Extinction coefficients and properties of Pinatubo aerosol determined from Halogen Occultation Experiment (HALOE) data

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. D22, PAGES 28,333-28,345, NOVEMBER 27, 01 Extinction coefficients and properties of Pinatubo aerosol determined from Halogen Occultation Experiment (HALOE) data K.-M. Lee, J. H. Park, 2 S. T. Massie, 3 and W. Choi 4 Abstract. Relative extinction coefficients as a function of wavelength are determined for stratospheric aerosols from the Mount Pinatubo eruptions in June of 1991, using the Halogen Occultation Experiment (HALOE) data at latitudes o- ø in the northern hemisphere from November 1991 to February Extinction coefficients at each of the eight HALOE channels are obtained from the ratio of two transmittance profiles of consecutive occultation measurementseparated by ø longitude, one loaded with aerosols larger than the other during the early stage of aerosol dispersion after the eruptions. These coefficients are compared to theoretical Mie calculation values. Composition and a single mode particle size distribution are derived as a function of altitude. The retrievals indicate that the weight percentage of H2SO 4 for 45 occultation cases is larger than the equilibrium value by about 5 wt %, while the size distribution parameters are within the range of those measured in situ at Laramie, Wyoming. 1. Introduction Stratospheric aerosols originated from the eruptions of Mount Pinatubo in June of These particles had diverse effects on the global atmospheric environment, in particular, upon chemical composition [Brasseur et al., 1990; Grant et al., 1994; Tie et al., 1994] and temperature [Labitzke and McCormick, 1992; Angell, 1993] fields. They also perturbed radiation fields by scattering solar radiation and absorbing infrared radiation, thus affecting the climate system [Hansen et al., 1992]. Quantitative understanding of radiative forcing requires information on particle composition and size distributions [Lacis et al., 1992], together with the spatial distribution of the aerosol. Extensive measurements of the composition and particle size distributions of Pinatubo stratospheric aerosols have been carried out by, among others, Deshler et al. [1992, 1993], Sheri- dan et al. [1992], and Pueschel et al. [1994]. These measurements indicated that most of the aerosol particles are composed of liquid H2SO4/H and that volcanic ash particles are present up to about km until at least March On the basis of analyses of diverse measurements, Russell et al. [1996] pointed out that weight fractions of H2SO 4 are in the range of 65 to 80% for most cases of stratospheric temperature and humidity. Inference of aerosol properties from satellite-basedata has been reported by Grainget et al. [1995] using Improved Stratospheric and Mesospheric Sounder (ISAMS) data and Hervig et al. [1998] using Halogen Occultation Experiment (HALOE) data, respectively, on the Upper Atmosphere Research Satellite (UARS). Grainget et al. [1995] estimated aerosol parameters from ISAMS data using relationships between surface area, volume density, effective radius, and the absorption coefficient. The relationships were also used by Hervig et al. [1998] to infer aerosol properties from HALOE data. Direct retrievals of aerosol properties are discussed by Wang et al. [1989] using Stratospheric Aerosol and Gas Experiment II (SAGE II) data and by Echle et al. [1998] using Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) data, respectively. Results from these remotely sensed data are based on inversion methods applied to transmission or emission measurements at individual wavelength channels. These inversion methods are dependent on uncertainties of absorption by interfering gases. In this study, we introduce a new ratio method that uses two transmittance profiles to obtain relative aerosol extinction coefficients as a function of wavelength. The current technique can be used for cases when two transmittance profiles have different aerosol extinction signatures relative to each other. The technique is applied to HALOE data, from which we infer aerosol composition and particle size distribution information during the time period from November 1991 to February 1992 when aerosol-loaded air masses are not well mixed. We begin with a brief description of Mie theory, present satellite-based observations of signal profiles, and describe how aerosol properties are derived along with associated error budgets. Department of Astronomy and Atmospheric Sciences, Kyungpook 2. Aerosol Extinction National University, Taegu, Korea. 2Atmospheric Science Division, NASA Langley Research Center, Aerosol properties, such as particle size distribution and Hampton, Virginia, USA. composition, can be inferred from observed aerosol extinction 3Atmospheric Chemistry Division, National Center for Atmospheric coefficients (km- ) using the theoretical expression of extinc- Research, Boulder, Colorado, USA. tion coefficient as a function of size distribution and refractive 4School of Earth and Environmental Sciences, Seoul National Uniindex. When the aerosol is composed of liquid H2SO4/H, in versity, Seoul, Korea. particular, the refractive index depends on the weight fraction Copyright 01 by the American Geophysical Union. Paper number 00JD /01/00JD0001 $09.00 of H2SO 4 [Remsberg et al., 1974; Palmer and Williams, 1975; Tisdale et al., 1998]. The extinction coefficient/3 at wavelength X for a population of aerosols is theoretically defined as 28,333

