1. Chapter 12: Scattering and Absorption by Particles
around 1 cm
100 um < r < 3 mm
50 um < r < 100 um
10 um < r < 50 um
0.1 um < r < 10 um
r < 0.2 um
0.1 nm
deep UV
thermal IR
radar
Summary of Scattering Regimes: Note Particle Sizes
and wavelengths of radiation!!

2. Light Scattering Basics (images from Wallace and Hobbs CH4).
Angular Distribution of scattered radiation (phase function) x
Dipole scattering
Sphere, radius r, complex refractive index n=mr + imi
mr=1.5 Qs x 2
W. P. Arnott, AAAR tutorial, Sept. 2007 2

3. Small Particle Limit Size parameter x << 1. Helps understand:
Radar back scatter by hydrometeors
Absorption proportional to particle volume
Rayleigh scattering regime

4. Aerosol Optical Properties: Absorbing particles. Review
F0 (W/m2)
Pext (W) = F0 ext
Pabs (W) = F0 abs
Psca (W) = F0 sca
Optical power removed by ext=abs+sca.
For small optical depths,
and D < 0.1 µm:
I(L)/I(0) = e(-L L),
L(1/m) ≈ S.O.C (m2/g) x r (g/m3),
L = path length,
r = aerosol concentration by mass. 
particle
mass
Absorption dominates for D < 0.1 µm (Rayleigh scattering).
Aside: For non-absorbing aerosols, Extinction=Scattering. Note the strong dependence of the scattering coefficient on diameter!
1/r
Rayleigh

5. General Mie Theory: Optics of Homogeneous Spheres of radius r and refractive index m Sum of Complex Terms

6. Definitions: Optical Coefficients for Particles
Extinction coefficient for particle mono dispersions
Extinction coefficient for particle dispersions
Sheridan, P. J., W. P. Arnott, J. A. Ogren, B. E. Anderson, D. B. Atkinson, D. S. Covert, H. Moosmuller, A. Petzold, B. Schmid, A. W. Strawa, R. Varma and A. Virkkula (2005). "The Reno aerosol optics study: Overview and summary of results." Aerosol Science & Technology 39: 1-16.
Nebulized, dried
Ammonium Sulfate
532 nm
Slowik, Jay, G., Eben S. Cross, Jeong-Ho Han, Paul Davidovits,Timothy B. Onasch, John T. Jayne, Leah R. Williams, Manjula R. Canagaratna, Douglas R. Worsnop, Rajan K. Chakrabarty, Hans Moosmüller, William P. Arnott, Joshua P. Schwarz, Ru-Shan Gao, DavidW. Fahey, Gregory L. Kok, and Andreas Petzold (2007). An Inter-Comparison of Instruments Measuring Black Carbon Content of Soot Particles. Aerosol Science and Technology, 41:295–314, 2007. 6
W. P. Arnott, AAAR tutorial, Sept. 2007 6

7. Small Particle Approximation of Mie Theory for Spheres

8. Mass Absorption Coefficient

9. Use of Mass Absorption Coefficient For Cloud Droplets

10. Accelerating Dipole Moment Produces Rayleigh Scatteringq  -
dipole moment =P=Qx=E0
=polarizability + E0 x - +
Charge Q
Acceleration of dipole moment: Scattered E field!!!

11. Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole
Refer to last page
for polarization
states.
horizontal polarization
vertical polarization
average of both

12. Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole
vertical polarization
state
3D rendering
horizontal polarization
state
The Peanut!
Average of both
polarization states.

13. Mie Theory for Water Spheres (non absorbing)
Like sunset
Maximum, relative maxima and minima, approximate theory due to Rayleigh.
Generally m is a function of wavelength

14. Mie Theory for Water Spheres: m=1.33, Visible Wavelengths

15. Mie Theory for Absorbing and Scattering Spheres
modest ni has the largest absorption for modest size parameters.

16. Mie Phase Functions for Water Spheres
Note the dipole character for small x
and the primary and secondary rainbows
for large x.

