Short Course On Radar Meteorology

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  • 1. ATMOS A short course on radar meteorology Tobias Otto Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 1
  • 2. AT Radar MeteorologyMOS 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 Earths atmosphere. Reference: AMS Glossary Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 2
  • 3. AT MicrowavesMOS HF 3 - 30 MHz VHF 30 - 300 MHz mobile UHF 300 - 1000 MHz KNMI Windprofiler phones L 1 - 2 GHz S 2 - 4 GHz C 4 - 8 GHz X 8 - 12 GHz PARSAX Ku 12 - 18 GHz KNMI WLAN Weather K 18 - 27 GHz Radar Ka 27 - 40 GHz V 40 - 75 GHz IDRA W 75 - 110 GHz mm 110 - 300 GHz Cloud Radar Reference: Radar-frequency band nomenclature (IEEE Std. 521-2002) Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 3
  • 4. AT Microwaves and WaterMOS scatteringelectromagnetic wavesfrequency ≈ 2.4 GHzwavelength ≈ 12 cm T. Otto absorption Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 4
  • 5. A T Water and Radar M O S radar received powerPARSAX on top of EWI faculty time T. Otto Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 5
  • 6. AT Information in microwavesMOS Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. 1. Amplitude y x can be related to the strength of precipitation / rain rate A A z Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 6
  • 7. AT Information in microwavesMOS Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. 1. Amplitude y x can be related to the strength of precipitation / rain rate 2. Frequency Doppler shift, relative radial velocity of the precipitation z Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 7
  • 8. AT Information in microwavesMOS Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. 1. Amplitude y x can be related to the strength of precipitation / rain rate 2. Frequency Doppler shift, relative radial velocity of the precipitation z 3. Phase can be used to measure refractive index variations Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 8
  • 9. AT Information in microwavesMOS Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation. 1. Amplitude y can be related to the strength of x precipitation / rain rate 2. Frequency Doppler shift, relative radial velocity of the precipitation 3. Phase z can be used to measure refractive index variations 4. Polarisation hydrometeor / rain drop shape Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 9
  • 10. AT Radar MeteorologyMOS 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 Earths atmosphere. Reference: AMS Glossary Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 10
  • 11. AT Radar Equation for a Point TargetMOS antennae range R Pt transmitter Gt target σ Pr receiver Gr isotropic backscattered power density antenna at receiving antenna Pt .. transmitted power (W) Gt .. antenna gain on transmit Pt 1 Gr 2 R .. range (m) Pr   Gt     σ Gr .. radar cross section (m2) .. antenna gain on receive 4R 2 4R 2 4 Pr .. received power (W) power density incident effective area of on the target the receiving antenna Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 11
  • 12. AT Radar Equation for a Point TargetMOS antennae range R Pt transmitter Gt target σ Pr receiver Gr radar constant target characteristics Pt .. transmitted power (W) Gt .. antenna gain on transmit Pt Gt Gr    2 R .. range (m) Pr  4   R σ .. radar cross section (m2) 3 4 Gr .. antenna gain on receive free-space Pr .. received power (W) propagation Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 12
  • 13. AT From Point to Volume TargetsMOS - the radar equation for a point target needs to be customised and expanded to 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 the radar cross sections of all scatterers in the resolution volume V (range-bin):   range bin i V  unit volume i Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 13
  • 14. AT Radar Resolution VolumeMOS antenna beam-width θ c range R radar resolution volume r  (range-bin) 2B 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 Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 14
  • 15. AT Range Resolution of a Pulse RadarMOS Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 15
  • 16. AT Range Resolution of a Pulse RadarMOS 1 2 3 e.g. pulse duration 1 µs 300m  c  (s )  m f0 Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 16
  • 17. AT Range Resolution of a Pulse RadarMOS 1 2 3 c  2 • each target 1 consists of the sum of the sample backscattered signals of a volume with response the length c·τ/2 target 2 • for a pulse radar, the optimum sampling rate of response the backscattered signal is 2/τ (Hz) target 3 response Now we sample the backscattered signal. Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 17
  • 18. AT Radar Equation for Volume TargetsMOS PGt Gr  2  R 2 2 c Pr  t   V    i  i 44 R 2 16 ln 2 B unit volume  R 33 44 unit volume c V   r  2 2B 2     c r V     R tan   θ/2   2  2 B R tan(α) ≈ α (rad) for small α  rad  c r  2 c 1 2B V  R 2   4 2 B 2 ln 2 volume reduction factor due to Gaussian antenna beam pattern Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 18
  • 19. AT Radar Cross Section σMOS Pbackscattered 2  (m ) Sincident Pbackscattered .. backscattered power (W) Sincident .. incident power density (W/m2) 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 Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 19
  • 20. AT Radar Cross Section σMOS Monostatic radar cross section of a conducting sphere: a .. radius of the sphere normalised radar cross section  .. wavelength Rayleigh region: a <<  Resonance / Mie region: electrical size Optical region: a >>  Figure: D. Pozar, “Microwave Engineering”, 2nd edition, Wiley. Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 20
  • 21. AT Radar Cross Section σMOS  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:  K Di6 5 2 D .. hydrometeor diameter i   .. wavelength  4 |K|2 .. dielectric factor depending on the material of the scatterer Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 21
