Droplet number uncertainties associated with CCN: an assessment using observations and a global model adjoint

We use the Global Modelling Initiative (GMI) chemical transport model with a cloud droplet parameterisation adjoint to quantify the sensitivity of cloud droplet number concentration to uncertainties in predicting CCN concentrations. Published CCN closure uncertainties for six different sets of simplifying compositional and mixing state assumptions are used as proxies for modelled CCN uncertainty arising from application of those scenarios. It is found that cloud droplet number concentrations ( Nd) are fairly insensitive to the number concentration ( Na) of aerosol which act as CCN over the continents ( ∂ lnNd/∂ lnNa ∼ 10–30 %), but the sensitivities exceed 70 % in pristine regions such as the Alaskan Arctic and remote oceans. This means that CCN concentration uncertainties of 4–71 % translate into only 1– 23 % uncertainty in cloud droplet number, on average. Since most of the anthropogenic indirect forcing is concentrated over the continents, this work shows that the application of Köhler theory and attendant simplifying assumptions in models is not a major source of uncertainty in predicting cloud droplet number or anthropogenic aerosol indirect forcing for the liquid, stratiform clouds simulated in these models. However, it does highlight the sensitivity of some remote areas to pollution brought into the region via long-range transport (e.g., biomass burning) or from seasonal biogenic sources (e.g., phytoplankton as a source of dimethylsulfide in the southern oceans). Since these transient processes are not captured well by the climatological emissions inventories employed by current large-scale models, the uncertainties in aerosol-cloud interactions during these events could be much larger than those uncovered here. This finding motivates additional measurements in these pristine regions, for which few observations exist, to quantify the impact (and associated uncertainty) of transient aerosol processes on cloud properties.


