Vertical cloud structure of warm conveyor belts – a comparison and evaluation of ERA5 reanalyses, CloudSat and CALIPSO data

Warm conveyor belts (WCBs) are important cyclone-related airstreams that are responsible for most of the cloud and precipitation formation in the extratropics. They can also substantially influence the dynamics of the cyclone and the upperlevel flow. So far, most knowledge about WCBs is based on model data from analyses, reanalyses and forecast data, with only a few observational studies available. The aim of this work is to gain a detailed observational perspective on the vertical cloud and precipitation structure of WCBs during their inflow, ascent and outflow, and to evaluate their representation in the new 5 ERA5 reanalysis dataset. To this end, satellite observations from the CloudSat radar and the CALIPSO lidar are combined with an ERA5-based WCB climatology for nine Northern Hemisphere winters. Based on a case study and a composite analysis, the main findings can be summarised as follows: (i) WCB air masses are part of deep, strongly precipitating clouds, with cloud-top heights at 9-10 km during their ascent, and an about 2-3 km deep layer with supercooled liquid water co-existing with ice above the melting layer. The maximum surface precipitation occurs when the WCB is at about 2-4 km height. (ii) 10 Convective clouds can be observed above the inflow and during the ascent. (iii) At upper levels, the WCB outflow is typically located near the top of a 3 km deep cirrus layer. (iv) There is a large variability between WCBs in terms of cloud structure, peak reflectivity, and associated surface precipitation. (v) The WCB trajectories with the highest radar reflectivities are mainly located over the North Atlantic and North Pacific, and – apart from the inflow – they occur at relatively low latitudes. They are associated with particularly deep and strongly precipitating clouds that occur not only during the ascent, but also in the 15 inflow and outflow regions. (vi) ERA5 represents the WCB clouds remarkably well in terms of position, thermodynamic phase and frozen hydrometeor distribution, although it underestimates the high ice and snow values in the mixed-phase clouds near the melting layer. (vii) In the lower troposphere, high potential vorticity is diabatically produced along the WCB in areas with high reflectivities and hydrometeor contents, and at upper levels, low potential vorticity prevails in the cirrus layer in the WCB outflow. The study provides important observational insight into the internal cloud structure of WCBs, and emphasises the 20 ability of ERA5 to essentially capture the observed pattern, but also reveals many smalland mesoscale structures observed by the remote sensing instruments but not captured by ERA5.

To characterise the vertical cloud and precipitation structure of the WCBs, and to gain insight into the meteorological environment they are embedded in, satellite observations from the CloudSat radar and the CALIPSO lidar are combined with ERA5 reanalyses from the ECMWF. The period chosen for the study extends from December 2006 to the end of January 2016, and the analysis is confined to Northern Hemisphere winter (December-February). Winter 2011/2012 is excluded from the study, as CloudSat was not part of the A-Train during that time period. 100

Satellite observations
Reflectivity profiles from the Cloud Profiling Radar (CPR) onboard the polar-orbiting CloudSat satellite (Stephens et al., 2002Tanelli et al., 2008) are used. The CPR is a nadir-pointing radar operating with a frequency of 94 GHz (∼ 3 mm, Wband). It provides cloud information with a vertical resolution of 485 m (oversampled to produce an effective resolution of 240 m) between the surface and 30 km altitude. The horizontal resolution is about 1.7 km in along-track direction (resulting 105 from a pulse integration period of 0.16 s), and 1.4 km in cross-track direction. In the present study, we use CloudSat reflectivity data provided by the raDAR/liDAR (DARDAR) project (Delanoë and Hogan, 2010, see below), which is interpolated to a grid with 1.1 km horizontal and 60 m vertical resolution. The minimum detectable signal of the CPR is −30 dBZ. Absorption mainly by liquid water results in a two-way attenuation of the radar signal, which can amount to more than 10 dBZ km −1 below the melting layer and even lead to a full attenuation of the radar signal in strongly precipitating systems (Mace et al., 2007; 110 Marchand et al., 2008). Reflectivity values between about −30 dBZ and −15 dBZ typically represent non-precipitating clouds, values between −15 dBZ and 0 dBZ drizzle or light rain, and values greater than 0 dBZ rain with increasing intensity (Stephens and Haynes, 2007;Haynes et al., 2009). According to Haynes et al. (2009), unattenuated near-surface reflectivity values of more than 0 dBZ (−5 dBZ) are almost certainly associated with significant surface rain (snow) rates of at least 0.03 mm h −1 . Radar signals likely contaminated by surface or clear air clutter are filtered out in the present analysis with the CloudSat cloud mask 115 from the 2B-GEOPROF product (Marchand et al., 2008). The effect of surface clutter is most pronounced below 1.2 km height (Marchand et al., 2008), which reduces the ability to investigate the cloud structure at the height of the WCB inflow.
Ice water content (IWC) profiles are obtained from the DARDAR cloud product, version v1 (Delanoë and Hogan, 2010).
They are derived using a variational method that combines CloudSat radar reflectivities, CALIPSO lidar attenuated backscatter and infrared radiometer data of the Moderate Resolution Imaging Spectroradiometer (MODIS) on-board the Aqua satellite 120 (for details see Hogan, 2008, 2010). In addition, the ice cloud estimates depend on thermodynamic variables like temperature, pressure and specific humidity from the "ECMWF-AUX" dataset, which contains ECMWF variables interpolated to the CloudSat radar bin. The CloudSat and CALIPSO products used to derive the IWC data are highly complementary and sensitive to very different powers of particle size. The radar is able to measure and penetrate optically thick clouds, but it cannot detect optically thin clouds with a reflectivity value below the minimum detectable signal of the radar (−30 dBZ). On the other providing a more detailed picture of the structure and microphysical properties of the hydrometeors than could be obtained by the individual sensors. The IWC retrievals consist of the entire frozen hydrometeor fraction, without distinction between small ice crystals and sedimenting snow flakes. For each IWC value the associated uncertainty is estimated. Uncertainties can arise, 130 for instance, from instrumental and measurement errors of the satellites, differences in the radar and lidar footprints, and errors associated with assumptions used in the variational scheme. They are expressed as one standard deviation percentage errors in the natural logarithm of the IWC and can reach up to about 60%. Despite these significant uncertainties, the DARDAR cloud product currently comprises one of the most accurate estimates of ice clouds properties (Stein et al., 2011;Eliasson et al., 2013). Like the reflectivity profiles, the IWC data is available on a grid with 1.1 km horizontal and 60 m vertical resolution. 135 2.2 ERA5 reanalyses ERA5 reanalyses from the ECMWF (Hersbach et al., 2020) are used for the WCB identification and the characterisation of the meteorological environment. ERA5 is based on the Integrated Forecast System model version cycle 41r2 that was operational in 2016. The reanalyses have a spectral resolution of T639 (corresponding to ∼31 km) on 137 vertical levels and a temporal resolution of 1 h. In this study, the fields are interpolated to a regular grid with 0.5 • horizontal resolution. 140 In ERA5, the parameterization of stratiform clouds and large-scale precipitation is based on an advanced version of the scheme developed by Tiedtke (1993) and includes prognostic variables for water vapour, cloud liquid water, cloud ice, rain, snow and grid box fractional cloud cover (ECMWF, 2016; see also Forbes and Ahlgrimm, 2014). Interactions between the various water species are described with parameterisations for condensation, deposition and freezing via stratiform and convective processes, evaporation, sublimation and melting, as well as the generation of precipitation via autoconversion, accretion 145 and snow riming. Precipitating particles have a terminal fall speed and can be advected between grid boxes by the threedimensional wind. Supercooled liquid water can exist at temperatures between 0 • C and the homogeneous freezing threshold at −38 • C. When ice and supercooled liquid co-exist, the ice crystals grow at the expense of the liquid water droplets via the Wegener-Bergeron-Findeisen mechanism. Convection is parameterised by a bulk mass flux scheme based on Tiedtke (1989), with a modified convective available potential energy closure (Bechtold et al., 2014). It considers deep, shallow and midlevel 150 convection. The collective behaviour of a range of cumulus clouds in a grid cell is represented by a single pair of plumes describing the updraft and downdraft mass fluxes associated with the cloud ensemble, including the processes of entrainment of environmental air into the cloud, and detrainment of cloud condensate into the environment.

