The radar observations from the three flights are displayed in Fig. . Observations for flight B984 stem from the HAMP MIRA radar on board the HALO aircraft, which operates at a frequency of 35 GHz and has been characterized and calibrated by . Its observations have been downsampled to a vertical resolution of 210 m and a horizontal resolution of roughly 700 m in order to reduce the computational complexity of the retrieval and to better match the field of view of the passive observations, which, at an altitude of 5 km, vary between about 900 m for the low-frequency channels and 200 m for the high-frequency channels.

The radar observations for flights C159 and C161 stem from the CloudSat Cloud Profiling Radar (CPR, ), which operates at 94 GHz. Since the CloudSat observations were affected strongly by ground clutter, the first five bins located completely above surface altitude were set to the reflectivity found in the sixth bin above the surface. The CPR observations have a vertical resolution of 240 m and a horizontal resolution of about 1.4 km. The horizontal distance between subsequent observations is 1.1 km.

While the radar observations for flight B984 come from an airborne radar, the observations for flights C159 and C161 stem from a spaceborne sensor. The high velocity of the spaceborne sensor causes significant temporal delay between co-located observations from the radiometers and the radar. Figure  displays the delay between co-located radar and radiometer observations with respect to the along-track distance for the three flight scenes. While the delays for flight B984 remain mostly within 5 min, they reach values exceeding 30 min for the two other flights.

The in situ measurements that are relevant to this study are measurements of bulk ice water content using a Nevzorov hot-wire probe and PSDs recorded using DMT CIP-15 and CIP-100 probes, which measure size-resolved particle concentrations with resolutions of 15 and 100 µm, respectively. In situ measurements are available only for flights B984 and C159, which each consist of two parts: a high-level run during which the aircraft flew above the cloud system to perform the remote-sensing observations and a low-level run during which the aircraft flew at lower altitude through the cloud to perform the in situ measurements. A detailed view of the high- and low-level runs for the two flights is provided in Fig. . For flight C159, this view reveals a noticeable horizontal offset of 3 to 4 km between the ground tracks of radar and radiometer observations. Even larger deviations occur between certain parts of the low-level run and the ground tracks of the remote-sensing observations.

An overview of the measured IWC and PSDs is provided in Fig. . While for flight B984 the measured IWC is mostly consistent with the radar observations, there are clear disparities between the measured IWC and the CPR reflectivities for flight C159. This indicates that there may be considerable differences between the regions of the cloud that were sampled during the in situ sampling and the part that was observed by the CloudSat CPR.

The PSD profiles for flight B984 show a clear size-sorting pattern with a gradual decrease in the concentration of particles smaller than 200 µm and a simultaneous increase in the concentration of larger particles. For flight C159, high concentrations of small particles are encountered at low altitudes which decrease with altitude. For larger particles no systematic variation with altitude is observed.

The synergistic retrieval algorithm used in this study is based on the optimal estimation framework and retrieves distributions of frozen and liquid hydrometeors together with water vapor by simultaneously fitting a forward model to the active and passive observations. Since the algorithm is described in detail in the following section only outlines its main features and how it has been adapted to the flight data.

The retrieval input consists of a single radar profile and the corresponding spatially closest radiometer observations. Background properties of the atmosphere and the surface, such as temperature and wind speed, as well as a priori profiles for relative humidity and liquid cloud water are taken from the ERA5 hourly reanalysis . The output of the retrieval are two parameters of the PSDs of frozen and liquid hydrometeors as well as liquid cloud water content (LCWC) and relative humidity. Hydrometeor PSDs are represented using the approach proposed by : At each level in the atmosphere the concentration of hydrometeors with respect to the volume equivalent diameter Deq is given by 1NDeq=N0*FDeqDm, where F is a fixed function that specifies the shape of the normalized PSD, and N0* and Dm are the retrieved parameters. The N0* parameter is retrieved in log⁡ space while Dm is retrieved in linear space. Relative humidity is retrieved in a transformed space based on an inverse hyperbolic tangent transformation and cloud liquid water content in log⁡ space. A listing of all retrieval targets and corresponding a priori assumptions is provided in Table .

