Adaptation of Dry Nephelometer Measurements to Ambient Conditions

Mar 3, 2005 - Also addressed is a systematic error in the dry scattering coefficients measured with a nephelometer previously discussed in the literat...
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Environ. Sci. Technol. 2005, 39, 2219-2228

Adaptation of Dry Nephelometer Measurements to Ambient Conditions at the Jungfraujoch REMO NESSLER,† ERNEST WEINGARTNER,* AND URS BALTENSPERGER Laboratory of Atmospheric Chemistry, Paul Scherrer Institut (PSI), CH-5232 Villigen PSI, Switzerland

In a numerical study the influence of relative humidity (RH) on aerosol scattering coefficients σ was investigated. Based on a core/coating aerosol model, RH enhancement factors for scattering, ξ(RH) ) σ(RH)/σ(RH ) 0), were calculated for the wavelengths λ ) 450, 550, and 700 nm for a summer and a winter case. The investigation was adapted to the situation (e.g., chemical composition, particle size distributions, hygroscopic behavior) of the high-alpine site Jungfraujoch (JFJ, 3580 m asl), where long-term measurements of dry aerosol scattering coefficients are performed at these wavelengths. The presented results are therefore representative of the lower free troposphere above a continent. The RH enhancement factors at a specific RH strongly depend on the average particle size. For example, at RH ) 85% they vary between ∼1.2 and ∼2.7 in summer and between ∼1.4 and ∼3.8 in winter. It is shown that there is a strong relationship between ξ and the Ångstro¨ m exponent a˚ (based on scattering only) of the dry aerosol, which is directly derived from the dry scattering measurements. This allows for parametrizing ξ for a specific wavelength and season with a˚ and RH. The parametrization is applicable for RH up to ∼90%sfor higher RH the underlying hygroscopic models become unreliablesand for a˚ between ∼ -0.25 and ∼2.75, which covers the range observed at the JFJ. Also addressed is a systematic error in the dry scattering coefficients measured with a nephelometer previously discussed in the literature, which arises from nonidealities in the angular intensity distribution of the light inside the instrument. This effect also depends strongly on the particle size and can be described by a correction factor C that can be parametrized with a˚. The scattering coefficient corrected for measurement artifacts at ambient RH for specific wavelength and season therefore can be estimated from the uncorrected dry nephelometer scattering coefficient σneph as σ(a˚, RH) ) C(a˚) × ξ(a˚, RH) × σneph. As additional information only ambient RH data are needed. The 95% confidence bound of this total correction ranges from less than 5% for low RH and large a˚ up to ∼40% for high RH and small a˚. * Corresponding author phone: +41563102405; fax: +41563104525; e-mail: [email protected]. † Also affiliated with the Laboratory for Air and Soil Pollution (LPAS), Swiss Federal Institute of Technology, CH-1510 Lausanne, Switzerland. 10.1021/es035450g CCC: $30.25 Published on Web 03/03/2005

 2005 American Chemical Society

Introduction Atmospheric aerosol particles significantly influence the Earth’s radiation budget. The effects occur in two distinct ways: Particles with diameters in the range 0.1 < D < 1 µm are highly effective in scattering andsdepending on their chemical compositionsabsorbing incoming solar radiation. These processes are known as the direct effect. The indirect effect refers to the fact that soluble particles with D J 100 nm additionally may act as cloud condensation nuclei and thereby alter the microphysical and hence the radiative properties and the lifetime of clouds. The direct effect can result in positive or negative radiative forcing, depending on the chemical composition and the microphysical properties of the aerosols and the albedo of the underlying surface. The indirect effect is thought to result in negative global mean radiative forcing, which may be negating the positive forcing due to all greenhouse gases. However, the uncertainty is still very large. Indeed, aerosols are one of the greatest sources of uncertainty in the assessment of global climate forcing (1, 3, 4). A key parameter governing the aerosol radiative forcing is the single scattering albedo (5). It can be determined by simultaneous measurements of absorption and scattering coefficients. A convenient instrument to provide the latter ones is an integrating nephelometer. Nephelometer measurements (using the model TSI 3536, which operates at the wavelengths λ ) 450, 550, and 700 nm) have been performed at the Jungfraujoch (JFJ) High Alpine Research Station within the World Meteorological Organization’s (WMO) Global Atmosphere Watch (GAW) program since 1995. The goal of this program is to provide a long-term monitoring of the trends as well as an early warning system for changes in the atmosphere in general, and, concerning aerosols, to determine the spatio-temporal distribution of aerosol properties related to climate forcing and air quality up to multi-decadal time scales (6). The JFJ is located in the Swiss Alps at 3580 m asl. Due to its high elevation it resides prevalently in the free troposphere and is not affected by regional pollution sources. During the warmer months the JFJ is influenced by injection of planetary boundary layer air as a result of thermal convection. Consequently most extensive aerosol parameters undergo an annual cycle, exhibiting maxima in the summer months and minima in the winter months (7). The JFJ is thus representative of the lower free troposphere above continental areas. The scattering coefficients measured with a nephelometer require a number of corrections. A first correction is necessary by the optical construction of the nephelometer. Nonidealities in the angular (primarily the truncation of the near-forward scattering) and to a far less extent in the wavelength sensitivity cause systematic measurement errors. Although modest for typical accumulation-mode particles, they increase strongly for coarse-mode particles (8). A second correction arises from the sampling technique associated with most in situ aerosol measurements. Usually such measurements have to be performed by inducting the ambient air into a housing. This process may change the temperature (T) and the relative humidity (RH), and, this being the case, the measured aerosol properties differ from the ambientsthe climate-relevants ones. At a place exposed to such harsh weather conditions as the JFJ (average temperature below 0 °C even in summer, average annual RH of 74%) this is particularly true. Since the temperature of the laboratory and the instrumentation is kept at 20-30 °C, the RH of the measured aerosol typically drops below 10% (9). Furthermore, many researchers keep the RH deliberately at defined low values by modest heating VOL. 39, NO. 7, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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to ensure comparability between different nephelometer measurements (10). For example, ratios of the scattering coefficient at 85% RH to that at 30% RH between 1.01 and 1.51 were found for biomass burning aerosols in Brazil (12), ratios of the scattering coefficient at 85% RH to that at 40% RH between ∼1.0 and ∼3.3 were measured at a testbed site covering north central Oklahoma and south central Kansas (13), and values of the same ratio between ∼1.5 and ∼2 were measured on Kaashidhoo Island in the Republic of the Maldives (14). All results refer to a wavelength of 550 nm. The objective of this paper is to present a method that allows derivation of ambient scattering coefficients from dry scattering coefficients measured with a nephelometer without the need of any additional measurements other than ambient RH. The approach basically relies on two correction factors: one to correct for the nephelometer nonidealities (earlier discussed in the literature (10)), and one to correct for the changes caused by the drying of the aerosol (hygroscopic correction). The analysis is adapted to JFJ conditions. Consequently, the results are representative of the lower free troposphere above a continent. For this aerosol type hardly any information about the humidity effect on scattering is available so far (1). Since the method itself is not restricted to free troposphere aerosol, we suggest similar analyses for other aerosol types. Because of data availability, the present study focuses on a winter and a summer case, which are expected to mark the extrema of the continuous JFJ annual cycle (see above). The presented method is the result of model calculations. Its experimental verificationse.g., by means of a combined dry/ humidified nephelometer systemsis the objective of future work. A parallel examination of the RH effect on absorption coefficients is reported in Nessler et al. (2).

