The spatial resolution of the AIRS measurements is 13.5 km at nadir. Nine AIRS measurements (3 × 3), called a “golf ball” (see grey circles in Fig. 1), correspond to one footprint of the Advanced Microwave Sounding Unit (AMSU). NASA AIRS L2 standard products include atmospheric temperature and water vapour profiles as well as surface skin temperature and ice/snow flag (Susskind et al., 2003, 2006; Chahine et al., 2006) at the spatial resolution of an AMSU footprint. The AIRS-LMD (AIRS clouds retrieved at the Laboratory of Dynamic Meteorology) cloud retrieval makes use of these products as ancillary data and has been described in (Stubenrauch et al., 2010). Briefly, the retrieval methodology is based on a weighted χ2 method using radiances measured along the wing of the 15 µm CO2 absorption band. The χ2 method determines the cloud pressure level (pcld), for which the measured radiances provide the most coherent cloud emissivity. The method also yields IR cloud emissivity defined as εcld = (Iclear-Imeas)/(Iclear-Icld(pcld)), where Imeas is the measured radiance, Iclear is the clear sky radiance and Icld the radiance of an optically thick cloud at the pcld level estimated for the observed situation from a minimum in the χ2 vertical profile. The AIRS-LMD data set participated in the GEWEX cloud assessment (Stubenrauch et al., 2013) and performed well. In the case of multiple cloud layers, the retrieved properties correspond to those of the highest cloud layer, as far as its optical depth is above 0.1.

CALIOP (Cloud-Aerosol Lidar with Orthoganal Polarization), a two-wavelength polarization-sensitive nadir viewing lidar, provides high-resolution vertical profiles of aerosols and clouds. It uses three receiver channels: one measuring the 1064 nm backscatter intensity and two channels measuring orthogonally polarized components of the 532 nm backscattered signal. Cloud and aerosol layers are detected by comparing the measured 532 nm signal return with the return expected from a molecular atmosphere. The method utilizes an adaptive threshold test (Vaughan et al., 2009) and retrieved the height of the physical top height, rather than the effective radiative height. The method is capable of detecting the clouds with visible extinction as small as ∼ 0.01 km-1 though the detection efficiency decreases in this domain and, as Davis et al. (2010) have shown, the CALIPSO misses a certain fraction of sub-visible cirrus clouds. The retrieval algorithm is the same for the daytime and nighttime portions of the orbit, except that different detection thresholds are used for day and night. Analysis of the parallel and perpendicular polarization of 532 nm backscatter signals provides vertically resolved identification of cloud water phase according to the algorithm of Hu et al. (2007). For this analysis, we utilize ztop and zbase from version 3 of the CALIPSO L2 cloud data averaged to 5 km along the track (release v.3.01).

The GEOPROF L2 product (Haynes and Stephens, 2007; Haladay and Stephens, 2009; Mace et al., 2009) of version P1_R04 merges the millimetre wavelength cloud profiling radar (CPR) radar data (footprint of 2.5 km × 1.4 km) with those collected by CALIOP. CloudSat shares an orbit with CALIPSO, so that they probe nearly the same volumes of the atmosphere within 10–15 s of each other. This configuration combined with the capacity for millimetre radar to penetrate optically thick hydrometeor layers and the ability of the lidar to detect optically thin clouds has allowed Mace et al. (2009) to develop an approach for retrieving the vertical and horizontal structure of hydrometeor layers with unprecedented precision, ranging from optically thin cirrus and boundary layer clouds to deep optically thick precipitating systems. In this study, the GEOPROF product helps us to verify if the cloud base height for the selected overlap is consistent with the IWC profile provided in the DARDAR data set (see next section) and use the ztop values to “align” the IWC(z) profiles for the classification (Sect. 3.2).

