Clouds play a central role in the Earth's energy budget, as they are responsible for large variations in the reflected shortwave and emitted longwave radiation . The response of clouds to changing greenhouse gases and aerosols remains one of the largest uncertainties in understanding past and future climate changes . Significant advances have been made into modeling and observing the role of aerosols in liquid clouds e.g., especially through the use of retrievals of the cloud droplet number concentration e.g., but the impact of aerosols on high clouds remains uncertain . A large part of this uncertainty comes from the difficulty in retrieving cirrus cloud properties at a large enough scale to separate the roles of individual factors controlling the ice crystal number concentration (Ni).

A key microphysical property of ice clouds, the Ni links the aerosol environment to dynamic effects driving cloud updrafts and the generation of supersaturation . Through changes in the ice crystal size, changes in the Ni can have far-reaching implications for a cloud, impacting the radiative , precipitation and cloud lifetime properties . The Ni is often used as a prognostic variable in two-moment cloud microphysics schemes e.g.. This highlights a requirement to understand the controls on the Ni in order to improve our understanding and parameterization of cloud processes. While aircraft measurements of the Ni exist, they are restricted in space and time. They can also be affected by shattering of ice crystals at the instrument inlet and difficulties in measuring the smallest crystals . In this paper, the new DARDAR-Nice satellite dataset described in Part 1 allows the processes that control the Ni to be investigated globally.

It is known that the temperature plays a strong role in determining the ice crystal nucleation rate. The homogeneous nucleation rate is a strong function of temperature and supersaturation , with atmospherically relevant nucleation only taking place at temperatures colder than 235 K. This strong temperature dependence in the nucleation rate does not necessarily correspond to a strong temperature dependence in the Ni . A weak Ni temperature dependence was found by . found similar results, with a slight reduction in the Ni for the coldest measurements. Higher Ni values have been observed at cold temperatures during ATTREX than in , leading to a weak combined temperature dependence. However, using different datasets targeting different cloud types, and both showed an increase in Ni with decreasing temperature, demonstrating that there is still considerable uncertainty regarding the Ni temperature dependence.

The in situ homogeneous nucleation of ice crystals is also dependent on the supersaturation , which is often generated through cooling due to vertical air motion. Large-scale updrafts cannot reproduce observed cirrus properties on their own, the smaller scale variation in updraft provided by gravity waves is necessary and is occasionally able to produce cirrus in regions of large-scale subsidence . These small-scale updrafts can produce Ni values as high as 50 000 L-1 , highlighting the important role that vertical motion can play in determining the Ni.

Although ice can form by in situ nucleation, many ice crystals also form through the freezing of liquid condensate. This liquid-origin cirrus often originates from high updraft regions in mixed-phase clouds, forming thicker cirrus than those composed of in situ ice (; ). Synoptic-scale updrafts can also produce liquid-origin cirrus in the midlatitudes . The Ni formed through these liquid-origin processes is also strongly dependent on the cloud-scale updrafts, with higher updrafts maintaining higher ice supersaturations and producing larger Ni values .

Aerosol also plays a role in determining the Ni, although its impact is complicated by variations in ice crystal nucleation pathways and aerosol properties. While any particle can theoretically act as a homogeneous nucleation center given a high enough supersaturation, in practice these aerosols are often hydrophilic liquid aerosols . Increases in the aerosol number can result in an increase in Ni through increased homogeneous nucleation. However, in many situations, the Ni is limited by dynamical concerns, which limits the impact of aerosols .

A second class of aerosols, known as ice nucleating particles (INP) are able to nucleate ice heterogeneously and can freeze liquid water droplets at temperatures warmer than 235 K. At these warmer temperatures, the presence of INP will often control the Ni near nucleation locations , as they form the sites for creating an ice crystal, although the nucleating ability of these INP is also a strong function of temperature . As heterogeneous nucleation can take place at a lower supersaturation than homogeneous nucleation, the introduction of INP has the ability to prevent homogeneous nucleation by depressing the supersaturation. As the Ni produced through homogeneous nucleation events is typically higher than the INP concentration (and so the Ni from heterogeneous nucleation), this implies that the introduction of INP into a clean atmosphere can reduce the Ni . In situ and satellite studies have provided some evidence for a possible decrease in Ni with increasing aerosol based on regional and hemispheric differences in ice crystal properties, although it has proved difficult to conclusively link these Ni changes to a change in INP.

