Numerical simulations and airborne measurements are used to evaluate the impact of physical processes on synoptically forced, midlatitude cirrus ice concentrations. The agreement within a factor of 2 between ice concentrations measured with independent techniques (replicators and optical imaging probes) provides confidence in the accuracy of the in situ measurements. We use a computationally efficient modeling approach that incorporates the key cirrus physical processes, such that thousands of cloud cases can be simulated and the model results can be statistically compared with observations. One-dimensional simulations with detailed treatments of cloud microphysical processes are driven by temperatures and vertical winds extracted from meteorological analyses. Small-scale temperature and vertical wind perturbations associated with mesoscale waves are superimposed on the analysis fields. We find that in simulations with only homogeneous freezing nucleation, ice concentration statistics are very sensitive to the specified mesoscale wave vertical wind perturbations. With the frequency distribution of vertical winds adjusted to agree with aircraft observations, we obtain good agreement between the simulated and observed ice concentration frequency distributions. Both the observations and simulations indicate that relatively high ice concentrations (≥1000 L−1) occur rarely in these clouds (less than 1% of the time). Simulations including both homogeneous and heterogeneous nucleation indicate that even with moderate concentrations of ice nuclei (20 L−1), heterogeneous nucleation is an important ice production process, particularly for relatively low ice concentrations and warm temperatures. With enhanced ice nuclei concentrations (100 L−1), heterogeneous nucleation dominates ice production in the model. We find that it is critically important to include the impact of sedimentation on the evolution of ice concentrations when comparing model results with observations. Ice crystal collection efficiencies are poorly constrained at low temperatures, and we find that aggregation can significantly reduce ice concentrations. Sensitivity tests indicate that neither the agreement between observed and simulated ice crystal statistics nor the sensitivities indicated by the simulations are significantly affected by model assumptions such as the time periods simulated, geographic domain covered, trajectory paths calculated, or ice crystal habit assumed.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Cirrus clouds are an important component in the Earth's climate system. Because of their location in the cold upper troposphere, cirrus can significantly reduce the outgoing longwave radiation. They also reflect incoming solar radiation, but on balance, they typically exert a direct radiative warming influence on the climate system [Ackerman et al., 1988]. Deposition growth and sedimentation of cirrus ice crystals regulate upper tropospheric humidity, which is in turn important for the radiation budget. The climate sensitivity (surface temperature response to increasing CO2) predicted by global models is strongly sensitive to the representations of cirrus microphysical properties [Sanderson et al., 2008; Mitchell et al., 2008].
 In this study, we focus on midlatitude synoptic cirrus ice concentrations. Development of physically based cirrus parameterizations for use in climate models requires an understanding of how environmental conditions and physical processes control the evolution of cirrus microphysical properties. We focus here on understanding the processes controlling cirrus ice concentration, which is a key physical property of cirrus clouds. Additionally, recently developed cirrus parameterizations include ice concentration as a prognostic variable.
 Given limited availability of vapor for ice growth, ice concentration will affect the size to which ice crystals grow and hence their fallspeeds. For a given ice mass, cirrus extinction increases with ice concentration. The ice concentration in the initial stage of cirrus formation is controlled by nucleation processes. Modeling studies have shown that ice number concentration produced by homogeneous freezing of aqueous aerosols is primarily controlled by cooling rate and temperature [Jensen and Toon, 1994; Kärcher and Lohmann, 2002], and therefore, temperature variability driven by mesoscale gravity waves can be very important for cirrus microphysical properties [Haag et al., 2003; Kärcher and Ström, 2003; Hoyle et al., 2005; Comstock et al., 2008]. The relative importance of heterogeneous and homogeneous nucleation processes depends on the concentration of heterogeneous ice nuclei (IN) and the cooling rates driving cirrus formation [DeMott et al., 1997; Kärcher et al., 2006]. As cirrus evolve after the initial nucleation of ice crystals, various processes (e.g., aggregation, entrainment dilution, and differential sedimentation) generally decrease ice concentration. The evolution of ice crystal size distributions can also depend on the interplay between dynamical and microphysical properties. Radiatively driven, small-scale convective motions can generate patches of supersaturation within cirrus, promoting fresh nucleation of ice crystals and/or depositional growth. Under some conditions, small-scale variability in humidity and temperature fields can lead to patches in the cloud with relatively low ice concentrations and large crystals. These large crystals can sediment into the lower parts of the cloud, depleting vapor and potentially quenching subsequent nucleation [Spichtinger and Gierens, 2009].
