Calibration and measurement uncertainties of a continuous-flow cloud condensation nuclei counter (DMT-CCNC): CCN activation of ammonium sulfate and sodium chloride aerosol particles in theory and experiment

Experimental and theoretical uncertainties in the measurement of cloud condensation nuclei (CCN) with a continuous-flow thermal-gradient CCN counter from Droplet Measurement Technologies (DMT-CCNC) have been assessed by model calculations and calibration experiments with ammonium sulfate and sodium chloride aerosol particles in the diameter range of 20–220 nm. Experiments have been performed in the laboratory and during field measurement campaigns, covering a wide range of instrument operating conditions (650–1020 hPa pressure, 293–303 K inlet temperature, 4–34 K m −1 temperature gradient, 0.5–1.0 L min −1 flow rate). For each set of conditions, the effective water vapor supersaturation ( S eff , 0.05–1.4%) was determined from the measured CCN activation spectra (dry particle activation diameters) and Kohler model calculations. High measurement precision was achieved under stable laboratory conditions, where the relative standard deviations of S eff were as low as ±1%. During field measurements, however, the relative deviations increased to about ±5%, which can be mostly attributed to variations of the CCNC column top temperature with ambient temperature. The observed dependence of S eff on temperature, pressure, and flow rate was compared to the CCNC flow model of Lance et al. (2006). At high S eff the relative deviations between flow model and experimental results were mostly less than 10%, but at S eff ≤0.1% they exceeded 40%. Thus, careful experimental calibration is required for high-accuracy CCN measurements – especially at low S eff . A comprehensive comparison and uncertainty analysis of the various Kohler models and thermodynamic parameterizations commonly used in CCN studies showed that the relative deviations between different approaches are as high as 25% for (NH 4 ) 2 SO 4 and 12% for NaCl. The deviations were mostly caused by the different parameterizations for the activity of water in aqueous solutions of the two salts. To ensure comparability of results, we suggest that CCN studies should always report exactly which Kohler model equations and parameters were used. Provided that the Aerosol Inorganics Model (AIM) can be regarded as an accurate source of water activity data for highly dilute solutions of (NH 4 ) 2 SO 4 and NaCl, only Kohler models that are based on the AIM or yield similar results should be used in CCN studies involving these salts and aiming at high accuracy. Experiments with (NH 4 ) 2 SO 4 and NaCl aerosols showed that the conditions of particle generation and the shape and microstructure of NaCl particles are critical for their application in CCN activation experiments (relative deviations up to 18%).

particles in the diameter range of 20-220 nm. Experiments have been performed in the laboratory and during field measurement campaigns, extending over a period of more than one year and covering a wide range of operating conditions (650-1020 hPa ambient pressure, 0.5-1.0 L min −1 aerosol flow rate, 20-30 • C inlet temperature, 4-34 K m −1 temperature gradient). For each set of conditions, the effective water vapor 10 supersaturation (S eff ) in the CCNC was determined from the measured CCN activation spectra and Köhler model calculations.
High measurement precision was achieved under stable laboratory conditions, where relative variations of S eff in the CCNC were generally less than ±2%. During field measurements, however, the relative variability increased up to ±5-7%, which can 15 be mostly attributed to variations of the CCNC column top temperature with ambient temperature.
To assess the accuracy of the Köhler models used to calculate S eff , we have performed a comprehensive comparison and uncertainty analysis of the various Köhler models and thermodynamic parameterizations commonly used in CCN studies. For Substantial differences between the CCNC calibration results obtained with (NH 4 ) 2 SO 4 and NaCl aerosols under equal experimental conditions (relative deviations of S eff up to ∼10%) indicate inconsistencies between widely used activity parameterizations derived from electrodynamic balance (EDB) single particle experiments (Tang and Munkelwitz, 1994;Tang, 1996) and hygroscopicity tandem 10 differential mobility analyzer (HTDMA) aerosol experiments (Kreidenweis et al., 2005). Therefore, we see a need for further evaluation and experimental confirmation of preferred data sets and parameterizations for the activity of water in dilute aqueous (NH 4 ) 2 SO 4 and NaCl solutions.
The experimental results were also used to test the CCNC flow model of Lance vapor supersaturation is established along the centerline of the column. The aerosol sample enters the column at the top center of the column, and particles with a critical supersaturation less than the centerline supersaturation are activated as CCN (for definitions of supersaturation and critical supersaturation see Sect. 3.1). The residence time in the column (∼6-12 s, depending on flow rate) enables the activated 15 particles to grow into droplets that are sufficiently large (>1 µm) to be detected separately from unactivated particles (usually <<1 µm). An optical particle counter (OPC) at the exit of the column determines the concentration and size distribution of droplets in the size range of 0.75-10 µm. Droplets larger than 1 µm are considered to be activated CCN. 20 The effective water vapor supersaturation (S eff ) in the CCNC is determined by ∆T=T 3 −T 1 , which is the temperature difference between the top (T 1 , set ∼3 K higher than the sample temperature) and the heated bottom of the column (T 3 , maximum ∼50 • C, limited by OPC operating conditions). In this study, ∆T and S eff have been varied in the range of 2-17 K (corresponding to gradients of 4-34 K m −1 ) and 25 0.05-1.3%, respectively. Shifting from one supersaturation level to another requires approximately 0.5-3.5 min, depending on the size of the step, and whether it is from lower to higher supersaturations (shorter time) or vice versa (longer time). The calibration setup used in this study was similar to the one described by Frank et al. (2006b), and is illustrated in Fig. 1. Calibration aerosol was generated by nebulization of an aqueous salt solution (solute mass concentration ∼0.01%) of ammonium sulfate ((NH 4 ) 2 SO 4 , purity >99.5%, supplier: E. Merck, Darmstadt) or 5 sodium chloride (NaCl, purity >99.99%, supplier: Alfa Aesar GmbH & Co KG), using a TSI 3076 Constant Output Atomizer operated with particle-free pressurized air (2.5 bar, 2 L min −1 ). The polydisperse aerosol was dried to a relative humidity of <15% by dilution with particle-free dry air (∼30 L min −1 ). The excess flow was vented through a filter (HEPA) or into a fume hood/exhaust line, where care was taken to keep 10 overpressure in the system as low as possible (mostly <20 Pa). The dry aerosol (0.5-2 L min −1 ) was passed through a bipolar charger/radioactive neutralizer 555 MBq) to establish charge equilibrium, and a differential mobility analyzer (DMA; TSI 3071 Electrostatic Classifier) with closed loop sheath air flow (10 L min −1 ) was used to select monodisperse particles. To adjust the particle number concentration, 15 the monodisperse aerosol was diluted with particle free air (0-1 L min −1 ) in a small mixing chamber (glass, ∼10 cm 3 , built in-house) at the DMA outlet. After dilution, the monodisperse aerosol flow was split into two parallel lines and fed into a condensation particle counter (CPC; TSI 3762; 1 L min −1 ) and into the CCNC (0.5-1 L min −1 ). For the calibration experiments, the number concentration of monodisperse aerosol particles 20 was kept below ∼3×10 3 cm −3 to avoid counting errors caused by coincidence.

