The ultimate purpose of this study is to investigate the contribution of ice nucleation parameterizations to the difference in estimating anthropogenic aerosol indirect forcing.Three physically-based ice nucleation parameterizations,respectively developed by Liu and Penner(2005,hereafter LP),Barahona and Nenes(2009,hereafter BN) and Kärcher et al.(2006,hereafter KL) are analyzed in this paper.The LP parameterization is derived from fitting the simulation results of a cloud parcel with constant updraft velocities.The number of nucleated ice crystals is a function of relative humidity,temperature,aerosol number concentration and updraft velocity.The BN parameterization is derived from an approximation to the analytical solution of air parcel equations.One advantage of BN parameterization is that the heterogeneous nucleation may be described by different nucleation spectra,derived either from the classical nucleation theory,or from observations.In KL parameterization,the competition between different freezing mechanisms is treated by explicitly calculating the evolution of the water vapor saturation ratio within one host-model's time step.It is worth noting that,in this parameterization,the ice crystal number concentration produced via homogeneous freezing is not sensitive to the sulfate aerosol number concentration in most cases,except for the highest(4 m·s^-1) updraft velocities.The offline experiments show that the ice crystal number concentration calculated from KL parameterization was not sensitive to sulfate aerosols number concentration in most cases,whereas the ice crystal number concentration calculated from the LP and BN parameterizations increased with the increasing sulfate aerosols number concentration.Compared to the BN and KL parameterizations,it is relatively easy for heterogeneous ice nucleation to inhibit homogeneous ice nucleation with LP parameterization.However,the ice crystal number concentration calculated from LP parameterization is usually higher than BN and KL parameterizations.Aside from the default LP parameterization in the CAM5 model,the BN and KL parameterizations were implemented in CAM5 for comparison.The occurrence frequency of homogeneous freezing from simulation with LP parameterization is less than BN and KL parameterizations.However,all of the simulations show that the occurrence frequency of homogeneous freezing is less than 0.1,which is in consistent with the observations.Furthermore,there is no remarkable difference among these three parameterizations in the ice crystal number concentration or cloud radiative forcing,and all of the simulation results show generally high agreements with cirrus cloud observations.This suggests that the model's capability to simulate cirrus clouds is not sensitive to physically-based ice nucleation parameterizations.The CAM5 experiment using the KL parameterization predicts a much smaller anthropogenic aerosol long wave indirect forcing(LWCF,0.05 W·m^-2) than that using the LP(0.36 W·m^-2) and BN(0.33 W·m^-2) parameterizations.This indicates that ice nucleation parameterization plays an important role in estimating anthropogenic aerosol indirect forcing.Previous studies showed that the annual global mean change in LWCF from pre-industrial times to present-day estimated from the ECHAM5 model with KL parameterization was 0.05—0.20 W·m^-2,which was much less than the estimate(0.40—0.52 W·m^-2) given by the CAM5 model with LP parameterization.It appears that this difference can be mostly explained by ice nucleation parameterizations.