 Developing an understanding of the processes that control cirrus ice concentration is not possible without accurate measurements of ice concentration. Until recently, airborne in situ measurements of cirrus microphysical properties have generally been unreliable (particularly for small (<50 μm) ice crystals) because of the potential presence of shattering artifacts and poor time response of older imaging probes [e.g., Field et al., 2003; McFarquhar et al., 2007; Jensen et al., 2009; Korolev et al., 2011]. The recent Department of Energy (DOE) SPARTICUS (Small Particles In Cirrus) and NASA MACPEX (Midlatitude Cirrus Properties Experiment) airborne campaigns were focused on providing extensive data sets of cirrus microphysical properties with new instrumentation designed to address the problem of shattering artifacts. In addition to the physical design of the cloud probes to limit shattering artifacts, postprocessing techniques using particle interarrival times are used to identify and remove clusters of particles resulting from shattering events.
 The approach typically taken to compare cirrus simulations with observations is to focus on a particular cloud system [e.g., Fridlind et al., 2004; Jensen et al., 2005; Comstock et al., 2008]. While this case study approach has merit, it can be problematic because of the challenge of adequately specifying the initial environmental conditions and the forcing that drives cloud formation at sufficiently small spatial and temporal scales. The problem is particularly acute for cirrus clouds because upper tropospheric relative humidity is poorly represented in meteorological analyses, and because mesoscale waves (unresolved in the analyses) are very important for cirrus formation processes. When comparing observed and simulated cirrus properties, it can be difficult to distinguish problems with the initial conditions and forcing from problems with the representation of cloud microphysical processes.
 Here we use numerical simulations to evaluate the physical processes controlling the evolution of cirrus ice concentrations. Rather than use the case study approach, we present statistical comparisons between simulated and measured ice concentrations. The model is designed to include key physical processes, while being efficient enough to simulate thousands of cirrus systems, providing a statistically significant set of cirrus properties. We include a parameterization for mesoscale wave perturbations of temperature and vertical wind, and we evaluate the relative importance of heterogeneous and homogeneous ice nucleation. Section 2 describes the measurements used from the SPARTICUS and MACPEX campaigns. Section 3 describes the modeling approach. In section 4, we present the comparisons between observed and simulated ice concentrations, and we evaluate the relative importance of different processes using model sensitivity tests. In section 5, we evaluate the robustness of our results in the context of sensitivities to a number of key model assumptions. Lastly, in section 6, we summarize and discuss the implications of the results.
2 SPARTICUS and MACPEX Observations
 The SPARTICUS campaign was designed to provide a relatively long-term data set of midlatitude cirrus properties, with an emphasis on coordination of the aircraft measurements with ground-based (the DOE Southern Great Plains (SGP) site in northern Oklahoma) and satellite (primarily CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO)) remote-sensing observations. Learjet flights were conducted from January to June 2010, out of Rocky Mountain Metropolitan Airport. The operations area covered the central U.S., with most flights either flown over the SGP site or coordinated with CloudSat/CALIPSO over passes (Figure 1). A total of 200 flight hours (190 research flight hours and 10 test flight hours) were flown. Over 27 h of cirrus measurements were collected.
 The Learjet payload included a number of cloud microphysics probes, as well as measurements of state parameters and water vapor concentration. Here we focus on measurements made with the 2-Dimensional Stereo (2-D-S) probe. The 2-D-S probe is an optical array imaging probe with a pixel size of 10 μm [Lawson et al., 2006]. In addition to probe tips designed to reject shattering artifacts, particle interarrival times are used to identify and remove clusters of particles resulting from shattering [Baker et al., 2009].
 The MACPEX mission was an intensive, month-long (March–April 2011) campaign focused on measurements of midlatitude cirrus and stratospheric humidity. Fourteen science flights with the NASA WB-57 were conducted out of Ellington Airfield, Texas. The operations included active targeting of cirrus using near real-time satellite imagery and communication with the pilots. Ten flights targeted synoptic cirrus and three targeted anvil cirrus, resulting in a total of about 18.5 h of cirrus sampling. Most of the clouds sampled were over the south-central U.S. (Figure 1).
 The WB-57 payload included an extensive set of microphysics instruments measuring ice crystal size distributions, ice crystal habits, and bulk ice water content. In addition, several hygrometers were flown, as well as instruments to measure aerosol size distribution and meteorological conditions. We again primarily use the 2-D-S probe for measurements of ice concentrations, but we also compare the 2-D-S measurements with those from the Video Ice Particle Sampler (VIPS). The VIPS is an electro-optical instrument used to collect and image a continuous sample of cloud particles with sizes as small as 10 μm [Schmitt and Heymsfield, 2009]. Particles are collected continuously on a looped clear plastic belt coated with silicone oil. The portion of the belt exposed to the atmosphere is imaged by a high-resolution video microscope. The raw video is broken down into individual frames which are then analyzed with the help of an interactive computer program. The VIPS was optimized to measure particle size distributions between 10 and 200 μm. In addition to these cloud measurements, we use temperature, pressure, and vertical wind measurements from the Meteorological Measurement System (MMS) [Scott et al., 1990].
