In this section we present a series of cases that illustrate the performance of the scheme. The next section will analyze some of the detailed aspects of the scheme. The “ICE” case is the basic version of the scheme. It can be compared to a control case, ‘CNTL,’ that uses saturation adjustment to a ‘hybrid’ (liquid and ice) RH dependent on temperature from −20 < T < 0°C as in CAM3. Within this range some ice supersaturation can exist. The CNTL case also has ice nucleation fixed as a function of temperature as described in MG2008 using Cooper . The ‘FIXIN’ case has supersaturation, but uses ice nucleation following Cooper  as described in MG2008. The ‘ICEHI’ case is a version of the ‘ICE’ case with higher ice nuclei and ice crystal number concentrations. Higher concentrations result from increasing the crystal number from homogeneous freezing by using all sulfate particles in the Aitken mode. These cases are summarized in Table 2.
3.1. CAPT Experiments
 To evaluate the role of the ice scheme in mixed phase clouds, we compare CAM simulations to field observations collected during the Atmospheric Radiation Measurement (ARM) program's MPACE project [Verlinde et al., 2007]. MPACE was conducted near Barrow, Alaska in October 2004 and during the experiment there was a significant mix of deep and shallow clouds, as well as a high proportion of mixed phase clouds. To compare CAM with the observations, we utilize a weather forecasting approach [Phillips et al., 2004] as applied in the Cloud Associated Parameterization Testbed (CAPT) [Xie et al., 2008]. Model output for the grid-box closest to Barrow is examined for the second day of forecasts that are initialized every day in October 2004 with reanalyses produced by the Modern Era Retrospective-Analysis for Research and Applications (MERRA) project (http://gmao.gsfc.nasa.gov/research/merra/).
 Figure 1 illustrates the hourly mean cloud fraction as a function of time and pressure from observations and model simulations. The observations (Figure 1, top) are from the Active Remotely Sensed Cloud Locations algorithm [Clothiaux et al., 2000] which uses signals from the cloud radar and lidar at Barrow. The lower two panels illustrate the model's hourly mean cloud fraction from the CNTL simulation which does not permit ice supersaturation (Figure 1, middle) and the ICE simulation with the revised ice microphysics (Figure 1, bottom) including ice supersaturation and nucleation. The quantity from the model is not identical to that of the observations. Addressing the sources of differences between the model definition and that retrieved from upward-pointed radars and lidars is not easily done. While we don't have any expectation of bias, there are a number of difficult issues involved such as instrument sensitivity for detection of hydrometeors and differences between a point observation averaged over time (which is the observation) and an grid-box area-averaged quantity from the model. But, both model versions simulate a reasonable progression of middle and high cloud in response to various frontal passages. A prominent difference is the much larger amount of boundary-layer clouds in the ICE simulation in better agreement with the observations. These boundary layer clouds were observed to be mixed phase (Figure 2) and the presence of supercooled liquid allows these clouds to be long-lived due to turbulence driven by the strong cloud-top longwave cooling that occurs only when cloud liquid is present. Surface fluxes also play a role, but are similar in these simulations. While the ICE simulation produces an appreciable amount of supercooled liquid, the CNTL simulation simulates essentially no supercooled liquid and thus simulates very low amounts of boundary-layer cloud. Perhaps the absence of supersaturation in the CNTL simulation allows more condensation and thus has depleted the available humidity. Relative to the CNTL simulation, the presence of significant amounts of supercooled liquid in the ICE simulation leads to a greatly improved simulation of the downward longwave radiation at the surface (not shown).
Figure 1. Height-time profile of cloud fraction (%) for Barrow, Alaska, during October 2004: (top) as observed from ARM cloud radars and lidars Active Remotely Sensed Cloud Locations algorithm [Clothiaux et al., 2000], (middle) CNTL simulation, and (bottom) ICE simulation. Simulations use the CAPT weather forecast approach.
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Figure 2. Height-profile of quantities averaged over the period 1200 UTC 9 October to 1200 UTC 10 October during MPACE. (left) Cloud fraction (%). (middle) Liquid water content. (right) Ice water content. Observations in black. Cloud fraction observations are from Active Remotely Sensed Cloud Locations (ARSCL) [Clothiaux et al., 2000]; liquid and ice water content are from Shupe et al. . Simulations for CNTL (green dash), ICE (blue dash), and ICEHI (red) shown.
