This study examines the impact of a new cloud thermodynamic phase parameterization on climate simulation. The new parameterization is based on CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation) observations and replaces the default parameterization in the Community Atmosphere Model version 4. It is shown that the application of the new cloud phase parameterization results in a small increase in global-mean liquid water path (LWP) and a small decrease in global-mean ice water path (IWP). Large regional increases in LWP mainly occur in tropical regions such as the western Pacific warm pool and northeastern Indian Ocean and middle latitudes, while large decreases in IWP occur in the midlatitude storm track regions. The increase in zonal-mean cloud water content occurs at temperatures between −15°C and −30°C and cloud fraction increases occur at higher altitudes near the −30°C isotherm. Two other sensitivity experiments that favor more ice-phase clouds also increase cloud fractions at the same altitudes, but decrease cloud water content at slightly lower altitudes. It is found that relative humidity increases at the same altitudes where the cloud fraction increases, caused by radiative cooling that is induced by cloud fraction increases but not changes in cloud water content. This result points to a deficiency in cloud fraction parameterizations that rely solely on ambient humidity without taking cloud water/ice content into account. Zonal-mean cloud albedo forcing is sensitive to LWP in mixed-phase clouds and the comparison with observations suggests that the CALIPSO and default parameterizations perform well in the extratropical regions.
 Modeling mixed-phase clouds, in which cloud water and ice coexist, in general circulation models (GCMs) has been a difficult task because of the complicated microphysical processes involved in determining their formation and the lack of characterization of unresolved dynamic and thermodynamic environments within a grid box length of hundreds of kilometers. These clouds occur in the temperature range of 0 to −40°C [Roger and Yau, 1989; Pruppacher and Klett, 1997]. (We loosely define the clouds with temperatures between 0°C and −40°C as mixed-phase clouds.) It is generally accepted that homogeneous nucleation – formation of ice particles in supercooled drops without the presence of foreign substrate – becomes effective for the cloud droplets at temperatures colder than −38°C and heterogeneous nucleation – with the participation of foreign substrate to form ice particles – is the dominant mechanism for forming ice particles in the atmosphere at temperatures warmer than −38°C. The details of heterogeneous nucleation processes are, however, highly dependent upon many factors such as the amount of ice nuclei present in the atmosphere and their physicochemical properties, ambient temperature, amount of supersaturation and updraft speeds. The last three factors depend upon the details on subgrid-scale description of unresolved cloud-scale dynamics and thermodynamics in the GCM.
 The mass fraction of supercooled liquid clouds in a GCM grid box – the cloud thermodynamic phase parameterization – is generally assumed to be a function of ambient temperature based upon early aircraft measurements of continental clouds [e.g., Feigelson, 1978; Bower et al., 1996; Korolev et al., 2003], i.e., typically piecewise linear between the low and upper temperature thresholds [Fowler and Randall, 1996; Klein et al., 2009], where the low threshold corresponds to 0% liquid and the upper threshold corresponds to 100% liquid. The thresholds, especially the low threshold, vary strongly among GCMs and thus the mass fraction of supercooled water clouds can be very different for a given ambient temperature between 0 and −40°C. For example, the relative amount of liquid at an ambient temperature of −15°C varies from 12% to 83% in the six single column models (SCMs) participating in a model intercomparison study of Arctic mixed-phase clouds [Klein et al., 2009; Morrison et al., 2009]. Because of the significant differences in radiative properties (optical depth and infrared emissivity) between liquid and ice clouds, the radiative effect of mixed-phase clouds produced from different cloud thermodynamic phase parameterizations plays a critical role in determining climate feedbacks [e.g., Li and Le Treut, 1992; Gregory and Morris, 1996; Tsushima et al., 2006]. As greenhouse gases increase, GCM-simulated storm tracks move poleward [Yin, 2005] and so do the associated water clouds. It has been found that many of the clouds within storm tracks are supercooled water clouds [Hogan et al., 2004; Hu et al., 2010; Zhang et al., 2010]. When water clouds move poleward, the reduction of solar insolation at higher latitudes causes a concomitant reduction in global albedo. A recent GCM intercomparison study indicates that the difference in cloud albedo feedback among different GCMs is primarily a result of the differences in the poleward redistribution of cloud liquid water due to differences in cloud thermodynamic phase parameterizations [Tsushima et al., 2006]. The models that produce more supercooled water clouds have higher climate sensitivities.
 Not all cloud thermodynamic phase parameterizations use the piecewise linear function discussed above or directly impose such a relation. Doutriaux-Boucher and Quaas  fitted a relation with 1.7 power of a function of the ambient temperature and a low threshold of −32°C to match the GCM-modeled cloud top temperature in the mixed-phase cloud range with polarimetric satellite observations. The 40-year European Center for Medium-range Weather Forecasts (ECMWF) reanalysis (ERA40) used a similar power (2.0) of a function of the ambient temperature but with a higher threshold of −23°C [Weidle and Wernli, 2008]. An overestimate of ice clouds between 0 and −30°C was identified, compared to the same polarimetric satellite observations. Rather than simply prescribing the liquid mass fraction as a function of ambient temperature, several studies formulated physically based treatments of condensational growth of water droplets and depositional growth of ice crystals that could result in relations that are consistent with aircraft measurements [Lohmann and Roeckner, 1996; Del Genio et al., 1996; Rotstayn et al., 2000]. Del Genio et al.  results were consistent with those of Feigelson  while those of Rotstayn et al.  were similar to those of Bower et al. .