Determination of 50% activation diameters
In every calibration experiment, the CCNC was operated at five different ∆T values in the range of 2-17 K. For each ∆T, multiple scans were performed, in which the Introduction EGU range of 18-220 nm. At each D, the number concentration of total aerosol particles (condensation nuclei, CN) was measured with the CPC, and the number concentration of CCN was measured with the CCNC (∼60 s waiting time to adjust to the new particle concentration plus 20-30 s averaging time). The activated particle fraction, or CCN efficiency (CCN/CN), was calculated from the averaged concentrations of CN and 5 CCN. From every scan of particle diameters at constant ∆T, we obtained a spectrum of CCN/CN over D ranging from no activation to full activation. The CCN efficiency spectrum was fitted with a cumulative normal distribution function using a nonlinear least-squares fitting routine (Gauss-Newton method, Matlab, MathWorks, Inc.): (1) 10 where erf is the error function, a is the maximum value of f CCN/CN , D 50 is the particle diameter at f CCN/CN =a/2, and σ is the standard deviation of the cumulative normal distribution function. Exemplary CCN efficiency spectra and their fits are illustrated in Fig. 2a.
When the DMA selects particles of a given electrical mobility, the particles are 15 not all singly charged. There are also multiply (mostly doubly) charged particles that have the same electrical mobility, but which are larger in diameter. Since the probability of three charges or more is rather low, only doubly charged particles will be mentioned here. Because of their larger diameter, the doubly charged particles activate at a lower supersaturation than the singly charged particles of the same electrical 20 mobility. Therefore, doubly charged particles appear in the activation curve (CCN/CN vs. D) of a chemically homogeneous aerosol as a plateau at smaller diameters (see Figs. 2a and 3). The height of this plateau corresponds to the number fraction of doubly charged particles. It usually becomes larger for larger particle sizes (i.e., smaller supersaturations), because the probability of double charges becomes higher 25 (Wiedensohler, 1988). Furthermore, the height of this plateau depends on the shape of the number size distribution of the generated aerosol particles. The broader the size distribution is, the higher is the concentration of large particles, and the higher 8200 Introduction EGU is the fraction of doubly charged particles selected by the DMA. When the fraction of activated doubly charged particles detected among the CCN is high, it is necessary to correct the activation curves for this bias. The effect of this correction on further calculations will be discussed in Sect. 4.1. The correction can be done by calculating the amount of doubly charged particles from the number size distribution of measured 5 aerosol particles assuming a bipolar charge distribution and then subtracting them from the CCN/CN ratio as described in Frank et al. (2006a). An alternative method to fit the activation curves so that only the information from the singly charged particles is used, is to fit the sum of two cumulative Gaussian distribution functions to the measured CCN efficiency spectrum. This method yields 6 fit parameters defined in analogy to 10 Eq.
(1) (a 1 , a 2 , σ 1 , σ 2 , D 50,1 , D 50,2 ). The midpoint of the first, lower distribution function (D 50,1 ) can be regarded as the diameter at which half of the doubly charged particles are activated; the midpoint of the second, upper distribution function (D 50,2 ) is taken as the diameter at which half of the singly charged particles are activated (D 50 ). However, this technique is only applicable when there are enough data points at the plateau of 15 the doubly charged particles to be fitted. This method also makes the assumption that the fraction of doubly charged particles is constant over the whole size range. A simpler method to correct the activation curves for doubly charged particles is to determine their fraction from the level of the smaller plateau in the activation curve and to subtract this value from the CCN/CN ratio at each diameter, assuming that the 20 fraction of activated doubly charged particles is constant over the whole particle size range. The activated fraction of singly charged particles can then be calculated as follows: In this equation the indices "1" or "2" refer to the fraction of singly or doubly charged 25 particles of a variable. The indices "1+2" describes the measured concentration or fraction consisting of singly and doubly charged particles, respectively. (1) is fitted to the corrected CCN efficiency spectrum to obtain D 50 .

Determination of effective supersaturation (S eff )
The diameter at which 50% of the monodisperse aerosol particles are activated, i.e., D 50 as obtained from the fit to the experimental data, can be regarded as the critical dry particle diameter for CCN activation, D c , i.e., the effective diameter which 5 is required for particles of the given composition to be activated as CCN at the given supersaturation. According to Köhler theory (Sect. 3), D c can be related to a critical supersaturation, S c , which is the minimum supersaturation required to activate particles of the given size and composition as CCN, and can be calculated from basic physicochemical parameters of the particle material in aqueous solution. Therefore, Köhler model calculations as detailed in Sect. 3 (model VH4.1 unless mentioned otherwise) were used to derive S c from D 50 . S c can be regarded as the effective water vapor supersaturation in the CCNC (S eff ) at the given operating conditions (∆T, p, T 1 , Q). From each of the multiple CCN efficiency spectra recorded at each of the 15 temperature differences investigated within a calibration experiment, we obtained one data point in a calibration diagram of S eff vs. ∆T. A linear calibration function, f s =k s ∆T + S 0 , was obtained by a linear least-squares fit to these data points. One exemplary calibration line is illustrated in Fig. 2b EGU difference (∆T inner ) between the exit and the entrance of the column. Lance et al. (2006) compared the simulated instrument responses for calibration aerosol against actual measurements. They indicated that the supersaturation strongly depends on ∆T inner which may be only a fraction of the temperature difference imposed by the TECs at the outer wall of the column (∆T =T 3 −T 1 ). It is assumed that the inner 5 temperature at the entrance of the column (T 1,inner ) equals the entrance temperature measured outside the column, i.e., T 1 . The temperature drop across the wall -the quotient of ∆T inner to ∆T -is called the thermal efficiency η (η≤1) and varies with the operating conditions. η has to be determined to predict the S eff of the instrument and can be calculated if the thermal resistance (R T ) of the column is known. R T is a 10 material property and varies between instruments. Following the procedure suggested by Lance et al. (2006), we calibrated the thermal resistance of our instrument before estimating the thermal efficiency and the supersaturation in the CCNC under different operating conditions. The supersaturation was first determined experimentally by calibrating the CCN counter with ammonium 15 sulfate particles of known size at different ∆T values and inferring S eff by converting the critical diameter into S c via Köhler theory. The VH4. 3 Köhler model (cf. Sect. 3.4) was used to calculate S c , because the parameters B 1 − B 5 of Lance et al. (2006) were based on a van't Hoff factor model with i s =3. The calibration line (S eff vs. ∆T ) did not go through the origin of the coordinate system, but intercepted the x-axis at a certain 20 ∆T 0 (cf. Fig. 2b). Since the model assumes that S=0 if ∆T inner =0 and thus ∆T =0, we shifted the calibration line to the left by subtracting its ∆T 0 from each ∆T, which led to a new calibration line of S eff vs. ∆T* (∆T*=∆T -∆T 0 ). Each pair of ∆T* and S eff was taken to determine ∆T inner by solving Eq. (16) in Lance et al. (2006) iteratively. The thermal efficiency η was calculated dividing ∆T inner by ∆T*. The thermal resistance 25 R T , valid for our CCNC unit, was calculated by solving Eq. (15) in Lance et al. (2006). R T was used to model the effective supersaturation for any operating condition (T 1 , p, Q) of the CCNC. For a given ∆T, ∆T* was calculated by subtracting a mean value of ∆T 0 =1 K and inserted into Eq. (15) in Lance et al. (2006)

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wall temperature difference, ∆T inner , was determined by multiplication of η with ∆T*, and finally, S eff was calculated using Eq. (16) in Lance et al. (2006).

