The CRISTA instrument was flown twice on space shuttle missions in 1994 and 1997 in a free-flyer configuration . During both missions the instrument made around 8 d of nearly global measurements in the mid-IR (5–15 µm), with a still today unprecedented horizontal resolution for a limb sounder. This was possible by the implementation of three telescopes with crossing viewing directions, which results in a rather dense measurement net (Fig. ) – even in the tropics (not presented). With an along-track sampling of 200/400 km and three viewing directions the typical gaps between the orbits in the Equator and midlatitude region are filled with measurements. Additionally, the pointing capability of the satellite allowed CRISTA-2 to extend the latitudinal coverage up to 74∘ N and S away from the more restricted coverage defined by the orbit inclination of 57∘ (fixed value for CRISTA-1 coverage). The rather good vertical resolution and sampling of 1.5 and 2.0 km helps cirrus clouds to be detected and the exact location with respect to the tropopause to be determined with quite a high accuracy .

The typical horizontal averaging along the line of sight of a limb sounder is in the order of 200–300 km, where the narrow field of view helps to keep this uncertainty in an adequate range, but this limits the accuracy of the retrieved limb ice water path (IWP) (see also Sect. 2.3 for details) from CRISTA.

The exact position of the cloud along the limb path (line of sight) remains unknown in limb measurements and is not retrievable. Simplified assumptions, e.g. a fixed horizontal cloud extent, are necessary to solve this issue in a retrieval process for target parameters like ice water content (IWC) or extinction e.g..

Modified instruments like a limb imager allow substantial improvements in macroscopic cloud parameters with refined observation and retrieval techniques e.g. 2D/3D and tomographic retrieval techniques, . However, the CRISTA measurement capabilities are still unique for the limb IR technique. Extremely low cloud optical thicknesses are detectable, which results in a very high detection sensitivity for IWC (> 5 × 10-6 gm-3), vertical IWP (2 × 10-4 gm-2), and extinction (8 × 10-4–10-2 km-1) . The IWC value represents only 1/10 of the CALIOP detection threshold , and the extinction threshold represents the upper limit of the measurement range of IR limb sounders. For extinctions > 10-2 km-1 the IR spectrum saturates and becomes optically thick in the limb, and the instrument loses sensitivity for optically thicker clouds.

Radiative flux calculations have been performed using the offline version of the SOCRATES (Suite Of Community RAdiative Transfer codes based on Edwards and Slingo) radiative transfer model with six bands in the short wave (SW), nine bands in the long wave (LW), and a delta-Eddington two-stream scattering solver at all wavelengths. This version has been used extensively in previous studies for calculating radiative effects from several atmospheric agents, including contrails e.g. , water vapour e.g., ozone e.g., and aerosols .

The model simulates ice cloud radiative effects using the parameterisation for ice cloud bulk optical properties. Radiative flux calculations are performed for specified ice cloud fraction, ice crystal effective radius, and mass mixing ratio. Our sensitivity simulations consider three different ice crystal shapes: spherical particles, hexagonal cylinders , and aggregates based on 83 representative size distributions measured during the CEPEX campaign (). The diurnal variations in the SW are simulated by calculating the daily average SW radiative effects based on 24 instantaneous values (i.e. model runs with a 1 h time resolution) using pre-calculated solar zenith angles (SZAs) at the profile location. Clear-sky conditions below the cloud base are assumed in the radiative calculations. For the sake of a simplified setup we ignored multi-layer clouds. This disregards a potentially reduced radiative input in the long wave from underlying cold cloud tops with lower temperatures than the surface. Changes in the albedo with time or geographical location are considered by an incorporated time-dependent 2D model of global albedo values.

In order to guide the model in a realistic cloud parameter space, the simulations were set up based on the CRISTA-2 measurements. IWC and extinction estimates as well as accurate cloud top heights with respect to the tropopause height are retrieved from the satellite and meteorological reanalysis datasets. ECMWF's fifth-generation reanalysis, ERA5 , is used for temperature, ozone, and specific humidity information at the profile location of CRISTA-2. Additionally, ERA5 pressure and geopotential height are applied to transform the vertical coordinate altitude for the satellite into pressure levels for the model. The derivation of lapse rate tropopause height and pressure from ERA5 follows the method of .