Delanoë and Hogan (2010) have adapted a variational method using the synergy of radar, lidar, and infrared radiometer from airborne and ground-based measurements (Delanoë and Hogan, 2008) to CALIPSO-CloudSat-MODIS satellite observations to retrieve vertical profiles of visible extinction coefficient, IWC, and De. The variational scheme finds a state vector x, which minimizes the square-root sum of the differences between the observed (y) and calculated radiances. The components of the observation vector y are the following: radar reflectivity factor, apparent lidar backscatter as well as IR radiance and IR radiance difference if the radiometer is used. Note that in the version we are using the IR radiances are not assimilated. The components of x are the visible extinction coefficients at different altitudes, extinction-to-backscatter ratio, and number concentration parameters at different altitudes.

The solution (state vector x) is found by minimizing a cost function using Gauss–Newton iteration, as described fully by Delanoë and Hogan (2008). A key input to the retrieval algorithm is an observational error covariance matrix, which includes both instrument and forward-model errors (Delanoë and Hogan, 2008, 2010). The resulting DARDAR (for liDAR + raDAR) products contain the profiles of the ice cloud related parameters on a 60 m vertical grid, which have been used in a number of studies (Bardeen et al., 2013; Battaglia and Delanoë, 2013; Ceccaldi et al., 2013; Delanoë et al., 2011, 2013; Deng et al., 2013; Eliasson et al., 2012; Faijan et al., 2012; Gayet et al., 2014; Huang et al., 2012; Jouan et al., 2012, 2014; Mason et al., 2014; Stein et al., 2011a, b).

ERA-Interim global atmospheric reanalysis is produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), covering the period from 1989 until now. Dee et al. (2011) give a detailed description of the approach and the data. The data assimilation scheme is sequential: at each time step, it assimilates available observations to constrain the model built with forecast information obtained in the previous step. The analyses are then used to make a short-range model forecast for the next assimilation time step. Gridded data products (at a spatial resolution of 0.75∘ latitude × 0.75∘ longitude) also include 6-hourly dynamic parameters such as horizontal and vertical large-scale winds. A common proxy for the intensity of the vertical motions in the atmosphere is the vertical pressure velocity at 500 hPa level, w500 (e.g. Bony and Dufresne, 2005; Martins et al., 2011). In addition, we also use vertical winds just underneath the cloud (wbase) and at the radiative height of the cloud (wcloud) to study correlations between the shape of the cloud IWC profile and the atmospheric dynamics.

Figure 1 illustrates a typical single-day coverage of AIRS and CALIPSO-CloudSat at a specific observation time (13:30 at the equator crossing time). Whereas the AIRS swaths cover areas about 1000 km, the active instruments only cover a 90 m–1.4 km wide track near the middle of the AIRS swaths. Since the instruments share the same orbit, one can impose strict overlapping criteria to get a high-quality data set.

Our colocation starts with the AIRS data and searches the other data sets for the observations closest to the centres of individual AIRS footprints (usually, three per each golf ball). A blown-up part in the upper-right corner of Fig. 1 shows an example of the overlapping measurements: for favourable conditions, the AIRS footprint can cover up to three CALIPSO L2 samples at 5 km resolution and up to 10 GEOPROF/DARDAR L2 samples at the spatial resolution of a CPR footprint (1.7 × 1.4 km). One has to keep in mind that “ideal” overlaps like the one shown in Fig. 1 are not so frequent: if the closest CALIPSO or DARDAR footprint lies outside the AIRS footprint, then the case is skipped.

Table 2 complements Fig. 1 and shows the statistics for the components of the collocated data set. As one can see, with the rigid colocation criteria used in this work the average distance between the centres of the samples is about 6 km. The fraction of the data selected is small, but the number of overlaps per day is still on the order of ∼ 1 × 104. The temporal deviation between the observations is defined by the distance between the satellites and is less than 2 min. The ERA-Interim atmospheric reanalysis deviates on average much more because of its rather coarse spatial and time resolution. The resulting collocated data set comprises the variables listed in Table 1.

