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 From March to May 2001, aerosol size distributions and chemical compositions were measured using differential mobility analyzers (DMA), an aerodynamic particle sizer (APS), Micro-Orifice Uniform Deposit Impactors (MOUDI), and denuder samplers onboard the Twin Otter aircraft as part of the Aerosol Characterization Experiment (ACE)-Asia campaign. Of the 19 research flights, measurements on four flights that represented different aerosol characteristics are analyzed in detail. Clear-column radiative closure is studied by comparing aerosol extinctions predicted using in situ aerosol size distribution and chemical composition measurements to those derived from the 14-wavelength NASA Ames Airborne Tracking Sun photometer (AATS-14). In the boundary layer, pollution layers, and free troposphere with no significant mineral dust present, aerosol extinction closure was achieved within the estimated uncertainties over the full range of wavelengths of AATS-14. Aerosol extinctions predicted based on measured size distributions also reproduce the wavelength dependence derived from AATS-14 data. Considering all four flights, the best fit lines yield Predicted/Observed ratios in boundary and pollution layers of 0.97 ± 0.24 and 1.07 ± 0.08 at λ = 525 nm and 0.96 ± 0.21 and 1.08 ± 0.08 at λ = 1059 nm, respectively. In free troposphere dust layers, aerosol extinctions predicted from the measured size distributions were generally smaller than those derived from the AATS-14 data, with Predicted/Observed ratios of 0.65 ± 0.06 and 0.66 ± 0.05 at 525 and 1059 nm, respectively. A detailed analysis suggests that the discrepancy is likely a result of the lack of the knowledge of mineral dust shape as well as variations in aerosol extinction derived from AATS-14 data when viewing through horizontally inhomogeneous layers.
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 Quantifying the effect of atmospheric aerosols on the climate system requires knowledge of their physical, chemical, and optical properties, as well as of their temporal and spatial variability. Aerosol Characterization Experiment (ACE)-Asia was designed to study the aerosol in the atmosphere of east Asia, one of the Earth's most significant and complex anthropogenic aerosol sources. With widespread fossil fuel and biomass burning, coupled with large outbreaks of mineral dust, the atmospheric aerosol leaving the Asian continent is, arguably, the most complex on Earth. Through simultaneous measurement of aerosol microphysical, chemical, and radiative properties from a variety of platforms, the ACE-Asia campaign provided data to assess the climate impact of Asian aerosol.
 A fundamental question that underlies prediction of aerosol climatic effects is how accurately aerosol radiative properties can be predicted based on measured in situ microphysical and chemical properties. If it can be demonstrated that columnar aerosol extinction and other radiative properties (e.g., absorption, angular distribution of scattering) can be accurately predicted given the knowledge of atmospheric aerosol size and composition, then models that predict these properties can be confidently used to predict climatic effects of aerosols. This so-called radiative closure has been attempted with varying degrees of success in several field campaigns using a variety of overdetermined measurements and modeling techniques [Clarke et al., 1996; Hoff et al., 1996; Hegg et al., 1997; Howell and Huebert, 1998; Redemann et al., 1998; Collins et al., 2000]. ACE-Asia was planned to provide an unprecedented opportunity to perform aerosol radiative closure studies from a number of platforms. This paper focuses on radiative closure between the aerosol extinction calculated using in situ measurements of aerosol size distributions and chemical compositions aboard the CIRPAS Twin Otter aircraft and those derived from the 14-wavelength NASA Ames Airborne Tracking Sun photometer (AATS-14), which flew on the same aircraft.
 ACE-Asia was conducted in east Asia from late March to early May 2001. Intensive field measurements were conducted off the coast of east China, Korea, and Japan. A detailed description of the campaign is given by B. Huebert et al. (submitted manuscript, 2002) (Overview paper). The CIRPAS Twin Otter flew 19 scientific missions out of Iwakuni Marine Corps Air Station, Japan. Four of those missions sampling different air masses provided ideal conditions for detailed analysis of predicted and observed clear-column aerosol extinction, and we address these four cases in detail in the present paper.
2. Aerosol Size Distribution Measurements
 The suite of instruments related to this study, which are deployed on the Twin Otter, are listed in Table 1. Measurements and data reduction for each instrument are described in detail in this section. Because it is essential to assess the uncertainty associated with the eventual radiative closure, and because some of that uncertainty results from uncertainties in the aerosol size and composition measurements, we devote attention to a careful analysis of the measurements on which the radiative closure is based.
Table 1. Measurements Made Onboard the Twin Otter That are Related to This Study
Aerosol size distribution
Differential mobility analyzer system
Aerosol size distribution
Aerodynamic particle sizer
Tandem DMA system
Inorganic anions, elements
30 min to 1 h
30 min to 1 h
Aerosol optical depth
14-wavelength Sun photometer
Aerosol scattering coefficient
TSI 3563 nephelometer
Pressure, temperature, RH
2.1. Differential Mobility Analyzer (DMA)
 Two DMA systems, operated in parallel inside the main cabin of the Twin Otter, were deployed during ACE-Asia [Wang et al., 2003]. One of the two systems measures the dry aerosol size distribution by passing the aerosol flow through a Nafion drier prior to the measurement. The other measures the aerosol size distribution at ambient relative humidity (RH) by using an active RH controller [Wang et al., 2003]. The aerosol sample was introduced in the Nafion tubes housed in a stainless steel shell, and the control of the aerosol RH was achieved through controlling the RH of the countercurrent purge flow between the Nafion tubes and the stainless steel shell. A feedback cascade algorithm was used to achieve good control accuracy. The size measurement sections of the two systems downstream of the drier and active RH controller are identical. The main components of the measurement section are a cylindrical DMA (TSI Inc., model 3081) and a condensation particle counter (TSI Inc., model 3010), which has a 50% counting efficiency at 10 nm. All the flows associated with the DMA are monitored and maintained by feedback controllers to compensate for environmental changes during airborne measurement. Using the scanning mobility technique, each DMA system generates a size distribution from 15 nm to 1 μm diameter every 100 s. Both DMA systems were carefully calibrated prior to and during ACE-Asia, and accurately recovered both the peak size and number concentration of monodisperse calibration aerosols as small as 30 nm diameter. The aerosol sample flows for the DMA systems were drawn from the Twin Otter community inlet, which was shared by other instruments in the main cabin. For the particle size range measured by the DMA systems (diameters smaller than 1 μm), the aerosol transmission efficiency through the community inlet has been established to be 100%. Data from DMA systems were analyzed using the data inversion procedure described by Collins et al. .
