Particle scattering, backscattering, and absorption coefficients: An in situ closure and sensitivity study

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D21, 8122, doi:10.1029/2000jd000234, 2002 Particle scattering, backscattering, and absorption coefficients: An in situ closure and sensitivity study Heike Wex, Christian Neusüß, 1 Manfred Wendisch, Frank Stratmann, Christian Koziar, Andreas Keil, 2 and Alfred Wiedensohler Institute for Tropospheric Research, Leipzig, Germany Martin Ebert Umweltmineralogie, Technische Universität Darmstadt, Darmstadt, Germany Received 7 December 2000; revised 6 September 2001; accepted 8 October 2001; published 11 September 2002. [1] Comparisons between measured and calculated aerosol scattering, backscattering, and absorption coefficients were made based on in situ, ground-based measurements during the Melpitz INTensive (MINT) and Lindenberg Aerosol Characterization Experiment 1998 (LACE 98) field studies. Furthermore, airborne measurements made with the same type of instruments are reviewed and compared with the ground-based measurements. Agreement between measured and calculated values is on the order of ±20% for scattering and backscattering coefficients. A sensitivity analysis showed a large influence on the calculated particle scattering and backscattering coefficients resulting from sizing uncertainties in the measured number size distributions. Measured absorption coefficients were significantly smaller than the corresponding calculated values. The largest uncertainty for the calculated absorption coefficients resulted from the size-dependent fraction of elemental carbon (EC) of the aerosol. A correction for the measured fractions of EC could significantly improve the agreement between measured and calculated absorption coefficients. The overall uncertainty of the calculated values was investigated with a Monte Carlo method by simultaneously and randomly varying the input parameters of the calculations, where the variation of each parameter was bounded by its uncertainty. The measurements were mostly found to be within the range of uncertainties of the calculations, with uncertainties for the calculated scattering and backscattering coefficients of about ±20% and for the absorption coefficients of about ±30%. Thus, to increase the accuracy of calculated scattering, backscattering, and absorption coefficients, it is crucial to further reduce the error in particle number size distribution measurement techniques. In addition, further improvement of the techniques for measuring absorption coefficients and further investigation of the measurement of the fraction of EC of the aerosol is necessary. INDEX TERMS: 0305 Atmospheric Composition and Structure: Aerosols and particles (0345, 4801); 0365 Atmospheric Composition and Structure: Troposphere composition and chemistry; 0394 Atmospheric Composition and Structure: Instruments and techniques; KEYWORDS: closure study, sensitivity study, scattering coefficients, absorption coefficients, nephelometer, PSAP Citation: Wex, H., C. Neusüß, M. Wendisch, F. Stratmann, C. Koziar, A. Keil, A. Wiedensohler, and M. Ebert, Particle scattering, backscattering, and absorption coefficients: An in situ closure and sensitivity study, J. Geophys. Res., 107(D21), 8122, doi:10.1029/2000jd000234, 2002. 1. Introduction [2] Atmospheric aerosol particles influence the Earth s radiation budget by scattering and absorbing incoming solar radiation. Parameters that control the influence of aerosol particles on climate include (a) vertical profiles of the particle single scattering albedo, which are derived from 1 Now at Bruker Saxonia, Analytik GmbH, Leipzig, Germany. 2 Now at Met Office, Farnbourough, England, UK. Copyright 2002 by the American Geophysical Union. 0148-0227/02/2000JD000234 particle absorption and scattering coefficients, (b) vertical profiles of the phase function of the particles or equivalent parameters, such as the asymmetry parameter, which can be derived from the particle size distribution, and (c) vertical profiles of the particle extinction or scattering coefficient. There are, however, uncertainties associated with the measurements of these quantities and with the models which are used to derive these quantities from available measurements, e.g. the Mie-model or radiative transfer calculations. Thus, there are also uncertainties associated with the determination of the influence of atmospheric aerosol particles on climate [Intergovernmental Panel on Climate Change LAC 4-1

LAC 4-2 WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY (IPCC), 1996]. It is therefore a major objective of this paper to evaluate the uncertainty of measured aerosol properties such as particle scattering, backscattering, and absorption coefficients, and to evaluate the applicability of the models used in the calculations. [3] To estimate the uncertainty of different measurement techniques and accompanying numerical conversions, comparisons of measured and derived aerosol properties have been made. Such studies are often referred to as closure studies, and Quinn et al. [1996] reviews some of these closure studies. In former closure studies on optical aerosol properties, measurement-model comparisons were made for scattering and backscattering coefficients for marine aerosol [Quinn et al., 1995; Quinn and Coffman, 1998]. The results presented in these studies were based on data from the Pacific Sulfur/Stratus Investigation 1991 (PSI 91), the Marine Aerosol and Gas Exchange 1992 (MAGE 92), and the first Aerosol Characterization Experiment 1995 (ACE 1). Measured number size distributions averaged over impactor sampling periods were used as input parameters in a Mie-model to calculate scattering and backscattering coefficients, with the aerosol modeled as an external mixture of one component containing sulfate and a second component containing sea salt. The results were compared to average scattering and backscattering coefficients measured with a nephelometer. Agreement within a range of experimental uncertainty of 30 to 40% was found for the comparison of measured and calculated scattering coefficients in the work of Quinn et al. [1995] and for the scattering coefficients of the submicrometer size range in the work of Quinn and Coffman [1998]. Calculations for scattering coefficients in the super-micrometer size range and for backscattering coefficients in general yielded