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Data Quality

Data Quality. Measurement variance: Z. Using a square law receiver, the variance is: Where Ps is the signal power, Pn is the noise power, M is the total number of samples, and Mi is the number of independent samples. Measurement variance: Z.

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Data Quality

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  1. Data Quality

  2. Measurement variance: Z • Using a square law receiver, the variance is: • Where Ps is the signal power, Pn is the noise power, M is the total number of samples, and Mi is the number of independent samples

  3. Measurement variance: Z • The total number of samples M is determined by PRT and dwell time • There may be considerable correlation from sample to sample. • The degree of correlation depends on • wavelength, • PRT, • beamwidth • Pulsewidth • Spread of velocities in the resolution volume

  4. Measurement variance: V • Assuming a large number of samples:

  5. Measurement variance • Some observations • As spectrum width increases VAR(Z) decreases, but VAR(V) increases • The variance of both V and Z decrease with decreasing wavelength • The variance of both decrease with increasing samples (dwell time) • These calculations do not take into account radar artifacts!

  6. Unambiguous Range and Velocity • Doppler dilemma • Long PRT (Ts) = long range and small Nyquist velocity • Short PRT = short range and large Nyquist velocity

  7. Second Trip for Alternate Txmit Radars • LDR is positive for second trip • LDR is negative for third trip

  8. Second Trip for Alternate Txmit Radars

  9. Bragg Scatter • “Radar backscattering from the turbulent clear atmosphere is caused by irregular small-scale fluctuations in the radio refractive index produced by turbulent mixing” Ottersten (1969, Radio Science)

  10. Bragg Scatter • When scattering comes from turbulent fluctuations in refractive index and these obey the k-5/3 law (i.e., the inertial subrange of fully developed, isotropic turbulence), the Bragg reflectivity comes from variations of refractive index at scales near l/2 and is expressed by • hB = 0.38 l(-1/3) Cn2 (Knight and Miller, 1998) • Cn represents a measure of the strength and variability of the refractive-index field • There will be reflections due to any refractive index variations ~ l/2

  11. Bragg Scatter • But we don’t use h! • Recall, we use equivalent reflectivity Ze • Ze assumes spherical liquid drops • Takes into account wavelength

  12. Bragg Scatter • So, • And the ratio of Bragg Z values at two wavelengths:

  13. Bragg Scatter • Some examples of Bragg scatter Z ratios for different wavelength pairs: • S- and C-band • (10/5)^(11/3) = 12.7 • 10*log10(12.7) = 11 dB • S- and X-band • (10/3)^(11/3) = 82.6 • 10*log10(82.6) = 19.2 dB • S- and Ka-band • (10/0.86)^(11/3) = 8.1X103 • 10*log10(8.1X103) = 39.1 dB

  14. Bragg Scatter Knight and Miller (1998)

  15. Bragg Scatter Knight and Miller (1998)

  16. Bragg Scatter from S-PolKa S-band reflectivity (dBZ) Ka-band reflectivity (dBZ)

  17. Attenuation • Gaseous • Liquid • Attenuation • Differential attenuation

  18. Attenuation: Gaseous • Absorption by O2 and H2O vapor • Attenuation depends on transmit frequency, atmospheric, T, P concentrations of H2O and O2 • O2 changes predictably with altitude • H2O vapor is highly variable

  19. S-band: 2.8 GHz Ka-band: 35 GHz Attenuation: Gaseous • Ka-band atmospheric attenuation is much stronger than at S-band • Well separated at different humidity values Therefore, it is possible to retrieve path-integrated humidity 25.5 g m-3 12.75 g m-3 2.55 g m-3 Attenuation (dB km-1, one-way) 0.25 g m-3 0.0 g m-3 From Lhermitte (1987) Frequency (GHz)