2.2. Aerodynamic Particle Sizer (APS)
 An APS (TSI model 3320), which has a measurement range of 0.5–20 μm in aerodynamic diameter, was mounted under the left wing of the Twin Otter. The APS infers particle size by measuring the velocity of particles inertially accelerated in an expanding air stream; large particles undergo smaller acceleration and achieve lower velocity than small particles. Note that the APS does not measure the traditional aerodynamic particle size, for reasons that are explained below.
 Independent of the sampling pressure, i.e., aircraft altitude, the velocity of expanding air downstream of the APS nozzle reaches 150 m/s. The particle Reynolds number inside the acceleration region is defined as
where ρg is the density of air, is the particle volume-equivalent diameter, where V is the volume of the particle. vg is the air speed in the instrument, vp the speed of the accelerated particle, and η the viscosity of air. For polystyrene latex (PSL) particles with diameters of 1.0, 2.1, 5, and 15 μm, the corresponding values of Rep in the acceleration region are 0.65, 4.8, 24, and 103, respectively [Wang and John, 1987]. Therefore, the interaction of the particle and the surrounding air often lies well outside the Stokes regime (Rep < 0.05). Under the ultra-Stokesian condition (Rep > 0.05), the particle speed after acceleration is a function of particle aerodynamic size as well as the density of the particle [Wilson and Liu, 1980; Baron, 1984]. In an attempt to quantify the effect of particle density on APS measurement, Wang and John  found that within the resolution of the instrument, inside the detection volume, two particles with the same velocity, i.e., the same APS response, have the same acceleration. This finding enables accurate interpretation of APS measurements provided with calibration data. Cheng et al.  generalized the analysis to include particle shape and slip correction factor. For two particles with the same APS response, the following relationship holds:
where subscript 1 denotes the calibration particle (In the present case, spherical PSL particles, density = 1.05 g/cm3), and subscript 2 denotes the particle of interest. ρp is the particle density, C the slip correction factor, κ the dynamic shape factor, and (1 + aReb ) the ultra-Stokesian correction factor. For a spherical calibration particle, κ = 1, a = 1/6, and b = 2/3. The slip correction factor and the Reynolds number are evaluated at the APS sensing volume, which has a lower pressure and temperature than the ambient condition as a result of the expansion of the air stream. Given the calibration particle diameter, Dp1, and its density, ρp1, the volume-equivalent diameter of the measured particle, Dp2, can be derived using equation (2) with knowledge of its density, ρp2, the dynamic shape factor, κ, and the ultra-Stokesian correction (1 +
 The density of the measured particle is calculated using the constructed size-resolved particle chemical composition, together with its water content, which is calculated using the gas–aerosol thermodynamic model, ISORROPIA [Nenes et al., 1998]. The details of the density calculation are described subsequently. In this study, particles are assumed to be spherical, a reasonable assumption for hygroscopic aerosols in the marine boundary layer (MBL), where most often the aerosols are deliquesced as a result of high RH. For particles at low RH and nonhygroscopic particles, such as mineral dust, the assumption of sphericity does not necessarily hold. Lack of knowledge of dust particle shape as well as its dynamic shape factor κ, and the ultra-Stokesian correction factor (1 + is a source of uncertainty in APS measurements. Uncertainties in the aerosol extinction calculation resulting from the assumption of spherical particles is estimated by using data on nonspherical agglomerate particles measured by Cheng et al. .
 The APS occasionally detects recirculating particles within the detection region, leading to so-called artificial particles [Stein et al., 2002]. The particles involved are generally small in size but, due to recirculation, cross the detection laser beams multiple times with a reduced speed. As a result, when this occurs, these small, but slow particles are misinterpreted as large particles. While on a number concentration basis, these artificial particles represent only a very small fraction of the total particles detected, because these particles are interpreted as large (>5 μm), this could introduce significant errors into an aerosol extinction calculation. These artificial particles can be removed by applying a matrix data mask to the correlated APS data, which is a simultaneous measurement of the particle speed and scattering intensity as they cross the laser beams [Stein et al., 2002]. Based on the principle that large particles scatter more light than small particles, a particle sized to be large (slow speed) but associated with little light scattering is identified as artificial and removed from the data. Figure 1 shows an example of the correlated data, which were taken during Research Flight 9 on 14 April 2001. The x axis is the light scattering channel, which increases in the direction of increasing intensity of light scattered by particle. The y axis is the time of flight channel, which increases with increasing particle time of flight between the two detection laser beams, i.e., aerodynamic particle size. The data mask is represented by a straight line in the two-dimensional time of flight-scattering intensity space. Particles appearing below the line are identified as artificial and removed. The mask given by the dashed line (TSI carbon mask) is based on the calculation of light scattered by black carbon particles; the solid line is a custom mask constructed based on ACE-Asia data. Analysis of data using each of the two data masks is considered in the case studies.
 The commercial APS has been engineered for laboratory measurement. A special inlet for airborne sampling was developed by MSP Corp. to minimize impaction particle losses when transporting particles in a high speed air stream to the instrument. The flow rate of the APS inlet system, 100 L/min, is equal to the product of the average aircraft cruising speed, i.e., 50 m/s, and the cross-sectional area of the inlet diffuser tip. The actual instantaneous flow rate may be somewhat different from the average value, 100 L/min, and the resulting uncertainty in predicted aerosol extinction is discussed subsequently. After entering the inlet diffuser, the flow slows down significantly. The ID of the inlet diffuser tip is 0.66 cm and the ID at the end of the 7° diffuser is 2.54 cm. The flow then enters a virtual impactor, where it is split in a 25/75 ratio. The flow division is achieved by a flow splitter with two carefully sized orifices, the performance of which was confirmed experimentally under typical flight conditions. A small fraction (5 L/min) of the major flow after the division (75 L/min) is sampled by the APS, and the remainder of the flow (70 L/min) is removed from the system with the minor flow.