WCB identification
The ERA5-based WCB trajectories are calculated with a slightly modified version of the algorithm developed by Madonna 155 et al. (2014). Based on the Lagrangian Analysis Tool (LAGRANTO; Wernli and Davies, 1997;Sprenger and Wernli, 2015), trajectories are started every 6 h from an equidistant grid in the lower troposphere and calculated forward for 48 h. For the climatological analysis, the starting points are located every 80 km in the horizontal direction and vertically every 20 hPa between 1050 and 790 hPa, consistent with Madonna et al. (2014). For the case study, the horizontal resolution of the starting grid is increased to 40 km. To be classified as WCB air parcels, the trajectories must experience a strong ascent of at least 160 600 hPa within 48 h in the vicinity of an extratropical cyclone, whereby extratropical cyclones are identified as two-dimensional objects based on the algorithm of Wernli and Schwierz (2006), refined in Sprenger et al. (2017). To exclude rapid ascent associated with tropical cyclones, the WCB trajectories are required to be north of 25 • N during their ascent phase (at time 24 h). With respect to the WCB identification method by Madonna et al. (2014), two modifications are made: (i) Very fast ascending trajectories that fulfil the 600-hPa ascent criterion in the first part of the 48-h period and thereafter descend again 165 are also selected. For those trajectories the pressure difference between times 0 and 48 h can be lower than 600 hPa and therefore they would have been neglected as WCB trajectories by the approach of Madonna et al. (2014). Compared to the original method, this leads to an increase in the number of identified WCB trajectories by about 35% (K. Heitmann, personal communication). (ii) WCB trajectories with a small distance to each other are clustered and considered to belong to the same WCB, with a clustering method similar to the one described in Catto et al. (2015). When one of the trajectories in the cluster is 170 collocated with a surface cyclone for at least one time step during the ascent, all the trajectories in the cluster are considered as WCB trajectories. Compared to the original algorithm, where every single trajectory is required to be collocated with a surface cyclone, this leads to a further increase in the number of WCB trajectories by about 10%. Despite the significant increase in the number of identified WCB trajectories with respect to the original WCB identification criterion, tests have shown that the modifications do not affect the findings of this study.

Matches between WCB trajectories and CloudSat -CALIPSO overpasses
To combine the ERA5-based WCB trajectories with the satellite data, all WCB trajectories are selected that are overpassed 180 by the CloudSat -CALIPSO satellites. Since the individual satellite profiles along the tracks are available every about 0.16 s and therefore much more often than the hourly ERA5 data, the ERA5 fields are assumed to be representative for a 1-h time range of ± 30 minutes around each full hour. A match between a WCB trajectory position and the satellites' track occurs when the trajectory is located within 50 km horizontal distance of the satellite orbit during this 1-hour window (see Fig. 2b). In total, 509'042 matches are identified between individual WCB trajectories and A-Train overpasses in the nine winters. These 185 matches are associated with about 9'000 different WCB clusters.
In the climatological study, several satellite profiles are attributed to each matching WCB trajectory. They are then averaged to increase the representativity of the observations (see schematic illustration in Fig. 1). In total, 113 satellite profiles are averaged per WCB match -that is, the profile with the closest distance to the WCB air parcel, plus the 56 preceding and the 56 succeeding profiles. With a distance of 1.1 km between each satellite profile, the 113 assigned profiles correspond to a 190 track segment length of about 124 km and therefore approximately the effective horizontal resolution of ERA5 (four times the horizontal grid spacing), i.e., the smallest scale the model is able to resolve fully (see Abdalla et al., 2013). This allows for a better comparison between the observations and the model data. Consistent with earlier work (Illingworth et al., 2007;Delanoë et al., 2011), it is assumed that the narrow satellite track is representative for the three-dimensional model grid box. 195 In addition to the analysis of the entire climatology of matching WCB trajectories, those with highest reflectivity values given by CloudSat are investigated separately. More specifically, from all 509'042 matches, in each 0.5 km height bin the 5% with highest reflectivities at their respective height are selected and referred to as "strong WCBs". These top 5% in terms of reflectivity are assumed to be the strongest cloud-and-precipitation producing WCB air parcels. Comparison of the entire climatology and the subcategory of "strong WCBs" allows to assess differences between the two categories in the cloud and 200 precipitation structure, the geographical distribution, and the meteorological environment.

