ATM 507 Lecture 25 Text reading Chapter 15 Paper Due Dec. 9 Review Session Dec. 9 Final Dec. 12 (10:30 AM-12:30 PM) Today s topic Aerosol Optical Properties 1
Aerosol Optical Properties There are a number of books on this subject alone: Van de Huslt, Bohren and Huffman, etc. This presentation is based primarily on Seinfeld and Pandis, Chapter 15 and Aerosol Technology by Hinds, Chapter 16. 2
Extinction, Scattering and Absorption Extinction Attenuation of light along the axis of propagation Extinction = Absorption and Scattering Absorption EM energy converted to thermal energy (vibrational, rotational, and ultimately translational) less light in the system Scattering EM energy along axis of propagation re-radiated in other (all) directions 3
Definitions C ext = extinction cross-section (single particle) units: m 2 C scat = scattering cross-section C abs = absorption cross-section C ext = C scat + C abs A = cross-sectional area of the particle - note that this area is based on the optical or physical diameter of the particle Combining the optical cross-sections and the optical area one obtains a dimensionless quantity - 4
Particle Extinction Efficiency Q ext = C ext /A dimensionless ratio of effective extinction area and optical size-based area Similar relations for scat and abs Q depends on composition (through the index of refraction), and The ratio of light wavelength and particle diameter (through the size parameter) Q is the fundamental building block of Aerosol Optics. The theory describing Q can and does get pretty complex. (Anybody take advanced E&M?) 5
Independent Variables used to determine Q The first variable is the index of refraction which depends on composition and wavelength. Wavelength of incident radiation (λ) and physical (optical) diameter of the particle (D p ) are combined into Size Parameter: α = (πd p )/ λ This is the ratio of the particle s circumference to the wavelength of the incident light 6
Index of Refraction Absolute N = n + ik (where vacuum has an index of exactly 1) Typically the index is normalized to the index of the surrounding medium (N 0 ) - m = N/N 0 N 0 most commonly refers to air, where N 0 = 1.00029 + 0i at 589 nm Note that N (= N 0 = 1.00029) and m (= 1.0) are nearly identical for air, but for generality m is used for derivations. 7
Index of Refraction II m = n + ik The real part (n) of the index of refraction represents the non-absorbing (scattering or refracting) component The imaginary part (k) represents the absorbing component (Hinds gives the alternate expression for m = m (1 ai) = m m ai In this case a is related to the absorption coefficient of the bulk material: b abs = 4πa/λ) Both real and imaginary parts are functions of wavelength and composition. 8
Index of refraction III There are two absorbing species in this table - carbon is a strong absorber, while mineral dust is a weak absorber. 9
Extinction, Absorption, and Scattering Efficiencies (Q parameters) Q ext = f(m, α) as are Q scat and Q abs The simplest case is for a spherical chemically pure particle Even those equations are rather complicated. Investigation of the results usually involves the consideration of three regimes α << 1 Rayleigh scattering regime (particles small compared to the wavelength of light) α 1 Mie scattering regime (the complicated part!) α >> 1 Geometric scattering regime (particles large compared with the wavelength of light) 10
Single Scattering Albedo ω 0 = Q scat /Q ext = C scat /C ext =SSA ω 0 = the fraction of light extinction (i.e., light that interacts with the particle and is scattered or absorbed) that is scattered by a particle 1 - ω 0 = the fraction of light extinction that is absorbed by a particle SSA is an important and useful parameter for radiative forcing and therefore dynamics and climate connections. 11
Extinction Coefficient For a population of monodisperse, spherical particles at number concentration N, the extinction coefficient (units: m -1 ) is related to the dimensionless extinction efficiency by b ext πd = 4 2 p NQ ext (Hinds calls this σ e instead of b ext.) For a distribution of sizes and compositions, one needs to sum and/or integrate over these variables (and potentially over wavelength) Calculated extinction (and scattering) coefficients using measured size distributions and indices of refraction are an important part of closure studies 12
Extinction in the Atmosphere In the Beer-Lambert Law, the extinction of radiation is an exponential function of the extinction coefficient and the geometric path length I/I 0 or F/F 0 = exp(-b ext z) {or exp(-σ e L)} The optical depth is given by τ = b ext z (dimensionless) In the general case, both gases and aerosols contribute: b ext = b eg + b ea = b abs + b scat = b ag +b aa +b sg +b sa 13
Molecular Rayleigh Scattering (A digression from aerosol scattering) b sg (m 0-1) 2 /λ 4 m 0 = index of refraction of air = 1.00029 Note very strong wavelength dependence Total Rayleigh optical depths (TOA to sea level) for a clear standard atmosphere Wavelength τ R 300 nm 1.224 400 nm 0.364 550 nm 0.098 700 nm 0.037 1060 nm 0.007 14
Aerosol Optical Depth Aerosol optical depth in the visible ranges from To 0.05 clean, pristine environment (with no recent volcanic eruptions), 1.0 locations near sources of intense particle emissions (i.e., large wildfires) 15