The relative role of heterogeneous and homogeneous nucleation in the atmosphere is unclear, making it difficult to develop observational constraints on the impact of aerosols on the Ni e.g.. In addition, changing conditions over the life cycle of a cloud can result in a switch between nucleation mechanisms ; nucleation is also not the only control on the Ni. The rarity of INP suggests that other processes, such as ice multiplication, are required to explain the Ni observed in the lower atmosphere .

These four factors (temperature, supersaturation/updraft, ice origin and aerosol environment) are all thought to influence the Ni in high clouds, but significant uncertainties remain in assessing the role of these factors on the Ni. First, although they have been investigated using aircraft and balloon measurements , the ice origin and in-cloud updraft are difficult to determine from observations at a global scale and over a significant period of time. A recent classification has shown some skill at determining these quantities when compared to a convection permitting model and is used in this work to account for this issue.

Second, the Ni is a difficult property to measure at a global scale. Aircraft measurements are limited in space and time and have been afflicted by shattering of crystals on the tips of measurement probes, casting doubt on some earlier measurements of the Ni . Additionally, due to the highly variable nature of cirrus clouds and their strong sensitivity to environmental conditions, it can be difficult to separate the relative roles of aerosol and dynamics .

The retrieval presented in Part 1 of this work has demonstrated that the Ni can be retrieved using a combined radar–lidar retrieval, and that this compares well to new in situ aircraft measurements where shattering is accounted for. Combined with simultaneous retrievals of the ice water content, this allows the global distribution of the Ni and the factors that control it to be investigated. Using reanalysis aerosol concentrations and a proxy for the INP concentration, the impact of aerosols on high clouds is also investigated, highlighting avenues for future research into cirrus cloud processes.

The Ni dataset used in this work (DARDAR-Nice) has been described in detail in Part 1 of this work , so only the main features are outlined here. The DARDAR-Nice product is based on the DARDAR retrieval , a combined raDAR–liDAR retrieval of ice cloud water content (IWC) and ice crystal effective radius using data from the CloudSat and CALIPSO satellites at approximately 13:30 LST (local solar time). Only daytime data from the period from 2006 to 2013 is used in this work due to constraints in the reanalysis data availability. The properties are retrieved at a horizontal resolution of 1.7 km and a vertical resolution of 60 m. Both the DARDAR IWC and the DARDAR-Nice Ni retrieval compare favorably to in situ aircraft data . The best agreement is at temperatures below -30 ∘C, where the retrievals are more accurate due to the dominance of unimodal ice crystal size distributions and reduced ambiguity in the cloud phase.

To investigate the controls on ice crystal nucleation, a more in-depth study is performed of the Ni near the cloud top (Ni(top)). As the cloud top is the location of the coldest temperature in the cloud, it has the highest theoretical nucleation rates. Although the cloud top is close to the nucleation region in wave clouds e.g., this is not always the case and the Ni(top) can be rapidly reduced by differential sedimentation and entrainment e.g.. However, as the coldest temperature, it provides a limitation on the maximum nucleated Ni within the cloud, restricting the impact of temperature variability due to the vertical extent of the cloud. The cloud top is taken to be the top 120 m of the cloud and only the uppermost cloud layer (in multilayer situations) is used to avoid issues with ice being seeded by ice crystals falling from overlying layers. The data are also restricted to locations where the retrieval has gone through at least two iterations, limiting the impact of prior assumptions about the cloud structure.

Four main controls on the Ni(top) are considered in this work: temperature, cloud-scale updraft, ice origin and aerosol. Temperature data in this study are taken from the ECMWF ERA-Interim reanalysis . Information about the cloud-scale updraughts and the ice-origin (liquid/ice) cannot yet be directly obtained at a global scale using satellites. To provide an indication of these cloud properties, the IC-CIR classification from is used. This classification is based on the assumed cirrus source (orographic, frontal, convective or synoptic) and determined at 13:30 LST using cloud retrievals from the MODIS instrument and reanalysis data. This classification selects orographic clouds by assuming the product of the topographic variation and the wind speed is related to the in-cloud updraft, similar to global climate model parameterizations e.g.. The Oro 2 and Oro 1 regimes are the regimes with the respective highest and second highest sextiles of the parameterized in-cloud updraft. Frontal and convective regimes are selected as connected regions of high level cloud that intersect with reanalysis fronts and regions of large-scale updraft, respectively. Finally, the synoptic regime is taken as a residual, with clouds being considered synoptic if they do not fit any of the other classes. Through comparisons with convection permitting model data and classifications based on reanalysis data, this classification has been shown to provide useful information on the cloud scale updrafts and the ice origin. While not a direct retrieval of these properties, it does allow some inferences to be made regarding the response of the Ni to these factors. The results in this paper are restricted to daytime data, which in turn restricts it to 13:30 LST due to the orbit of the satellites used to construct the DARDAR-Nice dataset.

