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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.

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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.Radar: The Quickest Path to dbZNote: Key results are circled by a red box like this. The homework assignment is also given by a red box.Definitions: Optical Coefficients for a Flat SurfaceSunlightI0 (W/m2)SunlightI0 (W/m2)Black SurfaceArea A (m2)a = albedo = 0Absorptance = (1-a) = 1Arbitrary SurfaceArea A (m2)a = albedoAbsorptance=(1-a)Power Scattered,Power AbsorbedPsca = 0Pabs = I0 Aabs = APower Scattered,Power AbsorbedPsca = I0 A aPabs = I0 A(1-a)abs = (1-a) ADefinitions: Optical Coefficients for a Surface and a ParticleBeam of SunlightI0 (W/m2)SunlightI0 (W/m2)Thing (particle, molecule, flea, etc)Absorption, less light through thing.Scattering, light redirected by thing.Arbitrary SurfaceArea A (m2)a = albedoAbsorptance=(1-a)Power Removed From BeamI0 ext = PextI0 abs = PabsI0 sca = PscaPower Scattered,Power AbsorbedPsca = I0 A aPabs = I0 A(1-a)abs = (1-a) Aabs=(1-)extOptics of N identical (particles / volume)Light beam area = Azdzz+dzPower removed in dz: = I(z) N A dz extBouger-Beer“law”(direct beam only!)Monodispersons and PolydispersionsnrN particles / volume.All of radius r.Radar Theory Part 1Radar Theory Part 2: Key Results!!!This is what is reported on radar graphs!!!Radar Theory Part 2: Typical Values of ZdbZClear air mode of NEXRAD: -28 dbZ to 28 dbZ.Precipitation mode of NEXRAD: 5 dbZ to 75 dbZ.Light rain: 20 dbZ.Rain Fall Rate for MonodispersionRadar Theory Part 3: Rainfall Rate Estimate From RadarDefinition of rainfall rate and what happens after rain hits the surface. Rainfall rate depends on the mass of water droplets and their fall speed.Rainfall Rate AnalogyFalling rain: Coffee is beingpoured at some rate.Height of coffee = HRainfall Rate = Height of Coffee / time elapsed pouring it.Rainfall Rate = dH / dtRain Drop Fall SpeedRain Drop Fall Speed: A balance of Forces, Drag and GravityFall Speed Is a Function of Size: Note the Shape in Terminal FlowUgggh!NOT!!!Radar Theory Part 3: Rainfall Rate Estimate From RadarThis is one relationship used to get rainfall rate (depth / time) from radar. Problem: People have developed many such relationships! Which is correct, if any?????Definitions: Optical Coefficients for ParticlesExtinction coefficient for particle mono dispersionsExtinction coefficient for particle dispersionsSheridan, 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 Sulfate532 nmSlowik, 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, 2007.16W. P. Arnott, AAAR tutorial, Sept. 2007Light Scattering Basics (images from Wallace and Hobbs CH4).Angular Distribution of scattered radiation (phase function)xxSphere, radius r, complex refractive index n=mr + imiDipole scatteringxxmr=1.5xQsx17W. P. Arnott, AAAR tutorial, Sept. 2007Polarization Diverse Radar: Coming to the NWS in the next few years. 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.

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