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!!

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

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

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

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

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

Small Particle Approximation of Mie Theory for Spheres

Mass Absorption Coefficient

Use of Mass Absorption Coefficient For Cloud Droplets

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

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

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.

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

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

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

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

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.

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

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

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.

Radar: The Quickest Path to dbZ Power received is proportional to 1/d2. (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: http://en.wikipedia.org/wiki/NEXRAD

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.

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.

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

Radar Theory Part 1

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

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

Radar Bright Band: Strong Scattering from Melting Hydrometeors http://www.radar.mcgill.ca/bright_band.html

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.

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

Rain Fall Rate for Monodispersion

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.

Rain Drop Fall Speed

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

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

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?????

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

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.

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

NEXRAD System Today Gap

Supplemental and similar information for radar

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)

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).

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

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:

Introduction to Meteorological Radar 46

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

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

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

Example: Weather Echoes Microwave Transmitter Receiver

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.

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

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

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

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

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

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

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.

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

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

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 200-300%). 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