Key concepts: Extinction, absorption, and scattering cross sections, coefficients, and mass scattering efficiencies for gases, particles, and bulk samples. Distinguish the direct beam from the diffuse beam for transmitted light. Beer’s ‘law’ ONLY describes the direct beam!!!! Optical depth as a coordinate, replaces the vertical coordinate for radiation transfer. Particle dispersions, mono versus polydisperse distributions. First link of cloud microphysics (cloud condensation nuclei number) with cloud optical depth in the visible. Chapter 7: Atmospheric Transmission
Given flux I0 incident on the air:substance boundary.Calculate the Flux Transmitted to Point X: Air: nr=1.00006, ni=1e-10 Substance: nr=1.67, ni=0.2 I0 0 x
Air: nr=1.00006, ni=1e-10 Substance: nr=1.67, ni=0.2 Given flux I0 incident on the air:substance boundary.Calculate the Flux Transmitted to Point X: R 1 1-R=T I0 0 x Answer: Propagator from 0 to x.
Air: nr=1.00006, ni=1e-10 Substance: nr=1.67, ni=0.2 What if we divide the substance into particles?Calculate the Flux Transmitted to Point X: I0 0 x N identical particles / volume v = particle volume a = average particle projected area. ext = a Qext = Single Particle Extinction Cross Section. Qext=Extinction Efficiency. ext = abs+sca , ext= ext(nr,ni,) Pext = I0ext = Power (watts) removed by a single particle from I0 by extinction.
Air: nr=1.00006, ni=1e-10 Substance: nr=1.67, ni=0.2 What if we divide the substance into particles?Calculate the Flux Transmitted to Point X: I0 0 x N particles / volume v = particle volume a = average projected area for each particle. ext = a Qext = Particle Extinction Cross Section. Qext=Extinction Efficiency. ext=N ext=Extinction Coefficient. Assume sca= N sca x <<1 .(single scattering assumption). I(x)=I0 exp(- ext x) Otherwise, use multiple scattering theory (to be developed soon)
What if we divide the substance into particles?Calculate the Flux Transmitted to Point X: reflection direct I0 absorption diffuse (scattered) reflection Direct Beam: I(x)=I0 exp(- ext x) Transmission Coefficient for the Direct Beam: tdirect=exp(- ext x) Otherwise, use multiple scattering theory: I(x) = Idirect + Idiffuse More Generally, Captures fate of photons: tdirect + tdiffuse + r + a = 1 transmission + reflection + absorption coefficients = 1. Often calculate ‘r’ and ‘t’, and obtain ‘a’ as residual.
Single Particle Perspective: Assume ext ≈ abs , sca ≈ 0 (particle size much less than the wavelength, deep in the Rayleigh range. Size parameter << 1.) Deq absorption Gross, Special Purpose, ad-hoc Approximation: abs = a[1-exp(-Deq/)]. Let Deq=v/a. =/(4ni)=skin depth. Limits: Deq<< , (1-e-small)≈small, abs = 4niv/ Deq>> , (1-e-large)≈1, abs = a . v = particle volume a = particle projected area
Air: nr=1.00006, ni=1e-10 Substance: nr=1.67, ni=0.2 What if we divide the substance into particles?Calculate the Flux Transmitted to Point X: I0 0 x N particles / volume v = particle volume a = average projected area for each particle. abs= N abs x. Deq<< , abs = 4niv/ I(x)=I0 exp(- 4nivNx/ ) vN=C=(Particle Volume)/Volume C=Concentration (e.g. ppmv) I(x)=I0 exp(- 4nixC/ )
Air: nr=1.00006, ni=1e-10 Substance: nr=1.67, ni=0.2 Compare x I0 0 (Assumes no particle scattering,dilute (C<<1), weak absorption). C=volumetric concentration.
Homework: Compare Mie Theory for Spheres with the simple model for absorption below. Gross Special Purpose Approximation: abs = a[1-exp(-Deq/)]. Let Deq=v/a. =/(4ni)=skin depth. v=4r3/3. a=average projected area=r2 for a sphere. D=2r. Deq=2D/3. • Cases in a 3 matrices for fixed nr and variable D and ni: • (calculate the percentage error of the model and Mie theory.) • = 0.5 um. nr=1, nr=1.33, nr=1.5 • D=0.01 um, 0.1 um, 1 um, 10 um. • ni=0.001, ni=0.01, ni=0.1, ni=1.
Table for Homework (one for each real refractive index, 1.0, 1.333, and 1.5). Fill each empty table with a percentage error as defined below.
Air: nr=1.00006, ni=1e-10 Compare: Bulk Substance, Gas, and Particles Bulk Substance: nr=1.67, ni=0.2 x I0 0 Gas (Assumes no particle scattering,dilute (C<<1), weak absorption). C=volumetric concentration. Particles
Single Scatter Albedo Definition Single scatter albedo Why do we call it that?