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 The boundary-layer mixed phase clouds observed during 9–15 October were sampled by aircraft and have been the subject of numerous modeling studies ([Klein et al., 2009; Solomon et al., 2009], among others). Figure 2 shows the average for a 1 day (9–10 October) period of cloud fraction and liquid and Ice Water Content (IWC) from remote sensor retrievals [Shupe et al., 2008] and model simulations. Simulated IWC includes snow (precipitating ice). The ICE and ICEHI simulations correctly simulate an overcast cloud with appreciable amounts of liquid and that produces ice and snow that falls out of the cloud. However, both simulations underestimate the amount of supercooled liquid by 50% (Figure 2, middle) and overestimate the amount of ice and snow by 50% (Figure 2, right). These biases also appear when comparing model simulations relative to the aircraft retrievals [McFarquhar et al., 2007b] and during the whole of the 6 day period with mixed phase boundary-layer cloud. The biases in supercooled liquid are a common feature of many models for this case [Klein et al., 2009]. Although many factors may contribute to this bias, it is noteworthy that the model simulates a snow crystal number concentration of nearly 100 L−1. The ice crystal concentration in clouds is <1 L−1. Thus most of the ice and snow number concentration is snow. The total ice and snow concentration far exceeds the observed ice number concentration of 2 L−1 [McFarquhar et al., 2007b] for large crystals (and would include snow). This suggests that the model's snow production is too strong, at least for this region and time.
 High snow numbers are due to freezing of all supercooled rain instantaneously at temperatures less than −5°C. This was included to prevent excessive supercooled rain in the Arctic spring that negatively impacts sea ice distributions. In an experiment where this freezing threshold is reduced to −40°C (FRZ), total ice and snow numbers simulated by CAPT are only 1 L−1. In this test the immersion freezing of some fraction of the rain mass is allowed above this temperature threshold following the formulation described in MG08. The FRZ case does improve agreement with observations for the MPACE case, but degrades general simulations because the sea ice model does not treat supercooled liquid precipitation.
 The performance of the scheme can also be evaluated by looking at the climatological (average) representation of ice number, the total mass of ice and the in-cloud ice water content compared to observations. Results are averages from 3 year runs with fixed present day sea surface temperatures and aerosol emissions after a 1 year spin up. Simulations are performed at 1.9° latitude by 2.5° longitude horizontal resolution with 30 vertical levels up to 3 hPa. Upper tropospheric vertical resolution is about 1 km and is shown as vertical ticks on Figure 4a (some ticks are omitted in the boundary layer for clarity).
 The ice mass mixing ratio fraction (or ice fraction, FICE) with respect to temperature is illustrated in Figure 3 following that of Korolev et al. [2003, Figure 5]. Figure 3 shows a series of probability distribution functions (PDFs) in different temperature ranges from observations (Figure 3a) and from output of the ‘ICE’ case (Figure 3b). Model output is only shown for mixed phase conditions when ice and liquid are present (qi and ql > 0). Ice mass fraction is calculated at each model point (1000–100 hPa and 90°S–90°N) and time, as is temperature, and then the PDFs are constructed from monthly means of each, point by point. The shape of a joint PDF of instantaneous values is similar.
 The transition from ice to liquid occurs between −2°C and −20°C in observations and −5°C and −20°C in the simulation. In the ICE simulation, the maximum frequency at an ice fraction of 0.6 is between −10°C and −15°C. There is not enough ice mass fraction (relative to the observations) at temperatures warmer than −15°C, indicating a slightly more narrow transition temperature range in the simulations, but a reasonable mean mixed phase transition. The ICE simulation is closer to the observations than the CNTL simulation, or the simulations described by Gettelman et al. [2008, Figure 4] using MG2008.
 The ice mass, or ice water content (IWC), is an important component of understanding the radiative distribution and impact of high clouds, and has been shown to vary widely between observations and between observations and models [Waliser et al., 2009]. Differences in retrieved IWC arise due to the sensitivity of instruments to different parts of the ice PSD, and saturation of active and passive sensing wavelengths by ice and liquid. Differences in simulated ice arise from coarse representations of the size distribution and segmentation of ice into up to three species (ice, graupel, and snow) in models (CAM has only two: ice and snow).
