Parameterization of cloud droplet activation using a simplified treatment of the aerosol number size distribution

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2007jd009485, 2008 Parameterization of cloud droplet activation using a simplified treatment of the aerosol number size distribution Niku Kivekäs, 1 Veli-Matti Kerminen, 1 Tatu Anttila, 1 Hannele Korhonen, 1,2 Heikki Lihavainen, 1 Mika Komppula, 1 and Markku Kulmala 3 Received 10 October 2007; revised 5 February 2008; accepted 10 April 2008; published 14 August [1] The number-to-volume concentration ratio, R, defined as the number concentration of particles larger than a certain cut-off diameter divided by the total particle volume concentration, can be used for expressing aerosol number size distributions in a simplified way. Earlier studies have shown that R shows less variability than random size distributions would produce. In this article the parameter R was used to develop a new parameterization for estimating the cloud droplet number concentration (CDNC). The parameterization is a function of four input parameters: the total submicron volume concentration (V tot ), number-to-volume concentration ratio with a 0.1-mm cut-off diameter (R(0.1 mm)), soluble fraction of the particle volume (e) and air updraft velocity (v up ). The parameterization was derived by finding the best fit to a series of simulations made with an adiabatic air parcel model simulating cloud droplet activation, and the model input parameters were varied over a range typical for northern European background air. Results from the parameterization were compared with cloud droplet concentrations measured in Northern Finland, and a good agreement was found. The new parameterization demonstrates that if the value of R(0.1 mm) can be estimated or parameterized without knowing the whole particle number size distribution, cloud droplet number concentrations can be estimated relatively accurately by using only the four parameters mentioned above. This would reduce significantly the computer resources needed for calculating CDNC in large-scale atmospheric models. Citation: Kivekäs, N., V.-M. Kerminen, T. Anttila, H. Korhonen, H. Lihavainen, M. Komppula, and M. Kulmala (2008), Parameterization of cloud droplet activation using a simplified treatment of the aerosol number size distribution, J. Geophys. Res., 113,, doi: /2007jd Introduction [2] Our ability to simulate the behavior of the Earth s climate system is seriously hindered by the general lack of understanding on how atmospheric aerosol particles interact with clouds [e.g., Chen and Penner, 2005; Lohmann and Feichter, 2005; Penner et al., 2006; Lohmann et al., 2007]. [3] The first step of aerosol-cloud interactions involves the activation of aerosol particles into cloud droplets. This process determines the total cloud droplet number concentration (CDNC), which is an essential parameter when investigating the influences of clouds on radiation and ultimately on climate. The number concentration of cloud droplets depends on the size distribution and chemical composition of aerosol particles participating into cloud droplet activation, on the cloud updraft velocity, and on various dynamical effects related to the transportation water 1 Research and Development, Finnish Meteorological Institute, Helsinki, Finland. 2 School of Environment, University of Leeds, Leeds, UK. 3 Department of Physical Sciences, University of Helsinki, Helsinki, Finland. Copyright 2008 by the American Geophysical Union /08/2007JD vapor between the gas phase, growing aerosol particles and cloud droplets [e.g., Kulmala et al., 1993; Charlson et al., 2001; Nenes et al., 2001]. During the last decade or so, a lot of effort has been put on investigating the complex interplay between these factors. As a result, effective parameterizations capable of predicting CDNC under different atmospheric conditions have been developed for use in atmospheric models [Abdul-Razzak and Ghan, 2000; Nenes and Seinfeld, 2003; Fountoukis and Nenes, 2005; Romakkaniemi et al., 2005; Ming et al., 2006]. More recently, it has been demonstrated that current cloud droplet activation parameterizations are applicable to large grid boxes used in global modeling frameworks [Meskhidze et al., 2005; Peng et al., 2005]. [4] Using sophisticated parameterizations for predicting the CDNC in large-scale models requires detailed information on the aerosol number size distribution and chemical composition. In many cases, no such information is available and a simpler approach is needed. The only practical solution to this is to relate CDNC to some bulk aerosol property or to a combination of easily available parameters. Examples of aerosol properties used for this purpose include sulfate mass concentration [e.g., Boucher and Lohmann, 1995], total aerosol number concentration [e.g., Chuang et 1of9

