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.
Figure 3. Zonal mean of the annual mean (a) total IWC and (b) filtered cloud IWC (non-convective and non-precipitating) from CloudSat observation. Unit is (mg m−3).
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 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.
Figure 4. Zonal mean of the annual mean cloud IWC from (a) filtered CloudSat (non-convective and non-precipitating), (b) ERA-Interim, and (c) UCLA AGCM. The contours are the standard deviations (contour interval is 0.1 mg m−3).
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 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.
Figure 5. (a) Multilayer Taylor diagram of the annual mean cloud IWC for the ERA-Interim (red) and UCLA AGCM (green). The reference data set “Obs” is from CloudSat observation. (b) Portrait diagram display of relative error metrics for the multilayer cloud IWC for the ERA-Interim and UCLA AGCM. See text for the definition of relative error.
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 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.
Figure 6. Annual mean cloud IWC (mg m−3) from (a and b) filtered CloudSat (non-convective and non-precipitating, (c and d) ERA-Interim, and (e and f) UCLA AGCM at 300 and 500 hPa.
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 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.
Figure 7. Zonal mean of the seasonal mean cloud IWC (Dec-Feb, Mar-May, Jun-Aug, and Sep-Nov) from (a, b, c, and d) filtered CloudSat (non-convective and non-precipitating), (e, f, g, and h) ERA-Interim, and (i, j, k, and l) UCLA AGCM. The contour interval is 1 (mg m−3).
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 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.
Figure 8. Seasonal mean cloud IWC (Dec-Feb, Mar-May, Jun-Aug, and Sep-Nov) at 300 hPa from (a, b, c, and d) filtered CloudSat (non-convective and non-precipitating), (e, f, g, and h) ERA-Interim, and (i, j, k, and l) UCLA AGCM. The unit is (mg m−3).
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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.
Figure 10. Zonal mean of the annual mean cloud IWC from sensitivity experiments on the autoconversion time scales with (b) constant time scale, (c) effect of differential IR heating only, (d) effect of environmental static stability only, and (e) 1.4 times larger of the constant time scale used in (b). (a) Also shown is the control simulation same as in Figure 4c. The contour interval is 1 (mg m−3).
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 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).
Figure 11. Zonal mean of the annual mean cloud IWC from (a) sensitivity experiment on the temperature threshold (−23°C to 0°C) for all the saturated water vapor and cloud liquid to deposit to cloud ice. (b) Also shown is the IWC difference between the sensitivity experiment (Figure 11a) and control (Figure 10a). The contour interval is 1 (mg m−3) for the sensitivity experiment (Figure 11a) and 0.5 (mg m−3) for the difference (Figure 11b).
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 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
|Experiments||ΔTotal Cloud Cover (%)||ΔOLR (W m−2)||ΔNet SW at TOA (W m−2)||ΔNet Radiative Flux at TOA (W m−2)|
|dIR+ constant τi,eff||1.52||−3.41||−2.25||1.16|
| + constant τi,eff||−1.52||4.42||3.85||−0.56|
|Constant τi,eff * 1.4||2.05||−3.79||−2.11||1.68|
|Deposition temperature threshold (−40∼−5 to −23∼0°C)||0.01a||0.16||0.5||0.34|