 The most accurate cloud phase information can be determined from both layer integrated backscatter and depolarization ratio obtained by CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) measurements from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite [Hu et al., 2001, 2007, 2009]. With cloud temperature information from the collocated Imaging Infrared Radiometer (IIR) measurements and cloud water paths from collocated Moderate Resolution Imaging Spectroradiometer (MODIS) measurements, Hu et al.  compiles global statistics of the frequency of occurrence, liquid water content, liquid water path, and their temperature dependence. For clouds with temperatures between −40°C and 0°C, they found that the liquid mass fractions and liquid water paths are significantly higher than the ones from previous studies using passive remote sensing measurements [Doutriaux-Boucher and Quaas, 2004; Weidle and Wernli, 2008; Choi et al., 2010] and the ones used in all GCMs [e.g., Smith, 1990; Ose, 1993, Kristjánsson, 1994; Boucher et al., 1995; Doutriaux-Boucher and Quaas, 2004; Weidle and Wernli, 2008]. A new cloud thermodynamic phase parameterization was proposed that has the potential to benefit cloud models and cloud parameterizations used in climate models to improve their ice-phase microphysics parameterizations.
 The goal of this study is to investigate the effects of different cloud phase parameterizations on climate simulation. A control experiment using the default cloud phase parameterization in the Community Atmosphere Model version 4 (CAM4) [Collins et al., 2006; Gent et al., 2011] and three sensitivity experiments were performed. The first sensitivity experiment implemented a new cloud thermodynamic phase parameterization [Hu et al., 2010] in CAM4, denoted by Hu. The second experiment used the formula of the ECMWF Integrated Forecasting System, denoted by ERA40_f thereafter (note that the results from ERA40 reanalysis are labeled as ERA40 in the rest of the paper). The third one, denoted by mid_f, used the mass fraction of supercooled liquid water that is an average of the formulae of Hu and ERA40_f. The results from the control and the three sensitivity experiments were compared with satellite and ground-based observations, in particular, with the vertical distributions of cloud water and ice contents from the state-of-the-art satellite active remote sensing observations.
Section 2 describes the CAM4 and experiment design, with an emphasis on the cloud thermodynamic phase parameterizations used in the control and sensitivity experiments. The simulated results from the control and sensitivity experiments are analyzed and compared with observations in Section 3. A summary is given in Section 4.
2. Model Description and Experiment Design
 The GCM used in this study is the Community Atmosphere Model version 4 [Collins et al., 2006; Gent et al., 2011]. A finite-volume dynamical core [Lin, 2004] with grid spacing of 1.9° × 2.5° in the horizontal and 26 levels in the vertical is chosen for this study. In CAM4, deep convection is parameterized using the mass flux scheme of Zhang and McFarlane , which includes a subgrid-scale convective momentum transport following Richter and Rasch . The calculation of convective available potential energy (CAPE) is modified to include the dilution effect of an entraining plume in place of the standard undilute non-entraining plume used in CAM version 3 (CAM3). A combination of the mass flux approach [Hack, 1994] and large-scale condensation are used in CAM4 to parameterize shallow cumulus and stratocumulus clouds. Midlevel convection is parameterized following Hack . The radiative transfer scheme is basically the same as CAM3, as detailed in Collins et al. .
 The cloud parameterization includes macrophysical and microphysical parts, as detailed in Rasch and Kristjánsson  and Zhang et al. . The macrophysical part determines the large-scale net condensation rate with a self-consistent treatment of the evolution of water vapor, heat, cloud fraction, and in-cloud condensate [Zhang et al., 2003] while the microphysical part includes the microphysical processes within prognostic equations for the mass of cloud ice and liquid. These masses are combined into a single variable called “total condensate” in the macrophysical calculation. The total condensate is partitioned into cloud ice and liquid according to ambient temperature. Condensed water from convective detrainment can either form precipitation or additional stratiform water. Convective precipitation can evaporate into its environment. Cloud fraction is determined from three diagnostic relationships for the amounts of low-level stratocumulus clouds [Klein and Hartmann, 1993], convective clouds [Xu and Krueger, 1991] and layered cloud systems, while their maximum value is chosen to represent cloud fraction for the grid area. The in-cloud mixing ratios, the grid volume mean quantities divided by cloud fraction, are used in the microphysical parameterization that converts condensate into precipitate and determines the evaporation. Liquid and ice mixing ratios are independently advected, diffused and transported by convection and also subject to (minimal) sedimentation. The falling condensate, i.e., snow and rainwater, are diagnosed. Five processes are included to convert condensate to precipitate: the auto-conversion of liquid to rain, the collection of cloud water by rain from above, the auto-conversion from ice to snow with its threshold value varying linearly between 0°C and −20°C, the collection of ice by snow, and the collection of liquid by snow.