Figure 2 illustrates the information available in the collocated data set, for typical examples of high-level ice clouds, with IWP (ice water path) increasing from 9.0 to 303 g m-2. In this figure, we supplement the IWC vertical profiles with AIRS zcld (horizontal red lines), CALIPSO ztop and zbase (blue lines), and GEOPROF ztop and zbase (green lines). It is interesting to trace the behaviour of these values with changing IWP: whereas CALIPSO and GEOPROF ztop match on all four panels, CALIPSO and GEOPROF zbase match at IWP < 100 g m-2, while the CALIPSO lidar cannot probe the lower boundary of thicker clouds; AIRS zcld corresponds to the radiative height close to the maximum backscatter signal from CALIPSO (Stubenrauch et al., 2010); for high-level ice clouds it lies generally 1 to 2 km below cloud top, depending on the vertical accumulation of optical depth (Liao et al., 1995; Holz et al., 2008); it seems to correspond to the IWC peak height up to IWP of about 30 g m-2, while for thicker clouds the corresponding optical depth is reached earlier. We explain all these features by the capabilities of the instruments and by physics of observations, and we find them to be consistent with the results presented elsewhere (e.g. Stubenrauch et al., 2013, and references therein). For the analysis, we have selected only high ice clouds, using AIRS cloud pressure (pcld < 440 hPa) and DARDAR profile information on the occurrence of liquid or ice. To ensure high quality of the selected subset, we filtered out the cases, for which DARDAR ice cloud peak height is beyond the GEOPROF ztop and zbase limits of the layer, closest to the AIRS cloud. This removes 18 % of the collocated data, and the mismatches are explained by different spatial resolution of the compared data sets, by the uncertainties of pcld→zcld conversion associated with temperature/H2O profiles, and by the GEOPROF cloud boundary thresholds.

Figure 3 shows the comparison of height for all high ice clouds in the collocated and filtered data set. In Fig. 3a, we compare the AIRS cloud height with the DARDAR IWC(z) peak height. As one can see, for clouds above ∼ 10 km the highest probability density (in red) almost follows a 1 : 1 line, while for the lower clouds AIRS tends to be ∼ 2–3 km higher. This is linked to the optical thickness of the cloud and its correlation with the vertical extent: for geometrically thicker clouds, AIRS retrieves the radiative height, while active instruments are capable of penetrating deeper. In Fig. 3b, AIRS cloud height is compared with the CALIPSO top: 80 % of the clouds are below the CALIPSO cloud top boundary; we assign the remaining 20 % to difference in sample size of these two instruments (5 km × 0.06 km vs. 15 km × 15 km) and to accuracy in AIRS cloud height determination (1 km). The purpose of Fig. 3c is to show the spread of the IWC(z) profile within the cloud: for the clouds peaking in the 8–13 km region, their ztop is usually just 1 km higher than the peak; however, the distribution is broad and for a significant fraction of clouds with smaller emissivity the IWC(z) maximum is much lower than the ztop. This is consistent with the AIRS vs. DARDAR peak plot in Fig. 3a: the IWC peak of extended cloud layers is closer to cloud base.

Figure 4 presents average cloud emissivity and vertical extent in relation to IWP. As one can see, average IR cloud emissivity increases with IWP and then saturates at ∼ 0.7–0.9 for IWP values greater than ∼ 100 g m-2. However, for the same large IWP, the mean is smaller in winter midlatitudes than in summer midlatitudes. It is interesting to note the peculiarity of ε(IWP) curves in the low IWP domain (Fig. 4a, c), where ε increases for IWP values less than ∼ 4–7 g m-2. One has to keep in mind that the same amount of water can form clouds of different optical depths (and emissivities): for thin clouds, the ice crystal size distribution centres around lower values compared to that of thicker clouds. We justify this explanation by building the ε(IWP) distributions only for De > 40 µm (not shown for the sake of clarity). These distributions do not have a feature at IWP ≈ 4–7 g m-2; instead, the ε(IWP) increases monotonically and then reaches saturation. The relationship between the vertical extent of the ice cloud (Δzcld) and its IWP is shown in Fig. 4b, d. Here one has to note the difference between the summer and winter hemispheres: both single and multi-layer clouds show a saturation of Δzcld in the winter hemisphere at IWP ≈ 70 g m-2 that corresponds to higher ice water densities in the storm tracks. Another remarkable feature of the Δzcld(IWP) is a nearly linear dependence on log(IWP) (with the exception for aforementioned saturation effects in winter hemispheres). This allows reducing the number of variables in the statistical classification we seek to develop.

