1. Assignment #2 If air with precipitation water content of 1 g/m 3, assuming mono size distribution (all hydrometeors have same size) How many raindrops would be in 1 m 3 (total number density N) if all raindrops have diameter (D) of 1 mm? Calculate 10log(N*D 6 ), units in mm 6 /m 3. How many snowflakes would be in 1 m 3 if all snowflakes have diameter of 5 mm and density in 0.3 g/cm 3 ? Calculate 10log(N*D 6 ), units in mm 6 /m 3. How many hails would be in 1 m 3 if all hails have diameter of 10 mm and density in 0.9g/cm 3 ? Calculate 10log(N*D 6 ), units in mm 6 /m 3.

2. Precipitation Content Basic units: g/m 3 Simple interpretation: Mass of water in a unit volume Extreme values: 0.1 gram/m 3 in light drizzle 10 gram/m 3 in rain in hurricane eyewall Example: A distribution of 1000 1-mm raindrops per cubic meter would have a precipitation content of about 0.5 grams/m 3.

3. Relationship of the Reflectivity Factor to other Meteorological Quantities Precipitation content (W): The mass of condensed water substance (water or ice) present in the form of precipitation-sized particles (detectable with radar), per unit volume. Where:  m j is the contribution to the total mass from each raindrop j

4. Precipitation Rate Basic units: m 3 /(m 2 sec) = m/s Standard units: mm/hr Simple interpretation: Depth of accumulated rainfall on a runoff-free surface Extreme values: 0.1 mm/hr in light drizzle 1000 mm/hr in a hurricane eyewall Example: A distribution of 1000 1-mm raindrops per cubic meter, falling at their terminal fall speed of 4 m/s in the absence of vertical motion, would give a precipitation rate of 2.1  10 -6 m/s or about 7.5 mm/hr.

5. Relationship of the Reflectivity Factor to other Meteorological Quantities Precipitation rate (R): The volume of precipitation passing downward through a horizontal surface, per unit area, per unit time. Where:  r j is the contribution to the rainfall rate from each raindrop j w j is the fall velocity of each drop j

6. What is the fall velocity of a raindrop? For drops with diameters between 0-2 mm (most drops) the fall velocity is proportional to diameter Terminal velocity of raindrops In still air (Foote and duTroit 1969) so what is the relationship to the radar reflectivity?

7. Problem: Illustration of inequality Consider two drops 1 mm and 2 mm Therefore: There is no exact Relationship between rainfall Rate and radar reflectivity Nevertheless, rainfall rates are qualitatively related to the radar reflectivity factor, and radar scientists have sought empirical relationships of the type: where Z R is the value of Z when R = R 0

8. Relationship of Z to Precipitation Rate Methods of determining Z-R relationships 1. The direct method: Values of Z and R are measured by a radar and raingages. The data are compared using correlation statistics and a Z-R relationship is determined from a best fit.

9. Relationship of Z to Precipitation Rate Methods of determining Z-R relationships 2. The indirect method: Values of Z and R are calculated from the same measured raindrop size distribution. Methods to measure raindrop size distributions Mechanical: stained filter paper: Uses water stains in filter paper to estimate raindrop sizes (used originally by Marshall and Palmer) Impact disdrometer: Uses raindrop’s momentum when striking surface to estimate its size.

10. Ground Based Optical disdrometers Airborne Optical disdrometers Foil impactors Determine drop sizes by shadows recorded on optical arrays Foil impactors: determine drop sizes from impact craters

11. Example of raindrop images collected with an airborne optical array spectrometer in a shower in Hawaii with the largest raindrop ever recorded in nature (courtesy Ken Beard)

12. Typical measured raindrop size distributions

13. Measurement Issues The measurement used to arrive at a Z-R is an issue too…………. Comparison of aircraft 2D-P measurements (truncated and untruncated) to disdrometer (Joss- Waldvogel) measurement. Truncated (at 1 mm) 2D-P measurement is closer to disdrometer measurement…..small drops? DSD instrumentation is an issue (e.g., impact-type disdrometers have sensitivity problems at the small drop end of the spectrum e.g., drops < 1 mm diameter).