 The cirrus clouds observed during MACPEX and SPARTICUS in the central and south central U.S. had two basic generating mechanisms, namely uplift of moist air by wave motions on a variety of scales and deep convective outflow. Wave motions varied from the near-planetary scale uplift of air from the tropics to the predominant cirrus altitudes of 200–300 hPa, to synoptic-scale midlatitude cyclones, to gravity waves. Most of the cirrus observed during both SPARTICUS and MACPEX was wave-related. Moreover, the cirrus that was convective, especially during SPARTICUS, also involved some upper level wave activity that allowed the cirrus to be maintained.
 The dominant cirrus generation mechanisms during SPARTICUS and MACPEX were jet stream cirrus due to upward flow from low latitudes (11 flights during all phases of SPARTICUS and five flights during MACPEX), midlatitude cyclone development, both involving the full depth of the atmosphere (12 flights during January–April of SPARTICUS and two flights during MACPEX), and those involving upper level waves only (six flights during all phases of SPARTICUS and two flights during MACPEX). The distribution of cirrus types observed was quite similar during the two experiments.
2.1 2-D-S/VIPS Comparison
 For the comparison between the MACPEX VIPS and 2-D-S measurements, we use the following criteria to select relatively uniform, statistically significant cloud samples: (1) continuous cloud sample of at least 45 s, (2) 2-D-S concentration larger than 15 μm to remain within 0.4 and 2.5 times the mean concentration over the averaging period (see discussion below about the first 2-D-S size bin (5–15μm)), (3) VIPS concentration to remain within 0.4 and 2.5 times the mean concentration over the averaging period, and (4) VIPS measurements not overwhelmed by large ice loading during the averaging period. The last criterion excludes anvil cirrus cases with large ice water contents. We identified 74 45 s time periods meeting these criteria. The majority of these cases (58) were from the flight of 23 April, during which relatively continuous clouds were sampled at 36 and 38 kft over the Texas/Oklahoma border.
 Figure 2 shows examples of the 2-D-S/VIPS size distribution comparisons. In general, the agreement is very good, both in terms of the ice crystal sizing and the concentrations. The two comparisons in the bottom row of Figure 2 are representative of the comparisons for which ice concentrations were larger than 20 L−1(including most of the cases on 23 April). The top row of Figure 2 shows examples of less frequent cases when the ice concentration is low, and VIPS indicates considerably more small (<100 μm) crystals than does 2-D-S. These cases occurred in the lower parts of cirrus clouds where a predominance of large crystals (sedimenting from above) is expected. In these cases, large particles could have been clipped due to the small field of view of each VIPS image. Also, differences in particle opacity could have led to large particles being split into smaller particles by the VIPS analysis software.
 In nearly all of the 2-D-S size distributions, the concentration in the first size bin (5–15 μm) is considerably larger than the concentrations in the next few larger bins, and the first bin often contributes significantly to the overall ice concentration. Without continuous nucleation of new crystals, it is difficult to understand how ice crystals smaller than 15 μm could persist in all parts of the clouds. Under even moderately supersaturated/subsaturated conditions, either deposition of vapor will rapidly grow the crystals to larger sizes, or sublimation will rapidly eliminate the small crystals. For example, at 200 hPa and 220 K with an ice saturation ratio of 1.2, a 15 μm crystal will double its size in about 10 min. Complete sublimation at a saturation ratio of 0.8 will occur even faster. The 2-D-S depth of field is proportional to the square of the particle radius, resulting in a significant concentration boost in the first size bin compared to larger bins. The uncertainty in the depth of field is largest for the smallest bins. In light of these facts, we have chosen to omit the first size bin in our calculations of ice concentration from the 2-D-S measurements.
 The comparison between 2-D-S and VIPS ice concentrations (in the VIPS size range) from the averaging periods described above is shown in Figure 3. Most of the comparisons having 2-D-S concentrations greater than 20 L−1falling within a factor of 2 and little indication of a systematic bias between the two instruments. As discussed above, when the 2-D-S concentration is relatively small, the VIPS concentration is often considerably higher than the 2-D-S concentration. The comparisons are particularly good for the 23 April flight. The concentration and size of the particles were ideal for the way the VIPS was set up on that day. Also, the collection belt had recently been replaced leading to fewer artifacts. Estimation of the uncertainties in concentrations and size distributions measured by these types of instruments (optical array imaging probes and replicators) is challenging, involving issues such as sample volume determination and corrections for out-of-focus images. However, the relatively good agreement between these independent measurements provides some confidence in the accuracy of the measured ice concentrations.