Table 3 shows the latitudinal behaviour of cloud emissivity, IWP, vertical extent and proportion of ice within the cloud, separately for single-layer and multi-layer cloud scenes (identified by GEOPROF). We draw the readers' attention to two types of IWP values in Table 3: median and mean IWPs. The median IWPs are calculated over the ensemble of corresponding cloudy scenes, while the mean IWPs represent both cloudy and clear sky scenes together. The latter distribution shows a common three-peak pattern (cf. Eliasson et al., 2011) while the median values are more representative for strongly skewed distributions, which is the case of the IWP. As one can see, single layer high clouds are thicker both in geometrical and in optical sense. One can note the following differences: (a) median IWP values differ more strongly than cloud emissivities that is related to cloud emissivity saturation for thick clouds; (b) the vertical extent Δzcld of single layer clouds is ∼ 0.7 km larger than that of top ice clouds in multi-cloud scenes; (c) the geometrical ratio of ice layer thickness with respect to total layer thickness (Δzice/Δzcld) is larger for single layer clouds. We associate the latter difference with multi-layer mixed-phase clouds, for which the conditions at the lower boundary of high ice cloud are favourable for changing the phase from ice to water.

We have analyzed the IWC profiles with respect to cloud IWP, vertical extent, latitude, and atmospheric dynamics. The objectives of this analysis are the following: (a) establishing a minimal basis of primitive shapes, which one can use for approximating IWC(z), (b) building a statistical model for these primitive profiles, and (c) estimating the energetic effects of clouds with the same ice water path (IWP) but different IWC(z). A “minimal basis” in this context means that the individual elements of the suggested set of IWC profiles should not be linearly dependent with respect to any of the atmospheric and cloud variables. We have “aligned” the IWC profiles using the GEOPROF ztop values, calculated the vertical extent of the ice cloud using the GEOPROF zbase and ztop values, determined the IWP by integrating the DARDAR IWC(z) within these limits, normalized the IWC profiles to IWP, and compared them with a set of primitive shapes. An initial set of shapes consisted of the following: (1) “rectangular” or constant IWC; (2) “upper triangle”; (3) “isosceles triangle”; (4) “tilted triangle”; (5) “lower triangle”; (6) “trapezoid”; and (7) “isosceles trapezoid”, illustrated in Fig. 5a. The “tilted triangle” was built using the average top-to-peak and base-to-peak IWC(z) gradients normalized by the IWP. The other shapes are empirical approximations. It is important to note here that using a fixed set of profile shapes does not mean using the same IWC gradient within the same type: the real IWC values are always bound to the IWP of the cloud through normalizing.

To check the redundancy within these seven primitive profile shape types, we have used the statistics built over the globe for 1 month, January 2007 (the results do not change significantly for any other period). For each collocated event and for each primitive shape, we have calculated ζ, a standard rms of the model IWC profile deviation from the real IWC(z) profile. As a result, we have obtained seven sequences of ζ values and performed a “round robin” correlation analysis of these sequences. As the linear correlation coefficients in Table 4 show, a set of seven profile shapes appears to be redundant since some pairs of profile shapes are strongly correlated, with the correlation coefficients of about 0.8–0.9 (marked in bold), so it is logical to reduce the basis. The first profile to keep is a standard one (rectangular), which is approximated by a constant-within-layer IWC and which corresponds to an assumption currently used in the retrieval of cirrus bulk microphysical properties (e.g. Guignard et al., 2012). The profiles #2 (upper triangles) and #5 (lower triangles) are uncoupled from the others, so they should also be included to a reduced basis. In addition, we keep shape #7, which fills a gap between #2 and #5 and which is more physically sound compared to #1 (sharp changes in concentration are unlikely in high ice clouds, especially in the tropics, (e.g. Liao et al., 1995). The reduced set of profiles #1, #2, #5, and #7, illustrated by representative examples of the data and their approximations in Fig. 5, does not contain linearly dependent elements.