Methods The study presented in this paper is primarily based on the analysis of modeled dry and ambient scattering coefficients. The input parameters for the model are derived from measured hygroscopic properties, size distributions, and data on the chemical composition. Both the concepts and the measurements used for the modeling are briefly described in the following. Hygroscopic Growth. The aerosol hygroscopic behavior can be addressed in terms of hygroscopic growth factors g(RH) ) D(RH)/D(RH ) 0), where D is the particle diameter. Hygroscopicity measurements of the JFJ aerosol served two purposes in this study. On one hand, hygroscopic growth factors g(RH) measured as a function of RH (humidograms) were used to model the relationship between dry and ambient aerosol diameters for the fine-mode (see below) aerosol. On the other hand, hygroscopic growth factors measured at a constant RH of 85% allowed for deriving lacking information about the aerosol chemical composition by means of a hygroscopicity closure (see below). Hygroscopic Growth at the Jungfraujoch. The aerosol hygroscopic behavior at the JFJ was investigated extensively during the two cloud and aerosol characterization experiments (CLACE1 and CLACE2) performed in winter 2000 (February to March) and summer 2002 (July), by means of a low-temperature hygroscopicity tandem differential mobility analyzer (H-TDMA). Both campaigns provided humidograms as well as g(RH ) 85%) time series. The results relevant for the present paper are given in Weingartner et al. (11) and Nessler et al. (9) (CLACE1, winter) and Weingartner et al. (15) (CLACE2, summer). Briefly, they are as follows. (i) In summer, as well as in winter, the hygroscopic growth distributions were mainly characterized with one single narrow mode, showing that the particles were to a large extent 2220

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internally mixed. (ii) Neither in summer nor in winter did the humidograms reveal deliquescence or efflorescence, i.e., no hysteresis was detected. (iii) Consequently, the RH dependence of the growth factor in both cases was characterized by a smooth function, the parametrization of which contains the whole information about the hygroscopic behavior. (iv) In summer the hygroscopic growth factors were considerably lower and the onset of hygroscopic growth occurred at larger RH than in winter. For the winter case we used the hygroscopic growth parametrization given in Nessler et al. (9) for the 250-nm dry particles (largest measured particles) to determine the diameter of the ambient particles. For the summer case we fitted g(RH) data for 100-nm dry particles (largest particles for which humidograms were measured) from Weingartner et al. (15) with the empirical model

(

ln(g) ) γ1x + γ2x2 + γ3x3

x ) ln 1 -

RH 100

)

(1)

where RH is given in percent and the free parameters γ1, γ2, and γ3 were adjusted in the least-squares sense. Equation 1 is a generalization of the frequently used parametrization ln(g) ) γx (11, 16-18), which failed in our case because of the slow increase of g with RH. Although still of minor importance (and only relevant for RH J 85%), the Kelvin effect starts to play a role for particles as small as 100 nm. To obtain a growth curve representative for the fine-mode particles that contribute most to the scattering, we thus converted the fitted curve to the curve corresponding to 250nm dry diameter by correcting for the Kelvin effect. It is parametrized according to eq 1 with γ1 ) -0.018, γ2 ) 0.050, and γ3 ) -0.013. The fitting procedures underlying the parametrizations yield an uncertainty ∆g ) 0.03 for both the summer and the winter case. Hygroscopic Growth Factors of Multicomponent Aerosols. For the hygroscopicity closure (see below) it was necessary to estimate the hygroscopic growth factor g of a mixed particle from the growth factors of its components. A common approach to do so is to use the Zdanovskii-Stokes-Robinson (ZSR) relation (19, 20), which assumes independent hygroscopic behavior of the different components. Supposing volume additivity the ZSR relation can be written as

( ) ∑V g

3 j j

g)

j

∑

1/3

(2)

Vj

j

where Vj and gj are the volumes and the hygroscopic growth factors, respectively, of the individual components. Experimental results often indicate a fair agreement with ZSR predictions (18, 21, 22), but according to a more detailed analysis of literature data (22) positive or negative interactions between different compounds are possible, depending on mixed species and concentrations. We also used the aerosol inorganic model AIMIII to derive the hygroscopic growth factor of the inorganic part of the JFJ aerosol (see below). This chemical thermodynamic model was developed for the aerosol system H+-NH4+-Na+SO42--NO3--Cl--H2O and enables the distribution of water and ions to be calculated between liquid, solid, and vapor phases for ambient conditions (23). Discrepancies between the ZSR relation and AIMIII amount to only a few percent above the deliquescence RH. Microphysical and Chemical Aerosol Properties. Aerosol Model. For the fine-mode particles (dry diameter Ddry e 1