2 28,334 ' LEE ET AL.: PINATUBO AEROSOL PROPERTIES fo mx) dn(r) dr ]3(X) = -r2qe(x, dr, (1) = x)]. (3) Note that if the reference signal r, is completely free of aerosol, then an absolute amount of aerosol extinction can be obtained. This ratio method provides extinction coefficients at eight wavelength regions, while Herrig et al. [1993] retrieve where r is the aerosol radius, Qe is the Mie extinction efficiency extinction at four correlation channel wavelengths. factor, and dn/dr is the particle size distribution. The efficiency factor is a function of the Mie size parameter, x = 2 rr/x, and We analyze data from the HALOE experiment [Russell et al., 1993]. Fifteen sunrise and sunset occultations take place the complex refractive index, m x = mr+ imi, which in turn each day along an almost constant latitude circle, with separadepends on aerosol composition. Thus, using measured values tion of about ø between successive measurements. HALOE of/3 and knowing certain parameter values of (1), aerosol size distribution and composition can be inferred. has four gas filter correlation channels to measure HF, HC1, CH4, and NO, centered at 2.45, 3.40, 3.46, and 5.26 m, respectively, and four broadband channels to measure CO2, 2.1. Observed Aerosol Extinction Coefficients NO2, H, and 03, centered at 2.80, 6., 6.60, and 9.85 m, There are various methods of computation to retrieve aerorespectively. Vacuum path signals are used exclusively in our sol extinction coefficients from passive satellite remotely analysis of the gas filter data. sensed data. Herrig et al. [1993, 1995] discuss inversion tech HALOE data. During the first 6 months after the niques that derive absolute values of aerosol extinction for the Mount Pinatubo eruptions, aerosol-loaded air masses were not well mixed, and numerous cases of two consecutive occultation HALOE channels. These techniques rely on knowledge of the gaseous absorption within each channel. For example, the profiles having distinct signatures of aerosol layers, as well as HALOE CH 4 channel used by Herrig et al. [1993] is a gas filter having different aerosoloading, were found. We have chosen correlation channel which contains two paths, one with CH 4 45 cases in the latitude range of 0- ø in the northern hemigas (used to correlate atmospheric CH 4 absorption) and the sphere from November 1991 to February It is difficult to other a vacuum path. The correlation signal, that is less deshow statistics on transmittance profiles of 45 cases because of pendent on aerosol extinction, provides CH 4 mixing ratio. various altitude ranges of aerosol layers. However, we show Then, the retrieved CH 4 amount is used to obtain an absolute three representative cases now and statistics on the relative extinction ratios of 45 cases derived from the current ratio aerosol extinction value using the vacuum path signal of the same correlation channel. This result depends on retrieved technique in the next section. CH 4 mixing ratio and instrument function uncertainties. Three examples that have different vertical structures are We discuss and apply a new ratio technique that makes use shown in Figure 1 for the eight HALOE channels: December of two consecutive occultation signal profiles. We assume that 6, 1991, occultation 22 (48.6øN, 337.9øE; solid line) and occulthe gaseous profiles of the two occultations are similar but the tation (48.6øN, 1.9øE; dotted line) when the reference proaerosol profiles are different, and that the extinction coeffifile is nearly free of aerosol interference at altitudes where cient is constant within the wavelength range of each channel. extinction by aerosols in the other profile is significant (Figure We have chosen cases when the aerosol layer of one occultala), February, 1992, occultation 9 (48.9øN, 161.1øE; solid tion is different from the other and retrieved gaseous profiles line) and occultation 11 (48.8øN, 137.1øE; dotted line) when are very close to each other, which we confirmed using the the reference profile is similar to the other but with less interoperational HALOE inversion software, during the time when ference by aerosol (Figure lb), and February 27, 1992, occul- Pinatubo aerosols were not well mixed. The ratio of the two tation 3 (24.5øN, 2.0øE; solid line) and occultation 5 (24.1øN, profiles, then, eliminates gaseous absorption and the instru øE; dotted line) when the two profiles are nearly identical ment function. except for aerosol layer centered at about km (Figure lc). The HALOE transmittance profile, r(z, X), is a function of The first column displays transmittance signals for the two altitude z, averaged over each channel's wavelength interval, consecutive sunset occultations, the second column displays and can be expressed for the i th occultation location as the relative optical depth profiles obtained from the ratios of the two transmittance signals (equation(3)), and the third r,(z, X) = exp [-/3,(z,,k)L]%as(Z,,k), (2) column displays relative optical depths but normalized by the peak value of aerosolayer of each channel. For all channels in where rgas is the transmittance of gaseous absorption which is Figures la-lc the profiles of relative optical depths (second normalized by the exo-atmospheric signal; thus the instrument and third columns) show similar patterns; that is, in the case of function is eliminated. The aerosol extinction portion, exp December 6, for instance, a region above 29 km with value very [-/3i(z, X)L], is separated from other factors assuming the close to 0 (indicating that the gaseous profiles at the two extinction coefficient is constant over a channel interval, where locations are very close above 29 km and most likely similar a L is the total path length. The parameter/3i, defined as the few kilometers below 29 km), a distinct layer between 28 and absolute extinction coefficient is therefore the measure of total 21 km, and a region below 21 km. The values below 21 km for extinction along the tangent path length. In our analysis, it is Figure la, 19 km for Figure lb, and 23 km for Figure lc have assumed that along the horizontal observation ray path (on the large fluctuations because of either very small signals (due to order of 400 km) the distribution of aerosol is homogeneous. saturation) or the presence of opaque clouds. Only aerosol For a given channel the ratio of transmission of one profile layers can create the nearly same profile structures for all at location (a) to that at adjacent location (b) can be used to channels in Figures la-lc. define the relative extinction coefficient/3a,, or relative optical The third column profiles of eight channels in Figures la-lc depth/3a,,l: are then averaged, respectively, and the averages of normal- /3a,b(z, X)L = [/3a(z, X)-/3b(z, X)]L ized relative optical depths are shown in Figures 2a-2c along with their standard deviations. Note that the standard devia- tions are less than 5% in the region of aerosol layers (i.e.,

