코 사례분석 이상굴절에 의한 에코(3 May,2003) - 빔갇힘현상(Ducting) Pressure (hPa)
Temperature(℃)
Dewpoint Temp.(℃)
dN/dz
995
10.6
5.6
-657
990
14.0
-9.0
-228
984
18.6
-19.4
-27
965
-20
850
11.2
-17.8

18. 에코는 없으나 비가 오는 경우

19. 추
강수에코가 관측되지만 실제 비가오지않는경우

20. 5. Attenuation of microwaves
Attenuation by atmospheric gases
attenuation(or extinction)
= absorption + scattering
attenuation by clear air at sea level

21. (2) Attenuation of microwaves by water and ice
For water content of 1 g/m3
= 3cm : attenuation : ∼0.1 dB/km
= 10cm : attenuation : ∼0.01 dB/km
For ice content of 1 g/m3
= 3cm : attenuation : ∼ dB/km
= 10cm : attenuation : ∼0.008 dB/km

23. (3) Attenuation of microwaves by raindrops
(3) Attenuation of microwaves by raindrops depends on radar wavelength and rainfall rate (R : mmh-1)
= 3.2cm
two-way attenuation : R1.31 dBkm-1
= 5.7 cm
two- way attenuation : R1.17 dBkm-1
= 10 cm
two-way attenuation : R dBkm-1
※ The attenuation produced by snowflakes is less than that produced by raindrops at low precipitation rates, but it is not easy to relate to precipitation rate

25. (4) Simulation of attenuation effect by precipitation
(a) Modification of the profile of a shower 20 km in width in which the intensity R of the precipitation varies by 10 mm h-1 : RM, minimum detectable intensity.
(b) Modification of the profile of a shower 20 km in width in which the intensity R of the precipitation varies by 5mmh-1 km-1 : RM, minimum detectable intensity. (After Treussart 1968 and Clift 1985.)

26. Magnitude of attenuation due to hydrometeors
Orders of magnitude of attenuation due to hydrometeors at 5cm wavelength(after Crozier 1986)
ln general, attenuation decreases with increasing temperatures for liquid hydrometeors and increase with increasing temperature for solid water particles

27. ATTENUATION of Radar Signal
Gases (oxygen, water vapor)
(1.5 db/100 km)
Hydrometeors (rain, snow, hail)
Increases rapidly with decreasing wavelength
Negligible at S-band (10 cm)
Moderate at C-band (5 cm)
Pronounced at X-band (3 cm)
(nearly proportional to Rainrate)
Radome attenuation is an additional problem at C- and X-band.