The coupled global atmospheric-ocean models used for transient simulations in the IPCC AR4 report differences in the present-day shortwave forcing of more than 2 W/m2. We show here that about 1.3 W/m2 of this spread could be explained by the different methods used to calculate cloud droplet number concentration (CDNC) from aerosol mass concentrations. Although we cannot rule out that other forcing agents could yield comparable uncertainties, this strongly points to the aerosol indirect effect as the main contributor to the wide spread in the shortwave forcing reported in IPCC AR4.
 More than three decades ago, Twomey  stated the first hypothesis on how anthropogenic aerosols may influence climate through their impact on clouds. According to this hypothesis, often termed the first aerosol indirect effect, an increase in atmospheric pollution will lead to an increase in cloud albedo, all else being equal.
 Several decades and hundreds of publications later, aerosol indirect effects on climate are still a puzzle to the scientific community [Baker and Peter, 2008], adding uncertainty to future climate projections. While the number of hypotheses on how aerosols may affect clouds, and thereby climate, have increased over this time period, the first aerosol indirect effect (AIE) is the only effect which can be calculated as a pure forcing directly comparable to other natural and anthropogenic forcing agents. In the Intergovernmental Panel on Climate Change (IPCC) fourth assessment report (AR4), the first aerosol indirect effect (AIE) was singled out as the most uncertain contributor to the net anthropogenic forcing of climate [Forster et al., 2007]. Despite the fact that this effect, also named the cloud albedo effect, has been studied extensively in recent decades, the level of understanding of this effect was in IPCC AR4 still characterized as low, radiative forcing estimates varying between −0.22 and −1.85 W/m2. Hence, the highest estimates predict the AIE forcing to be comparable to that of greenhouse gases, but of opposite sign. Nevertheless, out of the coupled model simulations presented in IPCC AR4 predicting climate change over the next century, only 9 out of 23 included aerosol indirect effects [Meehl et al., 2007].
 Prediction of aerosol indirect effects in numerical models requires a method for calculations of cloud droplet number concentration (CDNC) in the model based on aerosol mass or number concentration. In this paper, we investigate different methods applied to predict CDNC in the IPCC AR4 transient ocean-atmosphere simulations that included the AIE, 4 methods in total. We carry out this CDNC scheme intercomparison in the Integrated Forecasting System (IFS) modelling framework, developed at the European Centre for Medium-Range Weather Forecast (ECMWF). The purpose is to provide an estimate of the spread in anthropogenic forcings caused by the prediction of CDNC alone, by performing a series of model experiments varying the CDNC scheme while all other aspects of the modelling framework are kept unchanged. The uncertainty range for the shortwave radiative forcing (SWRF) of the coupled model simulations in IPCC AR4 [Meehl et al., 2007] spans from −1.6 W/m2 to +0.6 W/m2 for the year 2000. It is suggested that a major contributor to this wide range of SWRFs is the variety of parameterization of the aerosol indirect effect among the models.
2. Model Description and Setup
2.1. Integrated Forecasting System
 The global atmospheric modeling tool in this study is the Integrated Forecasting System (IFS), which is the operational forecast model from ECMWF. An extended version of the IFS is also the atmospheric component of an Earth system model currently under development, namely the EC-Earth model (http://ecearth.knmi.nl/).
 All simulations were carried out using a Semi-Lagrangian dynamical core at T95 spectral truncation, 40 levels in the vertical and a dynamical timestep of one hour. The physical schemes in the model most relevant for this study are the warm cloud microphysics scheme and the radiation scheme. The treatment of warm stratiform cloud microphysics follows Tiedke . Cloud condensate and cloud cover are prognostic variables, while precipitation release is diagnosed. Warm-phase clouds form in a model grid box when the relative humidity exceeds a critical height-dependent threshold, and dissipate as a result of evaporation and/or precipitation processes. The cloud droplet effective radius (re) is calculated based on cloud droplet number concentration and liquid water content, following the formulation of Martin et al. :
where LWC is the liquid water content, ρw is the density of water, Nl is the cloud droplet number concentration and k is a constant (k equals 0.67 over continents, and 0.80 in maritime air masses). Shortwave radiative properties of liquid clouds as a function of cloud droplet effective radius are calculated following Fouquart .
2.2. Description of the Aerosol Treatment
 As the focus of this study is to assess the forcing uncertainty introduced by applying various CDNC schemes, we prescribed the monthly average aerosol mass concentrations. The aerosol fields are the same as used by Chen and Penner  and Penner et al. , and include anthropogenic and natural sulfate, black carbon, anthropogenic and natural organic matter, and mineral dust and seasalt aerosols divided into two size categories.