Definitions: Optical Coefficients for a Flat Surface Sunlight I0 (W/m2) Sunlight I0 (W/m2) Black Surface Area A (m2) a = albedo = 0 Absorptance = (1-a) = 1 Arbitrary Surface Area A (m2) a = albedo Absorptance=(1-a) Power Scattered, Power Absorbed Psca = 0 Pabs = I0 A abs = A Power Scattered, Power Absorbed Psca = I0 A a Pabs = I0 A(1-a) abs = (1-a) A
Definitions: Optical Coefficients for a Surface and a Particle Beam of Sunlight I0 (W/m2) Sunlight I0 (W/m2) Thing (particle, molecule, flea, etc) Absorption, less light through thing. Scattering, light redirected by thing. Arbitrary Surface Area A (m2) a = albedo Absorptance=(1-a) Power Removed From Beam I0 ext = Pext I0 abs = Pabs I0 sca = Psca Power Scattered, Power Absorbed Psca = I0 A a Pabs = I0 A(1-a) abs = (1-a) A abs=(1-)ext
Optics of N identical (particles / volume) Light beam area = A z dz z+dz Power removed in dz: = I(z) N A dz ext Bouger-Beer “law” (direct beam only!)
Monodispersons and Polydispersions n r N particles / volume. All of radius r.
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. 18 W. P. Arnott, AAAR tutorial, Sept. 2007
Light Scattering Basics (images from Wallace and Hobbs CH4). Angular Distribution of scattered radiation (phase function) x x Sphere, radius r, complex refractive index n=mr + imi Dipole scattering x x mr=1.5 x Qs x 19 W. P. Arnott, AAAR tutorial, Sept. 2007
Coated-Sphere influence of an aqueous coating on aerosol optics. • Contours are the scattering enhancement factor. It is larger than the absorption factor. W. P. Arnott, AAAR tutorial, Sept. 2007
Mass Efficiency Factors For Abs Sca and Ext. (In general, Ext and Scaare not related to particle mass). Why do this then? Example: numerical models for weather can easily predict the mass of condensed water or ice. These quantities then need to be somehow converted into cloud droplets and ice crystals, rain drops, snow flakes, hail, graupel, etc. What determines n(r)? Role of CCN?
Aerosol Optical Properties: Absorbing particles. For small optical depths, and D < 0.1 µm: I(L)/I(0) = e(-Bext L), Bext(1/m) ≈ S.O.C (m2/g) x M (g/m3), L = path length, M= 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!
Optical Depth from kext, kabs, ksca: Example, Water Vapor I0 Examples: kabs = 8.8 m2/g at 532 nm for diesel soot. ksca = 3.8 m2/g at 532 nm for Mexico City A L Pwater I
Precipitable Water (mm) Amount of water, expressed as a depth or as a mass, which would be obtained if all the water vapor in a specified column of the atmosphere were condensed and precipitated. A Pwat
Precipitable Water Amount, Pwat, (mm) Amount of water, expressed as a depth or as a mass, which would be obtained if all the water vapor in a specified column of the atmosphere were condensed and precipitated. 1992 Precipitable Water Amount Pwat measurement methods.
Optical Depth from kext: Liquid Water Path ztop Liquid Water Path zbot Somewhere there has to be an integral over z!
Shortwave Cloud Optical Depth: North Central Oklahoma USA Barnard JC,Long CN (2004) A Simple Empirical Equation to Calculate Cloud Optical Thickness Using Shortwave Broadband Measurements. Journal of Applied Meteorology 43(7): 1057.
Sengupta, M, Clothiaux, E E, Ackerman, T P, Kato, S and Min, Q (2003). Importance of Accurate Liquid Water Path for Estimation of Solar Radiation in Warm Boundary Layer Clouds: An Observational Study. Journal of Climate 16(18): 2997-3009. 600 g/m2
Cloud Condensation Nuclei: Cloud droplets (D≈20 um) grow on areosols (D≈0.2 um)
t Smax drop growth activation S aerosol Cloud Droplet Formation • Steps are: • Parcel cools as it rises • Exceed the dew point at LCL • Generate supersaturation • Droplets start activating as S exceeds their Sc • Condensation of water • becomes intense. • S reaches a maximum • No more droplets form
Aerosol Indirect Effect The impact of aerosols on cloud radiative properties
The climatic impact of aerosols on cloud properties is called the aerosol indirect effect A high concentration of aerosols overseed cloud droplets to generate highly concentrated, narrowly distributed cloud droplet spectra This can increase the cloud albedo up to 30% reducing the amount of radiation reaching the surface Narrowly distributed cloud droplet spectra prevent the formulation of precipitation and could increase cloud lifetime that further cools the Earth’s surface (Matsui et al., 2004) What is the Aerosol Indirect Effect?
