1 Introduction

The estimation of anthropogenic aerosol indirect forcing (AIF) is important for the projection of future climate change (Boucher et al., 2013). Compared with warm clouds, much less attention has been paid to anthropogenic AIF through cirrus clouds (Myhre et al., 2013; Seinfeld et al., 2016). Although increasingly more general circulation models (GCMs) are including the treatment of aerosol–cirrus interactions (Liu et al., 2007; Gettelman et al., 2010; Barahona et al., 2014), it is often hard to clearly separate the anthropogenic ice AIF (i.e., anthropogenic AIF through cirrus clouds) from other AIFs (i.e., anthropogenic AIFs through warm clouds and mixed-phase clouds) without significant modifications of these GCMs. Thus, very few published papers present the anthropogenic ice AIF (Gettelman et al., 2012). Furthermore, compared with warm clouds, there are more uncertainties in representing cirrus clouds in GCMs because of the lack of observations. Thus, it is necessary to quantify the uncertainties in quantifying anthropogenic ice AIF. This study tries to fill this gap.

The uncertainties in estimating anthropogenic AIF by GCMs stem largely from two sources. First, GCMs themselves have substantial uncertainties in representing cloud processes including aerosol–cloud interactions. These uncertainties are an inevitable outcome of the limited understanding of realistic cloud processes and the scale disparity between GCMs and realistic cloud processes in the atmosphere (Seinfeld et al., 2016). Second, the change in the aerosol state itself from pre-industrial (PI) to present-day (PD) is uncertain. This uncertainty is caused by uncertainties in aerosol emissions and atmospheric aerosol processes (Boucher et al., 2013; Carslaw et al., 2013). In this study, we focus on the first kind of uncertainties.

Here, the Community Atmosphere Model version 5 (CAM5) is used to quantify the ice AIF. To separate the ice AIF from other AIFs, we adopt a new approach in which ice nucleation parameterization is driven by prescribed PD or PI aerosols. Sensitivities of ice AIF to several uncertain processes and parameters in CAM5 are investigated. The remainder of this paper is organized as follows. We introduce the model description and modifications in Section 2. Section 3 presents the sensitivity of ice AIF to different ice nucleation parameterizations and the uncertainties in the cloud microphysics scheme. Conclusions and discussion are given in Section 4.

2 Model and experiments 2.1 CAM5

The CAM5 model (Neale et al., 2012) is used in this study. Stratiform cloud microphysics in CAM5 is based on the MG scheme, which predicts the mass and number mixing ratios of cloud liquid and cloud ice, and diagnoses the mass and number mixing ratios of rain and snow (Morrison and Gettelman, 2008). The MG scheme is a framework of all cloud microphysics processes, such as activation of cloud condensation nuclei, accretion of cloud droplets and ice by rain, and sedimentation. In the MG scheme, each cloud microphysics process is described by empirical formula or parameterization. Note that, in the original MG scheme, ice nuclei concentrations are a function of temperature and not coupled to aerosol characteristics. To enable the CAM5 model to treat the aerosol indirect effects on cirrus clouds, the physically based ice nucleation parameterization of Liu and Penner (2005; hereafter LP) was applied in the MG scheme by Gettelman et al. (2010).

Here, the aerosol processes in CAM5 are treated with a three-mode (i.e., Aitken, accumulation, and coarse modes) aerosol module (Liu et al., 2012), which is coupled to the MG scheme for aerosol–cloud interactions. In the default CAM5, sulfate aerosols in the Aitken mode is used for homogeneous freezing and dust in the coarse aerosol mode is taken as potential ice nucleating particles (INPs). It is necessary to point out that the online calculated aerosols also drive the droplet activation parameterization, and the ice nuclei concentrations in mixed-phase clouds are a function of supersaturation and not coupled to aerosol characteristics.

There are two methods to diagnose the subgrid vertical velocity (W_sub), which is used to drive the ice nucleation parameterization. One is derived from the turbulent diffusion coefficient (Morrison and Gettelman, 2008), and the other is diagnosed from the turbulence kinetic energy (Gettelman et al., 2010).

The MG scheme distinguishes cloud ice and snow as two different classes of solid-phase condensates. The crystal/snow separating diameter (D_cs) has been used as a major tuning parameter in GCMs. Simulation results show that cirrus cloud properties are very sensitive to this tunable parameter (Zhang et al., 2013b). Unfortunately, it is difficult to directly constrain the D_cs value from observations (Eidhammer et al., 2017). Different D_cs values have been used in the MG scheme. In the version of CAM5 used in this work, the default value of D_cs is 400 μm, while D_cs has been set to 200 μm in an earlier version of CAM (Morrison and Gettelman, 2008).