  • 22. AT Radar Equation for Weather RadarMOS Pt Gt Gr   R  c  K 2 2 2 5 2 Pr      i   Di6 4  R 3 4 4 16 ln 2 B unit volume unit volume  Pt Gt Gr  c3 1 2 Pr  K  Dei  R 2 2 6 1024 ln 2 B 2 unit volum radar constant radar reflectivity factor z, purely a property of the observed precipitation Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 22
  • 23. AT Radar Reflectivity Factor zMOS 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: z  Pr CR2 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 Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 23
  • 24. AT Summary of the assumptions made so farMOS 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 approximated by a Gaussian function • far-field of the radar antenna, using linear polarisation • so far, we neglected the propagation term (attenuation) Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 24
  • 25. AT Radar MeteorologyMOS 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 Earths atmosphere. Reference: AMS Glossary Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 25
  • 26. AT Radar Reflectivity Factor zMOS  mm6  z  D  m3   i 6   spans over a large range; to compress it into a smaller range of numbers, a logarithmic scale is preferred  unit volume  1 m3   dBZ  z one raindrop equivalent to Z  10 log10  3  D = 1mm 1mm6m-3 = 0 dBZ  1mm / m  6 raindrop diameter #/m3 Z water volume per cubic meter 1 mm 4096 36 dBZ 2144.6 mm3 4 mm 1 36 dBZ 33.5 mm3 Knowing the reflectivity alone does not help too much. It is also important to know the drop size distribution. Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 26
  • 27. AT Raindrop-Size Distribution N(D)MO  N0S z  D   D N ( D)dD  7  6! unit volume i 6 6 0 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: N D   N 0 exp  D  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) Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 27
  • 28. AT Reflectivity – Rainfall Rate RelationsMOS reflectivity (mm6m-3) z   D 6 N ( D)dD D  liquid water content (mm3m-3) LWC  6  D D 3 N ( D)dD raindrop volume  rainfall rate (mm h-1) R 6  D D 3v( D ) N ( D )dD 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 z  aRb 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 Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 28
  • 29. AT Summing-upMOS - 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 power which is related to the amplitude of an electromagnetic wave, what about frequency, phase and polarisation? … more after a short break … Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 29
  • 30. AT 2nd Part - OutlineMOS  radar geometry and displays  Doppler effect  polarisation in weather radars Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 30
  • 31. AT 2nd Part - OutlineMOS  radar geometry and displays  Doppler effect  polarisation in weather radars Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 31
  • 32. AT Radar DisplayMOS PPI (plan-position indicator): RHI (range-height indicator): Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 32
  • 33. AT 2nd Part - OutlineMOS  radar geometry and displays  Doppler effect  polarisation in weather radars Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 33
  • 34. AT Doppler EffectMOS http://en.wikipedia.org/wiki/File:Dopplerfrequenz.gif 2vr  fd  vr ,m ax   target  4Ts 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 Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 34
  • 35. AT Weather Radar Measurement Example (PPI)MOS Reflectivity (dBZ) Doppler velocity (ms-1) Data: IDRA (TU Delft), Jordi Figueras i Ventura Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 35
  • 36. AT Combining Reflectivity and Doppler VelocityMOSDoppler Processing (Power Spectrum):Mapping the backscattered power ofone radar resolution volume into theDoppler velocity domain. Power Doppler Width Mean Doppler Doppler Velocity Velocity Figures: Christine Unal Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 36
  • 37. AT 2nd Part - OutlineMOS  radar geometry and displays  Doppler effect  polarisation in weather radars Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 37
  • 38. AT Can Polarimetry add InformationMOS  yes, because hydrometeors are not spheres - ice particles - hail 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 - raindrops 1987. http://commons.wikimedia.org/wiki/Category:Hail Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 38
  • 39. AT Measurement PrincipleMOS transmit Zhh (dBZ) Zhv (dBZ) receive Zvh (dBZ) Zvv (dBZ) Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 39
  • 40. AT Measurement PrincipleMOS transmit Zhh (dBZ) Zhv (dBZ) receive - Zvh (dBZ) Zvv (dBZ) = Zdr differential reflectivity Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 40
  • 41. AT Hydrometeor ClassificationMOS rain aggregateslayer ice crystals melting (snow) Reflectivity Differential Reflectivity Z hh  10 log CR Phh dBZ  dB Phh 2 Z dr  10 log Pvv Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 41
  • 42. AT Measurement PrincipleMOS transmit Zhh (dBZ) Zhv (dBZ) receive - Zvh (dBZ) Zvv (dBZ) = LDR (dB) linear depolar- isation ratio Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 42
  • 43. AT Linear Depolarisation RatioMOS melting clutter ground layer Reflectivity Linear Depolarisation Ratio Z hh  10 log CR Phh dBZ  dB Phv 2 LDR  10 log Pvv Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 43
  • 44. AT Estimation of raindrop-size distributionM N D   N 0 exp  D OS concentration (m-3mm-1) slope parameter (mm-1) 1. the differential reflectivity Zdr depends only on the slope parameter Λ, so Λ can be directly estimated from Zdr 2. once that the slope parameter is known, the concentration N0 can be estimated in a second step from the reflectivity Zhh Data: IDRA (TU Delft), Jordi Figueras i Ventura Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 44
  • 45. AT Summing-upMOS - 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, - … Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 45
  • 46. ATMOS A short course on radar meteorology Tobias Otto e-mail t.otto@tudelft.nl web 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. Delft University of Technology Remote Sensing of the Environment (RSE) Tobias Otto: A short course on radar meteorology. 46