A short course on radar meteorology

1. Tobias Otto A short course on radar meteorology

2. Radar: Radio Detection And Ranging An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy. Radar Meteorology: The study of the atmosphere and weather using radar as the means of observation and measurement. Meteorology: The study of the physics, chemistry, and dynamics of the Earth's atmosphere. Radar Meteorology Reference: AMS Glossary

3. mobile phones KNMI Windprofiler KNMI Weather Radar WLAN IDRA Cloud Radar Microwaves HF 3 - 30 MHz VHF 30 - 300 MHz UHF 300 - 1000 MHz L 1 - 2 GHz S 2 - 4 GHz C 4 - 8 GHz X 8 - 12 GHz Ku 12 - 18 GHz K 18 - 27 GHz Ka 27 - 40 GHz V 40 - 75 GHz W 75 - 110 GHz mm 110 - 300 GHz PARSAX Reference: Radar-frequency band nomenclature (IEEE Std. 521-2002)

4. T. Otto Microwaves and Water scattering electromagnetic waves frequency ≈2.4 GHz wavelength ≈ 12 cm absorption

5. radar T. Otto Water and Radar received power PARSAX on top of EWI faculty time

6. Information in microwaves Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. Amplitudecan be related to the strength of precipitation / rain rate y x A A z

7. Information in microwaves Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. Amplitudecan be related to the strength of precipitation / rain rate 2. FrequencyDoppler shift, relative radial velocity of the precipitation y x z

8. Information in microwaves Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. Amplitudecan be related to the strength of precipitation / rain rate 2. FrequencyDoppler shift, relative radial velocity of the precipitation 3. Phasecan be used to measure refractive index variations y y x z

9. Information in microwaves Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. Amplitudecan be related to the strength of precipitation / rain rate 2. FrequencyDoppler shift, relative radial velocity of the precipitation 3. Phasecan be used to measure refractive index variations 4. Polarisationhydrometeor / rain drop shape y x z

10. Radar: Radio Detection And Ranging An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy. Radar Meteorology: The study of the atmosphere and weather using radar as the means of observation and measurement. Meteorology: The study of the physics, chemistry, and dynamics of the Earth's atmosphere. Radar Meteorology Reference: AMS Glossary

11. isotropic antenna backscattered power density at receiving antenna power density incident on the target effective area of the receiving antenna Radar Equation for a Point Target range R antennae Pt Gt transmitter target σ Pr Gr receiver Pt .. transmitted power (W) Gt .. antenna gain on transmit R .. range (m) σ .. radar cross section (m2) Gr .. antenna gain on receive Pr .. received power (W)

12. targetcharacteristics radar constant free-space propagation Radar Equation for a Point Target range R antennae Pt Gt transmitter target σ Pr Gr receiver Pt .. transmitted power (W) Gt .. antenna gain on transmit R .. range (m) σ .. radar cross section (m2) Gr .. antenna gain on receive Pr .. received power (W)

13. From Point to Volume Targets • the radar equation for a point target needs to be customised and expandedto fit the needs of each radar application(e.g. moving target indication, synthetic aperture radar, and also meterological radar) • radar has a limited spatial resolution, it does not observe single targets (i.e. raindrops, ice crystals etc.), instead it always measures a volume filled| with a lot of targets •  volume (distributed) target instead of a point target • to account for this, the radar cross section is replaced with the sum of theradar cross sections of all scatterers in the resolution volume V (range-bin):

14. Radar Resolution Volume antenna beam-width θ radar resolution volume (range-bin) rangeR c .. speed of light B .. bandwidth of the transmitted signal (the bandwith of a rectangular pulse is the inverse its duration B=1/τ)  Δr is typically between 3m - 300m,and the antenna beam-width is between 0.5° - 2° for weather radars

15. Range Resolution of a Pulse Radar

16. Range Resolution of a Pulse Radar 1 2 3 e.g. pulse duration 1 µs 300 m f0

17. target 1 response target 2 response target 3 response Range Resolution of a Pulse Radar 1 2 3 • each sample consists of the sum of the backscattered signals of a volume withthe length c·τ/2 • for a pulse radar, the optimum sampling rate of the backscattered signal is 2/τ (Hz) Now we sample the backscattered signal.

