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Chapter 12: Scattering and Absorption by Particles around 1 cm 100 um < r 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!! Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Light Scattering Basics (images from Wallace and Hobbs CH 4). Angular Distribution of scattered Light Scattering Basics (images from Wallace and Hobbs CH 4). Angular Distribution of scattered radiation (phase function) x x Sphere, radius r, complex refractive index n=mr + imi Dipole scattering x Qs x x mr=1. 5 x W. P. Arnott, AAAR tutorial, Sept. 2007 2 pat arnott, atms 360

Small Particle Limit Size parameter x << 1. Helps understand: • Radar back scatter Small Particle Limit Size parameter x << 1. Helps understand: • Radar back scatter by hydrometeors • Absorption proportional to particle volume • Rayleigh scattering regime Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Aerosol Optical Properties: Absorbing particles. Review Optical power removed by ext=abs+sca. F 0 (W/m Aerosol Optical Properties: Absorbing particles. Review Optical power removed by ext=abs+sca. F 0 (W/m 2) Pext (W) = F 0 ext Pabs (W) = F 0 abs Psca (W) = F 0 sca For small optical depths, and D < 0. 1 µm: I(L)/I(0) = e(-L L), L(1/m) ≈ S. O. C (m 2/g) x r (g/m 3), L = path length, r = aerosol concentration by mass. • Absorption dominates for D < 0. 1 µm (Rayleigh scattering). particle mass Rayleigh Pat Arnott, ATMS 749 Atmospheric Radiation Transfer 1/r • Aside: For non-absorbing aerosols, Extinction=Scattering. Note the strong dependence of the scattering coefficient on diameter!

General Mie Theory: Optics of Homogeneous Spheres of radius r and refractive index m General Mie Theory: Optics of Homogeneous Spheres of radius r and refractive index m Sum of Complex Terms Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Definitions: Optical Coefficients for Particles Extinction coefficient for particle mono dispersions Sheridan, P. J. Definitions: Optical Coefficients for Particles Extinction coefficient for particle mono 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. 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, David. W. 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. W. P. Arnott, AAAR tutorial, Sept. 2007 Extinction coefficient for particle dispersions Nebulized, dried Ammonium Sulfate 532 nm 6 pat arnott, atms 360

Small Particle Approximation of Mie Theory for Spheres Pat Arnott, ATMS 749 Atmospheric Radiation Small Particle Approximation of Mie Theory for Spheres Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mass Absorption Coefficient Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Mass Absorption Coefficient Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Use of Mass Absorption Coefficient For Cloud Droplets Pat Arnott, ATMS 749 Atmospheric Radiation Use of Mass Absorption Coefficient For Cloud Droplets Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Accelerating Dipole Moment Produces Rayleigh Scattering P E 0 q + x + Charge Accelerating Dipole Moment Produces Rayleigh Scattering P E 0 q + x + Charge Q Pat Arnott, ATMS 749 Atmospheric Radiation Transfer =P=Qx= E 0 =polarizability dipole moment Acceleration of dipole moment: Scattered E field!!!

Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole Refer to 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 Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole 3 D Rayleigh Scattering Phase Function: Angular Distribution of Light Scattered by a Dipole 3 D rendering vertical polarization state horizontal polarization state The Peanut! Average of both polarization states. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mie Theory for Water Spheres (non absorbing) Like sunset Maximum, relative maxima and minima, Mie Theory for Water Spheres (non absorbing) Like sunset Maximum, relative maxima and minima, approximate theory due to Rayleigh. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Generally m is a function of wavelength

Mie Theory for Water Spheres: m=1. 33, Visible Wavelengths Pat Arnott, ATMS 749 Atmospheric Mie Theory for Water Spheres: m=1. 33, Visible Wavelengths Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mie Theory for Absorbing and Scattering Spheres modest ni has the largest absorption for Mie Theory for Absorbing and Scattering Spheres modest ni has the largest absorption for modest size parameters. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mie Phase Functions for Water Spheres Note the dipole character for small x and Mie Phase Functions for Water Spheres Note the dipole character for small x and the primary and secondary rainbows for large x. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mie Phase Functions for Water Spheres: Log[p( )] for details Glory (strong backscattering, rainbow, 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. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mie Theory for Water and Ice Spheres Absorption feature good for phase determination. Pat Mie Theory for Water and Ice Spheres Absorption feature good for phase determination. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Mass Absorption Coefficient for Cloud Water Spheres, Microwaves Microwave remote sensing for cloud water Mass Absorption Coefficient for Cloud Water Spheres, Microwaves Microwave remote sensing for cloud water path L: TB = T = [1 -exp(-k. L)] T (Rayleigh Jeans Approximation for brightness temperature) T microwave radiometer Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Zenith Microwave Transmittance: Cloud Free Atmospheres Water Vapor Rotational Lines Choose microwave frequencies for 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. Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Radar: The Quickest Path to db. Z Power received is proportional to 1/d 2. Radar: The Quickest Path to db. Z Power received is proportional to 1/d 2. (inverse square law). Doppler shift: Indicates speed. Power received: Responds to hydrometeor concentration. Non polarized operation d Polarized and non polarized operation Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Polarization: Allows for hail and rain discrimination From: http: //en. wikipedia. org/wiki/NEXRAD