 The total counting efficiency of the APS measurement, ηt, is
where ηs is the transmission efficiency of the airborne inlet system and ηAPS is the counting efficiency of the APS. ηs is determined using uranine-tagged oleic acid particles, which are generated by a TSI vibrating orifice aerosol generator. The efficiency was calculated from the mass of aerosol collected on the 5 L/min APS tube with respect to the total mass entering the sampling system at 100 L/min flow rate, multiplied by the flow split ratio (i.e., 20). The ηs used in this study is presented in Figure 2.
 The counting efficiency of the APS is a product of aspiration (ηasp), transmission (ηtran), and detection (ηdet) efficiencies:
 The aspiration and transmission efficiencies characterize the superisokinetic sampling of the APS inner inlet and the particle deposition on the inner nozzle, respectively. The detection efficiency is defined as the fraction of particles entering the detection area that are counted.
 While APS counting efficiency APS has received a lot of attention, the only study of the counting efficiency of the most recent model 3320, that deployed on the Twin Otter, is apparently that of Armendariz and Leith . The counting efficiency of Armendariz and Leith  and that of an earlier model (3310) of Kinney and Pui  are shown in Figure 3. The APS 3320 studied by Armendariz and Leith  was equipped with an earlier version firmware (Version 1.78), which produces problematic correlated data. As a result, the removal of artificial large particles by applying mask to correlated data is not possible, and Armendariz and Leith  reported the counting efficiency of particle only smaller than 5 μm based on the noncorrelated data. The data show that the counting efficiency of the APS 3320 begins at 30% for 0.5 μm diameter particles, increases to 100% for 0.9 μm particles, then drops to 60% for 5 μm particles. The nonunity counting efficiency around 0.5 μm is probably due to the low detection efficiency, a result of low scattering light intensity of submicron particles. The counting efficiency reached 90% at 0.7 μm, suggesting the detection efficiency is at least 90% and most of the particle at this size scatter enough light to be detected. In this study, particles larger than 0.7 μm are assumed to scatter enough light to be detected, and the counting efficiency is not a strong function of the particle refractive index. Only APS measurements above 0.7 μm were used in aerosol extinction calculations.
Kinney and Pui  studied the product of the aspiration and transmission efficiencies (ηaspηtran) of the earlier 3310 model. Since the APS 3320 has a similar design of the inlet geometry and similar flow characteristics to those of the 3310 model, the detection efficiency of the APS 3320 within the overlap region of the two measurements can be approximated by the ratio of reported efficiencies (Figure 3). Assuming the detection efficiency is constant for particles larger than 2 μm, the counting efficiency of the APS 3320 can be extrapolated from Kinney and Pui's results to diameters exceeding 5 μm. The assumption of a constant detection efficiency is supported by the detection efficiency derived in the overlap region, which shows little variation. To account for the potential error in the extrapolation of the APS counting efficiency, a ±50% uncertainty is assumed for the APS concentration over the extrapolation size range in the uncertainty analysis of the aerosol extinction calculation.
2.3. Integration of Size Measurements
 Adjusting the DMA and APS measurements to ambient size distributions, which are needed for extinction calculations, requires knowledge of measurement conditions inside each instrument as well as the response of aerosol size to the RH change. For the DMA system with active RH control, the RH inside the instrument was generally maintained at the ambient level and little correction was needed. However, when the aircraft sampled air masses with rapid RH variation, the RH inside the instrument lagged somewhat behind the ambient RH. The RH inside the DMA was continuously monitored and recorded. Determining deviation of the APS measurement RH from the ambient RH inside the APS is more complicated than for the DMAs since neither RH nor temperature of the sample flow is directly measured. Assuming no heat exchange between the aerosol flow and the conduit wall, the temperature of the air stream increases about 1.2°C as the flow decelerates in the diffuser. The residence time of the airflow before reaching the APS is about 0.4 s, which is sufficient for particles up to 20 μm diameter to adjust to the decreased RH. Before reaching the sensing volume, the RH of the aerosol flow once again changes as a result of acceleration through the APS nozzle. However, the resulting lower temperature and higher RH will not further change the particle size, since the time between acceleration and detection is about 1 μs. Since the water vapor concentration is conserved during transport of the air stream to the APS, the RH of the APS measurement was calculated from the ambient RH assuming a 1.2°C increase in temperature. The sensitivity of calculated aerosol extinction to the amount of APS ram heating is discussed later.
2.4. Aerosol Chemical Composition and Mixing State
 Backcalculation of the ambient particle size distribution from each instrument's data requires knowledge of the size response to RH. Interpretation of APS data requires the particle density, which, in turn, generally necessitates knowledge of aerosol chemical composition and mixing state. The construction of aerosol chemical composition is discussed in this section, and the two sections following focus on the calculation of the aerosol size response to RH and aerosol density. On board the Twin Otter, a set of 8 Micro-Orifice Uniform Deposit Impactors (MOUDI) and three denuder samplers were deployed to characterize aerosol chemical compositions. The sample flow rate of the MOUDI is 100 L/min. Each MOUDI has 5 stages that collect particles within predetermined aerodynamic diameter ranges. However, to reduce the sampling time, only one stage of each MOUDI was used to collect particles (below 3 μm) during the ACE-Asia campaign. The 8 MOUDIs enable sampling of multiple representative air mass during each flight. The MOUDI sample filters were extracted using deionized water (HPLC grade) through mechanical shaking for 20 min. The filter extracts were then analyzed for the metallic elements (total mass including soluble portion, “cations,” and insoluble portion) using an inductively coupled plasma-atomic emission spectrometer (ICP-AES, model Jarrell Ash 955), and water-soluble anionic species using a standard ion chromatography (IC) system (model DIONEX DX-500) (S. Gao et al., Aerosol chemistry, and light-scattering and hygroscopicity budgets during outflow from East Asia, submitted to Journal of Atmospheric Chemistry, 2002).