18. volume reduction factor due to Gaussian antenna beam pattern Radar Equation for Volume Targets 2 r θ/2 tan(α) ≈ α (rad) for small α R

19. Pbackscattered Sincident .. backscattered power (W) .. incident power density (W/m2) Radar Cross Section σ Depends on: • frequency and polarisation of the electromagnetic wave • scattering geometry / angle • electromagnetic properties of the scatterer • target shape  hydrometeors can be approximated as spheres

20. Resonance / Mie region: a  .. radius of the sphere .. wavelength Radar Cross Section σ Monostatic radar cross section of a conducting sphere: Rayleigh region: a <<  normalised radar cross section electrical size Optical region: a >>  Figure: D. Pozar, “Microwave Engineering”, 2nd edition, Wiley.

21. D  |K|2 .. hydrometeor diameter .. wavelength .. dielectric factor depending on the material of the scatterer Radar Cross Section σ • hydrometeors are small compared to the wavelengths used in weather radar observations: weather radar wavelength 9cm max. 6mm raindrop diameter • Rayleigh scattering approximation can be applied;radar cross section for dielectric spheres:

22. Radar Equation for Weather Radar radar constant radar reflectivity factor z, purely a property of the observed precipitation

23. Radar Reflectivity Factor z To measure the reflectivity by weather radars, we need to: - precisely know the radar constant C (radar calibration), - measure the mean received power Pr, - measure the range R, - and apply the radar equation for weather radars: Summary: Radar observations of the atmosphere mainly contain contributions from hydrometeors which are Rayleigh scatterers at radar frequencies. This allowed us to introduce the radar reflectivity factor z, a parameter that - only depends on the hydrometeor microphysics and is independent on radar parameters such as the radar frequency, - i.e. the reflectivity within the same radar resolution volume measured by different radars should be equal

24. Summary of the assumptions made so far In the derivation of the radar equation for weather radars, the following assumptions are implied: • the hydrometeors are homogeneously distributed within the range-bin • the hydrometeors are dielectric spheres made up of the same material with diameters small compared to the radar wavelength • multiple scattering among the hydrometeors is negligible • incoherent scattering (hydrometeors exhibit random motion) • the main-lobe of the radar antenna beam pattern can be approximatedby a Gaussian function • far-field of the radar antenna, using linear polarisation • so far, we neglected the propagation term (attenuation)

25. Radar: Radio Detection And Ranging An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy. Radar Meteorology: The study of the atmosphere and weather using radar as the means of observation and measurement. Meteorology: The study of the physics, chemistry, and dynamics of the Earth's atmosphere. Radar Meteorology Reference: AMS Glossary

26. 1 m3 one raindrop D = 1mm equivalent to 1mm6m-3 = 0 dBZ Radar Reflectivity Factor z • spans over a large range; to compress it into a smaller range of numbers, a logarithmic scale is preferred Knowing the reflectivity alone does not help too much. It is also important to know the drop size distribution.

27. Raindrop-Size Distribution N(D) where N(D) is the raindrop-size distribution that tells us how many drops of each diameter D are contained in a unit volume, i.e. 1m3. Often, the raindrop-size distribution is assumed to be exponential: concentration (m-3mm-1) slope parameter (mm-1) Marshall and Palmer (1948): N0 = 8000 m-3mm-1 Λ = 4.1·R-0.21 with the rainfall rate R (mm/h)

28. Reflectivity – Rainfall Rate Relations reflectivity (mm6m-3) liquid water content (mm3m-3) raindrop volume rainfall rate (mm h-1) terminal fall velocity • the reflectivity measured by weather radars can be related to the liquid water content as well as to the rainfall rate: power-law relationship the coefficients a and b vary due to changes in the raindrop-size distribution or in the terminal fall velocity. Often used as a first approximation is a = 200 and b = 1.6