Köhler theory and models
In this section, consistent and precise specifications and distinctions of different types of Köhler models frequently used to calculate critical supersaturations for the CCN 5 activation of ammonium sulfate and sodium chloride particles will be presented. Model results and differences will be compared and discussed in Sect. 4.6.

Basic equations and parameters
According to Köhler theory (Köhler, 1936;Pruppacher and Klett, 1997;Seinfeld and Pandis, 1998), the condition necessary for an aqueous solution droplet to be in equilibrium with water vapor in the surrounding gas phase can be expressed by the following basic equation (Kreidenweis et al., 2005;Koehler et al., 2006): The water vapor saturation ratio, s, is defined as the ratio of the actual partial pressure of water to the equilibrium vapor pressure over a flat surface of pure water at the 15 same temperature. Expressed in percent, s is identical to the relative humidity (RH), which is typically used to describe the abundance of water vapor under sub-saturated conditions. Under supersaturated conditions (s>1, RH>100%), it is customary to describe the abundance of water vapor by the so-called supersaturation S, which is expressed in percent and defined by: a w is the activity of water in the aqueous solution, and Ke is the so-called Kelvin term, which describes the enhancement of the equilibrium water vapor pressure due to surface curvature.

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Under the common assumption that the partial molar volume of water can be approximated by the molar volume of pure water (Kreidenweis et al., 2005), the Kelvin term for a spherical aqueous solution droplet with the diameter D wet is given by: M w and ρ w are the molar mass and density of water, and σ sol is the surface tension of 5 the solution droplet. R and T are the universal gas constant and absolute temperature, respectively. Deviations from this approximation are generally negligible for the dilute aqueous solution droplets formed by hygroscopic salts like ammonium sulfate and sodium chloride at s≈1 (Brechtel and Kreidenweis, 2000;Kreidenweis et al., 2005). To describe a w and σ sol as a function of droplet composition, various types of equations, 10 parameterizations, and approximations have been proposed and can be used as detailed below. For a given type and mass of solute (dissolved substance), a plot of s vs. D wet generally exhibits a maximum in the region where s>1 and S>0. The saturation ratio and supersaturation at this maximum are the so-called critical saturation s c and 15 critical supersaturation S c , respectively, which are associated with the so-called critical droplet diameter, D wet,c . Droplets reaching or exceeding this diameter can freely grow by condensation of water vapor from the supersaturated gas phase and form cloud droplets (Pruppacher and Klett, 1997;Seinfeld and Pandis, 1998).
Aerosol particles consisting of soluble and hygroscopic substances, such as 20 ammonium sulfate and sodium chloride, generally take up water vapor and already form aqueous solution droplets at s<1 (hygroscopic growth). The ratio of the droplet diameter, D wet , to the diameter of a compact spherical particle consisting of the dry solute, D s (mass equivalent diameter of the dry solute particle), is defined as the (mass equivalent) growth factor of the dry solute particle, g s :

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x s is the mass fraction of the solute in the droplet, and ρ s is the density of the dry solute (cf. Table 1). Equations (3), (5), and (6) can be used to describe the hygroscopic growth and CCN activation of aerosol particles (D wet as a function of s -or vice versa -for any given value of D s ), if a w , ρ sol , and σ sol are known as a function of droplet composition, which is usually described by the solute mass fraction x s , molality µ s , or 5 molarity c s . The molality is defined as the amount of substance (number of moles) of solute, n s =m s M −1 s , divided by the mass of solvent, i.e., by the mass of water in an aqueous solution, m w =n w M w . M s is the molar mass of the solute (cf. Table 1), m s is the mass of the solute, and n w is the amount of substance (number of moles) of water in the 10 solution.
The molarity is defined as the amount of substance divided by the volume of the solution in units of mol L −1 . Mass fraction, molality, and molarity of the solute are related by: The scaling factor 10 −3 m 3 L −1 is required to relate the molarity in mol L −1 to the other quantities, which are generally given in SI units. Depending on the types of parameterizations used to describe a w , ρ sol , and σ sol , different models can be used to calculate the critical supersaturation S c for any given 20 value of D s . The different options considered and compared in this study are outlined below and discussed in Sect. 4.6.
In the Köhler model calculations used for CCNC calibration, the experimentally determined critical dry particle diameter D c (i.e., the fit parameter D 50 , or a shape corrected value as detailed in Sect. 3.6) was taken as the dry solute mass equivalent Introduction EGU diameter D s , corresponding to a solute mass of m s =π 6 ρ s D 3 s . The CCNC column top temperature (T 1 ) was taken as the model temperature T .

Activity parameterization (AP) models
For the activity of water in aqueous solution droplets of (NH 4 ) 2 SO 4 , NaCl, and other salts, Tang and Munkelwitz (1994) and Tang (1996) have presented parameterizations 5 derived from electrodynamic balance (EDB) single particle experiments as polynomial fit functions of solute mass percentage (100 x s ): The polynomial coefficients a q for (NH 4 ) 2 SO 4 and NaCl at 298 K are listed in Table 2.
An alternative parameterization of a w has been proposed by Kreidenweis et al. (2005), who derived the following relation between a w and the growth factor of dry solute particles (g s ) determined in measurements with a hygroscopicity tandem differential mobility analyzer (HTDMA): The coefficients k a , k b , and k c for (NH 4 ) 2 SO 4 and NaCl are listed in Table 2.

15
Low (1969) provided a table of a w for ammonium sulfate and sodium chloride for molalities of 0.1-6 mol kg −1 . For the calculation of S c , however, this range of molalities is insufficient and has to be extrapolated below 0.1 mol kg −1 . We have tested this approach with a third order polynomial fit, but the results were very different from the parameterizations given above (deviations up to a factor of 2 in S c ) and are not 20 discussed any further. For the density of aqueous solution droplets of (NH 4 ) 2 SO 4 , NaCl, and other salts, Tang and Munkelwitz (1994) and Tang (1996) ρ w is the density of pure water in kg m −3 (e.g., 997.1 kg m −3 at 298 K) and the coefficients for (NH 4 ) 2 SO 4 and NaCl at 298 K are listed in Table 3.

5
Under the assumption of volume additivity (partial molar volumes of solute and solvent in solution are equal to molar volumes of pure substances; Mikhailov et al., 2004), ρ sol can also be calculated by The simplest parameterization of ρ sol used in this study was approximating it by the 10 density of pure water, either with a constant value of 997.1 kg m −3 or a temperature dependent one. The temperature dependence of the density of pure water can be described by Pruppacher and Klett (1997): Here t is the temperature in • C (t=T -273.15 K) and A 0 =999.8396 kg m −3 , The deviations caused by using different parameterizations and approximations of ρ sol turned out to be small, as will be detailed below (Sect. 4.6). 20 For the surface tension of aqueous salt solution droplets, Seinfeld and Pandis (1998) proposed the following parameterization: for NaCl. σ w is the surface tension of pure water as detailed below, and c s is the molarity of the solute. Alternative concentration-dependent parameterizations (Hänel, 1976;Weast and Astle, 1982;Chen, 1994;Gysel et al., 2002) exhibited only small deviations in σ w in the concentration range of interest (<1% for µ s <1 mol kg −1 ).