The cloud detection capabilities and the high detection sensitivity for cirrus clouds by IR limb sounders have been demonstrated in various studies and for various instruments. The detection method is based on a colour ratio of the emissions in a CO2 and minor ozone band at a wavenumber region around 792 cm-1 and an atmospheric window region at 830 cm-1. The so-called cloud index is high (CI > 4) for optically thin and cloud-free conditions and shrinks to values close to 1 when becoming optically thick in the limb direction. We applied a cloud index threshold of 3 for cloud top height detection, a robust threshold, applied and evaluated in various studies e.g. . The method was developed originally for the CRISTA satellite instrument but has been successfully adopted due to its high efficiency to other IR limb sounders, like the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument on the Envisat satellite or more recently on airborne instruments .

The CRISTA observations were used to define the macro- and microphysical cloud parameter required for the SOCRATES run. In total 161 profiles with cirrus clouds around the tropopause were selected from the CRISTA-2 dataset in the regions highlighted in Fig. . These regions are restricted to latitudes > 60∘ N, which are not well covered by in situ instruments. The clouds formed under a specific dynamical situation where a Rossby wave breaking event over the Atlantic transported a high water vapour amount to high latitudes over Europe and triggered the ice cloud formation in regions with sufficiently cold temperatures, although the temperatures were usually too warm and additional temperature fluctuation by gravity waves would be necessary but were not resolved in the applied reanalysis data . To keep the number of modelled profiles for our study at a reasonable size as well as to choose well-characterised UTC events, we limited our analysis to 2 d and defined regions as highlighted in Fig. . This restriction allows sensitivity studies over various micro- and macrophysical parameters with the SOCRATES model.

showed that the cloud index value in the optically thin part of cloud measurement correlates well with the limb-integrated surface area density along the limb path (ADP) (equivalent to a limb IWP), and they generated lookup tables for various altitudes and latitudes. In addition, taking the effective radius of the particles into account (predefined for the model runs with 5, 10, and 30 µm), it is possible to estimate the mean IWC along the line of sight under the assumption of a tangent height layer homogeneously covered by the cirrus cloud. A constant path length through the cloud of 200 km has been applied. Usually, the path length depends on the tangent point altitude with respect to the real cloud top (not the detected instrument-based cloud top height; because of the limited vertical resolution and sampling of the instrument, the real cloud top height (CTH) can be lower or higher than the detected CTH). In addition, the cloud path length depends on the size of the field of view. Consequently, for a horizontally and/or vertically large cloud extent the limb cloud path can become extremely long (150 to 400 km for 1 to 3 km, respectively, at vertical resolution). In the current analysis, we are mainly interested in the cloud top region, up to 1–2 km below the cloud top, where the cloud is usually still optically thin, and an effective cloud path of ≃ 200 km is a reasonable assumption for the rather small field of view of 1.5 km of CRISTA . Finally, it needs to be highlighted that the cloud base height is difficult to retrieve for limb measurements. Obviously, for optically thick clouds in the limb (and nadir) direction, the cloud bottom is not visible. In addition, for optically thinner clouds, limited altitude coverage (hmin > cloud base height, CBH) makes it impossible to determine a CBH for many limb sounders (e.g. MIPAS, CRISTA) especially for vertically thick clouds. Consequently, for the sensitivity study with SOCRATES we decided to use predefined cloud thicknesses (Δz) of 0.5 and 2 km.

For a newer and airborne-based IR limb sounder, showed the ability to retrieve CTH and CBH. The predefined thicknesses for the SOCRATES study are in the range of the maximum of the Δz probability density (∼  600 m), and Δz = 2 km is in the maximum range of the UTC thickness detected by the airborne instrument, where roughly 5 %–6 % of the events show a Δz > 2 km.

The following procedure is applied for the interpolation of the CRISTA IWC to the SOCRATES grid. If more than one tangent height in a single profile is affected by clouds, then the values (IWC) are used for the linear interpolation on the vertical grid down to cloud bottom altitude. If the predefined cloud thickness overlaps the minimum altitude of the measurement with IWC > 0, then the model levels of the cloud are kept constant with the IWC of the lowest altitude.

In summary, IWC is estimated from the retrieved CTH and ADP or the ADP-equivalent limb IWP, where the effective radius and cloud thickness are predefined (0.5 and 2 km). The CRISTA measurements were taken in August 1997, which means under rather high solar zenith angle conditions with many hours of sunlight. For contrast we mirrored the CRISTA observation to February conditions to simulate contrapuntal winter-like events with respect to meteorological (ERA5) and solar conditions and used these for a rough estimate of the seasonal dependence of the CRE of UTCs (see Sect. ).