3 . ß LEE ET AL.: PINATUBO AEROSOL PROPERTIES 28,3 December 6, 1991,_., 3o HF 3o - ß 2o HCI 3O -... ß - : ''N'O..., ' 3O ß 4. --,.- -" 'o ' Tronsmittonce Relotive opticol depth (o) Normolized relotive opticol depth Figure 1. Transmittance profiles of the HALOE channels for (a) sunset occultations and 22 on December 6, 1991, (b) sunset occultations 9 and 11 on February, 1992, and (c) sunset occultations 3 and 5 on February 27, The left column displays transmittances for the two adjacent measurements, the second column displays relative optical depths (equation(3)) for the HF, CO2, HC1, CH4, NO, NO2, H, and 0 3 channels, respectively, as a function of tangent height, and the third column displays normalized relative optical depths (values are normalized to the peak of aerosolayer as 1) km for Figure 2a, 19- km for Figure 2b, and km for Figure 2c). These three examples demonstrate the accuracy of the ratio technique to derive relative optical depth from HALOE data Relative optical depths and relative extinction ratio. The current ratio technique provides relative optical depth for all HALOE channels. In order to use these data in calculations of the aerosol properties, the ratio of two relative optical

4 28,336 LEE ET AL.: PINATUBO AEROSOL PROPERTIES E ß < hf 3o February, 1992 ' ' x.. ß......,.., E õ ß < E ß Z < E -o ß <,. E 3O ß Z <,_, ß Z <,_, 03 õ Transmittance O '" ' ': Relative opticol depth (b) Figure 1. (continued) Normolized relotive optical depth depths at two channels (u and v), R,m,v, is defined (hereafter defined as relative extinction ratio) by Rum,,(z) = /3a,b(z, u)/13a,,(z, v), (4) where the superscript m denotes a measured quantity. Figures 3a-3c show the relative extinction ratios of the eight channels at various altitudes, using the extinction of the HF channel as a reference, for the occultation data shown in Figures la-lc. The relative extinction ratios at five tangent alti- tudes of the first two cases (i.e., December 6 and February ) show similar wavelength dependence, while the third case for February 27 shows much larger values for the HC1 and CH 4 channels (see section 2.3). Figure 3d shows the average of 395 data sets of 45 cases (each case having data at several altitudes) used in this study, along with the standard deviations. The standard deviations of 45 cases for eight channels are in the range of 5-%, which are proven to be due to variation of aerosol properties as well as measurement errors (see subse-

5 LEE ET AL.: PINATUBO AEROSOL PROPERTIES 28,337, E 0 HF... t v '. 3o 2s February 27, 1992,... ' ' ' '..,.,, HCI E 'Z..... C'H' ' ' 50 2 ' E ß <.... :i" ß... : ' Tronsmittonce Relotive optical depth (c) Figure 1. (continued) Normalized relotive opticol depth quent discussion in sections 4 and 5). We will next determine aerosol properties by comparing theoretical relative extinction ratios to those derived from the HALOE observations. The development above assumes that the aerosol extinction coefficient is constant for the wavelength range of each channel. Hervig et al. [1995] indicate that extinction coefficients for 75 weight (wt) % of H2SO 4 at the 50% filter point and at the center of the filter are different by less than 6%, except for the 03 channel. The 03 channel signal in altitude region of the aerosol layer is, in addition, saturated (or weak); thus the 03 ratio calculation contains a large error. Further, the CH 4 and HC1 channels are closely located in wavelength and do not offer additional information. Therefore, in our computation for aerosol properties, data from six channels (i.e., CO2, HF, CH4, NO, NO2, and H ) are used.

6 28,338 LEE ET AL.: PINATUBO AEROSOL PROPERTIES 3O December 6 I 991 Average of 8 channels ' 2: (o) 2.9 Derived from HALOE data Dec SS22/SS...,'F'' ' d ' ',' ' 'ch ' ' 0'' ' d.' ' 0' ' '0'.'' Z(km) T(K) \ (a)...,... ' Averoge opticol depth Standard Deviation Wovelength (/ rn). February, '... '.... Average of 8 channels.3o.9 Feb--92 SS09/SS1 1 Z(km) T(K) (b) (b)... i...,..., O.O O 1.5 Average optical depth.....3o Average of February 27, O.O O Standard Deviation -r 2 (c)._o i I i... i Wavelength (/ rn) Feb SS05/SS05...,'F' ' d.'' 0' ' 'ch ' ' /0' ' 0.' ' 0' ' '0 '' Z(km) T(K) ; I '.'.:::.. -:...::.....;::,. ";i:;;;;:.. ß. / -:.'..... ":'":" ===============================...:..::-.'-:... ß ::. (c) 2 t I O.O O I.5 O.O O Average optical depth Standard Deviation Figure 2. Average of normalized relative optical depths of eight channels for cases shown in Figures la-lc and their standard deviations: (a) December 6, 1991, (b) February, 1992, and (c) February 27, i... i... i Wavelength (/ rn) Average of Relative Extinction Ratio... [... [... [... [......,... [...!... (d) 2.2. Theoretical Aerosol Extinction Coefficients We compared our HALOE-derived aerosol extinction ratios (Figure 3 determined by equation (4)) and theoretically calculated values with inputs from various sources. Deshler et al. [1992] and Sheridan et al. [1992] reported that -- 98% of the Pinatubo aerosol particles were composed of liquid H2SO4/ H. Complex refractive indices of liquid H2SO4/H in the infrared region have been measured by Remsberg et al. [1974] for 75 and 90 wt % of H2SO 4 and by Palmer and Williams [1975] for six different wt % of H2SO 4. Tisdale et al. [1998] determined the optical constants at 2 K from 45 to 80 wt % and provided third-order polynomials to fit the indices for any weight fraction of H2SO 4. In the calculations of the Mie efficiency factors at the HALOE wavelengths, we adopt data by Palmer and Williams [1975], which cover a larger range of Wavelength (/ m) Figure 3. Relative extinction ratios (or ratio of relative optical depth defined by equation (4) with a reference of the HF channel) calculated from the HALOE data for three cases shown in Figure 1: (a) December 6, 1991, (b) February, 1992, and (c) February 27, (d) The average of 395 data sets of 45 cases and their standard deviation of each channel (as vertical bars). H2SO 4 concentration, along with a wavelength interpolation and a Lorentz-Lorenz temperature correction [Luo et al., 1996]. Measurements of aerosol size distributions at Laramie, Wy-

