What does radar measure?

1. What does radar measure? Hydrometeors: rain drops, ice particles Other objects: e.g. birds, insects.

2. Weather radar equations • To convert equations for distributed targets into weather radar equations, we must determine the radar reflectivity of arrays of precipitation particles. • This problem can be divided into three parts: • Finding the radar cross of a single particle; • (b) Finding the total radar cross section for the entire contributing region • (c) Dividing the total cross section by the effective volume of the contributing region to obtain the average radar reflectivity havg

3. First Assumption: Particles are all spheres Small raindrops and cloud droplets: Spherical Large raindrops: Ellipsoids Ice crystals Varied shapes Graupel and rimed particles Can be spherical Hail May or may not be spheres The scattering properties and radar cross sections of spherical particles have been calculated and are well understood.

4. The angular patterns of the scattered intensity from particles of three sizes: (a) small particles, (b) large particles, and (c) larger particles Rayleigh scattering pattern

5. What is the fundamental difference between the Rayleigh, Mie, and Optical regimes? With Rayleigh scattering, the electric field is assumed to be invariant in the vicinity of the particle

6. Second assumption: The particles are sufficiently small compared to the wavelength of the impinging microwaves that the scattering can be described by Raleigh Scattering Theory How small is small? From the figure above, the radius of the particle, a, must be (~ 1/6 of the wavelength)

7. p Einc Dielectric Sphere (water drop) incident plane wave A plane wave with electric field Einc induces an electric dipole p in a small sphere. The induced dipole is parallel to the direction of Einc which is also the direction of polarization of the incident wave.

8. From Rayleigh scattering theory, the dipole moment p induced in a spherical particle is proportional to the particle’s volume (D3), the material the particle is made of (K: ice or water) and the magnitude of the incident electric field (Einc). (1) And the intensity of the scattered electric field at the location of the particle is: [The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge.] (2)

9. Combining (1) and (2) we get: (3) To determine the radar cross section • divide (3) by Einc • (b) Square both sides of the resulting equation • (c) Multiply by 4pr2 (4)

10. What is K? K is a complex number representing the scattering (real part) and absorption characteristics of the medium Permittivity of medium where Permittivity of vacuum Values of Water Ice 0.176 for ice particles (0.208 is used when snowflake sizes are expressed as the diameters of water drops obtained by melting the ice).

11. (4) The radar cross section For an array of particles, we determine the average radar cross section (5) Now we determine the radar reflectivity: (6)

12. The quantity is of utmost importance in radar meteorology It is designated with the symbol Z, and is called the radar reflectivity factor In logarithmic units: It is the quantity that is displayed on a radar screen.

13. Relationship between the radar reflectivity and the radar reflectivity factor: (7) Recall the radar equation for a distributed target: Combining:

14. THE RADAR EQUATION FOR WEATHER TARGETS Radar characteristics Target characteristics constants where Z in normally expressed in logarithmic units

15. The weather radar equation: review of the assumptions • 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 uniform throughout the contributing region and constant over the period of time needed to obtain the average value of the received power.

16. The Weather radar equation: review of the assumptions 4. All of the particles have the same dielectric factor; that is, they are all either water droplets or ice particles. 5. The main lobe of the antenna is adequately described by a Gaussian function. 6. Microwave attenuation over the distance between the radar and the target is negligible. 7. Multiple scattering is negligible. Multiple scattering and attenuation are related so if one is true the other is too. 8. The incident and back-scattered waves are linearly polarized.

17. Review of the impact of the second assumption: The particles are sufficiently small compared to the wavelength of the impinging microwaves that the scattering can be described by Raleigh Scattering Theory How small is small? From the figure above, the radius of the particle, a, must be (~ 1/6 of the wavelength)

18. Validity of the Rayleigh Approximation for weather targets Valid Raindrops: 0.01 – 0.5 cm (all rain) Snowflakes: 0.01– 3 cm (most snowflakes) Hailstones: 0.5 – 2.0 cm (small to moderate hail) l = 10 cm Raindrops: 0.01 – 0.5 cm (all rain) Snowflakes: 0.01– 1 cm (small snowflakes) Hailstones: 0.5 – 0.75 cm (small hail) l = 5 cm Raindrops: 0.01 – 0.5 cm (all rain) Ice crystals: 0.01– 0.5 cm (single crystals) Graupel: 0.1 -- 0.5 cm (graupel) l = 3 cm Raindrops: 0.01 – 0.15 cm (cloud and drizzle drops) Ice crystals: 0.01– 0.15 cm (single crystals) l = 0.8 cm