Introduction
The ability of atmospheric aerosols to act as cloud condensation nuclei (CCN) remains one of the largest sources of uncertainty in current global climate modelling efforts (Solomon et al., 2007).This is because aerosols are chemically-complex and are derived from a variety of primary emissions sources as well as secondary gas-to-particle conversion in the atmosphere.Given this complexity, there is a need for an extensive global observational dataset that can be used to improve the representation of aerosol-cloud interactions in models.
Measurements of CCN spectra (i.e., CCN concentration over a range of water vapour supersaturation) have been made for decades (e.g., Twomey, 1977;Hudson, 1993, and references therein) and have yielded CCN datasets at a number of locations worldwide.While providing information on the spatiotemporal variation of CCN concentrations and the total particle size distributions, many of these pioneering studies lacked the detailed aerosol composition information needed to fully explain the observed CCN variability.Recent improvements in instrument capabilities have greatly improved the state of the art for measuring the chemical composition and CCN activity of aerosols.This includes the development of the Particle-Into-Liquid Sampler (PILS, Weber et al., 2001)  water-soluble aerosol composition, the Aerodyne Aerosol Mass Spectrometer (AMS, Jayne et al., 2000;Jimenez et al., 2003) for measuring non-refractory aerosol composition, and the Droplet Measurement Technologies Continuous-Flow, Streamwise, Thermal-Gradient CCN Counter (CCNC, Roberts and Nenes, 2005;Lance et al., 2006) for measuring CCN activation and droplet growth rates.Together with traditional and newer techniques for measuring the aerosol size distribution (e.g., Wang and Flagan, 1989;Flagan, 2004;Cai et al., 2008;Olfert et al., 2008), these robust and commercially-available instruments have enabled a multitude of field studies that have comprehensively characterised the compositional and size dependence of ambient CCN.With this information, it is now possible to empirically evaluate our theoretical understanding of aerosol-cloud interactions using in situ field data.
CCN concentrations are almost exclusively predicted in models with Köhler theory (Köhler, 1936), which has been shown to adequately capture the CCN activity of single-and multi-component aerosol by a large number of laboratory studies (e.g., Cruz and Pandis, 1997;Raymond andPandis, 2002, 2003;Giebl et al., 2002;Padró et al., 2007).However, atmospheric aerosols are often much more complex than those created in the laboratory, so application of Köhler theory-based models and parameterisations must necessarily make simplifying assumptions regarding the aerosol mixing state and composition in order to reduce their computational burden.To evaluate the uncertainty associated with these simplifying assumptions, a number of "CCN closure" studies have been performed, where the aerosol size distributions and chemical compositions measured in the field are used with the simplifying assumption scenarios to predict CCN number concentrations (N CCN ), which are then compared to concurrent CCN measurements with a CCNC.The deviation between the measured and predicted concentrations is interpreted as the uncertainty introduced by that set of simplifying assumptions.
While quantifying the uncertainty in our predictive understanding of CCN concentrations is important, it represents only one link in our understanding of the aerosol-cloud indirect effects on climate.The second link is the combination of CCN concentrations with cloud dynamics (e.g., ambient liquid water content, updraft velocity, and droplet condensational growth rates) to determine the overall cloud droplet concentration (N d ), which, in turn, affects the cloud albedo (A cld ) and radiative properties.Studies have combined ambient measurements of N d with cloud parcel model simulations using measured N CCN and dynamical parameters to perform "cloud droplet closure" (e.g., Hallberg et al., 1997;Chuang et al., 2000;Snider and Brenguier, 2000;Snider et al., 2003;Conant et al., 2004;Meskhidze et al., 2005;Fountoukis et al., 2007).The agreement between predictions and measurements has generally been quite good despite large observed aerosol variability in some studies, with aver-age N d predicted-to-measured ratios on the order of 0.71-1.2and some larger ratios reported by Hallberg et al. (1997).
In addition to these field studies, model simulations are an important tool for examining the sensitivity of N d to changes in CCN and other parameters by selectively turning on and off certain effects.For example, Lance et al. (2004) used a large number of 1-D parcel model simulations to look at the competing influences of aerosol chemistry and cloud updraft velocity in determining N d under a wide variety of conditions.They found that chemical effects can account for 28-100 % of the variability in N d for both marine and continental environments.Rissman et al. (2004) extended the droplet parameterisation of Abdul-Razzak et al. (1998) to include the effects of surfactants and derived the analytical sensitivities of N d with respect to the parameterisation inputs, and reached a similar conclusion that N d can be up to 1.5times as sensitive to aerosol composition and surface tension effects as it is to cloud dynamical effects under certain atmospherically relevant conditions.Sotiropoulou et al. (2006) used a droplet parameterisation to propagate the CCN closure uncertainties observed by Medina et al. (2007) during the ICARTT campaign to uncertainties in N d .Using a campaignaverage, prescribed CCN spectrum and size distribution in the parameterisation, they found the uncertainty of N d to be 50 % of that for N CCN over a range of conditions.Ervens et al. (2010) also modelled the sensitivity of N d uncertainty to N CCN uncertainty and found that a 100 % overprediction of N CCN leads to only a 15 % overprediction in N d .
The above studies (and others) highlight the influence of aerosols versus cloud dynamics on cloud properties, and motivates future work with larger scale models to better understand where clouds are most sensitive to aerosol composition effects.Toward this, Sotiropoulou et al. (2007) parameterised the CCN uncertainty from the ICARTT study in terms of supersaturation and used this relationship with the global N d and N CCN outputs from the NASA Goddard Institute for Space Studies Version II' (GISS II') general circulation model (GCM) to quantify the resulting errors in N d , aerosol indirect forcing, and autoconversion rate.This is achieved by running two present-day simulations: a base case simulation with normal present day emissions and a perturbed case simulation where the size distribution is varied to alter the CCN concentration according to the ICARTT uncertainty.Their results suggest that a global average CCN prediction error of 10-20 % translates into a 7-14 % uncertainty in N d and a 10-20 % uncertainty in aerosol indirect forcing (Sotiropoulou et al., 2007).While this study gives important first-order constraints on how CCN uncertainty may affect global indirect forcing estimates, the approach does not account for regional differences in the uncertainty of N CCN or how the model perturbation may induce other, nonlinear effects in the simulation.A thorough discussion of some of these challenges is presented by Lee et al. (2011), who have developed a new statistical method for estimating model sensitivities to input uncertainties and, more recently, used it to rank parametric uncertainties in cloud droplet formation model parameters (Lee et al., 2013).
There is also a large body of literature related to quantifying aerosol-cloud interactions through correlations of ground-based, airborne and satellite remote sensing measurements.In these studies, the logarithmic sensitivity of N d to N a is found through linear regression of in situ data or of proxies for N a such as aerosol optical depth or aerosol index.Reported regression slopes vary widely from 0.1-1.0(Nakajima and Schulz, 2009;McComiskey and Feingold, 2012, and references therein).Within this wide range, sensitivities over ocean tend to fall within 0.4-0.5 (Nakajima and Schulz, 2009).McComiskey and Feingold (2012) examined how inferred ∂N d /∂N a varied across ground-based, airborne, and satellite platforms, with mean values of 0.48 ± 0.15, 0.58 ± 0.20, and 0.27 ± 0.13 across the different categories of studies, respectively.Low values from satellite-derived measurements were attributed to the effect of aggregating measurement data across scales and not constraining liquid water path in the analysis, which tend to dampen the observed response (McComiskey and Feingold, 2012).The authors note that while this biases inferences of the cloud albedo effect low, it may be more representative of the full aerosol-cloud interactions system, including feedbacks.The sensitivities derived in this work from a physically-based, cloud model parameterisation complement these previous studies by providing a global picture of aerosol-cloud interactions without having to make assumptions with regard to liquid water path constraints; however, given the coarse resolution of the model, this approach does not completely avoid the scale problem discussed by McComiskey and Feingold (2012).
In summary, while there have been several studies to date examining the sensitivity of cloud droplet number concentration uncertainty to uncertainties in CCN number concentration, there is still no clear estimate of the global magnitude of this uncertainty or how it varies regionally.In this study, we address these questions by combining data obtained from over thirty-five published CCN closure studies with simulations conducted with the adjoint of the Kumar et al. (2009) cloud droplet parameterisation, recently developed by Karydis et al. (2012).The adjoint tracks the sensitivity of model output (i.e., N d ) to inputs concurrently with the forward model execution and without perturbing the simulation parameters.Thus, it is able to calculate the sensitivity of N d to aerosol number concentration, N a , or a large number of other parameters with analytical precision and requires only a single model run.In the following sections, we briefly discuss the published datasets and the adjoint model before comparing and contrasting the simulation results with observations.The goal of this work is to improve the understanding of the global and regional sensitivities of modelled cloud droplet number to the CCN concentration uncertainty introduced through simplified model assumptions regarding aerosol mixing state and chemical composition.This will in-form both future planning of field measurement studies focused on CCN, as well as efforts to quantify model uncertainty and variability.