FIGURE 1. Aerosol model for fine-mode particles. The diameter D1 of the insoluble core is the same for the dry and the ambient aerosol, ambient whereas the total diameters Ddry differ by the amount 2 and D2 of water contained in the coating of the ambient aerosol (hygroscopic behavior). Dambient (RH ) 0%) ) Ddry 2 2 . µm) we used the following model (cf. Figure 1). Both the dry and the ambient aerosol consist of a homogeneous insoluble spherical core and a homogeneous coating of uniform thickness. For the dry particle the coating is composed of only dry soluble material, whereas for the ambient particle the coating is a homogeneous mixture of the soluble material and a certain amount of water, which is in equilibrium with the ambient RH (hygroscopic behavior). An excellent agreement between measured scattering coefficients and model calculations based on such a coated sphere model has been reported (24). The coarse-mode particles (Ddry > 1 µm) were considered as homogeneous insoluble spheres (no hygroscopic behavior), based on the fact that they mainly consist of mineral dust, which experiences no significant hygroscopic growth. Furthermore, the chemical composition was supposed to be the same within the whole fine-mode and coarse-mode range, respectively. Note that this assumption implies a constant ratio between D1 and Ddry 2 over the whole fine-mode range as well. The threshold value Dth ) 1 µm as separation between fine and coarse mode is based on a study conducted at the JFJ by Streit et al. (25). Aerosol Size Distributions. Nyeki et al. (26) and Weingartner et al. (27) presented aerosol size distributions measured at the JFJ using an optical particle counter (OPC, 0.1 e D e 7.5 µm) and a scanning mobility particle sizer (SMPS, 18 e D e 750 nm), respectively. For the time period from March 1997 to May 1998 the two data sets overlap. We combined the corresponding fifteen monthly averages using the SMPS data for the fine mode and the OPC data for the coarse mode and fitted them with the sum of three log-normal distributions (two of them representing the fine mode (27), and one representing the coarse mode). By varying the resulting geometric standard deviations, median diameters, and coarse-mode concentrations within the (15% interval of the fitted parameters we finally obtained 496 size distributions considered representative for the JFJ aerosol. The log-normal parameters of the corresponding number size distributions lie within the following intervals: 0.016 e Dmed e 0.14 µm, I 0.11 e Dmed e 0.61 µm, 0.30 e Dmed II III e 3.86 µm, 1.47 e σI e 3.06, 1.23 e σII e 2.07, 1.07 e σIII e 2.90, 0 e NII/NI e 0.85 and 0 e NIII/NII e 0.08, where σi, Dmed , and Ni, i ) I, II, III, i are the geometric standard deviations, median diameters, and number concentrations, respectively, of the three modes. Chemical Composition. The chemical composition of the JFJ aerosol was investigated by Kriva´csy et al. (28) and Henning et al. (29). The first study is based on measurements from summer 1998 (July to August) and focuses on organic

compounds in particles with Ddry e 2.5 µm, whereas the second one treats water soluble inorganic ions separately in the fine and coarse mode measured during 1.5 years starting in July 1999. Restricted by the support in AIM III and the availability of refractive indices data, in the present study only nitrate (NO3-), sulfate (SO42-), chloride (Cl-), ammonium (NH4+), sodium (Na+), and hydrogen (H+) were considered of the inorganic ions. However, these species account for 97% of the total mass of water soluble inorganic ions. The neglected ions were replaced by a proper amount of H+ to establish electro-neutrality. The two data sets by Kriva´csy et al. (28) and Henning et al. (29) were then merged using the following assumptions. First, the chemical composition of the aerosol fraction with Ddry e 2.5 µm is equal or at least very similar to that of the aerosol fraction with Ddry e 1 µm. Second, due to the continuous JFJ annual cycle (cf. Introduction) the chemical composition of the JFJ aerosol is (nearly) the same each summer. The resulting chemical composition of the JFJ summer fine mode is shown in the second column of Table 1 in terms of mass fractions. The indicated uncertainties correspond to the standard deviations of the mean and thus represent the atmospheric variability. WSOC, WINSOC, and EC stand for water soluble organic carbon, water insoluble organic carbon, and elemental carbon, respectively. The water soluble inorganic ions are in the following referred to as SI. To calculate the refractive indices (cf. eq 10) associated with the summer fine mode, the mass fractions were converted into volume fractions. The necessary density data are listed in column 3 of Table 1. Representative density values for WSOC and WINSOC in the literature are still contradictory, resulting in large uncertainties (represented by the standard deviations of the mean of the different literature values). The same is true for elemental carbon. Compared to that, the uncertainties of the inorganic species are considered negligible. The resulting summer volume fractions are given in column 4 of Table 1. The uncertainties are calculated according to quadratic error propagation (assuming independent uncertainties). With WINSOC and EC forming the insoluble core it follows that D1/Ddry 2 ) 0.67 ( 0.04. Because data of the organic fraction are available only for summertime, the chemical composition for wintertime was estimated. To do so, we postulated consistency between the differences in the hygroscopic behavior and the differences in the chemical composition (hygroscopicity closure) according to eq 2 under the following simplifying assumptions: (a) the composition and therefore the hygroscopic growth factors of the individual fractions (SI, WSOC, WINSOC, EC) remain constant throughout the year, (b) what changes are their relative contributions to the total fine mode. This procedure is motivated by the fact that the SI chemical composition indeed shows little seasonal variation (29) and that there is a strong correlation between the hygroscopic growth factor and the amount of organics. First, the hygroscopic growth factors for SI, WSOC, WINSOC and EC were derived at RH ) 85%, where the JFJ summer and winter hygroscopic growth factors were found to be 1.37 ( 0.01 (15) and 1.53 ( 0.03 (11), respectively, for 250-nm dry diameter. We considered WINSOC and EC as nonhygroscopic, i.e., having a hygroscopic growth factor of 1. The SI hygroscopic growth factor was calculated using AIM III and found to be 1.590 ( 0.002. This value is representative for particles with Ddry J 250 nm (see the 2 discussion about the Kelvin effect above). The WSOC hygroscopic growth factor finally followed from the preceding results and the ZSR relation eq 2 and was found to be 1.2 ( 0.1. As an additional constraint, it was assumed that the ratios between WSOC, WINSOC, and EC remain constant throughVOL. 39, NO. 7, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Chemical Composition and Selected Microphysical Properties of the JFJ Fine-Mode Aerosol