 A pair of low-flow denuder samplers were used to collect filter samples for analysis of Organic Carbon (OC), and Elemental Carbon (EC) using a thermal–optical carbon analyzer [Mader et al., 2002]. A single high-volume particle trap impactor–denuder sampler was used to collect samples for the determination of water-soluble organic carbon and individual compounds comprising the OC. Calibration experiments determined the collection efficiency of the denuder sampler is over 90% for particle with 2.3 μm diameter or smaller [Mader et al., 2002].
 None of the above samplers produced size-dependent information on chemical composition; thus, the following assumptions are made in order to construct the size-resolved chemical composition. Since the concentration of NH4+ was not determined, the NH4+ concentration is estimated using the molar ratio, NH4+/(2SO42− + NO3−). Table 2 lists recent studies of aerosol chemical composition in east Asia. Ammonium to sulfate plus nitrate molar ratios among the studies range from 0.59 to 0.89. A ratio of 0.75 is assumed in this study. Based on previous observations that sulfate, nitrate, OC, and EC are found primarily in small particles [Wilson, 1997], and dust and sea salt are most likely to reside in larger particles, the aerosol mass was divided into fine and coarse modes. The size boundary between the two modes will be discussed below. The fine mode consists of NH4+, SO4−, NO3− OC, and EC, and the coarse mode includes sea salt and dust. when the mass size distributions of the fine and coarse modes are lognormal distributions with the same geometric standard deviation, for aerosol with diameter Dp, the mass ratio of the two modes could be written as
where fcoarse(Dp) and ffine(Dp) are the mass fractions of coarse mode and fine mode in the total mass of aerosol with diameter Dp, respectively. Dp0 is the particle diameter at which the mass fractions of the fine mode and the coarse mode are equal to each other, 50%, which is the “size boundary” between the two modes. α is a positive number that ensures that the fine mode and coarse mode dominate the total mass at small and large particle sizes, respectively. It will be shown subsequently that the calculated aerosol extinction is insensitive to the value of α, and a value of 3.3 is assumed in this study. Dp0 is selected such that when equation (5) is combined with the in situ aerosol size distributions, the calculated fine mode mass of aerosol matches the MOUDI and denuder sampler measurements. The mass ratios among the chemical species of the fine mode are assumed as constants, which are determined from MOUDI and denuder sampler measurements. The assumption of constant mass ratio among fine mode chemical species is supported by onboard Aerosol Mass Spectrometer size and chemically resolved mass concentration measurements, which showed the mass ratios between SO4/NH4/NO3/Organics were approximately independent of size in the submicron size range [R. Bahreini et al., Aircraft-based aerosol size and composition measurements during ACE-Asia using an aerodyne aerosol mass spectrometer, manuscript in preparation, 2002]. For the partition of sea salt and dust within the coarse mode, the majority of the coarse mode is assumed to be sea salt in the boundary and pollution layers, and dust in the free troposphere (with the exception of the 23 April case discussed later). These assumptions are necessary, since none of the samples is size resolved, and the filters do not include all the mass above 3 μm diameter. For each flight, size-resolved chemical compositions were generated for each layer.
Table 2. The Concentration of NH4+, SO42−, and NO3− During Recent Studies of Aerosol Chemical Composition in East Asia (Unit: μg/m3)
 A Tandem DMA system was onboard the Twin Otter for measurement of aerosol hygroscopic properties (D. Collins et al., manuscript in preparation, 2002). The system employs two high flow DMAs to maximize the counting statistics. Hygroscopic properties of particle with diameters ranging from 40 to 586 nm were measured. During most of the ACE-Asia flights, the Tandem DMA data showed that aerosols of the same dry size grew to similar final size, i.e., similar water uptake when exposed to high humidity, suggesting that the particles were internally mixed. Based on these observations, the present analysis assumes internally mixed aerosols. While the mixing state of supermicron particles is not available from hygroscopicity measurements, the assumption of an internally mixed aerosol in this size range should not cause significant errors, since frequently the supermicron aerosols were dominated by a single component, sea salt or mineral dust.
2.5. Calculation of Aerosol Size Response to RH
 Given aerosol chemical composition, the size response to varying RH was determined using the thermodynamic equilibrium model, ISORROPIA [Nenes et al., 1998]. ISORROPIA describes the sodium–ammonium–chloride–sulfate–nitrate–water aerosol system, and predicts the equilibrium water content, as well as the concentration, of chemical species in both aqueous and solid phases of aerosol at given RH and temperature.
 For RH between the crystallization and deliquescence points, particles can exist in either the metastable state (deliquesced) or equilibrium state (crystallized). Usually, the state of the aerosol can be determined by comparing the two size distributions measured by the DMA systems. As described above, the RH within one DMA (termed the “ambient” DMA) was maintained at ambient level by using an active RH controller. However, the size distribution measured by the “ambient” DMA is not always the true size distribution of the ambient particles. Since the RH of the aerosol flow first decreases as the flow enters the inlet, the deliquesced aerosol may be crystallized due to the initial RH decrease, and remain crystallized even after the RH later recovers to the ambient level. Therefore, we can be confident that the ambient aerosol is deliquesced only when the aerosol measured by the “ambient” DMA is deliquesced, which is evidenced by a shift of the size distribution measured by the “ambient” DMA toward larger sizes as compared to the dry distribution. When particles measured by the “ambient” DMA are crystallized (identical size distributions from the two DMA systems), the true state of the ambient aerosol is less clear, especially when the ambient RH is just above the crystallization point. In this case, it is assumed that the aerosols within the boundary layer are deliquesced, and aerosols within elevated pollution layers and in the free troposphere are crystallized. Uncertainties associated with this assumption will be investigated subsequently. Organic carbon, elemental carbon, and mineral dust are considered nonhygroscopic, and are only present in the solid phase of the aerosol. This assumption is more likely to hold for elemental carbon and mineral dust, but not necessarily for many organic species likely to be present [Saxena et al., 1995].