Finally, it is necessary to point out that the shape parameter (μ) of the gamma size distribution is assumed to be 0 for ice crystals (i.e., exponential distribution) in the MG scheme, whereas observations show 0.5 < μ < 2.5 ( Heymsfield et al., 2002; Morrison and Grabowski, 2008). For ice particles with a certain mass and number, this assumption leads to overestimation of the number concentration for large ice particles, which then impacts the relevant cloud microphysical processes, such as the accretion of cloud ice by snow and the fall velocity (Khain et al, 2015).

2.2 Modifications to the standard CAM5

First, we improve the treatment of ice nucleation in a more realistic manner by including the effects of pre-existing ice crystals on ice nucleation in cirrus clouds (Shi et al., 2015). Second, a maximum distance for air parcel ascent (DH_max) is introduced to reduce the maximum ice supersaturation (S_imax) that the rising cloud parcel could reach within one model time step (20–30 min), as model-diagnosed W_sub actually represents the vertical velocity fluctuation rather than the constant updraft velocity needed by ice nucleation parameterization (Shi and Liu, 2016). If S_imax is less than the homogeneous freezing supersaturation threshold (S_ihom), homogeneous freezing cannot occur—undoubtedly, considering DH_max can reduce occurrence frequency of homogeneous freezing (Fre_hom). Unfortunately, there are too few observed Fre_homvalues to constrain the DH_max value (Cziczo et al., 2013). In this study, DH_max is a tunable parameter used for the restriction of Fre_hom. Finally, we modify the cirrus cloud formulas in the MG scheme to allow non-zero μ. The μ-relevant ice processes (i.e., number and mass weighted ice-crystal fall velocity, effective radius, ice deposition and sublimation rate, accretion of cloud ice by snow, and autoconversion of cloud ice to snow) are calculated based on the gamma size distribution (i.e., non-zero μ) instead of the default exponential distribution (i.e., zero μ).

Besides the above modifications, to investigate the sensitivity of ice AIF to different ice nucleation parameterizations, two other ice nucleation parameterizations developed by Kärcher et al. (2006, hereafter KL) and Barahona and Nenes (2009, hereafter BN) are implemented in the MG scheme. Thus, there are three options available (LP, BN, and KL) for calculating new-formed ice crystal number concentration in the MG scheme. All three ice nucleation parameterizations are developed based on the ice formation process in an adiabatically arising air parcel, in which the competition between homogeneous freezing on sulfate aerosol particles and heterogeneous freezing on INPs is considered. Although the microphysical processes are similar in the three corresponding air parcel models, model results are not quite similar in some extents because of different parcel model assumptions (e.g., nuclei spectra to represent the heterogeneous freezing) and different numerical solution methods (e.g., the homogeneous freezing competition among different sizes of sulfate aerosol particles). Furthermore, the approaches for deriving these ice nucleation parameterizations from the corresponding air parcel models are also different. For example, the LP parameterization is derived from fitting parcel model results. The BN parameterization is derived from the analytical solution of parcel model equations. The KL parameterization explicitly calculates the evolution of ice supersaturation in the rising air parcel. Therefore, it is possible for significant differences in newly formed ice number concentration (N_i) calculated from the three parameterizations.

Here we compare the three ice nucleation parameterizations (i.e., LP, BN, and KL) used in this study. In Fig. 1, N_i is shown as a function of sulfate aerosol number concentration (N_so4, Fig. 1a) and dust number concentration (N_dust, Fig. 1b), calculated from the three parameterizations. N_i calculated from the LP and BN parameterizations increases with increasing N_so4 (a tenfold increase in N_so4 roughly doubles N_i), whereas N_i calculated from the KL parameterization is not sensitive to N_so4 except at very low N_so4. The reason is that the numerical solution method of homogeneous freezing used in the KL parameterization neglects the competition among different sizes of sulfate aerosol particles, which results in very small sensitivity of N_i to N_so4 (Liu and Shi, 2018). Our parcel model using this KL approach can reproduce a nearly zero sensitivity of N_i to N_so4 (figure omitted), which is similar to the KL results in Fig. 1. Under these low N_so4 conditions all sulfate aerosols will be activated to ice crystals. This is the reason why N_i calculated from the KL parameterization increases with increasing N_so4. Although N_i calculated from the LP and BN parameterization show the same trend, N_i from LP is larger than BN under most conditions (Fig. 1a). The main reason is that the homogeneous nucleation rate is calculated using different methods in the corresponding air parcel models. It is clear that the homogeneous freezing forms most ice crystals as N_dust used for heterogeneous freezing is only 10 L^–1. Compared with N_i with an updraft velocity of 0.1 m s^–1, N_i with an updraft velocity of 0.5 m s^–1 increases by a factor of ~10. With the aid of INPs, heterogeneous freezing tends to occur at lower S_i than that required by homogeneous freezing (S_ihom), preventing the homogeneous freezing from occurring or reducing the homogeneous freezing ice crystal number (Spichtinger and Gierens, 2009). Taking the BN parameterization driven by an updraft velocity of 0.1 m s^–1 as an example, N_i decreases with increasing N_dust under 1 L^–1 < N_dust < 10 L ^–1 (Fig. 1b). The reason is that ice crystals produced by heterogeneous freezing deplete the water vapor in the parcel, and then reduce the homogeneous freezing ice crystal number. At N_dust > 10 L ^–1, homogeneous freezing is completely shut off, and N_i from heterogeneous freezing increases with increasing N_dust. Here, the competition between homogeneous and heterogeneous freezing is considered in all three parameterizations.