(NH4)2SO4 (NH4)3H(SO4)2 NH4NO3 NH4Cl Na2SO4 WSOC WINSOC EC

summer mass fractiona [%]

density [g m-3]

summer volume fraction [%]

winter volume fraction [%]

refractive index

21 ( 8 19 ( 7 11 ( 1 0.27 ( 0.08 0.73 ( 0.11 22 ( 2 20 ( 4 6 .0 ( 0 .4

1.77b 1.83c 1.72b 1.519b 2.7b 1 .3 ( 0 .3 d 1 .3 ( 0 .3 d 1 . 7 ( 0 .7 e

17 ( 7 16 ( 6 10.1 ( 1.3 0.27 ( 0.09 0.43 ( 0.06 26 ( 7 24 ( 7 6(2

33 ( 10 30 ( 9 19 ( 4 0 .5 ( 0 .2 0 .8 ( 0 .2 8(3 7(3 1 .7 ( 0 .7

1.528 ( 0.008f 1.51 ( 0.01g 1 .6 ( 0 .1 h 1.52i 1.48i 1.48 ( 0.08j 1.48 ( 0.08j 1.7 ( 0.7 + (0.48 ( 0.08)ik

a Combined data from Kriva ´ csy et al. (28) and Henning et al. (29). b Data from Lide (46). c Data from Dunn et al. (47). d Based on Horvath (41), Dick et al. (48), and values for several organic species from Saxena et al. (49). e Based on combined data from Hess et al. (50), Horvath (41), and Lide (46). f Based on combined data from Toon et al. (51), Horvath (41), and Seinfeld and Pandis (42). g Data from Foshag (52). h Based on combined data from Weast (53) and Horvath (41). i Value linearly extrapolated from aqueous solution data from Lide (46). j Based on combined data from Horvath (41) and Schmid et al. (54). k Based on combined data from Twitty and Weinman (55), Shettle and Fenn (30), Levoni et al. (56), Schult et al. (57), Hess et al. (50), Horvath (41), Seinfeld and Pandis (42), and Lesins (58).

out the year. Other possible assumptions, e.g., the SI and EC fractions as well as the ratio (WINSOC + WSOC)/sulfate remaining constant throughout the year or the ratios WINSOC/WSOC and EC/SI remaining constant throughout the year, did not lead to physically reasonable, i.e., nonnegative volume fractions, within the considered uncertainty. The according results are presented in column 5 of Table 1. They further imply D1/Ddry 2 ) 0.43 ( 0.06 for wintertime. This corresponds to a soluble volume fraction of 0.92 ( 0.03, which is in excellent agreement with the value reported in Weingartner et al. (11). Because of its primary sources the JFJ coarse-mode aerosol does not show much seasonality (29). In the present study it was regarded as mineral dust, i.e., dust-like aerosols as given by Shettle and Fenn (30), independently of the season. Scattering Coefficients. For both the homogeneous (3134) and the coated (35) sphere the problem of light scattering is exactly solvable. In either case it is possible to calculate the amplitude (scattering) functions S1 and S2 (36, 37). For the homogeneous sphere they depend on the scattering angle θ, the size parameter x ) πDλ-1 (with D being the diameter of the sphere and λ being the wavelength of the incident light), and the complex refractive index m of the sphere. For the coated sphere they depend on the scattering angle θ, the size parameters x1 ) πD1λ-1 (D1 denoting the diameter of the core) and x2 ) πD2λ-1 (D2 denoting the total diameter of the sphere), and the complex refractive indices m1 and m2 of the core and the coating, respectively. Integration over θ yields the (dimensionless) scattering efficiency Q of a single particle:

1 Qt(λ,m,D) ) x

∫

π

0

{|S1(θ,x,m)| + |S2(θ x,m)| } sin θ dθ (3a)

Qt(λ,m1,m2,D1,D2) )

2

1 x2

∫

π

0

2

{|S1(θ,x1,x2,m1,m2)|2 +

|S2(θ,x1,x2,m1,m2)|2} sin θ dθ (3b) where eq 3a stands for the homogeneous sphere and eq 3b stands for the coated sphere. Henceforth, we will only give the equations for the coated sphere explicitly, from which the according (simpler) equations for the homogeneous sphere may easily be deduced. The subscript t in eqs 3a and 3b is used to indicate that Qt refers to the “true” value of the scattering efficiency, as it would be measured by an ideal instrument. The (real) nephelometer, however, measures a different quantity, because of nonidealities in the angular (8, 2222

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38) and the wavelength (8) sensitivities. The latter were shown to be of secondary importance (10) and will therefore be neglected here. The scattering efficiency as measured by a nephelometer, Qn, may then be expressed by replacing sin(θ) in eq 3 with the real angular sensitivity function f(θ)

1 Qn(λ,m1,m2,D1,D2) ) CR x2

∫ {|S (θ,x ,x ,m ,m )| π

1

0

1

2

1

2

2

+

| S2(θ,x1,x2,m1,m2)| } f(θ)dθ (4) 2

The constant CR takes into account the gas calibration of the nephelometer, which corrects for the nonidealities for sufficiently small particles (Rayleigh regime). For the TSI 3563 nephelometer, f(θ) has been measured by Anderson et al. (8). Henceforth the subscripts t and n will be used to distinguish between the “true” and the nephelometer quantities, respectively. Provided that only single scattering occurs, which is the case as long as no optically very thick layers (e.g., cumulus clouds) are considered, the dry scattering coefficient σdry due to an ensemble of aerosols characterized by the particle size distribution ∂N/∂log Ddry 2 is given by

σdry (λ,m1,m2,N) ) t

∫

∞

0

2

dry Qt (λ,m1,m2,D1(Ddry 2 ),D2

πDdry ∂N 2 ) × 4 ∂ log Ddry 2 d log Ddry (5) 2

σdry n (λ,m1,m2,N) )

∫

∞

0

2

dry Qn (λ,m1,m2,D1(Ddry 2 ),D2 )

πDdry ∂N 2 × 4 ∂ log Ddry 2 d log Ddry (6) 2

dry Note that D1 depends on Ddry 2 , i.e., D1 ) constant × D2 in our model, with the constant being a function of the chemical composition and thus of the season. To characterize the effect of the angular nonidealities we define the factor C as

C)

σdry t σdry n

(7)

where C is near unity for very small particles and increases with particle size (10). Note that in this paper statements about the particle size always refer to the average property of an ensemble of polydisperse particles.