 In the control experiment, the mass fraction of total condensate, as used in the standard CAM3 and CAM4, is a fixed linear function of ambient temperature (T), ramping from pure liquid at temperatures above Tmax = −10°C (T > Tmax) to pure ice for T < Tmin, where Tmin = −40°C. The mass fraction of supercooled liquid water between Tmax and Tmin is given by
A sensitivity experiment (ERA40_f) used the formula:
for temperatures between 0°C and −23°C. The condensate is pure ice when T < −23°C for ERA40_f. Formula (2) is currently used in the ECMWF Integrated Forecasting System. In another sensitivity experiment (Hu), we use the formula for the fraction of supercooled liquid water presence (or occurrence fraction) obtained from the CALIPSO observations [Hu et al., 2010]. The formula is given by the following sigmoid function
where P(T) = 5.2918 + 0.3694T + 0.06635T2 + 0.006367T3 + 2.33 × 10−4T4 + 2.97 × 10−6T5 is a polynomial fit to the observed relations between the fraction of supercooled water presence, f (T), and ambient temperature. It is assumed that the mass and occurrence fractions of supercooled liquid water are statistically equivalent when applying (3) in a GCM. There are large uncertainties in the retrieval of the mass fractions from satellite [Hu et al., 2010]. Hu et al.  showed that these two fractions are statistically equal within the uncertainties. Additionally, a direct implementation of the observed occurrence fraction in GCM to individual clouds is not possible.
 The mass fraction of the supercooled water phase cloud as a function of ambient temperature is plotted for formulae (1), (2) and (3) in Figure 1. The mass fraction of the supercooled water is larger from (3) than that from (1) when the ambient temperature is between −26°C and −10°C but smaller when the ambient temperature is between −40°C and −26°C. The mass fraction of the supercooled water from (2) is always smaller than that from either (1) or (3) in the −40°C to 0°C range. Another experiment, denoted by mid_f in Figure 1, uses the fraction of supercooled liquid water that is an average of the formulae of Hu and ERA40_f. As mentioned earlier, these formulae are used to partition the fraction of total condensate from convective detrainment or large-scale condensation into liquid and ice forms. Microphysical processes determine the amount of cloud liquid, cloud ice, and precipitate at the end of each time step. Thus, the differences resulting from these formulae in climate simulation may not as large as those appearing in Figure 1.
 The control and sensitivity experiments were run for a ten-year duration starting from 00Z September 1, 1990 using CAM4 with the resolution mentioned above. These experiments were forced by specifying climatological SST and sea ice with monthly mean annual cycles while coupled with the Community Land Model over land [Oleson et al., 2004; Gent et al., 2011]. The initial atmospheric conditions were obtained by mapping the high-resolution (T159) ERA40 [Uppala et al., 2005] to the coarse-resolution CAM4 grid in a way that is consistent with the low-resolution topography.
 It should be mentioned that the distinction between cloud liquid and ice is not solely dependent on temperature in nature. For example, cloud liquid fraction in mixed-phase clouds is actually higher at lower cloud temperature in the Arctic [e.g., Boudala et al. 2004; Liu et al., 2007; Xie et al., 2008]. As climate models gradually adopt the two-moment cloud microphysics parameterization and explicitly represent relevant microphysical processes in mixed-phase clouds, the phase parameterizations are replaced by other parameterizations related to the treatment of Bergeron-Findeisen [e.g., Fan et al., 2011] and ice nuclei parameterizations in mixed-phase clouds [e.g., DeMott et al., 2010; Liu et al., 2011].
 CAM version 5 (CAM5) implements a double-moment cloud microphysical scheme that prognoses both the mass mixing ratio and number concentration of cloud condensates [Morrison and Gettelman, 2008]. Microphysical processes in mixed-phase clouds (e.g., ice nucleation and Wegener-Bergeron-Findeisen process) are explicitly treated in the scheme. An updated treatment of ice nucleation, vapor deposition on ice crystals and ice supersaturation [Gettelman et al., 2010] are used to replace the single-moment cloud microphysical scheme that was used in CAM4. The effective sizes of cloud condensates can be calculated from model-predicted mass mixing ratios and number concentrations. Thus, cloud radiative and microphysical properties can respond to aerosol changes. Because of these significant changes from CAM4 to CAM5, results from a ten-year CAM5 simulation are also included in the following sections. The same configuration as the control run with CAM4 was used.
 Since the primary objective of this study is to investigate the effects of different cloud phase parameterizations on climate simulation, we will show prominent results related to the global distributions of cloud liquid water path (LWP) and cloud ice water path (IWP) in the temperature range of −40°C and 0°C, and the meridional cross sections of liquid water and ice water content and cloud fraction. We will also show relative humidity, radiative heating, and top-of-the-atmosphere (TOA) solar radiative forcing to interpret the results of the sensitivity experiments. State-of-the-art satellite observations from CloudSat, CALIPSO, MODIS, and CERES (Clouds and the Earth's Radiant Energy System [Wielicki et al., 1996]) and reanalysis data are used to provide some constraints on the fidelity of the simulations.
