This study validates the cloud ice water content (IWC, non-precipitating ice/non-snow) produced by a unique prognostic cloud ice parameterization when used in the UCLA atmospheric general circulation model against CloudSat observations, and also compares it with the ERA-Interim reanalysis. A distinctive aspect of this parameterization is the novel treatment of the conversion of cloud ice to precipitating snow. The ice-to-snow autoconversion time scale is a function of differential infrared radiative heating and environmental static stability. The simulated IWC is in agreement with CloudSat observations in terms of its magnitude and three-dimensional structure. The annual and seasonal means of the zonal-mean IWC profiles from the simulations both show a local maximum in the upper troposphere in the tropics associated with deep convection, and other local maxima in the mid-troposphere in midlatitudes in both hemispheres associated with storm tracks. In contrast to the CloudSat values, the reanalysis shows much smaller IWC values in the tropics and much larger values in the lower troposphere in midlatitudes. The different vertical structures and magnitudes of IWC between the simulations and the reanalysis are likely due to differences in the parameterization of various processes in addition to the ice-to-snow autoconversion, including ice sedimentation, temperature thresholds for ice deposition and cumulus detrainment of cloud ice. However, a series of sensitivity experiments supports the conclusion that the model with a constant autoconversion time scale cannot reproduce the correct IWC distribution in both the tropics and midlatitudes, which strongly suggests the importance of physically based effects on the autoconversion timescale.
 Ice clouds play extremely important roles in the radiation budget of the Earth [e.g., Liou, 1986; Stephens, 2005; Yue and Liou, 2009]. They reflect solar radiation, and absorb and emit terrestrial radiation. Using satellite observations, Liou  showed that ice clouds regularly cover about 20–30% of the globe. Wylie et al.  reported high clouds (mostly ice clouds) in 33% of the National Oceanic and Atmospheric Administration (NOAA) High Resolution Infrared Radiometer Sounder data from 1979 to 2001. Despite the recognized importance of ice clouds, large quantitative uncertainties remain in our understanding of their generation, maintenance and decay mechanisms. These uncertainties result in major obstacles to the development of reliable cloud ice schemes for General Circulation Models (GCMs). In addition, there has been a lack of global observational data sets of cloud properties such as high resolution vertical profiles of ice water content (IWC) to constrain mass concentrations of cloud hydrometeors [Waliser et al., 2009].
 The cloud profiling radar onboard the National Aeronautics and Space Administration (NASA) CloudSat satellite (launched in 2006 [Stephens et al., 2008]) has been providing a new global view of the vertical structure of clouds, in particular the structure of cloud condensate including IWC at a higher vertical resolution than other satellites (e.g., Earth Observing Systems' Microwave Limb Sounder, EOS MLS). Using a combined CloudSat/CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) cirrus cloud algorithm, Sassen et al.  reported a global average frequency of cirrus cloud occurrence of 16.7% during the period 15 June 2006 through 15 June 2007. Stubenrauch et al.  present a six-year global climatology of cloud properties obtained from observations of the Atmospheric Infrared Sounder (AIRS) onboard the NASA Aqua satellite, and evaluate the retrieved AIRS cloud properties with combined CloudSat/CALIPSO observations. They found global cloud amount to be between 66% to 74%, to which high clouds (cloud mid-layer pressure lower than 440 hPa) contribute about 40%. The largest fraction of high clouds (thin cirrus, cirrus, and high opaque clouds, such as anvils) occurs in the tropics.
 Using the EOS MLS and CloudSat IWC vertical profiles, Waliser et al.  discuss how to make meaningful comparisons of satellite cloud condensate retrievals with model simulations for tropospheric ice clouds. They also discuss shortcomings in the simulation of IWC in contemporary climate models. The cloud profiling radar on CloudSat is sensitive to large hydrometeors and IWC. For a meaningful comparison between the retrieved and simulated IWC, convective and precipitating particles, such as snow, graupel, and hail must be excluded from the retrievals since the effects of such large particles are not included in the calculation of IWC in most conventional prognostic ice cloud parameterizations used in climate models. Waliser et al.  further suggest that radiation calculations that use IWC calculated in this way are also affected by excluding such large hydrometeors in the parameterizations. These processes should be included in the development of cloud ice parameterizations. Indeed, the radiative impacts of large hydrometeors (i.e., snow) have been included in National Center for Atmospheric Research (NCAR), Community Atmosphere Model, Version 5 [Gettelman et al., 2010], and their results demonstrated improvement in the simulated ice clouds and radiation fields.
Table 1 compares various cloud microphysics schemes utilized in the selected World Climate Research Programme (WCRP) phase 3 and 5 of the Coupled Model Intercomparison Project (CMIP3 and CMIP5) models. We also list the schemes used in the University of California Los Angeles atmospheric GCM (UCLA AGCM) and the model that produces the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis. There are different degrees of complexity of microphysics schemes among these models. For all of the selected CMIP3 models, only single-moment schemes (prognosing mass mixing ratios only) were implemented in the cloud microphysics schemes. However, two-moment schemes (prognosing both mass and number mixing ratios) for AGCM parameterizations for both cloud ice as well as other species such as cloud water (e.g., NCAR CESM1.0 and GFDL CM3) are becoming more widely used. The primary goals of such two-moment schemes in AGCMs are largely to improve the treatment of cloud-aerosol interactions, and to allow for a more physically based representation of cloud droplet and ice nucleation on aerosols and therefore indirect aerosol effects. Other than the various microphysics processes implemented in these climate models, of high relevance to our study is the representation of the ice-to-snow autoconversion time scale, which varies widely between models from a simple constant to a physically based formula (e.g., UCLA AGCM). With the availability of CloudSat observations, it is now possible to evaluate the impact of these parameterized microphysics processes on the simulated three-dimensional structure of cloud ice.