Ship Tracks Ship Ship Exhaust CDNC = CCN (# cloud condensation nuclei)
Cloud Optical Depth and Cloud Condensation Nuclei Particles CCN: ( dust, soot, smoke), ( sea salt, sulfate, phytoplankton) I0 CCN ≈ 200 nm diameter Water Vapor & Cloud Droplet Ir Water Vapor & CCN cloud H It Cloud optical depth LWP = Cloud Water Mass / Area Qext = Cloud droplet extinction efficiency CCN = # cloud condensation nuclei source: http://en.wikipedia.org/wiki/Cloud_condensation_nuclei
Aside: Asymmetry Parameter of Scattering, g. -1<g<1 nr=1.33 =0.6328 D=20 um g=0.874 Is() I0
‘Typical’ Water Droplet Cloud Optical Properties Deff = 20 um Variance = 0.1 Why does the single scatter albedo go so low at around 3 microns? Why does the asymmetry parameter go so large at around 3 microns? COMPLEX REFRACTIVE INDEX OF WATER: Visible in black.
Cloud Albedo (Reflectance) and Transmittance: Simple Model Cloud optical depth Ir cloud H LWP = Cloud Water Mass / Area Qext = Cloud droplet extinction efficiency CCN = # cloud condensation nuclei It I0 nr=1.33 =0.6328 D=20 um g=0.874 figure 1 source: http://en.wikipedia.org/wiki/Cloud_condensation_nuclei
Derive the relationship between and CCN given on the previous slide. Reproduce Figure 1 on the previous slide. Calculate the R and T coefficients in Figure 1 for water droplets with diameters of 5 microns, and 10 microns. You will have to recalculate the asymmetry parameter. Calculate the climate sensitivity to water droplet number by calculating dR/dCCN. In words, how does the cloud albedo (reflectance) change with CCN? Assume all of the variation in R is due to CCN; hold all other parameters fixed. Explore and explain your solution as a function of total optical depth . Why is this solution only an approximation of dR? Make a plot of the asymmetry parameter g and the extinction efficiency Qext for cloud droplets varying in size from 1 micron to 20 microns. Explain your results. Try to reproduce the figure on the next slide using the simple model. Interpret your results. Interpret this figure. Homework Problem #2
Cloud Liquid Water Path, Effective Radius, And Cloud Albedo Does this make sense? Why? grams / m2 Global Survey of the Relationships of Cloud Albedo and Liquid Water Path with Droplet Size Using ISCCP.Preview By: Qingyuan Han; Rossow, William B.; Chou, Joyce; Welch, Ronald M.. Journal of Climate, 7/1/98, Vol. 11 Issue 7, p1516.
Optical Model for Light Absorption by Soot Bottom Line: Light absorption measurements by small particles can be used to determine the mass concentration of black carbon. This is the same way we measure many trace gases, like CO2, CO using IR. See: Lee, K O., R. Cole, R. Sekar, M. Choi, J. Zhu, J. Kang, and C. Bae, 2001. Detailed characterization of morphology and dimensions of diesel particulates via thermophoretic sampling. SAE Paper 2001-01-3572.
Pancakes Layers of Smoke from Siberian Forest Fires Observed Over North Central Oklahoma, 27 May 2003(Photo by Roy Woods, the CIRPAS Twin Otter Co-pilot) 0.5 to 1 km thick Arnott, W. P., J. W. Walker, H. Moosmüller, R. A. Elleman, H. H. Jonsson, G. Buzorius, W. C. Conant, R. C. Flagan, and J. H. Seinfeld, (2006). Photoacoustic insight for aerosol light absorption aloft from meteorological aircraft and comparison with particle soot absorption photometer measurements: DOE Southern Great Plains climate research facility and coastal stratocumulus imposed perturbation experiments. Journal of Geophysical Research 111, D05S02, doi:10.1029/2005JD005964. 43 W. P. Arnott, AAAR tutorial, Sept. 2007
The Distribution of Scattered Radiation (Phase Function) Geometrical Optics Rayleigh Resonance Incoming light direction Adapted from http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html W. P. Arnott, AAAR tutorial, Sept. 2007 44
Example of a morning when the Mexico City Plume Goes South to Popocatepetl Volcano. near forward scattering by particles sca = 30 degrees r << r ~ r >> 45 W. P. Arnott, AAAR tutorial, Sept. 2007
Plane Parallel Atmosphere, Solar Intensity from the Ground, and Atmospheric Optical Depth m
Optical Parameters for Analysis of Absorption and Scattering Single Scattering Albedo, ω Ratio of Scattering to Extinction Dark, absorbing aerosol: ω<0.5 Diesel Soot: ω(550 nm)=0.3 “White”, highly scattering aerosol: ω>0.85 Rice Straw fuel: ω(405 nm)=0.88 47
Optical Parameters for Analysis of Absorption and Scattering Ångström exponent of absorption, b Common assumption of Ångström exponent model: for Black Carbon b=1 Diesel Soot: b=1 Rice Straw: b(405/870)=2.8 48 W. P. Arnott, AAAR tutorial, Sept. 2007
Chamise Rice Straw Ponderosa Pine 49 W. P. Arnott, AAAR tutorial, Sept. 2007
Fern (Puerto Rico), Rice Straw & Ceanothus (a flowering shrub) Duff: Alaskan & Ponderosa Pine Duff Flowering Shrubs: Chamise, Manzanita, Sage & Rabbitbrush Pines: Southern Pine, Lodgepole Pine, & Ponderosa Pine 50 W. P. Arnott, AAAR tutorial, Sept. 2007