3.1. Changes in Supercooled Liquid and Ice Water Content and Cloud Amount
 The cloud fraction-weighted pressure for clouds within the −40°C–0°C temperature range provides a concise measure for the vertical location of mixed-phase clouds. The choice of this temperature range provides a consistent definition although supercooled liquid and ice clouds coexist in temperature ranges that are different among the experiments (Figure 1). The global distribution of the annual mean vertical location of the mixed-phase clouds is shown in Figure 2 for the control experiment. The mathematical definition is given by , where p is the pressure of the mixed-phase cloud in the −40°C–0°C temperature range of a GCM grid box, cf represents the mixed-phase cloud fraction, and subscripts i and k represent the ith GCM grid box and the kth level, respectively. Because of the latitudinal gradient in temperature, the mixed-phase clouds are associated mostly with boundary layer clouds in the polar regions (north of 60°N and south of 60°S), the middle level clouds between 800 hPa and 400 hPa in the midlatitudes (between 30°S and 60°S, and between 30°N and 60°N), and high-level clouds above 400 hPa in the subtropical and tropical region between 30°S and 30°N.
 The difference between the sensitivity and control experiments in the annual-mean LWP, vertically integrated liquid water content, in the 0°C and −40°C range for all kinds of clouds in each GCM grid box can provide a good measure of the change in supercooled water resulting from the use of different cloud phase parameterizations. In the control experiment (Figure 3a), large LWPs with magnitudes greater than 100 g m−2 appear in the tropical convective regions such as the intertropical convergence zone (ITCZ) and midlatitude oceanic storm track regions of both hemispheres. Moderate LWPs with magnitudes of ∼50 g m−2 appear in the region north of 50°N and near the large LWP regions. The global mean LWP is 49.7 g m−2. Compared to the control experiment, the global mean LWP from the Hu experiment increases by 1.9 g m−2 (Figure 3b), i.e., ∼4% of the global mean of the control experiment. Large regional increases in supercooled LWP, with magnitudes of greater than 10 g m−2 or 20–30% of the regional LWPs in the control experiment, mainly occur in tropical convective regions such as the tropical western Pacific warm pool and northeastern Indian Ocean, and middle/high latitudes centered at 60°S and 60°N (over continents, in particular), where tropical convection and extratropical storms are active, respectively. The decrease of supercooled water is much larger in the other sensitivity experiments; i.e., by 18.2 and 32.6 g m−2 in the global means for the mid_f and ERA40_f experiments, respectively. For the ERA40_f experiment, the largest regional decreases, with magnitudes greater than 60 g m−2 or 40–50% of the regional LWPs in the control experiment, occur in the tropical western Pacific and maritime continental regions and midlatitude storm track regions (Figure 3d). These are regions with the largest LWPs in the control experiment. The Arctic is another region where LWP decreases by over 50%. For the mid_f experiment, the regional patterns in LWP changes are similar to those in ERA40_f except for proportionally smaller magnitudes (Figure 3c), as expected.
 The global distribution of cloud IWP in the −40°C–0°C range of the control experiment is generally similar to that of the LWP of supercooled liquid clouds (Figure 4a). As noted earlier, some ice clouds in this temperature range do not coexist with supercooled liquid water clouds. The ratio of IWP to LWP, however, varies from region to region. It is ∼10% in the tropical regions, ∼20% in the southern storm track regions and greater than 30% in the northern middle/high latitudes. The global mean of IWP is 12.6 g m−2, which is 25.4% of the global mean LWP in the control experiment. The global mean IWP from the Hu experiment decreases by 2.3 g m−2 or 18.3% of that of the control experiment (Figure 4b). A surprising result is that the cloud IWP increases slightly in a few convectively active areas or decreases by less than 1 g m−2 in the rest of the region between 30°S and 30°N (Figure 4b). This is due to the fact that in the −26°C and −40°C range the ice water fraction is higher in the Hu experiment than in the control experiment (Figure 1). In the Southern Oceans and north of 45°N, however, the decreases in IWP are mostly between 4 and 8 g m−2 or 10–20% of the control experiment, which contribute to the decrease in the global mean IWP in this experiment.
 For the other two sensitivity experiments, ERA40_f and mid_f, we expect that their IWPs are larger in any region than those in the control experiment, based upon formula (2). This is the case for the mid_f experiment except for small areas in the southern high-latitude regions (Figure 4c) where significant decreases in IWP occur. The increases are most pronounced in large regions of tropical western Pacific, northeastern Indian oceans, and southern and northern middle/high latitudes, with magnitudes greater than 10 g m−2. The global patterns in the ERA40_f experiment (Figure 4d) are generally similar to those in the mid_f experiment except that there are significant decreases in the middle latitude of northern hemisphere and the high latitude of the southern hemisphere. Because of these differences, the increase in the global mean IWP from the ERA40_f experiment is only 3.0 g m−2, compared to 4.1 g m−2 in the mid_f experiment. This result implies that there are some processes that indirectly impact the simulation of mixed-phase clouds, which cannot be explained by the different cloud phase parameterizations alone (Figure 1). These include the microphysical conversion processes between ice and snow and dynamic/radiative processes that can change cloud macrophysical properties, although deficiencies or inconsistencies within the complicated cloud parameterization components cannot be ruled out. Detailed explanations for this result will be given in section 3.2.