Particle shape and roughness are very important parameters for correctly modelling the radiative effect of cirrus clouds and references therein. Cirrus particles can have very complex particle shapes for a review see. Various studies show less complexity for the cold cloud top regions, especially in the tropical tropopause region, where quasi-spherical particles with radii smaller than 50 µm seem to dominate the particle size distribution and where complex ice aggregates are less frequently observed . It is reasonable that cirrus at the tropopause and in the lower stratosphere (cloud top) at midlatitudes and high latitude also have less complex shapes than optically thick ice clouds in the free troposphere.

In this study we use the properties of three particle shapes: (a) aggregates, a specific composition of ice crystal habits ; (b) spherical ice particles as a simplification for the in situ observed quasi-spherical particles in the cloud top region, which are typically best described by droxtals or Chebyshev particles ; and (c) hexagonal cylinders (or columns or prisms). reported that the ice crystals observed in high cirrus clouds (with cloud temperature < -50 ∘C) were predominantly hollow or solid hexagonal columns. As described for example by the parameterised optical properties for the hexagonal ice particle are based on and over a parameterised bimodal particle size distribution from .

Cloud optical depth (τ) is an important parameter when investigating the cooling or warming potential of cirrus clouds e.g.. We computed τ from the CRISTA cirrus cloud detection by the CI–IWC relation prepared in lookup tables of ADP or limb IWP versus CI with respect to cloud altitude and a further correlation between extinction ke and IWC/Reff with ke = const ⋅ IWC/Reff, with const = 1.4 × 103, IWC in gm-3, Reff in micrometres, and ke in km-1 . Finally, a simple integration of ke over the cloud layer thickness (Δz) results in the vertical optical depth τ = ∫kedz, which is used for the SOCRATES input (Fig. ).

The vertical information content of the ice parameters measured by CRISTA is limited. If more than one tangent height is affected by clouds in a single profile, then the values (IWC and consequently ke and τ) are used for the interpolation on the vertical grid of SOCRATES. If the predefined cloud thickness Δz overlaps the minimum altitude of CRISTA, then the model levels of the cloud are kept constant with the IWC of the lowest altitude. The CRISTA-based optical depth (Fig. b) covers the full range of UTCs from extremely low τ<0.0005 up to a maximum of τ≃0.05, where the maximum is still in the range of SVCs.

For a crosscheck of the τ approach we also followed an estimation method for the optical depth by τ=1.5⋅IWP/(ρICE⋅Reff) e.g. with Reff in micrometres and ρICE the mass density of ice in gcm-3. Probability density functions (PDFs) of retrieved (Fig. a) and estimated (not shown) τ look very similar, which gives us confidence that the retrieved IWC, IWP, and extinctions retrieved from CRISTA are in a reasonable range. Figure a and b show the distribution of IWP and optical thickness retrieved from the CRISTA data. The similarities in the PDFs highlight the close link between both parameters.

A summary of all different model scenarios (36 in total) for SOCRATES is presented in Table  together with the mean model results of the cloud radiative effect of all CRISTA profiles with cirrus clouds in the regions of interest (see Fig. ) accounted for in the simulations. An example of the model input profiles (cloud index, temperature, specific humidity, and IWC) and the output profiles of SW and LW flux profiles for all-sky (as) cloudy and clear-sky (cs) non-cloudy conditions is presented in Fig. . The CRE is defined as the sum of SW and LW effect of the all-sky minus clear-sky fluxes (F) at the top of the atmosphere in Wm-2: CRE=(FSWas-FSWcs)+(FLWas-FLWcs).

LW, SW, and total flux (CRE) are saturating above the cloud top (< 100 hPa) with virtually constant values (Fig. b), and a simple definition of the top of atmosphere (ToA) radiative effect is applicable by means of the pressure levels 20 to 0.6 hPa. The latter pressure value is the minimum pressure level in the model run.