19. Validity of the Rayleigh Approximation for weather targets Invalid l = 10 cm Hailstones: > 2.0 cm (large hail) Snowflakes > 1 cm (large snowflakes) Hailstones: > 0.75 cm (moderate to large hail) l = 5 cm Raindrops: 0.01 – 0.5 cm (all rain) Snowflakes > 0.5 cm Hail and large graupel l = 3 cm Drops > 100 microns All ice particles except small crystals l = 0.8 cm

20. Reflectivity calculation for hail storms from different radar frequencies

21. Reflectivity calculation for hail storms from different radar frequencies

22. When the assumptions built into the radar equation are not satisfied, the reflectivity factor is referred to as: The Equivalent Radar Reflectivity Factor, Ze

23. Units of Z One would think the standard units of Z would be m6/m3 = m3 But no… The standard units for Z are mm6/m3 If these units are not used, you will be off by 10-18

24. Range of radar reflectivity factor in weather echoes WSR-88D Precipitation Mode WSR-88D Clear Air Mode 75 dbZ = giant hail 45-50 dbZ = heavy rain 25 dbZ = snow -28 dbZ = haze droplets

25. Nebraska record hailstorm 2003 75 dBZ

26. Heavy rain in Hurricane Andrew’s Eyewall = 45 dBZ

27. Snowstorm over Great Lakes: ~ 25-30 dBZ

28. Clear air echoes (few small insects) -12 dBZ

29. Echoes in clear air from insects Common is summer. Watch for echoes to expand area as sun sets and insects take off for their nocturnal travels

30. Echoes from birds and bats Birds take off radially from roosts in morning producing concentric rings of echo. Bats do the same at night. Migrating birds will produce small echo clusters that move across screen. Birds departing At 1114 UTC

31. Blocked beams (topography or buildings) Blocked beam

32. The bright band an enhancement of radar reflectivity at the melting level when snowflakes falling From above aggregate and develop wet surfaces. Note convective and stratiform regions of squall line. Precipitation estimates in stratiform region must be carefully examined because of bright band effects

33. Why there is a bright band? Recall |K2| for water is about 0.93 and for ice is about 0.176 When ice particles falling below 0oC, they start to melt, beginning from the surface. Therefore, they keep the size of the ice particle but coated with water. So the radar received power difference would be: P ice coated with water / P ice = 0.93/0.176 = 5.284 dBZ Zice coated with water = 10log Zice *5.284 = 10logZice + 10log(5.284) = dBZ Zice + 7.2 dBZ After totally melted, the ice particles becoming rain drops. The density increased from ~0.4 g/cm3 to 1 g/cm3 and the particle size decreased, so the reflectivity decreased.

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

35. An extreme example of bright band contamination of precipitation estimation – radar estimates 6 inches of precipitation in a winter storm on January 31, 2002!

36. Different radar displays

37. NEXRAD (WSR-88D) Operations and Scanning Procedures

38. Plan-Position Indicator (PPI) Scanning procedure Echoes close to the radar are at a low elevation Echoes far from the radar are at a high elevation Data collected on a cone are projected onto a plane

39. WSR-88D Volume Scanning Procedures Precipitation mode scan geometry Severe weather scan geometry Saves time…fewer elevations

40. Clear air mode: Fewer elevations, slower antenna rotation to achieve greater sensitivity for sensing clear air turbulence, insects and clouds, light drizzle or light snowfall.

41. Radar reflectivity: A measure of the power scattered back to the radar from objects in the path of a radar beam. Proportional to the sum of the sixth power of the diameter of all the particles illuminated by a pulse provided the particles are much smaller than the radar wavelength.

42. Base reflectivity: Echo intensity at the lowest scan level (0.5o) measured in dBZ

43. Composite reflectivity: Maximum echo intensity at any scan level measured in dBZ

44. “Precipitation” mode

45. “Clear air” mode (often used for snow) Radar parameters set to increase sensitivity

46. Storm Total Precipitation: Measured in inches fallen after an NWS selected start time.

47. Storm total precipitation is the primary tool for flash flood forecasting

48. Vertically integrated liquid (VIL): VIL is the integration of reflectivity within a column of air. Once thought to be related to potential hail size, but not really a good predictor.

49. Radial velocity: Velocity component along the radar beam direction (knots)

50. Radial Velocity A measure of the component of the wind along the direction of the radar beam