Table 1. Intercomparison of Cloud Microphysics Parameterizations Used in the Selected WCRP CMIP3 and CMIP5 Models, as Well as UCLA AGCM and ERA-Interim Model
Ice-to-Snow Autoconversion Time Scale
UCLA AGCM v7.1
mixing ratio of cloud liquid, ice
autoconversion ; Bergeron-Findeisen; condensation; cumulus detrainment of water vapor, cloud liquid, cloud ice; deposition; evaporation; freezing; melting; sublimation
number concentrations (N) and mixing ratio of cloud droplets and cloud ice (q)
activation of cloud condensation nuclei or deposition/condensation-freezing nucleation on ice nuclei to form droplets or cloud ice (N only); condensation/deposition (q only); accretion; autoconversion; cumulus detrainment; evaporation; heterogeneous freezing; homogeneous freezing; melting; sedimentation; sublimation; ice supersaturation and nucleation are allowed
τ = constant; (the autoconversion is also determined by size distributions)
 In this study, we validate a prognostic cloud ice parameterization used in the UCLA AGCM with CloudSat observations, and compare the results with IWC values from the latest reanalysis data set from the ECMWF (ERA-Interim). The emphasis is on the introduction of a physically based ice-to-snow autoconversion parameterization in the UCLA AGCM, and the AGCM's ability to represent the horizontal and vertical profiles of IWC. Several sensitivity experiments are performed to gain insight on the importance of different physical processes in the model parameterizations. The remainder of the paper is organized into five sections. Section 2 introduces the data sets and model. Section 3 describes the prognostic cloud ice and bulk microphysics schemes in the UCLA AGCM. Section 4 compares simulated IWC in the UCLA AGCM with CloudSat observations and the ECMWF ERA-Interim reanalysis. The results of the sensitivity experiments are also presented in Section 4. Section 5 summarizes and draws conclusions.
2. Data Sets and UCLA AGCM
2.1. CloudSat Observations and the ECMWF ERA-Interim Reanalysis
 The primary observational data we use are the IWC retrievals from CloudSat Version 4 (RO4), which covers the period from June 2006 to July 2008. These particular data are produced using a retrieval algorithm that includes a temperature threshold [Austin, 2007]. In this algorithm, the water contents for both liquid and ice phases are retrieved for all heights using separate assumptions, then a composite profile is created by using the retrieved ice properties at temperatures colder than −20°C, the retrieved liquid properties at temperatures warmer than 0°C, and a linear combination of the two in intermediate temperatures. This reduces the total IWC as the temperature approaches 0°C.
 The total IWC values from CloudSat are larger than those from the analysis and model simulations by a factor of two to three since the retrievals from CloudSat are sensitive to multiple sizes of ice particles, both slow-falling (near-floating) and fast-falling forms [Waliser et al., 2009]. In most conventional GCMs, including the UCLA AGCM and the ECMWF model version used in the ERA-Interim reanalysis, only the small ice particles associated with clouds are represented in the prognostic cloud ice variable, whereas the larger particles associated with precipitating snow and convective cores are represented diagnostically [Tompkins et al., 2007; Li et al., 2008; Waliser et al., 2009]. As stated in the introduction, to make meaningful model-data comparisons, all CloudSat RO4 IWC [Stephens et al., 2008] retrievals that are associated with convective cloud types (using CloudSat cloud classifications) or that are flagged as exhibiting surface precipitation are omitted [Li et al., 2008; Woods et al., 2008; Waliser et al., 2009]. We then obtain an estimate of cloud ice which serves as a constraint for the prognostic ice cloud variable in typical GCMs. Ideally, precipitating profiles from the models should also be excluded to obtain an equivalent cloud ice estimate to the non-precipitating/non-convective CloudSat data. This, however, has to be done while the model was being integrated, and will be a meaningful filtering only if the model resolution is high enough and comparable to CloudSat footprint. Since we cannot perform such calculations over the ERA-Interim, we assume this issue only has minimum impact on our comparison because model precipitation in a GCM represents the mean within a grid box with a horizontal resolution of about 200 km by 200 km and a column physics time step of one hour, whereas CloudSat has a footprint of about 1–2 km.
 We also use the latest global reanalysis data set - ERA-Interim - from ECMWF [Dee et al., 2011]. The cloud microphysics scheme of the model cycle 31R1 used in the ERA-Interim reanalysis allows for ice phase supersaturation [Tompkins et al., 2007] and includes a new scheme for ice crystal sedimentation and snow autoconversion rate. The cloud ice fields in ERA-Interim, however, are not directly constrained, as ice cloud observations are not assimilated directly. Hence the cloud ice fields are largely determined by the model physics. More details on the model cycle 31R1 can be found at http://www.ecmwf.int/research/ifsdocs/CY31r1/index.html. IWC data from this reanalysis are available at a horizontal resolution of 1.5° latitude and 1° longitude and 37 pressure levels in the vertical. The monthly means of the daily mean IWC fields are used for the period from 1989 to 2009.
2.2. Atmospheric Model: UCLA AGCM
 The UCLA AGCM includes parameterizations of the major physical processes in the atmosphere. The parameterization of cumulus convection, including its interaction with the planetary boundary layer (PBL), is a prognostic version of the original Arakawa-Schubert cumulus parameterization [Arakawa and Schubert, 1974] designed by Pan and Randall . The parameterization of radiative processes is based on work by Harshvardhan et al. [1987, 1989] and the parameterization of PBL processes is based on the mixed-layer approach of Suarez et al. , as revised by Li et al. . Surface heat fluxes are calculated following the bulk formula proposed by Deardorff  and modified by Suarez et al. . The model also includes parameterizations of prognostic cloud liquid water and cloud ice [Köhler, 1999] and the effects of cumulus clouds on the radiative transfer. A detailed description of the parameterization of prognostic cloud ice and the bulk microphysics scheme follows in the next section. Further details of the model are provided by Arakawa  and Mechoso et al. . The UCLA AGCM is coupled to the first generation of the Simplified Simple Biosphere Model (SSiB) [Xue et al., 1991]. Several sources of data [Dorman and Sellers, 1989; Xue et al., 1996a, 1996b] have been used to determine the vegetation types that specify monthly climatological land surface properties (e.g., leaf area index, green leaf fraction and surface roughness length) in SSiB. In the configuration used here, SSiB has three soil layers and one vegetation layer.