 Figure 4 compares the mass of ice and snow (total frozen condensate) in the ICE simulation with CloudSat version 5.1 [Waliser et al., 2009] and Microwave Limb Sounder (MLS) [Wu et al., 2009] version 2.2 total IWC satellite retrievals. CloudSat is an active 96 GHz cloud radar with horizontal footprints of 1.3 km cross track, 1.7 km along track and 240 m vertical range. MLS is a microwave limb-viewing instrument with 200 km along track, 7km cross track and 4 km vertical resolution. Both are in a similar 1330 local equatorial crossing time orbit. Both zonal mean vertical (Figure 4b) and horizontal (Figure 4d) distributions are shown for CloudSat, with the zonal mean MLS IWC measurements as the contour lines in Figure 4b. There are still large uncertainties in the retrieval of IWC from satellites [Waliser et al., 2009]. For example, CloudSat retrievals make assumptions about ice crystal number concentration and cloud phase as a function of temperature. MLS is saturated by thick and dense clouds [Wu et al., 2009].
Figure 4. (a and b) Zonal mean and (c and d) ∼225 hPa maps of ice and snow path (mg m−3) from ICE case (Figures 4a and 4c) compared to CloudSat (colored contours) satellite observations (Figures 4b and 4d). Microwave Limb Sounder observations are also shown in Figure 4b (lines) with contour intervals on the same scale.
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 The simulated IWC distribution peaks in midlatitudes at 800 hPa at >20 mg m−3 in Figure 4a, higher in the Southern Hemisphere, in agreement with CloudSat IWC observations (Figure 4b). At midlatitudes in both CAM and CloudSat, ice mass peaks in the storm track regions over the oceans. Overall the ICE simulation seems to have correct ice and snow magnitude at midlatitudes, lower ice and snow mass in the tropical upper troposphere, and slightly lower overall altitudes relative to CloudSat retrievals. The lower altitude may be due to the significant fraction of snow in the ICE simulation (which is averaged in altitude as it falls over the time step). The lower simulated altitude might also be due to the liquid ice partitioning as a function of temperature by CloudSat and the simulation. If model ice occurs at warmer temperatures (Figure 3), or CloudSat prescribed ice at colder temperatures, simulated ice and snow would occur lower in the atmosphere than CloudSat.
 In the upper troposphere at ∼225 hPa, the magnitude of IWC+SNOW in the model (Figure 4c) is less than observed from CloudSat (Figure 4d), mostly because the mass in CAM appears to be shifted lower in altitude. In CloudSat, at least 2/3 of the mass of ice phase species is likely ‘precipitating’. The CAM ICE simulation is similar. The horizontal distribution in the simulations (Figure 4c) reproduces the distribution of the ice phase, but with lower magnitude than CloudSat (Figure 4d).
 Figure 5 shows the annual zonal mean of ice mass mixing ratio (not including snow, Figure 5a), ice effective radius (Figure 5b) and ice number concentration (Figure 5c). The ice mass mixing ratio peaks in the tropical upper troposphere near 250–300 hPa at 3 mg kg−1. The ice and snow mass peaks slightly lower at 10 mg kg−1 (Figure 4a). The polar regions and midlatitudes do not have much ice mass (it is mostly snow in Figure 4a). Ice effective radius increases closer to the surface, with higher altitude cirrus clouds having smaller sizes (20 μm) and larger sizes (50–60 μm) found at lower altitudes. Ice number in the region of maximum mass is around 0.1 cm−3 (or 100 L−1). Ice nucleation with higher numbers is seen at altitudes above this (pressure < 200 hPa). Ice multiplication (due to shattering of rimed ice crystals) and further nucleation is seen in the mixed phase region (600–800 hPa). At 250 hPa, ice number concentrations are higher over land (typically 100–300 L−1), and lower over the oceans and in the Arctic over land (20–50 L−1). Higher concentrations over land appear to be due to more ice nucleation in the simulations, a result of (1) higher turbulence and vertical velocity as well as (2) more heterogeneous nuclei (dust) and sulfate for homogeneous freezing. Note that CloudSat and CAM ice mass peaks over tropical land convective regions (Figures 4c and 4d), but over oceans in midlatitudes.
Figure 5. Annual zonal mean latitude height plots of (a) cloud ice mass, (b) cloud ice effective radius, and (c) ice number from ICE simulations. Plots have been thresholded by where ice mass is larger than 0.2 mg kg−1.