2 al., 1997], number concentrations of sea-salt and sulfate particles [O Dowd et al., 1999], and mass concentrations of sulfate, organic matter and sea salt [Menon et al., 2002]. None of these parameterizations take properly into account changes in the shape of the aerosol number size distribution, although the particle size is one of the most important aerosol properties determining its ability to form cloud droplets [e.g., Dusek et al., 2006]. [5] In this paper, we will derive a simple cloud droplet activation parameterization that uses two quantities related to aerosol number size distribution: its submicron volume concentration and its number-to-volume concentration ratio. The first of these quantities is directly proportional to the overall aerosol burden, whereas the second parameter can be related to the shape of the aerosol size distribution in the size region relevant to cloud droplet activation. In addition to these two quantities, the new parameterization takes into account the bulk solubility of the aerosol particle population, as well as the air updraft velocity. The parameterization will be provided in a semiempirical form derived using a simple fitting algorithm based on numerical calculations with an adiabatic cloud parcel model. Predicted cloud droplet number concentrations obtained from the parameterization will be compared to those measured in field during a large number of cloud cases in northern Finland. The new parameterization can be applied in models that have incomplete information about the aerosol number size distribution, in addition to which it can be used to analyze field experiments related to cloud formation. Figure 1. An aerosol number size distribution dn/dlogd p as a function of d p, where n is the number concentration in cm 3 and d p is particle diameter in mm. Part of the distribution (7 530 nm) is the average number size distribution of 21 May The vertical lines are diameters mm, mm, mm, mm, mm, and mm. 2. Approach [6] In this work the problem of estimating the cloud droplet number concentrations (CDNC) was approached in the following way: First, the aerosol number-size distribution was described with two parameters, which were the submicron particle volume concentration and number-tovolume concentration ratio. Second, cloud droplet activation was simulated with an adiabatic air parcel model. Third, an empirical relation was searched to relate the simulated CDNC to four parameters: the two size distribution parameters mentioned above, a parameter representing the chemical composition of the particles and a parameter representing the meteorological conditions leading to cloud formation Representing the Shape of Aerosol Number-Size Distribution [7] A submicron aerosol volume concentration was chosen to describe the amount of particulate matter in the air. The limitation to submicron sizes was made in order to give a more accurate estimate of the number of particles participating in the cloud droplet activation. Number concentrations of supermicron particles are typically negligible compared with those of submicron particles, giving thereby a minor contribution to CDNC, whereas even a small concentration of supermicron particles can affect the particulate volume concentration significantly. [8] The aerosol volume concentration alone does not tell anything about the shape of the particle number-size distribution, although such information is needed to predict the number concentration of activated cloud droplets. We express the shape of the particle number-size distribution in terms of a particle number-to-volume concentration ratio, R(d c ), defined as Rd ð c Þ ¼ Nd> ð d cþ : ð1þ V tot Here N(cm 3 ) is the number concentration of submicron particles with a diameter d larger than d c ; d c is a chosen cut-off diameter and V tot (mm 3 /cm 3 ) is the total volume concentration of all submicron particles. The definition of R(d c ) can be interpreted as the cumulative particle number concentration above the cut-off diameter, scaled with the total particle volume concentration. By varying the cut-off diameter d c, the particle number size distribution can be described explicitly. The value of R(d c ) decreases monotonically with increasing value of d c and changes most rapidly in the region having a peak in the particle number size distribution (compare shape of distribution in Figure 1 with R values given in Table 1). [9] Since the volume of a particle is proportional to the third power of its diameter, the magnitude of the volume concentration of a size distribution is determined by its largest particles. The numerator in the definition of R(d c ) takes into account all particles larger than d c in diameter equally. When a constant d c is used, the value of R(d c ) provides information about the general shape of the distribution in the range d c < d <1mm: the larger the value of R(d c ), the higher the number concentration of particles near d c compared to those closer to 1 mm. [10] The main reason for using R(d c ) in our analysis is that in all aerosol systems investigated so far, this quantity has been found to vary much less than what random size distributions would produce [Van Dingenen et al., 2000; Hegg and Russell, 2000; Dusek et al., 2004; Eleftheriadis et al., 2006; Kivekäs et al., 2007]. In previous studies the cut-off diameter d c has been chosen to be between 80 and 120 nm. The variability of R depends on d c, being larger for 2of9