2.3 Prescribed aerosol data

Zhang et al. (2013a) introduced a new approach to CAM5, which allows the separation of the impact of aerosols on cold ice clouds from that on liquid clouds by using the prescribed aerosol capability. The prescribed PD and PI aerosol data are acquired from the baseline CAM5 simulations. In the default CAM5 model, aerosol characteristics, which are used for driving the ice nucleation parameterization and droplet activation parameterization, are online calculated from the aerosol module. To isolate the anthropogenic AIF on cirrus clouds from that on liquid-phase clouds, the ice nucleation parameterization is driven by the prescribed PD and PI aerosol data, respectively, whereas the droplet activation parameterization is still driven by the online PD calculated aerosol. In this study, each experiment has a pair of simulations (hereafter, PD and PI) with ice nucleation parameterization driven by the prescribed PD and PI aerosol data, respectively. Therefore, the difference between PD and PI simulations within one experiment only indicates the anthropogenic aerosol (i.e., the difference between PD and PI prescribed aerosol) indirect effects through cirrus clouds. Note that the anthropogenic ice AIF, which is calculated as the top-of-atmosphere radiative flux perturbation, not only comes from the changes in cirrus clouds but also from other radiation-relevant changes caused by rapid adjustments to anthropogenic aerosols (e.g., the interactions among ice, mixed-phase, and liquid clouds). Undoubtedly, this method also has shortcomings. Because the aerosol data used for driving ice nucleation is prescribed, the aerosol characteristics cannot respond to the influence of clouds and precipitation, such as wet removal of aerosols by precipitation. Also this method may inhibit the interactions among ice, mixed-phase, and liquid clouds through conversions of water vapor and cloud hydrometeors.

Evaluation of CAM5 aerosol simulations can be found in Liu et al. (2012). Here, the prescribed aerosol data used as inputs to the ice nucleation parameterization are shown in Fig. 2. Annual and zonal mean PD (for year 2000) sulfate aerosol number concentrations in the Aitken mode are higher than 100 cm^–3 in the tropical upper troposphere due to the new particle formation favored at colder temperatures. Unlike the sulfate aerosol number concentrations used for homogenous freezing, coarse mode dust number concentrations used for heterogeneous freezing are lower than 100 L^–1 in the upper troposphere, and even lower than 10 L^–1 over the Southern Hemisphere (SH). Compared with the PI (for the year 1850) aerosol concentrations, PD sulfate aerosol number concentrations are significantly increased, with normalized changes larger than 100% over the Northern Hemisphere (NH), and larger than 200% over the NH mid- and high latitudes. In contrast to sulfate aerosol, changes in dust number concentrations are not obvious. In this work, one sensitivity experiment uses higher INP number concentrations, following the study of Penner et al. (2015) in which coarse mode dust, 10% of accumulation mode dust, and 0.1% of accumulation mode soot are allowed to act as INPs. The total dust number concentrations (coarse mode + 10% accumulation mode) used for this experiment increase noticeably compared with the coarse mode dust. The 0.1% of accumulation mode soot concentrations, which can act as INPs, are very low (< 10 L^–1) in the upper troposphere. However, their changes from PI to PD are substantial.