CCN uncertainties from aerosol composition and mixing state
In this work, we use CCN prediction uncertainties measured at multiple locations worldwide as a proxy for CCN prediction uncertainty in models employing Köhler theory.These simplified mixing state and composition assumptions are characteristic of those used in large-scale models to compute CCN concentration and N d .In another form of CCN closure, some other studies in the literature use the aerosol hygroscopicity obtained from humidified aerosol growth factor measurements to predict CCN concentrations with typically good agreement (e.g., Kim et al., 2011;Kammermann et al., 2010;Vestin et al., 2007;Good et al., 2010;Gasparini et al., 2006;Dusek et al., 2003;Covert et al., 1998, and others).While important for assessing the uncertainties associated with using the same hygroscopicity to predict both subsaturated and supersaturated water uptake, this type of closure study is not included here as it is less relevant for comparing against mass composition-based models.
The studies shown in Table 1 reflect a diverse mixture of urban, rural, and marine sampling on both airborne and ground-based platforms.The majority of published studies focus on locations in North America, and CCN concentrations range from zero to a few thousand particles per cm 3 with the highest concentrations observed in the vicinity of local urban emissions sources (e.g., Houston, TX; Riverside, CA; Mexico City, Mexico) and within targeted biomass burning and ship plumes.Most studies report CCN concentration and closure data at a single or a few discrete supersaturations, and the tabulated values reflect the average across all supersaturations.Since closure results reported in the litera-ture are not described in the same way, we use our judgement in interpreting the closure results described in each study.In many cases the values tabulated in Table 1 reflect an average and standard deviation, while in some studies, the numbers represent the reported mean or median and the total range of observed variability.Given the different uncertainty metrics reported, we do not incorporate these in our analysis in Sect.3.4.A detailed description of each closure study location, measurements, and data analysis is given by the references in Table 1.
The CCN prediction uncertainties reported by the studies considered are shown in Table 2. Most closure analyses overpredict CCN concentrations.Typically, the external mixing scenarios produce lower predicted CCN concentrations than the ammonium sulfate or internal mixing scenarios.As discussed by Ervens et al. (2010), some studies report large CCN overpredictions on the order of 2-5-fold, which likely reflects the contribution of local emissions sources near the sampling locations that may produce a size-varying, externally-mixed aerosol that cannot be captured well from bulk chemical composition measurements.In some locations (e.g., Houston, TX, and Los Angeles, CA), airborne studies covering a wide horizontal and vertical sampling area report a smaller closure uncertainty than that from ground-based sites in the same area.These conflicting values probably stem from the more local nature of the ground measurements  versus the regional nature of airborne measurements.To capture the observed range of variability, we evaluate the uncertainties from both sets of measurements, recognising that the former are probably more relevant for finer-scale air quality modelling while the latter are probably more appropriate for comparison with coarser-resolution GCM climate predictions.

