This study investigates the sensitivity of the total anthropogenic aerosol effect to the treatment of rain within the global climate model (GCM) ECHAM5. A comparison between a prognostic (rain is stored within the atmosphere) and a diagnostic rain scheme (rain is precipitated out within one model time step) is conducted. Furthermore, the shape of the rain drop distribution within the prognostic rain scheme is varied. The prognostic rain scheme shifts the emphasis of the rain production process from autoconversion to accretion in better agreement with observations. Since the parameterization of the accretion process is independent of the cloud droplet number concentration, the total anthropogenic aerosol effect decreased by 0.5 to 0.9 Wm−2. Varying the rain drop distribution has a smaller influence on the total anthropogenic aerosol effect, changing it by 0.2 to 0.3 Wm−2.
 The total anthropogenic aerosol effect summarizes the impacts of aerosols on clouds and precipitation and, consequently, on the earth's radiative budget. This includes the aerosol indirect effects (AIE) and the smaller direct and semi-direct aerosol effects [see also Lohmann et al., 2007]. The first AIE (or cloud albedo effect) refers to decreasing cloud droplet sizes as the concentration of (anthropogenic) aerosols increases which leads to an increase in the cloud albedo and therefore, in the planetary albedo [Twomey, 1974]. Furthermore, it is more unlikely that the cloud droplets will grow to precipitation sized drops which presumably results in a prolonged lifetime of clouds within the atmosphere [Albrecht, 1989]. However, the magnitude of both of these effects is still very uncertain [Denman et al., 2007].
 The introduction of a prognostic rain scheme into the ECHAM5 GCM shifts the emphasis of the rain production from autoconversion (collisions and coalescence of cloud droplets) to accretion (collision and coalescence of cloud droplets with rain drops) in better agreement with observations [Wood, 2005; Posselt and Lohmann, 2008a, 2008b]. Wood  pointed out that autoconversion is important only within a thin layer near cloud top which cannot be resolved in a GCM and, thus, the parameterizations require considerable tuning. As the parameterization of the accretion process is independent of the cloud droplet number concentration, the total anthropogenic aerosol effect is smaller than using the standard diagnostic rain scheme [Posselt and Lohmann, 2008a, 2008b]. Please note, that, by mistake, only the anthropogenic aerosol effect of sulfate was calculated by Posselt and Lohmann [2008b] resulting in too low values for the total anthropogenic aerosol effect. In this study, we investigate whether the total anthropogenic aerosol effect is sensitive to parameters within the prognostic rain scheme, namely the assumed rain drop distribution.
 In this study, the ECHAM5-GCM [Roeckner et al., 2003] with the two-moment cloud microphysics scheme for cloud water and ice in stratiform clouds is used [Lohmann et al., 2007]. Aerosols are treated prognostically within the aerosol module HAM [Stier et al., 2005]. Recently, prognostic equations for the rain water mass mixing ratio and rain drop number concentration were additionally introduced into the ECHAM5 [Posselt and Lohmann, 2008a]. The rain quantities do not influence the radiation directly but cloud water and cloud cover do.
 Here, N denotes the total rain drop number concentration (in m−3), D is the rain drop diameter (in m) and Γ(μ) denotes the Gamma function. The Gamma distribution f(D) is characterized by the shape factor μ and the distribution parameter D0, which is proportional to the mean diameter .
ρw and ρa denote water and air density, respectively, and q the rain water mixing ratio (in kg kg−1). The exponential distribution is a special case of the Gamma distribution for μ = 1. An increase in μ results in a narrower size distribution where the largest and smallest drops are less emphasized. Figure 1 shows Gamma distributions with different μ for a constant rain drop number concentration and constant mean diameter.
 The bulk fall velocities for rain drop mass vq and number vN are obtained analogous to Posselt and Lohmann [2008a] using an approximated fall velocity relation of a single rain drop based on Rogers et al.  integrated over the drop size distribution f(D).
 The constants bv and b1 are given by bv = 3918 s−1 and b1 = 9.65 m s−1. The critical distribution parameter Dv has a value of Dv = b1/bv = 2463 μm. Using different fall speeds for mass and number enables gravitational sorting with larger drops being removed faster than smaller drops. The larger the shape factor, the lower is the ability of gravitational sorting as vq and vN converge with decreasing vq and increasing vN.