 In the present study, we use version 7.1 of the model with a horizontal resolution of 2.5° latitude and 2° longitude, and 29 layers in the vertical. The model top is 1 hPa. The distributions of greenhouse gases, sea ice, and ocean surface albedo are all prescribed corresponding to a monthly climatology. The atmospheric initial conditions are taken from a previous, multiyear model run starting on October 1st, 1982 from the NCEP/NCAR reanalysis [Kalnay et al., 1996]. The monthly varying SST fields for the AGCM simulations are taken from the climatology compiled by Reynolds and Smith . We performed a control and a series of sensitivity experiments. The control is twenty years long and each of the sensitivity experiments is three years long.
3. Prognostic Cloud Ice and the Bulk Microphysics Schemes in the UCLA AGCM
 In this section, we describe the prognostic cloud ice and bulk microphysics schemes in the UCLA AGCM. The reader is referred to Köhler  and Appendix A for more details. A bulk microphysics scheme of moderate complexity based on work by Ose  is assembled that uses water vapor (qv), cloud liquid water (ql) and cloud ice (qi) as prognostic variables and diagnoses rain (qr) and snow (qs) independently. Here qn is the mixing ratio of the bulk species n. The scheme includes descriptions of the dominant exchange processes between each pair of bulk species. The continuity equations for these five bulk-water species are expressed as follows:
where is the rate of change of bulk species n due to process m, A(qn) is the grid-scale advection of qn, and F(qn) is the advection by falling. The processes considered here are detrainment from cumulus convection (cum), condensation (cnd), deposition (dep), evaporation (evp), sublimation (sbl), autoconversion (auto), Bergeron-Findeisen process (bf), and melting (mlt). Figure 1 illustrates the microphysical exchange processes between the five bulk-water species. Each arrow is labeled according to the dominant microphysical process linking the corresponding bulk-water species. Here, we focus only on the microphysical and macrophysical (dynamical) processes for cloud ice. Cloud ice (qi) is treated as a separate prognostic variable, which allows for the incorporation of detailed cloud microphysics and the potential to advect cloud ice (equation (3)). We did not, however, include several microphysics processes in this parameterization, such as sedimentation of cloud ice, accretion and riming of cloud liquid water and ice by rain and snow. These processes also play a role in determining the profiles of cloud ice [e.g., Wacker and Seifert, 2001; Jakob, 2002; Spichtinger et al., 2006].
 The amount of precipitation generated in the cloud potentially involves all five bulk-water species. It also depends on sub-grid scale dynamical processes and parameters ranging from the particle size distribution to the cloud-scale geometry and motion field. However, the dominant process in the model that determines the precipitation generation is the autoconversion which represents the small scale collection processes converting small particles to larger precipitating particles. The representation of this process for ice to snow conversion is the focus of this paper.
3.2. Precipitation Formation and Autoconversion
 A suite of cloud resolving model (CRM) simulations were performed by Köhler  to investigate the degree to which GCM-unresolved cloud scales impact the evolution of large-scale layer clouds. The CRM was originally developed by Krueger  and is based on the two-dimensional (X-Z) anelastic equations. It features a third-order turbulence closure.
 Based on the CRM experiments, Köhler  showed that optically thick cloud layers decay significantly slower than expected if the microphysical autoconversion of cloud ice to snow was the only process at work. In their study, eight physical parameters, cloud layer thickness, normalized total water in cloud, environmental relative humidity, environmental static stability, cloud differential IR heating, cloud differential solar heating, maximum total water flux (a summation of all water phases), and total kinetic energy (the CRM parameterized turbulent kinetic energy plus the resolved eddy kinetic energy), were correlated with an effective autoconversion rate (τi,eff), defined as the flux of snow exiting the ice cloud at the bottom boundary.
 Among the eight physical parameters, the three with the highest correlations (all above 0.8) to the effective autoconversion rate were found to be (1) cloud differential infrared (IR) heating, (2) normalized total water in cloud and (3) kinetic energy. This result confirms the importance of the interactions among ice water, radiation and motion in the evolution of ice clouds. Another process having a weaker impact on prolonging ice cloud lifetimes was (4) the environmental static stability.
 These CRM-based results led to the following micro/macro-physical understanding of the decay of ice cloud layers. Ice cloud layers are destabilized against the prevailing environment by cloud differential IR heating, which is a function of cloud ice amount. This destabilization allows for the generation of kinetic energy. Ice water (including snow) concentrations increase near cloud base due to the falling of ice crystals. The vertical upward mixing of cloud ice and snow related to the kinetic energy, therefore, was found to be responsible for prolonging the life of cloud layers.
 The cloud IR destabilization and the resulting upward turbulent water fluxes involve subgrid-scale processes and must be parameterized in a GCM. These turbulent fluxes are shown to retard the effective production rate of snow exiting the cloud layer and thus act to sustain the cloud. An ensemble of ice cloud CRM simulations with varying cloud and environmental conditions was then used to obtain an empirical formulation that allows for an estimate of τi,eff from variables available in a GCM. Köhler  suggests that cloud differential IR heating ( in units [W m−2]) and environmental static stability ( in units [m s−2]) are the two most important independent factors. Here we define hg as a generalized liquid-ice moist static energy:
where cp is specific heat capacity of dry air at constant pressure, T is temperature, g is gravity, z is geopotential height, and Lc and Lf are the latent heating of condensation and freezing, respectively. The saturated hg* is obtained by using the saturated mixing ratio over ice q*i instead of qv.
 Application of multiple linear regression yields the following expression for the effective autoconversion time scale (τi,eff, hour) with a multiple correlation coefficient of 0.928:
 According to (8), optically thick clouds with dIR on the order of 200 W m−2 have decay time scales about 0.6 h larger than their zero-dIR optically thin counterparts.