2.2 Ice Concentration Statistics
 Here we present the statistics of ice concentration indicated by the SPARTICUS and MACPEX 2-D-S measurements. We restrict our analysis to synoptic cirrus (i.e., clouds that were not directly associated with deep convection) since we are not simulating deep convection with our model. Figure 4 shows frequency distributions of ice concentrations in synoptic cirrus from the two campaigns in different temperature ranges. A significant temperature dependence is expected both because ice concentration produced by homogeneous freezing increases with decreasing temperature, and because higher temperatures will more often correspond to lower parts of deep cirrus clouds. The expected variation with temperature is apparent in the measured ice concentrations, with higher ice concentrations occurring more frequently in colder clouds. Note that ice concentrations exceeding 1000 L−1occur infrequently (about 1% of the time in SPARTICUS and less than 0.1% of the time in MACPEX). Note that this result contrasts sharply with previously reported frequency distributions of midlatitude cirrus ice concentration. Kärcher and Ström  reported counterflow virtual impactor measurements of cirrus ice concentration, and Hoyle et al.  reported measurements from a variety of older cloud probes. Both of these studies indicated commonplace occurrence of ice concentrations greater than 1000 L−1. However, it has been shown that ice concentration measurements made with the older airborne cloud probes may be exaggerated by shattering artifacts [e.g., McFarquhar et al., 2007; Jensen et al., 2009].
 There are noticeable differences between the SPARTICUS and MACPEX ice concentration statistics. The SPARTICUS measurements indicate higher occurrence frequency of concentrations exceeding 1000 L−1than MACPEX. These high ice concentrations are mostly from a single cirrus case sampled on the SPARTICUS flight on 29 April. The large ice supersaturation and numerous small crystals in this cloud suggest a recent homogeneous freezing event (J. Comstock, personal communication). The ice concentration temperature dependence is weaker in SPARTICUS than in MACPEX, particularly for temperatures warmer than 235 K. These differences could be a result of the necessarily limited sampling provided by aircraft campaigns. Alternatively, the differences could result from the different time periods covered by the campaigns. However, the general similarity of the ice concentration frequency distributions from the two campaigns provides some assurance that the data sets generated by the aircraft measurements give a statistically representative sampling of cirrus microphysical properties in the region.
3 Modeling Approach
 Our approach here is to simulate the important cloud processes using a framework that is efficient enough to permit a large number of simulations and provide a statistically significant data set of cirrus properties for comparison with the observations. For this purpose, we use the “temperature-curtain” modeling approach [Jensen and Pfister, 2004]. Essentially, temperature and vertical wind time-height curtains are constructed by extracting temperature and vertical wind profiles versus time along trajectories using meteorological analyses. Wave-driven temperature and vertical wind perturbations are superimposed on these temperature curtains, which are in turn used to drive one-dimensional cloud simulations. The parameterization was originally developed for the tropical tropopause region, and we have modified parameters such as the tropopause pressure for application to the midlatitude upper troposphere. As discussed below, the wave amplitudes are tuned to approximate the distribution of vertical wind speeds measured during MACPEX. A temperature curtain example is shown in Figure 5. For comparison with the SPARTICUS and MACPEX data sets, we have generated 4880 temperature curtains using trajectories ending every 2.5° latitude and 2.5° longitude within the domain of 26–46°N and 87–112°W, and every 2 days within the time range March through April 2010. We must select a particular vertical level from which we start the back trajectories (in the results shown below, we use 323 K, which corresponds to an altitude of about 8–9.5 km), and the path taken by the trajectory will of course depend on the choice of this altitude. The sensitivity of the results to the initial trajectory altitude is addressed in section 5.
 For simulating cirrus cloud processes, we use the Community Aerosol and Radiation Model for Atmospheres (CARMA) [Toon et al., 1988; Jensen et al., 1998; Bardeen et al., 2008]. For this application, CARMA is configured such that sulfate aerosols are tracked in 60 size bins with radii ranging from 0.01 to 7.5 μm and a mass ratio between successive bins of 1.4. Ice crystals are tracked in 60 size bins with radii ranging from 0.01 to 4.7 mm and a mass ratio between successive bins of 1.8. We assume hexagonal column ice crystal habits with an aspect ratio of three. We specify the density of the ice crystals versus size following Heymsfield et al. . The vertical domain goes from the surface to 15 km, with a grid spacing of 100 m.