The ambient scattering coefficient σamb reads as

σamb (λ,m1,mamb (RH),N,RH) ) t 2

∫

∞

0

dry Qt(λ,m1,mamb (RH),D1(Ddry 2 2 ),g(RH)D2 )

2 π[g(RH)Ddry 2 ] × 4

∂N d log Ddry (8) 2 ∂ log Ddry 2 σamb (λ,m1,mamb (RH),N, RH) ) n 2

∫

∞

0

dry Qn(λ,m1,mamb (RH),D1(Ddry 2 2 ),g(RH)D2 )

2 π[g(RH)Ddry 2 ] × 4

∂N d log Ddry (9) 2 ∂ log Ddry 2 where g(RH) ) Damb (RH)/Ddry is the hygroscopic growth 2 2 amb factor and m2 (RH) is the complex refractive index of the coating at ambient conditions. We have g(RH ) 0%) ) 1, mamb (RH ) 0%) ) m2 and σamb(RH ) 0%) ) σdry. The Kelvin 2 effect was neglected, since it is only important for particles with Ddry 2 j 100 nm, which only contribute very little to the scattering coefficient at the nephelometer wavelengths. We therefore considered g and mdry 2 independent of the particle diameter in eqs 8 and 9. Test calculations showed indeed that the ambient scattering coefficients changed by less than 2% when taking into account the diameter dependence of g and mdry 2 caused by the Kelvin effect. Since we distinguish between fine- and coarse-mode particles, the integration limits in eqs 5, 6, 8, and 9 were accordingly adapted. Refractive Indices. There are a variety of mixing rules to determine an average or apparent refractive index of a multicomponent aerosol, but there is no theoretical basis for any of them (39). Frequently used are the Lorentz-Lorenz rule (40) and the assumption of a volume weighted average (41). In our case the two methods showed very similar results (differences smaller than 1% for the real parts and differences much smaller than measurement uncertainties for the imaginary parts). We therefore used the latter one because of its simplicity. The complex refractive index m ) m′ + im′′ of a mixture is then calculated as

∑V m ∑V m′ j

m)

j

j

j

)

∑ j

Vj

j

∑ j

∑V m′′

j

j

+i Vj

j

∑

j

(10) Vj

j

The data presented in Table 1 allow for calculation of the fine-mode refractive indices, i.e., the refractive indices of the core, m1, and the coating, m2, according to eq 10. With the assumption of constant ratios between WSOC, WINSOC, and EC, m1 is the same for the summer and the winter case, namely m1 ) (1.53 ( 0.07) + (0.09 ( 0.05)i. Although this is not a priori true for m2, the values for the summer case, m2 ) 1.51 ( 0.03, and the winter case, m2 ) 1.522 ( 0.014, turned out to be not significantly different. Seasonal differences in the humidity effect on scattering therefore arise basically from variations in the hygroscopic properties. The values for mamb (RH) followed from the m2 values by adding the proper 2 amount of water (mwater ) 1.33 (42)) and using eq 10. As coarse-mode refractive index we used for summer and winter the value mc ) 1.53 + 0.008i given by Shettle and Fenn (30) for dust-like aerosols. An uncertainty of 5% was assumed. Ångstro1 m Exponent. The A° ngstro¨m exponent (43) was originally introduced to describe the spectral variability of the atmospheric aerosol optical thickness and hence is intrinsically related to extinction. We follow an approach often used in connection with nephelometer studies (cf. e.g., Heintzenberg et al. (44) or Anderson and Ogren (10)) and define an A° ngstro¨m exponent a˚ based on scattering only -a˚ σdry n (λ) ) b ‚ λ

(11)

The factor b is related to the aerosol concentration and is not of interest in this study. In contrast to Anderson and Ogren (10), who calculated different A° ngstro¨m exponents for every nephelometer wavelength pair, we use a single one by fitting the three nephelometer scattering coeffcients σdry n (λ ) 450 dry nm), σdry (λ ) 550 nm), and σ (λ ) 700 nm) to the power n n law (11). The thus-derived values of a˚, which correspond to the scattering exponent as defined by Collaud Coen et al. (45), are very similar (discrepancies of about 1%) to the ones calculated for the wavelength pair 450 nm/700 nm. Parametrization of the Humidity Effect on Scattering. The humidity effect on scattering can be characterized by defining a RH enhancement factor

ξ(RH) )

σamb (RH) t

(12)

σdry t

similar in concept to the hygroscopic growth factor g(RH). Accordingly, ξ(RH ) 0%) ) 1. The empirical model eq 1 already used to describe the summer hygroscopic growth turned out to be a very satisfying parametrization for ξ(RH) as well

ln(ξ) ) a1x + a2x2 + a3x3

(

x ) ln 1 -

RH 100

)

(13)

where Vj and mj ) m′j + im′′j are the volumes and the complex refractive indices, respectively, of the substances in the mixture. Even though refractive indices are wavelength dependent, they can to a good approximation be considered as constant within the range of the nephelometer wavelengths.

Results and Discussion

Refractive index data for each considered species are given in the last column of Table 1. The indicated uncertainties are based on the discrepancies between different literature values and represent the standard deviation of the mean. The tabulated refractive indices themselves correspond to the average literature values. Exceptions are the refractive indices for NH4NO3 and NH4Cl, which were derived by linearly extrapolating aqueous solution data. The uncertainties originating from the fitting procedure are negligible compared to the uncertainties of the other refractive indices, all the more so as NH4NO3 and NH4Cl account for only a tiny fraction of the fine-mode volume.

On the basis of the refractive indices and the ratios D1/Ddry 2 presented above, we calculated for each of the 496 aerosol size distributions the following data (using eqs 5-8 and 12) at the wavelengths 450, 550, and 700 nm for the summer as dry well as the winter case: σdry t , σn , C and for RH between 0% and 99% (using increments of 3%) σamb (RH) and ξ(RH). The t ξ(RH) curves were then parametrized by fitting eq 13 to the calculated data. The wavelength dependence of the σdry n values yielded a˚. The thus-obtained data set built the basis for our investigation. Parametrization of the RH Enhancement Factor for Scattering. Since the scattering effciency varies with particle

Note that ξ(RH) and thus the parameters a1, a2, and a3 of its parametrization depend on the chemical composition and the size distribution of the aerosol particles as well as the wavelength of the incident radiation.