7 ß... i LEE ET AL.: PINATUBO AEROSOL PROPERTIES 28,339 oming (41øN, 4øE), for Pinatubo aerosols have been reported by Deshler et al. [1992, 1993], and a summary of the measurements up to April 1994 is given by Massie et al. [1996]. In describing the particle size distribution the most frequently employed form is the lognormal expression dr - N, In 2 (r/r,) -- - exp - -- (5) t=l F 2 In or, 2 In 2 or, ' where dn/dr is the number of particles in the radius interval dr; N i is the number density (particles cm-3), cr i is the geometric mean standard deviation (dimensionless) of r, and R i is the median radius (/ m), respectively, for mode i. Although Pinatubo aerosols are accurately represented by a bimodal distribution, the present study adopts a single mode expression. The single mode representation has been used by other studies [Wang et al., 1989; Herrig et al., 1998] using remotely sensed data. The reason for using a single mode expression is that extinction measurements at a limited number of infrared wavelengths are not sufficiento retrieve the six parameters of a bimodal distribution. Another reason is that remotely sensed infrared data are not accurate enough to distinguish small contributions from aerosols with small radii (less than txm), which are described by the first mode of a bimodal size distribution. When a single mode distribution is used, the number density N is eliminated in the expression of the ratio of the extinction coefficients at two wavelengths (u and v), and the relative extinction ratio is given by EjQe(x,, m,)jan R,, (z):, f, too,an,, (6) where the superscript c denotes calculated values and the subscript j runs over the number of radii bins. The value of Aris represents the fractional amount of the total number density in the jth radius range dr/ multiplied by z-r]: r 2{ q 2 1 In o- [ ln:<o/r) 2 o- 1 } /Xnj = z- exp - d 5. (7) 2.3. Theoretical Simulation of Extinction Ratio Theoretical values of relative extinction ratio from (6) can be compared to measured values obtained from (4) to infer size distribution parameters (R and o-) and composition. In order to understand dependency of relative extinction ratio on aerosol parameter values, the extinction ratios are computed for several different cases using (6) at the HALOE wavelengths. With most likely combinations of the size distribution parameters, calculated relative extinction ratios which matched the shapes of the HALOE-derived extinction ratios in Figures 3a-3c are shown in Figures 4a-4c for HgSO 4 concentrations varying from 65 to 85 wt %: R = 0. /xm and o- = 1. (Figure 4a), R = 0.34 txm and o (Figure 4b), and R = 0.37 txm and o- = 1.19 (Figure 4c). The values for each channel are normalized to that of the HF channel. The HALOE-derived extinction ratios clearly indicate the presence of HgSO4/HgO droplets. The extinction ratios, however, vary with H2SO 4 wt % changes in different ways. The extinction for the CH 4 (3.46 txm) channel increases with increasing HgSO 4 amount, while this trend is reversed for the COg, NO, Nag, and HgO channels (at 2.80, 5.26, 6., and 6.6 txm). A combination of larger R and smaller o- in Figure 4c Calculated from Mie theory R=0. /xm, cr=1. H2SO,(Wt %).,:,,,,: * 65.0./ '::i::.:. ß o ".'i.. : '"'%., A ':.: ' :.'.7 '.'x '?,..:..:::.. z []":"'::": *..:.:,... :::::::::::::::::::::::::::: Wavelength (/_z,m) R= ' /zm, cr=1.34 H2SO,(Wt %) i :;:. ß i ":'.'..:::: o 75.0 ß :½',,,,,.,:.,., :,x 80.o ß ':-E [] ':.'.:: '"'/,, ":'"'" :'9:..... ': ' i:]' "-'" 8.: ?:.:.:e:-::'-:-::'?? i::::p tq ". ' x" '.2.'-.":,'-'.:':"... ::.-.:-':::.':" --a:;. a.....:.:' lo Wavelength (/_z m) R=0.37 /zm, a= :!: o 75.0 t,, ),,, [] 85.0 i:'":'"'i, o.o i..;.! '"",-...,.',;!i i '""':': %...:.:.:.:.:.:..!?:& :'i [] [] '.. 'El' ' (o) (b) a :t8...:.:.:-:...-.:--.1'.11:--:..:...: lo Wavelength Figure 4. Relative extinction ratios (or ratio of relative optical depth defined by equation (6)), calculated at HALOE channel centers from Mie theory, for HgSO 4 concentrations varying from 65 to 85 wt % at 2 K. The median radius (R txm) and geometric mean standard deviation (o-), respectively, are (a) 0. and 1.3, (b) 0.34 and 1.34, and (c) 0.37 and Values are normalized to the HF channel. compared to the other two cases results in large extinction ratios for the HC1 and CH 4 channels. These examples of Figures 4a-4c are shown in order to give qualitative understanding of dependency of extinction ratios on various aerosol pa-... ( )