 Cloud processes treated include ice nucleation via homogeneous freezing of sulfate aerosols [Koop et al., 2000], heterogeneous ice nucleation on insoluble particles, deposition growth, sublimation, sedimentation, and aggregation. Heterogeneous nuclei are assumed to be active at an ice saturation ratio of 1.3. This is a somewhat arbitrary (but typical) threshold for activation of reasonably effective ice nuclei. In reality, heterogeneous nuclei would promote ice nucleation over a range of supersaturations, possibly resulting in limitation of the number of ice crystals produced because of competition between different ice nuclei. We use a coalescence efficiency of 0.1 for ice-ice collisions [Mitchell, 1988; Wang and Chang, 1993]; however, we note that ice coalescence efficiencies at low temperatures are essentially unconstrained and may be an important source of uncertainty in the simulations. The initial aerosol population is assumed to be log normally distributed with a concentration of 100 cm−3, a mode radius of 0.04 μm, and a sigma of 2.3. The choice of aerosol size distribution has only a secondary impact on calculations of ice concentrations produced by homogeneous freezing of aqueous aerosols [e.g., Jensen and Toon, 1994; Kärcher and Lohmann, 2002]. Temperature and vertical wind in the model at each time step are taken from the temperature/vertical wind curtains described above. Soundings and aircraft observations indicate that temperature variability driven by gravity waves is essentially ubiquitous in the upper troposphere. We use the parameterization described by Jensen and Pfister  to superimpose temperature and vertical wind perturbations driven by mesoscale waves. We have adjusted the wave parameters to provide approximate agreement between the model vertical wind speed frequency distribution and the MACPEX MMS observations (see section 3.1). The analysis water vapor field is used to specify the initial vertical profile of water vapor concentration in our simulations. This is a significant source of uncertainty for individual simulations; however, as discussed above, our intent here is to simulate the statistics of ice concentration in midlatitude cirrus. The sensitivity of the results to the initial humidity profiles is addressed in section 5.
 An example of the evolution of a cloud simulated with this approach is shown in Figure 6. Rapid cooling drives an increase in supersaturation, and homogeneous freezing nucleation produces ice concentrations exceeding 1000 L−1at about 10.6 km. Growth of these ice crystals rapidly depletes vapor in excess of ice saturation. As the larger crystals grow and sediment, a deep layer develops with considerably lower ice concentrations than those produced by the nucleation event. The high ice concentrations in the initial cloud layer decrease to less than 100 L−1over a few hours due to vertical mixing and differential sedimentation. It is clear from this example that simply comparing the ice concentrations at the point of nucleation to aircraft measurements made throughout the cloud would be misleading.
 This modeling framework omits physical processes that may be important for the evolution of ice concentrations in cirrus. First, the temperature-curtain approach is only strictly valid in the absence of vertical shear in the horizontal wind. Although wind shear will affect the column-integrated properties of cirrus, the omission of shear effects will not necessarily have a large impact on the vertical distribution of ice concentration statistics.
 A potentially more important limitation of our approach is the lack of feedbacks between cloud radiative heating, dynamics, and microphysics. Simulating these feedbacks would require a full cloud-resolving model approach. As discussed above, small-scale convection can result in variability in ice nucleation rates, entrainment of dry air, and potential quenching of ice nucleation in lower parts of the clouds. These effects should generally broaden ice concentration frequency distributions. It is worth noting, however, that radiative heating rates in midlatitude synoptic cirrus are generally quite small. Mace and Benson  showed that for cirrus with optical depths less than five, net radiative heating rates were no more than about 0.2 K d−1. Even for cirrus with optical depths greater than 10, the heating rates peaked at about 0.5 K d−1. The effects of this heating on cirrus evolution are competing with the continuous synoptic-scale and mesoscale temperature variability. Even synoptic-scale lifting of a few cm s−1 will give cooling rates on the order of 20 K d−1. Most of the cirrus cloud systems observed during SPARTICUS and MACPEX were optically thin, patchy clouds with relatively short lifetimes. In such clouds, the radiative-dynamics feedbacks are likely to have a second-order effect on the cloud evolution. These feedbacks are likely more important for thick, persistent cirrostratus.
 Although it is difficult to quantitatively evaluate the impact of processes not simulated with our approach on ice concentrations, we proceed here based on an assumption that the our approach includes the essential physical processes needed to explain the statistical distribution of ice concentration. The good agreement between observed and simulated ice concentrations (shown below) provides some support for this assumption.
3.1 Upper Tropospheric Vertical Wind Spectra
 The impact of wave-driven vertical motions on ice nucleation depends on the wave amplitudes. Since high-frequency waves generally have the largest amplitudes, they play a particularly important role. The MACPEX WB-57 payload included the Meteorological Measurement System (MMS) that measures temperature, pressure, and winds [Scott et al., 1990]. MMS calculates vertical winds by combining measurements of the aircraft motion and the air flow with respect to the aircraft. Integrating the vertical accelerometer measurement results in errors that are large compared to the vertical wind signal at low frequencies. As a result, we remove the vertical wind mean and overall trend for any given flight. In addition, we use a Fourier filter to remove all periods longer than 5 min (about 60 km wavelength). Performing these procedures gives us a precision of about 5 cm s−1.