 The global mean mixed-phase cloud amount, which is calculated using the maximum overlap assumption from the vertical profile of cloud fraction in the −40°C to 0°C range, from the control experiment is 18.9%, about one-third of the global mean total cloud amount. The global-mean mixed-phase cloud fraction increases by 1.8%, 2.7%, and 3.9% in the Hu, mid_f, and ERA40_f experiments, respectively, compared with the control. A large part of the cloud fraction increases in these sensitivity experiments occurs in the high-latitude regions (not shown). As shown later, the increases in relative humidity, not cloud water/ice content, are largely associated with the cloud fraction increases because of the diagnostic scheme used to diagnose nonconvective cloud fraction in CAM4 (section 2). In order to examine these relationships, vertical-meridional cross sections of cloud fraction and other variables are plotted (Figures 5–8). The cross section plots provide more information on the exact vertical location where cloud fraction increases relative to the control experiment, as compared to the horizontal distribution plots. For reference, isotherms of 0°C, −15°C and −30°C are overlaid on all cross section plots shown in this study so that the relationships of cloud variables with ambient temperature are easily visualized.
 The most significant changes in the cloud fraction from the sensitivity experiments occurs in the middle-level clouds at middle latitudes and low-level clouds south of 75°S (Figures 6a–6c). Middle-level clouds in middle latitudes are distinctive because they are mixed-phase and are often decoupled from surface fluxes of heat, moisture, and momentum [Fleishauer et al., 2002]. Their fraction is not only underestimated by GCMs with horizontal grid spacing of 100 km, but also by cloud resolving models (CRMs) with horizontal grid spacing of 1 km [Cheng and Xu, 2006]. It is not surprising that the multiscale modeling framework (MMF), in which a cloud-resolving model (CRM) is embedded in each atmospheric grid column of the host GCM to represent cloud physical processes, also underestimated the amount of middle-level clouds [Cheng and Xu, 2011]. On the other hand, GCMs that are able to simulate more middle-level clouds are crucial in determining the overall cloud response or climate sensitivity because middle-level clouds in the storm track regions have stronger positive albedo feedback due to the fact that storm tracks move polewards [Bender et al., 2010]. The sensitivity tests with different cloud phase parameterizations presented in this study all produce more middle-level clouds at the middle/high latitudes (Figures 6a–6c). Comparison against observations and physical interpretation of these results are discussed below.
3.2. Interpretation of the Changes of Cloud Properties in the Sensitivity Experiments
 How well do the mixed-phase clouds from the control and sensitivity experiments compare to the state-of-the-art observations? In this study, the merged data from CALIPSO, CloudSat, CERES and MODIS, denoted C3M, are used for the comparison. The observations from CALIPSO, CloudSat and MODIS are projected to CERES footprint with an average size of approximately 20 km × 20 km [Kato et al., 2010, 2011]. Four-year C3M data are temporally averaged, from July 2006 to June 2010. These footprint data are averaged in horizontal space to obtain the zonal mean profiles of cloud fraction, cloud water content and cloud ice content. Figure 5b shows the differences in cloud fraction between the control experiment and C3M while Figures 5d and 5f show the C3M cloud water content and cloud ice content, respectively.
 The control experiment shows a maximum cloud-fraction center in the tropical upper troposphere (150–300 hPa), which is produced by convective detrainment, and two other maximum centers in the southern and northern storm track latitudes (Figure 5a). Similar maximum centers also appear in cloud water content (Figure 5c) and cloud ice content (Figure 5e), except for slightly equatorward shifts of the storm track maximum centers and higher vertical locations of all maximum centers in cloud ice content than those in cloud water content.
 Compared to C3M data, the zonal-mean cloud fraction is underestimated for the mixed-phase clouds south of 20°S and north of 20°N with temperatures between −40°C and 0°C. Areas of underestimate with magnitudes larger than 10% are located between 55°S and 70°S and north of 50°N. There is also overestimate of high-level clouds in both the tropics (above 150 hPa or 13 km) and the extratropics (with temperatures less than −45°C) (Figure 5b). As shown later, this feature is primarily associated with the overestimate of the high-level relative humidity by more than 10% in CAM4, relative to the ERA40 reanalysis. Convective detrainment is very weak at these high altitudes and can thus be eliminated as a cause of the overestimate of these clouds, but the overestimate of ice water content can be related to the high-level detrainment (Figures 5e and 5f). These clouds are not the primary interest of this study and therefore will not be discussed further. Use of a satellite-instrument simulator could result in a more consistent comparison in cloud fraction between C3M and the CAM4 simulation, but such a simulator designed specifically for C3M data is not currently available.