Case study of a representative North Pacific WCB
In this Section we examine the cloud and precipitation structure of a representative WCB that occurred in January 2014 over the central North Pacific. The associated cyclone underwent an explosive deepening and was observed by the A-Train at the time of its strongest intensity (minimum sea level pressure of 975 hPa), around 00 UTC 3 January 2014. At this time the infrared 205 satellite image and the overlaid ERA5 fields in Fig. 2a reveal a comma cloud pattern with high clouds along the cold, the warm and the intense bent-back front, and a distinct dry slot that wraps around the storm centre below a cyclonically breaking upper-level wave, shown by the 2-pvu contour on 315 K. The yellow contour outlines the grid points where, according to the reanalysis data, at least one WCB air parcel is present somewhere in the vertical column. The large area encompassed by this contour indicates that the entire frontal region is influenced by WCB air. Note that these air parcels belong to WCB trajectories 210 with a range of different starting times and vertical positions, with some still located at low levels at the beginning of their twoday ascent, some in the middle of their ascent, and some already located in the upper troposphere at the end of their two-day ascent. As an example, Fig. 2b shows WCB trajectories with starting times at 06 UTC 2 January, and their position 18 h later (black dots), at the time of the satellite overpass.
The A-Train moved from the southeast to the northwest over the warm sector, the cold and the warm fronts of the mature 215 cyclone (blue line in Fig. 2a,b), and thereby simultaneously captured parts of the WCB inflow, ascent and outflow. In the warm sector, south of 27 • N, the reflectivity profile measured by CloudSat (Fig. 3a,b) reveals shallow-to-midlevel convection above the WCB inflow, which is corroborated by the negative vertical gradient in equivalent potential temperature (θ e ) between the surface and 4 km height. Between 27 • and 33 • N the WCB inflow is cloud-free and located below thin cirrus clouds in the WCB outflow that increase in thickness toward the cold front. At the cold front, between 33 • and 40 • N, and above large 220 parts of the surface warm front, between 42 • and 46 • N, most of the deep cloud system is associated with WCB air (see purple dots in Fig. 3b that mark WCB air parcels). The high reflectivities (Fig. 3a) and satellite-retrieved IWC values (Fig. 3c) below 6-8 km indicate strong precipitation in the form of snow above and rain or melting snow below the 0 • isotherm. Unlike radars operating at centimetre wavelengths, which exhibit a clear reflectivity peak at the melting layer, CloudSat's millimetre operating wavelength does not lead to a typical bright band at the melting layer, but rather a dim band with reduced reflectivities 225 (Sassen et al., 2007;Heymsfield et al., 2008). The dim band is due to snowfall attenuation and non-Rayleigh scattering effects, and it is evident both at the cold and at the warm front in the strongly precipitating cloud system (Fig. 3a). Above 6-8 km, at temperatures colder than about −20 • C, the lower reflectivity and IWC values suggest ice clouds rather than falling snow. At the cold front, in the unstable air south of 37 • N the presence of some narrow columns with particularly high reflectivities suggest convective WCB ascent embedded in the frontal cloud. In the northern part of the cold front, the higher static stability and 230 horizontally relatively uniform reflectivities point to a mainly stratiform cloud structure. At the warm frontal zone the WCB intersections with the satellite track indicate a gentle slantwise ascent along the tilted moist isentropes (Fig. 3b). North of 46 • N the associated ice clouds decrease in thickness with increasing distance from the surface warm front, as the cloud base slopes upward along the moist isentropes and the cloud-top height decreases. Figure 3d shows in colours the sum of the prognostic cloud ice and snow variables of ERA5, interpolated along the satellite 235 track. To allow for a better comparison with the observations, in Fig. 3e the satellite-retrieved IWC is shown as the running mean over 113 satellite profiles, which corresponds to a track length of 124 km and thereby approximately the effective resolution of ERA5 (i.e., four times the horizontal grid spacing, see Abdalla et al., 2013). As noted in Sect. 2.1, the observations and ERA5 are not entirely independent, as the satellite-retrieved IWC relies on thermodynamic variables from ECMWF analyses.
In particular, the retrieved IWC is based on temperature profiles from the ECMWF to locate the melting layer height, which 240 implies that by design the melting layer agrees well with ERA5. Despite this constraint, the satellite retrievals contain much additional information that is independent from the ECMWF data, such that the comparison with ERA5 is meaningful and provides important insight into the quality of the model data. Fig. 3d and e shows that ERA5 captures the location of the cloud system and the broad ice and snow structure remarkably well. The sum over the ice and snow values strongly increases toward the melting layer and peaks right 245 above the melting layer in the deep frontal clouds, where most of it is present as falling snow (see thin black contours in Fig. 3d). However, the model considerably underestimates the peak values between the melting layer and the −20 • C isotherm (maxima of 1050 mg m −3 in ERA5 compared to 1630 mg m −3 in the observations), which are most likely associated with mixed-phase clouds. The underestimation is particularly pronounced in the convective clouds south of 27 • N. The one standard deviation percentage errors associated with the IWC retrievals in this case study are about 20-30% in the thin ice clouds at 250 upper levels, 5-20% around the −20 • C isotherm and 10-40% near the melting layer (not shown). The differences between the observations and ERA5 near the melting layer are therefore outside the error range of the observations, even for values of 40%. Furthermore, along the entire cross section the cloud edges are less sharp in ERA5 than in the observations, and the transition between cloudy and cloud-free regions is smoother. Nevertheless, comparison with ERA5's predecessor, ERA-Interim, reveals a strong improvement in the ice cloud representation in ERA5 (Binder, 2016). In ERA-Interim, the agreement 255 with the observed IWC is very poor, in particular in the mixed-phase clouds, where the underestimation of the high values close to the melting layer amounts to several orders of magnitude. The significant improvement of the representation from ERA-Interim to ERA5 can mainly be explained by a major upgrade of the cloud and precipitation parameterisation (see also Delanoë et al., 2011;Forbes and Ahlgrimm, 2014): While ERA5 is based on prognostic variables for cloud ice, snow, liquid water and rain, in ERA-Interim precipitation and mixed-phase clouds are described by diagnostic formulations, and snow is In summary, the case study of this North Pacific WCB reveals that (i) WCB air parcels form part of vertically extended, strongly precipitating clouds, but not the entire frontal cloud system is WCB air, (ii) convection can occur in the WCB inflow and ascent region, consistent with previous studies (e.g., Crespo and Posselt, 2016;Oertel et al., 2019), and (iii) the ERA5 reanalysis with prognostic variables for snow and ice is able to capture the broad structure and distribution of the frozen 265 hydrometeor fraction associated with the WCB cloud, but the peak values are underestimated.

