pat arnott, atms 749 atmospheric radiation transfer chapter 12: scattering and absorption by...

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Chapter 12: Scattering and Absorption by Particles

Summary of Scattering Regimes: Note Particle Sizesand wavelengths of radiation!!

0.1 nm

r < 0.2 um

0.1 um < r < 10 um

10 um < r < 50 um

50 um < r < 100 um

100 um < r < 3 mm

around 1 cm

deep UV radarthermalIR

pat arnott, atms 360W. P. Arnott, AAAR tutorial, Sept. 2007 2

Light Scattering Basics (images from Wallace and Hobbs CH4).

Sphere, radius r, complex refractive index n=mr + imi

x

xx mr=1.5

Qs

Angular Distribution of scattered radiation (phase function)

x x

xDipole scattering


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

For small optical depths,

and D < 0.1 µm:

I(L)/I(0) = e(- L),

(1/m) ≈ S.O.C (m2/g) x (g/m3),

L = path length,

= aerosol concentration by 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!

particlemass

F0 (W/m2)Pext (W) = F0 ext

Pabs (W) = F0 abs

Psca (W) = F0 sca

Optical power removed by ext=abs+sca.

Rayleigh 1/r


General Mie Theory: Optics of Homogeneous Spheres of radius r and

refractive index mSum of Complex Terms

pat arnott, atms 360W. P. Arnott, AAAR tutorial, Sept. 2007 6

Definitions: Optical Coefficients for Particles

Extinction coefficient for particle mono dispersions

Extinction coefficient for particle dispersions

Nebulized, dried Ammonium Sulfate532 nm

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.

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.


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

E0

+

-

Charge Q-+

P

dipole moment =P=Qx=E0

=polarizabilityx

Acceleration of dipole moment: Scattered E field!!!


Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole

Refer to last pagefor polarization states.

horizontal polarization

vertical polarization

average of both


Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole

3D rendering

vertical polarizationstate

horizontal polarizationstate

The Peanut!Average of bothpolarization states.


Mie Theory for Water Spheres (non absorbing)

Maximum, relative maxima and minima, approximate theory due to Rayleigh.

Generally m is a function of wavelength

Like sunset


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 xand 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)

microwave radiometer

T


Zenith Microwave Transmittance: Cloud Free Atmospheres

Choose microwave frequencies for cloud emissivity measurement wheretransmittance is high!!! Water vapor is variable; choose low frequency.

WaterVapor

RotationalLines


Radar: The Quickest Path to dbZ

Non polarizedoperation

Polarized andnon polarizedoperation

Doppler shift:Indicates speed.Power received:Responds to hydrometeorconcentration.

Polarization:Allows for hailand rain discrimination

d

From: http://en.wikipedia.org/wiki/NEXRAD

Power received is proportional to 1/d2. (inverse square law).

Pat Arnott, ATMS360

DefinitionsRADAR is an acronym. RAdio Detection And Ranging.

NEXRAD Weather Radar: WSR88D

Advanced Research Project Agency (ARPA) Long-range Tracking and Identification Radar (ALTAIR). Ballistic Missiles and Space Surveillance (military).

Weather Surveillance Radar, 1988, Doppler.

pat arnott, atms 360

Radar: The Quickest Path to dbZ

1. Absorption, scattering and extinction cross sections.

2. Backscattering cross section.

3. Cross section in the Rayleigh limit (particle diameter is much smaller than the wavelength of the radiation.)

4. Radar cross section for a particle in the Rayleigh limit.

5. 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.

n

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

Rayleigh

Non Rayleigh

WSR-88D NWS Doppler Radar

strong backscatter by water drops

compared to that of ice!!


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 beingpoured 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


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?????

Pat Arnott, ATMS360

Precipitation Estimation using the

Z-R Relationship

R = aZb

where

R = Rain Estimation

a = 300

Z = Radar Reflectivity

b = 1.5

The equation used forthe 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


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.

Pat Arnott, ATMS360

Antenna Beamwidth

radians

D is the antenna diameter

λ is the wavelength of signal in air

Tradeoff: Small wavelengths (high frequencies) = small antennasBut small wavelengths attenuate more

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NEXRAD System TodayNEXRAD System Today

Gap

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Supplemental and similar information for radar

Pat Arnott, ATMS360

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)

Pat Arnott, ATMS360

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).

Pat Arnott, ATMS360

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

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Pulse Lengths for WSR-88D Radar[Weather Surveillance Radar, 1988, Doppler]

• Total radiated power in a radar pulse

• Range Resolution:

• Long Pulse:

• Short Pulse:

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Introduction to Meteorological Radar

Pat Arnott, ATMS360

Ene

rgy

Abs

orbe

d by

Atm

osph

ere

Radar Wavelength

35 GHz

94 GHz

MaximumPropagation

Distance

20-30 km

10-15 km

8 mm3.2 mm

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Pat Arnott, ATMS360

RADAR Echolocation(RADAR ~ RAdio Detection And Ranging)

“Microwave Echo-Location”

MicrowaveTransmitter

Receiver

Tx

Rx

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Target Spatial Orientation

Polarization Pt

PolarizationPs

Large Drops

Small Drops

Closer look at Large

drop

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Example: Weather Echoes

MicrowaveTransmitter

Receiver

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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.

Pat Arnott, ATMS360

Antennas

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

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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

Pat Arnott, ATMS360

Products Available

▪Reflectivity Images

▪Velocity Images (Doppler)

▪Precipitation Estimates

▪Vertically Integrated Liquid

▪Echo Tops

▪Animated Loops of Most Products

▪Many Other Products



Pat Arnott, ATMS360

Reflectivity Images

Base Reflectivity and Composite Reflectivity

Base Reflectivity

Composite Reflectivity

○0.5° elevation slice

○Shows only the precipitation at the lowest tilt level

○May underestimate intensity of elevated convection or storm cores

○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



Pat Arnott, ATMS360

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



Pat Arnott, ATMS360

Radar Loops



Pat Arnott, ATMS360

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.

Pat Arnott, ATMS360

ConventionalRadar (NEXRAD)

PolarimetricRadar (ARMOR)

POLARIMETRIC RADAR?

Pat Arnott, ATMS360

Polarimetric Variables1. 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

Research:

NCAR, CSU, NASA, UND, DLR, BMRC, NOAA-ETL

ARMOR

Operational:

NEXRAD, TV

vs

Small ZDR Large ZDR

Pat Arnott, ATMS360

• 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

Advantages of a Dual-Polarization RadarReally just a self-consistent way of obtaining a more complete description of the particle types and shapes present in a given volume of space.

vs

Small ZDR Large ZDRSmall drops Large drops

vs

Hail Rain

vs

Insects Rain

Mitigates the multiple Z-R issues!

pat arnott, atms 749 atmospheric radiation transfer chapter 12: scattering and absorption by...

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