2.3. Description of the Cloud Droplet Schemes
 Below follows a short presentation of the 4 methods applied to calculate cloud droplet number concentration (Nl) in this sensitivity study. In all cases Nl is given in cm−3.
 The representations of Nl as a function of sulfate mass presented by Boucher and Lohmann  (hereinafter referred to as BL95) have been used extensively in model studies of the aerosol indirect effects over the last decade. The empirical relationships in this paper are based on measurements from aircraft campaign carried out over North-America and the North and North-East Atlantic over different seasons and conditions. Based on these measurements, the following two relationships were obtained, for continental and maritime conditions, respectively:
where MSO4 is the sulfate mass concentration in μg/m3.
 The CDNC parameterization presented by Jones et al.  (hereinafter referred to as J01) was originally presented by Jones et al. , but was extended by J01 by taking not only sulfate but also seasalt aerosol concentrations into account. Based on simultaneous aircraft measurements of Nl and number concentrations of sulfate and sea salt aerosols (Na) from four regions (Pacific ocean, Summer 1987; South Atlantic, Winter 1991; British Isles, Winter 1990 and 1992; Azores, Summer 1992), the following relationship was presented:
 Here, Na represents all sulfate and sea salt aerosols (m−3), and Nmin = 5cm−3. It is assumed that seasalt and sulfate are externally mixed. The number of sulfate aerosols are predicted from the mass concentration of aerosol sulphur (m), following
where m is given in kgm−3. The number of seasalt aerosols is calculated as a function of windspeed following the parameterizations of O'Dowd et al. [1997, 1999].
 The relationships between Nl and aerosol mass concentrations presented by Menon et al.  (hereinafter referred to as M02) were based on partly the same field campaigns as those presented by BL95. However, they extended the BL95 approach by taking into account not only sulfate mass, but also seasalt and organic mass concentrations, obtaining the following relationships (for continental and maritime conditions, respectively):
where MSO4, MOM and MSS are the mass concentrations in μg/m3, of sulfate, organic matter and seasalt respectively.
Dufresne et al.  (hereinafter referred to as D05) presented modified versions of the relationships presented by BL95. By fitting (2) and (3) to satellite data from the POLDER instruments, they obtained the following relationship:
 CDNCs as a function of sulfate mass concentration based on Equations 1, 4, 6 and 8 are shown in Figure 1, illustrating the wide range of CDNCs arising from the four methods outlined above. For a given sulfate mass concentration, CDNC estimates span approximately one order of magnitude, especially when moderate amounts of organic matter are allowed to contribute to droplet formation by M02.
2.4. Model Setup
 For each CDNC scheme we carried out a pair of simulations; one with preindustrial (PI) aerosol concentrations and the other with aerosol concentrations corresponding to present day (PD) conditions. Anthropogenic changes in model parameters were thereafter calculated as the difference between the two simulations (subtracting PI values from PD values). We do not include the direct, semi-direct and second indirect aerosol effects in our simulations. Each simulation was carried out for 5 years, using climatological sea surface temperatures and sea ice extent. For all simulations, the CDNC is restricted to values higher than 5 cm−3.
3. Results and Discussion
 As evident from Figures 2a–2d, the four different CDNC schemes lead to significant differences in the CDNC values at 950 hPa (shown here for PD simulations). The highest CDNCs are produced by M02, while the D05 CDNC parameterization resulted in the lowest CDNCs. Similarly, as seen from Table 1, the anthropogenic changes in CDNC values at 950 hPa differ by one order of magnitude, leading to anthropogenic changes in the net radiative flux at the top of the atmosphere ranging from −0.62 W/m 2 to −1.94 W/m2. This range is dominated by the anthropogenic change in shortwave radiation, as the change in longwave radiation is always positive and never exceeds 0.12 W/m2 in any of the simulations. Generally, large anthropogenic changes in CDNC are expected to yield large AIEs. This is also confirmed by Table 1. However, the AIE is not only dependent on the anthropogenic CDNC perturbation, but also on the optical thickness of the unperturbed clouds. Typically, clouds with relatively low CDNCs are more susceptible to a CDNC perturbation than clouds with high CDNCs [e.g., Koren et al., 2008]. Consequently, the modest anthropogenic CDNC perturbation by D05 still leads to a significant AIE response of −0.62 W/m2, because the unperturbed clouds contain few cloud droplets in this case. Similarly, the high natural CDNC values of M02 correspond to a model state which is relatively insensitive to additional cloud droplets. Hence, a CDNC increase ten times larger than by D05 leads to an AIE of −1.94 W/m2, i.e., only about three times larger than the AIE by D05. Despite this CDNC saturation effect, the spread in AIE arising from varying the CDNC prediction is significant.