Climatological analysis of the WCB cloud structure
In this Section the WCB clouds and their meteorological environment will be characterised climatologically for nine Northern Hemisphere winters. We will first discuss the spatial distribution of the matches between WCB trajectories and the A-Train, and then investigate their vertical structure in satellite observations and reanalysis fields.  Atlantic storm track regions between about 30 • and 60 • . This spatial pattern reflects the winter climatological distribution of WCBs during their inflow, ascent and outflow (blue contours). In general, in the southwestern ocean basins most WCB air 275 parcels were observed in the inflow, i.e., when the WCB trajectories were below 2 km height (pressure levels > 800 hPa), in agreement with the climatological maximum of WCB starting positions (Madonna et al., 2014). In contrast, in the northeastern part of the oceans, at the end of the storm tracks, the majority of the matches occurred in the outflow, i.e., when WCB trajectories were above 7 km height (pressure levels < 400 hPa). Overall, the matches are distributed over a wide altitude range between the surface and 13 km height, with the highest numbers below 2 km in the inflow and in particular between 7 and 280 10 km in the midlatitude outflow (Fig. 4c). The latitude of the matches increases from about 25 • -50 • N in the WCB inflow to 35 • -75 • N for air parcels at 8 km height (mean and 10-90 interpercentile range in green in Fig. 4d), reflecting the poleward motion typically occurring during the WCB ascent. Note, however, that the WCB air parcels in the different height bins generally belong to different WCB trajectories -only in rare cases the same trajectory has been observed more than once by the narrow CloudSat-CALIPSO tracks. Matches above 8 km typically occurred again at lower latitudes (where the tropopause is higher 285 than in polar region), ranging from about 30 • to 60 • N for air parcels at 10 km height, and from 10 • to 35 • N for very high outflow above 12 km. These matches are most likely associated with WCBs in convectively active subtropical systems.
The matches with "strong WCBs", that is, the 5% of the air parcels in each 0.5 km height bin with the highest CloudSat radar reflectivities (see Section 2.5), are mainly located over the North Pacific and North Atlantic (Fig. 4b). Interestingly, in the inflow and early ascent (< 3.5 km) the mean latitude of the WCB air parcels with exceptionally strong reflectivities is further 290 north than the mean over all trajectories, with most air parcels located between 30 • and 60 • N (mean and 10-90 interpercentile range in blue in Fig. 4d). The opposite is true at higher altitudes, where the strong WCBs are typically located much further south than the entire climatology. Between 4 and 10 km height their mean latitude is approximately constant around 38 • N, and matches at higher levels occur again at very low latitudes and are probably related to subtropical cyclones. Note, again, that different WCBs contribute to the strong category in each height bin, and the general decrease in the mean latitude from inflow 295 to outflow observed for the strong WCBs does not imply an equatorward ascent. All in all, the analysis shows that WCBs with exceptionally strong radar reflectivities in their inflow occur further north than the mean of all matches, while higher than usual radar reflectivities in the WCB ascent and outflow are found further south.

Composites of reflectivity and DARDAR-retrieved IWC
To investigate the cloud structure of the WCBs during their inflow, ascent and outflow, we create vertical composites of the 300 satellite observations, separately for different WCB heights. Hereby, all matching WCB air parcels are classified into 0.5 km height bins, with the number of matches per bin shown in the histogram in Fig. 4c. We will first examine the composites associated with the entire climatology, and then compare them to the subcategory of strong WCBs. Figure 5 shows composites of vertical profiles of CloudSat reflectivity (Fig. 5a) and DARDAR-retrieved IWC (Fig. 5b) as a 305 function of the height at which the A-Train profile matched with a WCB trajectory. This height is referred to as z W CB . For instance, for matches at a height of z W CB = 3 km, the radar reflectivity shows median values exceeding −6 dBZ from near the ground to about 6 km altitude, whereas for matches above z W CB = 7 km, radar reflectivities are below −30 dBZ, if the median is calculated over all WCBs (Fig. 5a). Thus, with increasing z W CB the composites give insight into the vertical cloud structure associated with the WCB inflow (z W CB = 0-2 km), ascent (z W CB = 2-7 km) and outflow (z W CB >7 km), respec-310 tively. Comparison with the latitude-height distribution of the matches (green line in Fig. 4d) shows that up to z W CB ≈ 8 km the satellite composites can be interpreted as a -somewhat irregular -vertical cross section from south to north through poleward ascending WCB air. However, keep in mind that the matching WCB air parcels in the different height bins correspond to different WCB trajectories, such that Fig. 5 shows a composition of single WCB positions and not the development along individual trajectories. The calculation of median rather than mean profiles of the matches is motivated by the fact that in the 315 case of reflectivity the median allows us to take into account clear-sky values, and in the case of IWC the mean would be dominated by large values. As seen in the case study, several matches can occur on top of each other in the same cloud system (see purple dots in Fig. 3b). In these cases, in the composites the same satellite profile is taken into account for each match separately, i.e., it is present more than once along the x-axis. In summary, this sophisticated compositing approach is able to provide representative vertical profiles of observed radar reflectivity and IWC along WCBs in the Northern Hemisphere storm 320 track regions in winter.