To investigate a possible aerosol link to Ni, we use the “monitoring atmospheric composition and climate” (MACC) aerosol reanalysis product , which assimilates MODIS aerosol optical depth (AOD) retrievals into the ECMWF integrated forecast system. The MACC product provides altitude information for aerosols along with speciation information. Although the MACC speciation has not yet been validated, the MODIS cloud droplet number concentration shows a stronger sensitivity to hydrophilic aerosol types than hydrophobic aerosols, suggesting that the MACC speciation conveys useful information about the aerosol type . Further from sources, where ageing and other assumptions come into play, the speciation may be less accurate. In the upper troposphere, liquid aerosol is thought to be the dominant aerosol component , although recent studies have noted that glassy organic aerosols are abundant in the upper atmosphere and can act as INP at temperatures below -55 ∘C . This work takes the MACC total mass concentration as a measure of the liquid aerosol concentration – high (low) aerosol is more (less) than 6 µg m-3, with the caveat that this measure of aerosol may shift towards a measure of INP at the coldest temperatures considered in this work.

The response of the Ni to aerosol is likely to vary by aerosol type . Although MACC provides a dust speciation, it is not clear whether this can be used to determine the presence of INP. Previous studies have suggested that high altitude aerosol may be responsible for glaciating clouds between 0 and -35 ∘C . Based on this previous work, the glaciation of clouds between 0 and -35 ∘C is used as a proxy for the occurrence of INP.

Cloud phase is determined using the DARDAR phase detection algorithm v1.1.4;. This algorithm uses the different response of lidar backscatter and radar reflectivity to liquid and ice hydrometeors to identify glaciated clouds. Clouds with a peak in lidar backscatter at the cloud top are treated as liquid or mixed phase and those with only a strong radar return are treated as glaciated. Experience suggests that the retrieved phase can be unreliable for clouds less than 600 m thick, so these are excluded from this part of the analysis.

Using this cloud top phase product, a “glaciation index” is developed using the phase retrievals between 0 and -35 ∘C. As approximately half of cloud tops are glaciated at -20 ∘C, glaciated clouds with a top temperature warmer than -20 ∘C are identified as “warm ice”, and liquid topped clouds colder than -20 ∘C are identified as “cold liquid”. The warm ice pixels are taken to indicate the presence of INP within 100 km the approximate spatial scale of aerosol variability from, whilst the cold liquid pixels are taken to indicate a relatively INP-free environment. If both (or neither) are detected within 100 km, that pixel is excluded from the analysis. The cloud phase is only used for the uppermost cloud layer when determining this INP proxy to reduce the impact of overlying ice clouds seeding ice in lower layers. In addition, regions with nearby higher cloud layers (those within a 10:1 glide slope) are also excluded from the glaciation index. To reduce the impact of random errors in the phase retrieval, two or more neighboring pixels are required for a detection of warm ice or cold liquid. This glaciation index is produced for each DARDAR vertical profile and is then used as a proxy for the occurrence of INP at temperatures colder then -35 ∘C in that profile. The use of cloud glaciation as an INP proxy for colder temperatures in the atmosphere assumes that cloud glaciation is correlated to INP between 0 and -35 ∘C and that there is a sufficient vertical correlation in INP occurrence. These assumptions are discussed in Sect. .

This combination of reanalysis temperature and aerosol data, along with previously determined clouds regimes and a proxy for INP are used globally for daytime data over the period from 2006 to 2013 to investigate the role of different processes on the Ni.

The changes in Ni(top)5µm observed in the previous section have impacts throughout the depth of the cloud. Figure  shows how Ni and IWC information propagates vertically within a cloud. The cloud profiles are split into two categories, based on whether they have above or below median values of the cloud top properties (Ni(top), IWC(top)). The difference in the vertical structure of the clouds (in a similar manner to Fig. ) is shown, with red over blue indicating an increase in the retrieved quantity at a given distance from the cloud top for profiles that were above median in that property at the cloud top.