Table 1. Aerosol Indirect Effect and Corresponding Anthropogenic Changes in CDNC at 950 hPa for the Four CDNC Schemes
Figure 2e shows boundary layer CDNC derived from four years (2003–2006) of Moderate Resolution Imaging Spectroradiometer (MODIS) data using the methodology described by Bennartz . This study utilizes Level-3 daily atmospheric product, termed Atmospheric Daily Global Joint Product (Collection 5) available at the NASA Goddard Earth Sciences (GES) Distributed Active Archive Center (DAAC). The data is available on a 1 × 1 degree grid. In addition to the ocean-only data reported by Bennartz  we also present CDNC data over land in this study. This data is derived using the same methodology applied to MODIS cloud optical parameters over land. The accuracy of CDNC retrievals over water surfaces is discussed in detail by Bennartz . Over land surfaces the accuracy of the product might be further reduced by unresolved variations in surface albedo. The averaging period of 4 years ensures that random variations are sufficiently reduced to ensure a high accuracy of the average CDNC. However, in particular over land, the effects of undetected elevated aerosol layers above clouds might potentially lead to a systematic underestimation of retrieved CDNC, as discussed by Bennartz and Harshvardhan . For reasonably thin undetected aerosol layers, this effect will be about 20% at most and will thus be much smaller than the differences between the different CDNC schemes.
 As evident from Figure 2, M02 significantly overestimates CDNC compared to the MODIS data, while D05 underestimates CDNC, particularly over land. J01 and BL95 both compare favourably to the MODIS data, although J01 seems to predict too high CDNCs over the ocean. This overestimation is more pronounced at mid-latitudes, indicating that droplets formed on sea salt generated by high wind speeds may be causing this overestimation. It is interesting to note that BL95, representing the oldest and simplest CDNC scheme considered in this study, leads to the best comparison with observations. Comparing simulated CDNC at 850 hPa rather than 950 hPa will not significantly affect the above conclusions. However, the comparison is likely to be sensitive to the present-day aerosol fields, and simulations with aerosol fields deviating significantly from the ones employed here could lead to different conclusions. As the IFS has traditionally been employed in forecast rather than climate mode, it is reassuring that global cloud properties (liquid water path, ice water path and cloud cover) compare well with observed values (Table 2). Additionally, there is little variation in these variables for the different simulations. As aerosols effects on the hydrological cycle are not explicitly taken into account in this study, this is to be expected.
Table 2. Observed and Modeled Global Average Cloud Cover, Ice Water Path and Liquid Water Patha
 In this study, we have demonstrated that the various CDNC schemes applied in the coupled model simulations presented in the IPCC AR4 yield a first aerosol indirect effect ranging from −0.62 W/m2 to −1.94 W/m2, in simulations where aerosol fields and all other aspects of the model remained unchanged. This result indicates that most of the spread in the anthropogenic shortwave forcings from coupled simulations in the IPCC AR4 could possibly be explained simply by the different empirical relationships between aerosol mass and cloud droplet number concentration used in these models. However, there are also uncertainties associated with shortwave forcings arising from other processes, for instance the direct aerosol effect or land use changes. Additionally, the aerosol indirect effect is strongly dependent on model state (e.g., amount of low vs. high clouds) and pre-industrial vs. present-day aerosol fields. Hence, the same study carried out in a different model and/or with different aerosol fields could yield different results. Nevertheless, the spread in AIEs obtained in this study is significant, suggesting that the AIE is the primary contributor to the spread in estimates of anthropogenic shortwave forcings. Based on radiative transfer calculations for an idealized cloud case (i.e., fixed surface albedo, latitude, cloud cover, etc.), McComiskey and Feingold  found a set of different empirical relationships between CDNC and aerosol concentrations to yield a wide range of aerosol indirect forcings. Here, we have qualitatively confirmed their results in a non-idealized global context. Despite the wide uncertainty in AIE associated with empirical relationships, they are likely to be employed in global climate model (GCM) simulations for years to come, as they are relatively easy to implement in models and computationally inexpensive. The latter makes them particularly attractive for transient climate simulations. Hence, the AIE uncertainty range reported in this study should be kept in mind when comparing transient climate simulations in the future.
 We thank the European Centre for Medium-Range Weather Forecasts (ECMWF) for providing computing time within the special project SPCHCLAI and gratefully appreciate the user support for the help with the supercomputing facility. We are also thankful to the Swiss Federal Office of Meteorology and Climatology (MeteoSwiss) for supporting this study with additional computing time. Finally, we would like to thank two anonymous reviewers for comments that led to improvements of the paper.