Model description
Simulations were conducted with the NASA Global Modelling Initiative (GMI; http://gmi.gsfc.nasa.gov)chemical transport model (CTM) using offline wind fields and an online aerosol simulation module coupled with the Kumar et al. (2009) droplet activation parameterisation (Karydis et al., 2011).The GMI model is a modular CTM capable of multiyear, global simulations of aerosol concentrations and compositions (Rotman et al., 2001;Considine et al., 2005).The aerosol module used for this study is that of Liu et al. (2005), which uses emissions inputs for SO 2 , dimethyl sulfide, H 2 O 2 , elemental carbon (EC), organic carbon (OC), mineral dust, and sea salt from Liu et al. (2005).The online aerosol module outputs the global distribution of aerosol mass concentrations, which is used to drive the cloud droplet parameterisation and its adjoint.Before running the offline droplet activation parameterisation, the aerosol mass is first classified as one of four, externally-mixed aerosol modes: fossil fuels (SO 2− 4 , OC, and EC), biomass burning (OC and EC), marine (SO 2− 4 and sea salt), and mineral dust.The aerosol within each mode are assumed to be internally mixed and follow a prescribed size distribution as given by Chuang et al. (1997) and Radke et al. (1988) for fossil fuel aerosols, Anderson et al. (1996) for biomass burning aerosols, Lance et al. (2004) for marine aerosols, and d'Almeida (1987) for mineral dust aerosols.
The aerosol number concentration for each type is then computed using these size distributions and a mass fractionweighted average of the component densities (e.g., SO 2− 4 , OC, EC) as described in more detail by Karydis et al. (2011).
The aerosol number distributions are then used to drive, offline, a cloud droplet parameterisation (Kumar et al., 2009;Barahona and Nenes, 2007;Fountoukis and Nenes, 2005;Nenes and Seinfeld, 2003) that employs a physically-based method for calculating the aerosol CCN spectrum (i.e., the number of particles that act as CCN as a function of supersaturation) and the maximum supersaturation, s max , for ascending cloud parcels in the global model.The total cloud droplet number, N d , is then the value of the CCN spectrum at s max in each model grid cell.Recently, the adjoint of the cloud droplet parameterisation has been developed (Karydis et al., 2012), which calculates the sensitivity of N d to the parameterisation input parameters (i.e, aerosol concentration and composition) during the forward model run.This allows the simultaneous computation of both the mean parameter values and their sensitivities with analytical precision.

Model application
The model simulation represents a single, climatological year (in this case from March 1997 to February 1998), including a one-month spin up time that is not included in the analysis.This simulated time period was selected to complement the modelling study of Karydis et al. (2011).Meteorological fields were obtained from the GISS II' global climate model (Koch and Rind, 1998;Rind and Lerner, 1996), with a horizontal resolution of 4 • latitude by 5 • longitude and with 23 vertical layers from surface pressure to 0.01 hPa.The meteorological information in the simulation was updated every three hours.For the droplet parameterisation and its adjoint, a constant effective water uptake coefficient of 0.06 was assumed (Fountoukis et al., 2007), and realistic updraft velocities were prescribed based on observed values for stratocumulus clouds over land (w = 0.3 m s −1 ) and ocean (w = 0.15 m s −1 ) (Chuang et al., 2000;Guibert et al., 2003;Meskhidze et al., 2005).Employing prescribed aerosol properties and cloud updraft velocities for land and ocean introduces additional uncertainty in the model simulations that is not explored in this study, and which may influence the derived sensitivities.The model simulations have been previously evaluated against worldwide observations of cloud droplet number concentrations by Karydis et al. (2011) with reasonably good agreement.Nonetheless, in the next section, we use the observed CCN concentrations reported by the studies in Table 1 to evaluate the ability of the GMI model and emissions inputs to capture this regional variability.