2.6. Calculation of Particle Density
 At given RH and temperature, the aerosol density is calculated using the concentrations of both aqueous and solid phases of aerosol, which are provided by ISORROPIA. The density of the aqueous phase is calculated based on partial molar volumes,
where ρa is the density of the aqueous phase, ρ0 the density of pure water, ci the molality of each solute, Mi the molecular weight, the partial molar volume, and Vmixex the excess molal volume. In our calculation, it is assumed that no volume change associated with mixing of water and the solutes occurs, i.e., Vmixex = 0. The error in calculated density by assuming Vmixex = 0 does not exceed 5% over the concentration range of NaCl droplets. This suggests that the assumption should not introduce significant error in the analysis since the density calculation only affects the interpretation of APS data. For the size range measured by the APS, the aqueous aerosol phase, if any, is generally dominated by NaCl.
 The solid phase is assumed potentially to consist of 11 components, 8 of which are inorganic salts, and the other 3 are nonhygroscopic species: OC, EC, and mineral dust. The density of the inorganic salts are available from CRC , and the densities of OC, EC, and mineral dust are assumed to be 1.2 [Turpin and Lim, 2001], 1.25 [Horvath, 1993], and 2.5 g/cm3 [Volz, 1973], respectively. Once the densities of the aqueous phase and each component within the solid phase are determined, the calculation of aerosol density can be carried out.
 Through the calculation described above, data from the DMA and APS were used to determine the corresponding size distributions under ambient conditions. The agreement between ambient distributions derived from DMA and APS measurements usually fell within 20% in the size range within which the two instruments overlap. Figure 4 shows an example of ambient size distributions derived from DMA and APS measurements at 450 m during Research Flight 17 from UTC 0138 to 0209 on 27 April 2001. For the size distribution in the overlap range of the DMA and APS, a simple average of the DMA and APS distributions was used.
2.7. Effective Particle Refractive Index
 Given the chemical composition of an internally mixed particle, the optical properties are often calculated through the effective refractive index approach, assuming an equivalent homogeneous sphere with an effective, or average, refractive index, which is derived from the refractive index of each component within the aerosol. In our analysis, the refractive index of the aerosol is averaged over the aqueous phase and each component in the solid phase using the Bruggeman mixing rule [Bruggeman, 1935],
where i indicate the aqueous phase or the different components of the solid phase within the aerosol, fvi is the volume fraction, mi the refractive index of component i, and mav is the average aerosol refractive index that is being sought. With the aqueous phase composition given by ISORROPIA, the refractive index of the liquid phase can be obtained through the partial molal refraction approach [Moelwyn-Hughes, 1961]. The refractive indices of the 8 inorganic salts of the solid phase are taken from CRC , and OC and EC are assumed to have refractive indices of 1.55 + 0i [Larson et al., 1988] and 1.96 + 0.66i [Seinfeld and Pandis, 1998], respectively. With no available data on the refractive index of east Asia mineral dust, the refractive index of central Asia dust [Sokolik et al., 1993], 1.56 + 0.0032i, was used. The refractive index of each component is assumed constant within the AATS-14 wavelength range (363–1558 nm). Both experimental [Chýlek et al., 1988] and modeling studies [Videen and Chýlek, 1998] demonstrate that the aerosol extinction of a composite particle can be accurately predicted using refractive index derived from Bruggeman mixing rule. The aerosol extinction was also calculated using volume-averaged refractive indices to estimate the uncertainties introduced by the average method.
2.8. Optical Measurements and Calculation
 The 14-wavelength NASA AATS-14 was deployed on the Twin Otter. The AATS-14 continuously measured the optical depth of the column of air between the aircraft and the top of atmosphere. By subtracting from this value the optical depth due to Rayleigh scattering of gas molecules and absorption by O3, NO2, H2O, and O2–O2 [see Schmid et al., 2002], the aerosol optical depth (AOD) throughout the column of air between the altitude of the aircraft and the top of the atmosphere is calculated. The derivative of AOD with respect to altitude gives the aerosol extinction σext at different altitudes,
where τ(z, λ) is the AOD at wavelength λ, and z is the distance between the instrument and top of atmosphere. Prior to differentiation, τ(z, λ) is smoothed (in a nonbiased manner) to reduce effects of horizontal and temporal variations of AOD on the photometer-to-Sun path at a given altitude [e.g., Schmid et al., 2000]. Uncertainties in derived aerosol extinction introduced by the smoothing procedure are estimated as 0.005 km−1 [Schmid et al., 2000].
 To compare with extinction derived from the AATS-14 data, aerosol extinction is calculated using ambient aerosol size distributions together with effective refractive indices based on aerosol chemical compositions. For each particle diameter, the extinction cross section is calculated using Mie theory at the 13 wavelengths measured by the Sun photometer (One of the wavelength at 940 nm was used for the measurement of water vapor concentration, and the absolute error in derived the columnar water vapor, CWV, is conservatively estimated as 0.1 cm + 10% CWV [Schmid et al., 1996]. The aerosol extinction is an integration over the measured size range,
where Dp is the particle diameter over which the integral is performed. Dp1 and Dp2 are the minimum and maximum diameters of measurement, respectively. Qext is the extinction cross section based on Mie theory, m(Dp, RH, z) the effective refractive index of the particle, which is a function of the particle's size, composition, and (implicitly) ambient RH. n(Dp, z) is the particle size distribution at ambient conditions.
2.9. Uncertainty Analysis
 The degree to which clear-column radiative closure is achieved is judged by the closeness with which measured and calculated extinctions agree. To understand discrepancies between the calculated and measured σext, the uncertainties associated with the calculated aerosol extinction need to be addressed. The uncertainty sources, which are grouped into 7 categories, are listed in Table 3, together with the uncertainty levels assumed in the analysis. Many of the entries in Table 3 have been discussed above. To examine the uncertainty associated with aerosol mixing state, we carried out a complete calculation based on an externally mixed aerosol, in which 8 types of aerosol were assumed: (NH4)2SO4, NH4HSO4, H2SO4, NH4NO3, OC, EC, sea salt, and dust. For this externally mixed aerosol, the water content of hygroscopic aerosol and its density were calculated using data of Tang and Munkelwitz , Tang , and Tang et al. . The aerosol extinction is the summation of the contribution from each type of aerosol. The organic molecular weight per carbon weight, moc/mc, value of 2.1 ± 0.2 was used in our study [Turpin and Lim, 2001]. mions/mcarbon is the mass ratio of fine mode ions (NH4+, SO42−, and NO3−) from the MOUDI sample to total carbon from the denuder filter samples. The ±30% uncertainty assumed for this ratio accounts for the different cut sizes and uncertainties in the analysis of the MOUDI and denuder filter samples, as well as the aerosol hygroscopicity resulting for the assumption that OC and EC are nonhygroscopic. At increased mass ratio, the aerosol is more hygroscopic since more hydrophilic ions are present in the aerosol. The results of the uncertainty analysis are presented with each of the four cases studied.