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TABLE 2. Polynomial Parametrization, ai(λ,a˚) ) ∑k c(i) ˚k, of the Parameters a1, a2, and a3, Which Describe ξ(RH) According k (λ)a to Equation 13a Summer

Winter

a1 (×103)

a2 (×102)

a3 (×102)

c0 c1 c2 c3 c4

1.38 ( 0.07 4.32 ( 0.16 -0.736 ( 0.074

5.04 ( 0.17 13.0 ( 0.4 -1.94 ( 0.17

450 nm -3.81 ( 0.04 2.28 ( 0.09 -0.451 ( 0.042

c0 c1 c2 c3 c4

0.349 ( 0.111 5.26 ( 0.21 -0.875 ( 0.086

2.06 ( 0.23 15.6 ( 0.5 -2.28 ( 0.23

550 nm -4.51 ( 0.06 2.65 ( 0.13 -0.522 ( 0.061

c0 c1 c2 c3 c4

-2.01 ( 0.36 7.56 ( 0.56 -1.40 ( 0.20

-3.13 ( 0.38 19.3 ( 0.8 -2.72 ( 0.38

700 nm -5.60 ( 0.09 3.08 ( 0.20 -0.585 ( 0.091

a1 (×102)

a2 (×102)

a3 (×103)

-10.1 ( 0.4 -14.3 ( 0.7 1.97 ( 0.31

12.1 ( 0.1 9.14 ( 0.74 -7.30 ( 1.30 3.50 ( 0.83 -0.563 ( 0.170

6.68 ( 0.12 18.0 ( 0.7 -11.2 ( 1.2 4.75 ( 0.74 -0.806 ( 0.151

-11.8 ( 0.5 7.02 ( 2.72 -29.8 ( 4.8 15.8 ( 3.0 -2.62 ( 0.62

9.81 ( 0.08 13.6 ( 0.4 -8.82 ( 0.73 3.45 ( 0.46 -0.509 ( 0.095

2.50 ( 0.19 20.7 ( 0.7 -6.77 ( 0.71 0.811 ( 0.197

-8.57 ( 0.55 10.5 ( 3.0 -33.0 ( 5.3 15.2 ( 3.38 -2.26 ( 0.69

9.96 ( 0.13 11.7 ( 0.5 -3.36 ( 0.47 0.337 ( 0.129

2.92 ( 0.17 18.1 ( 0.3 -3.90 ( 0.15

a The a , a , and a values resulting from the shown c , c , c , c , and c coefficients are scaled as indicated by the scaling factors. Valid ranges: 1 2 3 0 1 2 3 4 -0.25 e a˚ e 2.75 and 0% e RH e 90%.

FIGURE 2. Relationships between the A° ngstro1 m exponent a˚ and the parameters a1, a2, and a3, which describe ξ(RH) according to eq 13, at the example of λ ) 450 nm. The situation for the other two wavelengths is very similar. In every graph each dot represents a value calculated with a different aerosol size distribution. The solid lines parametrize these relationships using polynomials up to order 4 (gained from least-squares fitting). R2 denotes the adjusted coeffcient of multiple determination. size, the humidity effect depends on the particle size. For constant RH, ξ(RH) decreases monotonically with increasing particle size provided that the aerosol size distribution is broad enough to smear out the Mie oscillations. Depending on particle size, ξ(RH ) 85%) varies for example between ∼1.2 and ∼2.7 in summer and between ∼1.4 and ∼3.8 in winter. This feature does not only result from the fact that the coarse mode is considered nonhygroscopic, it is also true for the fine mode itself, because due to the particle size dependence of the scattering coefficient the humidity effect is strongest for the smallest particles. Since the wavelength dependence of the scattering coeffcient is also sensitive to the particle size (10)ssmall particles are associated with large A° ngstro¨m exponents and vice versasthe humidity effect is related to the A° ngstro¨m exponent a˚. As can be seen from Figure 2, there exist strong relationships between a˚ and the parameters a1, a2, and a3, which parametrize ξ(RH) according 2224

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FIGURE 3. RH enhancement factors ξ as a function of RH modeled according to eqs 13 and 14 (solid lines) for a˚ ) 1.25 and λ ) 450 nm for the summer (a) and the winter (b) case as well as the corresponding 95% confidence bounds (dashed lines). Also shown are the RH enhancement factors calculated by means of eqs 5, 8, and 12, for four of the 496 representative JFJ size distributions, which were selected according to the criterion to lead to an A° ngstro1 m exponent of a˚ ) 1.25 with the given refractive indices (circles, crosses, triangles, and squares). The scatter in these latter RH enhancement curves arises from the fact that they are based on a data set which simulates the data uncertainty (see below). Graphs (c) and (d) illustrate the hygroscopic growth factors as a function of RH for the summer and the winter case. to eq 13. Thus, it is possible to express the RH enhancement factor as a function of λ, a˚, and RH only: ξ ) ξ (a1(λ,a˚), a2(λ,a˚), a3(λ,a˚), RH). For the parametrization of a1, a2, and a3, polynomials up to order 4 (cf. Table 2) turned out to be appropriate

ai(λ,a˚) )

∑c

(i) k

(λ) a˚k

i ) 1, 2, 3

(14)

k

The corresponding coeffcients of the polynomials are presented in Table 2. Figure 3 shows the RH enhancement factors ξ as a function of RH modeled according to eqs 13 and 14 for a˚ ) 1.25 and λ ) 450 nm for the summer (a) and the winter (b) case as

We therefore fitted the combined data to our parametrization model, which consists of two straight lines:

C(a˚) )

FIGURE 4. Relationship between the A° ngstro1 m exponent a˚ and the correction factor C accounting for angular nonidealities of the nephelometer. Since the situation is very similar for each wavelength as well as for summer and winter, these features are not distinguished in the graph. Every dot represents the calculated correction factor for a specific size-distribution/wavelength/season combination. The solid line corresponds to the parametrization (15) (least-squares fit based on all dots). R2 denotes the adjusted coeffcient of multiple determination. The dashed line corresponds to the correction presented by Anderson and Ogren (10). well as the corresponding 95% confidence bounds. Also shown are the RH enhancement factors, calculated by means of eqs 5, 8, and 12, for four of the 496 representative JFJ size distributions, which were selected according to the criterion to lead to an A° ngstro¨m exponent of a˚ ) 1.25 with the given refractive indices. The scatter in these latter RH enhancement curves arises from the fact that they are based on a data set, which simulates the data uncertainty (see below). The hygroscopic growth curves for the summer (c) and the winter (d) case complete the figure and demonstrate how hygroscopic changes are translated into scattering changes. Parametrization of the Angular Correction Factor. The factor C correcting for the angular nonidealities can also be parametrized in terms of a˚ (10). Figure 4 shows that for large values of a˚ (small particles) the correction is small and the relationship between C and a˚ is strong, but that for decreasing a˚ (increasing particle size) the correction gets larger and the relationship between C and a˚ becomes weaker. Since the situation is very similar for each wavelength as well as for the summer and the winter case, a single parametrization for all six cases is appropriate. The reason for the small difference between the different cases is the similarity of the summer and winter refractive indices (cf. above) and the fact that the effect of the angular nonidealities (basically the truncation of light scattered into the forward direction) is a function of the ratio between the wavelength and the particle size, which is of the same order of magnitude for all three wavelengths.

