University of Nevada, Reno. Thermal Infrared Radiative Forcing By Atmospheric Aerosol

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1 Univerity of Nevada, Reno Thermal Infrared Radiative Forcing By Atmopheric Aerool A diertation ubmitted in partial fulfillment of the requirement for the degree of Doctor of Philoophy in Phyic By Narayan Adhikari William P. Arnott, Ph. D. /Diertation Advior Augut, 2014

2 5 2 THEORETICAL ANALYSES OF AEROSOL MICROPHYSICAL AND OPTICAL PROPERTIES 2.1 Size ditribution function The ize of particle in the atmophere uually pan a wide range, which reult in a large tandard deviation in the normal (Gauian) ditribution for fit of the oberved particle ize. Aerool ize ditribution are repreented by a normal ditribution of the logarithm of the particle radii, called lognormal ditribution, in which the natural logarithm of radii i normally ditributed (Levoni et al. 1997). The lognormal columnar volume ize ditribution function!"($)! '($ i given by (Schuter et al. 2006)!"($)! '($ = *,-. '(/ exp 3 ('( $5'($ 6 )7,('(/) 7 8, (2.1) where C repreent the column volume of all particle per cro ection of atmopheric column which i obtained by integrating!"($) over all ize i.e.! '($ $ 6?@!"($) dlnr! '($ C =. (2.2) $ 6AB Thi parameter C control the overall caling of the ditribution. The quantity!"($)! '($ i normalized if C = 1.0. r C i the volume median, or modal radiu; half the particle are maller and half larger than r C. The modal radiu i the radiu of maximum frequency of the ditribution. The median and modal radii are identical for lognormal ditribution. S i called the geometric tandard deviation, which i related to the tandard deviation σ of the natural logarithm of the radiu lnr (i.e. the radiu in log pace) by S = e E. The dimenionle quantity S give the pread (or width) of the ditribution. The parameter r m and S are contant for a given ize ditribution. The value of S (mut be 1) lie in the range for realitic atmopheric aerool (Zender 2010). For monodipere particle, S 1. The factor 2π on the denominator come from the normalization

3 6 property of the Gauian function i.e., KL 5L exp H I7, J dx = 2π. The common unit for the volume ditribution dv/dlnr are µm 3 µm 2. The reaon behind the ue of volume concentration i that the optical effect of atmopheric aerool are more related to their volume rather than their number (Whitby 1978). The columnar particle number ize ditribution n(r) in the unit of number of particle per unit area per ize interval in the whole atmophere column i given by P Q n(r) = N(r, z)dz, (2.3) where N(r, z) i the local number concentration (number per unit volume) per ize interval. Auming pherical particle, we have RSRT' UT$RVW'X YS'ZCX T$XT S[ TV$ $ 6?@!"($) $ 6?@ \ $ 6?@.!"($) $ 6AB = dlnr = $ 6AB!'($ ] πr] n(r)dr = dr. (2.4) $ 6AB $!'($ Hence, n(r) i related to the volume ize ditribution oberved by an AERONET Cimel unphotometer a (Sayer et al. 2012) n(r) = ]!"($). (2.5) \-$^!'($ Eq. 2.5 i ued to integrate the individual particle ingle cattering propertie derived from the Mie theory for pherical homogeneou particle (Bohren and Hoffman 1983), or other for nonpherical particle. Fig. 2.1 depict example of meaured aerool bimodal lognormal volume ize ditribution at the Univerity of Nevada, Reno (UNR), which conit of fine and coare mode aerool. The bimodal ize ditribution can be given by a linear combination of two lognormal function given