Figure a gives an overview of the range and occurrence in the vertical IWP from the CRISTA estimates. The obviously very different vertical cloud thicknesses of 0.5 and 2.0 km result in a separation in the PDF of IWP with very small IWPs between 3 × 10-3 and 5 × 10-2 gm-2 for the 0.5 km cloud layers and an IWP ≃ 10-1 gm-2 for the 2 km extended cirrus. All modelled and observed cirrus clouds are optically thin in the limb and nadir direction and will be invisible for most passive nadir instruments. The lowest IWP values are equivalent to an IWC of 10-5 gm-3, which is 1 order of magnitude larger than the detection sensitivity of IR limb sounders and close to the so far lowest IWC values observed in in situ measurements 10-6 gm-3, .

The mean temperature of the modelled cloud layers is in the range of 210 to 250 K for August (Fig. c), peaking around 220 K, which is a typical tropopause temperature at this time of the season (see Fig.  or ). We applied no pre-selection based on temperature for the CRISTA cloud detection; consequently a few (11 out of 162) lower-altitude and warm cirrus are part of the SOCRATES calculations and are visible in the presented PDF at T > 240 K. These events have been detected 2 to 4 km below the tropopause but at cloud top heights of 8 to 9 km, which is relatively close to the typical tropopause height at the relatively high latitudes (60–70∘ N) of the measurements.

February temperature profiles have been selected from ERA5 and are not observationally based (longitude and latitude of the August cloud observations). The corresponding estimated cloud temperatures are lower than in August (the maximum of the probability distribution peaks at 210 K; not shown). Although the selected temperature profiles for February may not be realistic for the microphysical formation of cirrus (e.g. frequent CTHs are modelled in February significantly above the tropopause), it seams reasonable to use the profiles for T, specific humidity (SH), and O3 to define the background atmosphere conditions for the February scenarios in SOCRATES. However, these February simulations are only intended to provide rough CRE estimates for the discussion on the overall differences between summer and winter conditions.

An overview of the CRE of the individual profiles is presented for selected model setups in Fig.  by probability density functions (PDFs) for various Δz and particle shapes (colour-coded) and effective radius as well as for August (a, b) and February (c) background conditions. Relatively broad distributions of a negative CRE for hexagonal particles from -2 to 0.5 Wm-2 were found for Δz = 2 km, changing to a positive CRE for spherical particles (+0.5 to 2 Wm-2, Fig. a) for an effective radius of 10 µm. Overall, our simulations indicate contrasting behaviours between spherical and hexagonal particle shapes and between August and February conditions. Very similar distribution were found between hexagonal shapes and aggregates as shown for the large mode (Reff = 30 µm) but with similar agreement for both other size modes (Fig. b). Finally, for the small mode (Reff = 5 µm) and February conditions, the PDFs of spherical and hexagonal particles are shifted to positive CREs; only a minor contribution of the scenarios with hexagonal particles is able to produce a net cooling effect. The results are discussed in more detail in the discussion of Sect. .

Figure  gives a better representation of the SW, LW, and net effect with respect to the optical depth (Sect. ) of the modelled clouds. Figure a, c, e, and g show the CRE versus optical depth for four and eight model scenes – always for Δz = 0.5 and 2 km and August conditions with Reff = 10 µm and aggregate (Fig. a and b), spherical (Fig. c and d), and hexagonal particle shapes (Fig. e and f) – and finally for the large particle mode 30 µm and hexagonal particle shape. The exponential growth of SW and LW effects with increasing log⁡(τ) is obvious for all setups and especially well pronounced for the combination of Reff = 10 µm and aggregates as well as hexagonal particles. SW and LW effects are nearly in balance and changes in shape or radius can significantly change the net effect (black symbols in Fig. a, c, e, and g) from cooling to warming and vice versa. The interplay of SW and LW effects is visualised in more detail in Fig. b, d, f, and h. Deviations from the one-to-one line highlight the warming (above) and cooling (below) of the net cirrus CRE for each single cloud event modelled with SOCRATES. Smaller Δz induces a very similar ratio between LW and SW effects, illustrated by rather similar gradients and only smaller amplitudes in the LW–SW correlation. For summer conditions and particle shapes of aggregates the short-wave scattering effect can reach a very large cooling (extended day length), especially for larger optical depth values (τ > 0.01). This results in 10 scenarios (Table : scenes 01, 02, 05, 06, 17, 18, 25, 26, 33, 34) with an overall mean cooling potential (aggregates for 5, 10, and 30 µm; hexagonal shape only for 5 and 10 µm) presented in Fig. a–d. However, even smaller effective radii (< 10 µm) will result in even larger cooling effects for aggregates or similar complex particle shapes. For optically thin cirrus clouds (SVC and/or UTC), in situ measurements show typically Reff <≃ 100 µm and quasi-spherical shapes with some plates and rare trigonal shapes . Thus, aggregates are not a very plausible particle shape for the optically thinnest cirrus clouds observed by CRISTA.