2.4 Description of model experiments

In this study, the most uncertain aspects in the representation of cirrus clouds (including ice nucleation parameterization) that impact the estimation of anthropogenicice AIF were investigated. Table 1 summarizes all the experiments performed in this study. Compared with the default CAM5, the CTL experiment takes the pre-existing ice effects into account, and restricts the occurrence of homogeneous freezing with DH_max. Note that the effects of pre-existing ice and DH_max have been implemented in the development trunk of the CAM model (not yet released). As well as the CTL experiment, we carry out eight sensitivity experiments in three groups. Because ice nucleation is the root process for ice AIF, we first investigate the uncertainties of ice nucleation parameterization in group A. The CTL, ParaBN, and ParaKL experiments show the impact of different sensitivities of homogeneous freezing-produced N_i to N_so4. Comparison between the CTL and INP experiments shows the impact of uncertainties regarding INPs (i.e., heterogeneous freezing). Besides uncertainties in ice nucleation parameterization, how to drive the ice nucleation parameterization in GCMs can also significantly impact the ice nucleation process especially for homogeneous freezing. Unfortunately, cloud-scale vertical motions are poorly resolved in GCMs (e.g., the tunable parameter DH_max). The experiments in group B investigate the uncertainties in how to use ice nucleation parameterization (i.e., sensitivity to homogeneous nucleation occurrence). Finally, there are also some uncertainties about other cloud processes in the cloud microphysics scheme due to the lack of cirrus cloud observations or the coarse-resolution of GCMs. CAM5 simulation results show that cirrus cloud properties are very sensitive to some tunable parameter in the cloud microphysics schemes (Zhang et al., 2013b). The base state of cirrus clouds might significantly impact the estimation of anthropogenic ice AIF. Group C shows the sensitivity of ice AIF to some important uncertain variables (i.e, W_sub, D_cs, and μ) in the MG scheme.

All simulations in this study were run for 11 yr at a 1.9° × 2.5° horizontal resolution with 30 vertical levels and a 30-min time step, using prescribed sea surface temperatures and PD aerosol emissions. Each experiment had a pair of simulations with ice nucleation parameterization driven by PD and PI prescribed aerosols, whereas online calculated aerosols are used to drive the droplet activation parameterization for liquid clouds. The last 10 years’ results were used in our analysis.

3 Ice AIF and its uncertainty 3.1 Sensitivity to different ice nucleation parameterizations

Table 2 gives the global annual mean values of cloud radiative forcings, ice water path (IWP), high-cloud fraction (CLDH), column cloud ice number concentration (CDNI), and 60°S–60°N averages at 197 hPa of ice effective radius (R_i197) and cirrus cloud occurrence frequency (FRE197) from the PD simulations. Table 2 gives model results from all experiments. Here in this subsection, we only discuss about the sensitivity to the CTL, ParBN, and ParKL experiments. Results from other experiments will be analyzed in the following subsections. There are no remarkable differences in those variables listed in Table 2 among the CTL, ParBN, and ParKL experiments.

Figure 3 compares the variation of modeled N_i as a function of temperature against a compilation of field campaign data (Krämer et al., 2009). It should be noted that observed N_i might be overestimated due to the shattering of large ice particles, especially for relatively warm cirrus clouds (> 230 K) (Field et al., 2006). Here, we discuss modeled N_i from the CTL, ParBN, and ParKL experiments from the view of three temperature ranges, > 230 K, 205–230 K, and < 205 K. At temperatures above 230 K, we should keep in mind that the observed N_i might be overestimated and thus it is difficult to evaluate modeled N_i at these temperatures. In the temperature range of 205–230 K, modeled N_i from the CTL, ParBN, and ParKL experiments are close to the observations. There are no large differences among these three experiments. At temperatures below 205 K, modeled N_i from all experiments is obviously higher than observations. It is likely that some important mechanisms are missing in current GCMs. For example, aerosols rich with organic matter may become glassy below the glassy-transition temperature (approximately 205 K), thereby preventing homogeneous freezing from occurring (Jensen et al., 2010; Murray et al., 2010).

Figure 4 compares the probability distribution frequency (PDF) of modeled N_i against aircraft measurements from the Small Particles in Cirrus (SPARTICUS) campaign, which was carried out over the Southern Great Plains (SGP) site (36.6°N, 97.5°W). We sample instantaneous N_i over the field campaign site every three hours. Although the observation date has taken the shattering of ice crystals into account by using new probes and improved algorithms (Lawson, 2011), it is unclear to what extent very high N_i (> 1000 L^–1) is influenced by the ice shattering. Furthermore, it is important to point out that the observed N_i is from in situ aircraft measurements, while the modeled N_i represents the average of cloud fraction within a model grid cell (about 100 km). Therefore, the occurrence frequency of very high N_i from modelresults should be lower than observations. This point should be kept in mind when comparing modeled N_i with in-situ observations. Except for very high N_i, PDFs of modeled N_i from the CTL, ParBN, and ParKL experiments are close to each other, and agree well with observations.

Figure 5 shows the changes (PD minus PI) in the annual zonal mean in-cloud ice crystal number concentration (ΔN_i) from the CTL, ParBN, and ParKL experiments. Note that, in this work, we use “Δ” to indicate a change between PD and PI. As LP and BN parameterizations show moderate sensitivities of N_i to N_so4 (Fig. 1) and N_so4 is significantly increased from PI to PD over the NH (Fig. 2), ΔN_i from the CTL and ParBN experiments are statistically significant in the NH upper troposphere. In contrast, ΔN_i from the ParKL experiment is generally not statistically significant except in limited regions of the NH upper troposphere.