Definitions RADAR is an acronym. RAdio Detection And Ranging. NEXRAD Weather Radar: WSR 88 Definitions RADAR is an acronym. RAdio Detection And Ranging. NEXRAD Weather Radar: WSR 88 D Weather Surveillance Radar, 1988, Doppler. Advanced Research Project Agency (ARPA) Long-range Tracking and Identification Radar (ALTAIR). Ballistic Missiles and Space Surveillance (military). Pat Arnott, ATMS 360

Radar: The Quickest Path to db. Z 1. Absorption, scattering and extinction cross sections. Radar: The Quickest Path to db. Z 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. pat arnott, atms 360

Monodispersons and Polydispersions n N particles / volume. All of radius r. r pat Monodispersons and Polydispersions n N particles / volume. All of radius r. r pat arnott, atms 360

Radar Theory Part 1 pat arnott, atms 360 Radar Theory Part 1 pat arnott, atms 360

Radar Theory Part 2: Key Results!!! This is what is reported on radar graphs!!! Radar Theory Part 2: Key Results!!! This is what is reported on radar graphs!!! pat arnott, atms 360

Mie Radar Backscatter Efficiency for Water and Ice Spheres Non Rayleigh strong backscatter by Mie Radar Backscatter Efficiency for Water and Ice Spheres Non Rayleigh strong backscatter by water drops compared to that of ice!! Rayleigh WSR-88 D NWS Doppler Radar Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Radar Bright Band: Strong Scattering from Melting Hydrometeors http: //www. radar. mcgill. ca/bright_band. html Radar Bright Band: Strong Scattering from Melting Hydrometeors http: //www. radar. mcgill. ca/bright_band. html Pat Arnott, ATMS 749 Atmospheric Radiation Transfer

Radar Theory Part 2: Typical Values of Zdb. Z Clear air mode of NEXRAD: Radar Theory Part 2: Typical Values of Zdb. Z Clear air mode of NEXRAD: -28 db. Z to 28 db. Z. Precipitation mode of NEXRAD: 5 db. Z to 75 db. Z. Light rain: 20 db. Z. pat arnott, atms 360

Rainfall Rate Analogy Falling rain: Coffee is being poured at some rate. Height of 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 = d. H / dt pat arnott, atms 360

Rain Fall Rate for Monodispersion pat arnott, atms 360 Rain Fall Rate for Monodispersion pat arnott, atms 360

Radar Theory Part 3: Rainfall Rate Estimate From Radar Definition of rainfall rate and 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. pat arnott, atms 360

Rain Drop Fall Speed pat arnott, atms 360 Rain Drop Fall Speed pat arnott, atms 360

Rain Drop Fall Speed: A balance of Forces, Drag and Gravity pat arnott, atms Rain Drop Fall Speed: A balance of Forces, Drag and Gravity pat arnott, atms 360

Fall Speed Is a Function of Size: Note the Shape in Terminal Flow pat Fall Speed Is a Function of Size: Note the Shape in Terminal Flow pat arnott, atms 360

Radar Theory Part 3: Rainfall Rate Estimate From Radar This is one relationship used 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, atms 360

Precipitation Estimation using the Z-R Relationship The equation used for the Z-R relationship can 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 = a. Zb where R = Rain Estimation a = 300 Z = Radar Reflectivity b = 1. 5 Pat Arnott, ATMS 360

Polarization Diverse Radar: Now at the NWS • Radar sends out horizontally and vertically 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. arnott, atms 360 pat

Antenna Beamwidth radians D is the antenna diameter λ is the wavelength of signal Antenna Beamwidth radians 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 Pat Arnott, ATMS 360

NEXRAD System Today Gap Pat Arnott, ATMS 360 NEXRAD System Today Gap Pat Arnott, ATMS 360

Supplemental and similar information for radar Pat Arnott, ATMS 360 Supplemental and similar information for radar Pat Arnott, ATMS 360

NEXRAD RADAR • Named WSR-88 D • S-band radar • radiation wavelength is λ NEXRAD RADAR • Named WSR-88 D • 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, ATMS 360

More Definitions: NEXRAD and WSR-88 D NEXRAD or Nexrad (Next-Generation Radar) is a network More Definitions: NEXRAD and WSR-88 D 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-88 D, 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 slowscanning 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, ATMS 360

Clear-Air Wind Profiler Radar Acoustic Sounder (obtain Tv(z) and (u, v, w) winds in Clear-Air Wind Profiler Radar Acoustic Sounder (obtain Tv(z) and (u, v, w) winds in principle) Pat Arnott, ATMS 360