8 . 28,340 LEE ET AL.: PINATUBO AEROSOL PROPERTIES rameters. Detailed derivations of aerosol parameters, however, are discussed in the next section using the nonlinear least squares fit technique. 3. Retrieval of Aerosol Parameters Using Mie Theory Aerosol parameters are inferred using a nonlinear least squares fit technique [More, 1977]. We define the normalized residual, f(x), of extinction ratio with unknown aerosol parameters, x (i.e., composition, geometric mean standard deviation, and median radius), as f(x) = Rm,v(Z) - Rum, v(z), (8) where R,m,v is the measured extinction ratio determined by (4) and R, v is the calculated extinction ratio of (6). The parameters x are determined when the sum of squared residuals reaches a predefined small value (or change of the sum of squared residuals is negligible in iterative calculations). In our calculations the final solutions are nearly independent of the initial estimation of the parameters Selection of Extinction Ratios for Computation of Aerosol Parameters There are many possible ways of computing relative extinction ratios using the six channels (i.e., HF, CO2, CH4, NO, NO2, and H ) included in this study. Some of the extinction ratios provide information on size distribution parameters, while others provide aerosol composition information Extinction ratio sensitive to H2SO 4 amount and size distribution parameters. Figure 5a shows the sensitivities of the relative extinction ratios of two HALOE channels (equation (6)) with respecto H2SO 4 amount. The ratios for NO/HF (ratio of extinction coefficient for the NO channel to that for the HF channel), CO2/HF, NO/CH4, and CO2/CH 4 are very sensitive to H2SO 4 amount, while the ratio for HF/CH 4 is nearly constant. These sensitivities indicate which relative extinction ratios are best suited to retrieve the H2SO 4 concentration. Similarly, variations of the extinction ratio of two channels with respect to changes of the geometric mean standard deviation and median radius are plotted in Figures 5b and 5c, respectively. Among others, the ratio for CH4/HF is the most sensitive to size distribution parameters. Note that the relative extinction ratio for NO/CH 4 is constant with respect to both size distribution parameter variations. This is due to a constant value of the efficiency ratio for a large range of aerosol radius (see subsequent discussion in section 3.1.2). However, this characteristic is important in retrieving the aerosol composi- tion, as it does not depend upon the size distribution function Ratio of efficiency factors sensitive to radius. Extinction ratio sensitivity, with respect to the size distribution parameters, is examined in terms of the ratio of extinction O.5. 4 HF/CH H 0 H Composition (H2SO 4 Wt %) Geometric Meon Stondord Deviotion C02/HF... CO2/CH t... i... i... i... CH4/H - NO/HF (b) 9O 0H4/002 :: NO/C02 NO/HF e> 2 CH4/CO ry 1 NO/CO 2 NO/CH 4... (c) O Medion Rodius Figure 5. Variations of relative extinction ratios with (a) H2SO 4 amount, (b) geometric mean standard deviation, and (c) median radius. efficiency factors that varies with particle radius. The numerator and denominator in (6) are sums of the fractional con- Figure 6 shows the ratios of the efficiency factors of the centrations A% weighted by the efficiency factors Qe values, HALOE channels with respecto the HF channel (see Figure respectively. If the ratio of efficiency factors at two wavelengths 6a), and with respect to the CO2 channel (see Figure 6b), varies with radius, then the calculated extinction ratio varies calculated with 80 wt % of H2SO 4 at 2 K. The ratios shown with the size distribution parameters. Therefore variation of in Figure 6a vary by about a factor of 100 for a radius range the ratio of efficiency factors with radius provides information from 0.1 to 1.0/ m, while the ratios shown in Figure 6b vary by on the sensitivity of the extinction ratio to size distribution a factor of 10. The efficiency ratios are nearly constant below parameter variations and the retrievable size range [Heintzen- about 0.06/ m in Figure 6a and below about 0.2/ m in Figure berg et al., 1981]. 6b. The large sensitivities of the relative extinction ratio for 1.70

9 ._ LEE ET AL.: PINATUBO AEROSOL PROPERTIES 28, H2S04=80%, T=21 5 K 1 i I E O.OLOO Q (C H4)/Q.!..H...F.)... Q(_NO)/Q(H F) o.e x (o) J, i J L I I I I, I, t,, t I L t I, I, I, rodius 0u, m) H2S04--80%, T=2 i i K o.oool o.oool o.oolo O.OLOO HALOE derived Extinction (km-1) Figure 7. Correlation of absolute extinction coefficients for the NO channel between the retrieved results using the ratio technique and those from the HALOE archive for cases o 13a(Z, Q_(CH4)/Q(CO2 ) / Q(NO2)/Q(CO2) Q(NO)/Q(CO2) ( ) 0.1 I... " rodius ( m) Figure 6, Ratios of Mie efficiency factors as a function of radius for 80 wt % H2SO4 at 2 K. CHdHF with the size distribution parameters shown in Figures 5b and 5c are a consequence of the large variation of Qe(CH4)/ Qe(HF) with particle radius. Other interchannel ratios, e.g., Qe(NO)/Qe(CH4) (not shown), are almost constant up to about 0.6 m, providing little information on the size distribution. This is the reason why the extinction ratio for NO/CH 4 in Figure 5 is constant with respect to the size distribution parameters. On the basis of the sensitivity and efficiency factor analysis we have selected nine relative extinction ratios to retrieve aerosol composition and size distribution parameters: CO2/ HF, HF/H, NO/HF, CH4/CO2, CO2/NO, H/CO2, HF/ CH4, NO/CH4, and NO/H. The first four ratios provide better information on both composition and size distribution parameters, while the last two ratios provide better information on composition. aerosol. For these cases,/3b in (3) is nearly zero. Then, (3) can be expressed as X)L = (a(z, X)NL = -ln [ 'a(z, X)/%(Z, X)], (9) where K a is the extinction coefficient for the case of N equal to 1 cm -3, which is calculated using the composition and the geometr c ii1uall b L llual U U VIO LIUII OIIU 111CUIOIi 1 aoiu3 tlia[ at determined by the nonlinear least squares fit to the nine HA- LOE-derived extinction ratios. The absolute extinction coeffi- cients a for the tangent layers are determined using an onionpeeling method, with the path lengths L calculated by a simple geometric method. The calculations begin from an altitude where the aerosol signal is negligible (see the second column of Figure 1). Since (9) already eliminates the gaseous absorption by the ratio, the uncertain of gaseous absorption is reduced. However, it contains an error caused by the assumption that the reference transmittance is nearly free of aerosol contami- nation (see subsequent discussion on the error budget in section 5). In order to determine number density, out of 45 cases, whose reference transmittance profiles have minimal aerosol contamination, were