Table 3 gives the changes (PD minus PI) in global annual mean values for the variables listed in Table 2. The change in column cloud ice number concentration (ΔCDNI) from the ParKL experiment is 7.58 × 10⁶ m^–2, lower than that from the CTL (11.00 × 10⁶ m^–2) and ParBN (10.84 × 10⁶ m^–2) experiments. Note that homogeneous freezing usually occurs under high W_sub conditions because both pre-existing ice effects and DH_max are considered. If N_so4 is relatively low, most sulfate aerosols will be nucleated to become ice crystals under these high W_sub conditions. This is the reason why ΔCDNI from the ParKL experiment is not much lower than those from CTL and ParBN experiments. The change in ice water path (ΔIWP) from the ParKL experiment is 0.09 g m^–2, which is also lower than CTL (0.21 g m^–2) and ParBN (0.25 g m^–2) experiments. Note that the ice cloud fraction is diagnosed based on total water (vapor + ice) in the CAM5 model. Therefore, an increasing IWP might lead to positive changes in the high-cloud fraction (ΔCLDH). ΔCLDH from the CTL, ParBN, and ParKL experiments are 0.15, 0.26, and 0.20%, respectively. All experiments show that the averages of R_i197 decrease from PI to PD. ΔR_i197 from the CTL, ParBN, and ParKL experiments are –0.20, –0.32 and –0.19 μm, respectively. To analyze the changes in cloud top height, we calculated cirrus cloud occurrence frequency (FRE) at 121, 168, and 197 hPa (only FRE197 shown in Tables 2 and 3). All experiments showed that the averaged FRE at 121, 168, and 197 hPa are increased from PI to PD. These results indicate that cloud top height increase from PI to PD. ΔFRE197 from the CTL, ParBN, and ParKL experiments are 0.15, 0.24, and 0.08%, respectively. All three experiments show significant changes in longwave cloud forcing (ΔLWCF) and shortwave cloud forcing (ΔSWCF). The change in longwave cloud forcing (ΔLWCF) from the ParKL experiment (0.21 W m^–2) is weaker than those from the CTL (0.27 W m^–2) and ParBN (0.33 W m^–2) experiments. One possible reason is that ΔIWP from the ParKL experiment (0.09 g m^–2) is significantly lower than the CTL (0.21 g m^–2) and ParBN (0.25 g m^–2) experiments. ΔSWCF from the CTL, ParBN, and ParKL experiments are –0.24, –0.31, and –0.26 W m^–2, respectively.

3.2 Sensitivity to uncertainty of INPs

Here we discuss the impacts of uncertainty regarding INPs. Compared with the CTL experiment, 10% of accumulation mode dust and 0.1% of accumulation mode soot are also considered to be INPs in the INP experiment. The impacts of a higher number of INPs on ice nucleation are shown in Fig. 6. The occurrence frequency of homogeneous freezing (Fre_hom) from the INP experiment is reduced compared with the CTL experiment, due to the higher competition between homogeneous and heterogeneous freezing. In this work, Fre_hom indicates the occurrence frequency of homogeneous freezing under the condition of ice nucleation events. Both CTL and INP experiments show that Fre_hom is less than 10% in most regions except in the tropical upper troposphere and over the South Pole. This is consistent with the observation analysis that heterogeneous freezing is the dominant formation mechanism of cirrus clouds (Cziczo et al., 2013). The contribution of ice crystals from heterogeneous freezing (N_ihet) to total N_i is significantly increased over the NH in the INP experiment compared with the CTL experiment. Higher N_ihet from the INP experiment (not shown) could inhibit the production of ice crystals from homogeneous freezing (N_ihom). Thus, there are no significant differences in N_i between the INP and CTL experiments, but the relative contribution from homogeneous versus heterogeneous freezing changes. Furthermore, both the variations of N_i as a function of temperature and the PDFs of N_i over the SGP site are similar in the INP and CTL experiments (Figs. 3 and 4). The globalmean CDNI from the INP experiment (182.97 × 10⁶ m^–2) is close to that from the CTL experiment (185.68 × 10⁶ m^–2, Table 2). Unlike CDNI, ΔCDNI (Table 3) (i.e., difference in CDNI between PD and PI) from the INP experiment (9.10 × 10⁶ m^–2) is obviously less than that from the CTL experiment (11.00 × 10⁶ m^–2), owing to the more important role of heterogeneous freezing at the PI in the INP experiment. Correspondingly, ΔLWCF (0.14 W m^–2) from the INP experiment is much lower compared with the CTL experiment (0.27 W m^–2). However, ΔSWCF from the two experiments (–0.24 W m^–2) are same. Therefore, ΔCF from the INP experiment (–0.10 W m^–2) is much smaller than that from the CTL experiment (0.04 W m^–2). Note that the standard deviations of ΔCF from the INP and CTL experiments are 0.15 and 0.13 W m^–2, respectively. ΔCF in these two experiments are within their standard deviations.

