1. Chap. V Precipitation measurements
Scattering of electromagnetic waves
Reyliegh scattering
Backscattering Cross section
Rayleigh scattering Cross section
Radar Equations
Marshall-Palmer distribution
Derivation of Z – R relationship

2. 1. Scattering of electromagnetic waves
Amount of energy backscattered from hydrometeors depends on
particle concentration in the pulse volume
Size
Composition
relative position
particle shape
particle orientation

3. 2. Rayliegh scattering
DROP
SCATTERED ENERGY
INCIDENT ENERGY

4. 3. Backscattering Cross section
from Mie theory
Backscattering cross section :
for spherical drop
where r : radius
: size parameter
an, bn : coefficients for scattered field
normalized backscattering cross section ( ) :

5. 4. Rayleigh scattering Cross section
drop diameter (D) < wavelength ( )
where : dielectric factor
: complex refractive index
values of
for water (0°< T ≤20℃)
for ice

6. Dielectric factor for water and ice
Calculated values of the normalized backscattering cross section ( ) for water and ice sphere. The water curve applies at a temperature of 0 and a wavelength of 3.21 cm. The ice curve is valid for wavelengths from 1 to 10 cm (Herman and Battan, 1961)

7. Radar backscattering efficiency as a function of χ for a metal sphere of radius r (Skolnik, 1980).

8. 5. Radar Equations Rayleigh scattering approximation
Average returned power :
(1)
where G : antenna gain
C : radar constant
N : number of scatters/unit volume
|k|2 : dielectric constant
: radar reflectivity factor (mm6/m3)

9. radar reflectivity factor :
unit of : mm6m-3
Z (dBZ) =

10. Mie scattering (2) : radar reflectivity (cm2/m3) = (3)
= (3)
: equivalent(or effective) radar reflectivity factor

11. Equivalent radar reflectivity factor
reflectivity factor of a population of spherical water particles satisfying the condition of Rayleigh approximation and producing a signal received.
for snow and ice particles
: radar reflectivity factor for ice

12. Equivalent radar reflectivity factor
: measured by radar observations
: estimated by the following equation

13. Radar echo intensity(or power)
Depends on
precipitation rate
number density
particle size
particle phase
orientation

14. Measurement of precipitation
Average power received by radar
(4)
Empirical relationship between Z and R
(5)
Where Z : radar reflectivity factor (mm6/m3)
R : precipitation rate (mm/hr)
a, b : constants (depending precipitation)
From eqs. (4) & (5)
(6)

15. 6. Marshall-Palmer distribution
: parameters depending on precipitation
: rainfall rate (mm/hr)

16. Fig Distribution function (solid straight lines) compared with results of Laws and Parsons (broken lines) and Ottawa observations (dotted lines). From marshall and Palmer(1948).

17. 7. Derivation of Z – R relationship
(1) radar reflectivity factor
(1)
(2)
Marshall – Palmer drop size distribution
(3)

18. (2) Precipitation intensity
mass flux of precipitation particle
→ (4)
Ni(Di) : number density
Di : diameter
Wi Di: fall velocity
ρw : density of water
(5)
(6)
or (7)

19. Assume
(8)
(9)

20. (3) Z – R relationship (3) (9) (10) From eqs.(3) and (10), we have
(11)

22. (4) Reflectivity Factor - Rainfall Rate Relations
Typical empirical relationships between reflectivity factor
Z(mm6 m-3 ) and precipitation intensity, R(mm/hr) (Battan, 1973)

23. Categories of echo Intensity and Rainfall Rate
* Based on Z= 200R1.6, intensity of stratiform rain is not generally greater than 46 dBZ.
** Based on Z= 55R1.6, hail is likely at these levels at the echo in tensities greater than 50 dBZ.
# dBZ=log10Ze (mm6m-3) , where Ze is the equivalent radar reflectivity.

24. Interpretation of the Radar Reflectivity Scale
Because Z spans several orders of magnitude, it is generally expressed in
dBZ = 10 log10(Z) Ex: Z = 200 mm6/m3  23 dBZ
Type and Intensity
Reflectivity
Drizzle or clear air targets (insects)
0 dBZ
Very light rain or snow (A few raindrops or snowflakes)
10 – 15 dBZ
Light rain or snow (Typical spring/fall mm/hr)
20 – 30 dBZ
Moderate precipitation (3 – 10 mm/hr)
30 – 40 dBZ
Heavy rain (Summer showers: 20 mm/hr)
45 – 50 dBZ
Very heavy rain or hail (Thunderstorm core: 100 mm/hr)
dBZ
Strong ground echoes
> 60 dBZ

25. Factors affecting DSD formation and evolution
(5) Microphysical aspects of rain formation a b
Larger
raindrops
Smaller
Factors affecting DSD formation and evolution
Type of frozen particles aloft (unrimed snow, rimed snow, aggregated snow, graupel, hail)
Height and depth of the melting layer (bright band)
Evaporation, break-up, and coalescence below the melting level

26. 69 R(Z) relations (Battan 1973)

27. (6) Differential reflectivity
: horizontal and vertical reflectivities, respectively

29. Detection of Melting Layer
(0.8~2.6 dB)
: Horizontal radar reflectivity factor: 30-47dBZ
(0.9~0.97)
Boodoo et al. (JAMC, 2010, 49)

30. The King City 3.1º elevation PPI images of ZH
at 1320UTC 15 Jan 2007.

31. The King City 3.1º elevation PPI images of ZDR at 1320UTC 15 Jan 2007.

32. The King City 3.1º elevation PPI images of ρHV at 1320UTC 15 Jan 2007.

33. (7) Problems associated with precipitation measurements by radar
실제 지상에 강수가 있으나 radar beam overshooting으로 에코가 약하게 탐지됨.
low-level evaporation beneath the radar beam(에코보다 작은 강우강도);
관측고도 낮은 지형 위에 강우 생성으로 관측된 에코보다 더 강한 강우강도(orographic enhancement above hills )
bright band(밝은띠)
underestimation of the intensity of drizzle because of the absence of large droplets
radar beam in the presence of a strong inversion, causing it to intercept land or sea