For spheres (Fig. c and d) compared to aggregates (Fig. a and b) or hexagonal particles (Fig. e and f) the SW scattering efficiency is less pronounced and the cooling effect is generally smaller in amplitude and usually smaller than the LW warming for spheres. Hexagonally shaped particles are more realistic for high-altitude cirrus cloud particles , although they are usually observed at colder temperatures and not necessarily generally representative of UTCs at midlatitudes and high latitudes. Figure e represents an example of the optical depth versus CRE and the LW versus the SW effect for 10 µm. The results are very similar to the aggregates, although the amplitude for SW, LW, and total CRE are slightly larger for aggregates than for hexagonal particles. As a consequence, for hexagonal ice crystal shapes a few more profiles with LW > SW are present (Fig. f and h). The larger effective radius (Reff = 30 µm; Fig. h and f) results in significantly smaller surface area densities, which reduces the SW effect. The LW can now dominate the SW more frequently and results for nearly 50 % of the profiles in a net warming effect (Fig. h) compared to the 10 µm runs (Fig. f) with cooling for most of the profiles.

In addition, we present in Fig.  the CRE versus optical depth relation for Reff =  5 µm and 10 µm of hexagonal and spherical particles for August and February conditions. The small mode again shows opposing effects for hexagonal and spherical particles, here with an extremely high SW cooling (up to 10 Wm-2) for hexagonal particles. The latter results in a net cooling for all profiles, and the situation is the opposite for spheres, where the majority creates a net warming effect.

There is a strong Reff dependency on the SW effect, where larger particles correspond to smaller surface area densities for constant IWC and consequently smaller SW scattering. Generally, 0.5 and 2 km cloud layers behave very similarly to changes in the parameter settings (LW is orange and red and SW lilac and blue in Fig. , Fig. ), whereby τ is a significant factor of ∼ 4 smaller in the CRE for Δz = 0.5 than for the Δz = 2 km cloud layers.

In addition, we tried to find a relation between the CRE and macrophysical parameters like the distance to the tropopause as well the temperature difference between cloud top and surface temperature. Figure  presents only results for Reff = 10 µm (5 and 30 µm differ only by an enhancement and reduction in magnitude, respectively, and no change in sign) for spherical (Fig. a) and hexagonal (Fig. b) particles for cloud top pressure minus tropopause pressure in pressure altitudes.

Although the interquartile range of the median values of the CRE are rather large (error bars), for Δz = 2 km there is a distinctive correlation starting a few kilometres (2–3 km) below the TP up to 0.5 km above the tropopause. In addition, for spherical as well for hexagonal particle shapes, the median indicates a weak negative gradient with cooling in the CRE with larger distances above the tropopause (> 0.5 to 2 km). Δz = 0.5 km events show a negative gradient but with smaller tendencies in the range of -1 to 3 km with respect to the tropopause. The gradient looks for aggregates and hexagonal particle shapes as opposed to spheres. Below the tropopause (≃ -1.5 km) the gradient is negative for most of the scenarios.

Mean cloud temperature should have an imprint on the CRE, because the emitted radiation of the cloud is directly related to the temperature. One of the major radiation effects by high cold clouds is a warming potential due to the emission at lower temperatures around the tropopause e.g.. The cloud radiative effect with respect to the cloud top temperature (CTT) minus surface temperature at the profile location is presented in Fig. . CTT is not directly related to the LW effect of clouds; it is the temperature difference between the cloud top and the LW-emitting layer in the atmosphere, an underlying cloud layer, or the surface temperature under clear-sky conditions e.g.. In addition, the optical thickness of the cloud layer is also an important parameter in this representation; the smaller the optical thickness, the smaller the LW effect and consequently the smaller and less significant the sensitivity to the temperature difference. A completely transparent cloud (τ=0) has a negligible LW effect. This appears nicely in the different behaviour of the Δz = 2 km and dz = 0.5 km scenarios in Fig. , where the vertically thin clouds (red, scaled by a factor 4) show no or only weak trends in the CRE with respect to the temperature difference. For all particle sizes and shapes for the vertically thick and consequently optically thicker cloud layers (blue) a linear relation becomes obvious; the smaller the negative temperature difference, the smaller CRE. Although the scatter – the error bars represent the interquartile range – is sometimes even large for the 2 km cloud cases, this appears only for temperature bins with small event numbers (N<5). In contrast, the Δz = 0.5 km scenes always show a relatively large interquartile range with respect to the median and only a weak indication of similar trends (significantly smaller gradients) like in the Δz = 2 km scenes (Fig. a and d).