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 To explore the ice content in a different way, we compare the in-cloud ice water content in the simulations (including snow) to empirical fits based on observations. The inclusion of snow inside of clouds for in-cloud qi > 0.05 mg kg−1 does not substantially alter the PDF (we seek to assess total ice in the cloudy portion of the grid box, not snow without cloud). The fits for comparison are based on in situ observations that do not generally separate precipitation from suspended crystals. Figure 6 compares a joint PDF of IWC as a function of temperature from the ICE simulation with several different empirical formulations from Wang and Sassen , Schiller et al. , Wood and Field , Wilson and Ballard  and Liou . All are fits to observations, with those of Wood and Field  and Wilson and Ballard  functions of the background water vapor. The observed variability about the empirical fits is large, and variations between them are also large. Thus these relationships are not a strong constraint on IWC-temperature relationships. The simulations have increasing IWC with temperature as observed, and the peak of the distribution at IWC < 7 mg m-3 agrees with observations in the 220–250 K temperature range.
Figure 6. In-cloud ice water content (IWC) and in-cloud snow in mg m−3 as a function of temperature from the ICE run (gray-shaded joint PDF). Data from 80°S–80°N and 500–200 hPa. Snow is added when in-cloud ice mass is greater than 50 ppmm and cloud fraction is greater than 0.05. Various empirical fits to observations shown from Wang and Sassen : black solid, Liou : black dashed, Wood and Field : red, Wilson and Ballard : gray, and Schiller et al.  for different regions (yellow dash-dotted: Arctic, green solid: midlatitudes, cyan dotted: tropics, and purple dashed: global). Those of Wood and Field  and Wilson and Ballard  are functions of the background water vapor and are shown for 5, 10, 20, and 50 ppmm with thicker lines corresponding to more water vapor. 50 ppmm shown only for T > 233 K.
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 Figure 7 illustrates the number of ice particles (including snow in clouds with ice number concentration > 1 L−1) in the ICE simulation as a function of temperature. Instantaneous data up to 120 hPa make up the PDF for all latitudes. Ice concentrations peak between 30 L−1 at 235 K to 10 L−1 at 255K. At colder temperatures (T < −35°C), ice nucleation is rapid. Most near surface Arctic points are clustered near 255K and 10 L−1. The simulated ice crystal concentrations are compared to empirical fits of ice nuclei concentrations in Figure 7. These are not the same quantity, as ice crystal number concentrations can be altered by processes other than nucleation (e.g., depletion by sedimentation or autoconversion, ice multiplication, etc). Gultepe et al.  found average ice crystal concentrations of 3–10 L−1 at temperatures above 230K. The dotted line is from Prenni et al. , a recalculation of Meyers et al.  (solid line) to fit MPACE observations. Also shown are estimates by Cotton et al.  and Fletcher  (on which Cotton et al.  is based). The ice numbers from Cooper  are used by the CNTL and FIXIN case (and fixed at 220 L−1 for T < −35°C as in MG2008). Values of 100 L−1 seen for CAPT MPACE simulations occur at temperatures from 235–250 K and are largely due to high snow number concentrations.
Figure 7. Ice number (ice and snow number) as a function of temperature for the ICE case using instantaneous output from 1000 to 120 hPa and all latitudes. Also shown are fits to observations for ice crystal concentrations as a function of temperature based on the study by Fletcher  (dashed) and Cooper  (3-dot dashed). Fits to observations of ice nuclei are shown for the studies by Meyers et al.  (solid) and Prenni et al.  (dotted), and the parameterization of ice nuclei concentration are from the study by Cotton et al.  (dash-dotted).
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3.3. Ice Nucleation
 Ice nucleation in the ICE formulation of the model includes both homogenous freezing of sulfate solution droplets and heterogeneous freezing on dust. Figure 8a shows the fractional contribution of homogenous freezing to total ice crystal formation in the ICE case. At high altitudes and high latitudes of the Southern Hemisphere, homogenous freezing dominates ice nucleation. Note that some of the regions where homogenous freezing dominates are in the stratosphere in polar regions, due to cold temperatures. Not much water is available there for growing nucleated particles, and hence there are not many clouds in these regions of the stratosphere. In the Northern Hemisphere, especially in midlatitudes at levels where significant ice is produced (400–200 hPa), homogenous freezing is about half of the total ice nucleation. A significant fraction of simulated ice nucleation in the ICE run (Figure 8a) is from heterogeneous freezing on dust. In the ICEHI case (Figure 8b), the total number of activated ice nuclei is based on a larger number of sulfate aerosols (homogenous freezing). As a result, in the ICEHI case, ice nucleation (where ice is significant from the surface to 200 hPa in high latitudes and 300–100 hPa in the tropics) is almost entirely dominated by homogenous freezing. In both cases tropical cirrus clouds are dominated by homogenous freezing at pressures less than 150 hPa. This indicates not much dust is present in the upper troposphere, or the conditions are not right for nucleation, and is consistent with observed ice nuclei composition, even over land [DeMott et al., 2003a]. However, given significant mineral dust loading, dust dominates ice crystal residuals.