 The vertical structures of the zonal- and annual-mean cloud liquid water content from the control experiment are very different from the C3M observations. The control experiment shows high water content with magnitudes over 51 mg kg−1 at the middle latitudes and the tropics, in particular, for the −30°C to 0°C temperature range (Figures 5c and 5d), whereas the C3M water content does not exceed 31 mg kg−1. The cross-section of cloud ice content from the control experiment is very similar to that of the C3M observations, but the simulated magnitudes (with maxima less than 11 mg kg−1) are a factor of 2–3 smaller than the C3M observations, whose maxima exceed 26 mg kg−1 (Figures 5e and 5f). Salzmann et al.  also reported a similar large discrepancy between observation and simulation. However, these differences may not be entirely due to the deficiencies of the model because the retrieval of cloud phase is difficult with observations. The presence of large snow particles and drizzle that affect radar reflectivity add further complications in deriving liquid and ice water contents. C3M relies on CloudSat-derived cloud phase (2B CWC-RO, Revision 4). The CWC-RO algorithm deems all ice if the air temperature is below −20°C and all liquid when the air temperature is above 0°C. It partitions ice and liquid contents linearly in the −20°C–0°C range (R. Austin, Level 2B radar-only cloud water content (2B-CWC-RO) process description document, v5.1, 2007, http://www.cloudsat.cira.colostate.edu/dataICDlist.php?go=list&path=/2B-CWC-RO). During the C3M processing, vertically integrated CloudSat-derived ice and liquid water contents are normalized to IWP/LWP retrieved from MODIS. This ensures that vertically integrated, normalized ice and liquid water content agree with IWP/LWP retrieved from MODIS [Kato et al., 2011]. Thus, uncertainties in the C3M cloud ice/water contents are attributed to both CloudSat and MODIS retrievals.
 As indicated earlier, all three sensitivity experiments alleviate the underestimate of cloud fraction associated with the mixed-phase clouds in the control experiment (Figures 6a–6c). Compared to the control experiment, the largest increase in cloud fraction is 1–3% centered at the −30°C isotherm in the Hu experiment while the largest increase in liquid water content with is 3 mg kg−1 and is located in a layer with higher temperatures (between the −30°C and −15°C isotherms; Figure 6d). This increase in liquid water content is accompanied by decreases in cloud ice content centered between −30°C and −15°C isotherms in the extratropics (Figure 6g). In the other two sensitivity experiments (Figures 6b and 6c), the amplitudes of cloud fraction increases are larger (>5% in the ERA40_f experiment) and at the same vertical location as in the Hu experiment. The liquid water content, however, decreases by more than 10 mg kg−1 (with a maximum over 40 mg kg−1 in ERA40_f) in the vertical span bounded by the −5°C and −30°C isotherms (Figures 6e and 6f), accompanied by an increase in ice water content with a magnitude larger than 4 mg kg−1 in the vertical span bounded by the 0°C and −15°C isotherms (Figures 6h and 6i). Both the increases in cloud liquid water content in the Hu experiment and those in cloud ice content in the ERA40_f and mid_f experiments are located below the heights of the significant cloud fraction increases in all these sensitivity experiments. This result suggests that changes in thermodynamics, represented by relative humidity (Figure 7), resulting from radiative cooling are directly responsible for the cloud fraction increases because cloud fraction is diagnosed from the ambient relative humidity regardless of the amount of cloud water/ice present in the GCM grids. Relative humidity increases and the maximum radiative cooling, as detailed below, are located at the same or slightly higher altitudes than the vertical span where the cloud fraction increases occur. Further discussion on radiative cooling is given shortly.
 Another feature worth noticing is the reduction of ice water content near 500 hPa at the middle latitudes of the ERA40_f experiment relative to the control experiment (Figure 6i), which contributes to the smaller increase of IWP in the Southern Ocean region and the reduction of IWP in the northern midlatitudes, compared to the mid_f experiment (Figure 6h). The larger autoconversion rate from ice to snow is the most likely mechanism for the depletion of ice because all condensate is assigned to be ice in this experiment when the ambient temperature is less than −23°C while cloud liquid is present in the other three experiments. The autoconversion occurs only when ice water content exceeds a threshold. This explanation can also be used to explain the reduction of IWP at the southern high latitudes in the mid_f and ERA40_f experiments (Figures 4c and 4d) because of the lower temperatures than its northern counterpart (refer to the vertical location of the −15°C isotherm in Figures 6h and 6i).
 The longwave radiative heating rate from the control experiment and the difference between the control experiment and C3M retrieval are shown in Figures 8a and 8b. The C3M radiative heating profiles are obtained from a radiative transfer model with cloud input from CloudSat, CALIPSO and MODIS measurements and the calculated TOA radiative fluxes are constrained by CERES observations. Shortwave radiative heating is not shown due to a lack of diurnal samplings. Further details can be found in Kato et al. [2010, 2011]. In the lower and middle troposphere, the areas with positive biases with magnitudes greater than 0.2 K day−1 generally correspond to the areas where there is an underestimate of cloud amount (compare Figures 8b and 5b). The negative biases in the tropical upper troposphere (above −30°C isotherm) with magnitudes greater than −0.4 K day−1 may be related to a potential overestimate of cloud ice content in the C3M data, as explained earlier. Comparing the sensitivity experiments with the control experiment, it is clear that longwave cooling is associated with the cloud fraction increase in the mixed-phase temperature range (Figures 8c–8e), while the warming above the cooling zone in the tropics is related to the decreases in cloud fraction around 200 hPa in the tropics of the sensitivity experiments (Figures 6a–6c). This warming decreases the relative humidity and thus leads to the decrease of cloud fraction. Similar features are also present at the lower altitudes (between 0°C and −15°C isotherms) of the middle/high latitudes (Figures 8c–8e). These results only illustrate the consistency among relative humidity (Figure 7c–7e), cloud fraction and radiative cooling/heating in the model, but give no indication of the cause and effect.