The CRE versus optical depth similar to Fig.  is presented in Fig.  with an additional binning along the corresponding y axis and the computation of median and percentiles per bin for the CRE. The median and the interquartile range are presented, with the interquartile range as an error measure to better visualise the variability for constant optical depth. The median and interquartile range are better suited than the mean and standard deviation to characterise data with high internal variability, extreme outliers, or skewed distributions. For spherical particles, the median follows the exponential increase in the CRE from the 0.5 and relatively small τ over the 2 km scenarios up to τ≃0.02 and the CRE up to 2 Wm-2, whereby the aggregates show nearly the opposite behaviour in the CRE, with a smaller amplitude and larger scatter (interquartile range error bars).

Table  summarises all SOCRATES setups and mean results on LW, SW and net radiative effect. The median values of the selected areas (Sect. ) give distinctive tendencies of the overall cloud warming or cooling effect for the UTCs. In total 161 cloud profiles have been selected from the CRISTA-2 data and represent variable conditions where optical thin cirrus clouds were formed at and above the tropopause north of 60∘ N. Using more realistic cloud occurrence frequencies would allow a more realistic assessment of the CRE of the UTCs.

The LW effect of scattering and trapping the IR radiation back into the direction of the ground dominates the SW cooling effect for most of the model scenes. For spherical particle shapes, both scenarios, winter and summer, result in a net warming effect in the range of 0.17 to 1.15 Wm-2 (August) and 0.13 to 0.93 Wm-2 (February) for Reff = 10 µm. These are generally larger values than the mean effects for aggregates or hexagonal particles, especially for summer conditions.

The LW warming is even more effective for larger particles where the resulting smaller surface area densities reduce the SW cooling. However, the SW cooling is also more effective for larger particles. Table  shows this fact for all simulations of spherical particles: for example, a between 10 and 30 µm effective radius has a ∼ 3 times higher SW and LW effect for the 10 µm effective radius (e.g. factor 6 higher for 30 to 5 µm).

The short-wave scattering effect depends strongly on the solar zenith angle and the duration of sunlit hours. For winter conditions the mean SW effect cannot compensate for the LW effect for aggregates and spheres, whereas for summer conditions the aggregates can change the sign for the CRE from warming to cooling. SW is enlarged from -0.63 to -3.44 Wm-2 and results in a mean CRE of +0.81 (February) to -0.64 Wm-2 (August). This change in sign – from warming to cooling – does not appear for spherical particles. In contrast to aggregates the CRE stays positive from winter to summer and even shows a slightly enhanced CRE (e.g. 0.93 to 1.15 Wm-2 for 10 µm and Δz = 2 km). The SW effect of spherical particles is by far smaller than the one for aggregates.

As mentioned in Sect. 2, we used the profiles for T, SH, and O3 to define the background atmosphere conditions for February scenarios in SOCRATES. The CRISTA-based input (CTH and IWC, indirectly IWP, extinction, optical depth) are simply mirrored into these February conditions. While these simulations do not represent actual February UTC CRE simulations, they are intended to provide a basis for discussions on the more general differences between summer and winter conditions.

For winter (February) conditions the short-wave cooling becomes smaller due to reduced daylight hours (taking also into account the rather high geographical latitudes), which results in a general warming effect for all particle shapes and effective radii. The change from cooling to warming for aggregates and hexagonal particles with Reff = 10 µm is illustrated in Fig. c and d. In addition, the albedo varies for this change from a mean α = 0.15 to 0.5, which has a drastic effect on the LW radiance input coming from below the cloud. Similar to an underlying cloud, this can have a significant effect on the net SW or LW effect.