Figure 8. Zonal mean fractional contribution to ice crystal number from homogenous freezing from (a) ICE and (b) ICEHI experiments.
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 The horizontal distribution of the fraction of homogenous freezing at ice levels (232 hPa) is illustrated in Figure 9 for the ICE case. Heterogeneous nucleation is important in regions over and downwind of dust producing regions, especially the Sahara desert and S. Africa, Australia, and the Gobi desert over central Asia and the N. Pacific. The simulation predicts significant heterogeneous ice nucleation on dust throughout the Arctic and the N. Hemisphere, while the S. Hemisphere is dominated by homogenous freezing. Note that observations [Quinn et al., 2007] do suggest dust transport into the Arctic is a component of Arctic haze (aerosols).
Figure 9. Map of the fractional contribution to ice crystal number from homogenous freezing from the ICE experiment at 232 hPa.
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 The immediate prerequisite for ice nucleation is ice supersaturation [Kärcher and Lohmann, 2002; Kärcher and Haag, 2004]. When ice supersaturation reaches a threshold between water and ice saturation [Koop et al., 2000] or a threshold sufficient to activate heterogeneous ice nuclei, ice nucleation occurs. Thus representing the distribution of supersaturation is both a driver of and an effect of ice nucleation. Humidity observations in the upper troposphere from the Atmospheric Infra Red Sounder (AIRS) satellite [Gettelman et al., 2006a] and the Measurements of ozone, water vapor, carbon monoxide and nitrogen oxides by Airbus in-service aircraft (MOZAIC) project [Gierens et al., 1999] indicate an exponential decrease in the probability of occurrence of ice supersaturation as humidity gets higher, and rare instances of humidities approaching water saturation. Figure 10 shows a Probability Density Function (PDF) of relative humidity (RH is calculated over ice and liquid for both observations and the model: ramped between 0°C and −20°C). The region represented (500–200 hPa) has temperatures mostly below −20°C, so this can be thought of as simply RH over ice.
Figure 10. Probability distribution function (PDF) of relative humidity (RH) from instantaneous model output from ICE (green) and CNTL (black) simulations, as well as from AIRS (blue) and MOZAIC (red) observations. RH is merged (liquid and ice) RH as described in the text.
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 The ICE simulation matches AIRS and MOZAIC observations of ice supersaturation. Both the ICE and CNTL simulations have a high frequency of RH = 100% due to in-cloud points that are not seen in observations due to sampling. The CNTL model has virtually no supersaturation, and the supersaturation is only diagnosed because a combined liquid-ice relative humidity is used in a specified ‘mixed phase’ temperature region (0°C to −20°C). The ICE case has significant supersaturation (global frequency 7.8%). The calculation is performed on instantaneous model output averaged over the meridional and vertical range of MOZAIC aircraft data (from 30°S–60°N and 500–200 hPa). Simulated supersaturation is higher than AIRS (global frequency 1.3%), and lower than MOZAIC (global frequency 18%) observations, but within the range of uncertainty from these two data sources [Gettelman et al., 2006a]. Total frequency is lower. AIRS single profile RH uncertainty is about 20% under ice conditions [Gettelman et al., 2006b].
 The simulated zonal mean frequency of supersaturation is compared to AIRS in Figure 11. AIRS water vapor has a minimum threshold of ∼20ppmm. No data is available from pressures less than 150 hPa, in the stratosphere, or in regions of deep convection. The general pattern with higher frequencies (of 30%–50%) near the surface at high latitudes and low altitudes, is reproduced by the ICE simulation, with an expected higher frequency than AIRS. As a nadir IR sensor, AIRS cannot see the most humid columns within or adjacent to clouds, and so there is an expected dry bias to the AIRS all sky observations, and hence a lower frequency of supersaturation.
 Both AIRS and the ICE simulation have a higher frequency of ice supersaturation in the Southern than Northern hemisphere middle and high latitudes (Figure 11). Ovarlez et al.  attribute this to differences in aerosol populations, while Gettelman et al. [2006a] note that this could be simply due to different temperature variance. Kahn et al.  did not see hemispheric differences in temperature variance however.