Table 3. Assumed Levels of Uncertainty Associated With Properties Required for Calculation of Aerosol Extinction From Aerosol Size Distribution and Composition Measurements
 During ACE-Asia, 19 Twin Otter research flights were conducted out of Iwakuni Japan (B. Huebert et al., submitted manuscript, 2002). Among those 19 missions, four flights sampling different air masses presented conditions ideal for detailed analysis of clear-column radiative closure.
3.1. Research Flight 14, 23 April 2001
 During Research Flight 14, the Twin Otter flew to 33°N and 134°E, SE of Shikoku Island; the flight track is shown in the top two panels of Figure 5. Three layers were sampled in detail. Two layers were within the MBL, and centered at 30 and 600 m. The third layer was within the free troposphere and centered at an altitude of 1900 m.
 The total particle number concentration showed little variation within each layer, except for occasional spikes, which may represent small regions in which recent nucleation events occurred. The total particle number concentrations were about 2200 and 500 cm−3 for the two MBL layers and the free troposphere layer, respectively. The size distributions, together with the aerosol extinction distributions at 525 nm, were averaged for each layer (Figure 5). The aerosol extinction distributions are calculated at 525 nm since that wavelength is close to the peak solar irradiance wavelength and is one of those measured by AATS-14. All distributions shown correspond to aerosol at ambient conditions. Within the boundary layer, size distributions at both altitudes are bimodal, with the major mode occurring at 70–80 nm, and the smaller mode at 20 nm. which may reflect result of recent nucleation events. The size distribution in the free troposphere layer was monomodal, with peak concentration at 140 nm. The aerosol extinction distributions indicate that submicron particles dominated total aerosol extinctions of all three layers at 525 nm.
 As discussed above, the MOUDI and denuder sampler data were used to construct the size-resolved chemical compositions of the layers, which are shown in Figure 5. Unlike other flights, the MOUDI sample taken in the free troposphere contained little Ca and Si, suggesting no significant mineral dust present. All three layers contained significant OC in the submicron size range, while only the layer at 600 m altitude contained significant EC.
 The bottom panels in Figure 5 compare calculated aerosol extinctions using size distributions with those derived from the Sun photometer measurements, as well as showing vertical profiles of temperature, RH, and total particle concentration during the spiral. To facilitate comparison, the Sun photometer-derived aerosol extinction has been averaged to correspond to the DMA measurement interval. Comparison of vertical profiles of aerosol extinction at wavelengths 525 and 1059 nm is presented. As noted earlier, the uncertainty in aerosol extinction derived from AATS-14 measurement is ±0.005 km−1, which is introduced by the AOD smoothing procedure. [Schmid et al., 2000]. The uncertainty, σ, in the predicted aerosol extinction based on the aerosol size distribution can be estimated by,
where σi is the uncertainty in predicted aerosol extinction associated with each individual uncertainty (Table 3). Except for the point near 600 m altitude (near the boundary of the free troposphere and MBL), the discrepancies between the aerosol extinctions lie within the estimated uncertainties. The disagreement near 600 m is likely a result of low vertical resolution of the DMA measurement, this is supported by the fact that the aerosol extinction derived from Sun photometer measurement at 600 m agrees with that predicted from the particle concentration measured by DMA during the 600 m leg (UTC 0405–0425, prior to the profile). Aerosol extinctions are also averaged over the boundary layer and the free troposphere, and the results are presented in Figure 5 as a function of wavelength. In both layers, the aerosol extinction calculated from the size distributions successfully reproduces the wavelength dependence from the AATS-14.
Figure 6 shows the estimated uncertainties in the aerosol extinction calculation associated with each uncertainty category at 525 and 1059 nm. At both wavelengths and in both layers, the estimated uncertainty associated with the accuracy of aerosol size and concentration measurements dominates the overall uncertainty. Uncertainties introduced by assumptions concerning aerosol chemical composition are estimated to be generally within 10%. Estimated uncertainties for radiative closure calculated at 1059 nm are significantly larger than those at 525 nm. This is due to the uncertainties associated with APS measurement of supermicron particles, which contribute proportionately more to the total extinction at longer wavelength. The uncertainty due to the aerosol state, deliquesced versus crystallized, is negligible for this profile, since in both layers the aerosol state can be accurately identified by comparing dry and “ambient” size distributions measured by the DMA system, that is, deliquesced at boundary layer and crystallized in free troposphere. The uncertainty arising from the refractive indices and the method used to compute the particle effective refractive indices is less than 10%, and this will hold also in the other three cases.
 The derivation of aerosol extinction from AATS-14 data is based on the assumption that the path between the Sun and the Sun photometer passes through horizontally homogeneous layers. The scattering coefficients measured by the onboard TSI 3-color nephelometer (model 3563) within each layer are used as an assessment of the layer homogeneity. Figure 7 shows that the variation of scattering coefficients is small within each layer, suggesting that the assumption of horizontally homogeneous layers is supported for this flight, at least for layers sampled by the Twin Otter's horizontal legs. (As noted by Russell et al.  and Schmid et al. , horizontal and temporal variations of any attenuating layers above the aircraft can affect Sun photometer-derived extinction, but that does not appear to have occurred in this example.).