3 Table 1. Number Size Distribution in Figure 1 Presented With R(d c ) a d c, mm N(d > d c )/N tot (%) V(d > d c )/V tot (%) R(d c ), mm a The total particle number concentration N tot of the distribution is 1402 cm 3 and total volume concentration V tot is 6.08 mm 3 /cm 3. smaller values of d c. By using a cut-off diameter of 100 nm, the average values of R(0.1 mm) in northern European background air were found to be approximately 200 ± 70 mm 3 [Kivekäs et al., 2007]. A seasonal pattern for R was found, and it was found to correlate well with the seasonal pattern of the ambient temperature. At higher temperatures the value of R was, on average, higher and varied more [Kivekäs et al., 2007]. In this parameterization, a value of 100 nm was used for d c Other Variables in the Cloud Droplet Activation [11] The activation behavior of an aerosol particle is affected not only by its size but also by the amount and properties of water-soluble material in it. In this respect, potential influencing factors are the cocondensation of water and highly soluble vapors during the particle growth into cloud droplet, gradual dissolution of slightly soluble compounds inside the growing particle, partitioning of watersoluble compounds between the surface and bulk liquid of the particle, and the resulting decrease in the particle surface tension and its mass accommodation coefficient for water vapor [e.g., Kulmala et al., 1996; Laaksonen et al., 1998; Facchini et al., 1999; Chuang, 2006; Sorjamaa and Laaksonen, 2006]. The relative importance of these chemical effects vary from case to case, but in many circumstances the particle activation behavior can be described with a sufficient accuracy when knowing the amount of water soluble material in it [Abdul-Razzak and Ghan, 2005; Erwens et al., 2005]. For this reason, the soluble volume fraction e was chosen as the only parameter describing the chemical composition of the particles. [12] The maximum supersaturation reached by a convective air parcel under given conditions cannot be measured directly, nor can it be modeled without a considerable amount of information considering the particle size distribution. However, the vertical updraft velocity (v up )ofthe rising air parcel, along with information regarding the particle size distribution and its hygroscopic properties, has been shown to be a good way to estimate the maximum supersaturation reached [e.g., Nenes et al., 2003] Simulating Cloud Droplet Activation [13] Cloud droplet activation was modeled using a model simulating an adiabatically rising air parcel with a fixed updraft velocity. The potential deactivation of cloud droplets due to kinetic limitations associated with droplet growth [see, e.g., Kulmala et al., 1993; Nenes et al., 2001] are accounted for in the model used here [Anttila and Kerminen, 2002; Korhonen et al., 2005]. The solubility of particles is accounted in the model as soluble fraction by assuming that the particles consist of insoluble substances and soluble matter behaving like ammonium sulphate. [14] The model was used to obtain the number concentration of activated particles and the size of the smallest particles that activate from a given aerosol number-size distribution with a given soluble fraction rising with a given updraft velocity. Each model run was initialized with two lognormal modes, one in the Aitken and one in accumulation mode size range. The mean size (d p ), number concentration (N p ) and geometric standard deviation (s) ofthe mode in accumulation range, as well as the values of e and v up, were varied between the runs. [15] The values of modal parameters describing the accumulation mode were chosen to represent conditions typical for northern European background air [Tunved et al., 2003]. The soluble fraction and updraft velocity were varied in the range expected to be encountered in the atmosphere (Table 2). All value combinations were simulated. All parameters had also a weight factor attached to each of their value, being one in the more extreme cases and two or three for more typical conditions. No weighting for N p and s were applied. The weight factor of any simulation was the product of the weight factors of each individual variable. As a result, the weight factors of the simulations varied from 1 to 12. The larger the weight factor of a simulation, the more importance that simulation had when the numerical values in the parameterization were fitted. The values of the parameters and the corresponding weight factors are presented in Table 2. [16] For each combination of the accumulation mode parameters mentioned above, two simulations were made. In the first simulation the number concentration of Aitken mode particles was half of the accumulation mode particle number concentration, and in the second simulation it was twice that of the accumulation mode particles. In both cases the geometric standard deviation of the Aitken mode was 1.6 and the geometric mean diameter of the mode was 0.07 mm. The soluble fraction was same as for the accumulation mode. [17] In the simulations all particles that exceed 2.0 mm in wet diameter were considered as activated. This definition is Table 2. Variation of the Values of Particle Number Concentration N p, Accumulation Mode Mean Diameter d p, Geometric Standard Deviation of Accumulation Mode s, Soluble Volume Fraction of the Particles e and Updraft Velocity v up in the Simulations, and the Weight Factors Attached to Them Variable Unit Value 1 Weight 1 Value 2 Weight 2 Value 3 Weight 3 Value 4 Weight 4 N p cm d p mm s e v up m/s of9