The forward model and retrieval were made adaptive so that the ingested observations can be easily adapted to the different sensors and channels that were available for each flight. Low-frequency channels that are used only over ocean surfaces are deactivated over land by setting the corresponding channel uncertainty to 106 K. The atmospheric grid was limited to altitudes between 0 and 10 km and matched to the resolution of the radar observations. The latest stable release (version 2.4) of ARTS is used to implement the forward model used in the retrieval. The built-in single-scattering radar solver of ARTS is used to calculate radar observations and Jacobians. To account for the effect of multiple scattering in CloudSat observations, the attenuation due to hydrometeors is scaled at each atmospheric layer by a factor of 0.5 following Fig. 16 in . Passive radiances are calculated using the ARTS interface to DISORT , and their Jacobians are approximated using a first-order scattering approximation. Gaseous absorption is modeled using the absorption models from for N2 and O2. Following , absorption from water vapor is calculated using a combination of the AER database v3.6 for resonant absorption and the MT-CKD model version 3.2 for continuum absorption .

The retrieval residuals, i.e., the difference between simulated and real observations, for the large plate aggregate habit are displayed in Fig. . As the figure shows, the retrieval was able to fit both radar and radiometer observations fairly well for all flights. For flight B984, the radar residuals show some scattered deviations located at the edge of the cloud, which are likely discretization artifacts. Except for that, residuals for this flight remain well within 1 dB. The residuals for flight C159 exhibit four vertical stripes with significant residuals in the radar observations. In these regions, which correspond to significant scattering depressions in most passive channels up to 325 GHz, the simulations overestimate the radar reflectivity. Apart from this, there are some smaller regions where the simulations underestimate the radar reflectivity, but these remain limited to within few dB. For flight C161, moderate negative residuals in the radar observations can be observed in the right half of the convective core, which coincide with an overestimation of the scattering signal at 243 GHz.

Radiometer residuals for flight B984 are mostly within ±5 K but larger for flights C159 and C161. For these two flights, residuals exceeding 10 K are observed in the window channels up to 243 GHz as well as the outermost channels around the absorption lines at 118 and 183 GHz. Since these occur in profiles where precipitation is present and in which similar residuals can be observed in the radar observations and other channels that are sensitive to the lower parts of the atmosphere, a likely explanation is that they are caused by precipitation that is not observed by all sensors due to spatial and temporal co-location issues. In particular, the large residuals in the 243 GHz channel for flight C161 at around 100 km along-track distance may well be caused by the evolution of the convective cloud during the delay of about 30 min that separates the radiometer and radar observations.

For a more systematic analysis of the effect of the assumed particle shape on the retrieval residuals, their distribution for radar and radiometer channels around 183 GHz and above are displayed in Fig. . The distributions, which for most channels are close to or centered around zero, confirm that the retrieval generally fits the observations well. The largest deviations are observed for the 874 GHz channel and the 243 GHz channel for flight C161. For flights C159 and C161, the 874 and 664 GHz channels exhibit small systematic biases of opposite signs, which may indicate issues with the calibration or the modeling of water vapor absorption at these channels. Furthermore, it is interesting to note that the ice particle habit only has a minor impact on the residuals, indicating that the retrieval can compensate for mismatches in the assumed particle shape by adjusting the retrieval variables.

The retrieved bulk IWC and corresponding IWP for all three cloud scenes are displayed in Fig. . For all three flights, the ice particle shape has a significant effect on the retrieved amount of ice. In terms of IWP, the large-column aggregate and Evans snow aggregate habits yield the highest values, while the eight-column aggregate consistently yields the lowest IWP. The large plate aggregate and six-bullet rosette both yield values within the range of the other particle models with the six-bullet rosette leading to slightly higher IWP values than the large plate aggregate. In addition to the effect of the increased total retrieved water content, the particle habit also has a small effect on the vertical distribution of the ice hydrometeors, which is visible particularly for retrieved IWC in the convective core observed during flight C161.

The most important question regarding the hydrometeor retrieval is certainly whether the retrieved bulk properties are consistent with the in situ measurements. To compare the in situ measurements to the retrieval results, they were mapped to the radar observations using a nearest-neighbor criterion. For B984, retrieval results within a distance of 1 km of the flight path were then associated with the in situ measurements. Because of the mismatch between observations and in situ sampling paths, another approach was taken for flight C159. Here the retrieval results were mapped to the in situ measurements by selecting all retrieval results between 50 and 150 km along-track distance. Both the matched retrieval results and the vertically resolved distributions of measured and retrieved IWC are displayed in Fig. .