3.2. Research Flight 12, 19 April 2001
 Unlike the flight on 23 April, a pollution layer with high aerosol extinction was observed between the boundary layer and free troposphere during Research Flight 12 along 133°E to 38°N on 19 April 2001 (Figure 8). The Twin Otter flew 1-hour legs at 30 m (boundary layer) and 2000 m (pollution layer). The chemical composition of the pollution layer shows an enhanced contribution from nitrate, OC, and EC in the submicron size range, while the boundary layer is dominated by sulfate. The size distributions are monomodal except in the pollution layer. The size distribution of aerosol in the free tropospheric layer is similar to that of Research Flight 14, while in the boundary layer, the peak concentration size, 160 nm, is significantly larger than that of the previous case. Since neither MOUDI nor denuder filter samples were taken for the free tropospheric leg, the chemical composition from the previous flight on 17 April is used. Aerosol extinction during the spiral from UTC 0237 to UTC 0302 was calculated for the closure study. Agreement between observed and predicted aerosol extinction is not quite as close as for Research Flight 14. In the boundary layer, the aerosol extinction calculated from the measured size distribution is larger than that derived from Sun photometer measurement at an altitude of 50 m, while smaller than that derived from Sun photometer measurement at 550 m. The discrepancies exceed the estimated uncertainties. While it is not possible to pinpoint the exact reason, the discrepancies in the boundary layer could result from the differentiation of AOD data, the vertical resolution of the DMA measurement, and horizontally inhomogeneous layers, as indicated by the variation in aerosol scattering coefficients (Figure 9). The oscillations of AATS-14-derived extinctions with respect to the predicted extinction is caused by spatial variability of the overlying AOD. Counting statistics of the size distribution measurements could account for the somewhat different extinction spectra in the free troposphere. To avoid oversmoothing of the AOD, the aerosol extinction is occasionally allowed to become negative, as seen in Figure 8. The observed and predicted aerosol extinctions are averaged over each layer, and in good agreement at 13 wavelengths measured by the AATS-14.
Figure 10 shows the estimated uncertainties in the aerosol extinction calculation. Similar to Research Flight 14, the uncertainties associated with the accuracies of size and concentration measurements dominate the overall uncertainties in all calculations except in the free troposphere, where uncertainties introduced by the particle density become significant, especially at λ = 1059 nm. This is mainly a result of uncertainty in the mineral dust density, which is needed to interpret APS measurements for size distributions. Uncertainties due to the RH measurement and ram heating are negligible in both the pollution layer and free troposphere, because the ambient RH in each layer was very low, and the uncertainty in RH measurements does not encompass a change in size and calculated aerosol extinction of the crystallized aerosols.
3.3. Research Flight 11, 17 April 2001
 One focus of Research Flight 11 was to perform intercomparisons with R/V Ron Brown and the SeaWiFS satellite (Figure 11). The Twin Otter ferried to 33°N, 128°E, east of Cheju island. The Twin Otter performed one spiral at the time of the SeaWiFS overpass (UTC 0552). A pollution layer was found between the boundary layer and the free troposphere. A backtrajectory calculation indicated that the pollution layer originated from mainland China. Unlike Research Flights 12 and 14, a dust layer was found in the free troposphere exhibiting significant aerosol extinction. MOUDI and denuder samples were taken at altitudes of 40, 1380, and 2810 m, and the resulting data were used to construct aerosol chemical composition in the boundary layer, pollution layer, and free troposphere. Total particle number concentrations in these three layers were about 5000, 2000, and 500 cm−3, respectively. Aerosol number-versus-size distributions in all layers were monomodal to within the resolution of the linear y axis shown in Figure 11. Compared to the boundary layer, the particle sizes at which the peak aerosol concentration were observed in the pollution layer and free troposphere were larger, suggesting more aged particles aloft. Aerosol extinction shows an increased contribution from supermicron particles to the total extinction at increasing altitude. In the pollution layer the extinction mode at diameter 2000 nm results from a surface area-versus-size mode not resolved in the dN/dlogDp plot.
 Radiative closure is addressed for the aircraft spiral at the time of SeaWiFS overpass at UTC 0552. As shown in Figure 11, the size distribution-derived aerosol extinction is significantly smaller than that derived from the near-surface AATS-14 AOD measurement. Scattering coefficients measured during the flight are shown in Figure 12. Among all four cases that we consider here, the in-layer scattering coefficients displayed the most variability for this flight, especially within the pollution layer. The aerosol extinction calculated from the onboard measured size distribution is also supported by aerosol extinction derived from lidar measurement on R/V Ron Brown at the time of spiral (Figure 13), which shows a similar aerosol extinction and profile near the surface. Thus, the larger value of extinction obtained from AATS-14 is probably the result of temporal-horizontal variations of AOD on the photometer-to-Sun path during the Twin Otter ascent from minimum altitude to 300 m.
 For the pollution layer and free troposphere, the discrepancies between observed and calculated aerosol extinctions lie within the calculated uncertainties except for one point in the free troposphere (Figure 11). However, the aerosol extinctions calculated from measured size distributions are systematically smaller than those derived from AATS-14 measurements in the free troposphere. One possible cause is the error in the extrapolation of APS counting efficiency, which could significantly affect the aerosol extinction due to the large mineral dust particles.
 That mineral dust particles are spherical is also physically unlikely. Without knowledge of the shape, dynamic shape factor, and ultra-Stokesian correction factor of the mineral dust, the aerosol extinction of nonspherical dust is estimated using the data of doublet agglomerate particles of Cheng et al. . For doublet agglomerate particles consisting of two spheres, κ = 1.142, and the ultra-Stokesian correction factor is 1 + 0.1998 Rep0.6773. The aerosol extinction calculation of doublet agglomerates is based on the finding of Mishchenko et al.  that the extinction of large nonspherical particles can be accurately predicted by that of spherical particles with the same surface-equivalent diameter. The calculated aerosol extinction is averaged over the mineral dust layer (Figure 14). By assuming a doublet agglomerate shape, the aerosol extinction calculated from the size distribution data is significantly larger than that assuming simply spherical particles. As a result, the calculated aerosol extinction is closer to, although somewhat larger than, that derived from the AATS-14. The increase is 49% at 525 nm and 60% at 1059 nm. The significant increase in aerosol extinction is due to two factors. First, for the same APS response, the volume-equivalent size derived by assuming a doublet agglomerate shape is larger than that derived assuming a spherical shape; second, for the same volume-equivalent size, nonspherical particles have a larger extinction cross section because of larger surface-equivalent diameters. The uncertainties in predicted aerosol extinction using the doublet agglomerate model is also given in Figure 14.