Model validation
The observed CCN concentrations shown in Table 1 were measured using CCNCs set to prescribed supersaturations ranging from 0.068 % to 2.8 %.In many cases these prescribed supersaturations are higher than predicted in-cloud values, owing to instrument statistical or detection limitations or a desire to probe the CCN activity of Aitken mode particles.This makes it difficult to compare the observed CCN concentrations directly with the modelled droplet concentrations, which correspond to the CCN concentration at ∼ 0.1-0.2% supersaturation.To enable comparison and validate the model against the available CCN dataset, we used the GMI model output with the cloud droplet parameterisation and prescribed supersaturations over the range of experimental values.From the results shown in Table 3, it can be seen that the model is able to predict droplet number concentrations (which in this case is the same as CCN) over the same range as the observed CCN concentrations in 27 of the 36 studies.In nine others, however, the simulated and observed concentration ranges do not overlap and differ by roughly a factor of two (range of −50 % to 69 %).The discrepancies in these locations could be caused by variability in either the aerosol size distribution or number concentration (since s max is known and set equal to the experimental values).Quantifying the uncertainty associated with the modelprescribed size distributions in a meaningful way is not easily accomplished, while the uncertainty due to aerosol loading (derived from emissions uncertainty) is more straightforward.As discussed in the supplementary material, additional simulations were conducted with twice and one-half of the modelled climatological mean aerosol concentration in order to determine how transient aerosol concentrations affect the sensitivities derived in Sect.3.2.The results suggest that variability in the model aerosol loading introduces a small (∼ 5 %) uncertainty into the following N d uncertainty analysis.
Our analysis shows that increases in cloud supersaturation tends to increase the derived cloud droplet concentration sensitivity by roughly (14 ± 19) % per 0.1 % supersaturation units.Thus, while the derived sensitivities here are representative of climatologically-relevant stratifrom clouds, they constitute only a lower limit for more strongly-forced, convective clouds.

Global aerosol concentration (N a ) distributions
The simulated global annual mean aerosol concentration, N a , is shown in Fig. 1a and is found to be mostly anticorrelated with s max over the continents (not shown), consistent with a pronounced competition for water vapour associated with increases in CCN concentration.The highest concentrations (and lowest s max ) are seen over the eastern United States, Europe and east Asia from anthropogenic emissions.Higher concentrations are also predicted for the Southern Hemisphere near and downwind of biomass burning sources.; and the discrepancy between prediction and observations.Simulations were carried out using a prescribed s max equal to the instrument supersaturation range in each study.Meanwhile, the lowest concentrations (and highest s max occur in the pristine southern and subtropical oceans and the Alaskan-Canadian Arctic.The simulated global geometric mean aerosol concentration is 502 × ÷ 5.52 for a mean s max of (0.07 ± 0.03) %.
Simulated N a and N d at s max for each of the study locations are given in Table 4.While the s max in these locations is similar to the global average, the simulated N a and N d are much higher than the global average due to the past focus on conducting closure studies over the continents.In addition, in some regions, the simulated N a in Table 4 is considerably less than the maximum observed N CCN given in Tables 1 and  3 (e.g., during Canadian biomass burning, near Houston, TX, and in ship plumes near Monterey, CA).Since N CCN must be less than N a , these transients show the impact of local emissions sources that are not captured well by the simulated annual mean aerosol concentration.However, as shown in Sect.2.4, the uncertainty associated with incorrectly modelling these transients is small (∼ 5 %).