values lower than the measured values, even accounting for measurement uncertainties. [4] In this paper, data gathered in Germany during winter 1997 and summer 1998 are investigated. The measurements are described in section 2. Both ground-based and airborne measurements are investigated. Knowledge on the uncertainty of airborne measurements is needed, because these values can be used to derive vertical profiles of the optical aerosol properties needed for radiative transfer calculations. [5] Whereas the studies described above focused on marine aerosol, in this study we focused on continental aerosol particles. Therefore, an absorbing aerosol component must be included in the calculations, and in addition to scattering and backscattering coefficients, absorption coefficients are considered in the comparison of measured and calculated properties. Also, a comparison between measured and calculated total particle number concentrations is described. [6] A Mie-model was used to calculate the optical aerosol properties, with measured number size distributions and measured size-segregated information of the volume fraction of element carbon (EC) as input parameters. Refractive indices for the Mie calculations are based on a range of values reported in the open literature. To compare the resulting scattering and backscattering coefficients with those measured with a nephelometer, the nonlambertian angular behavior of the nephelometer was accounted for in the Mie calculations, as it has been done by Quinn et al. [1995] and Quinn and Coffman [1998]. Also similar to these studies, only dry particle properties are considered in this paper, and the scattering and backscattering coefficients are examined separately for the submicrometer particle fraction and for the total particle size range up to 10 mm. [7] The time resolution we used for comparing measured and calculated values was larger than in previous studies. Mie calculations were made for each of the measured number size distributions, yielding a 15-minute time resolution for the ground-based data sets and a 20-m vertical resolution for the airborne data sets. Also, both external and internal aerosol mixtures were examined, giving bounding values for the results of the Mie calculations. The calculations and comparisons between the measured and calculated values are described in section 3. [8] In addition to the comparisons, we evaluated the uncertainty of the results of the Mie calculations. This was done by (a) varying the individual input parameters of the Mie-code within their limits of uncertainty and (b) randomly varying all of the input parameters using a Monte Carlo approach. These results are described in section 4. 2. Experimental Design 2.1. Measurement Sites [9] The data used in this work were collected during two field campaigns. The first one took place at the field research station of the Institute for Tropospheric Research during November to December 1997. This station is located about 40 km northeast of Leipzig, Germany, close to the village of Melpitz. This first campaign is referred to as MINT (Melpitz INTensive). The second campaign is called LACE 98 (Lindenberg Aerosol Characterization Experiment 1998) [see Ansmann et al., 2002]. This study took place close to Falkenberg, about 80 km southeast of Berlin, Germany, during July to August 1998. Both measuring sites were situated on flat, open meadows in rural, continental areas. [10] During both campaigns, measurements were taken at the surface. Sample air was collected through PM10 inlets placed 7 m above the ground during MINT and 10 m during LACE 98. For each campaign two separate inlet systems were used: one for measurements of microphysical particle properties and absorption coefficients, and another one for impactor sampling and measurements of scattering and backscattering coefficients (for details, see Neusüß et al., 2002). [11] During LACE 98, similar measurements were taken with an aircraft (Partenavia P68B) [see Wendisch et al., 2002]. The Partenavia flew vertical profiles close to and above Falkenberg at altitudes up to 4 km. Flights preferably took place on days with clear sky. The isokinetic inlet system of the Partenavia is described by Maser et al. [1994]. 2.2. Ground-Based Measurements [12] The measured properties of atmospheric aerosol particles and the instrumentation used for the measurements are summarized in Table 1a. Ground-based measurements included the total particle number concentration, particle number size distributions, scattering, backscattering, and absorption coefficients, and the fraction of EC of the aerosol, derived from Berner impactor samples. The following sections specify the conditions of the ground-based measurements with respect to relative humidity, sampling

WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY LAC 4-3 Table 1a. Properties of Atmospheric Aerosol Particles and the Instrumentation Used for Ground-Based and Airborne Measurements Measured Property Specification Instrumentation total number concentration d p > 10 nm CPC (TSI 3010) a,b d p > 3 nm UCPC (TSI 3025) c,b number size distribution on ground 3 nm < d p < 800 nm TDMPS d 1 mm e < d p <10mm e APS (TSI 3310 and TSI 3320 f ) g,b airborne number size distribution 0.1 mm <d p <10mm PCASP h scattering and back-scattering coefficients l = 450, 550, and 700 nm integrating nephelo-meter (TSI 3563) b absorption coefficients l = 565 nm PSAP i,f fraction of EC thermodesorption method j 5-stage Berner impactor k a Condensation particle counter. b Manufactured by TSI, Inc., St. Paul, MN, USA. c Ultrafine condensation particle counter. d Twin differential mobility particle sizer, described by Birmili et al. [1999]. e Aerodynamic diameter. f Only used during LACE 98. g Aerodynamic particle sizer. h Passive cavity aerosol spectrometer probe, manufactured by Particle Measuring Systems, Inc., Boulder, CO, USA. i Particle soot/absorption photometer, manufactured by Radiance Research, Seattle, WA, USA. j Described by Neusüß et al. [2000]. k Described by Berner et al. [1979]. frequency, data processing, and corrections that had to be made to the measured, raw data. 2.2.1. Measurements at Low Relative Humidity [13] Due to temperature differences between the atmosphere and inside the measurement containers, the aerosol was dried within the sampling line before reaching the instruments. To ensure that the instruments placed inside the measurement containers measured the dry aerosol, dry sheath air was used for TDMPS (Twin Differential Mobility Particle Sizer) and APS (Aerodynamic Particle Sizer) measurements, keeping the relative humidity for these measurements below 5%. A diffusion dryer was also installed upstream of the nephelometer to ensure proper drying of the air prior to nephelometer measurements. The aerosol was dried in one of two diffusion dryer tubes while the other tube was regenerated by flushing with warm dry air. The diffusion dryer tubes were switched automatically once the relative humidity of the aerosol downstream of the dryers exceeded 20%. 