5
The simplest parameterization of σ sol used in this study was approximating it by the surface tension of pure water, either with a constant value of 0.072 N m −1 or a temperature dependent one. According to Seinfeld and Pandis (1998), the temperature dependence of the surface tension of pure water can be described by: Combination of Eqs. (3), (5), and (6) leads to the following version of the Köhler equation, which was taken as the basis for all activity parameterization (AP) model calculations: Depending on the applied type of water activity parameterization, we distinguish two 15 types of AP models: AP1 using the mass percentage-based parameterizations of Tang and Munkelwitz (1994) and Tang (1996), and AP2 using the growth factor-based parameterizations of Kreidenweis et al. (2005). In AP1 model calculations, x s was taken as the primary variable to calculate a w from Eq. (9); ρ sol from Eq. (11) with ρ w from Eq. (13); g s from Eq. (6); σ sol from Eq. (14) with 20 σ w from Eq. (15) and c s from Eq. (8); and s from Eq. (16) (base case AP1.1, Table 5). The maximum value of s (critical saturation ratio, s c ) was determined by the variation of x s (numerical minimum search for -s with the 'fminsearch' function, Matlab software), and via Eq. (4) it was converted into the corresponding critical supersaturation S c . In sensitivity studies investigating the influence of various simplifications and Introduction EGU were exchanged as detailed in Table 5, but the basic calculation procedure remained unchanged (test cases AP1.2-AP1.5). In AP2 model calculations, a w was taken as the primary variable to calculate g s from Eq. (10); ρ sol from Eq. (12) with ρ w from Eq. (13); x s =m s (m s +m w ), and m w =π 6 ρ w D 3 s g 3 s − 1 (volume additivity assumption); σ sol from Eq. (14) with σ w 5 from Eq. (15) and c s from Eq. 8; and s from Eq. (16) (base case AP2, Table 5). The maximum value of s (critical saturation ratio) was determined by variation of a w (numerical minimum search for -s with the 'fminsearch' function, Matlab software), and via Eq. (4) it was converted into the corresponding S c .

Osmotic coefficient (OS) models
10 According to Robinson and Stokes (1959), the activity of water in aqueous solutions of ionic compounds can be described by: ν s is the stoichiometric dissociation number of the solute, i.e., the number of ions per molecule or formula unit (ν NaCl =2, ν (NH 4 ) 2 SO 2 =3). Φ s is the molal or practical osmotic 15 coefficient of the solute in aqueous solution, which deviates from unity if the solution is not ideal (incomplete dissociation, ion-ion and ion-solvent interactions). Based on an ion-interaction approach, Pitzer and Mayorga (1973) derived semiempirical parameterizations, which describe Φ s as a function of solute molality µ s . The general form for electrolytes dissociating into two types of ions is: ν 1 and ν 2 are the numbers of positive and negative ions produced upon dissociation per formula unit of the solute (ν s =ν 1 +ν 2 ); z 1 and z 2 are the numbers of elementary charges carried by the ions ((NH 4 ) 2 SO 4 ν 1 =z 2 =2 and ν 2 =z 1 =1; NaCl ν 1 =ν 2 =z 1 =z 2 =1). EGU ionic strength is given by I=0.5 µ s (ν 1 z 2 1 + ν 2 z 2 2 ). A Φ is the Debye-Hückel coefficient which has the value 0.3915 (kg mol −1 ) 1/2 for water at 298.15 K. The parameters α and b are 2 (kg mol −1 ) 1/2 and 1.2 (kg mol −1 ) 1/2 , respectively. The coefficients β 0 , β 1 and C Φ depend on the chemical composition of the solute and have been tabulated by Pitzer and Mayorga (1973) for over 200 compounds (1:1, 1:2, and 2:1 electrolytes).

5
For ammonium sulfate and sodium chloride, at 298.15 K, the respective values and more recent updates from Mokbel et al. (1997) are listed in Table 4. The OS model calculations were performed in analogy to the AP1 model calculations as detailed above (with x s as the primary variable for the calculation of other parameters), except that a w was calculated from Eq. (17) with Φ s from Eq. (18) and µ s from Eq. (7).

Van't Hoff factor (VH) models
According to McDonald (1953) and the early cloud physics literature, the activity of water in aqueous solutions of ionic compounds can be described by the following form of Raoult's law, where the effects of ion dissociation and interactions are represented by the so-called van't Hoff factor, i s : For strong electrolytes such as ammonium sulfate and sodium chloride, the van't Hoff factor is similar to the stoichiometric dissociation number, and deviations of i s from ν s can be attributed to solution non-idealities (incomplete dissociation, ion-ion and ion-solvent interactions). The exact relation between i s and ν s or Φ s is given by 20 equating Eqs. (17) and (19). As detailed by Kreidenweis et al. (2005), the resulting equation can be approximated by a series expansion of the exponential term in Eq. (17), inserting n s n w =µ s M w (cf. Eq. 7) and truncation of the series. It follows then that:

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Deviations from this approximation are negligible for the dilute aqueous solution droplets formed by hygroscopic salts such as ammonium sulfate and sodium chloride at s≈1 (molalities <0.01 mol kg −1 ; relative magnitude of quadratic and higher terms of series expansion <1%). Combination of Eqs. (16) and (17) with µ s =m s (M s m w ), m w =π 6 D 3 wet ρ sol −m s , 5 g s D s =D wet , and i s ≈ν s Φ s leads to: For the dilute aqueous solution droplets formed by hygroscopic salts like ammonium sulfate and sodium chloride at s≈1, the contribution of the solute to the total mass of the droplet is low (m s /(π/6 D 3 wet ρ sol )<4% at D s =20 nm and <0.1% at 200 nm). If m s is 10 neglected, Eq. (21) reduces to: For the dilute salt solution droplets, differences between ρ w and ρ sol (<3% at D s =20 nm, <0.1% at 200 nm) and between σ sol and σ w (<1% at D s =20 nm, ∼0% at 200 nm) are also relatively small. With the approximations of ρ sol ≈ρ w and σ sol ≈σ w , Eq. (22) can be transformed into the following simplified and widely used form of the Köhler equation (e.g., Pruppacher and Klett, 1997; Seinfeld and Pandis, 1998):  (25) Under the assumption of complete dissociation and ideal solution behavior (Φ s =1), the van't Hoff factor is i s =2 for NaCl and i s =3 for (NH 4 ) 2 SO 4 solutions. For NaCl this approximation is quite common and the deviations from experimental results are small Gerber et al., 1977), but for (NH 4 ) 2 SO 4 it has been shown that i s has to be between 2 and 2.5 to achieve agreement between measured and calculated droplet diameters (Gerber et al., 1977;Pradeep Kumar et al., 2003). McDonald (1953) already remarked that the van't Hoff factor is not a constant value, but varies with the solute molality. Low (1969) The van't Hoff factor for ammonium sulfate was also parameterized by Young and 15 Warren (1992): (27) which is also valid for smaller molalities.
A further simplified Köhler equation (Eq. 22) was used to make VH3 model calculations. µ s was taken as a primary variable to calculate i s . i s , x s , ρ w , ρ sol , and σ sol were calculated as in VH1; D wet as in VH2; all parameters were inserted into Eq. (22) to calculate s. 10 The VH4 model used Eq. (23) to calculate s. µ s was taken as a primary variable to calculate i s . i s , x s , ρ w , σ w were calculated as in VH1. D wet was calculated from Eq. (6) which required the parameterization of ρ sol . Because the Köhler equation used for VH4 was derived assuming ρ sol as ρ w , the same approximation was also used to calculate D wet .
15 For all VH model calculations, the maximum value of s was determined by variation of µ s (numerical minimum search for -s with the 'fminsearch' function, Matlab software). The critical supersaturation S c was calculated from the maximum of s using Eq. (4).
In sensitivity studies investigating the influence of simplifications and approximations, individual parameterizations were exchanged as detailed in  (Seinfeld and Pandis, 1998): In the AA model calculations presented below, the widely used approximation A ∼ = 0.66 K T was inserted for the Kelvin term parameter A as defined in Eq. (24) (Seinfeld and Pandis, 1998) and different van't Hoff factors were tested (i s =2.2 or 3 5 for ammonium sulfate; i s =2 for sodium chloride). A comparison and discussion of critical supersaturations calculated with the different AP, OS, VH, and AA models specified above is given in Sect. 4.6. Unless mentioned otherwise the VH4.1 model has been used for CCNC calibration.
3.6 Particle shape corrections 10 Sodium chloride particles generated by nebulization of a NaCl solution and subsequent drying are usually of cubic shape (Scheibel and Porstendörfer, 1983;Krämer et al., 2000;Mikhailov et al., 2004). In a DMA, the particle size is selected according to the electrical mobility diameter, which assumes a spherical shape of the particles. In the case of cubic particles the diameter selected by the DMA would be overestimated by 15 4-5% which would thus result in an underestimation of the calculated S c . Therefore, it is necessary for the diameter to be corrected for the particle shape, which can be done as described, e.g., in Krämer et al. (2000). A shape factor χ is introduced, which is defined as the ratio of the drag force experienced by the particle in question to that of a sphere of equivalent mass: D B is the mobility equivalent diameter of the particle, i.e., the diameter which is selected by the DMA, D m is the mass equivalent diameter, i.e., the corrected diameter which 8215 Introduction EGU has to be used for further Köhler model calculations, and C(D B ) and C(D m ) are the slip correction factors for the respective diameters D B and D m . C(D) can be approximated by the empirical relation (Willeke and Baron, 2001): in which λ is the mean free path of the gas molecules (λ=68 nm in air at 298 K and 5 atmospheric pressure).
In a calibration of the CCNC using particles generated by an aqueous solution of sodium chloride, the particle size selected by the DMA is the electrical mobility diameter (D=D B ). The mobility equivalent diameters D B have to be transformed into mass equivalent diameters D m via Eq. (29). Using Eq. (30), Eq. (29) has to be solved 10 iteratively for D m , setting χ =1.08 as a shape factor for cubic shaped particles. The so determined D m are taken as the mass equivalent diameters of the dry salt particles (D s ) and used for all further calculations (such as determining D 50 using Eq. (1), and calculating S c as described in Sects. 3.1 to 3.5).
The nebulization of an ammonium sulfate solution is generally assumed to generate 15 particles of near-spherical shape. Recent investigations indicate that shape corrections may also be required for ammonium sulfate particles in studies aimed at high accuracy (Eugene Mikhailov, personal communication EGU effective water vapor supersaturation in the CCN counter, S eff . As outlined in Sect. 2.3, CCN efficiency spectra recorded by particle size selection with a differential mobility analyzer can be influenced by doubly charged particles (cf. Fig. 2a) which interfere with the determination of D 50 . The measured spectrum in Fig. 3a exhibits a high fraction of activated doubly 5 charged particles (plateau level ∼0.17). The fit with a single cumulative Gaussian distribution function (Eq. 1) strongly deviated from the measured data points and gave a D 50 value ∼2% smaller than the value obtained by fitting with two distribution functions. After correcting the measured spectrum with Eq.
(1) to the corrected spectrum gave the same D 50 value as the fit of two distribution functions 10 to the uncorrected spectrum, which can be regarded as the actual particle diameter of 50% activation. The ∼2% increase of D 50 led to a ∼3% relative decrease of the effective supersaturation determined by Köhler model calculations. The measured spectrum in Fig. 3b exhibits a low fraction of activated doubly charged particles (plateau level ∼0.06), and the fit with a single cumulative Gaussian distribution function (Eq. 1) agrees 15 well with all data points at CCN/CN >0.1. Therefore, the D 50 value obtained from this fit was only ∼0.5% smaller than the values obtained after correcting the spectrum with Eq. (2), or fitting with two distribution functions, and the relative change of S eff was only 0.7%. In our study, the observed fraction of activated doubly charged particles was 20 generally in the range of 0-0.25. In most cases the fraction was < 0.1 and a single cumulative Gaussian distribution (Eq. 1) fitted to the data points was used to determine D 50 (relative deviations of D 50 and S eff ≤1%). For plateau levels >0.1, two cumulative Gaussian distributions were used.

Measurement precision within a calibration experiment
25 Figure 2a shows the CCN efficiency curves and In this calibration experiment, the plateau level of activated doubly charged particles was <0.05 for all scans. The CCN efficiency spectrum was not corrected for doubly 5 charged particles, because in the previous section it was shown that their effect is <1% on S eff for such a small level. The fitting of a cumulative Gaussian distribution (Eq. 1) to the measured spectrum was used to determine D 50 . The D 50 values obtained from the fits were 178, 61, 45, 33, and 26 nm for the 5 different ∆T values (1.8, 5.1, 7.7, 11.7, and 15.6 K). The 95% confidence interval for D 50 was, on average, less than 2 nm, 10 which confirms the skill of the fit function used. The standard deviation of D 50 at a given temperature difference was very small, when the measurements were performed at nearly constant surrounding conditions (constant ambient pressure and temperature) over many hours (15 repeats per ∆T ; with a variation in ∆T of around ±0.03 K). It decreased with increasing supersaturation, ranging from 0.3-1.4% in diameter.

15
Using the D 50 values obtained from the CCN efficiency spectra, critical supersaturations S c were calculated as described in Sect. 3.4 using the VH4.1 model, and these were taken as the effective supersaturations in the CCNC, S eff . The supersaturations corresponding to the 5 set ∆T s (as mentioned above) were 0.06, 0.32, 0.52, 0.84, and 1.22%. The relative uncertainty in the supersaturation due to the 20 measurement uncertainty of D 50 (i.e., standard deviation of D 50 ) was as much as 2.2% (relative). The uncertainty decreased with increasing supersaturation.
From each CCN efficiency spectrum, the derived S eff was plotted versus the applied ∆T, and a linear calibration function was obtained by fitting (cf. Fig. 2b)  EGU higher supersaturations (S eff >0.1%), however, the calibration line agreed very well with the experimental data points (relative deviations ≤3%).

Variability within and between different measurement campaigns
We have operated our DMT-CCNC at a variety of locations and elevations. Calibration measurements were made during two one-month field campaigns in Guangzhou   5 and Beijing, China, at our home laboratory in Mainz, Germany, at a laboratory in Leipzig, Germany, and at two mountain stations, Hohenpeissenberg, Germany, and Jungfraujoch, Switzerland (Figs. 4a-d). In the first campaign in Guangzhou (Fig. 4a), the CCNC was running with a flow rate of 0.5 L min −1 at close to standard atmospheric pressure, and T 1 varied between 25 and 30 • C. A mean calibration line was calculated 10 to provide an average S eff to ∆T relationship over the whole field campaign. Here, the first calibration measurement was not taken into account, because it was measured at a T 1 that was much higher than during the rest of the campaign. It is evident that, in spite of the small variations in T 1 (25 to 26.7 • C), the measured calibration lines differed significantly from the mean line, and exhibited maximum deviations in S eff from the 15 average supersaturation of 5-7% (relative). The calibration lines from the second campaign in Beijing (Q=0.5 L min −1 , p≈1020 hPa; Fig. 4b), also scattered over time. Here, the maximum deviations in S eff from the average supersaturation were also in the range of 5-7%, although the variations in T 1 were a little more (25.4 to 29 • C).