{

β 2 - β1 R1 ‚ a˚ + β1, a˚ e s (15) where s ) R2 ‚ a˚ + β2, a˚ > s R2 - R1

At a˚ ) s the two lines intersect. The parameters R1, β1, R2, and β2 were found to be -0.214 ( 0.005, 1.417 ( 0.004, -0.050 ( 0.003, and 1.155 ( 0.005, respectively. Even though based on a different aerosol model, our findings are very similar to the results presented by Anderson and Ogren (10) (cf. Figure 4). However, when comparing the two parametrizations in the graph, note that the A° ngstro¨m exponent is not defined in exactly the same way in the two cases (see above). Combined Correction of the Dry Nephelometer Scattering Coeffcients. The combined effects of humidity and angular nonidealities are now parametrized as a function of λ, a˚, and RH only, and the “true” ambient scattering coefficient can be modeled as

σamb (λ,a˚,RH) ) σdry ˚ ) × ξ (a1(λ,a˚), a2(λ,a˚), t n × C(a a3(λ,a˚), RH) (16) using eqs 13-15 with the parameters given above and in Table 2. Besides the dry nephelometer data no additional measurements other than RH are needed. Equation 16 is applicable for RH up to ∼90%sfor higher RH the underlying hygroscopic models become unreliablesand for a˚ between ∼ -0.25 and ∼2.75, which corresponds to the interval on which the fitting procedures are based and which covers the range observed at the JFJ (45). Figure 5 shows the total correction factor as a function of RH and a˚ for the summer (a) and for the winter (b) case at λ ) 450 nm. The parametrizations underlying eq 16 are based on JFJ aerosol properties. Therefore, with the parameters given in this paper, eq 16 is representative for the lower free troposphere above a continent. For other aerosol types the parameters have to be adapted. Uncertainty Analysis. In the following discussion the ξ and C values calculated by means of eqs 5-8 and 12 will be referred to as “exact data”, whereas the ξ and C values resulting from the parametrizations given in eqs 13-15 will be referred to as “modeled data”. Two distinct kinds of uncertainties are present in the parametrizations of the humidity and angular correction factors. The first kind, which we call intrinsic uncertainties, is present even in the case of exactly known data. It arises from the scatter in the relationships between a˚ and the fit parameters a1, a2, and a3 (cf. Figure 2) as well as between a˚ and C (cf. Figure 4). The intrinsic uncertainties can be estimated by comparing the exact with the modeled ξ and C values. The second kind is related to the uncertainties of the data used to calculate the optical properties (e.g., refractive indices, chemical composition). To estimate the

FIGURE 5. Total correction factor (represented by the color scheme and the contour lines) as a function of RH and a˚ for the summer (a) and the winter (b) case for λ ) 450 nm. VOL. 39, NO. 7, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. Total Correction -0.5 e a˚ e 0.5

0.5 e a˚ e 1.5

1.5 e a˚ e 2.5

2.5 e a˚ e 3.5

humidity correction only

RH [%]

summer

winter

summer

winter

summer

winter

summer

winter

summer

winter

0 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90

17 18 18 20 21 24 27 30 33 41

17 19 22 25 27 29 30 31 33 37

7 18 18 20 21 24 27 30 33 41

3 19 22 25 27 29 30 31 33 37

8 8 10 11 14 17 20 23 31

9 12 15 17 19 20 21 23 27

4 4 6 7 10 13 16 19 27

5 8 11 13 15 16 17 19 23

0.5 1 3 4 7 10 13 16 24

2 5 8 10 12 13 14 16 20

influence of these uncertainties we used a Monte Carlo approach. The usual procedure would have been to repeat the calculation of all optical properties for each of the 496 size distributions and for every wavelength many times, each time varying the input parameters randomly within their uncertainties. This procedure was impossible since it would have exceeded the available computer power. Instead, we repeated the calculation only once, but we used for each of the 496 particle size distributions and for each wavelength a different set of m1, m2, mc, D1/Ddry 2 , Dth, and g(RH) values, reflecting their uncertainties. That is, each of this set was determined by choosing the following parameters from normal distributions around the original values with standard deviations according to their uncertainties: the mass fractions, densities, and refractive indices of the fine-mode constituents (the corresponding uncertainties are given in Table 1), the refractive index of the coarse mode (uncertainty 5%, see above), and the hygroscopic growth factors of the JFJ aerosol, g(RH) (uncertainty of the hygroscopic growth models ∆g ) 0.03, see above). Additionally, Dth was varied by choosing log(Dth) values from the normal distribution with standard deviation 0.1 around 0, which reflects the variability of the limit between coarse and fine mode as inferred from the fitted size distributions. The humidity and angular correction factors resulting from this calculation, which henceforth will be referred to as “noisy data”, can be compared with the corresponding modeled data. Furthermore, x% confidence bounds x can be estimated by determining x such that x% of the noisy data lie within the interval (1 ( x) × MD, where MD is the modeled data. A confidence bound defined in this way takes into account random measurement uncertainties and uncertainties arising from the natural variability of the parameters used to derive the parametrizations as well as the intrinsic model uncertainties. It does not account for any kind of systematic uncertainties, including possible inadequacies of the underlying aerosol model (see below). Because the uncertainties did not significantly differ for the different wavelengths, it was possible to base the uncertainty analysis on the combined data of all three wavelengths and thus increase the statistic. Table 3 lists 95% confidence bounds for the humidity and the angular as well as for the combined total correction. It reveals that for a˚ < 1.5 the total uncertainty up to RH ≈ 80% is dominated by the uncertainty of the angular correction, whereas for a˚ g 1.5 the humidity correction dominates the total uncertainty already for RH J 20%. The reason for this behavior is the dependence of the uncertainty of the angular correction (15) on a˚ (see below). The influence of the uncertainty of an arbitrary input parameter on the calculated optical properties can be determined by varying only this input parameter in the Monte Carlo simulation while holding all other parameters constant. Table 4 illustrates for the summer case how the uncertainties of different parameters affect the uncertainty of the humidity 2226