3.3 Sensitivity to homogeneous nucleation occurrence (DH_max)

Now we look at changes in the simulations resulting from different DH_max values. Figure 7 shows Fre_hom and N_i at 197 hPa from CTL, NoDH and DH400 experiments. The NoDH experiment shows that Fre_hom is larger than 10% except near dust source regions (e.g., Saharan Desert, Arabian Desert, and Gobi Desert) where the high dust INPs concentrations could prevent the homogeneous freezing from occurring in most conditions. After considering DH_max, Fre_hom from the CTL (DH_max = 450 m) and DH400 (DH_max = 400 m) experiments are less than 10% in most regions. The global mean Fre_hom is reduced from 15.16% in the NoDH to 4.24% and 3.50% in the CTL and DH400 experiments, respectively. As a result, the global mean N_i is reduced from 493.4 L^–1 in the NoDH to 356.9 and 318.1 L^–1 in the CTL and DH400 experiments, respectively. N_i usually becomes very high (> 1000 L^–1) once homogeneous freezing occurs, and the high N_i could persist for dozens of model time steps (Shi et al., 2015). Thus, the global mean N_i from the DH400 experiment is still high (> 300 L^–1, much larger than the INPs concentration) even if Fre_hom is reduced to 3.50%. Figure 3 shows that N_i from the NoDH experiment is higher than the CTL and DH400 experiments. Accordingly, Figure 4 shows that the PDF of N_i > 100 L ^–1 from the NoDH experiment is higher than that from the CTL and DH400 experiments.

The global mean CDNI from the NoDH experiment is 245.62 × 10⁶ m^–2, which is significantly higher than that from the CTL experiment (185.68 × 10⁶ m^–2, Table 2). As a result, the global mean LWCF (29.24 W m^–2) and SWCF (–56.15 W m^–2) from the NoDH experiment are stronger compared with the CTL experiment (LWCF of 26.65 W m^–2; SWCF of –53.84 W m^–2). The global mean ΔLWCF (0.32 W m^–2) and ΔSWCF (–0.27 W m^–2) from the NoDH experiment are also stronger than those from the CTL experiment (ΔLWCF of 0.27 W m^–2; ΔSWCF of –0.24 W m^–2, Table 3). The global mean CDNI (129.50 × 10⁶ m^–2) from the DH400 experiment, by contrast, is much lower than that from the CTL experiment (Table 2). As a result, the global mean LWCF (24.49 W m^–2) and SWCF (–52.04 W m^–2) from the DH400 experiment are weaker. ΔLWCF (0.17 W m^–2) from the DH400 experiment is also smaller compared with the CTL experiment (Table 3).

3.4 Sensitivity to cloud scheme uncertainties (W_sub, D_cs, and μ)

W_sub from the Wsub experiment is much larger than that from the CTL experiment (not shown). From Fig. 8, we can see that CDNI from the Wsub experiment is several times higher than the CTL experiment, as N_i is very sensitive to updraft velocity (Fig. 1). Compared with the CTL experiment, IWP from the Wsub experiment is increased, and both LWCF and SWCF become stronger (Fig. 8). Figure 3 also shows that N_i from the Wsub experiment is significantly higher than the CTL experiments. In Fig. 4, it is demonstrated that the PDF of N_i > 200 L ^–1 from the Wsub experiment is higher than that from others experiments. The global mean CDNI from the Wsub experiment (799.26 × 10⁶ m^–2) is three times larger than that from the CTL experiment (185.68 × 10⁶ m^–2, Table 2). The global mean LWCF and SWCF from the Wsub experiment are enhanced by 9.95 and –10.84 W m^–2, respectively. Although the global mean ΔCDNI from the Wsub experiment (34.61 × 10⁶ m^–2) is two times larger than that from the CTL experiment (11.0 × 10⁶ m^–2), the relative change (ΔCDNI/CDNI) from the Wsub experiment (4.3%) is less than that from the CTL experiment (5.9%). This might be the main reason why global mean ΔLWCF (0.19 W m^–2) and ΔSWCF (–0.20 W m^–2) from the Wsub experiment are weaker than those from the CTL experiment (Table 3). This also indicates that the sensitivity of SWCF and LWCF to N_i become weakerunder high N_i conditions. Figure 9 shows the changes in annual and zonal mean ΔLWCF, ΔSWCF, ΔCDNI, and ΔIWP. ΔCDNI from the Wsub experiment is larger than 50 × 10⁶ m^–2 between 40° and 70°N, which is several times larger than that from the CTL experiment. However, ΔLWCF from the Wsub experiment is close to that from the CTL experiment between 40° and 70°N. Compared with ΔLWCF, the fluctuation of ΔSWCF is more complicated because changes in warm clouds can also impact SWCF. ΔSWCF from the CTL experiment between 50° and 70°N (positive) has the opposite sign to those from the other experiments (negative). However, these ΔSWCF are within the ranges of 2 standard deviations.