 While the environmental static stability can be diagnosed directly from the GCM layers below and above the cloud layer, the differential IR heating dIR within a single layer is not calculated in current GCM radiation schemes. A simple analytical formula to determine the differential IR heating of a cloud layer was developed by Köhler . The key assumptions are that the cloud layer is a gray body with equal absorptivity and flux emissivityεf, and all absorption and emission occurs near the cloud boundaries. Under these assumptions the following expression can be derived:
 Here, QIR is the IR heating rate with being its cloud layer mean value, ρ is the air density, σ is the Stefan-Boltzmann constant, Fbotup is the upward IR flux at cloud bottom, Ftopdown is the downward IR flux at cloud top, Tbot is the cloud bottom temperature, Ttop is the cloud top temperature. Fbotup and Ftopdown are defined as positive quantities. The cloud radiative properties are calculated as a function of cloud water path and phase. Single column radiative transfer numerical experiments have verified the qualitative realism of this formulation. The range of dIR is shown to extend to values greater than 200 W m−2 for optically thick high, middle and low clouds.
 The required incoming boundary fluxes Fbotup and Ftopdown, and the broadband cloud flux emissivity εf (see Appendix A4) can be easily accessed or derived from GCM radiation and cloud schemes, respectively. An unavoidable complication is the direct interaction of cloud and radiation. In most current GCMs, a sequential cloud-radiation calculation is performed. However, the two equations (8) and (9) are directly linked through εf(τi,eff). In the absence of an analytical formulation of this interaction or a physical time step sufficiently smaller than the evolution time-scale, an iterative approach is mandated (see Figure 2). Note that the time step for the physics calculation in the UCLA AGCM is one hour.
4. Validation of the Prognostic Cloud Ice and the Bulk Microphysics Schemes
4.1. Horizontal and Vertical Profiles of Ice Clouds
 The major sources of cloud ice are detrainment from tropical convection and midlatitude baroclinic wave activity (storm tracks). In the tropics, detrainment of cloud ice from deep convection is the major source of cloud ice, such that one can expect large IWC in the upper troposphere where the largest cumulus detrainment takes place. A second lifting mechanism is common to midlatitude dynamics: Baroclinic instability waves create forced ascent associated with storms. The associated cloud systems have the lifetime of the responsible creation mechanism - several days.
Figure 3 shows the zonal mean of the CloudSat observed annual mean total and filtered cloud IWC (non-convective and non-precipitating). The magnitude of the filtered cloud IWC is smaller than that of the total IWC approximately by a factor of three. Nevertheless, the overall vertical structures are similar. Both total and filtered cloud IWC show three regions of local maxima. One is in the tropics at around 300 hPa and is associated with deep convection. The other two are in midlatitudes at approximately 600 hPa and correspond to the midlatitude storm tracks in each hemisphere. Compared to the total IWC, the filtered cloud IWC shows all three local maxima at a higher altitude, especially those in the midlatitudes, which are at about 500 hPa.
 Caution should be exercised when interpreting these results since the observed IWC is strongly affected by the attenuation effect over regions of strong convection where large ice particles are present [Matrosov, 2007; Sassen et al., 2007]. On the other hand, some small ice particles, like those in cold and thin cirrus clouds, may not be detected by CloudSat due to its sensitivity limit [Sassen and Wang, 2008]. Nevertheless, the CloudSat observations comprise by far the most accurate data set currently available. In the following text, all the comparisons are made against the filtered CloudSat cloud IWC (non-convective and non-precipitating). For brevity, we will only use the term “IWC” to represent the ice water content of small particles associated with ice cloud for the filtered CloudSat observations, ERA-Interim reanalysis, and UCLA AGCM simulations.
Figure 4 shows the zonal mean of the filtered annual mean IWC profiles from CloudSat (same as Figure 3b except for the different color scale), the reanalysis, and the AGCM control simulation. We also plotted the temporal standard deviations for each of the fields (contours). Compared to the CloudSat observations, the reanalysis shows the local maximum in the tropics at a much lower altitude. In the tropics, the reanalysis IWC maximum is at around 400 hPa and one third smaller in magnitude (∼3 mg m−3) than the observed. Outside the tropics, the maximum values are near the surface in high latitudes in both hemispheres. The UCLA AGCM simulation, on the other hand, realistically reproduces the overall vertical structure in both the tropics and midlatitudes. The magnitude in the tropics is around 2 mg m−3 larger than that in CloudSat. In midlatitudes, the IWC in the mid-troposphere is well simulated. There are, however, regions of large IWC near the surface in mid- and high-latitudes in the simulations as well as in the reanalysis which cannot be verified with the CloudSat retrievals due to surface clutter effects [Sassen and Wang, 2008]. The UCLA AGCM employs a unique single mixed-layer PBL parameterization after Suarez et al.  that allows for a PBL-top stratus layer. The large IWC in midlatitudes in Figure 4c are associated with parameterized PBL-top mixed phased stratus (figure not shown here). The standard deviations for the reanalysis and simulations are much smaller than the mean values. The slightly larger standard deviations in CloudSat are likely due to instantaneous CloudSat footprint (compared to model gridded mean values), small sampling numbers of only two years for CloudSat, or underestimate of atmospheric internal variability in both models.
 A multilayer Taylor diagram [Taylor, 2001] of the annual mean cloud IWC for the ERA-Interim (red) and AGCM control simulations (green) is shown in Figure 5a. The Taylor diagram relates three statistical measures of model fidelity: the “centered” root mean square error, the spatial correlation, and the spatial standard deviations. These statistics are calculated over the global domain (area-weighted). The reference data set “Obs” is from the two-year mean of CloudSat observations, and is plotted along the x axis. The radial distance from the origin is proportional to the standard deviation. The azimuthal angle represents the spatial correlation between the reanalysis/simulations and observations. The “centered” root mean square error between the reanalysis/simulations and observations is proportional to the distance between these two data points. Each horizontal field from both reanalysis and simulations is normalized by the corresponding standard deviations of CloudSat such that the multilayer fields can be shown on the same diagram. Due to the limit of radar sampling of CloudSat on detecting near surface cloud ice, we only performed the calculations from 700 hPa up to 100 hPa. In Figure 5a, we find that the cloud IWC in most layers is well simulated, except for the low correlation at 100 hPa and large standard deviation at 300 hPa. The low correlation at 100 hPa could be due to the UCLA AGCM difficulties in capturing the tropopause structure, but there is also some uncertainty in the high cloud IWC in the data as the CloudSat radar cannot detect small IWC in thin cirrus which can occur at these altitudes. The large standard deviation at 300 hPa is consistent with the larger cloud IWC seen in Figure 4. The reanalysis shows high correlations for most layers except for 100 hPa. The standard deviations are smaller above mid levels and larger at lower levels. This is also consistent with the zonal mean cloud IWC in Figure 4.