Milbrandt and Yau  and, recently, Seifert  provided a parameterization of μ depending on the mean diameter. Such a parameterization considers the changes in the shape of the rain drop distribution over time due to gravitational sorting. For rain drops Milbrandt and Yau  obtained the following expression for μ (with in m)
2.3. Model Setup
 The global simulations are conducted at a T42 horizontal resolution (∼2.8° × 2.8°) with 19 vertical model levels (uppermost layer at 10 hPa). The model time step of 30 minutes is divided into 30 sub-time steps for all processes involved in rain formation. The simulations are integrated for 5 years after a 3 month spin-up using climatological sea-surface temperatures and sea-ice extent.
 Sensitivity experiments with different values for μ, different approaches for the fall velocity (two-moment (different fall speeds for mass and number) versus a one-moment (same fall speed for mass and number)) and comparing the prognostic rain scheme with the diagnostic rain scheme are carried out (Table 1).
Table 1. Summary of Presented Global Simulations
simulation with the prognostic rain scheme [Posselt and Lohmann, 2008a] with 30 sub-time steps, different fall speeds for rain water mass vq and number vN using a Gamma distribution for rain drops with mu = 1
Same as MU-1, but applying the same fall speed vq for rain water mass and number
 Simulations MU-1 and DIAG are tuned so that the radiative balance at top-of-the-atmosphere (TOA) is within ±1 Wm−2. All other simulations use the same tuning parameters as MU-1. The imbalances of the non-tuned simulations are still small (within ±2–3 Wm−2). Furthermore, previous (non-published) simulations showed that the total anthropogenic aerosol effect is hardly affected by the tuning of the model.
 The total anthropogenic aerosol effect is defined as the change in the TOA net radiation due to anthropogenic aerosols and is estimated by comparing present-day (PD) to pre-industrial (PI) simulations. For the PI simulation, only natural aerosol emission representative of the year 1750 are used [Dentener et al., 2006].
Table 2. Annual Global Mean Precipitation (Ptot), Cloud and Rain Water Path (LWP, RWP) and Vertically Integrated Cloud Droplet Number (Nl), Cloud Cover (CC) and Shortwave Cloud Forcing (SCF) From Observations and the Model Simulations Described in Table 1
 Comparing simulation DIAG to simulation MU-1 reveals considerable changes. The cloud parameters LWP and Nl decrease considerably in MU-1 partly due to different tuning parameters. As the prognostic simulation stores rain in the atmosphere (rain water path, RWP), the hydrological cycle in MU-1 is decelerated resulting in longer cloud lifetimes (higher CC) and, thus, a slightly more negative SCF. The precipitation rate Ptot hardly changes due to the prescribed sea-surface temperature that largely controls the global mean evaporation from the surface.
 The usage of a one-moment fall speed scheme (MU-1m) as compared to the standard two-moment fall speed scheme in MU-1 leads to an increase in LWP and Nl, because the rain drops sediment more rapidly (lower RWP) so that more rain needs to be formed by the slower autoconversion process. This also leads to a slower hydrological cycle with higher CC and a more negative SCF. Employing narrower rain drop distributions (MU-10 and MU-PARA) has the opposite effect leading to a reduced LWP and Nl and increased RWP, resulting in a faster hydrological cycle due to increased accretion rates (see below), a shorter cloud lifetime (lower CC), and a less negative SCF as compared to MU-1.
 Employing a prognostic rain scheme results in changes in autoconversion and accretion rate as shown in Table 3. Within DIAG, the autoconversion is responsible for nearly 40% of the rain production whereas for the prognostic rain schemes autoconversion accounts for less than 10% which is in better agreement with observations [Wood, 2005]. This is the result from the repeatedly calculation of autoconversion and accretion on a smaller time step. The more vigorous accretion process removes more cloud water which in turn reduces autoconversion. Hence, the dependence on aerosol number is decreased because the autoconversion rate is the only rain producing process that depends on the cloud droplet number. This is especially important when evaluating aerosol induced changes between pre-industrial and present-day climate as discussed next.