Global cloud droplet concentration (N d )
distribution and relative sensitivity of N d to N a Simulated droplet concentrations, N d , are also shown in Table 4 and in Fig. 1b.The global distribution of N d is similar to that of N a , but with substantially lower concentrations (approximately five-fold on average).This is shown quantitatively in Fig. 2, as 50-100 % of aerosol form droplets at low concentrations, but the impact on N d of increasing N a gradually decreases above ∼100 cm −3 .This implies that the sensitivity of N d to aerosol depends on the activation fraction, which, in turn, is governed by N a and s max through the CCN spectrum.Low values of N a correlate with the highest s max and greatest cloud droplet sensitivity, while the highest N a correlate with the lowest s max and smallest cloud droplet sensitivity.The sensitivity decreases from 80-90 % at 10 cm −3 to nearly zero at 10 4 -10 5 cm −3 ; however, there is no clear trend in s max within this transition region (Fig. 2).This transition arises as aerosol concentration effects become more important than cloud dynamics in determining N d , and occurs around the inflection point of the sigmoidal fit function (N a ∼ 400 cm −3 ).As discussed by Karydis et al. (2012), the coarse mode of sea salt aerosol in the model can act as giant CCN (GCCN) in some regions (e.g., the North Atlantic Ocean).GCCN are large enough to activate at very low supersaturations and remove enough water vapour through their condensational growth that the local cloud s max is decreased.This means that fewer droplets can from in the presence of GCCN, resulting in an inverse-Twomey effect and potentially a reduction in shortwave cloud forcing (i.e., ∂N d /∂N a < 0).It is difficult to constrain the variability of GCCN, but they likely comprise a negligible fraction of overall measured in situ CCN concentrations.Consequently, for this study, we fix the sea salt partial N d sensitivity to values greater than or equal to zero (i.e., ∂N d /∂N a,seasalt ≥ 0), noting that the sensitivity may actually become negative in areas with close-to-zero sensitivities in Fig. 1.
The N d sensitivities shown in Table 4 indicate that most of the closure studies carried out in the past decade have taken place in moderately to heavily-polluted areas, where N d is weakly sensitive to changes in N a (∼ 10-30 %).Two studies in the Alaskan and Canadian Arctic show lower simulated  2007) simulated global cloud droplet number concentrations and anthropogenic aerosol indirect forcing using the GISS II' GCM and uncovered a similar global mean droplet concentration and geographical distribution as modelled here, but with nearly two-fold lower droplet concentrations in some continental regions.As expected, the spatial pattern of regional aerosol indirect forcing corresponded to the spatial pattern of N d .Thus, we expect the results of this study to be directly relevant for aerosol indirect forcing estimates even though the direct calculation of aerosol indirect forcing with a radiative transfer model is not performed here.

Global cloud albedo (A cld ) distribution and relative sensitivity of A cld to N a
The cloud droplet sensitivity discussed in the previous section provides important information regarding the potential sensitivity of clouds in a given region to changes in aerosol concentrations, but it says nothing about whether or not the clouds would form in the first place.This is because global and regional cloudiness is driven by dynamics (e.g., vertical updrafts) and moisture fluxes (e.g., water vapour mixing ratio) in addition to the presence of CCN.Quantifying these individual processes on a global scale is challenging; however, satellite measurements over the past decades have been able to discern global cloudiness with good accuracy.In this study, we use the global annually-averaged cloud albedo (A cld ) to capture all of these effects, which is computed as where A tsky and A csky are the total sky and clear sky albedos obtained from the NASA CERES mission satellite, respectively, and f cld is the daytime cloud fraction obtained from the MODIS mission satellite.Data were downloaded as annual averages for 2003 from the Giovanni online data system (Acker and Leptoukh, 2007).The global mean cloud albedo is 0.31.A cld directly captures the indirect effect of aerosols on clouds, while f cld indicates the extent to which clouds are present in a given area.The global distributions of A cld and f cld are shown in Fig. 3a and b.Synoptic scale dynamics play a large role in the observed distribution of f cld , with higher cloud fractions seen along the equatorial intertropical convergence zone (ITCZ) and in the mid-latitudes.Meanwhile, the observed cloud fraction is lowest in the subtropical subsidence zones.
In a landmark paper, Twomey (1991) defined the cloud albedo susceptibility to cloud droplet number as (Quaas et al., 2008) for a constant amount of liquid water and by making a number of simplifying assumptions regarding the radiative properties of liquid water droplets.Equation (2) indicates that A cld is at peak sensitivity to N d when A cld = 0.5, where Combining the satellite-derived ∂A cld /∂N d with the model-derived ∂N d /∂N a yields the overall sensitivity of cloud albedo to aerosol concentration, ∂A cld /∂N a , which is shown scaled by cloud fraction in Fig. 3d.Overall, the spatial distribution of the scaled albedo sensitivity is similar to the cloud droplet number sensitivity, except that the former exhibits decreased sensitivity in the subtropical subsidence zones, where both N d and cloudiness are low.The most sensitive regions are in the southern oceans and Arctic regions where a doubling of aerosol concentrations can be seen to induce the largest absolute change in albedo.Oreopoulos and Platnick (2008) also uncovered a similar spatial pattern of relative albedo sensitivity using MODIS satellite retrievals coupled with a detailed radiative transfer algorithm.They found distinct seasonal variation with the highest sensitivities found in coastal ocean upwelling zones throughout April-October and in the southern oceans during austral summer (Oreopoulos and Platnick, 2008).However, it is important to note that the sensitivities presented here do not include the mitigating effects of dynamical feedbacks (e.g., Koren and Feingold, 2011;Stevens and Feingold, 2009).Consequently, while the magnitude of this sensitivity may reflect an upper limit, the spatial distribution shown in Fig. 3d shows the key regions of the world where the sensitivity of cloud properties to aerosol is large.