 We also plot in Figure 5b a portrait diagram of relative error metrics [Gleckler et al., 2008] for the multilayer cloud IWC. For the root mean square error (Em) from a given layer (m) of the reanalysis/simulations, the relative error (E′m) is defined as:
where the Ē is the median root mean square error of all the layers in the reanalysis and simulations. By normalizing Em with Ē allows for a measure of how well a given layer compares with the typical model errors. Both reanalysis and simulations show relative smaller errors at 150 hPa and 100 hPa. This is mainly because the cloud IWC are much smaller comparing to other levels even with the low correlations and larger normalized centered root mean square errors in Figure 5a (100 hPa). Larger errors are found in the reanalysis at 500–700 hPa, which is consistent with the much larger cloud IWC at mid and low levels. The simulations show larger relative errors at 300 hPa and 400 hPa, which is consistent with larger cloud IWC seen in Figure 4.
Figure 6 shows the annual mean IWC from CloudSat, the ERA-Interim reanalysis, and the AGCM control simulation both at 300 and 500 hPa. The IWC pattern at 300 hPa from CloudSat (Figure 6a) shows large values over the major convective regions, such as the intertropical convergence zone (ITCZ) in the Pacific, Atlantic, and Indian basins, and the South Pacific convergence zone (SPCZ) and South Atlantic convergence zone (SACZ); as well as the major monsoon regions over Asia, Australia, the Americas, and Africa. The IWC at 300 hPa from both the reanalysis (Figure 6c) and the simulation (Figure 6e) show similar patterns, but different magnitudes. The reanalysis shows much smaller values of IWC while the simulation shows slightly larger IWC values except for the region over the Atlantic ITCZ. The IWC pattern at 500 hPa from CloudSat (Figure 6b) shows large values in midlatitudes in both hemispheres, which are associated with the midlatitude storm tracks. The reanalysis and simulation show similar patterns and values comparable to the CloudSat observations in midlatitudes. However, the reanalysis also shows values in the tropics that are comparable in magnitude to the midlatitude values. This is consistent with the vertical structure of IWC (Figure 4b) in the reanalysis, which shows a lower altitude IWC maximum in the tropics compared to CloudSat observations.
 We next examine the seasonal means of the zonal mean IWC. Figure 7 shows the Dec-Feb (DJF), Mar-May (MAM), Jun-Aug (JJA), and Sep-Nov (SON) IWC means from CloudSat. The seasonal mean vertical structures for the four seasons are similar to the annual mean, with one maximum in the tropics at 300 hPa and one in the midlatitudes in both hemispheres at 500 hPa. Nevertheless, the maxima also show seasonal variations. In the tropics, the IWC is largest in magnitude (over 10 mg m−3) north of the equator in JJA while the IWC is smallest in magnitude (around 6 mg m−3) south of the equator in DJF. The other two seasons both show maxima north of equator. In midlatitudes, the seasonal variations are less distinct in magnitude (∼7 mg m−3) in both hemispheres. In the northern hemisphere, the position of the maximum is closer to the equator in MAM at around 40°N. In SON, the maximum is displaced poleward to around 60°N. In the southern hemisphere, the position of the maximum is very similar in all seasons, staying at around 50°S. In JJA, the maximum extends equatorward to around 40°S.
 The seasonal mean vertical structures for the four seasons are similar to their annual mean for both reanalysis (Figures 7e, 7f, 7g and 7h) and the AGCM control simulation (Figures 7i, 7j, 7k and 7l). In the tropics, the IWC maximum in both the reanalysis and the simulation is strongest in JJA and weakest in MAM and DJF. In midlatitudes, the maxima in both the reanalysis and the simulation are weakest in JJA and strongest in DJF in the northern hemisphere. In the southern hemisphere, the maximum is weakest in DJF while the intensity is similar in the other three seasons for the reanalysis. The maximum is also weakest in DJF in the simulation, but is strongest in JJA.
 Seasonal variations in magnitude and position of the IWC maximum are further examined using global maps of IWC at 300 and 500 hPa. At 300 hPa (Figure 8), the IWC maximum of CloudSat and ERA-Interim reanalysis is in the tropics, and the variations indicated in Figure 7 are consistent with the changes in the position and intensity of the ITCZ convection. The simulations realistically reproduce the overall variations except have slightly larger values of IWC. At 500 hPa (Figure 9), the IWC of CloudSat, the reanalysis, and the simulations primarily reflect the signals associated with the storm tracks in midlatitudes in both hemispheres. The IWC is largest in the north Pacific and Atlantic due to frequent baroclinic wave activity in the northern winters in these regions, and is diminished due to the less frequent activity in the northern summers. The IWC variations are relatively insignificant in the southern hemisphere, though somewhat larger IWC values in JJA are seen in the CloudSat data and the reanalysis. The AGCM control simulation, however, shows more distinct seasonal variations of IWC with an enhancement in JJA and decrease in DJF.
4.2. Sensitivity Experiments on Autoconversion Time Scales and Temperature Threshold for Cloud Ice Deposition
 Differing degrees of complexity in the cloud microphysics schemes in the UCLA AGCM and in the model used to produce the ERA-Interim reanalysis (CY31r1) [Dee et al., 2011] complicate the interpretation of IWC comparisons. The major differences between the reanalysis and the simulation results could be due to differences in a number of parameterizations that directly affect the IWC, including detrainment of cloud ice from cumulus convection, ice sedimentation, the temperature-dependent mixed-phase assumptions for cloud ice and cloud liquid water, and the formulation of the ice-to-snow autoconversion. The ERA-Interim parameterization includes the sedimentation process, but not the ice to snow conversion dependence on differential IR heating and environmental static stability utilized in the UCLA parameterization. The ERA-Interim parameterization also has a different temperature threshold for pure ice phase cloud deposition. This temperature threshold is −40°C in the UCLA parameterization [Lord, 1978] and −23°C in the ERA-Interim parameterization (http://www.ecmwf.int/research/ifsdocs/CY31r1/index.html). The autoconversion formulations for ERA-Interim are also different for the temperature thresholds of T < −23°C and −23°C ≤ T < 0°C (note that a new cloud scheme formulation in the newer ECMWF operational model version 36R4 has a consistent treatment of ice-to-snow autoconversion across all temperatures and shows a significant decrease in the amount of cloud ice in the −23°C to 0°C temperature range, significantly improving the agreement of IWC with the CloudSat observations).