 Another way for assessing the impact of cloud phase parameterizations is to look at cloud albedo forcing. Cloud albedo forcing is an indicator of cloud reflectivity of solar insolation, defined as [Charlock and Ramanathan, 1985]: CFs = Rs0 − Rs, where Rs and Rs0 are the total and clear sky net downward fluxes of solar radiation at TOA, respectively. Cloud albedo forcing (αf) is obtained by dividing solar cloud radiative forcing by the solar insolation (S0), αf = CFs/S0. The zonal-mean cloud albedo forcing from the four experiments and the CERES Energy Balanced and Filled data [Loeb et al., 2009] are shown in Figure 9. It can be seen that the cloud albedo forcing has good correspondence with the amount of the liquid water in the mixed-phase and warm clouds at most latitudes. For example, the control experiment produces the largest liquid water in the mixed-phase clouds (Figure 3) and the largest cloud albedo forcing in the middle latitudes among all the experiments in this study. The more liquid water the clouds have, the larger the cloud albedo forcing is. This is because liquid water is optically thicker to solar radiation than ice water. The control and Hu experiments produce the most realistic cloud albedo forcing at the middle/high latitudes south of ∼30°S and north of ∼30°N because these two experiments have the most liquid water in the mixed-phase clouds. The ERA40_f experiment has the largest negative bias in cloud albedo forcing at the southern middle latitudes between 30°S and 70°S and north of 30°N because the LWP decreases by ∼50% for ERA40_f, but it is not offset by the increase in IWP (Figures 3e and 4e). The large increases in cloud fraction north of 75°N and south of 70°S of this sensitivity test (Figure 6c) offset the impact of the LWP decreases on the cloud albedo forcing so that its cloud albedo forcing is similar to that of the other experiments at these high latitudes.
 All the experiments overestimate cloud albedo forcing at low latitudes compared to the CERES observations (Figure 9). This result may be related to a number of factors. One of the factors may be the overestimate of the amount of low-level clouds by CAM4. The other factor is related to the overestimate of the liquid water because the cloud phase parameterization is applied to the entire cloud layer in the 0 to −40°C range. Another factor is that the cloud fraction is not necessarily related to the amount of cloud condensate, which can be seen in the small reductions of TOA cloud albedo forcing in the ERA_f and mid_f experiments even though LWPs are much smaller in these two experiments. Finally, according to Hu et al. , the low latitudes have less supercooled water than the middle and high latitudes in the mixed-phase clouds because of the availability of ice nuclei. In the future, we may use a formula that considers the dependence of supercooled water on latitude and altitude to further improve the simulation of mixed-phase clouds.
3.3. Comparison of the Mixed-Phase Cloud Simulations Between CAM5 and CAM4
 The differences between the CAM5 and CAM4 control experiments are shown in Figure 10, which are then compared with the differences between the sensitivity and control experiments with CAM4 (Figures 6–8). As in all of the sensitivity experiments with CAM4, CAM5 reduces the magnitude of the underestimate of mixed-phase cloud fraction in middle and high latitudes (Figure 10a), with increases of 5–25% over the CAM4 control experiment. Because the subgrid-scale cloud fraction is diagnosed using a formula proportional to the relative humidity in both CAM4 and CAM5, the differences between them are closely related to differences in relative humidity (Figure 10b). The relative humidity from CAM5 is 4–25% higher than from CAM4 in the middle and high latitudes, but is not more than ∼12% higher for mixed-phase clouds. Thus, relative humidity is a major factor directly contributing to the large cloud fraction differences in Figure 10a. As discussed earlier, cloud fraction influences the longwave radiation cooling and in return the radiative cooling increases the relative humidity in the sensitivity experiments with CAM4. However, the changes in longwave heating rate from CAM4 to CAM5 for the mixed phase clouds (Figure 10c) are generally similar to those of the three sensitivity experiments (Figures 8c–8e) except for the reduction of the positive biases in the low troposphere of CAM4 (Figure 8b).
 As stated in section 2, CAM5 does not use the temperature-dependent phase parameterization. The CAM5-simulated liquid and ice water contents (Figures 10d and 10e) resemble somewhat closely the C3M observations. But liquid water content and ice water content are, at least, a factor of two smaller than CAM4. Combining with the increase in cloud fraction, the comparison between CAM4 and CAM5 suggests that in-cloud liquid and ice water content in CAM5 are smaller than in CAM4. This partly explains the small differences in radiative heating rates in the mixed-phase cloud regions between CAM4 and CAM5 (Figure 10c) despite the larger cloud fraction in CAM5. Also, CAM5 underestimates cloud albedo forcing in the southern middle latitudes and northern high latitudes (Figure 9) due to the lack of supercooled water clouds. There is no significant difference in the tropical cloud albedo between the two models.
 In this study, we have examined the impacts of different cloud phase parameterizations on climate simulation. In the standard CAM4 (control simulation), the total condensate is partitioned into liquid and ice using a fixed linear function of ambient temperature, ramping from pure liquid at temperatures above −10°C to pure ice below −40°C. This type of formula has been commonly used in most GCMs with single-moment cloud microphysics [Klein et al., 2009]. In a sensitivity experiment (Hu), the partitioning of liquid and ice in mixed-phase clouds is based on CALIPSO observations. According to Hu et al. , the liquid phase fractions and liquid water paths from CALIPSO are significantly higher than the ones from previous studies using passive remote sensing measurements.