All WCBs
To quantify how often WCB matches occur on top of each other in the same cloud system, the contours in Fig. 5a,b show the relative WCB trajectory frequency, which is the number of matches in a certain 0.5 km profile height bin normalised by the total number of matches in the specific WCB height bin. For instance, a relative frequency of 10% at z W CB = 3.75 km and a profile height z prof = 9.75 km indicates that 10% of the WCB trajectories located between 3.5 and 4 km height have another about 36 • and 45 • N in the deep cold and warm frontal clouds (Fig. 3b). For matches at z W CB = 1 km height, only in 5% of the cases another WCB trajectory is located on top of them at 9.5-10 km height. The vertical area in between can either also be associated with WCBs (as in the case study between 36 • and 42 • N; Fig. 3b) or not (as between 30 • and 36 • N in Fig. 3b)the frequency values do not provide insight into the vertical connectivity of the WCB air. By definition, the frequency is 100% 330 along the diagonal line, and the slower its decrease away from the diagonal the more the observed reflectivity and IWC patterns are associated with WCB air.
In the reflectivity composite, the white areas indicate either clear air, or, in particular below about 0.8 km height, ground clutter, which both have been filtered out (see Section 2.1). In the IWC composite, the white areas indicate the absence of frozen hydrometeors. The cloud-top heights according to the radar reflectivities are everywhere lower than those according 335 to the IWC retrievals. This can be explained by the inability of the radar to detect thin ice clouds with reflectivities below −30 dBZ, whereas for the IWC retrievals the radar measurements are combined with lidar data that is strongly sensitive to optically thin ice clouds (see Section 2.1).
Overlaid on top of the observed fields are ERA5-based temperature contours (red dashed lines in Fig. 5a,b) and the dynamical tropopause (brown 2-pvu contour in Fig. 5a,b). From z W CB = 0 km up to about z W CB = 8 km, the melting layer and the 340 dynamical tropopause decrease in height (Fig. 5a,b), consistent with the increase in mean latitude (green line in Fig. 4d), while between z W CB = 8 and 14 km the transition from predominantly subpolar to subtropical outflow is associated with an increase in their heights. At the height of the WCB inflow (z W CB and z prof ≈ 0-2 km), liquid clouds with reflectivities of about −10 to −5 dBZ are present above the ground clutter (Fig. 5a), indicating some drizzle or light rain (Stephens and Haynes, 2007).
Above the inflow, the small non-zero median IWC values reveal the presence of thin ice clouds that extend up to about 9-10 km 345 height (Fig. 5b). As suggested by the low reflectivities below −30 dBZ, this is most likely non-precipitating cirrus. The 5% WCB trajectory contour approximately follows these ice clouds, indicating that a small fraction of them is associated with WCB air.
During the ascent (z W CB ≈ 2-7 km) WCBs form part of deep clouds, with cloud-top heights just below the ERA5-based dynamical tropopause at 9-10 km (Fig. 5a,b). The clouds have relatively high reflectivity values up to > 4 dBZ and -between 350 the melting layer and about −20 • C -high DARDAR-retrieved IWC with peaks at 260 mg m −3 , which indicates precipitation in the form of snow above and rain below the melting layer. The highest IWC values occur approximately at the height of the WCB, whereas the highest reflectivities are present just below the WCB slightly above the melting layer. The peak values, and therefore most likely the strongest surface precipitation, occur when the WCB trajectories are at a height of about z W CB = 3.5-4 km. Compared to the inflow, the WCB trajectory densities above and below the diagonal are higher in most of 355 the ascent region, indicating a stronger contribution of WCB air to the reflectivity and IWC profiles. Of course, there is a large case-to-case variability, and the median profiles contain cloud systems that are almost entirely formed by strongly ascending WCB air, and others where only a small part of the deep cloud is WCB air. The decrease in the WCB densities to only about 10% at cloud base and cloud top suggests that the latter is often the case, i.e., the WCB ascent is typically embedded in a deeper cloud that forms partially due to air parcels with a weaker ascent than required for the WCB criterion.

360
In contrast to the ascent, the WCB outflow (z W CB >7 km) is located within an about 3 km deep cirrus layer with low reflectivities below the sensitivity of the radar (Fig. 5a) and low IWC (1-10 mg m −3 , Fig. 5b). Their cloud bases and tops increase gradually with increasing outflow height, which suggests a predominantly slantwise ascent along the baroclinic zone, similar to the pattern observed in the case study north of 46 • N (Fig. 3). The deep cirrus layer and the extension of ice clouds above the WCB outflow level are in line with the findings of Wernli et al. (2016), who showed that the WCB outflow is often 365 associated with cirrus clouds that form by freezing of liquid droplets during the strong ascent, while above the outflow in situ ice cloud formation can occur in response to the strong lifting associated with the WCB.

Strong WCBs
Analogous to the satellite composites created for all WCB matches, Fig. 5c,d shows the median reflectivity and IWC profiles for the subcategory of strong WCBs, together with ERA5-based temperature contours and the dynamical tropopause. The 370 slight decrease in latitude with increasing height of the WCB matches (blue line in Fig. 4d) is reflected in a general increase in the melting layer height and the tropopause along the x-axis (Fig. 5c,d), in contrast to the decrease observed for the entire climatology ( Fig. 5a,b). It is again important to keep in mind that these composites cannot be interpreted in a Lagrangian way; the WCB air parcels in the different height bins generally belong to different WCB trajectories and the overall decrease in latitude with increasing z W CB does not imply an equatorward ascent.