 In this section, we explore possible explanations for the different zonal mean profiles of IWC in the ERA-Interim reanalysis and the UCLA AGCM control simulation in light of differences in the parameterizations of microphysical processes listed above. We perform two sets of sensitivity experiments in which either the autoconversion time scale (equation (8)), or diagnostic temperature threshold for pure ice phase cloud deposition were varied. The first set of experiments aims to determine the dominant macrophysical processes (differential IR heating and static stability of environment) in setting the autoconversion time scale. The second set of experiments is to examine the impact of changes in the temperature threshold for pure ice phase clouds as a prototype of the importance of microphysics.
4.2.1. Autoconversion Time Scale
 We perform three sensitivity experiments with the UCLA AGCM to test the impact of individual physical processes on autoconversion time scale (equation (8)). The first experiment applies a constant time scale: τi,eff = 0.97 hour, the second experiment uses a time scale that is a function of differential IR heating only: hour, and the third experiment uses a time scale that is a function of the environmental static stability only: hour.
Figure 10 shows the zonal mean of the annual mean IWC for the control and sensitivity experiments. The constant time scale experiment (Figure 10b) shows IWC values comparable to CloudSat observed in the tropics but smaller values than observed in midlatitudes. Figure 10e shows another experiment with time scale 1.4 times larger than that used in Figure 10b. The result shows IWC values comparable to the control simulation in the tropics but much larger values than control or CloudSat in the mid and low-troposphere in midlatitudes. An additional series of sensitivity experiments using other constant time scales (not shown) demonstrate that the model cannot reproduce magnitudes in both the tropics and midlatitudes comparable to control or observations, which strongly suggests the importance of physically based effects on the autoconversion time scale.
 It is apparent that the differential IR heating (Figure 10c) is the major contributor to longer autoconversion time scale (larger cloud IWC) seen in the control. The IR impact appears almost uniformly over all regions. The effect of environmental static stability (Figure 10d), on the other hand, acts to reduce the autoconversion time scale (smaller cloud IWC). Interestingly, this process acts differently in the midlatitudes and the tropics. Greater static stability in midlatitudes reduces IWC there most effectively. The realistic latitudinal contrast in the control simulation is therefore mostly due to this static stability term.
4.2.2. Temperature Threshold for Pure Ice Phase Cloud Deposition
 The particular CloudSat RO4 data used in this study are produced using retrieval algorithm that includes a temperature threshold [Austin, 2007]. In this algorithm, the total ice is reduced linearly as the temperatures go from −20° to 0°C. In a recent study by Delanoë et al. , the CloudSat IWC retrieved using a different algorithm shows an extension of larger IWC values in the lower troposphere, which indicates a level of uncertainty in the standard IWC products at warmer temperatures. Therefore, we performed a sensitivity experiment on cloud ice deposition in which the diagnostic temperature threshold for pure ice phase clouds is modified. Specifically, the boundaries of the linear regime are changed from the −40°C and −5°C currently used in the UCLA AGCM, to the values of −23°C and 0°C that are used in the ERA-Interim model (Figure 11).
 Since all liquid water is converted to ice at a higher temperature, this experiment (Figure 11a) generates much larger values of IWC, and the large values extend further into the lower troposphere compared to the control (Figure 10a). The differences are most pronounced around 400 hPa in the tropics and between 500 to 800 hPa in the midlatitudes in both hemispheres. The largest difference (∼5 mg m−3) is near 50°S at 600 hPa, which also suggests a strong impact of temperature threshold on the difference of cloud IWC between tropics and midlatitudes. Nevertheless, the overall patterns in the zonal mean of the annual mean IWC are similar. This suggests that the temperature threshold for the deposition process explains only part of the differences in the zonal mean IWC structure between the ECMWF CY31R1 model and the UCLA AGCM and is not the major contributor to the differences.
 There are however other plausible candidates to explain such a difference in the comparisons: (1) cloud ice sedimentation is included in the ERA-Interim model version for temperatures colder than −23°C, but is not parameterized in the UCLA AGCM; (2) there are differences in the thresholds for ice versus liquid phase cloud production from convective detrainment in ERA-Interim (all liquid warmer than 0°C to all ice colder than −23°C) compared to the UCLA AGCM (all liquid warmer than −10°C to all ice colder than −40°C, see Appendix A1); (3) there are differences in the magnitude of the autoconversion time scale which are significantly longer in the 0°C to −23°C temperature range in the ERA-Interim model version.
 Although these parameterization differences are not explored further in this paper, separate experimentation with a newer ECMWF model version (36R4) suggests the ice-to-snow autoconversion timescale in the 0°C to −23°C is the dominant reason for the higher IWC in the mid- to low-troposphere.