17. Mie Phase Functions for Water Spheres: Log[p()] for details
Glory (strong backscattering, rainbow, and corona are clearly visible. Fogbow is ‘rainbow’ for small size parameter.

18. Mie Theory for Water and Ice Spheres
Absorption feature good for
phase determination.

19. Mass Absorption Coefficient for Cloud Water Spheres, Microwaves
Microwave remote sensing for cloud water path L:
TB = T = [1-exp(-kL)] T (Rayleigh Jeans Approximation for brightness temperature) T
microwave radiometer

20. Zenith Microwave Transmittance: Cloud Free Atmospheres
Water
Vapor
Rotational
Lines
Choose microwave frequencies for cloud emissivity measurement where transmittance is high!!! Water vapor is variable; choose low frequency.

21. Radar: The Quickest Path to dbZ
Power received is proportional to 1/d (inverse square law).
Doppler shift: Indicates speed.
Power received:
Responds to hydrometeor concentration.
Non polarized
operation d
Polarized and non polarized operation
Polarization: Allows for hail and rain discrimination
From:

22. Definitions RADAR is an acronym. RAdio Detection And Ranging.
Advanced Research Project Agency (ARPA) Long-range Tracking and Identification Radar (ALTAIR). Ballistic Missiles and Space Surveillance (military).
NEXRAD Weather Radar: WSR88D
Weather Surveillance Radar, 1988, Doppler.

23. Radar: The Quickest Path to dbZ
Absorption, scattering and extinction cross sections.
Backscattering cross section.
Cross section in the Rayleigh limit (particle diameter is much smaller than the wavelength of the radiation.)
Radar cross section for a particle in the Rayleigh limit.
Radar cross section for N particles in the Rayleigh limit.
Note: Key results are circled by a red box like this. The homework assignment is also given by a red box.

24. Monodispersons and Polydispersions
N particles / volume.
All of radius r.

25. Radar Theory Part 1

26. Radar Theory Part 2: Key Results!!!
This is what is reported on radar graphs!!!

27. Mie Radar Backscatter Efficiency for Water and Ice Spheres
Non Rayleigh
strong backscatter by water drops
compared to that of ice!!
Rayleigh
WSR-88D NWS Doppler Radar

28. Radar Bright Band: Strong Scattering from Melting Hydrometeors

29. Radar Theory Part 2: Typical Values of ZdbZ
Clear air mode of NEXRAD: -28 dbZ to 28 dbZ.
Precipitation mode of NEXRAD: 5 dbZ to 75 dbZ.
Light rain: 20 dbZ.

30. Rainfall Rate Analogy Falling rain: Coffee is being
poured at some rate.
Height of coffee = H
Rainfall Rate = Height of Coffee / time elapsed pouring it.
Rainfall Rate = dH / dt

31. Rain Fall Rate for Monodispersion

32. Radar Theory Part 3: Rainfall Rate Estimate From Radar
Definition of rainfall rate and what happens after rain hits the surface. Rainfall rate depends on the mass of water droplets and their fall speed.

33. Rain Drop Fall Speed

34. Rain Drop Fall Speed: A balance of Forces, Drag and Gravity

35. Fall Speed Is a Function of Size: Note the Shape in Terminal Flow
Ugggh!
NOT!!!

36. Radar Theory Part 3: Rainfall Rate Estimate From Radar
This is one relationship used to get rainfall rate (depth / time) from radar.
Problem: People have developed many such relationships! Which is correct, if any?????