The threshold diameter D_cs that separates cloud ice and snow can significantly impact the autoconversion from cloud ice to snow in the MG scheme, and consequently exert a strong impact on the simulated IWP and LWCF (Gettelman et al., 2010; Zhang et al., 2013b). Compared with the CTL experiment, IWP from the Dcs200 experiment is significantly reduced due to a higher autoconversion rate from cloud ice to snow (Fig. 8). The global mean IWP from the Dcs200 experiment (10.35 g m^–2) is half of that from the CTL experiment (19.67 g m^–2), and much lower than the observation (25.8 g m^–2, Table 2). The global mean LWCF from the Dcs200 experiment is decreased by 2.0 W m^–2 compared with the CTL experiment (26.65 W m^–2). The global mean CDNI from the Dcs200 experiment (219.58 × 10⁶ m^–2) is increased compared with the CTL experiment (185.68 × 10⁶ m^–2). One possible reason is that the number-weighted ice-crystal fall velocity from the Dcs200 experiment is much smaller than that from the CTL experiment (not shown). The autoconversion rate from cloud ice to snow (i.e., D_cs) has significant impacts not only on cirrus clouds but also on warm clouds through the interactions among ice, mixed-phase, and liquid clouds. The Dcs200 experiment produces a higher liquid water path and higher column cloud droplets number concentration (not shown). This might be the main reasonwhy the global mean SWCF from the Dcs200 experiment (–55.42 W m^–2) is stronger than that from the CTL experiment (–53.83 W m^–2). The annual zonal mean distributions of ΔCDNI in the Dcs200 and CTL experiments are similar (Fig. 9). Compared with the CTL experiment, the Dcs200 experiment gives a weaker global mean ΔLWCF (0.23 W m^–2) and a stronger ΔSWCF (–0.32 W m^–2, Table 3). Thus, ΔCF from the Dcs200 experiment (–0.09 W m^–2) is less than that from the CTL experiment (0.04 W m^–2). Therefore, a smaller D_cs leads to a weaker ΔLWCF and a stronger ΔSWCF, and a lower ΔCF.

In the absence of any changes in ice number concentration or ice mass mixing ratio, an increase of μ results in a lower number concentration of larger ice crystals (not shown), and thus reduces the autoconversion rate from cloud ice to snow. This is a plausible explanation for the larger IWP in the Miu2 experiment (Fig. 8). Actually, the impacts of μ are complex because μ affects some other cloud microphysics (e.g., number and mass weighted ice-crystal fall velocities, and ice deposition and sublimation rate). The global mean IWP from the Miu2 experiment is increased to 38.06 g m^–2, much larger than the observation (25.8 g m^–2, Table 2). The Miu2 experiment produces much stronger LWCF (35.78 W m^–2) and SWCF (–62.27 W m^–2) compared with the CTL experiment. Because IWP from the Miu2 experiment between 40° and 70°S is high (> 40 g m^–2, Fig. 8), fluctuations of ΔIWP from the Miu2 experiment between 40° and 70°S are also large (Fig. 9). For the Miu2 experiment, the global mean ΔLWCF (0.35 W m^–2) and ΔSWCF (–0.47 W m^–2) are stronger than those from the CTL experiment (ΔLWCF of 0.27 W m^–2; ΔSWCF of –0.24 W m^–2); the global mean ΔCF (–0.12 W m^–2) is much smaller than that from the CTL experiment (0.04 W m^–2, Table 3). To sum up, μcan significantly impact cirrus cloud properties and anthropogenic ice AIF.

4 Conclusions and discussion

This study quantifies the anthropogenic ice AIF using CAM5 with a state-of-the-art treatment of ice nucleation. To separate the anthropogenic ice AIF, ice nucleation parameterization is driven by PD and PI prescribed aerosols, respectively, whereas online calculated aerosols with PD aerosol and precursor emissions are used to drive the droplet activation parameterization in both simulations. Compared with the fixed droplet number methodused in Gettelman et al. (2012), this method ensures that each experiment uses the same PD and PI aerosols to drive the ice nucleation process, thus focusing on the anthropogenic ice AIF.

One motivation for the development of cirrus clouds schemes in GCMs is to estimate ice AIF. However, there are same uncertainties in the cirrus cloud microphysics scheme (including ice nucleation parameterization) due to the lack of observation. In this study, we also try to determine the importance of each uncertainty to the estimation of anthropogenic ice AIF.