Table 3. Annual Global Means of the Vertically Integrated Autoconversion Rate (AUT), Accretion Rate (ACC) and the Fraction of the Autoconversion Rate to the Total Conversion Rate (AUT+ACC) for the Model Simulations Described in Table 1
kg m−2 s−1
kg m−2 s−1
3.2. Present-Day Versus Pre-industrial Simulations
 The differences between present-day and pre-industrial simulation are shown in Table 4 and in Figure 2. The changes in precipitation are rather small due to the prescribed sea surface temperatures (see above).
Table 4. Annual Global Mean Changes of Precipitation, Cloud Properties and Shortwave (SW) and Met (Net) TOA Radiation Due to Anthropogenic Aerosols for the Model Simulations Described in Table 1
 The aerosol-induced changes in LWP and Nl vary substantially between DIAG and the prognostic rain schemes. The major effect can be seen on the northern hemisphere where the changes in aerosol burden due to industrialization is largest (Figure 2). LWP and Nl are reduced by a factor of two for MU-1 and by a factor of 3 for MU-10 and MU-PARA. The narrower the rain drop distribution the higher the amount of rain stored in the atmosphere. This reduces the contribution of the autoconversion rate in the rain production process (as shown in Table 3) sufficiently to reduce the response to increasing aerosol burdens. Interestingly, the simulations MU-10 and MU-PARA yield quite similar results which implies that the gravitational sorting of rain drops leads to a narrowing of the rain drop distribution in MU-PARA. The impact of that narrowing is not captured by the exponential distribution (MU-1) but can very well be described by choosing a constant μ larger than 1 (in this case μ = 10).
 The application of the one-moment fall speed scheme in MU-1m results in larger differences of LWP and Nl than in MU-1. Especially in the southern hemisphere, MU-1m is closer to DIAG than to MU-1. Within the one-moment scheme no gravitational sorting takes place. Thus, the mean diameter of the drops remaining in the atmosphere is larger than for the two-moment scheme. This results in higher fall speeds and a faster removal of rain water from the atmosphere which is reflected in a lower RWP. Thus, the slightly higher autoconversion rate makes the MU-1m simulation more susceptible to changes in the aerosol burden.
 The changes in the TOA shortwave (SW) and net radiation due to anthropogenic aerosols are tied closely to the changes in LWP. The smaller the increase in LWP from pre-industrial conditions to present-day climate the smaller are the changes in the TOA SW and net radiation. The changes in the net (SW) radiation are 0.67 (0.64) Wm−2 less negative in MU-1 as compared to DIAG. Narrowing the distribution leads to a further reduction of the total anthropogenic aerosol effect of 0.21 (0.15) Wm−2 for MU-10 and 0.16 (0.27) Wm−2 for MU-PARA. The one-moment fall speed scheme increases the anthropogenic aerosol effect by 0.16 (0.22) Wm−2. The generally less negative total anthropogenic aerosol effect for the simulations with the prognostic rain scheme compared to DIAG is in better agreement with inverse estimates of the total anthropogenic aerosol effect [e.g., Hegerl et al., 2007].
 Employing a prognostic rain scheme, which represents a more physical treatment of the warm rain precipitation process, reduces the total anthropogenic aerosol effect substantially, by 0.5 to 0.9 Wm−2. The change from a diagnostic to a prognostic rain scheme reduces the importance of the autoconversion process that depends non-linearly on the cloud droplet number concentration. Hence, the rain production is less sensitive to changes in aerosol burden which reduces the total anthropogenic aerosol effect.
 The shape of the rain drop distribution also influences the total anthropogenic aerosol effect but to a lesser extent. A narrower distribution results in a less negative total anthropogenic aerosol effect of −1.3 to −1.35 Wm−2 as compared to −1.51 Wm−2 for the broad exponential distribution. The usage of a one-moment fall speed reverses the effect so that the total anthropogenic aerosol effect becomes more negative with −1.67 Wm−2.
 The rather large sensitivity of the total anthropogenic aerosol effect to the treatment of rain suggests that it is important to implement an appropriate parameterization for the rain drop distribution. However, the choice of μ is rather complicated due to the lack of knowledge about the “correct” rain distribution. Thus, extended measurements are necessary to fill this gap.
 The authors thank P. Spichtinger, A. Mühlbauer (ETH Zurich) and one anonymous reviewer for helpful comments and suggestions, S. Ferrachat (ETH Zurich) for technical support and the Swiss National Supercomputing Centre (CSCS) for computation time. This study contributed towards the Swiss climate research program NCCR Climate.