 The uncertainties in derived aerosol extinction (assuming spherical dust shape) are depicted for each layer in Figure 15. The uncertainties associated with the accuracy of the aerosol size and concentration measurements dominate the overall uncertainty except in the mineral dust layer, where the uncertainty from particle density, mainly the mineral dust, becomes comparable.
3.4. Research Flight 9, 14 April 2001
 The fourth of the cases studied focuses on the characterization of a mineral dust layer in free troposphere. The mineral dust layer during Research Flight 9 on 14 April exhibited the largest aerosol extinction among all cases studied. The Twin otter flight track, to 32.5°N, 132.5°E, south of Shikoku Island, the sampling of different layers, and the spiral for the radiative closure study are shown in Figure 16. APS data were not available during the sampling of the boundary layer and the beginning of the spiral; therefore, the analysis focuses on the pollution layer and the mineral dust layer in the free troposphere. Unlike previous cases, the total aerosol number concentration exhibits large variations within each layer. This could be a result of an ongoing mixing process of two different air masses, one of which is a polluted air mass with high particle number concentration. The mixing process is also evidenced by the RH profile during the spiral, which shows substantial vertical variation in the pollution layer. Aerosol extinction distributions are similar to those of Research Flight 11, on 17 April, with a bimodal distribution in the pollution layer and a significant contribution of supermicron particles to the total aerosol extinction in the mineral dust layer.
 Aerosol extinction closure is achieved again in the pollution layer on this flight. Similar to Research Flight 11 on 17 April, aerosol extinctions calculated from the measured size distributions are systematically smaller than those derived from Sun photometer measurements. The discrepancy is probably a combined result of horizontally inhomogeneous aerosol layers during the spiral, which is shown by the large variation of scattering coefficients during level flight in free troposphere (Figure 17), and inaccurate interpretation of APS data. The aerosol extinction is also calculated assuming a doublet agglomerate shape as described in the previous case, and the calculated aerosol extinction in the mineral dust layer is presented in Figure 18. The data suggest that the discrepancy could potentially be explained by the shape of the dust particles. The uncertainties in derived aerosol extinction are similar to those of Research Flight 11.
3.5. Summary of Measured and Calculated Aerosol Extinctions
Figure 19 shows measured and calculated aerosol extinctions over all four cases studied. (One data point near the surface during Research Flight 11 is excluded, where the aerosol extinction derived from AATS-14 measurement was probably corrupted as a result of horizontally inhomogeneous layers during the spiral.) The results show generally good agreement between aerosol extinction calculated from measured aerosol size distribution and chemical composition and those derived from Sun photometer measurements in boundary and pollution layers, where the slopes of the best fit are 0.96 and 1.03 at 525 nm and 0.94 and 1.04 at 1059 nm. For layers in the free troposphere, the slopes are 0.65 and 0.66 for 525 and 1059 nm, respectively. Possible reasons for underestimation of aerosol extinction from the size distribution data have been discussed above. When assuming a doublet agglomerate dust shape, the Predicted/Observed ratio is much closer to 1 at free troposphere: 0.95 ± 0.07 and 1.00 ± 0.07 for 525 and 1059 nm, respectively.
 As part of the ACE-Asia from March to May 2001, aerosol size distributions were measured using DMA and APS systems onboard the Twin Otter aircraft during 19 research flights. During the 19 missions, the atmosphere was often observed to be vertically layered, and a pollution layer with high aerosol extinction was frequently located between the boundary layer and free troposphere. Clear-column aerosol extinctions predicted using in situ aerosol size distribution and chemical composition measurements were compared to those derived from the 14-wavelength NASA AATS-14. The uncertainties associated with predicted aerosol extinction are studied. In the boundary layer, pollution layers, and free troposphere with no significant mineral dust present, extinction closure was achieved within the estimated uncertainties over the full range of wavelengths of AATS-14. The aerosol extinctions predicted based on measured size distributions also reproduce the wavelength dependence derived from AATS-14 data. In free troposphere dust layers, the aerosol extinctions predicted from the measured size distributions were generally smaller than those derived from the AATS-14 data. The uncertainty analysis suggests that the discrepancy is likely a result of the lack of the knowledge of mineral dust shape, as well as variations in aerosol extinction derived from AATS-14 data when viewing through horizontally inhomogeneous layers. For all four research flights studied, the uncertainty in predicted aerosol extinction associated with the aerosol size and concentration measurement accuracy dominates the overall uncertainty except in the dust layer, where the uncertainty introduced by lack of knowledge of dust density and shape becomes comparable. Considering all four cases, the best fit lines yield Predicted/Observed ratios in boundary and pollution layers of 0.97 ± 0.24 and 1.07 ± 0.08 at λ = 525 nm, and 0.96 ± 0.21 and 1.08 ± 0.08 at λ = 1059 nm, respectively. For free tropospheric layers, the ratio is 0.65 ± 0.06 and 0.66 ± 0.05 at 525 and 1059 nm, respectively, when dust particles are modeled as spheres. A nonspherical model of dust (doublet agglomerates) can produce agreement between predicted and observed extinction, via the combined effect of larger APS-derived particle size and larger extinction-to-volume ratios. The Predict/Observed ratios of nonspherical model are 0.95 ± 0.07 and 1.00 ± 0.07 at 525 and 1059 nm in free tropospheric layers.
 Continued development of aerosol instruments, especially those capable of accurately characterizing the size and the shape of large particles, and size-resolved chemical composition will improve the ability to perform radiative closure of atmospheric aerosol.
 We thank Brian Mader, Jose Jimenez, and Roya Bahreini for sharing their data. This work was supported by National Science Foundation grant ATM-0001934, Office of Naval Research grants N00014-96-1-0119, N00014-01-F-0404, and N00014-97-1-0132, National Aeronautics and Space Administration Program codes 622-44-75-10 and 291-01-91-45, and National Oceanographic and Atmospheric Administration order NAO2AANRG0129.