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Visibility Visibility is a subjective term We can define a quantity called visual range but only if we rely on the psychophysical concept of visual perception. To do this we define the INHERENT CONTRAST and the APPARENT CONTRAST in terms of the light intensities (or luminances) of the observed object and the background it is to be distinguished from 17
INHERENT CONTRAST C 0 = (B 0 -B )/B B 0 = luminance of object B = luminance of the background APPARENT CONTRAST C R = (B R -B R )/B R B R = luminance of object reduced by the scattering of intervening aerosol B R = luminance of background reduced by the scattering of intervening aerosol Consider the common case of an object viewed against the horizon. The contrast (between object and horizon) can be expressed as a familiar exponential function C R (L) = exp(-σ e L) or C R (x) = exp(-b ext x) Contrast decreases exponentially with the distance from the object. 18
Scattering coefficient unit conversions 0.5 km -1 = 500 Mm -1 (for reference this corresponds to a visual range of ~ 8 km) 2.0 km -1 = 2000 Mm -1 (this corresponds to a visual range of ~ 2 km) These examples show highly scattering atmospheres! 19
Visibility - II For good daylight viewing conditions, a contrast threshhold of 2% is usually employed for visual range determinations (i.e., apparent contrast is reduced to 2% of its inherent contrast, or there is a 98% contrast reduction). 0.02 = exp(-b ext x V ) Ln(0.02) = -b ext x V, or Visual range = x V = 3.912/b ext 20
Visibility - Examples On a hazy summer day, we may measure a scattering coefficient of 100 Mm -1 (=10-4 m -1 ) which corresponds to x V = 3.912/(10-4 m -1 ) 39 km Aerosol free conditions (sea level), or Rayleigh scattering only the Rayleigh scattering coefficient at 550 nm is approx. 11.6x10-6 m -1 (11.6 Mm -1 ) Maximum visual range is 337 km (sea level) A very clean day (with a deep blue sky) corresponds to an aerosol scattering coefficient of 10 Mm -1 which added to Rayleigh gives a total scattering of 21.6 Mm -1 and x V = 3.912/(2.16x10-5 m -1 ) 181 km 21
Measurements of Scattering NEPHELOMETER This instrument measures total scattering (actually, the angular response is somewhat truncated due to physical constraints). The clear scattering (air only - measured in a different cycle) is sometimes subtracted to yield the aerosol scattering coefficient. If there is no absorption, the nephelometer provides a direct measure of b ext (or σ e ), which can be used to determine the visual range or as the basis for a closure study. b scat (aerosol) = b sa typically < 200 Mm -1 22
Mass Scattering Efficiency Aerosol mass is the regulated quantity, and is the parameter used in most health studies. How does the scattering relate to aerosol mass loading? And conversely, can aerosol scattering measurements be used to determine mass loadings? The Mass Scattering Efficiency has units of m 2 g -1, and can be calculated directly if the scattering efficiency (Q), the size distribution, and the particle density is known. (Seinfeld and Pandis, Section 15.3 (22.3)). The equations in S&P are actually simplifications dealing with one type of aerosol and need to be generalized if the aerosol has multiple chemical species. (Again, the full equations are quite complex and will not be covered here!) 23
Mass Scattering Efficiency - II Empirically, we note that aerosol scatter has units Mm -1 (or 10-6 m -1 ), and that mass concentration has units µg m -3 (or 10-6 g m -3 ) σ sp = b ext /MC ( b scat /MC for weak absorption) Two useful papers: Chow et al., JAWMA 56: 398 (2006) Hand and Malm, JGR, 112: D16203 (2007) σ sp varies with location, season, and size cut (although fine particle scattering typically dominates) 24
Chow et al., 2006 (PM 2.5 scattering) Winter is smaller particles (inorganics?) Summer has more dust & is larger particles 25
Note that Fine scattering efficiency is always greater than Coarse MLR Multiple Linear Regression: b ext and MC i are knowns, system is solved for extinction (or scattering) efficiencies Partial The partial scattering method estimates the change in extinction due to the removal or addition of a single species 26
Closure Studies A closure study requires an overdetermined set of observations such that the measured value of an important system parameter can be compared to a value calculated with an appropriate model based on independent measurements. (i.e., use independent measurements of properties like composition and size to then calculate a bulk property) Reference: Quinn and Coffman, JGRD, 103:16,575 (1998) 27
Examples of Closure Mass closure - compare two or more of: Method 1 gravimetric Method 2 measure size distribution mass distribution (using estimated or measured density) Method 3 Measure components and sum (sulfate, nitrate, ammonium, OM, EC, dust, etc.) Scattering or Optical closure compare: Method 1 bulk scattering coefficient (Integrating Nephelometer) Method 2 Number size distribution (DMPS/APS) & chemical mass distribution (Impactor/IC, AMS, etc.) various model calculations to yield density, refractive index, true size/chemical distribution scattering efficiency from theory 28
Further Topics Measurement and Use of the SSA (Single Scatter Albedo) Measurement and Use of the Angstrom Exponent Humidity Effects deliquescence, aerosol growth, evaporation, crystallization Polarization, non-spherical particles, mixed particles Climate Connections Direct effect Indirect effect 29