 Frequency distributions of vertical wind speed from the MACPEX flights are shown in Figure 7, including both the campaign average distribution and distributions from individual flights. The vertical wind speed amplitudes varied greatly from flight to flight. The campaign-mean MACPEX vertical wind speed frequency distribution is not dissimilar from the distribution from the Interhemispheric Differences in Cirrus Properties due to Anthropogenic Emissions (INCA) midlatitude upper troposphere airborne campaign [Gayet et al., 2004]. Also shown in Figure 7 is the vertical wind speed frequency distribution produced by the combination of the synoptic-scale waves resolved in the MERRA analyses and our wave parameterization. The wave parameterization produces a vertical wind speed frequency distribution that is in reasonable agreement with the MACPEX observations up to about 1.7 m s−1, but the tail of the measured frequency distribution at higher vertical wind speeds that is present on some of the flights is not captured by the model. Homogeneous freezing driven by such large vertical winds could produce ice concentrations exceeding 10,000 L−1, which were not measured in the field experiment. This could simply mean that such high ice concentrations occur very rarely and do not persist.
 We begin by comparing the measured ice concentration statistics with those from the simulations with homogeneous freezing only. Figure 8 shows ice concentration frequency distributions separated into different temperature ranges. This set of simulations includes sedimentation and aggregation. The ice concentration frequency distributions are normalized within each temperature range. If we do not include subgrid-scale waves, then the simulated ice concentrations (red curves in Figure 8) are much lower than indicated by the observations. The synoptic-scale cooling rates resolved in the MERRA analyses simply do not drive homogeneous freezing nucleation events that produce sufficiently high ice concentrations. If we include the subgrid-scale vertical wind and temperature perturbations, then the simulated (green curves in Figure 8) and observed ice concentrations are in good agreement at temperatures below 225 K. The simulations do not produce the “hump” in the frequency distribution indicated by the MACPEX observations in the coldest temperature range; however, this feature is not present in the SPARTICUS ice concentration frequency distribution. In agreement with the measurements, the simulations indicate the occurrence of relatively high ice concentrations (>1000 L−1) occurs only rarely. In the warmest temperature range (225–235 K), the model underestimates ice concentrations somewhat. The cause of this discrepancy is unclear.
 Next, we present results from simulations including heterogeneous nucleation. IN measurements in the midlatitude upper troposphere typically indicate concentrations on the order of 5–20 L−1[DeMott et al., 2003a]. In anomalous conditions, IN concentrations can exceed 100 L−1 [DeMott et al., 2003b]. The MACPEX time period was characterized by heavy biomass-burning over the southwest United States, potentially producing unusually high IN concentrations. We present results from simulations with 20 and 100 L−1 IN. With NIN=20 L−1(Figure 9), heterogeneous nucleation only contributes significantly to the ice concentration in the warmest temperature range (225–235 K) or at the lowest ice concentrations. However, it is worth noting that ice concentrations lower than 20 L−1occur about 35% the time in the cirrus sampled during MACPEX. Heterogeneous ice nucleation will more effectively compete with homogeneous freezing as temperature increases because ice concentrations produced by homogeneous freezing decrease as temperature increases. Also, the warmest temperature range may typically represent the lower part of deep cirrus clouds. In the upper parts of cirrus, ice crystals will first be nucleated by heterogeneous processes (at relatively low supersaturations), followed by homogeneous freezing ice nucleation if the supersaturation continues to increase. Therefore, the crystals that grow largest will typically be those that were generated first by heterogeneous nucleation, and these larger crystals will sediment to the lower parts of the cloud.
 With higher concentrations of IN (NIN=100 L−1, Figure 10), ice crystals nucleated heterogeneously contribute significantly as a source of ice concentrations less than 100 L−1at temperatures colder than 225 K, and the IN dominate for all ice concentrations at temperatures warmer than 225 K. However, heterogeneous nucleation still does not completely prevent the occurrence of high ice concentrations at colder temperatures. In other words, even with 100 L−1 IN, there are still rapid cooling events that can drive the supersaturation high enough for homogeneous freezing to occur in some cases. The homogeneous freezing events are all driven by the subgrid-scale waves; with only the synoptic forcing from the MERRA analysis, homogeneous freezing never occurs in the simulations with 100 L−1 IN. Again, these high ice concentration events occur infrequently and do not persist for long periods of time. Heterogeneous nucleation generally produces lower ice concentrations than homogeneous freezing. As a result, inclusion of 100 L−1IN degrades the agreement with observed ice concentration frequency distributions compared to the set of simulations with homogeneous freezing only. The results presented here suggesting that heterogeneous nucleation can be an important mode of ice production in upper tropospheric cirrus under some conditions are consistent with recent analyses the composition of residual particles from sublimated ice crystals (Cziczo et al., personal communication).