4 7 by Eq. 2.1 for fine and coare mode. Fig. 2.1 (left) i a ize ditribution for a moke event in Reno on 26 Augut 2013 at 17:00 Local Standard Time (LST) meaured with AERONET (aerool robotic network) Cimel un photometer. The trong predominance of the fine mode implie the preence of mall moke particle. Fig. 2.1 (right) i the aerool ize ditribution derived from the MFRSR (multi filter rotating hadow band radiometer) data on 24 April 2013 at 14:29 LST during a dut torm event in Reno. The trong predominating feature of the coare mode particle over fine (or accumulation) mode i a typical characteritic of a dut outbreak epiode (Sicard et al. 2014). The volumetric parameter uch a volume median radiu, tandard deviation and volume concentration for each mode of both date are reported in Table 2.1. The value of the tandard deviation are taken to be 0.42 and 0.61 for the fine and coare mode, repectively (Dubovik et al. 2002). For the moke event, the ratio of fine to coare volume concentration wa 10.0, and for the dut event, the coare to fine volume concentration ratio wa 5.3. Figure 2.1 Bimodal lognormal aerool ize ditribution oberved in Reno: (left) during the Rim fire on 26 Augut 2013 at 17:00 LST meaured with the AERONET Cimel unphotometer and (right) during a dut torm on 24 April 2013 at 14:29 LST derived from the MFRSR data.

5 8 Table 2.1 Size ditribution function parameter for the Rim fire and dut cae Particle mode Concentration (µm 3 µm 2 ) Median radiu (µm) Standard deviation Coare 26 Augut April 2013 Fine Augut April Spectral bulk cattering propertie For a given ize ditribution n(r), the bulk (or mean) cattering propertie at a pecific wavenumber ν are obtained by integrating the ingle cattering propertie for individual particle over particle ize ditribution a follow (Yang et al. 2005; Baum et al. 2006): Q XIR (ν) = c d@e ($,f)g($)(($)!$ g($)(($)!$, (2.6) Q iwt (ν) = c jk? ($,f)g($)(($)!$ g($)(($)!$, (2.7) Q (ν) = Q XIR (ν) Q iwt (ν), (2.8) ω(ν) = c jk? (ν) c d@e (ν), (2.9) g(ν) = h o($,ν)c jk? ($,ν)g($)(($)!$ 6AB c jk? ($,ν)g($)(($)!$, (2.10) "($)(($)!$ r X[[ = ] \, (2.11) g($)(($)!$

6 9 where Q XIR (ν), Q iwt (ν), Q (ν), ω(ν), and g(ν) are the mean extinction efficiency, cattering efficiency, aborption efficiency, ingle catter albedo, and aymmetry parameter, repectively. The term r eff i the effective particle radiu, or the area weighted mean radiu of an aerool ditribution which characterize the radiation extinction propertie of the ditribution. V(r) i the volume of the individual particle and A(r) i the geometric projected area of a particle perpendicular to the incident plane. Similarly, Q XIR (r, ν), Q iwt (r, ν), and Q (r, ν) are the extinction, cattering and aborption efficiencie, repectively, for the individual particle at a pecific wavenumber. Thee quantitie are computed uing the Mie theory (which i decribed hortly in brief). The cattering aymmetry parameter i defined a the average value of the coine of the cattered angle, weighted by the intenity of the cattered radiation a a function of angle. It value i 1 for perfect forward cattering, 1 for perfect backcatter, and 0 for iotropic cattering. The cattering phae function P(θ, ν) pecifie the fraction of radiation cattered in a certain direction which i given by P(θ, ν) = h r(θ,$,ν)c jk? ($,ν)g($)(($)!$ 6AB c jk? ($,ν)g($)(($)!$. (2.12) The Henyey Greentein (H G) phae function i the mot widely ued model phae function, and i given by (Petty 2006) P 5t (θ, ν) =.5 o 7 (.K o 7 5, o WSiu) v 7, (2.13) where θ i the angle between the original direction of the incident photon Ω and the cattered direction Ω, uch that coθ = Ω. Ω. Thi function i iotropic for g = 0. For g > 0, the function can reproduce the oberved forward peak in the phae function of real particle.