14. To estimate Z and R, exponential approximations to raindrop size distributions are often developed The Marshall-Palmer Distribution Developed from raindrop samples collected in Canada on powdered sugar filter paper in 1948 by radar pioneers Marshall and Palmer

15. The Marshall-Palmer Distribution The Marshall-Palmer distribution stood as the standard for many decades although many subsequent studies showed that it was not universally applicable. The exponential distribution has properties that make it useful because it is easy to relate the drop size distribution to rainfall rate, precipitation content, and radar reflectivity

16. Radar scientists have tried to determine Z-R relationships because of the potential usefulness of radar determined rainfall for FLASH FLOOD NOWCASTING WATER MANAGEMENT AGRICULTURE (irrigation needs/drought impacts)

18. Z-R Variability: Convective/Stratiform Z=a 1 R b 1 Z=a 2 R b 2 10 log 10 Z R N(D) D Convective Stratiform D 0 strat > D 0 conv

19. There have been hundreds of Z-R relationships published – here are just a few between 1947 and 1960 – there have been 4 more decades of new Z-R relationships to add to this table since!

20. Z-R relationships are dependent on the type of rainfall (convective, stratiform, mixed), the season (summer, winter), the location (tropics, continental, oceanic, mid-latitudes), cloud type etc. For the NEXRAD radars, the NWS currently uses five different Z-R relationships and can switch between these depending upon the type of weather event expected.  Default WSR-88D (Z= 300R 1.4 )  Rosenfeld tropical (Z=250R 1.2 )  Marshall/Palmer (Z=200R 1.6 )  East Cool Season (Z=200R 2.0 )  West Cool Season (Z=75R 2.0 )

21. The single largest problem in applying Z-R relationships has been accounting for effects of the radar bright band The bright band: The melting level, where large snowflakes become water coated, but have not yet collapsed into small raindrops. Wet snowflakes scatter energy very effectively back to the radar

22. The bright band appears as a ring on PPI displays where the radar beam crosses the melting level

23. SNOW Few attempts have been made to develop Z-S relationships 1.Snow density varies significantly from storm to storm and within storms 2.Scattering by ice is non-Rayleigh (not spheres) and so the relationship between mass and Z is even less certain 3.Radars calibrated for rain (Z determined from K for rain, not ice, even in winter)

24. Measurements have been made of the size distributions of snowflakes and related to precipitation rates (melted equivalent), and Z-S relationships have been proposed but these relationships have largely been ignored in practice

25. Hail Very few attempts have been made to quantity hailfall from thunderstorms. Most work focuses on trying to identify whether hail is reaching the surface. This work is now focused on studies using polarization radar technology, which we will examine later in the course.

26. Doppler Radar From Josh Wurman NCAR S-POL DOPPLER RADAR

27. Doppler Shift: A frequency shift that occurs in electromagnetic waves due to the motion of scatterers toward or away from the observer. Doppler radar: A radar that can determine the frequency shift through measurement of the phase change that occurs in electromagnetic waves during a series of pulses. Analogy: The Doppler shift for sound waves is the frequency shift that occurs as race cars approach and then recede from a stationary observer

28. Sign conventions The Doppler frequency is negative (lower frequency, red shift) for objects receding from the radar The Doppler frequency is positive (higher frequency, blue shift) for objects approaching the radar These “color” shift conventions are typically also used on radar displays of Doppler velocity Blue: Toward radar Red: Receding from radar

29. Note that Doppler radars are only sensitive to the radial motion of objects Air motion is a three dimensional vector: A Doppler radar can only measure one of these three components – the motion along the beam toward or away from the radar

30. PROBLEM More than one Doppler frequency (radial velocity) will always exist that can fit a finite sample of phase values. The radial velocity determined from the sampled phase values is not unique

31. EXAMPLE VALUES OF THE MAXIMUM UNAMBIGUOUS DOPPLER VELOCITY Wavelength Radar PRF (s -1 ) cm 200 500 1000 2000 3 1.5 3.75 7.5 15 5 2.5 6.25 12.5 25 10 5.0 12.5 25.0 50 Table shows that Doppler radars capable of measuring a large range of velocities unambiguously have long wavelength and operate at high PRF

32. Folded velocities

33. Can you find the folded velocities in this image?

34. http://apollo.lsc.vsc.edu/classes/remote/graphics/airborne_radar_images/newcastle_folded.gif Folded velocities in an RHIVelocities after unfolding

35. The Doppler Dilema

36. Ways to circumvent the ambiguity dilema 1. “Bursts” of pulses at alternating low and high pulse repetition frequencies Measure reflectivityMeasure velocity Low PRF used to measure to long range, high PRF to measure velocity

37. A Guide to interpreting Doppler Velocity Patterns Rodger A. Brown and Vincent T. Wood National Severe Storms Laboratory NOAA Assignment #3

38. Multi Doppler analysis

39. Glen Romine When more than one radar views the same region of a storm, the pulse volumes have a different orientation, gain function relative to the particles and are generally not simultaneous…..