selected carefully. To justi the validi of the method for these cases, the retrieved absolute extinctions (km- ) values for the NO channel are compared in Fig- ure 7 to those from the HALOE archive. The o data sets show ve good correlation, with deviations of approximately 10% from each other. These deviations are within the uncer- tainties of the o data sets. The average number densi, calculated using the results of the HF, CH4, and NO channels, is used for later calculations of the aerosol volume densi, along with the geometric mean standard deviation and median radius retrieved from the nonlinear least squares fit Computation of Number Density 4. Results of Computations Herrig et al. [1998] and Wang et al. [1989] used HALOE and for Pinatubo Aerosols SAGE II data, respectively, to estimate the number density N by dividing the absolute extinction coefficient at wavelength X by the calculated extinction at the same wavelength for the We have applied the procedures described in the previous sections to analyze HALOE data from November 1991 to February For this period, aerosol-loaded air masses were case of N equal to 1 cm -3. For our study, the ratio technique not well mixed, and we have found 45 cases, for which the ratio is used to determine absolute extinction coefficients. For the technique can be applied, at middle latitudes (ø- ø ) in the early period of Pinatubo aerosols, several cases were found when the reference transmittances were contaminated little by northern hemisphere. Composition, geometric mean standard deviation, and median radius are calculated for all 45 cases

10 ._ 28,342 LEE ET AL.: PINATUBO AEROSOL PROPERTIES whose reference transmittance profiles have different aerosol extinction signatures with respect to other profiles that are to be ratioed. However, the number density was determined for cases whose reference transmittance profiles have minimal aerosol influence. 26. E December I i......,... I t 4.1. Composition, Geometric Mean Standard Deviation, and Number Density The result for December 6, 1991, is plotted in Figure 8a. Shown are the geometric mean standard deviation, median radius, the weight fraction of H2SO4, and the number density of the aerosol layer, with the uncertainties shown as horizontal bars (see section 5). For altitude region from 22.5 to.5 km the aerosol particles are composed of wt % H2SO4, the geometric mean standard deviation varies from 1.24 to 1.32, and the median radius is near 0.36/ m. The equilibrium weight percent of sulfuric acid was calculated using HALOE H and temperature data [Carslaw et al., 1995] and is indicated in the weight percent panel by the dotted line. When compared to the equilibrium compositio near 72 wt % of H2SO 4 at K, with H mixing ratios near 4.1 ppmv, the retrieved H2SO 4 concentrations are a little larger by about 7-10 wt %. Retrieved H2SO 4 concentrations of all 45 cases at altitudes of -28 km range from 75 to 85 wt %, median radii vary from 0.34 to 0.43/ m, and geometric mean standard deviations vary from 1.05 to The number densities for the cases range from 5 to 23 cm -3. Averages of aerosol parameters for 45 cases are shown in Figure 8b, with standard deviations of each parameter as dotted horizontal bars. These aerosol parameters are within the range of in situ measurements made at Laramie, Wyoming [Deshler et al., 1993; Herrig et al., 1995; Massie et al., 1996]. The effective radius, defined as the ratio of the third moment of the particle size distribution to the second moment, varies from 0.38 to 0.45/ m for all 45 cases. This is within the range of variations from November 1991 to February 1992 analyzed by Russell et al. [1996], using diverse measurements in the lower stratosphere. Figure 9 shows the differences of retrieved H2SO 4 and equilibrium concentrations as a function of pressure. The differences range from - 1 to 11 wt %, and they tend to increase with increasing pressure. In general, the retrieved H2SO 4 values are larger than the equilibrium values by about 3-8 wt %, with a mean near 5 wt %. Similar deviations for the Pinatubo aerosols were derived by Echle et al. [1998]. Using limb emission spectra at Kiruna on March 14-, 1992, they retrieved H2SO4 values larger than the equilibrium values by 2-8 wt % at altitudes of km. The deviation from the equilibrium value may be due, in part, to the fact that the aerosols are composed of both H2SO4/H droplets and volcanic ash, as indicated by Russell et al. [1996]. Volcanic ash particles have extinction spectra different from those of H2SOn/H droplets. The ability to retrieve aerosol composition relies on the selection of relative extinction ratios that are sensitive to com- position. The extinction ratios for NO/CH 4 and NO/H are, for instance, independent of the geometric mean standard deviation and median radius, but dependent upon the H2SO 4 concentration (see Figure 5). This indicates that the extinction ratios provide information on the composition regardless of the size distribution function. Thus we believe that the re- trieved composition is reliable provided that the refractive indices are correct I I I Geometric Mean Standard Deviation Median Radius (/zm) O H2SO 4 Weight % (O) 5 10 Number Density (cm-3) Average of Aerosol Parameters..., Geometric Mean Standard Deviation Median Radius (/zm) 28 E i H2SO, Weight % (b) Number Density (cm-3) Figure 8. Retrieved aerosol properties of geometric mean standard deviation, median radius, H2SO 4 wt %, and number density: (a) for sunset occultation 22 on December 6, Errors are indicated as horizontal bars. Equilibrium weight percent H2SO 4 values are plotted as a vertical dotted line with its own error bars. (b) Averages of aerosol parameters for 45 cases and their standard deviations (dotted horizontal bars) Comparisons With Others Unfortunately we could not find cases which could be compared directly to in situ measurements. This is due to the small number of cases for which our method was applied. Instead, we!