37. Precipitation Estimation using the Z-R Relationship
The equation used for
the Z-R relationship can be changed to produce different outputs. Private companies or researchers may use a different Z-R relationship for different geographical regions or climatic zones
R = aZb
where
R = Rain Estimation
a = 300
Z = Radar Reflectivity
b = 1.5

38. Polarization Diverse Radar: Now at the NWS
Radar sends out horizontally and vertically polarized pulses.
Hydrometeors like raindrops are flattened. The horizontal cross sections are larger than the vertical.
Therefore for large raindrops a the horizontal polarization backscatter amount is larger than the vertical amount.
Hail stones are more symmetrical and have less polarization diversity.

39. Antenna Beamwidth radians Tradeoff:
D is the antenna diameter
λ is the wavelength of signal in air
Tradeoff:
Small wavelengths (high frequencies) = small antennas
But small wavelengths attenuate more

40. NEXRAD System Today
Gap

41. Supplemental and similar information for radar

42. NEXRAD RADAR Named WSR-88D S-band radar
radiation wavelength is λ = 10.7 cm
Peak pulse power is 1 MW
Pulse duration is from 1.5 to 4.5 usec.
Tallahassee (right)

43. More Definitions: NEXRAD and WSR-88D
NEXRAD or Nexrad (Next-Generation Radar) is a network of 159 high-resolution Doppler weather radars operated by the National Weather Service, an agency of the National Oceanic and Atmospheric Administration (NOAA) within the United States Department of Commerce. Its technical name is WSR-88D, which stands for Weather Surveillance Radar, 1988, Doppler.
NEXRAD detects precipitation and atmospheric movement or wind. It returns data which when processed can be displayed in a mosaic map which shows patterns of precipitation and its movement. The radar system operates in two basic modes, selectable by the operator: a slow-scanning clear-air mode for analyzing air movements when there is little or no activity in the area, and a precipitation mode with a faster scan time for tracking active weather. NEXRAD has an increased emphasis on automation, including the use of algorithms and automated volume scans.
(wikipedia).

44. Clear-Air Wind Profiler Radar Acoustic Sounder (obtain Tv(z) and (u,v,w) winds in principle)44

45. Total radiated power in a radar pulse
Pulse Lengths for WSR-88D Radar [Weather Surveillance Radar, 1988, Doppler]
Total radiated power in a radar pulse
Range Resolution:
Long Pulse:
Short Pulse:

46. Introduction to Meteorological Radar46

47. Energy Absorbed by Atmosphere
94 GHz
35 GHz
Maximum
Propagation
Distance
Energy Absorbed by Atmosphere
10-15 km
20-30 km
3.2 mm
8 mm
Radar Wavelength 47

49. RADAR Echolocation (RADAR ~ RAdio Detection And Ranging) “Microwave Echo-Location”Tx Rx
Microwave
Transmitter
Receiver

50. Target Spatial Orientation
Large Drops
Polarization Pt
Small Drops
Closer look at Large drop
Polarization Ps

51. Example: Weather Echoes
Microwave
Transmitter
Receiver

52. Why Radar Can't (Usually) See Tornadoes
The network of WSR-88D Doppler radars across the US has certainly proven itself for the ability to detect severe weather. Tornado warnings, in particular, are much better now that National Weather Service forecasters have this fantastic new (new as of the early 1990s) tool.
But did you know that Doppler radar (usually) can't see an actual tornado? When Doppler radar is cited in a tornado warning it is generally because meteorologists see evidence the storm itself is rotating. It is a supercell thunderstorm or at least contains an area of rotation called a mesocyclone.
When can and when can't Doppler radar see a tornado? It's math! Let's figure it out. We'll be looking into two factors:
1) the earth is curved, and
2) the radar "beam" is 1 degree wide.

53. Antennas
Antenna is a transition passive device between the air and a transmission line that is used to transmit or receive electromagnetic waves.