For flight B984, the distribution of in situ-measured IWC values is well within the range of retrieved IWC values across all particle shapes up to an altitude of around 7 km. At these altitudes, the best match to the in situ measurements is achieved with the six-bullet rosette particle and the large plate aggregate. The eight-column aggregate underestimates the in situ-measured IWC while the large column aggregate and Evans snow aggregate overestimate it. Above 7 km all particles lead to results that underestimate the in situ-measured IWC. A likely cause for this is the high concentration of small particles as observed in the in situ measurements (see Fig. ) for which microwave observations lack sensitivity.

For flight C159, the distribution of retrieved IWC still covers the distribution of in situ-measured values for altitudes above 3 km but exhibits a tendency towards underestimation. Overall, the differences between the results for different habits are smaller for this flight. However, the uncertainties caused by the large sampling region as well as the potential co-location issues affecting the results make them less conclusive.

Finally, we want to address the question whether the representation of cloud microphysics within the retrieval forward model is consistent with the in situ-measured PSDs. For this, we calculate the PSDs corresponding to the retrieved bulk properties and compare them to the in situ measurements. The results of the comparison are displayed in Fig. . For flight B984, we find good agreement between retrieved and in situ-measured PSDs for larger particles (DMAX>200 µm) for the large plate aggregate and the six-bullet rosette. Since this is observed even at altitudes above 6 km, it confirms that the underestimation of IWC at these altitudes is likely caused by the high concentration of smaller ice particles. For flight C159, the retrieved PSDs deviate significantly from the in situ measurements. Although the six-bullet rosette and large plate aggregate seem to fit the tail (DMAX>1 mm) of the PSD for most altitudes except between 3–4 km, the measured PSDs deviate considerably at smaller sizes. This may also indicate that the assumed shape of the PSD may not be suitable for the observed cloud system.

A first important result of this study is the ability of the retrieval to find atmospheric states that are consistent with the observed radiances and radar reflectivities for all three flights. This in itself is not self-evident due to the uncertainties that still affect the modeling of ice-particle scattering at millimeter and sub-millimeter wavelengths. Previous studies that tried to directly validate sub-millimeter RT through clouds were limited to either tropical clouds or cirrus clouds . For flight B984, the radar and all passive observations were fitted up to small systematic biases no larger than 3 K. The deviations for the two other flights were generally larger, but these were likely caused by spatial and temporal co-location errors. This indicates that both the assumed optical properties as well as the retrieval forward model are consistent across the considered wavelengths. Furthermore, the two particle shapes for which the best agreement between retrieved and in situ-measured hydrometeor distributions was found for flight B984 were also those whose mass–size relationship yielded the best agreement between in situ measurements of IWC and PSDs. Since this ties the microphysical properties of the particles to their optical properties, it suggests that the modeling of these particles in the ARTS SSDB is physically consistent.

A rather unexpected result that emerged from this study is that the retrieval can fit the observations fairly well regardless of the assumed ice particle shape. This indicates that although the observations are sensitive to variations in ice particle shape, they alone cannot constrain it. This is in agreement with what has been reported in , namely that no correlation could be found between the particle shape yielding the best retrieval fit and the one yielding the most accurate retrieval results.

In an effort to better separate a potential signal from the ice particle shape in the retrieval residuals, we have investigated the relationship between retrieved IWP and the residual for different channels. Most channels that were available on all flights do not show a clear sign of a relation between the particle shape and the residuals. As an example for those channels we provide scatter plots of the retrieved IWP and the channel residual for the 325±3.5 GHz channel in Fig.  in the Appendix. We did, however, identify two channels from flight B984 that may exhibit a potential signal from the ice particle shape in the residuals. The scatter plots for these two channels are provided in Fig. . For the 325±9.5 GHz channel, all tested particles except the large plate aggregate seem to manifest a positive correlation between IWP and the residuals. For the 243±2.5 GHz, the six-bullet rosette, eight-column aggregate and large plate aggregate exhibit a weak negative trend in the residuals, while it remains positive for the large column aggregate and Evans snow aggregate. At least for these two channels the large plate aggregate seems to stand out as the ice particle shape yielding the smallest residuals across the retrieved range of IWP values.