Cloud droplet number uncertainties and implications for the indirect effect
In this section, the CCN closure uncertainties from Sect.2.1 (Table 2) and the modelled cloud droplet sensitivities from Sect.3.2 (Table 4) are combined to estimate the overall N d uncertainty arising from simplifying assumptions in Köhler theory that are typically applied in global modelling studies of aerosol-cloud interactions.Figure 4 gives the field measurement uncertainties for five of the six closure scenarios.
The left panels show the approximate spatial extent of those study areas located in North America and Europe and are coloured by the N CCN overprediction from Table 2.The right panels show the estimated N d overprediction N CCN .The colour scale for N CCN N CCN in Fig. 4 is twice that for N d N d , with light blue denoting zero overprediction (i.e., perfect agreement between Köhler theory predictions and measurements).For most regions in the continental United States and Europe, N d N d is quite small (∼ 0-20 %), despite large N CCN N CCN , which reflects the relative insensitivity of N d to aerosol concentration uncovered by the model for continental regions (Fig. 1c).Larger ∼ −10-20 %.Reported Arctic CCN uncertainties are considerably lower (Moore et al., 2011), but still have a large effect on N d N d because of the relatively low modelled droplet concentrations and relatively high modelled N d sensitivities in pristine regions.
Table 5 shows average uncertainty statistics for the six closure scenarios in this study.These mean values reflect the bias of past closure studies toward locations within the North American continent, which limits their generalisation over the globe.Additionally, the number of studies and the locations of those studies employing each closure scenario are different, which prevents direct cross-scenario comparison.However, the ratio of should be representative of the domain-averaged sensitivities, which can be directly compared despite different sample sizes.We find this ratio to be fairly invariant at 0.29-0.37 for N d N d ∼ 1-23 %.The N d uncertainty is consistent with the estimates of N d sensitivity made by Ervens et al. (2010) (∼ 15 %) using a parcel model and with average N d uncertainties of 7-14 % reported by Sotiropoulou et al. (2007) for the United States and Europe.Interestingly, the average N CCN uncertainties reported in the GCM study were also ∼ 10-20 %, suggesting a much larger N d sensitivity than we find here (i.e., ∼ 0.7 versus the 0.29-0.37found in this study).Sotiropoulou et al. (2007) also used the radiative transfer model embedded in the GISS II' GCM to express CCN prediction uncertainty in terms of cloud forcing.They find that a 10-20 % uncertainty in global N CCN results in a 0.1-0.2W m −2 shortwave cloud forcing uncertainty, which is 10-20 % of the anthropogenic indirect effect predicted in the model to be −1.00W m −2 .While this uncertainty is relatively small on a global scale, regional effects are likely to be more substantial.This is especially true when considering larger CCN prediction uncertainties than the range of 10-20 % assumed by Sotiropoulou et al. (2007), and which are suggested by some regional CCN closure studies in Table 2.