 The fraction of ice crystals produced by heterogeneous nucleation is shown in Figure 11. With 100 L−1IN, heterogeneous ice nucleation is a dominant pathway for production of ice crystals. Heterogeneous nucleation still contributes significantly to the occurrence of ice concentrations in the 10–20 L−1 range when the IN concentration is reduced to 20 L−1. The fraction of ice crystals produced by heterogeneous nucleation decreases for ice concentrations less than 10–20−1. This result is perhaps surprising given that homogeneous freezing generally produces larger ice concentrations than heterogeneous nucleation. However, the lowest ice concentrations generally occur at the lower edges of cirrus clouds where a small number of large ice crystals have sedimented. These regions may be dominated by larger crystals produced by heterogeneous nucleation earlier (i.e., at lower supersaturation) than ice crystals produced by homogeneous nucleation.
 Previous studies have shown that differential sedimentation has a significant impact on the evolution of ice concentrations in cirrus clouds [Barahona and Nenes, 2011; Jensen et al., 2012], and the example of the evolution of a simulated cirrus shown in Figure 6 suggests that sedimentation produces regions with relatively low ice concentrations as the cloud ages. To evaluate the impact of sedimentation in our simulations, we have run a set of simulations with ice crystal fallspeeds set to zero (Figure 12). Omitting sedimentation allows layers with high ice concentrations to persist, resulting in more frequent occurrences of ice concentrations exceeding 1000 L−1. Also, we find (not shown) that much of the ice in the warmest temperature range in our baseline simulation reached the lower part of the clouds as a result of sedimentation from above. Note that earlier studies using parcel models (excluding sedimentation) [Kärcher and Ström, 2003; Hoyle et al., 2005] predicted higher occurrence frequency of ice concentrations exceeding 1000 L−1than the results presented here. We conclude that inclusion of sedimentation is important when comparing simulated clouds with aircraft observations that necessarily include a range of cirrus ages and vertical locations. Also, it is important to include the effects of sedimentation on cirrus ice concentration in global model parameterizations.
 Lastly, we investigate the sensitivity of our results to ice crystal aggregation. As discussed above, the ice-ice collection efficiencies at low temperatures are essentially unknown, and the assumed values we are using may well be overestimates. We note that examination of the ice crystal images from the SPARTICUS campaign indicates commonplace occurrence of ice crystal aggregates in the lower parts of cirrus; therefore, aggregation must be important for production of large ice crystals. To bracket the range of aggregation effects, we present results from simulations with no aggregation in Figure 13. Aggregation necessarily decreases ice concentration, and we get the expected result that shutting off aggregation shifts the frequency distributions of ice concentrations toward higher values in all temperature ranges. Particularly, at the colder temperatures, the simulated occurrence frequency of concentrations greater than 1000 L−1 exceeds the observed frequency.
5 Additional Sensitivities
 Here we discuss the robustness of the results in the context of sensitivities to various model assumptions. The trajectory-curtain approach requires an assumption of an initial vertical level (potential temperature) for the back trajectories. Using a different initial potential temperature will change the path of the trajectory and correspondingly change the temperature and vertical wind time-height curtains. In the results shown above, we used 323 K (about 8–9.5 km) for the initial potential temperature. We have run additional sets of simulations with initial potential temperatures ranging from 315 to 335 K. Surprisingly, it turns out that the ice concentration statistics from these different sets of simulations are virtually indistinguishable. Likewise, using a set of trajectory curtains from March to April 2010 instead of 2011 has little impact on the results. One possible explanation of these results is that the meteorological influence on ice concentrations in cirrus clouds is dominated by the small-scale wave fluctuations that are not resolved in the analyses. In other words, the large-scale meteorological conditions will govern the overall formation of cirrus and perhaps also the bulk properties such as ice water content and extinction, but ice concentration is controlled by small-scale temperature fluctuations. In fact, this hypothesis is consistent with the fact that ice concentrations are generally dominated by subgrid-scale waves (Figure 8), and the fact that without these waves, the simulated ice concentrations are much lower than the observations.
 With a bin microphysics model, an assumption about the ice crystal habit must be made, which will affect the crystal fallspeed and deposition growth rates. We have chosen to represent the ice crystals as hexagonal columns with an aspect ratio of three. Simulations using different aspect ratios (or spherical ice crystals) give results that do not differ appreciably from the results presented above. We have also tried various experiments involving analysis of results from subsets of the model geographical domain and subsets of the model time period. Neither the agreement with observations nor the sensitivities presented are significantly affected. Lastly, we have run sets of simulations with the initial humidity profile increased or decreased by 50%. Again, the results are not significantly affected.