2.2.2. Measurements at 60% Relative Humidity [14] For sampling with Berner impactors (aerodynamic cut-off diameters of 50 nm, 140 nm, 420 nm, 1.2 mm, 3.5 mm and 10 mm), which were located outside the measurement containers, to minimize particle bounce, as recommended by Stein et al. [1994], the aerosol stream was kept at a relative humidity of 60% by heating or cooling the inlet tubes just upstream of the impactors. The aerosol mass from the impactor samples was determined gravimetrically at 60% relative humidity. Analysis of the chemical composition of the impactor samples was done [see Neusüß et al., 2002]. Part of the analysis was a thermodesorption method as described by Neusüß et al. [2000]. This yielded the mass fraction of the nonvolatile carbon (EC) contained in the aerosol for the five size ranges of the aerosol and at 60% relative humidity ( f(ec) mass,60% ). The reliability of the thermodesorption method, which was used to derive f (EC) mass,60%, recently was examined in an intercomparison study [Schmid et al., 2001]. Results from this intercomparison study will be described and included in the discussion in section 3.1.3. 2.2.3. Sampling Frequency [15] The sampling frequency for the measurements of the total number concentration (N meas ) and the scattering, backscattering, and absorption coefficients (s sc,neph, s bsc,neph, and s abs,psap, respectively) was one minute, whereas a complete number size distribution was measured every 15 min. Both N meas and s abs,psap were averaged over 15 min sampling intervals. Measurements of s sc,neph and s bsc,neph were made on particles with aerodynamic diameters up to 10 mm and 1 mm, respectively. This was achieved with a three-stage impactor (aerodynamic cut-off of 1 mm) with greased substrate plates located in one of two paths leading from the diffusion dryers to the nephelometer. The aerosol flow was switched every 15 min between these two aerosol paths. For the 15 minute averages of s sc,neph and s bsc,neph, the data was discarded for the first 5 min of sampling after switching. Sampling times in the Berner impactors varied form 8 to 24 h. To achieve higher time resolution, the sampling time was reduced during times of rapid changes in weather conditions or when aircraft measurements were simultaneously made. 2.2.4. Data Processing 2.2.4.1. CPC, UCPC, and TDMPS Particle Number Concentration and Number Size Distribution [16] The sampling efficiencies of all CPCs (Condensation Particle Counter) and UCPCs (Ultrafine Condensation Par- Table 1b. Average f(ec) V,dry for the Different Impactor Size Ranges, as Derived From the Measured f (EC) mass,60% a Stage 1 (50 140 nm) Stage 2 (140 420 nm) Stage 3 (420 nm 1.2 mm) Stage 4 (1.2 3.5 mm) Stage 5 (3.5 10 mm) MINT 40% 33% 24% 16% 13% LACE 98 23% 16% 11% 9% 9% a The size ranges of the impactor stages are given in terms of aerodynamic diameters.

LAC 4-4 WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY ticle Counter) used during MINT and LACE 98 were measured prior to the campaigns, by using a procedure described by Wiedensohler et al. [1997]. Inversion of the data measured with the TDMPS was done with an algorithm described by Stratmann and Wiedensohler [1996], which included measured transfer functions of the DMAs (Differential Mobility Analyzer) [Birmili et al., 1997]. Data measured with the APS were corrected for phantom counts following the procedure of Heintzenberg et al. [1998]. Aerodynamic diameters measured with the APS were converted to Stokes-equivalent diameters by assuming a density of the dry aerosol of 1.7 g/cm 3 (roughly corresponding to ammonium sulfate). Number size distributions measured simultaneously with the TDMPS and the APS were combined to yield a composite number size distribution as a function of Stokes-equivalent diameters. 2.2.4.2. Scattering and Backscattering Coefficients [17] For the measurement of scattering and backscattering coefficients with a nephelometer (s sc,neph and s bsc,neph ) the instrument was calibrated prior to each campaign by using CO 2 and particle-free air, as suggested by Anderson et al. [1996]. To verify the stability of the nephelometer, the calibration was repeated halfway during the campaigns. In addition, a zero baseline measurement was done once a day. The measured clean air constants differed less than approximately ±3%. [18] s sc,neph and s bsc,neph measured with the nephelometer are values integrated over angles from 7 to 170 and from 90 to 170, respectively. Also, the nephelometer light source shows a nonideal angular response. The nephelometer angular response was measured in a calibration experiment described by Anderson et al. [1996]. Instead of correcting the data measured with the nephelometer, the measured angular response was accounted for in the Mie calculations with which the scattering and backscattering coefficients were calculated from measured number size distributions. This yields calculated values simulating the ones measured with the nephelometer. 2.2.4.3. Absorption Coefficients [19] A PSAP (Particle Soot/Absorption Photometer) was used to measure absorption coefficients (s abs,psap ). These s abs,psap were corrected according to Bond et al. [1999]. The aerosol flow through the instrument was measured several times during the campaign, yielding a flow rate of 1.1 l/min instead of 1 l/min as indicated by the PSAP. The measured diameter of the sampling spot on several filters was 5.2 mm, which differs from 5.1 mm used in the automated data processing for the PSAP. Also, corrections due to the response of the PSAP to aerosol scattering and a correction of the internal calibration of the PSAP were used. Correction factors and their uncertainty, as given in the work of Bond et al. [1999], are (with F scat being the factor to correct for particle scattering and with F corr correcting for the internal calibration): F scat ¼ 0:02 0:02; F corr ¼ 1:2 0:2 [20] The overall correction applied to the measured s abs, PSAP yieldscorrectedabsorptioncoefficientss abs,psapcorr : s abs;psapcorr ¼ 0:9464 * s abs;psap F scat * s sc;neph;550nm F corr ð1þ ð2þ (with s sc,neph,550nm representing the scattering coefficients measured with the nephelometer at a wavelength of 550 nm). 