Since the large plate aggregate is one of the particles for which the best agreement between retrieved and in situ measurements was obtained, this may be viewed as an encouraging result indicating that sub-millimeter observations can, at least in combination with radar observations, be used to constrain the shape of ice particles in clouds. However, taking into account that these are observations from only one flight as well as the complicated statistics of the results from Fig. , it remains unclear whether these findings are statistically significant. A potential confounding factor may be the impact of the a priori assumptions on these results. Since the retrieval balances the residual with the deviation from the a priori, this may lead to a worse fit for the softer particles (large column aggregate, Evans snow flake) for which a much higher Dm must be retrieved for a similar scattering effect. While this effect may be desired in the retrieval to avoid the apparently excessive amounts of ice retrieved using these particle shapes, it is the combination of observations and a priori assumptions that constrains the particle shape and not the observations alone. We present these results here mainly for completeness and to serve as a potential basis for further investigation.

Nonetheless, even if indeed present, a potential signal from the ice particle shape in the results would be limited to a few Kelvin. This implies that future ice hydrometeor retrievals that make use of millimeter and sub-millimeter microwave observations must either account for the uncertainty caused by variations in ice particle shape or find ways to more accurately constrain the shape a priori. Moreover, for studies that seek to validate model predictions by comparing simulated and observed microwave observations, this implies that care must be taken to accurately characterize the ice particle shape. This is because agreement up to a few Kelvin between simulations and observations can be achieved for bulk water contents that vary by almost an order of magnitude (see Fig. ).

The lack of a distinct signal that constrains the ice particle shape even in the combined observations puts additional weight on the question of how to best represent ice particles in simulations of microwave observations. The habits that lead to the most accurate retrieval results in this study were the large plate aggregate and the six-bullet rosette. The channel residuals presented in Fig.  indicate the best fit for the large plate aggregate although it is unclear how robust these findings are. Furthermore, it is interesting to note that the large plate aggregate was also found to yield the best agreement between simulations based on a numerical weather prediction (NWP) model and satellite observations at frequencies between 19 and 190 GHz for stratiform snow in .

Nonetheless, these findings are based on observations from the single flight for which the retrieval results could be reliably compared with in situ measurements. This result can thus be seen as indication that these habits may work well for similar mid-latitude cloud systems, but more generally applicable conclusions would require further and more systematic investigation.

Since the results presented in were limited to simulations based on a high-resolution climate model, the validation of the retrieval using real observations remained an open issue. For flight B984, good agreement was found between retrieval results and in situ measurements. Although the retrieved IWC deviates from the in situ measurements at altitudes >6 km, the retrieved PSDs still match the in situ measurements well for particles with DMAX>200 µm. This indicates that the concentrations of these larger particles may be retrieved correctly but that the total IWC is underestimated due to the mismatch between assumed and actual PSD shape, the former of which lacks the very high concentration of small particles that are present in the in situ measurements. Although and show that the occurrence of high particle concentrations at sizes below 200 µm may be due to measurement inaccuracies of the CIP-15 probe, the measured PSDs correctly reproduce the measured IWC at these altitudes when the corresponding water content is calculated using any of the tested particle habits (Fig. ). Furthermore, the presence of a cloud layer with a large number of small particles was also reported by who investigated the same cloud system with combined radar–lidar observations.

For flight C159 no good agreement was found between retrieved and in situ-measured IWC and PSDs. However, some evidence suggest that this may be due to co-location: firstly, the flight path for the in situ sampling was found to be offset from the high-level run during which the observations were taken in the direction opposite to the wind at 800 mb (Figs. , ). Secondly, a clear backscattering signal is present in the CloudSat CPR observations even in regions where only negligible amounts of IWC are present in the in situ measurements (Fig. ). Thirdly, the residuals observed in Fig.  are indicative of additional co-location issues between radar and radiometer observations. Finally, also the comparison of retrieved and in situ-measured PSDs (Fig. ) seems to indicate large deviations between the observed and the assumed PSD shape.

Although the evidence from flight B984 suggests that the synergistic retrieval algorithm works well for retrieving ice hydrometeor concentrations, similar retrievals can be performed using only radar observations. A retrieval using only radar observations has the obvious advantage of requiring only a single sensor and being computationally much less complex. This naturally leads to the question of the added value that a synergistic retrieval can provide.

