Mesoscale Atmospheric Systems Radar meteorology (part 1) 04 March 2014 Heini Wernli with a lot of input from Marc Wüest
An example radar picture What are the axes? What is the resolution? What are the panels? What are the colours? What is the interpretation?
Radar principle Radio Detection and Ranging We send out an electromagnetic pulse and observe how much of it returns (the echo). The amplitude of the echo is called reflectivity. Thus, radar is an active remote sensing instrument. The goal is to detect precipitation particles. 3
Radar history
Radar history Magnetron after Randall and Boot 1940 Station of an English radar warning system at the Channel s coast 1935
Radar antennas at ETH (until a few years ago ) scanning C-band radar ETH for research purposes radar van IAC (X-band) together with standard meteorological instrumentation (now at University of Hohenheim)
Radar antennas airborne X-band radar during MAP (Mesoscale Alpine Programme in 1999) mobile scanning C-band radar DOW during MAP
Ranging Distance determined from the pulse s runtime maximum distance is limited by pulse repetition frequency (PRF) t max = 1/PRF
Electromagnetic spectrum
Magnetron The cavity magnetron is a high-powered vacuum tube that generates microwaves using the interaction of a stream of electrons with a magnetic field. http://en.wikipedia.org/wiki/magnetron
Radar frequencies / bands Band name frequency wavelength typical typical range (GHz) range (cm) frequency wavelength (GHz) (cm) MeteoSwiss radars: C-band Radar in research group of Alexis Berne (EPFL): X-band
Typical parameters of a weather radar variable symbol units Typical value remark Frequency f Hz 3000 MHz Wavelength λ m 10 cm λ=c/f Pulse duration τ s 1 µs Pulse length m 300 m length of a pulse in the atmosphere = cτ Pulse-repetition-frequency F s -1 400 s -1 often abbreviated as PRF Pulse-repetition-period T s 2.5 ms =1/F Duty cycle - - 0.0004 ratio of time where radar actually transmits Maximum power P W 1 MW 1 MW = 90 dbm Pulse energy W J 1 J Integral of power of pulse duration Average power P av W 400 W averaged over a pulse length
Scanning types: PPI (plan position indicator)
Height Hšhe [100 (10 3 Fuss) feet] Scanning types: RHI (range height indicator) 20 15 10 5 0 Elevation (Grad) [ ] 10 9 8 7 6 5.5 5 4.5 4 3.5 3 0 10 20 30 40 50 60 70 Distanz Distance (Meilen) [km] Note the different sample volumes à resolution! 2.5 2 1.5 1 0.5 0
Effect of earth curvature Exercise: What effect does earth curvature have on the height above ground for a radar beam leaving the antenna horizontally, at a R r r R Δh Δh distance of 100 km?
Typical radar problems 2 1 3 4 5 6 1. general quantification (D 6 ) 2. earth curvature 3. orographic enhancement beneath the beam 4. melting (bright band) 5. evaporation beneath the beam 6. anomalous propagation (anaprop)
Real antenna pattern: the gain function g(θ,φ) The power of main and side lobes elevation azimuth
Scattering cross section after Rayleigh Assuming the Rayleigh condition for a spherical particle of diameter D D < λ /16 then the Rayleigh scattering cross section σ is σ = π λ 5 4 K 2 D 6 K 2 is the dielectricity (a property of the material) ~ 0.93 for water ~ 0.18 for ice of density 0.917 gm -3
Scattering in general scattering cross section (normalized) particle perimeter / wavelength
Definition and unit of reflectivity Z Z = 1 V D 6 = 0 N ( ) D D 6 dd Z is the reflectivity factor or simply the reflectivity, which is shown on most radar pictures. example: 1 drop of D = 5 mm has Z like 15 625 drops of D = 1 mm mass: 65 mg compared to total 8180 mg The unit of Z is mm 6 / m 3, but more convenient are log units: dbz = Z Z 1mm m [ db] =10 log 6 3 Z = 10 mm 6 m -3 à 10 dbz Z = 100 mm 6 m -3 à 20 dbz Z = 1000 mm 6 m -3 à 30 dbz etc.
Review on important assumptions 1. The precipitation particles are homogeneous dielectric spheres with diameters small compared to the radar wavelength. 2. The particles are spread throughout the contributing region. If not then the equation gives an average reflectivity factor for the contributing region. 3. The reflectivity factor Z is constant over the period of time needed to obtain the average value of the received power. 4. All of the particles have the same dielectric factor; that is, they are all either water droplets or ice particles.
Drop-size distribution for rain The size distribution is of an approximate negative-exponential form, especially in rain that is fairly steady. Marshall and Palmer (1948) first suggested this approximation on the basis of summer observations in Ottawa: N( D) = N 0 e λd where N(D) dd is the number of drops per unit volume with diameters between D and D + dd in units of mm. Marshall and Palmer found the slope factor λ to depend on rainfall rate: λ( R) = 4.1 R 0.21 where λ has units mm -1 and R is given in mm/h. Rather remarkable, they also found that the intercept parameter N 0 is a constant given by N 0 = 8000 m -3 mm -1.
Drop-size distribution Marshall-Palmer doesn't hold for very small sizes nor necessarily for individual events, but seems to be the limiting form as individual samples are averaged.
Rain rate and drop-size distribution Given the size distribution of rain drops N(D) and the corresponding fall velocities v(d) then the rain rate is given by
Typical values of Z clouds drizzle rain heavy rain thunderstorm hail -30 to -20 dbz -10 to 0 dbz 10 to 30 dbz 30 to 45 dbz > 45 dbz > 55 dbz Reflectivity as a function of rainfall rate (using Marshall-Palmer) R (mm/h) 0.1 1 10 100 Z (mm 6 /m 3 ) 5 200 7950 316000 dbz 7 23 39 55
Nebraska record hailstorm 2003 (75 dbz)
Heavy rain in Hurricane Andrew s Eyewall (45 dbz)
Snowstorm over Great Lakes (~ 25-30 dbz)
Clear air echoes (few small insects) -12 dbz
Z-R relations MeteoSwiss uses an empirical relationship from yearlong comparison between radar reflectivities and rain gauge measurements. This relationship is Z = 300 R 1.5 Note that the exponent is close to 2 which could be explained by the D 6 (reflectivity) and D 3 (rain rate) ratios. Effects from dielectricity (snow vs. rain) lead to an exponent typically smaller than 2. Reflectivity as parameterized by MeteoSwiss (MCH) and using Marshall-Palmer) R (mm/h) 0.1 1 10 100 dbz (Marshall Palmer) 7 23 39 55 dbz (MeteoSwiss) 10 25 40 55
Radar images of MeteoSwiss Albis, La Dôle and Monte Lema available since ~ 90ies