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

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

2. Rayliegh scattering DROP SCATTERED ENERGY INCIDENT ENERGY

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 ( ) :

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

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)

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

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)

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

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

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

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

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

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)

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

Fig. 4.3. Distribution function (solid straight lines) compared with results of Laws and Parsons (broken lines) and Ottawa observations (dotted lines). From marshall and Palmer(1948).

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

(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)

Assume (8) (9)

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

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

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.

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 1 - 2 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) 55 - 60 dBZ Strong ground echoes > 60 dBZ

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

69 R(Z) relations (Battan 1973)

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

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)

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

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

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

(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