The change from net cooling to warming simulated for February conditions has been compared with the long time record analysis of CALIPSO by . It should be recapped that the cloud optical thicknesses < 0.01 (mainly UTCs) only play a minor role for the total CALIPSO-based CRE. showed the zonal mean seasonal variation in the total SW, LW, and net effect of ice cloud radiative effect, latitudinally resolved (Fig. 4). For ∼ 50 to 75∘ N significant changes over the seasonal cycle, from cooling in summer (March to August) to warming in winter (September to February), are observable. A net warming effect of 10–20 Wm-2 is observed during winter, and the net cooling effect can exceed 30 Wm-2 in southern midlatitudes to high latitudes and 20 Wm-2 in the northern midlatitudes to high latitudes. In the tropics, a strong net warming effect (10–20 Wm-2) persists over the whole year, mainly caused by high ice clouds with negligible seasonal variation in the zonal mean . Consequently, the CALIPSO results are in line with the simplified mirroring of the CRISTA measurements from summer to winter conditions for UTCs, while the amplitudes for UTCs are obviously much smaller, which is mainly a result of the different optical thicknesses of UTCs compared to ice clouds observed by CALIPSO. The tendency towards a change from cooling to warming is identical.

Various settings of UTC clouds have been modelled with SOCRATES for a first quantification of the cloud radiative effect of UTCs at midlatitudes and high latitudes. The original CRISTA-2 data have already been analysed regarding the cloud occurrence with respect to the tropopause by . However, the CRE was not analysed for these unexpected observations of UTCs well above the tropopause and with unprecedented high occurrence rates at high northern latitudes. A comprehensive study was missing where the cooling or warming potential of these clouds is investigated.

For larger effective radii as well for vertical thinner cloud layers (0.5 km) we observe smaller cooling and warming effects in the mean SOCRATES results (Table  and Sect. ). The determination of Δz would be an important parameter for a better future quantification of the CRE of UTCs. So far, there is no validated statistical information of the cloud thickness of UTCs available. Although the CALIOP data may miss a rather large part of the optically thinnest UTCs , the dataset is still the best set available for such an analysis. have analysed the cloud occurrence of stratospheric ice clouds (SICs) based on CALIOP data products. The studies by Zou and colleagues have not focused on the vertical extent of these clouds. showed for midlatitudes that the IR limb measurements by MIPAS give higher occurrence rates on SICs than CALIOP if both cloud occurrence frequencies are normalised in the tropics. This supports the notion that IR limb sounders are under specific conditions more sensitive in the detection of cirrus cloud than recent lidar in-space instruments. This circumstance was already discussed in earlier studies .

The best information on the Δz of UTCs retrieved from IR limb measurements is the more recent analysis of with data from the airborne GLORIA (Gimballed Limb Observer for Radiance Imaging of the Atmosphere) instrument during the airborne campaign WISE (Wave-driven ISentropic Exchange) in the North Atlantic in September and October 2017. Due to the excellent vertical resolution and fine sampling using a 2D infrared imaging detector, the data achieve a vertical sampling and resolution of 140 m. For the first time cloud bottom information was retrieved from extinction profiles.

The analysis shows that in the region investigated by WISE there is a maximum likelihood in cloud extent Δz of 500–625 m with likelihoods for Δz > 1.5 km of less than 25 % of the peak likelihood and in total only 10 % of all measured cloud events Fig. 8a. Note that for a typical Δz of 0.5 to 1 km a lower CRE is calculated than for Δz = 2 km (Fig. ). Generally, optical depth is a good estimator for the strength of the CRE even at very low optical depth, but the cloud vertical extent is obviously a critical parameter for τ and the CRE, and there seams a functional relation between the CRE, Δz, and τ (Fig. ).

Cloud top heights with respect to the tropopause show a week correlation with the CRE in the SOCRATES results especially below the tropopause with a decrease in mean CRE with warmer cloud temperatures (Fig. ). The variability in the net effect is very large (profile-to-profile variability), which makes it difficult to draw a final conclusion on a mean effect with the cloud top position with respect to the tropopause, but we found clear indications of an enhanced warming effect for optically thicker events at higher altitudes with respect to the tropopause.