7 10 The parameter Q XIR, Q iwt, Q, and g for a ingle homogeneou phere i obtained from the Mie theory in the form of an infinite erie (Hanen and Travi 1974): L Q XIR =, (2j + 1) ReÑa ~ 7 Üâ. Ü + b Ü à, (2.14) L Q iwt =, (2j + 1) Ña ~ Üa 7 Üâ. Ü + b Ü b Ü à, (2.15) Q = Q XIR Q iwt, (2.16) g = \ L ã Ü(ÜK,) Re Ña ~ 7 c jk? (ÜK.) Üa ÜK. + b Ü b ÜK. à + (,ÜK.) Üâ. ReÑa Ü(ÜK.) Üb Ü àå. (2.17) The heart of the Mie cattering problem lie in the computation of coefficient a Ü and b Ü, which are function of the ize parameter x (where x =,-$, and λ i the incident wavelength) and the è complex refractive index, and involve pherical Beel function. The erie converge whenever the number of term j in the erie i lightly larger than x, i.e., j i an integer cloet to (x + 4x ï v + 2) (Petty 2006). Higher order term correpond to light ray miing the phere. The infinite erie actually repreent the multipole expanion of the cattered light. The coefficient a Ü pecify the amount of electric multipole radiation wherea b Ü pecify the magnetic multipole radiation. For mall particle with a mall refractive index, only the electric dipole radiation i ignificant, and Rayleigh cattering take place. Fig. 2.2 illutrate the aymmetry parameter for Rayleigh and Mie cattering. For large particle all multipole with j x contribute. For much larger particle, uually x > 2000, computation of the Mie theory uffer both a computer time iue and a numerical preciion iue due to round off error a a conequence of the large value of j.

8 11 Figure 2.2 Illutration of the phae function for variou value of the aymmetry parameter (courtey: D. Mitchell). 2.3 Phyical characteritic of the aerool problem Thi ection preent a imple idea about the phyical characteritic of the aerool uch a total volume of the aerool per unit area of the atmopheric column above an intrument. Aume an aerool laden atmophere of volume V oberved by an intrument at the urface, whoe area i A and height i Z a hown in Fig. 2.3 (left). Figure 2.3 Aerool laden atmophere above an intrument at the urface: aerool ditributed over the whole column of the atmophere (left) and a cube repreenting the total volume of the aerool in a unit area (A=1 m 2 ) of the atmophere (right).

9 12 Referring to the fine mode concentration on 26 Augut 2013 (Table 2.1), we know that the total volume of all the aerool preent in a column of atmophere of 1 µm 2 area i µm 3, which i equivalent to the volume of 151 mm 3 in an area of 1 m 2. Thi i, in fact, the volume of all aerool particle when gathering them together in an area of a unit quare meter (Fig. 2.3, right, where A i aumed to be 1 m 2 ). Thi volume then repreent a cube of ide 5.3 mm in thi particular cae. I it not a tiny volume of matter dipered into the whole column of the atmophere, which we are dealing with? 2.4 Pedagogical model for IR radiative forcing by aerool We conider a implified atmophere containing water vapor and coare mode aerool uch a mineral dut (Fig. 2.4) where dut reide only in the boundary layer (0 3 km). Let T be the urface temperature and T T be the atmopheric temperature. Figure 2.4 A implified atmophere containing water vapor and coare mode aerool. The radiance at the TOA i given by R óòg (ν) = B(T, ν) expö Ñτ 7 ò +!ZiR τxir àú + B(T T, ν)ö1 expù Ñτ 7 ò +!ZiR τ àûú + B(T) τ!zir iwt H.Ko J expñ τ 7 ò, à, (2.18)