11 LEE ET AL.: PINATUBO AEROSOL PROPERTIES 28,343 4O 4 fit to Wyoming doto (Moy June 1997) '. { small particle ticnit Pressure (mb) Figure 9. Differences of retrieved H2SO 4 weight percent values from equilibrium values as a function of pressure. compare relationships among extinction, volume density, and composition with earlier statistical analysis of the Pinatubo aerosols Volume density versus extinction. Grainger et al. [1995] examined relationships between aerosol surface area, volume density, and effective radius based upon in situ Pinatubo aerosol measurements at Laramie, Wyoming, and showed that aerosol extinction is related to volume density and the effective radius. This method was extended by Massie et al. [1996] and Herrig et al. [1998] to understand the evolution, and to infer the properties of Pinatubo aerosol, respectively. A relationship between calculated extinction coefficients at 6. /xm and in situ volume density values are presented by Massie et al. [1996]. To compare with this, we calculate corresponding extinction coefficients and volume densities using retrieved aerosol properties of the cases for which the number density was determined. Results are shown in Figure 10, along with the fit to the in situ measurements given by Massie et al. [1996]. A good linear relationship between the extinction coefficient and the volume density is evident. The slope is in good agreement with the earlier analysis, but our extinction coefficients for a given volume density are smaller by about %. Though they to Wyoming 0 i,, i I i i I I i i i I i i,, Composition (H2SO 4 Wt %) Figure 11. Ratios of extinction at 5.26/am to volume density as a function of weight percent of H2SO 4. The solid line is the fit to the Wyoming data, and the dotted line is the small particle limit given by Hervig and Deshler [1998]. used the same optical data [Palmer and Williams, 1975], equilibrium H2SO 4 values were utilized instead of retrieved values. Our smaller extinction values are attributed to utilization of retrieved wt % H2SO 4 values that are larger than the equilibrium values. As shown in Figure 4, the extinction coefficient at 6./am decreases with increasing H2SO 4 amount. Therefore the larger H2SO 4 amount retrieved in this study results in extinction coefficientsmaller than those of Massie et al. [1996] Extinction per volume density versus weight percent of H2SO4 ß A relationship between extinction coefficient and H2SO 4 amount was reported by Herrig and Deshler [1998] using measurements of stratospheric aerosols at Laramie, Wyoming, from May 1991 to June Calculated using the equilibrium H2SO4 amount, their results show that the ratio of extinction coefficient at 5.26/am to volume density decreases with H2SO4 amount and that the spread (variance) of the ratio increases with decreasing H2SO4 amount (see their Figure 2). The corresponding ratio, calculated using our retrieved aerosol parameters, is shown in Figure 11 as a function of weight percent H2SO4. Included are the fit to the Wyoming data (solid line) and the small particle limit (dotted line), which is the lower limit of the ratio given by Hervig and Deshler [1998]. The ratios of our study decrease linearly with H2SO 4 amount, and are larger than the small particle limit. The slope, however, appears a little different from the fit to the Wyoming data. One possible reason for this could be differences in the aerosols during two different time periods. Their data cover a long period from May 1991 up to June We analyze particles within 7 months of the Pinatubo eruption. In spite of this, the magnitudes of our ratios are similar to those for the longer time period. o.1 i i i i ii i i i i I ii i i i i,, Extinction (kin-1) Figure 10. Volume densities calculated with the retrieved size distribution parameters, as a function of extinction at 6. /am. The solid line is the fit to the Wyoming data discussed by Massie et al. [1996]. 5. Error Analysis Sources of errors in our calculations are as follows: (1) uncertainties in the transmittances, (2) assumption that gas profiles at two consecutive occultations are the same, (3) assumption that the reference profile is contaminated by few aerosol particles for computation of number density, (4) assumption that the aerosol extinction coefficient (or refractive indices) within each channel is constant, (5) uncertainties in

12 28,344 LEE ET AL'.: PINATUBO AEROSOL PROPERTIES values of the refractive indices (both the absolute value, and by Harris et al. [1996] and Herrig et al. [1996]. The total error the interpolation and Lorentz-Lorenz correction), (6) assump- caused by these uncertainties in equilibrium H2SO 4 is estition of a single mode particle size distribution, and (7) assump- mated to be about 1 wt % at 24 km. The uncertainties for each tion that the aerosols are liquid H2SO4/H droplets. The first of the aerosol parameters are represented by horizontal bars in three error sources are related to uncertainties in the mea- Figure 8a. sured extinction coefficients, while the next four error sources are related to uncertainties in the calculations of the extinction ratios. 