4.2.3. Impact on Radiation Budget
 We further examine the changes of global annual mean radiation budget at top of atmosphere (TOA). Although the radiation budget at TOA in the current version of the AGCM is not in radiative balance (∼ several watts imbalance), it only creates minimum impact for the present study due to the prescribed SST. An adjustment of free parameters in the model parameterizations may be necessary to achieve the radiative balance for future studies. Table 2 summarizes changes of global annual mean total cloud cover, outgoing longwave radiation (OLR), net shortwave radiative flux at TOA, and net radiative flux at TOA from the sensitivity experiments in reference to the control simulation. Although robust values of the impact on the cloud cover and radiative budget at TOA may require longer integration or numerous ensemble simulations, results from these sensitivity experiments still provide useful information. For the global mean total cloud cover, we find that the effect of differential cloud IR heating tends to increase cloud cover, while the effect of environmental static stability tends to decrease it. Also, those effects seem to cancel each other out for the total cloud cover as suggested by the constant τi,eff experiment. Although the constant τi,eff experiment does not show significant changes in the total cloud cover, there is 0.39 (W m−2) change in the net radiative flux at TOA. For the deposition temperature threshold experiment, the impact on the total cloud cover is negligible. The change in the net radiative flux at TOA, however, also shows 0.34 (W m−2) difference. The changes in the net radiative flux at TOA from these experiments indicate changes of three-dimensional cloud distribution and the cloud types/optical depth (liquid or ice clouds) even though the global mean total cloud cover does not change much. This also indicates the sensitivity of radiation budget to the ways these physical processes are parameterized in climate models.
Table 2. Changes of Annual of Global Mean Total Cloud Cover (%), Outgoing Longwave Radiation (OLR, W m−2), Net Shortwave Radiative Flux at Top of Atmosphere (TOA) (W m−2), and Net Radiative Flux at TOA (W m−2) From the Sensitivity Experiments in Reference to the Control Simulation
ΔTotal Cloud Cover (%)
ΔOLR (W m−2)
ΔNet SW at TOA (W m−2)
ΔNet Radiative Flux at TOA (W m−2)
Values are not statistically significant at 95% confident level.
 In this study, we validate the simulated cloud IWC by a prognostic cloud ice parameterization and bulk-water microphysics scheme [Köhler, 1999] in the UCLA AGCM using CloudSat observations. We also compare the AGCM results with those from the ECMWF ERA-Interim reanalysis. The cloud profiling radar on CloudSat provides a new global view of the vertical structure of clouds from space, in particular the high vertical resolution structure of cloud condensates such as IWC.
 The prognostic cloud ice equation in the bulk-water microphysics scheme of the AGCM includes the processes of cumulus detrainment of cloud ice, deposition, sublimation, autoconversion, Bergeron-Findeisen process, and melting. For the autoconversion process, an empirical parameterization of the effect of upward turbulent water fluxes in cloud layers is formulated based on a suite of CRM simulations. The time-scale for conversion of cloud ice to snow was identified as the key parameter, and its parameterization was formulated based on the fact that this conversion was found to be highly correlated to differential cloud IR heating and environmental static stability.
 The annual and seasonal means of zonal mean profiles of IWC in the AGCM control simulation both show a local maximum at 300 hPa in the tropics associated with deep convection and another local maximum at 500 hPa in midlatitudes in both hemispheres associated with the storm tracks. The seasonal variations of IWC are consistent with seasonal changes in the intensity and position of convection in the tropics, and changes in baroclinic wave activity in midlatitudes. The AGCM simulated IWC is in close agreement with CloudSat observations in both structure and magnitude. The ERA-Interim reanalysis, however, shows much smaller values of IWC in the tropics but much larger IWC values in the lower troposphere in midlatitudes. These results are also consistent with the metric calculations shown in the Taylor diagram and portrait diagram of relative errors.
 Based on several sensitivity experiments varying the autoconversion time scale formulation, we found differential IR heating in the cloud layer to have the dominant effect on the autoconversion time scale (equation (8)). The role of the environmental static stability is to sharpen the contrast between mid-latitudinal and tropical ice clouds. This is a result of the stronger static stability in midlatitudes that reduces the IWC there more than in the tropics. The experiments suggested the importance of physically based effects on the autoconversion time scale since the model cannot reproduce the CloudSat IWC in both the tropics and midlatitudes with any constant (time/space invariant) autoconversion time scale. Sensitivity experiments on the diagnostic temperature range for ice cloud deposition were also performed to test whether this explains the large difference in ice clouds in the lower troposphere between UCLA and ECMWF models. Although these partially explain the differences in the IWC, the majority of the difference is likely to be due to different ice cloud sedimentation, different temperature thresholds for ice cloud convective detrainment, different autoconversion time scales for the 0°C to −23°C temperature range, as well as other differences in the model physics and dynamics.
 In summary, the success in simulating IWC in the UCLA AGCM depends on a well-balanced set of parameterizations of (1) cumulus convection and associated detrainment, (2) a moderate-complexity bulk-water microphysics scheme which prognoses cloud liquid and cloud ice and (3) a cloud macrophysical description of the interaction of motion, turbulence and falling ice particles as described here and developed by Köhler . Finally, it should be noted that a realistic IWC distribution was achieved in the UCLA AGCM by diagnosing physical parameters from a series of CRM experiments and employing them in a GCM without tuning the constant autoconversion time scale.
 We further examined the impact of differential cloud IR heating, environmental static stability, and the temperature threshold of ice deposition on the global total cloud cover and radiation budget at TOA from the sensitivity experiments in section 4. The results suggest that the changes in the net radiative flux at TOA can be as large as 0.39 (W m−2) even though the global mean total cloud cover does not change much (i.e., for the constant τi, eff and deposition temperature threshold experiments). Not only does the way these physical processes are parameterized affect the three-dimensional cloud distribution, but also the cloud phase, optical depths and the radiation budget in climate models.
 The methodology for comparison applied in this study follows Waliser et al.  and Li et al. . Accordingly, we filtered out convective clouds and surface precipitating cases from the CloudSat data. We then obtained an estimate of cloud ice which serves as a constraint for typical GCMs clouds. Ideally, for model-data comparisons with non-precipitating CloudSat estimates, precipitating profiles from the model should also be excluded during the model integrations. This is, however, a difficult task at this stage because model precipitation in a GCM represents the mean within a grid box with a horizontal resolution of about 200 km by 200 km and a time step of 1 h whereas CloudSat has a footprint of about 1–2 km and produces snapshots of cloud profiles. Thus, determination of a threshold for non-precipitation that is equivalent to CloudSat footprint is a challenge. One way to address this disparity on space and time scales could be the implementation of the Cloud Feedback Intercomparison Project (CFMIP) Observation Simulator Package (COSP) [Bodas-Salcedo et al., 2011] in climate models.