10 13 where ν i the wavenumber; B i the Planck function; τ 7 ò i the aborption optical depth of!zir water vapor; τ XIR, τ!zir!zir, and τ iwt are the extinction, aborption and cattering optical depth, repectively of coare mode aerool uch a dut; and H.Ko J repreent the probability of, cattering in the forward direction. Similarly the radiance at the BOA i given by R üòg (ν) = B(T T, ν)ö1 expù Ñτ 7 ò +!ZiR τ àûú + B(T) τ!zir iwt H.5o J expñ τ 7 ò, à, (2.19) where H.5o J repreent the probability for backward cattering. The econd term in Eq. 2.19,, therefore, ignifie the urface IR backcattering by atmopheric dut. The pectral radiative forcing at the TOA, ΔR óòg (ν) i obtained by ubtracting R óòg (ν) with dut from R óòg (ν) without dut. Therefore, ΔR óòg (ν) = B(T) expñ τ 7 ò àö1 exp!zir Ñ τxir àú B(T T ) expñ τ 7 ò àö1!zir expñ τ àú B(T) τ!zir iwt H.Ko J expñ τ 7 ò, à. (2.20)!ZiR Auming τ XIR and τ!zir are far le than 1, then Eq can be written a ΔR óòg (ν) = expñ τ 7 ò àöb(t)!zir τxir B(T T ) τ!zir ú B(T) τ!zir iwt H.Ko J expñ τ 7 ò, à. (2.21) Uing ω = je jk? je i.e., ingle cattering albedo, we have d@e ΔR óòg (ν) = expñ τ 7 ò à ãb(t)!zir τxir 1 (.Ko) B(T, T ) τ!zir å. (2.22) In the limit, ω 0, i.e., zero cattering approximation ΔR óòg (ν) = τ!zir expñ τ 7 ò à[b(t) B(TT )]. (2.23) We ee that, for a large value of τ 7 ò (i.e. moit atmophere), the dut radiative forcing at the TOA, ΔR óòg (ν) become mall. Alo, the forcing decreae with increaing atmopheric temperature T T. In the limit, ω 1 i.e., zero aborption approximation ΔR óòg (ν) = expñ τ 7 ò.5o à B(T) H J τ, iwt!zir. (2.24)

11 14 Apparently the backcattering of the urface emitted IR by the dut caue the radiative forcing to be important. If ΔR óòg (ν) > 0, le IR leave at TOA in the preence of dut and hence the atmophere get heated. Uing τ!zir = (1 ω)τ!zir XIR, Eq can be re written generally a ΔR óòg (ν)!zir = B(T) τ XIR expñ τ 7 ò à ã1 (.Ko), (1 ω) ü(ó? ) å. (2.25) ü(ó) The pectral radiative forcing at the BOA, ΔR üòg (ν) due to dut i obtained by ubtracting R üòg (ν) without dut from R üòg (ν) with dut i.e. ΔR üòg (ν) = B(T T ) expñ τ 7 ò àö1 expù (1 ω)!zir τxir ûú + B(T) ω τ!zir XIR H.5o J expñ τ 7 ò, à.!zir Auming mall τ XIR, we have ΔR üòg (ν)!zir = B(T) τ XIR expñ τ 7 ò.5o à ãω H J + (1 ω) ü(ó? ) å. (2.26), ü(ó) Notice that ü(ó? ) ~ ó ^? ü(ó) ^ ó^, and ó? H1 ó ó^ ó J\ 1 4 ó. Then ó ΔR üòg (ν)!zir B(T) τ XIR expñ τ 7 ò.5o à ãω H J + (1 ω) H1 4 ó Jå. (2.27), ó For the zero aerool aborption and emiion cae, ω = 1, ΔR üòg (ν)!zir = B(T) τ XIR expñ τ 7 ò.5o à H J. (2.28), Even though the dut aerool do not aborb IR at all, the backcattering of IR by the aerool contribute to IR radiative forcing. Alo, the aerool IR radiative forcing enhance in the drier atmophere. Thi offer poitive feedback on the climate warming. For a warmer planet, B(T) goe up and contribute to the poitive feedback. For ω 0, ΔR üòg (ν) = B(T T ) τ!zir expñ τ 7 ò à. (2.29) Eq i the zero cattering approximation, which can be ued to invetigate the perturbation due to any other greenhoue ga. The approximate forcing given in Eq and 2.26 were alo preented by Dufrene et al. 2002, though without the dependence on water vapor optical depth.