 Perhaps, the greatest uncertainty in the results of this study stems from the potential importance of processes not represented in the temperature-curtain modeling approach. As discussed above, we are not including the effects of wind shear or small-scale convection driven by cloud radiative heating. The latter process will likely broaden the ice crystal concentration frequency distribution; however, quantification of this effect would require a series of cloud-resolving model simulations with a range of environmental conditions—a task that is beyond the scope of this study. The agreement between ice crystal concentration statistics in the observations and the temperature-curtain simulations at least suggests that the model includes the most important processes. Even if wind shear and cloud-scale dynamics have important second-order effects, the dominance of ice nucleation processes (heterogeneous versus homogeneous) and small-scale temperature fluctuations in determination of cirrus ice concentrations may still hold.
6 Summary and Discussion
 In this study, we have used statistical comparisons between simulated and observed midlatitude synoptic cirrus to investigate the impact of cloud physical processes on ice concentrations. Extensive measurements of cirrus with the 2-D-S probe during the SPARTICUS and MACPEX field experiments provide the database of ice concentrations for comparison with the simulations. The 2-D-S measurements agree well with the VIPS probe measurements, both in terms of ice crystal sizing and concentration, in clouds with ice concentrations greater than 20 L−1(Figures 2 and 3). Ice concentration frequency distributions from SPARTICUS and MACPEX agree reasonably well (Figure 4), suggesting that the data sets provide an adequate representation of the climatology of ice cirrus ice concentrations for the regions and time periods sampled. The measurements indicate that concentrations exceeding 1000 L−1 occur rarely (less than 1% of the time).
 For simulation of cirrus formation and evolution, we use one-dimensional simulations with bin microphysics driven by temperatures and vertical winds extracted from meteorological analyses along trajectories. Mesoscale temperature and vertical wind perturbations that are not resolved in the analyses are superimposed on the fields used in the simulations, with the subgrid-scale wave parameterization tuned to agree with aircraft observations of vertical wind speed variability. Thousands of simulations are run in the geographical domain and time period of the field experiments to generate a statistically significant database of ice concentrations. With the baseline assumption that homogeneous freezing of aqueous aerosols is the dominant ice nucleation mechanism, the simulated and observed frequency distributions of ice concentration agree well, particularly for temperatures colder than ≃235 K (Figure 8).
 A key finding of this study is that mesoscale waves (unresolved in the meteorological analyses) play a dominant role in determining the ice concentration statistics. This result is perhaps expected given the strong sensitivity of ice concentration produced by homogeneous freezing to cooling rate. However, it turns out that the pathways of trajectories (and hence the synoptic-scale temperature and vertical wind evolution) have little impact on the frequency distributions of ice concentration. We note that the synoptic-scale forcing may well dominate bulk cloud properties such as ice water content and ice water path.
 Simulations including heterogeneous ice nuclei indicate that even with typical, relatively low upper tropospheric IN concentrations (≃20 L−1), heterogeneous nucleation competes effectively with homogeneous freezing, particularly for low ice concentrations (which occur frequently in both the observed and simulated cirrus) and at relatively warm temperatures (Figure 9). With enhanced IN concentrations (100 L−1), heterogeneous becomes the dominant pathway for production of ice crystals in general (Figures 10 and 11). Homogeneous freezing still occurs in rare cases at low temperatures, but overall, most of the ice crystals are produced by heterogeneous freezing.
 We have run a number of sensitivity tests to evaluate the robustness of the results given various model assumptions and uncertainties (e.g., time periods simulated, geographic domains simulated, ice crystal habit, trajectory paths, and initial relative humidity profiles). We find that neither the agreement between observed and simulated ice crystal statistics nor the sensitivities to physical processes indicated by the simulations are significantly affected by these model assumptions.
 Over the past several years, several parameterizations for ice nucleation have been developed for use in global models. These parameterizations treat homogeneous freezing [Kärcher and Lohmann, 2002; Barahona and Nenes, 2008] or both homogeneous freezing and heterogeneous ice nucleation [Kärcher et al., 2006; Barahona and Nenes, 2009; Liu and Penner, 2005]. In all of these parameterizations, vertical wind speed is a key parameter controlling the ice concentration produced by homogeneous freezing as well as the competition between heterogeneous and homogeneous ice nucleation. Of course, the global models do not resolve cloud-scale vertical motions, and therefore, some assumption must be made about the magnitude of subgrid vertical wind speeds that get passed to the parameterizations. One approach is to estimate the vertical wind speed using a turbulent kinetic energy (TKE) parameterization [Park and Bretherton, 2009]. However, the TKE is generally not very large in the upper troposphere, and the vertical wind speeds generated with this approach (5–10 cm s−1) are smaller than those generated by mesoscale waves in cirrus (see Figure 7). We recommend use of in situ vertical wind speed measurements to improvement of the representations of subgrid-scale vertical motions in global models.
 This work was supported by the NASA Radiation Science Programs and the DOE Atmospheric System Research Program.