2.2.4.4. Berner Impactor Fraction of EC [21] The mass fractions of EC determined from the Berner impactor samples at 60% relative humidity, f(ec) mass,60%, were converted to the volume related values for the dry aerosol, f(ec) V,dry, which were needed to derive refractive indices for the Mie calculations. For the conversion, an average particle growth factor of 1.13 for the particle growth between dry conditions and relative humidities of 60% was used. This value was taken from measurements of particle growth factors made during MINT and LACE 98 as reported by Neusüß et al. [2002]. For this value and a density of the dry aerosol of 1.7 g/cm 3, at 60% relative humidity the volume fraction of water in the aerosol is 30% and the mass fraction is 20%. This yields a conversion factor of 1.25 between f (EC) mass,60% and the mass fraction of EC of the dry aerosol. The density of EC was taken to be 1.5 g/cm 3. This value is the average of values given by Seinfeld [1986] for graphitic carbon (soot, 2 g/cm 3 ) and for loosely packed soot clusters (1 g/cm 3 )[Ouimette and Flagan, 1982]. With this follows a conversion factor of about 1.12 between the mass fraction and the volume fraction of the dry aerosol, leading to an overall conversion factor of 1.4 between f (EC) mass,60% and f(ec) V,dry : f ðecþ V ;dry ¼ 1:4 f ðecþ mass;60% ð3þ The average f(ec) V,dry for the different size ranges of the Berner impactor for MINT and LACE 98 are given in Table 1b. [22] From these considerations, the aerosol density at 60% relative humidity is 1.5 g/cm 3. This value was used to convert the aerodynamic diameters of the Berner impactor cut-offs to Stokes-equivalent diameters. These Stokesequivalent diameters were used to assign f (EC) V,dry, which was determined for the five different impactor stages, to the corresponding size ranges in the particle number size distributions. 2.3. Airborne Measurements [23] From the data taken on board the Partenavia during LACE 98 [see Wendisch et al., 2002] we used particle number size distributions measured with a PCASP (Passive Cavity Aerosol Spectrometer Probe) (described in Table 1a) and scattering and backscattering coefficients obtained with a nephelometer similar to the one used for the groundbased measurements in this study. Calibration of the PCASP was done using atmospheric aerosol. Diameters were compared to those measured with a DMA, whereas calibration of the particle number concentration was done by using a CPC for comparison. The calibration and data analysis of the PCASP are discussed in detail by Keil et al. [2001]. The nephelometer was used to measure s sc,neph and s bsc,neph at three different wavelengths. The Mie calculations were made such that the calculated values simulated s sc,neph and s bsc,neph, by accounting for the nephelometer angular nonidealities. The calibration of the nephelometer used for the airborne measurements was done similar to the calibration of the nephelometer used for the ground-based measurements.

WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY LAC 4-5 Table 2. Properties Examined in the Closure Studies, Variables Used for the Measured and Calculated Parameters, and Parameters Needed for the Calculations Property total number concentration scattering coefficients backscattering coefficients absorption coefficients Measured Parameter Calculated Parameter Input Parameters for the Calculations N meas N calc number concentrations obtained in the measurement of the number size distributions (N TDMPS and N APS ) s sc,neph s sc,mie N TDMPS ; N APS ; diameters obtained from the measurement of the number size distribution s bsc,neph s bsc,mie (d TDMPS and d APS ); refractive indices of the non-absorbing component (n non ) and of the s abs,psapcorr s abs,mie absorbing component (real part: n EC, imaginary part: I EC ); measured fraction of EC contained in the aerosol ( f (EC) V, dry ); cut-off diameters of the different impactor stages [24] To prevent cloud droplets from entering the sampling system, an impactor upstream of the instruments with a cutoffdiameterof5mm was used. Relative humidity and temperature were controlled just before the scattering chamber of the PCASP. These data showed that although the aerosol was not dried under controlled conditions, the relative humidity was less than 30% due to heating in the system. Data were taken with a time resolution of one second and were averaged to yield vertical profiles with a height resolution of 20 m for the particle number size distribution and for s sc,neph and s bsc,neph. 3. Comparison of Measured and Calculated Properties 3.1. The Ground-Based Data Set [25] For the ground-based data set, comparisons between measured and calculated properties were made for the total particle number concentration and for the scattering, backscattering, and absorption coefficients (see Table 2). 3.1.1. Particle Number Concentration [26] The measured number size distributions, composed of those measured with TDMPS and APS, were integrated to yield the total number concentration of the particles, N calc. The integrations were done separately for d p >10nm and for d p > 3 nm, corresponding to the measurements with the CPC and with the UCPC, respectively. For the MINT and LACE 98 data sets, 1768 and 1956 data-points, respectively, were evaluated. As a quantitative measure for the agreement between N calc and N meas, we defined the relative difference, (N), as follows: ðnþ ¼ N calc N meas N meas [27] Table 3 shows the average (N) of the MINT and LACE 98 time series for both d p > 10 nm and d p > 3 nm. Figure 1 shows scatterplots of N meas versus N calc, including the linear regression lines fitted to the data, the slopes of these lines, b, and the corresponding correlation coefficients, r. [28] Results for both campaigns yield systematically lower values for N calc (on average 20%), as can be seen by the negative (N) and by values for b being less than one (between 0.81 and 0.91). A loss of particles in the