 Given the increased knowledge from satellite observations and in situ measurements, as well as increased computational power, several important issues, both physically and numerically, are now being actively addressed in cloud ice parameterizations. The issues include more detailed and sophisticated microphysical processes (for example, wider use of two-moment schemes), radiatively active precipitation and finer vertical model resolutions. As stated in section 2, large size ice particles (convective or precipitating hydrometers) in the cloud ice schemes of most contemporary climate models are treated diagnostically, and are often assumed to be radiatively unimportant. Waliser et al. , however, show that the impact of these particles on the radiation budget is significant with possible impacts on the general circulation and global precipitation.
 Another important issue is the impact of vertical resolution on the simulated cloud IWC. Vertical resolution can affect the simulated column static stability, which in turn can affect cloud microphysics processes, such as the ice-to-snow autoconversion as shown in this study. A coarse vertical resolution could lead to an underestimation of column static stability and enhanced instability of vertical layers. A logical next step in the development of the cloud water/ice parameterization is to test the impact of vertical resolutions, and implementation of more detailed and sophisticated microphysics processes in AGCMs.
Appendix A:: Cumulus Cloud Interaction and Ice Microphysics
A1. Cumulus Detrainment of Water
 Cumulus convection can quickly transport large quantities of lower-tropospheric air to the upper troposphere. In doing so, it brings moisture including liquid droplets and ice crystals to the detraining level. Within the framework of the Arakawa and Schubert  cumulus parameterization, Lord  divided the cloud condensate into cloud liquid water and cloud ice according to air temperature. In this formulation, all condensate is liquid above −10°C and all is ice below −40°C. In between these two temperature thresholds, the condensate is partitioned into ice and liquid by linear interpolation. Note that the detrainment of cloud condensate is extremely sensitive to the details of the updraft microphysics as the amount of precipitate falling to the ground is typically an order of magnitude larger than the detrained cloud water.
 The cumulus convection scheme in the ERA-Interim parameterization is based on work by Tiedtke . The temperature thresholds for the partition of cloud condensate from the cumulus detrainment are also different (CY31r1) [Dee et al., 2011]. All cloud condensate is liquid above 0°C and all is ice below −23°C. These warmer temperature thresholds allow more cloud ice to form, and also have a larger impact in the tropics.
A2. Deposition and Bergeron-Findeisen Processes
 Deposition processes include nucleation (homogeneous and heterogeneous) of ice particles, and the effect of vapor diffusion on the cloud particles. Cloud droplets will freeze homogeneously at and below −35°C depending on droplet size [Heymsfield and Miloshevich, 1993]. The number density of effective ice nuclei is believed to roughly increase exponentially with decreasing temperature below 0°C and depends on aerosol composition [Houze, 1993]. The Bergeron-Findeisen process is based on the fact that the saturation mixing ratio of ice is lower than that of liquid water with the maximum difference at about −12°C. Thus, cloud ice crystals can grow to the expense of cloud liquid water, when both phases coexist.
 To parameterize condensation and deposition supersaturated water vapor is assumed to condense to cloud liquid water above Tl (= −5°C) and deposit to cloud ice below Ti (= −40°C) [Lord, 1978] with partitioning according to a linear interpolation with respect to temperature in between. This process is assumed to take place much faster than the physical time step (Δpt) of one hour and can be written as:
where fil(T) is the distribution function (see Figure A1). The saturation mixing ratio qx is calculated over liquid (ql) for T > −5°C and over ice (qi) otherwise.
 The Bergeron-Findeisen process is approximated by converting cloud liquid water into cloud ice with a time-scale τbf/fil
τbf = 1h is chosen rather arbitrarily.
A3. Sublimation and Melting Processes
 Ice crystals and snow sublimate to water vapor when the water vapor mixing ratio is below the corresponding saturation value. As suggested by Koenig and Murray , the formula given by Kessler  is used to describe the rate of sublimation of cloud ice and snow:
where Cer = 4.85 × 10−2s−1, qi is the saturation mixing ratio over ice, ρa is the density of air and ρa · qi,s is cloud ice and snow content in units of kg m−3, which for snow is calculated as the snow flux divided by the terminal velocity of snow vts.
 At temperatures above 0°C melting of cloud ice and snow occurs with the transformation to the corresponding size cloud droplet or raindrop taking place on timescales as short as 20 s [Ogura and Takahashi, 1971]. An instantaneous conversion of cloud ice and snow to rain is assumed to occur at temperatures above 0°C. For cloud ice, this implies that the ice crystals initially have enough mass so that they would start precipitating after the melting process. That assumption is supported by the observed size distributions of cloud ice crystals in warm ice clouds (De ≈ 100 to 150 μm) [Ou and Liou, 1995] that will melt above 0°C to drizzle-size particles.
A4. Broadband Cloud Flux Emissivity
 Starting from the plane parallel assumption, we further neglect the scattering of IR radiation by cloud particles and gas absorption (e.g., water vapor), and invoke the gray approximation for cloud liquid water and cloud ice, which assumes weak wavelength dependence in their absorption coefficients. We can then calculate the broadband cloud flux emissivity εf:
where the IR optical thickness can be approximated as τIR ≅ 0.5 · τsol = τsol,l + τsol,i, and the diffusivity factor as [Harshvardhan et al., 1987]. The solar optical thickness for cloud droplets (τsol,l) is written as:
and for ice crystal (τsol,i) is written as:
 Here, LWP is the liquid water path, IWP is the ice water path, and ρl is the density of liquid water. The effective cloud droplet radius re and effective crystal size De are chosen uniformly as 10 μm and 75 μm, respectively; a = −6.656 m2 kg−1 and b = 3.686·10−3 m3 kg−1 are empirical constants [Liou, 1992].
 We thank the three anonymous reviewers for their valuable comments on this paper. Computing resources were provided from the NCAR computational and information systems laboratory. Support for Hsi-Yen Ma was provided by the Regional and Global Climate and Earth System Modeling Programs of the Office of Science at the U.S. Department of Energy. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.