  20. Attenuation: Liquid At sea level and 20° C

  21. Attenuation: Liquid • Liquid attenuation is much stronger than gaseous • Depends on wavelength, T

  22. Attenuation: Liquid S-band reflectivity (dBZ) Ka-band reflectivity (dBZ)

  23. Attenuation: Liquid S-band reflectivity (dBZ) Ka-band reflectivity (dBZ)

  24. Attenuation: Liquid XPol Reflectivity S-Pol Reflectivity

  25. Attenuation: Differential Attenuation • Due to raindrop shape, the horizontal polarization (H) wave “sees” a larger cross section of liquid than the vertical (V)! • Therefore H experiences more attenuation than V

  26. Attenuation: Differential Attenuation • Recall ZDR = 10*log10(ZH/ZV) • So ZDR will be reduced by differential attenuation Other criteria:   i)   below bright band   ii) DM > 105 dBm (10 dB SNR)   iii)  PID not clutter! iv)   Z from 20 to 25 dBZ

  27. Attenuation: Correction • Attenuation and differential attenuation can be related to PHIDP • More sophisticated algorithms take advantage of self-consistency principle

  28. Results: Original Anagnostou et al (2006), FDP-based Single ray at 15 deg Azimuth Reflectivity difference: S – Xcorrected Mean = 0.4 dB Under-correction DBZ(S) – DBZ(X) Over-correction Mean difference of S-band and uncorrected X-band Z ~ -15 dB!!

  29. Side lobe contamination • All antennas transmit power in all directions • Directional antennas send the vast majority of power in a narrow beam • Leads to antenna gain

  30. The gain function in 2D Note that the width of the main beam is proportional to wavelength and inversely proportional to the antenna aperture Therefore: Large wavelength radars = big antenna Small wavelength radars = small antenna for same beam width Beam width (3 db down from peak) 10 cm 0.8 cm

  31. Side Lobe: S-Pol antenna pattern HH

  32. Side Lobe: S-Pol antenna pattern VV

  33. Side Lobe: S-Pol 2D patterns

  34. CHILL’s new Gregorian offset feed double reflector dish

  35. CSU CHILL pattern with new antenna

  36. Problems associated with sidelobes Horizontal “spreading” of weaker echo to the sides of a storm… Echo from sidelobe is interpreted to be in the direction of the main beam, but the magnitude is weak because power in sidelobe is down ~ 25 db. The problem is the worst in high reflectivity gradient situations

  37. Problems associated with sidelobes Vertical “spreading” of weaker echo to the top of a storm… Echo from sidelobe is interpreted to be in the direction of the main beam, but the magnitude is weak because power in sidelobe is down ~ 25 db.

  38. Where is the side lobe contamination visible? dBZ at 9.1 deg elevation angle

  39. Where is the side lobe contamination visible? ZDR at 9.1 deg elevation angle

  40. Where is the side lobe contamination visible? rhohv at 9.1 deg elevation angle

  41. Mie Scattering s /pa2 2pa/l From Rinehart (2004)

  42. Mie Scattering • Mie scattering region starts for particles of diameter ~ l/16. • For Ka-band Mie scattering is a factor at about 1 mm drops.

  43. Mie Scattering • The presence of Mie scattering means underestimated Ze • ZDR may be quite large in magnitude and noisy • Phase shift upon backscatter becomes important in Mie scattering – PHIDP is overestimated

  44. Optical Scattering • How will the ground clutter echoes compare between different wavelengths? • The same • Longer wavelength will have higher ground clutter Ze values • Shorter wavelength will have higher ground clutter Ze values

  45. Optical Scattering • How will the ground clutter echoes compare between different wavelengths: • The same • Longer wavelength will have higher ground clutter Ze values • Shorter wavelength will have higher ground clutter Ze values

  46. Optical Scattering • Ka-band a factor of 106, or 60 dB less sensitive to ground echoes s /pa2 2pa/l From Rinehart (2004)

  47. Background: What do the Radars See? Ka-band reflectivity, dBZ S-band reflectivity, dBZ Ground clutter contamination

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