4 Figure 2. Particle activation into cloud droplets and D50 activation diameter in real cloud (left) and in an adiabatic air parcel model (right). not entirely consistent with the Köhler theory, but was chosen because of practical reasons. By keeping the wet diameter limit low enough we made sure that all activated particles are accounted for. At the same time, the limit should be high enough to include only those yet unactivated particles that behave similarly to cloud droplets. When the activation limit was lowered below 2 mm, the limit started to influence the simulation results. Raising the limit up to 5 mm did not change the number of activated particles in the simulations. [18] The values of V tot and R(0.1 mm) were calculated for each dry size distribution. The effective dry particle activation diameter (termed here D50) was defined as the dry diameter of the lowest size bin that activated according to the definitions in the previous paragraph. In an adiabatic cloud model with chemically identical particles in each size bin, D50 is the sharp dry cut-size between activated cloud droplets and cloud interstitial particles. In real clouds, the value of D50 corresponds to the minimum dry diameter at which 50% of the particles with that diameter activate into cloud droplets (Figure 2) [Henning et al., 2002; Komppula et al., 2005]. 3. Parameterization 3.1. Derivation of the Parameterization [19] The cloud droplet number concentration was parameterized using four parameters. Two of them contained information about the aerosol number size distribution, being the total submicron volume concentration, V tot, and number-to-volume concentration ratio at 100 nm, R(0.1 mm). The two other parameters were the soluble fraction of particle volume, e, describing the chemical composition of the particles, and the air parcel updraft velocity, v up. The parameterization was made by finding the best fit to a set of 1152 simulations made with an adiabatic air parcel model. [20] The parameterization linking cloud droplet number concentration (CDNC) to V tot, R(0.1 mm), e and v up consists of three parts. The first part of the parameterization estimates the value of D50 using all of the four variables D50 ¼ ð0:016 ln V tot þ 0:0068 ln Rð0:1 mmþþ0:023þ e 0:13 v 0:37 up : ð2þ In equation (2) the constant factor attached to each parameter was estimated by linear fitting so that it gives the minimum sum of weighted differences between the simulated and parameterized values. The form of equation (2) is statistical, but it was chosen to meet realistic physical boundary conditions. For example, if the soluble fraction of particle mass or the updraft velocity of the air is zero, no activation is supposed to take place. The comparison between parameterized and simulated values of D50 gave a correlation coefficient (R 2 ) of The standard deviation of the difference between the parameterized and simulated values was 12%, and the difference was 46% at maximum (Figure 3). [21] In a paper by Kivekäs et al. [2007] the magnitude of R(d c ) was shown to depend inversely on the cut-off diameter d c. This dependency is used in the second part of the parameterization for relating R(D50) to R(0.1 mm): R 0:1 mm RD50 ð Þ ¼ 0:10 ð Þ : ð3þ D50 4of9

5 Figure 3. Parameterized versus simulated values of D50. The contours represent the number of scatter points per unit area, being (from in to out) 50%, 25%, and 5% of the highest number of scatter points per unit area in the picture. The thick straight line is 1:1. The constant factor of 0.10 in the fit was estimated by linear fitting so that it gives the minimum sum of weighted differences between the simulated and parameterized values. [22] The third and final part of the parameterization uses R(D50) and V tot to calculate the number of cloud droplets based on the definition of R(d c ), assuming that all particles with d > d c activate CDNC ¼ RD50 ð Þ V tot : ð4þ When parameterized values of CDNC were compared to the simulated values, a correlation coefficient (R 2 ) of 0.96 was found. The standard deviation of the difference between the parameterized and simulated values was 13%, and the difference was 53% at maximum (Figure 4) Sensitivity Studies [23] The contribution of each parameter to the results of the parameterization was studied in the following way: One parameter at the time was replaced with a constant value while other parameters were treated as described in the previous section. The results were compared to the simulated values of D50 and CDNC. [24] The variables that had the greatest influence on the parameterized value of D50 were the updraft velocity of the air and the aerosol volume concentration. This is expected, since the value of D50 depends on the maximum supersaturation reached by the raising air parcel, which depends strongly on these two quantities. When the updraft velocity was treated