29. Summing-up • electromagnetic waves and their interaction with precipitation • radar principle • radar equation for a point target • extension of this radar equation to be applicable for volume targets and for weather radars • the reflectivity was introduced, how it is determined from weather radar measurements, and its relation to rainfall rate (Z-R relations) But, so far we only considered the backscattered received powerwhich is related to the amplitude of an electromagnetic wave, what about frequency, phase and polarisation? … more after a short break …

30. 2nd Part - Outline  radar geometry and displays  Doppler effect  polarisation in weather radars

31. 2nd Part - Outline  radar geometry and displays  Doppler effect  polarisation in weather radars

32. Radar Display PPI (plan-position indicator): RHI (range-height indicator): Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

33. 2nd Part - Outline  radar geometry and displays  Doppler effect  polarisation in weather radars

34. Doppler Effect http://en.wikipedia.org/wiki/File:Dopplerfrequenz.gif target fd .. frequency shift caused by the moving target vr .. relative radial velocity of the target with respect to the radar λ.. radar wavelength Ts .. sweep time

35. Weather Radar Measurement Example (PPI) Reflectivity (dBZ) Doppler velocity (ms-1) Data: IDRA (TU Delft), Jordi Figueras i Ventura

36. Combining Reflectivity and Doppler Velocity Doppler Processing (Power Spectrum): Mapping the backscattered power of one radar resolution volume into the Doppler velocity domain. Power Doppler Width Doppler Velocity Mean Doppler Velocity Figures: Christine Unal

37. 2nd Part - Outline  radar geometry and displays  Doppler effect  polarisation in weather radars

38. Beard, K.V. and C. Chuang: A New Model for the Equilibrium Shape of Raindrops, Journal of the Atmospheric Sciences, vol. 44, pp. 1509 – 1524, June 1987. Can Polarimetry add Information  yes, because hydrometeors are not spheres - ice particles - hail - raindrops http://commons.wikimedia.org/wiki/Category:Hail

39. Measurement Principle transmit Zhh (dBZ) Zhv (dBZ) receive Zvh (dBZ) Zvv (dBZ) Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

40. Measurement Principle transmit Zhh (dBZ) Zhv (dBZ) - receive Zvh (dBZ) Zvv (dBZ) = Zdr differential reflectivity Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

41. Reflectivity Differential Reflectivity Hydrometeor Classification melting layer rain aggregates (snow) ice crystals Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

42. Measurement Principle transmit Zhh (dBZ) Zhv (dBZ) - receive Zvh (dBZ) Zvv (dBZ) =LDR (dB) linear depolar- isation ratio Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

43. Reflectivity Linear Depolarisation Ratio Linear Depolarisation Ratio melting layer ground clutter Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

44. Estimation of raindrop-size distribution the differential reflectivity Zdr depends only on the slope parameter Λ,so Λ can be directly estimated from Zdr once that the slope parameter is known, the concentration N0 can be estimated in a second step from the reflectivity Zhh concentration (m-3mm-1) slope parameter (mm-1) Data: IDRA (TU Delft), Jordi Figueras i Ventura

45. Summing-up • Doppler capabilities allow an insight into the dynamics and turbulence of precipitation • Polarisation can be successfully applied for weather observation because hydrometeors are not spherical, main applications are: • discrimination of different hydrometeor types, • suppression of unwanted radar echoes, i.e. clutter, • improving rainfall rate estimation, • estimation of raindrop-size distribution, • attenuation correction, • …

46. A short course on radar meteorology Tobias Otto e-mail t.otto@tudelft.nlweb http://atmos.weblog.tudelft.nl http://rse.ewi.tudelft.nl http://radar.ewi.tudelft.nl (for information on PARSAX)references R. E. Rinehart, “Radar for Meteorologists”, Rinehart Publications, 5th edition, 2010. R. J. Doviak and D. S. Zrnić, “Doppler Radar and Weather Observations”, Academic Press, 2nd edition, 1993. V. N. Bringi and V. Chandrasekar, “Polarimetric Doppler Weather Radar: Principles and Applications”, Cambridge University Press, 1st edition, 2001.