Sensitivity experiments of different ice nucleation parameterizations (i.e., CTL, ParBN, and ParKL experiments) show that longwave anthropogenic ice AIF (i.e., ΔLWCF) ranges from 0.21 (ParKL) to 0.27 (CTL) and 0.33 W m^–2 (ParBN), while shortwave ice anthropogenic AIF (i.e., ΔSWCF) ranges from –0.31 (ParBN) to –0.26 (ParKL) and –0.24 W m^–2 (CTL). Although the sensitivity of N_ihom to N_so4 in the KL parameterization is much weaker than those in the LP and BN parameterizatons, ΔCDNI from the ParKL experiment (7.58 × 10⁶ m^–2) is not much lower than those from the CTL (11.00 × 10⁶ m^–2) and ParBN (10.84 × 10⁶ m^–2) experiments. One possible reason is that N_ihom calcuated from the KL parameterization is sensitive to N_so4 under higher updraft velocity and lower N_so4 conditions, and many homogeneous freezing events occur under these conditions. The global mean ice anthropogenic AIF (i.e., ΔCF) from the ParKL experiment (–0.05 W m^–2) is less than the ParBN (0.02 W m^–2) and CTL (0.04 W m^–2) experiments.

Ice crystals can form heterogeneously on INPs at lower S_i, which can prevent the homogeneous freezing from occurring. Although Fre_hom is decreased due to a higher number of INPs (i.e., INP experiment), the global mean CDNI (182.97 × 10⁶ m^–2) is close to the CTL experiment (185.68 × 10⁶ m^–2) due to higher N_ihet. Furthermore, ΔCDNI (9.10 × 10⁶ m^–2) from the INP experiment is not much lower than that from the CTL experiment (11.00 × 10⁶ m^–2). One possible reason is that soot number concentration is significantly increased from PI to PD. ΔLWCF (0.14 W m^–2) from the INP experiment is significantly less than that from the CTL experiment (0.27 W m^–2), whereas ΔSWCF (–0.24 W m^–2) from the INP experiment is same as the CTL experiment. Thus, the INP experiment produces a much lower ΔCF (–0.10 W m^–2).

Although physically based ice nucleation parameterizations have considered the competition between homogeneous and heterogeneous freezing, to represent ice nucleation in a more realistic manner, it is still necessary for GCMs to restrict homogeneous freezing occurrence (Cziczo et al., 2013). The DH_max method used in this study was introduced in Shi and Liu (2016). DH_max can significantly reduce CDNI and ΔCDNI. ΔLWCF and ΔCF also become weaker after introducing DH_max.

We also investigate the sensitivity of anthropogenic ice AIF to uncertainties in the cloud microphysics scheme. W_sub derived from the turbulent diffusion coefficient can produce extremely high CDNI and ΔCDNI. However, ΔLWCF and ΔSWCF do not become stronger. Reducing D_cs leads to a weaker ΔLWCF and a stronger ΔSWCF, and a much weaker ΔCF. Non-zero μ can significantly impact cirrus cloud properties and enhance ΔLWCF and ΔSWCF. However, ΔCF is significantly decreased due to the non-zero μ. This group of experiments indicates that ice anthropogenic AIF depends on the base state of cirrus clouds.

The last two lines of Table 3 show ensemble statistics. Based on the statistical analysis of all experiments, the global mean ΔLWCF is estimated at 0.25 ± 0.07 W m^–2 (one standard deviation uncertainty), ΔSWCF is estimated at –0.29 ± 0.07 W m^–2, and total ΔCF is estimated at –0.04 ± 0.06 W m^–2. Although both longwave and shortwave ice AIFs are significant, the net ice AIF is rather weak. Note that the impacts of experiments in groups A and B on cloud properties (e.g., N_i, IWP, LWCF, and SWCF) are moderate compared with the experiments in group C (Figs. 3, 4 and Table 2). Including experiments of CTL, groups A and B (i.e., sensitivity experiments in the uncertainties on ice nucleation process), ΔLWCF is estimated at 0.24 ± 0.07 W m^–2, ΔSWCF at –0.27 ± 0.04 W m^–2, and the net ΔCF at –0.03 ± 0.07 W m^–2. These values are similar to those of all experiments.

This study focuses on uncertainties from the cloud microphysics scheme, especially for the treatment of ice nucleation. Sensitivity experiments suggest that improved understandings of the sensitivity of N_i to N_so4, the role of INPs, the spatial and temporal distribution characteristics of homogeneous freezing events, as well as the mean state of cirrus clouds properties, are necessary for constraining the ice AIF. It is worth noting that the uncertainty in aerosols is not considered in this work, which might also play an important role in estimating anthropogenic ice AIF.

Acknowledgments. We thank Kai Zhang for his assistance with prescribed aerosol code.