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

1. EM wave spectrum f = frequency c = speed of EM wave in free space = wavelength of EM wave Freaquency 30Hz 300Hz 3kHz 30kHz 300kHz 3MHz 30MHz 300MHz 3GHz 30GHz 300GHz 3THz 10km 1km 100m 10m 1m 10cm 1cm 1mm 0.1mm Wavelength VLF LF MF HF VHF UHF SHF EHF Band designations : L S C X Ku Ka W Broadcast band Microwave region

(1) Change of band width

(2) Range-height diagram

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

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

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

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 :

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 -∞

(1) Relationship between , and refractive conditions

(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

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

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

서해상 이상에코 출현(5월1일)

백령도 대기선도 분석(5월1일)

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

에코는 없으나 비가 오는 경우

추 강수에코가 관측되지만 실제 비가오지않는경우

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

(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 : ∼0.0004 dB/km = 10cm : attenuation : ∼0.008 dB/km

(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 : 0.0148 R1.31 dBkm-1 = 5.7 cm two- way attenuation : 0.004 R1.17 dBkm-1 = 10 cm two-way attenuation : 0.0006 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

(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.)

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

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.