Besides IWC, another important radiative characteristic of the cloud is the effective ice crystal size and its changes with height. The analysis of DARDAR De(z) profiles shows that they are not as diverse as the IWC profiles and can be represented with a trapezoid similar to profile #6 in Fig. 5a. Here, the only parameter needed to describe the vertical profile is the ratio of the upper and lower edges of the trapezoid (kAB, see a sketch in Fig. 6a). We have studied the best fit of this parameter for different IWPs and seasons, varying kAB in a broad range from 0.1 (almost the “upper triangle”) through 1.0 (rectangular) to 10 (almost “lower triangle”). As one can see in Fig. 6, for IWP < 2 g m-2 De(z) is almost constant (kAB≈1.1) and this coefficient demonstrates only a moderate increase up to IWP ≈ 10 g m-2. This is explained by the low density of the ice particles, which hinders the aggregation and buoyancy stratification. For IWP > 30 g m-2, De(z) is best represented by a trapezoid with a ratio of edges kAB=1.35–1.5. For these densities, the probability of ice particle aggregation is higher and the sedimentation of heavier particles increases their concentration towards the cloud base. It is interesting to compare the behaviour of kAB for winter and summer midlatitudes as we did for Δzcld(IWP) distributions in Fig. 4: in winter, kAB is larger than in summer, meaning stronger vertical De(z) gradients during this period. This behaviour is consistent with denser clouds in the storm tracks discussed above. However, De also depends on the mechanism of cirrus formation (e.g. in situ or as an anvil of a convective system), on the life stage of the system and on the environmental temperature and humidity. In this article, we do not study the De profiles in further detail, but, as the estimates in the next section show, the vertical profile of De affects the radiative properties of the cloud and should be taken into account in the analysis and modelling.

We have analyzed 3 years (2007–2009) of collocated data by searching for the best fit within the four primitive IWC(z) shapes: rectangular, isosceles trapezoid, lower triangle, and upper triangle. Then we have studied their relative occurrence with respect to IWP, cloud layering (single or multi), cloud vertical extent, vertical wind, latitude and underlying surface (land or ocean). As a first step, we have studied the probability of occurrence of these specific IWC profile shapes as a function of IWP. Table 5 presents the statistics separately for single-layer and multi-layer cloud scenes, respectively. As the median values of Table 3 have already indicated, about 75 % of all high ice clouds lie within the range of IWP < 100 g m-2. Within this IWP range, about 60 to 80 % of the IWC profiles may be represented by rectangular (constant IWC) and isosceles trapezoid shapes.

As one can see from the normalized IWP histogram values presented in Table 5a and b, the relative frequency of thick ice cloud occurrence is higher in a single- rather than in a multi-layer system. Qualitatively, the IWC profile shape type fractioning behaves the same way for single- and multi-layer cloud scenes: if joined, rectangular and trapezoid IWC shapes make up more than 70 % of all the shapes. Between these two types, trapezoid-like IWC shapes dominate both single- and multi-layer scenes, unless IWP < 10 g m-2. The remaining 20–40 % split into profiles with increasing (lower triangle) and decreasing (upper triangle) IWC towards cloud base. We observe, as expected, an increasing occurrence probability of lower triangle with increasing IWP. Upper triangle shapes mostly occur in clouds with IWP < 30 g m-2. This is consistent with the currently accepted ice cloud formation model: if the amount of ice in the cloud is low, the particles may form an “inverse” IWC profile, stimulated by updraft or by a favourable combination of water vapour and temperature profiles. If the cloud is thicker, the sedimentation of larger particles leads to a decrease of occurrence of this shape.