as a constant, the correlation (R 2 ) between the parameterized and simulated values of D50 was 0.35, and when the submicron aerosol volume concentration was kept constant, R 2 was Having a constant soluble fraction or R(0.1 mm) resulted in much higher correlation coefficients of 0.89 and 0.90, respectively, showing that the influence of these two parameters on the value of D50 was much weaker than those of V tot and v up. [25] The only input parameters affecting the parameterized CDNC directly (not only through D50) are the submicron aerosol volume concentration (V tot ) and R(0.1 mm). When the aerosol volume concentration was treated as a constant, there was no apparent correlation between the simulated and parameterized values of CDNC, which clearly demonstrates that the aerosol volume concentration is an essential quantity when searching for a simple parameterization for cloud droplet activation. Using a constant value for R(0.1 mm) gave a bit better results, but the correlation coefficient was still relatively low (R 2 = 0.46). When the updraft velocity or the soluble fraction of particle volume was treated as a constant, the correlation coefficients between the parameterized and simulated values of CDNC were 0.69 and 0.94, respectively. [26] The correlations between CDNC and either the updraft velocity or the soluble fraction were higher than the respective correlations between D50 and these two quantities. This shows that the later parts of the parameterization (equations (3) and (4)) can level down possible errors arising from the parameterized D50 (equation (2)). One might ask whether it is important to try to parameterize D50 at all. To answer this question, the sensitivity of the parameterization was studied also in such a way that the value of D50 was treated as a constant, and only the second and third part (equations (3) and (4)) were allowed to affect the results. As a result, the correlation coefficient between the parameterized and simulated values of CDNC was 0.65, which is significant but much lower than the R 2 of 0.96 obtained by using the full parameterization. [27] As a conclusion, the derived parameterization was found to be quite robust against inaccuracies or lack of data concerning the chemical composition of the particles, and also to some extent concerning the updraft velocity. On the other hand, inaccuracies in the total submicron volume concentration or number-to-volume concentration ratio can lead to very inaccurate results. 4. Comparison to Other Parameterizations [28] During the last few years, several parameterizations for cloud droplet activation have been developed [e.g., Fountoukis and Nenes, 2005; Abdul-Razzak and Ghan, Figure 4. Parameterized versus simulated values of CDNC. The contours and the thick straight line are as explained in the caption of Figure 3. 5of9

6 2000; Ming et al., 2006; Segal and Khain, 2006]. The parameterizations of Fountoukis and Nenes (referred hereafter as FN) and Abdul-Razzak and Ghan (referred hereafter as AG) have also been applied in large-scale modeling frameworks. In the comparison we have applied the formulations of FN and AG parameterization where lognormal representation of the aerosol number size distribution is used, requiring N p, d p and s of each mode as input parameters. Usually two modes are enough for parameterizing cloud droplet activation. Soluble fraction of particle mass is given separately for both modes and updraft velocity is given in these parameterizations in the same way as in our parameterization. That makes the total number of input parameters in these models nine (or eight, if all particles are assumed to have the same soluble fraction). [29] In order to get some idea about the performance of our parameterization in comparison to the FN and AG parameterizations, the same simulation conditions that were used in deriving our parameterization were also used to calculate the number of cloud droplets with the FN and AG parameterizations. The results were compared to those produced by our parameterization. No weight factors were used in this comparison. [30] The accuracy of our parameterization was found to be 2.1 ± 14.5% (average error ± one standard deviation). The same values for FN and AG parameterizations were 1.4 ± 11.5% and 4.8 ± 9.3%, respectively. Since our parameterization does not use N p as input parameter, the largest (in percents) errors of our parameterization occurred in cases when the number concentration of particles was small. When FN and AG parameterizations were used with only two size distribution parameters (That means neglecting the Aitken mode completely and assuming constant s for the accumulation mode), their accuracies were 31.1 ± 38.9% (FN) and 21.8 ± 36.6% (AG). This demonstrates that our parameterization can describe cloud activation with fewer parameters than FN or AG parameterizations in cases where Aitken mode particles contribute to the cloud droplet population. [31] The computational cost of these three parameterizations was also compared. Our parameterization is the most simple one and was also found to perform fastest. The AG parameterization was roughly one order of magnitude slower than our simulation, whereas the NS parameterization was about four orders of magnitude slower. It should be noted, however, that the FN parameterization has an iterative loop in it, and its computing time can be decreased significantly by optimizing the iteration algorithm, but probably not as much as four orders of magnitude. [32] In summary, our parameterization is almost as accurate as FN and AG, but is computationally more efficient. It also requires a smaller number of input parameters (four instead of nine or eight), making it a feasible option for models having limited information on the aerosol size distribution. 