54. Beam Height vs. Distance
Lowest elevation slice is 0.5° so it is not totally horizontal.
Earth’s curvature also plays a role.
Radar beam gets higher off the ground farther from the radar.
Makes low level precipitation invisible to radar at considerable distances.
From the National Weather Service
Greenville-Spartanburg, SC

55. Velocity Images (Doppler) Precipitation Estimates
Products Available
Reflectivity Images
Velocity Images (Doppler)
Precipitation Estimates
Vertically Integrated Liquid
Echo Tops
Animated Loops of Most Products
Many Other Products
From the National Weather Service
Greenville-Spartanburg, SC

56. Base Reflectivity and Composite Reflectivity
Reflectivity Images
Base Reflectivity and Composite Reflectivity
Base Reflectivity
Composite Reflectivity
Displays the maximum returned signal from all of the elevation scans
Better summary of precipitation intensity
Much less deceiving than Base Reflectivity
Subtle 3-D storm structure hidden
0.5° elevation slice
Shows only the precipitation at the lowest tilt level
May underestimate intensity of elevated convection or storm cores
From the National Weather Service
Greenville-Spartanburg, SC

57. Doppler Precipitation Estimate
Advantages and Limitations
Great for scattered areas of rain where no rain gauges are located
Has helped issue flash flood warnings more efficiently
Helps fill in the holes where ground truth information is not available
Much better lead time for warnings
Provides a graphical ‘map’ of rainfall for an entire region
Data can be overlaid with terrain and watersheds to predict reservoir and waterway crests
Estimates based on cloud water levels and not ground level rainfall
‘Hail Contamination’ causes highly inflated values
High terrain causes underestimates
Lower resolution than reflectivity images
Useful as a supplement, not replacement for ground truth information
From the National Weather Service
Greenville-Spartanburg, SC

58. Radar Loops From the National Weather Service
Greenville-Spartanburg, SC

59. What Next for NEXRAD? WSRP-2010D
Polarimetric radar
The next major upgrade is polarimetric radar, which adds vertical polarization to the current horizontal radar waves, in order to more accurately discern what is reflecting the signal. This so-called dual polarization allows the radar to distinguish between rain, hail and snow, something the horizontally polarized radars cannot accurately do. Early trials have shown that rain, ice pellets, snow, hail, birds, insects, and ground clutter all have different signatures with dual-polarization, which could mark a significant improvement in forecasting winter storms and severe thunderstorms. The deployment of the dual polarization capability to nexrad sites will begin in 2010 and last until 2012.

60. POLARIMETRIC RADAR? Conventional Radar (NEXRAD) Polarimetric
Radar (ARMOR) `

61. Polarimetric Variables
Reflectivity factor Z at horizontal polarization
- Measure of size and concentration of scatters
(dominated by SIZE)
2. Differential reflectivity ZDR
- Measure of median drop diameter→ SIZE/SHAPE
- Useful for rain / hail / snow discrimination→ SIZE/SHAPE/PHASE
3. Differential phase ΦDP (Specific Differential Phase- KDP)
- Efficient for accurate rainfall estimation→ NUMBER/SHAPE
- Immune to radar miscalibration, attenuation, and partial beam blockage
4. Cross-correlation coefficient ρhv
- Indicator of mixed precipitation → SHAPE/PHASE
- Efficient for identifying nonmeteorological scatterers
Operational:
NEXRAD, TV vs
Small ZDR Large ZDR
Research:
NCAR, CSU, NASA, UND, DLR, BMRC, NOAA-ETL
ARMOR

62. Advantages of a Dual-Polarization Radar
Really just a self-consistent way of obtaining a more complete description of the particle types and shapes present in a given volume of space.
More accurate rainfall estimation (10-20% max accumulation error as opposed to %).
Why? Because we collect information on drop size/shape/concentration and are able to mitigate hail contamination.
Identification of precipitation types and discrimination between meteorological and non-meteorological scatterers
Improvement in radar data quality: Self consistent way to calibrate using polarimetric variables vs
Small ZDR Large ZDR
Small drops Large drops
Mitigates the multiple Z-R issues! vs
Hail Rain vs
Insects
Rain