ð4þ TDMPS due to diffusion and deposition was found to be too small to account for this discrepancy. On the other hand, there is a possibility for an underestimation of the number concentration in the number size distributions for small particles with sizes of about d p < 50 nm, resulting from the uncertainty of the bipolar charge distribution in this size range [Wiedensohler, 1989]. Still, the source for the discrepancy between N meas and N calc is not clear. However, the standard deviations of the average (N) of 11% for MINT and 8% for LACE 98, and values for r between 0.88 and 0.98 indicate stable performance of the instruments, and thus good reproducibility of the data. 3.1.2. Ground-Based Scattering and Backscattering Coefficients [29] In the following, s sc,neph, s bsc,neph, and s abs,psapcorr are compared to the corresponding calculated values of these parameters. The values were calculated based on the measured number size distributions, composed of TDMPS and APS measurements. A Mie-code [Bohren and Huffman, 1983] was used for the calculations, yielding scattering, backscattering, and absorption coefficients s sc,mie, s bsc,mie, and s abs,mie. Calculations for s sc,mie and s bsc,mie were made for 450, 550, and 700 nm. For s abs,mie a wavelength of 565 nm was used. The upper limits of the particle diameter in the Mie calculations were set corresponding to the conditions of the preimpactor upstream in the nephelometer, i.e. to either 1 mm or10mm. These upper limits, given in terms of aerodynamic diameters, were converted to Stokesequivalent diameters for the dry aerosol, assuming a particle density of 1.7 g/cm 3 for the diameter conversion calculation. Refractive indices needed as input parameters for the Mie-model were calculated from f(ec) V,dry, the average values of which are given in Table 1b. The refractive indices were derived and used separately for the five different size ranges of the impactor measurements. The time resolution for the determination of the refractive indices was determined from the time resolution Table 3. Average Relative Differences (N) Between N meas and N calc and the Corresponding Standard Deviations MINT LACE 98 >10nm 18% ± 11% 21% ± 7% >3nm 30% ± 11% 17% ± 9%

LAC 4-6 WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY [31] For internal mixtures, the aerosol was assumed to be a homogeneous internal mixture of EC and nonabsorbing components. The refractive index ~ m was derived as a volume-mixture between the two components [e.g., Horvath, 1998]: ~m ¼ f ðecþ V;dry ~m EC þ 1 f ðec Þ V;dry ~m non ð5þ Figure 1. Comparison of N meas and N calc. The straight lines represent linear regression fits to the data, where b is the slope and r is the correlation coefficient of the fits. of the impactor measurements. Two extremes for the state of mixture of the particles were used to derive the refractive indices: external and internal mixtures. [30] For external mixtures, the particle number concentration measured in each size bin of the number size distribution was divided in a fraction of EC corresponding to f(ec) V,dry, representing the absorbing fraction of the aerosol, and in a nonabsorbing component. The refractive indices assigned to these two components were chosen as an average over a range of values given in the open literature (see Table 4). The refractive index used for the nonabsorbing component was ~ m non = 1.53 10 7 i. The real part of the EC component was set to 1.75 and the imaginary part was set to 0.555i, 0.54i, and 0.53i at wavelengths of 450, 550, and 700 nm, respectively, following the wavelength dependence given by d Almeida et al. [1991]. At the wavelength of 565 nm the same values were used than for 550 nm. [32] A comparison of ~m derived here and the refractive indices derived from an analysis of individual particles for six days of the LACE 98 campaign by Ebert et al. [2002] is shown in Figure 2. The relative difference between the refractive indices derived from various databases corresponding to different approaches is about 1% for the real part of the refractive index. For the imaginary part, the relative differences range between 1% and 20% for 4 of the 6 days. For 1 August and 6 August, however, the relative differences are 97% and 44%, respectively. For these two cases, however we achieved a difference of only about 20% between the values calculated in this work and data derived from photometer measurements on dried filter samples as described by Bundke et al. [2002], the values of which are also given in the work of Ebert et al. [2002]. Altogether the comparison of results from different studies made for the LACE 98 campaign justifies the use of our calculated refractive indices. [33] Although internal and external mixtures of aerosols are treated separately, atmospherical aerosol particles are probably a partial mixture of an internally and an externally mixed aerosol. Thus, the Mie calculations for the external and the internal mixture give the bounding values for the probable true values. [34] For the MINT data set, 720 data-points were evaluated for d p <1mm and 724 data-points for d p <10mm. LACE 98 contributed 508 and 510 data-points, respectively. Figure 3 shows the time series of s sc,neph and s sc,mie for the 550 nm wavelength and d p <10mm for the LACE 98 data set. s sc,mie and s bsc,mie calculated for the external mixture are generally larger than for the internal mixture. On average, s sc,mie calculated for the external mixture is a Table 4. Refractive Indices in the Open Literature for a Wavelength of About 550 nm a,b Source Elemental Carbon/Soot Organic Carbon Ammonium Sulfate Residue International Critical Tables [1928] 1.52 to 1.54 Dalzell and Sarofim [1969] 1.56 0.46i c 1.57 0.53i d D Alessio et al. [1975] 1.57 0.56i Lee and Tien [1981] 1.90 0.55i Ouimette and Flagan [1982] 1.56 0.47i e Hasan and Dzubay [1983] 1.97 0.65i 1.5 ± 0.1 1.52 1.59 0.089i (intern) 1.58 ± 0.5 (extern) Sloane [1984] 1.90 0.55i 1.55 1.53 1.53 0.005i Seinfeld [1986, 1998] 1.96 0.66i f Covert et al. [1990] 1.95 0.66i D Almeida et al. [1991] 1.75 0.44i 1.43 10 8 i Tang and Munkelwitz [1994] 1.53 1.544 a Values given here cover the same range as those given in Horvarth [1993]. b Further information on sources for refractive indices: Smyth and Shaddix [1996]. c Soot collected from acetylene flame. d Soot collected from propane flame. e Loosely packed soot clusters. f Graphitic carbon.

WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY LAC 4-7 factor of 1.16 larger than values calculated for the internal mixture. Relative differences between calculated and measured values for the scattering (sc), backscattering (bsc), and the absorption (abs) are defined similar to equation 4 as: ðscþ ¼ s sc;mie s sc;neph s sc;neph ð6þ Figure 2. Comparison of refractive indices calculated for internally mixed aerosol with refractive indices calculated from single-particle analysis by Ebert et al. [2002]. [35] Table 5 and Table 6 list the average relative differences between calculated and measured values for all three wavelengths for d p <10mm and for d p <1mm, respectively. [36] Scatterplots for s sc,neph versus s sc,mie and for s bsc,neph versus s bsc,mie at a wavelength of 550 nm and d p <10mm for the LACE 98 data set are shown in Figure 4, including the linear regression lines, b, and r. Values for b averaged over the three wavelengths at which measurements and Mie calculations were performed are given in Table 7. In general, for scattering and backscattering coefficients, it is b < 1 for an internal mixture and b > 1 for an external mixture. Thus, measured values generally are lower than the corresponding calculated values for external mixtures and larger than the corresponding calculated values for internal mixtures. For d p <10mm, 43% of all the s sc,neph and s bsc,neph for MINT and 61% for LACE 98 are enclosed by the s sc,mie and s bsc,mie obtained from the Mie calculations for the internal and external mixtures, even without accounting for any measurement and calculation uncertainties. For d p <1mm, the respective percentages are 45% for MINT and 39% for LACE 98. s sc,neph and s bsc,neph measured at 450 nm wavelength are close to the s sc,mie and s bsc,mie for the external mixture. With increasing wavelength, s sc,neph and s bsc,neph are closer to s sc,mie and s bsc,mie for the internal mixture. This can be seen by the average (sc) and (bsc) in Tables 5 and 6. This result can be explained by a larger fraction of the aerosol being externally mixed for small particles, which are also less aged, and an Figure 3. LACE 98 time series of s sc,neph and s sc,mie for d p <10mm at a wavelength of 550 nm. Measurements are represented by squares. The results of the Mie calculations are bounded by the upper and lower limits of the grey area, where the upper and lower limits correspond to calculations for external and internal mixtures, respectively. Breaks along the x-axis represent times during which no impactor measurements were taken.

LAC 4-8 WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY Table 5. Average (sc), (bsc), and (abs) for d p <10mm and the Corresponding Standard Deviations (sc), % (bsc), % (abs), % l, nm Extern Intern Extern Intern Extern Intern MINT 450 9 ±13 35 ± 13 2 ±14 45 ± 14 550 1 ± 15 24 ± 15 6 ± 15 33 ± 16 700 50 ± 27 14 ± 28 29 ± 21 18 ± 21 LACE 98 450 8 ± 9 9 ±8 5±11 20 ± 10 550 16 ± 10 0 ± 10 11 ± 9 11 ± 8 565 33 ± 44 171 ± 86 700 24±13 9±13 9±12 9 ±11 increasing fraction of the aerosol being internally mixed for large particles. [37] For the scattering coefficient for d p <1mm, especially for the LACE 98 data, calculated values exceed the measured values, especially toward larger wavelengths. This can be seen in Table 6 from the average (sc), which reaches large positive values even for the internal mixture. Also, b is larger than one for both internal and external mixtures for d p <1mm for LACE 98 (see Table 7). This behavior can be explained by a loss of particles of sizes slightly smaller than 1 mm in the preimpactor of the nephelometer. The preimpactor was used with an incorrect aerosol flow rate during LACE 98. Particles near 1 mm in diameter have a stronger effect on the scattering for the longer wavelengths used in the Mie calculations. They also have a larger effect on scattering than on backscattering, because the proportion of forward scattered light increases with increasing particle size. Thus, a lack of measured particles in this size range in the nephelometer can cause the kind of deviations between measured and calculated values observed here. [38] In general, both campaigns show comparable results. Average standard deviations of (sc) and (bsc) for d p < 10 mm are ±18% for MINT and ±10% for LACE 98 (Tables 5 and 6). The average r of the linear regression lines are 0.92 and 0.98 for MINT and LACE 98, respectively. This indicates stable performance of the instrumentation and an increase in the reproducibility of the data from MINT to LACE 98. The increased reproducibility of the data can be explained by the different TDMPS systems used during MINT and LACE 98. During MINT the sample- and sheath-airflows of the TDMPS were checked manually once a day, whereas during LACE 98 the TDMPS flows were adjusted automatically after each scan. Still, good overall reproducibility as determined by stable performance of the instruments was achieved for both campaigns, especially for d p <10mm, for which measurements were not influenced by the preimpactor of the nephelometer. 3.1.3. Ground-Based Absorption Coefficient [39] Figure 5 shows the LACE 98 time series of s abs,psapcorr and s abs,mie. Values for the average (abs) are given in Table 5. Scatterplots for s abs,psapcorr versus s abs,mie and the corresponding b and r are shown in Figure 6. s abs,mie calculated for the internal mixture are generally larger than for the external mixture. The range between s abs,mie for the external and the internal mixtures is larger than for the scattering coefficients, with an average factor between s abs,mie for the external and internal mixtures of 0.49. The fraction of all s abs,psapcorr enclosed by the results of the Mie calculations for the external and internal mixtures is 19%, with an average (abs) of 33% for the external and 171% for the internal mixtures, and with b = 1.09 for the external and b = 1.91 for the internal mixtures. These deviations are larger than the ones observed for scattering and backscattering coefficients, and the s abs,mie are generally larger than the s abs,psapcorr for both external and internal mixtures. On the one hand this could originate in a systematic underestimation of the absorption coefficient from the PSAP. On the other hand, as shown in section 4.2, s abs,mie is sensitive to f(ec) V,dry and also to the refractive indices, which are derived based on f(ec) V,dry, although these parameters have hardly any effect on s sc,mie and s bsc,mie. Indeed, the parameter f(ec) mass,60%, and therewith also f(ec) V,dry, as used this study appear overestimated. This assumption is based on a recent intercomparison study Table 6. Average (sc) and (bsc) for d p <1mm and the Corresponding Standard Deviations (sc), % (bsc), % l, nm Extern Intern Extern Intern MINT 450 16 ± 19 14 ± 17 19 ± 20 27 ± 17 550 31 ± 23 5 ± 21 29 ± 22 11 ± 19 700 114 ± 43 71 ± 41 64 ± 32 14 ± 27 LACE 98 450 21 ± 12 5 ± 10 15 ± 12 8 ±10 550 34 ± 14 21 ± 12 24 ± 11 5 ± 9 700 50 ± 20 39 ± 18 23 ± 16 10 ± 14

WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY LAC 4-9 Figure 4. Comparison of s sc,neph with s sc,mie and of s bsc,neph with s bsc,mie for d p <10mm ata wavelength of 550 nm for the LACE 98 data set. Squares and triangles represent data for the external and internal mixtures, respectively. The straight lines represent linear regression fits to the data, where b is the slope and r is the correlation coefficient of the fits. [Schmid et al., 2001]. In a round-robin test, three different filter samples were analyzed at 16 different laboratories. Values of the kind of method used to determine f (EC) mass, 60% for this work agreed with the average of the values of the 16 laboratories for one sample, whereas for the other two samples it exceeded the average value significantly. On average, the kind of method used in this work yielded values which were 33% larger than the average values of all 16 laboratories. Considering an overestimation of f(ec) mass,60% of 33% in the Mie calculations for this work, values calculated for s abs,mie decreased about 30% compared to those derived for the uncorrected f (EC) mass,60%, whereas s sc,mie and s bsc,mie changed by less than 1% for the calculations for the external mixture and by less than 5% for the internal mixture. (abs) decreases to 14% ±31% for the external and to 94% ± 69% for the internal mixture, with corresponding values for b of 0.98 and 1.59, respectively, and with r of about 0.83. The percentage of all s abs,psapcorr enclosed by the results of the Mie calculation for the external and internal mixtures increases to 68%. However, although the round-robin test indicates an overestimation of f (EC) mass,60%, the degree of overestimation can not be derived based on only three, highly variable data-points from the round-robin test. Also, no commonly accepted method exist for EC determination in atmospheric particles. The comparisons by Schmid et al. [2001] are based on the average values of the participating laboratories. Thus, a systematic correction of f (EC) mass,60% in this work was rejected, although the source for the discrepancy between s abs,psapcorr and s abs,mie is assumed to originate in an overestimation of the measured values of f (EC) mass,60%. [40] High standard deviations of the average (abs) of 44% for the external and 86% for the internal mixtures were observed, together with low values of r of 0.76 for the external and 0.8 for the internal mixture. This indicates less stability in the PSAP data, compared to other data Table 7. Average Slopes of the Linear Regression Fits for the Comparison of s sc,neph With s sc,mie and of s bsc,neph With s bsc,mie for External and Internal Mixtures, and for the Different Size Ranges at Which Measurements and Calculations Were Made MINT LACE 98 Extern Intern Extern Intern d p <10mm s sc 1.05 0.67 1.10 0.98 s bsc 1.07 0.51 1.08 0.88 d p <1mm s sc 1.40 1.00 1.29 1.17 s bsc 1.29 0.75 1.22 1.03

LAC 4-10 WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY Figure 5. The LACE 98 time series of s abs,psapcorr and s abs,mie at a wavelength of 565 nm. Measurements are represented by squares, with error bars indicating the uncertainty of the measured values due to corrections according to Bond et al. [1999]. The results of the Mie calculations are bounded by the upper and lower limits of the grey area, where the upper and lower limits correspond to calculations for internal and external mixtures, respectively. used in this work. This possibly is induced by the response of the PSAP to the filters used for the measurements and to the particle load on them, because the correction for the scattering on the filters was done according to Bond et al. [1999] and considered the instantaneous scattering of the atmospherical aerosol, but disregarded the changing load on the filters. Also, the relative humidity of the sampling air was not controlled during the measurements with the PSAP, causing fluctuations in the instrument performance. There is therefore a need for further investigation of the PSAP performance, to increase the stability of the measurement. Controlling the relative humidity of the measured aerosol and changing the filters used for the PSAP measurement from a filter transmission of 0.7 [Bond et al., 1999] is strongly recommended. 3.2. Airborne Data Set [41] Similar to the ground-based data, a comparison of s sc,neph and s bsc,neph with s sc,mie and s bsc,mie was made for the LACE 98 airborne data set for flights on 1, 10, and 11 August. To avoid data analysis problems associated with inlet problems, data were taken from smooth downward flight legs. Calculations were made with the modified Miecode described in section 3.1.2, using particle number size distributions measured with the PCASP. An analysis of individual aerosol particles was available for the times the flights were made [Ebert et al., 2002]. The analysis indicates a majority of the aerosol particles consisted of internally mixed particles of carbon and sulfate. The Mie calculations for the airborne data set were made for the internal mixture of the particles only, and were made for the three wavelengths at which the nephelometer makes measurements. The refractive indices were taken from the ground-based measurements. For this, the refractive indices calculated with equation 5 for the three impactor stages from 140 nm to 3.5 mm were averaged. For 1, 10, and 11 August, at l = 550 nm the averaged values used for the Mie calculations with the airborne data were 1.542 0.03i, 1.545 0.038i, and 1.552 0.054i, respectively. [42] Figure 7 shows the vertical profiles of s sc,neph and s sc,mie and the corresponding (sc) and (bsc) at a wavelength of 550 nm. The average values of (sc) and (bsc) for all three wavelengths are listed in Table 8. Figure 8 Figure 6. Comparison of s abs,psapcorr with s abs,mie for the LACE 98 data set. Squares and triangles represent data for the external and internal mixtures, respectively. The straight lines represent linear regression fits to the data, where b is the slope and r is the correlation coefficient of the fits.

WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY LAC 4-11 Figure 7. Vertical profiles of the LACE 98 airborne data set for s sc,neph and s sc,mie at a wavelength of 550 nm for three different flights on 1, 10, and 11 August. Also shown are the vertical profiles for (sc) and (bsc).

LAC 4-12 WEX ET AL.: IN SITU CLOSURE AND SENSITIVITY STUDY Table 8. Average (sc) and (bsc) for the Airborne Data Set and the Corresponding Standard Deviations a Date of Flight (sc) 450 nm (bsc) 450 nm (sc) 550 nm (bsc) 550 nm (sc) 700 nm (bsc) 700 nm 1 August 10 ± 11 12±19 7±16 9±17 9±17 1±55 10 August 49 ± 26 78 ± 213 20 ± 74 39 ± 126 48 ± 35 37 ± 138 11 August 16 ± 16 30 ± 54 11 ± 24 23 ± 20 5 ±25 8 ±25 a Values are given in %. shows scatterplots for s sc,neph versus s sc,mie and for s bsc,neph versus s bsc,mie, including the linear regression lines fitted to the data, b, and r. [43] The average (sc) and (bsc) for the airborne data set are similar to the values for the ground-based data set for the data gathered during the flights on 1 and 11 August. Values for b, averaged over the three different flights, range from 0.91 to 1.14 for the scattering coefficients, increasing with increasing wavelength, and range from 0.8 to 0.98 for the backscattering coefficients, indicating a good correlation between measured and calculated data. [44] On 10 August, the average (sc) and (bsc) are around 40%. Standard deviations for 10 August are about ±45% for the scattering and about ±160% for the backscattering coefficients. Generally, 10 August had low aerosol concentrations, besides a layer with high aerosol concentrations at a height of about 3 km. Below the 3-km layer, s sc,neph measured with the nephelometer at 550 nm varied from <10 5 1/m down to 10 6 1/m, and the number concentration of aerosol particles was about 500 particles/ cm 3. The large discrepancies between measured and calculated values on 10 August can be partly explained by poor counting statistics in the instrumentation, especially for measurements of the number size distribution, and also by possible inlet losses, which have a larger influence in case of low aerosol concentrations. Also, as can be seen in Figure 8, especially for the 550 nm wavelengths, the strongest deviations from the linear regression lines that compare measured and calculated values occur on 10 August. These deviating values occurred when the aircraft entered a layer with high aerosol concentrations, and are possibly due to time differences in the response of the different instruments to the quickly changing aerosol conditions. Nevertheless, a clear linear relation between measured and calculated data is observed, indicated by r, which is about 0.98 for the scattering coefficient and about 0.94 for the backscattering coefficient (see Figure 8). [45] Altogether the comparisons between measured and calculated values for the airborne data set yield about the same results as those for the ground-based data set, although it is much more difficult to achieve stable instrument operation in an aircraft than on the ground. This information therefore confirms that the instruments were stable during the airborne measurements, and this knowledge is useful for determining columnar aerosol properties based on in situ measurements. 4. Sensitivity Study [46] To quantify the influence of the uncertainties of the different input parameters of the Mie-model on s sc,mie, s bsc,mie, and s abs,mie, a sensitivity study was done for the LACE 98 data set. The sensitivity of s sc,mie, s bsc,mie, and s abs,mie toward the different input parameters was determined by repeating the Mie calculations, varying each input parameter individually (section 4.2). The overall uncertainty of s sc,mie, s bsc,mie, and s abs,mie was determined with a Monte Carlo approach, where Mie calculations were made repeatedly, each time varying all input parameters randomly, and the magnitude of the variation of each parameter was bounded by their uncertainty (section 4.3). 4.1. Uncertainties [47] The parameters tested in the sensitivity study are listed in Table 9. Deviations for these parameters were considered to be normally distributed around the original value with standard deviation s, which are also listed in Table 9. A range of ±3s around the original value contains 99% of the values possible for the parameter. The uncertainties of the different input parameters as given in Table 9 represent a conservative estimate of the maximum uncertainties for these parameters, ensuring that agreement between measured and calculated values is not based on excessively large uncertainties. [48] The uncertainty of the number concentration and of the particle sizing are considered separately for the TDMPS and APS measurements. This includes uncertainties in the CPC, UCPC, APS, and DMA measurements as well as uncertainties due to the TDMPS-inversion program and the conversion from aerodynamic to Stokes-equivalent diameter. [49] Furthermore, f (EC) V,dry derived from chemical analysis and the impactor cut-off diameters used for the partitioning of the number size distributions contained uncertainty as well. This involves uncertainties in sampling, analyzing and in the conversion from values measured at 60% relative humidity to dry conditions for these two parameters. [50] The uncertainties of the refractive indices were chosen such that the range covered by the uncertainties agreed with the range of the values for the refractive indices listed in Table 4. 4.2. Single Parameter Variation [51] Mie calculations were done for the entire groundbased LACE 98 time series, in which each of the input parameters was varied separately to (original value + s), whereas the other parameters remained fixed. Thus, the influence of the parameter variation on the result of the Mie calculation was determined independently. For a wavelength of 550 nm, the average relative differences between the results of the Mie calculations with the varied and with the original parameters are given in Table 10 for external and internal mixtures. Varying the input parameters to (original value - s) gave about the same shifts in the results but in the opposite direction. The shifts for the wavelengths of 450 and 700 nm were similar to those for 550 nm. [52] The largest influence on s sc,mie and s bsc,mie stems from uncertainties in the measurement of the number size