375
At the height of the WCB (along the diagonal), but also above and below, the reflectivities exceed those of all matches by 10-25 dBZ. Above the melting layer this goes along with DARDAR-retrieved IWC values that are a factor of 5-5000 larger than those of all matches (Fig. 5d). This confirms that the top 5% of the matches in terms of radar signal are indeed very strongly cloud-and-precipitation-producing WCB trajectories. Deep clouds extending from the surface to the tropopause occur not only in the ascent region, but -in contrast to all matches -also above the inflow and in the outflow. The cloud-top height 380 according to the IWC pattern is at 10 km above the air parcels in the WCB inflow, at 11 km for the ascending ones and at 11-14 km for the outflow, and it is thus everywhere higher than for the entire climatology. The decrease in the WCB trajectory densities away from the diagonal is much slower than for all matches, implying a stronger contribution of WCB trajectories to the formation of the deep clouds. Presumably, WCB trajectories in the inflow, ascent and outflow are often located on top of each other in the same cloud system, as in the case study at the cold front (Fig. 3b). These results also indicate that a vertically 385 deep layer of trajectories fulfilling the WCB criterion is likely leading to particularly high reflectivities and intense surface precipitation. The peak reflectivities (13.9 dBZ compared to 4.2 dBZ for all matches) occur at the height of the ascending WCB and not below as for all matches, and the signal decrease below the WCB indicates strong snow and rain attenuation. The IWC maxima (1180 mg m −3 compared to 260 mg m −3 for all matches) are collocated with the reflectivity maxima. They extend over several WCB heights along the diagonal, from about z W CB = 2.5 km to z W CB = 5 km, in contrast to the rather localised 390 peak at z W CB = 3.5-4 km observed for all matches. A secondary reflectivity and IWC maximum occurs at z W CB > 12 km in the middle troposphere, below the WCB outflow, and the low latitude of these matches (Fig. 4d) suggests that it is most likely associated with subtropical cyclones.

Meteorological environment in ERA5
To analyse the WCB clouds and the differences between all and strong WCBs in more detail, we complement the satellite 395 observations with model data from ERA5. This allows us to gain insight into the meteorological environment associated with the matches, and, at the same time, to compare the modelled ice and snow water content with the DARDAR observations. To this end, vertical profiles of the ERA5 fields are interpolated to the position of the matches, and composites equivalent to those discussed in the previous Section are created. Again, we will first examine the fields for all WCB matches and then compare them with the subcategory of strong WCBs.

All WCBs
The vertical composites of various ERA5 fields are shown in Fig. 6, separately for different WCB heights. Except for the frozen and liquid hydrometeor content the mean rather than the median profiles are shown in each height bin, as the fields are slightly smoother, but the median profiles are very similar. The frozen hydrometeor fraction, i.e., the sum of the prognostic cloud ice and snow variables (Fig. 6a), resembles the observed pattern in Fig. 5b remarkably well. However, in the ascent region between the 405 melting layer and about −20 • C the peak values are underestimated (160 mg m −3 in ERA5 vs. 260 mg m −3 in the observations), whereas above the inflow and below the outflow the values are overestimated, and the cirrus layer associated with the outflow is considerably deeper than in the observations. Also the transition between cloudy and cloud-free regions is smoother. Since the composites consist of a large number of satellite profiles, the mean errors associated with the IWC retrievals are much lower than the single values in the case study, with maximum errors of 0.17% coinciding with the maximum observed IWC 410 values (not shown). The difference between the IWC values in ERA5 and the observations are therefore much larger than the observational uncertainty range, both for the underestimated values in the ascent region and the overestimated values above the inflow and below the outflow. The underestimation of the peak values close to the melting layer is consistent with the case study. It occurs in a 2-3 km deep layer with mixed-phase clouds (Fig. 6b), which are known to be difficult to simulate and associated with large uncertainties in many numerical weather prediction and climate models (e.g., Morrison et al., 2003;415 Illingworth et al., 2007;Klein et al., 2009;Delanoë et al., 2011).
The ice clouds in ERA5 coincide with high relative humidities with respect to ice (RH ice ; Fig. 6c). The values are close to saturation (> 80%) along most of the WCB on the diagonal, and they are particularly high in a deep layer in the ascent region, where the strong updraft continuously leads to new ice cloud formation. At lower altitudes, the inflow and especially the ascent regions are also associated with high cloud liquid water and rain water contents (Fig. 6b). The liquid hydrometeor 420 fraction extends from the surface up to about 5-6 km height, with a 2-3 km deep layer of supercooled liquid water co-existing with ice above the melting layer. The highest liquid hydrometeor values occur during the WCB ascent (z W CB at ≈ 2-4 km) slightly below the WCB and the melting layer, in the lower part of the vertically extended cloud. Accordingly, also the surface precipitation has a maximum when the WCB is at 2-4 km height, with values of about 1.8 mm h −1 (solid green line in Fig. 7). Surface precipitation is also high in the WCB inflow (1.2-1.5 mm h −1 ), whereas it is rather weak below the outflow 425 (0.3 mm h −1 ). For z W CB > 6 − 7 km, the frozen and liquid hydrometeors are vertically disconnected (Fig. 6a,b), consistent with the tongue of relatively low RH ice < 70% in between (Fig. 6c). This suggests that the weak surface precipitation evident for z W CB > 6 − 7 km (Fig. 7) is not associated with the WCB, but with the low-level warm clouds present at 1-2 km height below the WCB (Fig. 6b). Throughout the inflow, ascent and outflow, most of the surface precipitation is associated with the large-scale cloud scheme (Fig. 7). Convective precipitation is significantly lower, but has a small peak in the inflow and early 430 ascent. The presence of convection in the inflow is further corroborated by very low moist static stability values (i.e., weak vertical gradients in equivalent potential temperature, dθ e /dz) in that region (Fig. 6d,e). Higher stabilities are present below the ascending WCB, where the tilted moist isentropes indicate a lifting over the cold or warm front (Fig. 6d). At higher altitudes during the ascent, at and above the height of the WCB, the stabilities are again lower and indicate some convective motion.
The strong cloud and precipitation formation goes along with elevated PV values in the lower and middle troposphere, and 435 low PV in the WCB outflow (Fig. 6f). The elevated low-and mid-level PV (> 0.5 pvu) extends over a broad and deep region in the inflow, ascent and early outflow (z W CB at ≈ 1-10 km) and coincides with increased stability (Fig. 6e). Two areas with particularly high PV (> 0.7 pvu) are located slightly below the ascending WCB (z W CB at ≈ 2-5 km; Fig. 6f). One of these two high low-level PV areas is located between the melting layer and the observed and modelled snow and ice maximum at WCB height (Figs. 5b and 6a), and it coincides with the radar reflectivity maximum (Fig. 5a). Most likely, latent cooling of the 440 melting layer, as well as latent heating due to freezing of cloud water and vapour deposition on ice particles along the WCB, both contribute to the PV maximum in between. The agreement with the observations indicates that in addition to the good representation of cloud ice and snow in ERA5, the reanalysis data is able to capture the cloud-diabatic processes associated with WCBs and their impact on the dynamics very well. The second area with high low-level PV (at z W CB ≈ 2-3 km) is located below the melting layer at 1-2 km profile height and coincides with the maximum in the modelled cloud rain and liquid water 445 content (Fig. 6b), which suggests that here the PV production is mainly associated with latent heating due to condensation, and potentially some below-cloud cooling due to rain evaporation. This PV maximum is not accompanied by a corresponding maximum in reflectivity (Fig. 5a), probably as a result of the two-way attenuation of the radar signal close to the surface in strongly precipitating systems. In the WCB outflow, the PV values are anomalously low (< 0.2 pvu; Fig. 6f) and coincide with reduced vertical stability (Fig. 6e). As a consequence of the low-PV air in the outflow, the tropopause above is elevated, and a 450 sharp vertical PV gradient is established between the low values at WCB height and the high values in the stratosphere. The elevated tropopause also goes along with an increased vertical gradient in equivalent potential temperature and a layer with peak vertical stability in the stratospheric air above the WCB outflow (Fig. 6d,e), which is referred to as tropopause inversion layer (TIL; Birner et al., 2002). As discussed by Kunkel et al. (2016), the TIL typically forms above the WCB, because (i) the low-level cloud-diabatic processes lead to an increase in the vertical motion and an enhancement of static stability above the 455 updraft region, and (ii) the upward transport of moisture into the tropopause region and the formation of high-level ice clouds goes along with strong radiative cooling at the tropopause, which contributes to a further enhancement of the TIL.