Pulse Lengths for WSR-88 D Radar [Weather Surveillance Radar, 1988, Doppler] • Total radiated Pulse Lengths for WSR-88 D Radar [Weather Surveillance Radar, 1988, Doppler] • Total radiated power in a radar pulse • Range Resolution: • Long Pulse: • Short Pulse: Pat Arnott, ATMS 360

Introduction to Meteorological Radar Pat Arnott, ATMS 360 Introduction to Meteorological Radar Pat Arnott, ATMS 360

Energy Absorbed by Atmosphere 94 GHz 35 GHz Maximum Propagation Distance 10 -15 km Energy Absorbed by Atmosphere 94 GHz 35 GHz Maximum Propagation Distance 10 -15 km 20 -30 km 3. 2 mm 8 mm Radar Wavelength Pat Arnott, ATMS 360

Pat Arnott, ATMS 360 Pat Arnott, ATMS 360

RADAR Echolocation (RADAR ~ RAdio Detection And Ranging) “Microwave Echo-Location” Tx Rx Microwave Transmitter RADAR Echolocation (RADAR ~ RAdio Detection And Ranging) “Microwave Echo-Location” Tx Rx Microwave Transmitter Receiver Pat Arnott, ATMS 360

Target Spatial Orientation Large Drops Polarization Pt Small Drops Polarization Ps Closer look at Target Spatial Orientation Large Drops Polarization Pt Small Drops Polarization Ps Closer look at Large drop Pat Arnott, ATMS 360

Example: Weather Echoes Microwave Transmitter Receiver Pat Arnott, ATMS 360 Example: Weather Echoes Microwave Transmitter Receiver Pat Arnott, ATMS 360

Why Radar Can't (Usually) See Tornadoes • The network of WSR-88 D Doppler radars Why Radar Can't (Usually) See Tornadoes • The network of WSR-88 D 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 1990 s) 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, ATMS 360

Antennas • Antenna is a transition passive device between the air and a transmission Antennas • Antenna is a transition passive device between the air and a transmission line that is used to transmit or receive electromagnetic waves. Pat Arnott, ATMS 360

Beam Height vs. Distance ○ Lowest elevation slice is 0. 5° so it is 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, ATMS 360

Products Available ▪ Reflectivity Images ▪ Velocity Images (Doppler) ▪ Precipitation Estimates ▪ Vertically 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 Pat Arnott, ATMS 360

Reflectivity Images Base Reflectivity and Composite Reflectivity Base Reflectivity ○ 0. 5° elevation slice Reflectivity Images Base Reflectivity and Composite Reflectivity Base Reflectivity ○ 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 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 Pat Arnott, ATMS 360

Doppler Precipitation Estimate Advantages ● Great for scattered areas of rain where no rain Doppler Precipitation Estimate Advantages ● 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 and Limitations ● 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 Pat Arnott, ATMS 360

From the National Weather Service Greenville-Spartanburg, SC Radar Loops Pat Arnott, ATMS 360 From the National Weather Service Greenville-Spartanburg, SC Radar Loops Pat Arnott, ATMS 360

What Next for NEXRAD? WSRP-2010 D Polarimetric radar The next major upgrade is polarimetric What Next for NEXRAD? WSRP-2010 D 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 socalled 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 dualpolarization, 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, ATMS 360

POLARIMETRIC RADAR? Conventional Radar (NEXRAD) Polarimetric Radar (ARMOR) Pat Arnott, ATMS 360 POLARIMETRIC RADAR? Conventional Radar (NEXRAD) Polarimetric Radar (ARMOR) Pat Arnott, ATMS 360

Polarimetric Variables 1. Reflectivity factor Z at horizontal polarization - Measure of size and Polarimetric Variables 1. Reflectivity factor Z at horizontal polarization - Measure of size and concentration of scatters NEXRAD, TV (dominated by SIZE) 2. Differential reflectivity ZDR Operational: Small ZDR - Measure of median drop diameter→ SIZE/SHAPE Large ZDR vs - Useful for rain / hail / snow discrimination→ SIZE/SHAPE/PHASE 3. Differential phase ΦDP (Specific Differential Phase- KDP) Research: - Efficient for accurate rainfall estimation→ NUMBER/SHAPE NCAR, CSU, 2. - Immune to radar miscalibration, attenuation, and partial beam NASA, UND, blockage DLR, BMRC, NOAA-ETL 4. Cross-correlation coefficient ρhv 1. - Indicator of mixed precipitation → SHAPE/PHASE ARMOR - Efficient for identifying nonmeteorological scatterers Pat Arnott, ATMS 360

Advantages of a Dual-Polarization Radar Really just a self-consistent way of obtaining a more 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. Small ZDR Large ZDR Mitigates the multiple Z-R issues! Small drops Large drops vs • Identification of precipitation types and discrimination between meteorological and non-meteorological scatterers Hail Rain vs Insects Rain vs • Improvement in radar data quality: Self consistent way to calibrate using polarimetric variables Pat Arnott, ATMS 360