 We have shown that the application of the new cloud thermodynamic phase parameterization in CAM4 results in an increase in global- and annual-mean liquid water path (LWP) by 1.9 g m−2 (4%) and a decrease in global- and annual-mean ice water path (IWP) by 2.3 g m−2 (18%) for temperatures between −40°C and 0°C, compared to the control experiment with the default parameterization. The maximum regional increase in LWP, with a magnitude of greater than 10 g m−2 or 20–30%, mainly occurs in the tropical regions such as the western Pacific warm pool and northeastern Indian Ocean and middle latitudes. The maximum regional decreases in IWP, with magnitudes of 8 g m−2 or ∼20%, occurs between 40°S and 70°S and north of 45°N while the regional IWP increases slightly or decreases by less than 1 g m−2 in the tropical and subtropical regions. The maximum increase in the zonal-mean cloud liquid water content (LWC) occurs between temperatures of −30°C and −15°C, while the largest increase in the cloud fraction is centered at the −30°C isotherm. The largest decrease in the zonal-mean cloud ice water content (IWC) is spread over a wider temperature range, but peaks between the −30°C and −15°C isotherms.
 To understand the results from the Hu experiment, we performed two additional experiments, one with the cloud thermodynamic phase parameterization used in the ERA40 reanalysis that produces pure ice for temperature less than −23°C, and the other with supercooled liquid fraction between the Hu and ERA40_f experiments. The results from these two experiments resemble those in the Hu experiment except for the sign and magnitude of LWP and IWP changes from the control experiment and altitudes of the maximum changes in cloud LWC and IWC. However, changes in cloud fraction are located in the same vertical extent as in the Hu experiment despite significant decreases/increases at slightly lower altitudes in LWC/IWC in these two experiments. Other subtle differences in the regional IWP distribution are also noticeable at high latitudes.
 Although all experiments were compared with observations from CloudSat, CALIPSO, CERES and MODIS (C3M), uncertainties in the C3M vertical profile data would not enable us to discriminate the overall performance of the simulations of mixed-phase clouds. It is, however, found that the zonal-mean cloud albedo forcing has good correspondence with the amount of the liquid water in the mixed-phase clouds at low and middle latitudes. The control and Hu experiments produce the most realistic cloud albedo forcing at the middle/high latitudes south of ∼30°S and north of ∼30°N, compared to the CERES observations, because these experiments have the most liquid water in the mixed-phase clouds. The experiment with ERA40 parameterization has the largest negative bias of cloud albedo forcing between 30°S and 70°S and north of 30°N because the LWP decreases by ∼50%, but it cannot be offset by the increase in IWP. The large increases in cloud fraction north of 75°N and south of 70°S in this sensitivity test offset the impact of the LWP decreases on the cloud albedo forcing so that its cloud albedo forcing is similar to that of other experiments at the high latitudes. At low latitudes, cloud albedo forcing is overestimated in all experiments, pointing to deficiencies in other aspects of cloud parameterizations in the CAM4 such as the cloud fraction diagnosis based solely upon ambient relative humidity but not on cloud water/ice content.
 We have briefly compared the mixed-phase clouds and their liquid and ice water contents from a ten-year simulation of CAM5 with the control and sensitivity experiments with CAM4. As in all the sensitivity experiments with CAM4, CAM5 reduces the underestimate of mixed-phase cloud fractions in middle and high latitudes but produces smaller amounts of liquid and ice water content when compared to CAM4. The higher relative humidity in CAM5 is a major factor directly contributing to the larger mixed-phase cloud fraction. Because of smaller in-cloud liquid and ice water content, CAM5 underestimates the cloud albedo forcing in the southern middle latitude and northern high latitudes.
 As previously mentioned, a common feature among the three sensitivity experiments is that the heights of significant cloud fraction increases are located above those of the increases/decreases in cloud water content or cloud ice content, compared to the control experiment. This result suggests that changes in thermodynamics, represented by relative humidity (Figure 8), resulting from radiative cooling are directly responsible for the cloud fraction increases because cloud fraction is diagnosed from the ambient relative humidity. Relative humidity increases and the maximum radiative cooling are located at the same or slightly higher altitudes than the vertical span where the cloud fraction increases occur.
 If the inconsistency between the decrease of cloud water content and the increase of cloud fraction were removed, the impact of cloud-phase parameterizations would be greater among the different sensitivity experiments. The cloud fraction parameterization of Xu and Randall , which relates cloud fraction to both the ambient relative humidity and cloud condensate, can be implemented to further test the different cloud-phase parameterizations and to improve the simulation of mixed-phase clouds. New results will be reported in a separate study, along with other modifications to the Hu parameterization discussed earlier.
 This work has been supported by DOE Atmospheric System Research Program under Interagency agreement DE-SC0005450. This work was also partially supported by NASA Modeling, Analysis and Prediction program managed by David Considine. The computation resources from NCAR BlueGene supercomputer were provided by the Teragrid organization. Thanks to Kirk Ayers and Zachary Eitzen of SSAI for reading drafts of this paper.