5. Comparison to Ambient Measurements 5.1. Measurement Data [33] The parameterization results were compared to measured cloud droplet number concentrations. The measurements were made at the Pallas Sodankylä Global Atmosphere Watch (GAW) station [Hatakka et al., 2003]. The station is located in northern Finland near the northern limit of the boreal forest zone. There are no major local or regional pollution sources nearby. At Pallas there are several measurement sites, of which two were used in this study. The lower altitude site Matorova ( N, E, 340 m above sea level) is located on the top of a small hill in the middle of a 100 m 100 m clearing in boreal forest. The other measuring site, Sammaltunturi ( N, E, 560 m above sea level), is located some 6 km south-west from Matorova on the top of a local mountain (arctic roundtopped hill called field) some 100 m above the tree line and some 300 m above the surrounding area. Aerosol size distributions were measured at both sites with similar DMPS measurement systems [Komppula et al., 2003]. [34] The lower altitude site (Matorova) is always under the cloud base, but there are periods when the higher altitude site (Sammaltunturi) is inside a cloud. During such periods the activated fraction of particles in each size class can be calculated from the particle number-size distributions at the two sites. Activated particles were removed in the sampling system of the DMPS. Therefore the number concentration of activated particles in each size class can be calculated by subtracting the number concentration of the particles in each size class at the higher altitude site from that at the lower altitude site [Komppula et al., 2005]. [35] We studied a set of 33 cloud events. The chosen data set did not include the cases where meteorological conditions before and after the cloud event were so different that they cannot be assumed to represent the same air mass. Also cases where particle number concentration was outside the simulated range ( cm 3 ) were excluded. [36] The size distribution parameters V tot and R(0.1 mm) were calculated from the number size distributions measured below the cloud during the cloud events. No data concerning the chemical composition of particles in individual cloud events were available. The range of typical soluble fractions of the particle volume was estimated from the hygroscopicity data collected during two cloud measurement campaigns at the site. This was made using the method by Swietlicki et al. [1999]. We found that the soluble fractions varied mostly between 0.25 and 0.55 during the times of the campaigns (data not yet published). A value of 0.4 was taken here as the soluble fraction for all the cloud events. [37] No information on the air updraft velocity during the cloud events was available. The updraft velocity would have to be measured near the cloud base where the activation takes place and during the time of activation. This is very difficult with a ground based platform carrying automated measurements [Verheggen et al., 2007]. The lack of measured data forced us to use a constant value for updraft velocity in all cloud events. A value of 0.4 ms 1 was chosen. This value gave the best fit between the measured and parameterized cloud droplet number concentrations and it lies in the physically realistic range of air updraft velocities. [38] There are also other factors that may influence the formation and development of a cloud droplet population, such as availability of condensable water, the ambient temperature at the time and place of cloud formation, 6of9

7 measured value. This shows that the parameterization has a potential to be applied to real atmospheric conditions. [40] Since there was not enough information available concerning the soluble volume fraction of the measured particles, and no information at all concerning the updraft velocity of air during the cloud events, the correlation cannot be as high as it could be when using the full parameterization. As brought out in the sensitivity analysis, the influence of the soluble fraction on CDNC is not as high as the effects of the other parameters considered here. Therefore the error caused by the missing solubility information can be estimated to be small. [41] The correlation coefficient between the parameterized and measured values of CDNC was very close to that obtained between the parameterized and simulated values of CDNC, when v up was treated as constant in the sensitivity analysis. This indicates that most of the difference between the parameterized and measured values of