Strong WCBs
The vertical composites of the ERA5 fields for the subcategory of strong WCBs are shown in Fig. 8. Again, the reanalysis correctly captures the broad structure and distribution of ice and snow along the WCBs (compare Fig. 8a and Fig. 5d), but 460 underestimates the peak values in the mixed-phase layer (540 mg m −3 in ERA5 vs. 1180 mg m −3 in the observations). The observational uncertainty of the IWC values is slightly larger than for the entire climatology, with maximum values of about 1% in the ascent region near the melting layer (not shown), but the difference between the observed and ERA5-based IWC maxima is still significantly larger than the uncertainty range of the observations. Consistent with the satellite measurements ( Fig. 5c,d), throughout the inflow, ascent and outflow the modelled clouds associated with the strong WCBs are considerably deeper than those associated with the entire climatology, their hydrometeor contents are higher, the layer with mixed-phase clouds is deeper (Fig. 8a,b), and RH ice is higher (Fig. 8c). This goes along with considerably higher surface precipitation along the entire WCB, with peak values above 3 mm h −1 when the air parcels are at 3.5 km height, and significant amounts also in the inflow and below the outflow (solid blue line in Fig. 7). In contrast to all WCB matches, there is no gap between the frozen and liquid hydrometeors throughout the inflow, ascent and outflow (Fig. 8a,b), consistent with the higher RH ice (Fig. 8c). This 470 suggests that also above z W CB ≈ 6 km the surface precipitation is coming from the WCB, and not from the low-level warm clouds as in the case of all matches. Along the entire WCB, most of the precipitation is again associated with the large-scale cloud scheme. The strongest convective precipitation occurs for WCBs around 4-5 km height and is potentially linked to a local minimum in moist static stability in the lower troposphere in that region (Fig. 8d,e). High values in the convective precipitation are also present at z W CB > 12 km, where high reflectivities and IWC values have been observed below the WCB outflow in 475 Fig. 5c,d. The presence of convection in this region is further supported by the high θ e values (Fig. 8d), the weak stratification ( Fig. 8e) and the high RH ice (Fig. 8c) throughout the depth of the troposphere. As mentioned in Section 4.2.2, this secondary cloud and precipitation maximum is most likely linked to subtropical cyclones.
The stronger cloud and precipitation formation in the subcategory of strong WCBs is reflected in stronger low-level PV production, in particular for WCBs in the inflow and early ascent, with peak values > 0.9 pvu (Fig. 8f). In contrast to the 480 entire climatology, where the highest PV values are located just below the WCB, for the strong category they occur along the WCB on the diagonal and coincide with the observed reflectivity and ice and snow maxima (Fig. 5c,d). Along the WCB, we expect the strongest latent heating due to condensation, freezing and vapour deposition on ice, consistent with the relative humidity maximum (Fig. 8c). Thus, the positive PV maximum coincides with the latent heating maximum, which is in line with the findings from previous studies (e.g., Wernli and Davies, 1997). In the WCB outflow, the PV values are anomalously 485 low (< 0.2 pvu). As for the entire climatology, above the outflow the tropopause is elevated and a tropopause inversion layer is evident (Fig. 8e,f).

Summary and discussion
In this study, ERA5 reanalyses have been combined with satellite observations from the polar-orbiting CloudSat radar and CALIPSO lidar to gain a detailed observational perspective on the vertical cloud structure of WCBs during their inflow, ascent 490 and outflow, and to evaluate their representation in ERA5. To this end, more than 500'000 matches between the satellite observations and ERA5-based WCB trajectories (corresponding to about 9'000 different WCB clusters) were evaluated during nine Northern Hemisphere winters in a composite analysis and a detailed case study. The majority of the matches occurred over the ocean basins in regions of high climatological WCB frequencies and can therefore be considered as representative.
The satellite observations revealed that the WCBs form part of vertically extended, strongly precipitating clouds, in particular 495 during their ascent, with cloud-top heights at 9-10 km. In some cases the entire cloud system is associated with WCB air, but often the cloud parts below and above the WCB air parcels form in air with a comparatively weak ascent below the WCB threshold. Convection can occur above the WCB inflow and during the ascent, in agreement with recent studies on convection embedded in WCBs (e.g., Crespo and Posselt, 2016;Flaounas et al., 2016;Oertel et al., 2019). In the upper troposphere, after the main ascent phase, the WCBs are typically located near the top of an about 3 km deep layer with cirrus clouds.