6. Summary and Conclusion The error caused by the first source contributes little to the Aerosol parameters have been derived for November 1991 total error in our calculation since the transmission error is less to February 1992 for ø-øn latitude. To determine relative than 0.3% [see Russell et al., 1993]. The second assumption extinction coefficients (or relative optical depths) of the aerocontributes a small error in the measured extinction ratios sols as a function of wavelength from HALOE transmittance since we have selected two consecutive measurements which data, we used a signal-ratio technique that is not affected by have very close transmittance profiles above the aerosol layer (see Figure 1). We estimate a variation of 5% between the two transmittance profiles, caused by gaseous absorption of differgaseous absorption and the instrument function. The two signals should have different aerosol signatures with respect to each other. Then, the ratio of relative optical depths (i.e., ent amounts. Errors in the measured extinction ratios associrelative extinction ratios) have been used to infer aerosol propated with this variation is 10%. Uncertainty due to the third error source (i.e., uncertainty of aerosol in the reference signal) is estimated, using aerosol amount provided by the HALOE archived data, to be less than 10%. The fourth assumption contributes little error in the calculated extinction coefficients. For the HALOE CO2 channel, for instance, the mean extinction coefficient is different from the center value by less than 1%. For the other channels included in this study the differences are much smaller. erties, i.e., composition and size distribution parameters, employing a nonlinear least squares fit technique. Finally, the number density was calculated using these results for cases when the reference profiles are nearly free of aerosols. Retrieved results show that the weight percent H2SO 4 values are larger than the equilibrium values by about 5 wt %, and that the geometric mean standard deviation and median radii values are within the range of in situ measurements made at Laramie, Wyoming. Although some uncertainties are involved Uncertainties of refractive index (i.e., the fifth error source), in the results, we believe that the retrieved composition and which is caused by interpolation and Lorentz-Lorentz correction as well as uncertainties in their absolute values, could cause an important error in the calculated extinction ratios. Refractive indices of Tisdale et al. [1998] for 75 wt % of H2SO 4 and 2 K at the HF (2.45 /am), CO2 (2.80/am), CH 4 (3.46 size distribution parameters are reliable. The scatter diagram of extinction coefficient at 6. /am versus volume density, calculated from the retrieved results, shows a linear relationship, and is in good agreement with a similar calculation [Massi et al., 1996]. In addition, when plotted with respecto /am), NO (5.26/am), and H (6.60/am) channels are different from those of Palmer and Williams [1975] by (real/imaginary parts) 0.5%/53%, 1%/5%, 1%/33%, 0.7%/23%, and 2%/%, respectively. We use these differences as estimated uncertainties in the refractive indices for each of the channels. Retrieved H2SO 4 weight percent, the calculated ratio of extinction coefficient at 5.26 /am to volume density is larger than the small particle lower limit, and lies within the climatological range given by Herrig and Deshler [1998]. These comparisons indicate that the ratio technique is a powerful method to determine aerosol extinction coefficients. results using the data by Tisdale et al. [1998] and those by Palmer and Williams [1975] yield typical differences in geomet- The deviation of the retrieved weight percent of H2SO 4 from ric mean standard deviation, median radius, composition, and the equilibrium value, by approximately 5 wt %, may be attribnumber density of about 10, 5, 2, and %, respectively. uted to uncertainties in the values of the refractive indices. Total errors in the retrieved results coming from all sources However, possibilities of compositions other than H2SO4JH have been estimated by a Monte Carlo method by introducing solution, or the possibility that the actual concentrations are random errors to each of the adopted parameter values. For higher than equilibrium values, cannot be ruled out. This topic instance, analysis has been done by introducing random errors will be investigated further. (given by a Gaussian distribution with a standard deviation equal to the estimated error) to each of the measured extinction ratios. Then, we retrieve aerosol properties from the er- Acknowledgments. The authors are grateful to the HALOE team who provided transmittance data for our study. The work in Korea has ror-introduced extinction ratios. The procedures are carried been supported by the Korean Ministry of Science and Technology and out 70 times, and the standard deviation of each aerosol pa- by the Japanese National Institute for Environmental Studies, and in rameter is defined as the uncertainty. Similar analysis has been the United States by NASA grants NAS and S X. The done for calculated extinction coefficients with error- National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation. W. Choi was also supported by the introduced parameter values. The resulting total error of the BK21 Program of the Korean Ministry of Education. analysis is assumed to be the root-sum-square of each uncertainty. 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Yue, Inference of stratospheric aerosol composition and size distribution from SAGE II satellite measurements, J. Geophys. Res., 94, , W. Choi, School of Earth and Environmental Sciences, Seoul National University, Seoul 1-742, South Korea. (wchoi@plaza.snu.ac.kr) K.-M. Lee, Department of Astronomy and Atmospheric Sciences, Kyungpook National University, 1370 Sankyuck-dong Buk-gu, Taegu , South Korea. (kmlee@bh.knu.ac.kr) S. T. Massie, Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, CO 807, USA. (massie@acd. ucar.edu) J. H. Park, Atmospheric Science Division, NASA Langley Research Center, Hampton, VA 23681, USA. (j.h.park@larc.nasa.gov) (Received December ll, 00; revised April 17, 01; accepted June 11, 01.)