The top row of Fig.  shows that Ni5µm information propagates a significant distance through the cloud. Clouds with an increased Ni(top)5µm maintain a higher Ni5µm at distances at least 3km from the cloud top in all regimes. However, as shown in the second row, vertical information about the Ni100µm does not propagate nearly as far through the cloud. The vertical propagation is the highest in the synoptic regime. The vertical propagation of IWC information is very similar to the Ni100µm, with the relationship to the cloud top IWC being significantly reduced more than 500 m from the cloud top.

The large vertical propagation of the Ni5µm indicates that the changes in Ni5µm at the cloud top found in the previous section can have considerable impacts at lower levels in the cloud. However, the lower vertical propagation of the information about the larger crystals (Ni100µm, IWC) would support the suggestion that the growth of the ice crystals after nucleation is primarily controlled by meteorological factors that do not play a large role in the nucleation processes that control Ni100µm. Note that the temperature of the cloud top and the distance from the cloud top can still play a large role in determining the Ni (Figs.  and ).

These results show that the Ni(top)5µm is strongly affected by several factors including temperature (Fig. ), cloud type (Fig. ) and updraft (Fig. ), and that changes in the Ni(top)5µm can be maintained at large distances from the cloud top (Fig. ). The dependence of the Ni(top)5µm on the in-cloud updraft and the relationship to reanalysis liquid aerosol (Fig. ) at temperatures between -35 and -60 ∘C is consistent with the impact of homogeneous nucleation processes on the Ni(top)5µm. This is supported by the relationship of the Ni(top)5µm to the INP proxy (Fig. ), where a reduction in Ni(top)5µm with increasing INP could be indicative of an INP suppression of homogeneous nucleation . The relationship with INP is also consistent with heterogeneous nucleation having a strong role to play in determining the Ni(top)5µm in synoptic cirrus clouds at temperatures colder than -60 ∘C.

Uncertainties in the retrieval have been covered in Part 1 of this work . However, there are a few points to note with regards to the relationship of the Ni to other cloud and meteorological properties. Although there is significant uncertainty in the Ni retrieval, many of these uncertainties are random errors and not systematic functions of the meteorological properties investigated here. Even ice crystal shape, which can be a major issue in ice cloud retrievals, is a function of temperature (to first order) and so does not impact the majority of the results which are presented in this work stratified by temperature. The geographical variations in Fig. b show a similar pattern to those from , with high Ni(top) observed in mountainous regions and a reduced Ni(top) in the tropics. The similarity of the results from these two different retrieval products, each with a different physical basis supports the conclusions drawn from these datasets regarding the global distribution of Ni. There is also little evidence to suggest that there are large biases caused by the retrieval only being able to use one instrument (radar or lidar). Cases where only the lidar detects a cloud are often characterized by monomodal ice distributions, which are well represented by the parameterization. As such, these cases are retrieved with similar accuracy to the full radar–lidar retrieval .

The cloud phase classification is of critical importance to the warmer clouds included in this study and there is evidence of the misclassification of a small number of cases at temperatures warmer than -35 ∘C (Fig. ). This can make it difficult to interpret results at these temperatures, so they are not a focus of this work. The change in phase of these clouds as a function of aerosol is likely to dominate the radiative response of clouds to aerosols at these temperatures.

There are a number of limitations of this study that could be addressed in future work. The lack of information about the location of INP is a serious issue when investigating the impact of aerosol on Ni. While the INP proxy in this work is able to provide a qualitative estimate of the role of INP in determining the Ni, for a quantitative estimate a better proxy or measure of the global INP concentration is required.

Additionally, the impact of meteorological covariations makes it difficult to assign causality to the aerosol–Ni(top) relationships observed in Fig. . The lack of a complete picture of the atmosphere makes it difficult to directly control for meteorological variability. The causal link between aerosol and Ni(top) is thought to be strong e.g., but the lack of observations of in-cloud updrafts also limits how accurately the impact of aerosol on the Ni can be determined. Although the cloud regimes used have some ability to constrain the cloud-scale updraft , the updraft is a critical component in determining the Ni through its influence on the supersaturation. The in-cloud updraft is assumed to be largely independent of the aerosol properties in this work, but it is possible that the reanalysis aerosol is related to the in-cloud updraft, such that more aerosol is vertically transported in conditions with high in-cloud updrafts. In this case, a positive correlation between the Ni and MACC reanalysis aerosol could be generated. However, as MACC does not explicitly simulate in-cloud updrafts, the impact of this confounding issue is likely to be small.