20
Before and after each field campaign, we always calibrated the CCNC in our home laboratory (Mainz, p≈1020 hPa). In December 2005, we performed a calibration measurement using the same experimental setup over several days. The instrument was stopped in between measurement runs only to make small changes (change of dilution flow, liquid flow, etc.). The period was divided into five individual calibration 25 experiments with the resulting calibration lines shown in Fig. 4c. The five calibration lines differed from an average curve by up to 2% (relative) in supersaturation.
In 2006, we made three more calibrations experiments (Fig. 4c)

EGU
The time between each experiment was more than one month and the experimental setup was newly arranged every time. The three calibration lines obtained also scattered around a mean curve by up to 2-3% in supersaturation. From Fig. 4c, it can be seen that the slope of the mean calibration line was considerably smaller (10.4%) than it was for the measurements in December 2005. We assume that the 5 performance of the CCNC changed during this time. Over the complete one-year period, the supersaturation calibrated against ∆T in our laboratory varied by up to ±6% from the average S eff . Figure 4d shows the calibration lines measured during field campaigns at mountain stations (Hohenpeissenberg, 900 m a.s.l.; Mt. Jungfraujoch, 3570 m a.s.l.) and in a laboratory near sea level (Leipzig). It illustrates that the supersaturation obtained at a given ∆T decreases significantly with pressure, which will be discussed in more detail in Sect. 4.5.
For the two field campaigns on Mt. Jungfraujoch we found a similar long-term trend as for the lab experiments. The calibration line in 2007 has a 16% lower slope than 15 that in 2006, whereas the calibration lines within one campaign hardly differ from each other.

Application of the CCNC flow model
Four calibration experiments performed at different locations, altitudes and flow rates (cf. Table 5; MZ05, MZ10, JF05, JF08) were used to determine the thermal resistance 20 (R T ) of our CCN instrument according to the procedure described in Sect. 2.4 and based on the model described by Lance et al. (2006). Figure 5 shows the calculated R T as a function of ∆T. It can be seen that R T varies with ∆T, and differs between the different calibration runs. The overall average R T calculated for ∆T ≥3 K was 1.78 K W −1 , which was assumed to be the valid thermal resistance for our CCNC

EGU
Using the average R T , the calibration lines of the example conditions shown in Table 7 were modeled as described in Sect. 2.4 and compared with the experimentally determined curves (Fig. 6). Except for the calibration experiment MZ10, the modeled lines agree well with the experimentally determined curves -also for HP05, which had not been included in the determination of R T . Only in the low supersaturation range 5 (<0.1%) did the model deviate strongly from the measured S eff by up to 28% (relative). At high S eff , the relative deviations between model predictions and measurement values were on average +0.4% for MZ05, -3.5% for JF08, +2.3% for JF05, and +5.8% for HP05. Individual data points deviated by up to ∼8%. For the MZ10 example, the modeled S eff was on average 73% too high. This discrepancy might be due to instabilities during the calibration experiment, indicated by relatively large deviations of the measured data points from linearity.
As outlined in Sect. 2.4, the parameterizations of Lance et al. (2006) used to determine the thermal resistance of the CCNC were based on a van't Hoff factor model with i s =3. Accordingly, the best agreement between flow model and experimental 15 calibration results was achieved when using the VH4.3 Köhler model to calculate S eff from D 50 . Figure 6 also shows the measured calibration lines for which the S eff was calculated using the VH4.1 Köhler model (the one that we used in general for our calculations). For the example cases MZ05, JF08, JF05, and HP05, the modeled S eff was then on average 11%, 14%, 8%, and 6% lower than the experimental S eff , 20 respectively. The modeled calibration line for MZ10 agreed better with the experimental data calculated with the VH4.1 Köhler model than with the experimental data calculated with VH4.3, but especially the low S eff were still up to ∼60% too high. 4.5 Dependence of supersaturation on temperature, pressure, and flow rate As shown in Sect. 4.3 (Fig. 4), the relation between S eff and ∆T depends on T 1 , p, 25 and Q. Here

EGU
To investigate the dependence of S eff on T 1 , we used all calibration lines measured at a flow rate of 0.5 L min −1 and standard atmospheric pressure to calculate S eff at ∆T =5 K, which corresponds to an inner-column temperature gradient of ∼8 K m −1 (subtraction of ∆T 0 ≈1 K and divison of ∆T*≈4 K by the column length of 0.5 m; cf. Sect. 2.4). When plotted against T 1 (Fig. 7a), the experimentally 5 determined S eff values exhibit a near linear decreasing trend with an average slope of ∆S eff /∆T 1 =-0.0057% K −1 . The observed dependence agrees fairly well with flow model calculations for the same conditions (Q=0.5 L min −1 , p=1020 hPa, and ∆T =5 K) yielding a slope of ∆S eff /∆T 1 =-0.0049% K −1 . Both values are of similar magnitude but somewhat higher than the -0.0034% K −1 calculated by Roberts and Nenes (2005) for 10 an inner-column temperature gradient of 8.3 K m −1 . Note, however, that the observed variability of S eff at T 1 ≈299 K was of similar magnitude as the observed and modeled differences between 296 K and 303 K. Figure 7b illustrates the dependence of S eff on pressure. All calibration lines presented in Fig. 4 were used to calculate the effective supersaturation at ∆T =5 K, and 15 the obtained values were plotted against pressure. The observed near-linear increase of S eff with p was 0.037% per 100 hPa at Q=0.5 L min −1 , which is of similar magnitude as the flow model result (0.027% per 100 hPa) and the value reported by Roberts and Nenes (2005) (∆S eff /∆p=+0.03% per 100 hPa for 0.5 L min −1 and dT /dZ=8.3 K m −1 ). Figure 7c shows the dependence of S eff on the flow rate of the CCNC. All calibration 20 lines measured at ∼1020 hPa and ∼650 hPa were used to calculate S eff at ∆T =5 K, and the obtained values were plotted against Q. The observed increase of S eff with Q was 0.029% per 0.1 L min −1 at sea level, and 0.042% per 0.1 L min −1 at high altitude. The model slopes were ∆S eff /∆Q=+0.048% per 0.1 L min −1 at 1020 hPa and ∆S eff /∆Q=+0.030% per 0.1 L min −1 at 650 hPa, respectively. The corresponding value 25 reported by Roberts and Nenes (2005) was somewhat higher: ∆S eff /∆Q=0.06 % per 0.1 L min −1 for 1000 hPa and dT /dZ=8.3 K m −1 . Figure 8 illustrates the observed average relative change of supersaturation

EGU
(∆S eff /S eff ) caused by changes of column top temperature, pressure, and flow rate as a function of ∆T.
The relative decrease of S eff with increasing T 1 was ∼2% K −1 at high ∆T and decayed near-exponentially to ∼0.5% K −1 at ∆T =2 K (Fig. 8a). The relative increase of S eff with increasing p was ∼1% per 10 hPa at high ∆T and grew near-exponentially to ∼ 2.3% 5 per 10 hPa at ∆T =2 K. At high ∆T the relative increase of S eff with increasing Q was ∼15% per 0.1 L min −1 for the measurements at p≈1020 hPa and ∼25% per 0.1 L min −1 at p≈650 hPa. For the 650 hPa measurements, the deviation increased with decreasing ∆T to up to ∼30% per 0.1 L min −1 at ∆T =2 K, but for the measurements at ≈1020 hPa it decreased to almost -30% per 0.1 L min −1 at ∆T =2 K. The latter is most likely due 10 to instabilities in the calibration experiment performed at 1 L min −1 and p≈1020 hPa (MZ10, cf. Fig. 6).