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TABLE 4. Summer Casea RH [%]

i) (95 [%]

g) (95 [%]

(9m) [%]

Dth) (95 [%]

(F) 95 [%]

mf) (95 [%]

0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90

0.4 0.6 1 1 2 3 5 9 14

0.4 1 2 4 6 9 10 11 10

0.1 0.3 0.7 0.9 2 3 4 7 13

0.1 0.2 0.4 0.7 1 2 3 5 6

0.0 0.1 0.3 0.5 0.8 1 2 3 6

0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 4

a (i) denotes the 95% confidence bound due to the intrinsic model 95 g) (m) (Dth) (F) mf) , 95 , 95 , 95 and (95 denote the 95% confidence uncertainty, and (95 bounds due to the uncertainties in the hygroscopic growth, the refractive indices of the fine-mode constituents and of the coarse mode, the finemode threshold value Dth, the densities of the fine-mode constituents, and the mass fractions of the fine-mode constituents, respectively.

correction. Note that the intrinsic model uncertainty (i) x (column 2) is always superposed to the uncertainty (p) x arising from the uncertainty of an arbitrary parameter p. The uncertainty considerations based on the noisy data thus can only reveal the uncertainty (p,i) x , which includes the intrinsic uncertainty, and not (p) itself. However, (i) x x is more of statistical than of systematic character and can be assumed independent of all other uncertainties. Therefore, it holds (p)2 (p) that (p,i)2 ≈ (i)2 x x + x , such that x can be extracted from (p,i) x . The values given in Table 4 were obtained in this way. The separation is actually very accurate. This can be seen from the fact that the total uncertainties resulting from quadratic summation along the rows of Table 4 agree with the values from Table 3 (second-to-last column) within 1%. By far the most important contribution to the uncertainty of the humidity correction comes from the uncertainty in the hygroscopic growth. It is followed by the intrinsic model uncertainty and the uncertainties of the refractive indices of the fine-mode constituents and the coarse mode, the threshold value Dth, the densities of the fine-mode constituents, and the mass fractions of the fine-mode constituents. In contrast to the humidity correction, the uncertainty of the angular correction strongly depends on the particle size and therefore on the A° ngstro¨m exponent. For a˚ J 1.5 (only small scatter in the C values in Figure 4) the uncertainty is small and arises primarily from uncertainties in the refractive indices of the fine-mode constituents and of the coarse mode. But for a˚ j 1.5 (large scatter in the C values in Figure 4) the uncertainty rapidly increases with decreasing a˚ and is dominated by the intrinsic model uncertainty. All other uncertainties are of minor importance over the whole A° ngstro¨m exponent interval. In the following some possible systematic errors are discussed, which may add to the random uncertainties

addressed so far. An idea about the uncertainty introduced by the aerosol model used for the study can be obtained by repeating all the calculations with a different aerosol model. In case of the fine mode we did so using the simpler homogeneous sphere model (classical Mie model). The thus-obtained RH enhancement factors are typically lower than the ones obtained with the shell model. However, the differences are very small. The largest deviation amounts to less than -4%. The differences for the angular correction factors are even smaller, not even reaching 1%. Further test calculations addressed the model assumption that the coarse mode is nonhygroscopic. They showed that the ambient scattering properties even for size distributions with large coarse-mode contributions changed by less than 1%, when taking into account a weak hygroscopic growth of the coarsemode particles as sometimes observed during Saharan dust events at the JFJ. The estimation of the winter fine-mode chemical composition involved some simplifying assumptions. Their failure would affect the estimates of the soluble volume fraction and the ratio between WINSOC and EC. Bundke et al. report for a 10% error in the soluble volume fraction an error of 3% in ξ at most (40). A wrong WINSOC to EC ratio causes a wrong refractive index m1. An error of 6% in its real part or of 20% in its imaginary part were found to result in an error up to 9% in ξ (40). The uncertainty considerations also allow deciding whether the winter humidity effect on scattering is significantly different from the summer humidity effect. For λ ) 450 nm and λ ) 550 nm it was found that for a˚ J 1 the humidity effect is over the whole RH range significantlys referring to the 5% level of significancessmaller in the summer than in the winter case, whereas for a˚ j 1 the difference is not significant at low RH. However, for RH J 40% the domain of significant difference expands linearly to smaller a˚ values, such that at RH ≈ 80% the summer humidity correction is for all A° nstro¨m exponents significantly smaller than the winter humidity correction. From RH ≈ 80% to RH ≈ 85% the domain of significant difference shrinks very rapidly, confining itself to large a˚ values. For still higher RH the difference is not significant anymore, independently of the A° nstro¨m exponent. For λ ) 700 nm the situation shows the same qualitative behavior, but the boundary of the domain of significant difference is shifted toward higher a˚ values, never falling below a˚ ≈ 0.5. Data availability allowed for this study investigation of only a summer and a winter case. However, since the aerosol properties measured at the JFJ undergo an annual cycle with its extremal values in summer and winter (cf. the Introduction), these two situations are expected to represent the minimum and the maximum of a recurrent oscillation. In a first approximation and until further experimental data will be available, the correction factors for any other season may therefore be estimated by interpolating them between the summer and the winter situation according to the annual oscillation of any other aerosol parameter measured at the JFJ, i.e., in a sinusoidal way. Because the difference between the summer and the winter correction, even where it is significant in the RH-a˚domain, is never very large compared to the uncertainty, this procedure is expected to yield correction factors within reasonable uncertainty for the whole year. In the RH-a˚domain, where the difference between summer and winter correction is not significant, the use of a seasonally constant factor (average between summer and winter case) is appropriate.

Acknowledgments The financial support and the meteorological data of MeteoSwiss (Global Atmosphere Watch) are highly appreciated. In addition, we thank the International Foundation High

Altitude Research Stations Jungfraujoch and Gornergrat (HFSJG), which made it possible for us to carry out our experiments at the High Altitude Research Station at Jungfraujoch. We also thank Tad Anderson for providing us with the angular sensitivity function of the TSI 3563 nephelometer and Martin Gysel for fruitful discussions about hygroscopic growth factors.

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Received for review December 23, 2003. Revised manuscript received December 4, 2004. Accepted December 15, 2004. ES035450G