40. Multiple Doppler Retrieval of Wind Fields

42. How Quad Doppler wind retrieval from airborne radars works SQUALL LINE reflectivity shaded fore radar scan aft radar scan

43. How Quad Doppler wind retrieval from airborne radars works SQUALL LINE reflectivity shaded

44. How Quad Doppler wind retrieval from airborne radars works SQUALL LINE reflectivity shaded

45. Raw unedited data ground previously leveled

46. Final clean edited radar sweep!

47. Wind Output @ 3.5 km cross-section to be shown later NRL P-3 track NOAA P-3 track

48. Vertical cross-section A A’ A

49. Some real cases during SALLJEX field campaign are available at: http://trmm.chpc.utah.edu/old_web/salljex/

50. Polarimetric Radar

51. Long-standing Problems Distinguishing, ice and liquid phases of precipitation using radar Identifying specific hydrometeor populations, such as hail or supercooled water Quantifying, rain, snow and hailfall rates using radar.

52. Multi-Parameter Measurements Standard Doppler radar (Z HH, V r,  ) Polarization radar (signals of two different polarizations are processed): Many parameters can be derived (Measurements of two or more parameters of the radar signal) * Note notation: Z HH Transmitted at horizontal polarization Received at horizontal polarization

53. Linear Polarization (Doviak and Zrnić, 1993) http://www.nssl.noaa.gov/~schuur/radar.ht ml E E Electromagnetic Waves

54. Circular Polarization Practical use of circular polarization: Tracking aircraft in precipitation. Light to moderate rain: removal of a large portion (e.g. 99%) of the precipitation echo (transmitted right-hand circular polarized waves become, when scattered from small spherical drops, left-hand polarized). E

55. (Pruppacher and Klett, 1997) 4 mm 3.7 mm 2.9 mm 2.7 mm 1.8 mm 1.4 mm Differential Reflectivity Z DR Z DR [dB] = 10 log( ) – Depends on axis ratio oblate: ZDR > 0 prolate: ZDR < 0 – For drops: Z DR ~ drop size (0 - 4 dB) z HH z VV

56. Z DR (cont.) Z DR = 10 log( ) (Pruppacher and Klett, 1997) z HH z VV – For ice crystals: columns (1 – 4 dB) plates, dendrites (2 – 6 dB)

57. Z DR (cont.) Z DR = 10 log ( ) (Pruppacher and Klett, 1997) z HH z VV (Hobbs, 1974) – For hail: (-1 – 0.5 dB) – For graupel: (-0.5 – 1 dB) – For snow: (0 – 1 dB)

58. Z DR (cont.) Independent of calibration Independent of concentration (but can depend on how the concentration is distributed among various sizes Is affected by propagation effects (e.g. attenuation)

59. LDR [dB] = 10log( ) Linear Depolarization Ratio LDR (Pruppacher and Klett 1997) 4 mm 3.7 mm 2.9 mm z HV z HH Spheroidal hydrometeors with their major/minor axis aligned or orthogonal to the electric field of the wave: LDR - dB Detects tumbling, wobbling, canting angles, phase and irregular shaped hydrometeors: large rain drops (> -25 dB) Hail, hail and rain mixtures (-20 - -10 dB) wet snow (-13 - -18 dB) 8

60. Differential Propagation Phase Φ DP Φ DP [deg.]= Φ HH – Φ VV ΦHH, ΦVV: cumulative differential phase shift for the total round trip between radar and resolution volume). ΦHH, ΦVV = differential phase shift upon backscatter + differential phase shift along the propagation path

61. (Photos: Scott Ellis) NSF funded S-band dual polarization Doppler radar Highly mobile (fits in 6 sea containers) Antenna diameter 8.5 m Beam width 0.91 deg Range resolution 150 m S-Pol (NCAR)

62. Chill (CSU) NSF funded S-band dual polarization Doppler radar Antenna diameter 8.5 m Beam width (3 dB) 1.1 deg Range resolution 50, 75, 150 m

63. Koun WSR-88D Radar (NSSL Norman, OK) Polarimetric upgrade of NEXRAD radar, completed in March 2002

64. Wyoming King Air Cloud Radar (UW) K-band Dual/single polarization Doppler radar Beam width 0.4 – 0.8 deg (depending on antenna type) Antenna configurations down, side, up

66. Results

67. Assignment #3 Read the slides from the website: http://trmm.chpc.utah.edu/class/5230/homework.html