The CRE is not only affected by τ, but the atmospheric background conditions (temperature profile, CTH location, surface albedo, microphysical quantities) can also result in situations where even similar background conditions and constant τ result in a very different CRE. This makes the prediction of a net cooling or warming difficult. Even LW and SW effects turn out to be very different depending on the optical depth (Fig. ). Global measurements with a sophisticated occurrence frequency statistic, where the cloud detection is weighted with the area covered by clouds, are necessary. The subsequent radiation model runs would then allow the overall CRE of UTCs in the tropopause region to be better quantified.

followed a very similar procedure with the combined CALIPSO–CloudSAT ice cloud data products (DARDAR: ; 2C-ICE: ). These data may not include the correct number of UTCs due to a lack of detection sensitivity (see Sect. ) and will consequently to some extent underestimate the total cloud coverage and occurrence of cirrus clouds. The results achieved by Hong and colleagues are presented for ice cloud optical depths τ > 10-2, a value where the limb measurements are starting to saturate. The analysis of Hong and colleagues lacks the optically thinnest range of τ = 10-4–10-2, where IR limb sounders are most sensitive. A combination of IR limb and space lidar measurements would be an excellent combination to cover the full range of the optical depth of cirrus clouds (τ = 10-4 to > 20) for a comprehensive view on the radiative effect of cirrus clouds. argue that subvisual cirrus (τ<0.03) display only weak SW and LW radiative effects because of their infrequent occurrence global mean < 5 %; , and this results in a global mean value of CRE = 0.05 Wm-2 Table 4,. However, as already argued above, the applied cloud dataset misses a significant number of UTCs and the overall radiative effect for SVCs and UTCs is underestimated. Our study shows that the radiative effect of these additional UTCs will be small but relevant, in the range of the CRE median of -2.43 to 2.28 Wm-2 (Reff = 5 µm) assuming a 100 % occurrence rate (with a single profile maximum of net cooling of -9 Wm-2 and net warming of ∼ 6 Wm-2; Fig. ). For summer conditions only aggregates and hexagonal particles have the potential for a net cooling effect. If a more realistic UTC coverage of 10 (20) % is assumed , the CRE is reduced to a still not irrelevant range of -0.24 (-0.48) to 0.22 (0.45) Wm-2.

The numbers of the radiative forcing caused by UTC calculated here can be put into perspective by the radiative forcing determined for CO2 and other greenhouse gases. In a similarly designed study, analysed SW, LW, and the net radiative effect of a stratospheric water vapour (SWV) enhancement as well as the effects of contrail cirrus in a comparison of various radiative transport models. An overall global change in SWV from 3.0 to 3.7 ppmv resulted in a net radiative forcing (LW + SW) of 0.22 to 0.49 Wm-2 depending on the specific model. This is a similar value and range as for the 10 µm particle size in the CRE results for UTCs presented above (Table ), with a mean 100 % cloud-cover – clearly an overestimate of the real atmosphere. A typical contrail cirrus with an optical depth of 0.3 and a 100 % coverage resulted in a CRE of -14 to -7 Wm-2 for a high SZA (75∘) and a positive CRE of 12–23 Wm-2 for a low SZA (30∘). Similar to the UTCs focused on for this study, the CRE of optically thin contrails is very sensitive to the SZA; depending on the sunlight hours and the maximum SZA, the overall CRE can change from negative to positive effects. Finally, Myhre and colleagues made a more realistic estimate of the global coverage of contrails and the resulting CRE. Four models deliver a rather good consistency in the range of 9.3 to 15 mWm-2 (warming), which is significantly smaller than the estimates found above for 10 % and 20 % coverage of global UTCs with Reff = 10 µm. Only if we further reduce the global coverage to 1 % (to be consistent with the contrails coverage), is the CRE of UTCs in the range of -22 to 18 mWm-2 for Reff = 5 µm and -5 to 9 mWm-2 for 10 µm, where the warming of hexagonal shapes and aggregates fits well with the contrails. However, these estimates indicate a significantly larger CRE for UTCs than contrails.

Although the presented study specifies only first estimates of the CRE under various conditions, the results presented here show the priority to better constrain the number (coverage) and vertical thickness of UTCs in the lower stratosphere and tropopause region. This would help to determine how important it is to consider UTCs in future climate model simulations. This would also help to prove whether UTCs are at least to some extent considered in the current very common cloud dataset composed of radar and lidar space measurements e.g..

Such optically thin clouds, like those reported above, may be important for the radiation budget of the upper troposphere and lower stratosphere and thus for modifying the mean tropopause temperature. They may thus indirectly control the amount of water vapour entering the stratosphere and influence circulation pattern. Radiative vertical flux profiles could be converted to heating rates e.g., and a large cloud heating rate was shown to strongly modulate circulation patterns e.g.. This activity could be the topic of follow-up work of the present study.