Deviations between different Köhler model calculations
To characterize the uncertainties related to Köhler model calculations, critical supersaturations were calculated for ammonium sulfate and sodium chloride particles To test the influence of different parameterizations of the solution density and surface tension on S c , we calculated S c for ammonium sulfate particles based on the AP1.1 model using alternative parameterizations for ρ sol and σ sol . Assuming volume additivity to calculate ρ sol (AP1.2), instead of calculating it from the experimental parameterizations by Tang and Munkelwitz (1994)  EGU by up to 1.5% and setting σ sol =0.072 N m −1 (AP1.5) caused a 2% lower S c at most. For all these test cases, the deviation in S c decreased with increasing particle diameter. For the largest diameters, the approximations of ρ sol and σ sol had no significant influence on S c . The same test cases, when applied to sodium chloride, brought smaller deviations 5 in S c than for ammonium sulfate, namely -0.1% for AP1.2, -0.4% for AP1.3, -0.6% for AP1.4, and -1% for AP1.5 at most. To investigate the different water activity parameterization models and their impact on S c , the model approaches of AP1.2, and AP2 were applied to both ammonium sulfate and sodium chloride particles. The parameterizations of ρ sol and σ sol were 10 fixed in each case. For ammonium sulfate, the S c calculated with a w by Kreidenweis et al. (2005) (AP2) was up to 2.7% higher than the S c calculated with a w by Tang and Munkelwitz (1994) (AP1.2). The deviation in S c decreased for smaller diameters down to a ∼1% lower S c for 20 nm. For sodium chloride, S c was ∼5% smaller for the AP2 model calculations than for AP1.2 over the whole diameter range.

15
The OS model was compared with the AP model and resulted, for ammonium sulfate, in a 7-15% lower S c (for 20 and 200 nm, respectively) with the OS model than with AP1.1. For sodium chloride, the S c was between 2.9 and 4.9% (for 200 and 20 nm, respectively) higher with the OS model. The VH1.1 model was compared with the AP1.1 model and resulted for ammonium sulfate in a 7.1 to 13.7% lower S c (for 20 20-200 nm, respectively) with the VH1.1 model than with AP1.1.
The results of the different VH models were compared for ammonium sulfate particles. Here, ρ sol and σ sol were parameterized as dependent on temperature and composition in all cases. For the van't Hoff factor, the composition dependent parameterizations (Eqs. 26 and 27) were always used. Only the Köhler equation was 25 changed resulting in the three test cases VH1.1, VH2.1, and VH3.1. The non-simplified VH model (VH1.1) resulted in a S c between 1.85 and 0.05% for particle diameters between 20 and 200 nm. The simplification of i s ≈ν s Φ s (VH2.1) led to a value of S c which was up to 0.3% lower than calculated with the VH1.1 model. EGU assumption that the contribution of the solute to the total mass of the droplet is so low that it could be neglected (VH3.1) resulted in an up to 2% higher S c than that calculated with VH1.1. The influence of approximating solution densities and surface tensions by those of pure water was practically the same for base cases VH1-VH3 as for AP1 (∼1% for ρ sol ; ∼2% for σ sol ).

5
The VH4.1 model assumed, furthermore, that ρ sol can be approximated with ρ w . The critical supersaturations which were obtained by the VH4.1 model had up to 0.6% higher values than those calculated with VH1.1. A further simplification of case VH4.1 was to assume a constant van't Hoff factor. Using i s =2.2 (VH4.2) led to a higher S c than with VH4.1. The deviation increased with particle diameter up to 10%. Using 10 i s =3 (VH4.3) led to a lower S c than with VH4.1. The deviation decreased with particle diameter from 15.3% at 20 nm to 5.6% at 200 nm. The analytical approximation model results (AA.1) were compared for ammonium sulfate particles with the AP1.1 results (±2.5% deviation in S c ), with the VH1.1 results (up to 19% higher S c ), and with the OS model results (up to 21% higher S c ). For 15 sodium chloride the AA.1 model calculations were compared with the AP1.1, with OS, and with VH4.2. The AA.1 calculations resulted in a S c which was 8-10%, 3-7%, and ∼8% higher than the respective compared model results.
To examine how sensitive S c is to variations in the temperature, we compared the VH4.1 model (with T =298.15 K) with VH4.4 (with T =303.15 K). Calculations with the 20 VH4.4 model resulted in a ∼4% lower S c than with VH4.1. Further, we investigated how much the S c of NaCl particles would be underestimated if no shape correction were applied to the particle diameter. Calculating S c from the uncorrected D s using the AP1.1 model resulted in a 5.8-7.4% lower S c than was calculated from the corrected diameters. Introduction  Fig. 11. Note: for calculating S eff with the NaCl-AP2 model, a shape correction was not applied, because the water activity parameterization used in this model already included shape corrections for NaCl (Kreidenweis et al., 2005).
For ammonium sulfate, AP1. EGU NaCl-AP1.1 was 4-5% higher than NaCl-AP2 in the whole supersaturation range, indicating that the underlying thermodynamic data sets for aqueous solutions of NaCl determined in EDB experiments (AP1.1) and HTDMA experiments (AP2) are not fully consistent. The NaCl-OS model based on data from NaCl bulk solution measurements was 3-5% higher than NaCl-AP1.1 and 10% higher than NaCl-AP2.
Upon comparison of ammonium sulfate and sodium chloride, each of the two model types AP1.1 and AP2 yielded different calibration lines. The S eff values obtained from the (NH 4 ) 2 SO 4 calibration experiment were 3-8% higher for AP1.1 and 11-13% higher for AP2 than the S eff values obtained from the NaCl calibration experiment. These deviations indicate that the applied thermodynamic parameterizations for ammonium 10 sulfate are not fully consistent with those for sodium chloride, neither with regard to the underlying EDB data sets (AP1.1) nor with regard to the HTDMA data sets (AP2).
The agreement indicates that the concentration-dependent van't Hoff factors of Low (1969) and Young and Warren (1992) for (NH 4 ) 2 SO 4 are consistent with the activity parameterizations of both Tang (1996) and Kreidenweis et al. (2005) for NaCl. In any case, the calibration line obtained with the (NH 4 ) 2 SO 4 -VH4.1 model lies in the middle of 20 both the (NH 4 ) 2 SO 4 and the NaCl calibration lines displayed in Fig. 11. Therefore, the VH4.1 model indeed appears to be best-suited for CCNC calibration with ammonium sulfate, as long as the discrepancies between the different activity parameterizations from hygroscopic growth experiments (EDB: AP1; HTDMA: AP2; bulk solution: OS and VH1.1-VH4.1) have not been resolved. 25 As outlined in Sect. 3.6, recent investigations indicate that for ammonium sulfate particles shape corrections may also be required to achieve high accuracy (Eugene Mikhailov, personal communication).
Taking the shape irregularities into account, all ammonium sulfate calibration lines EGU would be lifted by a few percent depending on envelope shape and porosity of the particles, respectively (Mikhailov et al., 2004). In this case, (NH 4 ) 2 SO 4 -AP1.1 and (NH 4 ) 2 SO 4 -AP2 would significantly exceed NaCl-OS and deviate even more from NaCl-AP1.1 and NaCl-AP2. On the other hand, (NH 4 ) 2 SO 4 -VH4.1 would still agree well with NaCl-AP1.1.