Summary and conclusions
Modelling simulations conducted with the GMI chemical transport model and cloud parameterisation adjoint are used to interpret and extend the results of thirty-six published CCN closure studies in the literature to estimate the overall uncertainty in cloud droplet number concentration from applying Köhler theory-based parameterisations with simplifying assumptions.We find that the prediction of cloud droplet number is most susceptible to CCN uncertainty at low aerosol concentrations (N a < 100 cm −3 ) and becomes insensitive to N CCN uncertainty for concentrations above 10 4 cm −3 .Thus, pristine areas such as the Arctic and remote oceans are found to be most sensitive (> 70 %), while the sensitivity over continental regions is on the order of 10-30 %, which is consistent with some previous estimates.While the simplifying assumptions employed by past CCN closure studies produce significant overprediction of N CCN when compared to observations, the impact of these uncertainties on the prediction of N d is on the order of ±10 % over most of the continental United States, but as high as 30-50 % in the Alaskan Arctic, Houston, TX and Los Angeles, CA, where the highest N CCN prediction uncertainties were observed.
This work shows that the regional sensitivity of N d to N CCN is important when assessing the uncertainty in cloud droplet number and albedo and, hence, indirect forcing, associated with simplified assumptions regarding CCN.Most CCN closure studies to date have been located in continental regions, and future measurements of CCN and aerosol properties should focus on more remote regions to improve the coverage of the global dataset.Much of the past global anthropogenic indirect forcing has been over the continents, and the results of this study indicate that uncertainties in estimating the global aerosol indirect effect arising from the simplified composition assumptions in models are relatively small.Two questions remain, however, that motivate future research.First, climate models may employ prescribed size distributions for aerosol composition modes, which are likely to be a large source of uncertainty; however, the closure studies employed in this study use measured size distribution information.Consequently, size distribution effects are not reflected in the N CCN proxy.Second, the impact of transient events such as long-range pollution transport or seasonal biogenic emissions sources on changing CCN concentrations remains unclear; the regional sensitivities uncovered in this study indicate that these events may have an important climatic impact.This motivates future field measurements directed at measuring CCN in the southern oceans and Arctic, where observations are limited and seasonal variations have been shown to be significant.These datasets would provide important information to quantify the impact of, and uncertainty associated with, how transient pollution events might influence predictions of CCN concentrations and, hence, clouds and climate.
for measuring R. H. Moore et al.: Droplet number prediction uncertainties from CCN

Fig. 1 .
Fig. 1.Simulated global spatial distribution of the annual mean N a (A), N d (B) and logarithmic sensitivity of N d to N a (C).
N d N d values are observed in California, in the Alaskan and Canadian Arctic, and in the Amazon rainforest, although only one closure scenario is considered in the Amazon study.In Los Angeles, the large N d N d reflects the large (nearly five-fold) CCN overprediction reported by Cubison et al. (2008) and Ervens et al. (2010) for all closure scenarios.In the Los Angeles basin and California Central Valley, Moore et al. (2012a) report smaller values of N CCN N CCN that vary from −59 to 79 %, and which translate into N d N d

Fig. 2 .Fig. 3 .Fig. 4 .
Fig. 2. Simulated N d (left) and sensitivity of N d to N a (right) plotted versus simulated N a for all grid model grid cells.Each point reflects one grid cell of the global annual mean values shown in Fig. 1, and are coloured by the grid-cell s max .

Table 1 .
Summary of past CCN closure studies using measured aerosol compositions and size distributions for predictions.

Table 2 .
CCN number concentration percent overprediction ( N CCN /N CCN )×100 % for different closure scenarios reported by the studies in Table1.

Table 3 .
Summary of regional observed CCN number concentration, N CCN ; simulated aerosol number concentration, N a ; simulated cloud droplet concentration, N d ; the logarithmic cloud droplet concentration sensitivity, ∂lnN d

Table 4 .
Comparison of regional simulated aerosol number concentration, N a ; simulated cloud droplet concentration, N d , at s max ; the logarithmic cloud droplet concentration sensitivity, ∂ ln N d ∂ ln N a ; the satellite-derived cloud fraction, f cld ; cloud albedo, A cld ; and semi-logarithmic albedo sensitivity ∂A cld ∂ ln N a.Satellite data were obtained from the NASA Giovanni database for CERES and MODIS satellites, as discussed in the text.All reported results are annual arithmetic means (± one standard deviation), except for N a and N d , which are geometric means ( × ÷ one geometric standard deviation).

Table 5 .
Percent overprediction of CCN concentration field study, with equal weighting given to each study location regardless of area.Reported are the mean ± one standard deviation across the 36 different datasets.Since individual field studies do not apply all scenarios, the overprediction values cannot be directly compared; however, the domain-averaged sensitivity ratios a and higher simulated s max and sensitivity of N d to N a (∼ 70 %).The global mean sensitivity is 0.46 ± 0.22.Sotiropoulou et al. ( N