500
According to ERA5, high low-level PV occurs below the ascending WCB in the lower part of the vertically extended cloud. The strongest low-level PV production occurs at about 3 km height between the melting layer and the ascending WCB and coincides with the radar reflectivity maximum. It is most likely produced by a combination of diabatic heating due to freezing of cloud water and depositional growth of ice particles at the WCB height and diabatic cooling from snow melting below. A second area with particularly strong low-level PV production occurs at about 1-2 km height, below the WCB and 505 the melting layer, in a region with strong cloud-condensational heating, and possibly some below-cloud evaporative cooling.
The occurrence of the strongest positive PV anomalies below rather than at the WCB height is surprising, and the potentially important contribution of various in-and below-cloud microphysical processes to the low-level PV production is in line with the findings from recent modelling studies (Joos and Wernli, 2012;Crezee et al., 2017;Attinger et al., 2019).
The WCB trajectories with the highest reflectivity values ("strong WCBs") have mainly been observed over the North At-510 lantic and North Pacific, and -except in the inflow -at relatively low latitudes (∼ 38 • N). They are associated with particularly deep and strongly precipitating clouds that occur not only during the ascent, but also in the inflow and outflow region. Compared to the climatology of all WCBs, the hydrometeor content is considerably higher and the surface precipitation is stronger.
The low-level PV production is larger and has its peak in the inflow and early ascent at the height of the WCB, and it coincides with high reflectivities and hydrometeor values. The agreement of the positive PV anomaly with the region of strong cloud for-515 mation is characteristic for strongly ascending WCB air masses, where the PV anomaly, which is produced below the diabatic heating maximum, is advected upward toward the heating maximum (Wernli and Davies, 1997).
The comparison between the satellite retrievals and ERA5 showed that the reanalyses are able to capture the main structure of the WCB clouds in terms of position and thermodynamic cloud phase. The spatial pattern of the frozen hydrometeor fraction (ice and snow) is in good agreement with the observations, in particular at high altitudes, where most of the frozen fraction 520 is present as ice rather than falling snow. However, the peak values in the mixed-phase cloud regime near the melting layer are underestimated by a factor of 1.6 for the entire climatology and a factor of 2.4 for the subcategory of strong WCBs.
This corroborates the findings from many other studies that mixed-phase clouds are difficult to simulate accurately (e.g., Illingworth et al., 2007;Delanoë et al., 2011). The co-existence of ice, supercooled liquid water and water vapour, and the complex interaction of various microphysical processes, render their understanding and parameterization in numerical weather 525 prediction and climate models particularly challenging. Nevertheless, compared to the older reanalysis dataset ERA-Interim (Dee et al., 2011), where the microphysical parameterisations are based on simplified diagnostic relationships for snow and mixed-phase clouds, the improved scheme in ERA5 with prognostic variables for cloud ice, snow, liquid water and rain leads to a much more realistic representation of the WCB cloud pattern (Binder, 2016). This is consistent with the findings from Delanoë et al. (2011) and Forbes and Ahlgrimm (2014), who also compared CloudSat-CALIPSO observations with two ECMWF 530 models with schemes similar to the ones in ERA5 and ERA-Interim, respectively, and found a significant improvement in the ice-cloud parameterization with the upgrade from the diagnostic to the prognostic representation of mixed-phase clouds and precipitation. As a caveat of the present study, it should be noted that the DARDAR-retrieved IWC depends on thermodynamic variables like temperature, pressure and specific humidity from ECMWF analyses and is therefore not entirely independent of the ERA5 data being evaluated. This illustrates the challenge of finding completely independent observations to validate cloud 535 variables in model data. Nevertheless, the satellite retrievals contain much additional information not incorporated in ERA5 and thereby they allow for a meaningful comparison of the two data sets.
Following earlier studies (e.g., Illingworth et al., 2007;Delanoë et al., 2011), in the present analysis it has been assumed that the cloud structure observed along the narrow two-dimensional satellite track is representative for the entire three-dimensional volume of the model grid box. Despite a quite good agreement between ERA5 and the observations, it is possible that this 540 assumption is not entirely justified and the clouds observed by the satellite are not representative for the larger-scale features. As proposed by Delanoë et al. (2011), additional information on the large-scale environment could be obtained from other instruments onboard the A-Train satellites with a wider swath width, in order to better assess the representativity of the measurements.
The CloudSat and CALIPSO measurements have provided a much needed, detailed observational perspective into the in-545 ternal cloud structure of WCBs, and have revealed many small-and mesoscale structures not resolved by the temporally and spatially much coarser-resolution model data that has mainly been used so far to study WCBs. The measurements complement the insight gained on WCBs from recent modelling studies with high-resolution convection-permitting simulations (e.g., Oertel et al., 2020). In future work, the large number of WCB trajectories observed by CloudSat and CALIPSO could still be exploited in more detail, both in case studies and climatological analyses. They could be classified, for instance, according to 550 different criteria like the position relative to the cyclone centre and the stage of the cyclone life cycle, the ascent behaviour (slantwise vs. convective), the outflow curvature (cyclonically vs. anticyclonically), the amplitude of the low-level positive and upper-level negative PV anomalies or the geographical region, in order to assess whether different types of WCBs have common characteristics. It would also be insightful to extend the climatological analysis to different seasons and the Southern Hemisphere, to investigate potential seasonal and hemispheric differences in the WCB cloud structure. Finally, the study 555 could be repeated with data from other models. In particular, it would be interesting to evaluate the representation of WCBs in operational numerical weather prediction models at different lead times, which might allow for the identification of systematic forecast errors. matches between the WCB trajectories and the satellite data are available from the authors upon request.
Author contributions. M.S. calculated the ERA5 WCB climatology. H.B. performed all other analyses in this study and wrote the paper. All co-authors contributed to the interpretation of the results and writing of the paper.