It is also possible that using cloud glaciation as a proxy allows other meteorological covariations, which could generate apparent relationships between the INP and Ni. However, the in-cloud updraft is of a second-order importance in determining the cloud top phase compared to the INP concentration . The inclusion of a glide-slope test when determining the INP proxy means that it is also unlikely that clouds are being glaciated by undetected ice falling from higher cloud layers. The separation into cloud regimes also limits the impact of these kind of meteorological covariations, which might be expected between different regimes, but would be weaker within them.

The behavior of the Ni retrieval in this work follows the expected behavior of the Ni determined in several previous studies based on satellite remote sensing, in situ, theoretical and modeling results. This provides further evidence that the DARDAR-Nice Ni retrieval described in is able to retrieve the Ni in a variety of situations.

Few global studies exist of the controls on the ice crystal number concentration (Ni), especially regarding the role of aerosols. In this study, the DARDAR-Nice Ni retrieval from Part 1 is used to investigate possible controls on the Ni at a global scale for the period from 2006 to 2013. A special emphasis is placed on the Ni at the cloud top (Ni(top)), due to the close proximity to ice crystal nucleation locations within many high clouds .

Strong relationships between the Ni(top) and updraft, cloud type and particularly temperature are observed (Figs.  and ), with a higher Ni(top) for crystals larger then 5 µm (Ni(top)5µm) being found at colder temperatures in all regimes, which is consistent with an increased nucleation rate at lower temperatures. Fewer crystals larger than 100 µm, (Ni(top)100µm) are found at the coldest temperatures, possibly due to the reduced depositional growth rate meaning that they sediment from the cloud top region before they can grow to a sufficient size.

Many of the regimes show an increase in the Ni100µm and a decrease in the Ni5µm with increasing distance from the cloud top (Fig. ) due to the size sorting impact of sedimentation. The rate of change of the Ni moving away from the cloud top depends on the regime, with much slower changes in the synoptic regime indicating a role of meteorological factors in determining ice crystal growth rates. This is supported by the weaker temperature dependence of the Ni within clouds compared to the Ni(top) (Fig. ), which may also explain the apparent weak dependence of Ni on temperature and INP found in previous studies. Given the large difference between the Ni(top) and the Ni deeper in the cloud, this may suggest that the cloud top would make a good target for future in situ campaigns examining the controls on ice nucleation.

There are indications of homogeneous nucleation or possibly the freezing of liquid droplets determining the Ni(top). At temperatures just colder than -35 ∘C, there is a peak in the upper quantiles of the Ni(top)5µm (Fig. ). This peak is related to the updraft strength in the cloud, with the reliably high updrafts in the orographic regime giving it the strongest peak (Fig. ). This is further supported by the relationship between the Ni(top)5µm and the MACC reanalysis aerosol (Fig. ), with an increased Ni(top)5µm being observed in high aerosol environments. This indicates a possible dependence on the liquid aerosol concentration, particularly for smaller crystals, although this analysis cannot make a conclusive statement about the causality of this relationship. An investigation into the covariances between the MACC reanalysis aerosol, the DARDAR-Nice Ni and meteorological factors is an important target for future work.

As previous work has suggested that INP occurrence is related to cloud glaciation, the glaciated fraction at -20 ∘C is used as a qualitative proxy for INP occurrence (Fig. ). At temperatures between -50 and -35 ∘C, there is a reduction in Ni(top)5µm with increasing INP (Fig. ), which may indicate an INP suppression of the homogeneous nucleation , providing further supporting evidence for the role of homogeneous nucleation in determining the Ni(top). At colder temperatures, some regimes show an increasing Ni(top), and the Ni(top)100µm in particular, which may be evidence of heterogeneous nucleation controlling the Ni(top) and shifting the size distribution towards larger crystals. However, as with the relationship to liquid aerosol, meteorological covariations could be generating these relationships. Further studies are required to separate the role of these different mechanisms in controlling the Ni(top) and to isolate the role of aerosols in these relationships.

While changes to the Ni(top) are important for radiative considerations, changes in the Ni(top) can have implications for the cloud many kilometers below the cloud top (Fig. ). This far reaching impact into the life cycle of ice and mixed-phase clouds demonstrates the importance of developing strong observational constraints on the controlling factors of the Ni. The results presented in this work provide a global context for existing theory and in situ measurement based hypotheses about cloud properties, highlighting areas for future research to further constrain ice and mixed-phase cloud processes.