Conclusions
Table 10 summarizes the CCNC calibration and measurement uncertainties determined in this study. Under stable operating conditions, the effective water vapor supersaturation in the DMT-CCNC can be adjusted with high precision. The relative standard deviations of repeated measurements in laboratory experiments were as low as ±1% for S eff >0.1%, but increased up to ±7% during field measurements, which is mostly due to variations of the CCNC column top temperature with ambient temperature. The observed dependence of S eff on temperature (T 1 ), pressure (p), and aerosol flow rate (Q) in the CCNC can be approximated by the following gradients: (∆S eff /S eff )/∆T 1 ≈-2% K −1 at p≈1020 hPa and Q=0.5 L min −1 ; (∆S eff /S eff )/∆p≈+0.1% 15 hPa −1 at Q=0.5 L min −1 and T 1 ≈299 K; and (∆S eff /S eff )/∆Q≈+0.15% (mL min −1 ) −1 at p≈1020 hPa and T 1 ≈299 K. At high supersaturations (S eff >0.1%), the experimental data points generally agreed well with a linear calibration function (S eff vs. ∆T ; relative deviations ≤3%). At S eff <0.1%, however, the calibration line deviated by up to ∼40% from experimental data 20 points, indicating that in this range S eff does not linearly depend on ∆T and special care has to be taken to obtain reliable measurements. Besides careful calibration, it may be beneficial to operate the CCNC at particularly low flow rates (<0.5 L min −1 ) to achieve high precision at low S eff .
In the course of several field and laboratory measurement campaigns extending over a period of about one year, we found a systematic decrease of the slope of the calibration line by about 10-15% which could not be reversed by standard cleaning EGU procedures and may require a full refurbishing of the instrument to be reversed. In any case, we recommend careful and repeated calibration experiments during every field campaign to ensure reliable operation and to obtaine representative uncertainty estimates for the CCN measurement data. Besides experimental variabilities, Table 10 also summarizes calibration and 5 measurement uncertainties related to data analysis and Köhler model calculations.
If the influence of doubly charged particles is not taken into account in the fitting of CCN efficiency spectra, the 50% activation diameter can be underestimated, and the effective supersaturation can be overestimated by up to ∼3%. In Köhler model calculations, the approximation of the density and surface tension 10 of aqueous salt solutions by those of pure water can lead to relative underestimations of S eff which are small (-1% and -2%, respectively), but not negligible with regard to measurement precision under stable operating conditions. Most importantly, however, the Köhler model results obtained with different parameterizations and approximations of the activity of water in aqueous solution deviate by up to 25% for (NH 4 ) 2 SO 4 15 and 15% for NaCl, respectively. To ensure the comparability of results, we suggest that CCN studies should always report exactly which Köhler model equations and parameterizations of solution properties were used for instrument calibration.
After the subtraction of a constant temperature offset and the derivation of an instrument-specific thermal resistance parameter (R T ≈1.8 K W −1 ), the experimental 20 calibration results could be fairly well reproduced by the CCNC flow model of Lance et al. (2006). At S eff >0.1% the relative deviations between flow model and experimental results were generally less than 8%, when the same Köhler model approach was used. At S eff ≤0.1%, however, the deviations exceeded 20%, which can be attributed to non-idealities which also cause the near-constant temperature offset. Therefore, EGU approach used in the CCNC flow model (constant van't Hoff factor i s =3) deviates substantially from the more realistic modeling approaches tested and compared in this study. It yields by far the lowest S eff values. Substantial differences between the CCNC calibration results obtained with (NH 4 ) 2 SO 4 and NaCl aerosols under equal experimental conditions (relative 5 deviations of S eff up to ∼10%) indicate inconsistencies between widely used activity parameterizations derived from electrodynamic balance (EDB) single particle experiments (Tang and Munkelwitz, 1994;Tang, 1996) and hygroscopicity tandem differential mobility analyzer (HTDMA) aerosol experiments (Kreidenweis et al., 2005).

ACPD
Nevertheless, the concentration-dependent van't Hoff factors of Low (1969) and Young and Warren (1992) for (NH 4 ) 2 SO 4 were found to be consistent with the activity parameterizations of both Tang (1996) and Kreidenweis et al. (2005) for NaCl. Moreover, the calibration line obtained with the (NH 4 ) 2 SO 4 -VH4.1 model generally applied for CCNC calibration with ammonium sulfate in this study lies in the middle of both the (NH 4 ) 2 SO 4 and the NaCl calibration lines. Indeed, the VH4.1 model 15 appears to be best-suited for CCNC calibration with ammonium sulfate, as long as the discrepancies between the different activity parameterizations from hygroscopic growth experiments (EDB: AP1; HTDMA: AP2; bulk solution: OS and VH1.1-VH4.1) have not been resolved. Our investigations indicate a real need for further evaluation and experimental confirmation of preferred data sets and parameterizations for the 20 activity of water in dilute aqueous (NH 4 ) 2 SO 4 and NaCl solutions.  Table 2. Polynomial coefficients used to calculate the water activity with Eq. (9) or (10). The coefficients a 1 , a 2 , a 3 , and a 4 for (NH 4 )2SO 4 and NaCl at 298 K are given in Tang and Munkelwitz (1994) and in Tang (1996), respectively. The coefficients k a , k b , and k c are the Kelvin corrected values for (NH 4 ) 2 SO 4 and the Kelvin and shape corrected values for NaCl, taken from Kreidenweis et al. (2005).  Tang and Munkelwitz (1994) and in Tang (1996) Fig. 8. Dependence of effective supersaturation on temperature (T 1 ), pressure (p), and flow rate (Q) in the CCNC averaged over all calibration experiments with ammonium sulfate aerosol. Every data point corresponds to the slope of a linear fit to all values of ∆S eff /S eff at a given ∆T plotted against T 1 , p, or Q, respectively. ∆S eff /S eff is the relative deviation between S eff from an individual calibration line and the mean value of S eff for all calibrations performed at Q=0.5 L min −1 and p≈1020 hPa (black triangles) or 650 hPa (blue triangles), respectively. The dashed lines are first-order exponential decay fit functions. 7,2007 Calibration and measurement uncertainties of a CCN counter  Fig. 11. Calibration lines of effective supersaturation (S eff ) vs. temperature difference (∆T ) obtained from one experiment with ammonium sulfate and one experiment with sodium chloride particles under equal conditions. The data points were calculated from measured D 50 using different Köhler models; the lines are linear fits. Note that (NH 4 ) 2 SO 4 -AP1.1 is near-identical to (NH 4 ) 2 SO 4 -AP2.