CDNC at Pallas was due to the lack of information concerning the air updraft velocity. If there were other sources of error, they had a smaller effect and were masked by the error associated with the air updraft velocity. Figure 5. Parameterized versus measured cloud droplet number concentrations at Pallas during 33 cloud events with updraft velocity 0.4 ms 1. The error bars show the parameterization results when updraft velocity was varied ±0.2 ms 1. The figure is divided to concentration ranges cm 3 (top) and cm 3 (bottom). The straight lines are 1:1. freezing, mixing, entrainment and large-scale cloud dynamics [Verheggen et al., 2007]. Most of these effects vary much even over small spatial and temporal scales, and are therefore impossible to be resolved in climate or chemical transportation models with large grid boxes and several relatively long time steps. The effects of these factors are not included in the parameterization Results and Error Analysis [39] The parameterized and measured values of cloud droplet number concentration are shown in Figure 5. Since the value of updraft velocity is very uncertain, the parameterization was also run with updraft velocities 0.2 and 0.6 ms 1 and the results are shown as error bars in Figure 5. The correlation coefficient between the parameterized and measured data was The largest offsets produced by the parameterization were within 52% of the measured value, and 78% of all offset values were within 25% of the measured value. Also 75% of the parameterized values were within the error bar range from the corresponding 6. Summary and Conclusions [42] An empirical parameterization was developed for calculating the cloud droplet number concentration (CDNC) from the total submicron volume concentration of particulate matter (V tot ), number-to-volume concentration ratio with 0.1 mm cut-off diameter R(0.1 mm), soluble fraction of particle volume (e) and air updraft velocity (v up ). The parameterization was made by searching the optimal fit to the D50 activation diameter and CDNC values of a set of 1152 simulations made with an adiabatic air parcel model. In the simulations, the Aitken mode particle number concentration, accumulation mode particle number concentration, mean diameter of accumulation mode particles, geometric standard deviation of accumulation mode, soluble volume fraction of the particles and updraft velocity of the air parcel each varied within ranges typical for northern European background conditions. [43] The parameterization was able to reproduce the effective dry activation diameter (D50) and CDNC from the simulations with very high accuracy. The correlation coefficients (R 2 ) between the parameterized and simulated values of D50 and CDNC were both The contribution of each parameter to the parameterization results was studied by keeping one parameter constant at time. The most important parameters were found to be V tot and R(0.1 mm). Also keeping v up constant reduced the accuracy of the parameterization, but the effect of keeping the soluble volume fraction constant had very little effect. [44] The parameterization was compared with two other existing parameterizations [Fountoukis and Nenes, 2005; Abdul-Razzak and Ghan, 2000] in terms of accuracy and computing time. The new parameterization was found to be close to these two parameterizations in terms of accuracy, and more effective in terms of computing time. It also requires less input parameters. 7of9

8 [45] The parameterization results were further compared with measured cloud droplet activation data obtained from the Pallas GAW station in northern Finland. There was no information about the air updraft velocity and particle soluble volume, so they were both treated as constants. The parameterization was able to reproduce the measured CDNCs reasonably well, with a correlation coefficient of [46] The parameterization needs some kind of estimation for the values of R(0.1 mm) when more detailed particle number size distribution data are not available. Typical values of R(0.1 mm) in aged aerosol lie in the range mm 3 in both marine and continental air. In air where Aitken mode is prominent, the values of R(0.1 mm) are larger, being usually in the range mm 3. However, more extreme cases have also been reported, R(0.1 mm) being less than 50 mm 3 or more than 500 mm 3 [Dusek et al., 2004; Eleftheriadis et al., 2006; Kivekäs et al., 2007] This uncertainty creates a need for more investigations on the behavior of R(0.1 mm) in different environments. [47] A parameterization like the one presented in this work is computationally cheap and reasonably accurate as well as robust against some inaccuracies in the input data. It can be used in large-scale atmospheric models to reduce the computational time. The parameterization presented in this work has been created to perform under conditions typical for northern European background air. In the future, the applicability of this kind of parameterization needs to be studied in other types of environment. [48] Acknowledgments. This work was supported financially by the Tor and Maj Nessling Foundation and the European Union. 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