To investigate this, the results of the combined and an equivalent radar-only retrieval for flight B984 are displayed in Fig. . For the large plate aggregate and six-bullet-rosette habits, the results of the combined and the radar-only retrieval are largely similar down to an altitude of about 3.5 km, below which the radar-only retrieval tends to overestimate the in situ IWC. In contrast to the combined retrieval, the results of the radar-only retrieval exhibit almost no impact from the particle habit. While the radar-only retrieval remains mostly unaffected by the habit choice, using a different habit in the combined retrieval may cause systematic overestimation (Evans snow aggregate and large column aggregate) or underestimation (eight-COLUMN AGGREGate).

A similar comparison is shown in Fig.  for the retrieved PSDs. The PSDs are largely similar for both retrievals for altitudes above 4 km. Below that, however, the radar-only retrieval overestimates the particle concentrations, while the combined retrieval matches the in situ measurements well for the large plate aggregate and six-bullet rosette habits. This indicates that the combined retrieval utilizes the complementary information in the radar and passive observations to match both moments of the PSD, whereas the radar-only retrieval can only match one of them.

The tendencies observed for the retrieved IWC in Fig. 14 are even more pronounced when the IWP is calculated along the sampling path of the in situ measurements. The resulting retrieved IWP values are displayed in Table . The radar-only retrieval systematically overestimates the reference IWP for all tested particle shapes. The combined retrieval leads to even stronger overestimation when the large column aggregate or the Evans snow aggregate are used as ice particle shapes, while the eight-column aggregate leads to a strong underestimation of the true IWP. With the six-bullet rosette and the large plate aggregate used as ice particle shapes, the combined retrieval yields results that are closest to the in situ measurements. Thus, while the incorporation of passive observations increases the sensitivity to the representation of hydrometeors, it can help to improve the retrieval of IWP given that a suitable particle model is used in the retrieval.

These results thus suggest that combining radar with passive microwave observations helps to constrain the PSD of ice hydrometeors for sufficiently large particle sizes (DMAX>200 µm). Since for air- and space-borne observations only microwave observations can sense the base of thick clouds, this is a unique synergy between these types of observations.

While these results were obtained for a Ka band cloud radar, we do not expect them to change much for a W band radar. Although the habit may have a stronger effect on the retrieval results of a W band radar due to its higher frequency, the underlying problem remains that the radar observations provide only a single piece of information per range bin. To retrieve the two moments of the hydrometeor PSD, the retrieval thus has to rely on a priori information, which cannot accurately describe the distributions in all clouds. Although the passive observations provide only a comparably small amount of additional information, our results indicate that the retrieval is able to use that to better constrain the retrieved hydrometeor distributions.

Since microwave radiative transfer simulations in cloudy atmospheres remain a challenging problem, it is important to also consider the limitations of the simulations and derived results that were presented in this study. The simplifications that were applied in the simulations are the following:

Horizontal photon transport between the retrieved profiles is ignored.

found that neglecting photon transport in simulations of sub-millimeter observations across a footprint of 6 km incurs only a small random error with biases <0.5 K, so it is likely also small for the simulations presented here. For flight B984, the horizontal averaging of the radar observations leads to a profile width of 700 m which is fairly close to the width of the radiometer field of view which varies between about 900 and 200 m at an altitude of 5 km. The effect of beam inhomogeneity is therefore expected to be small for this flight. For flights C159 and C161, the radar beam has an along-track width of about 1.4 km, which is larger than that of the radiometers, so these observations may be affected to a larger extent than those for flight B984.

Neglecting the finite spectral resolution of the passive channels can lead to an error of up to 2.1 K for satellite observations that are affected by ozone absorption . Since the passive observations used in this study were all taken from altitudes below 10 km the effect of this approximation is likely negligible.

The effect of multiple scattering for air-borne radar observations is generally negligible . For CloudSat observations, however, the higher frequency and the considerably wider footprint will increase the effects of multiple scattering on the observations. Although the simulations account for the signal-enhancing effect of multiple scattering by layer-wise reduction of the attenuation, the presence of multiple scattering may still add to the uncertainty in the simulations for flights C159 and C161.

Finally, there is the potential presence of oriented particles in the cloud. The different ice habits used in this study all assume totally random orientation of the ice particles. Systematic vertical orientation of particles of a given shape in the cloud would effectively alter their scattering properties. For observations at nadir, particle orientation can increase the extinction of the large plate aggregate of up to 20 % . To first order, the increase in extinction can be expected to cause a similar overestimation of the retrieved IWC. This, however, is still considerably lower than the differences observed due to different ice habits.