To address the influence of large-scale vertical winds, we have analyzed the IWC profile shape statistics with respect to vertical wind w500, wbase (at GEOPROF zbase), and wcloud (at the AIRS zcld) and split it to three dynamic situations: strong updraft (w < -175 hPa day-1, 6 % of all the cases), “calm atmosphere” (-175 hPa day-1 < w < 175 hPa day-1, 93 %), and strong downdraft (w > 175 hPa day-1, 1 %), like those used in Stubenrauch et al. (2004). The analysis shows that changes in relative occurrence of IWC profile shapes are only noticeable for strong downdraft within the cloud (see values in brackets in Table 5), while filtering the statistics based on w500 and wbase did not lead to conclusive results. As one can see in Table 5, dynamic effects are only well traceable with lower triangles: strong downdrafts correspond to additional 3–11 % occurrence, and the added occurrence grows with IWP. We assign these effects to the following mechanisms: (a) in the case of a downdraft, the whole cloud becomes sub-saturated and the small ice crystals at the top sublimate much faster than the large ones (the size of crystals in the ice cloud increases from top to bottom, see Fig. 6), giving rise to lower triangle profiles; (b) downdraft leads to more intensive aggregation of ice crystals within an existing layer of less buoyant ice crystals beneath – this works only when the ice crystal aggregation is noticeable (warm cirrus and completely frozen mixed phase clouds; Kienast-Sjogren et al., 2013). It is interesting to note that the situation does not inverse in the case of strong updrafts and the occurrence of upper triangle profiles does not increase. When a strong updraft takes place, a homogeneous freezing is triggered and a lot of small ice crystals appear within the whole cloud (Kärcher and Lohmann, 2002) that leads to an increase in the occurrence of rectangular-type profiles.

In a further step, we address the effects of other factors, which might be important for the statistical IWC profile classification. These are cloud vertical extent Δzcld, latitude (season), and underlying surface type (land or ocean). The ultimate goal is to reduce the number of variables to a necessary minimum. We already know from Fig. 4b, d that cloud vertical extent is almost linearly dependent on the logarithm of IWP, so we only keep IWP for the classification. As for the latitude, Fig. 7 presents the fraction of lower triangles as a function of latitude and IWP. This profile shape is the third one in frequency of occurrence (Table 5) and its radiative effects are expected to differ from those of the first two types (see Sect. 4.2 for the discussion). In Fig. 7, we separate the statistics for single-layer and multi-layer cloud scenes and for ocean and land. As the comparison of Fig. 7a, c with Fig. 7b, d shows, the surface does not have a significant influence on the relative occurrence, thus allowing to merge the statistics for land and ocean. On the other hand, single- and multi-layer scenes in Fig. 7a, b and Fig. 7c, d show different patterns, justifying considering them separately. Latitudinal variability for single-layer scenes (Fig. 7a, b) is noticeable in the high IWP domain (> 300 g m-2), but as Table 5 shows, these cases represent less than 20 % of single layer clouds and less than 10 % of all clouds.

Summarizing, we suggest using the statistical classification of the IWC profile shape based solely on IWP. We explain relative consistency of the IWC profile shape type fractioning by a similarity of cloud formation processes in the atmosphere: regardless of the pressure/temperature/humidity profile, geographic location, and season, the physics of ice nucleation remains the same: once the supersaturation conditions and (in the case of a heterogeneous freezing) the ice nuclei exist, the clouds start forming; once formed, ice crystals start growing and sedimenting; reaching the zone with kinetic temperature greater than frost point temperature leads to ice sublimation.

As mentioned above, ice clouds affect radiative energy balance in the atmosphere in several ways: reflecting and scattering the incoming solar radiation, reflecting and scattering terrestrial and atmospheric radiation coming from below, and emitting infrared radiation in all directions. For a fixed IWP, each of the aforementioned components can depend on the profile of absorbing/scattering/emitting particle concentration. In this section, we address radiative effects in the long-wave (LW, 10–3280 cm-1) and short-wave (SW, 820–50 000 cm-1) bands. To quantify them, we will use surface radiative flux (SRF), top of the atmosphere radiative flux (TOA), and atmospheric contribution (ATM = TOA - SRF). In a numerical experiment described below, we estimate the effects of the shape of IWC profiles using five typical atmospheric scenarios: subarctic and midlatitude summer and winter as well as the tropics. The atmospheres were considered up to the mesopause region. The detailed description of atmospheric scenarios and vertical profiles of temperature and atmospheric constituents can be found in Feofilov and Kutepov (2012).