In this study, radar and in situ data from the HALO-(AC)3 campaign are analyzed. During the campaign organized by the Transregional Collaborative Research Centre TR 172 (AC)3, three research aircraft were employed to study the Arctic atmosphere. The main objectives of the campaign included investigating warm-air intrusions into the Arctic and marine cold-air outbreaks (MCAOs) and collecting collocated measurements with up to three aircraft . The synoptic situation during the campaign is described in . The instrumentation on board the Polar aircraft is similar to that used during the Airborne measurements of radiative and turbulent FLUXes of energy and momentum in the Arctic boundary layer (AFLUX) and the Multidisciplinary drifting Observatory for the Study of Arctic Climate – Airborne observations in the Central Arctic (MOSAiC-ACA) campaigns described in . During the majority of flights analyzed in this study, north and northeasterly wind transported cold-air masses from the central Arctic to the main measurement area in the Fram Strait.

We focus on data collected by Polar 5 and Polar 6, two Basler BT-67 aircraft operated by the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI; ). A total of 11 flights with Polar 5 and 13 with Polar 6 were conducted in March and April 2022 during HALO-(AC)3 in the vicinity of Svalbard. Closely collocated and nearly coincident measurements were obtained with the W-band cloud radar component of the Microwave Radar/radiometer for Arctic Clouds MiRAC-A; on board Polar 5 and a variety of in situ cloud probes mounted under the wings of Polar 6 . Figure a shows a conceptual sketch of how collocation was achieved: while Polar 6 was flying low and in-cloud, Polar 5 was following in close proximity on the same track above. The slight offset between the two planes was necessary so that dropsondes could be released safely from Polar 5.

Figure  shows (a) all flight tracks of Polar 6 and (b) flight tracks of both aircraft for flights with collocated segments. The overlapping lines show close spatial collocation. The sea ice concentrations (SICs) at the campaign beginning and end indicate the variable sea ice conditions. All 13 Polar 6 flights resulted in over 60 h of flight time and about 32 h of cloud particle measurements. A total of 31 % of the total flight time during the flights shown in Fig. b was conducted as collocated, which we define as both aircraft having a maximum horizontal distance of 5 km within a 5 min time window. From a total of about 11.8 h of collocated flight time, 4.6 h are collocated cloud measurements (this corresponds to a distance of approximately 1300 km assuming a typical speed of 80 m s-1). The analyzed data cover a temperature range of -31 to -1 °C and an altitude range of in-cloud measurements from close to the ground to 1760 m.

During HALO-(AC)3, a variety of in situ cloud data were collected. This study uses microphysical cloud data collected from three different cloud instruments, the Cloud Droplet Probe CDP;, the Cloud Imaging Probe CIP;, and the Precipitation Imaging Probe PIP;. All three probes were installed under the wings of Polar 6 (Fig. ) and operated by the German Aerospace Center (DLR). The CDP is a forward-scattering optical spectrometer. The instrument measures cloud particles in the size range 2.8 to 50 µm by the intensity of forward-scattered laser light underlying Mie theory. Larger cloud particles are measured via optical array probes (OAPs). Here, two-dimensional shadow images of the cloud particles are recorded as the particles pass through the instrument's sampling area. The data collected by the CIP and PIP differ in pixel resolution. Both instruments consist of a 64-diode array, with the CIP covering a size range from 15 to 960 µm (15 µm resolution) and the PIP covering from 103 to 6.4 mm (103 µm resolution). By combining CDP, CIP, and PIP, a continuous particle size distribution is derived, including all hydrometeors from 2.8 to 6400 µm. We apply the same processing methods for the OAP data as those used for the AFLUX and MOSAiC-ACA campaigns . The operating principles of the instruments, processing, uncertainties, and applied corrections are described in detail by and .

Liquid water content (LWC) and total water content (TWC) were measured with a Nevzorov probe . The probe was operated with a new sensor head, which featured an LWC sensor and two TWC cones with diameters of 8 and 12 mm . The Nevzorov probe contains sensing elements which are regulated to provide a constant temperature (110 °C during the HALO-(AC)3 campaign). Droplets and ice particles momentarily cool the sensing elements when they impinge. In consequence, the sensors draw more power as they heat and evaporate impinging water in order to maintain their temperature, which can be used to estimate bulk LWC and bulk TWC. The measurement range of the Nevzorov probe extends from approximately 0.01 to 3.0 g m-3. Uncertainties of the Nevzorov depend very much on the atmospheric conditions that are present . Nevzorov probe measurements made during HALO-(AC)3 are only available for flights in April due to technical difficulties in March. Air temperature was measured with a Pt100 mounted in a Rosemount housing at the noseboom of Polar 6. The measurements were corrected for adiabatic heating in the housing.

With the collected data, we are unable to distinguish between larger liquid droplets and small solid ice particles due to low-resolution images consisting of only a few pixels. We therefore assume all cloud particles with sizes larger than 50 µm to be ice crystals and all cloud particles with sizes smaller than 50 µm to be liquid droplets, similarly to . For the majority of low-level Arctic MPCs, this is appropriate to assume . This assumption is based on the good agreement between Nevzorov probe LWC and LWC calculated from the particle size distribution (PSD) assuming particles smaller than 50 µm to be liquid droplets where both measurements are available (R2 = 0.83; Nevzorov and PSD LWC sum up to 973 and 983 g m-3, respectively, and lie within 1 % of each other). Additionally, we do not expect that this assumption will lead to significant biases due to radar reflectivities (that we simulate from in situ PSDs) being dominated by large particles.

The Microwave Radar/radiometer for Arctic Clouds MiRAC; was designed for operation on board the research aircraft Polar 5. During HALO-(AC)3 the active radar component (MiRAC-A) was operated on board Polar 5 in the same constellation as during MOSAiC-ACA. MiRAC-A is a 94 GHz frequency-modulated continuous-wave (FMCW) radar, which was mounted with an inclination angle of 25° backward in a belly pod under Polar 5. The radar measurements have been quality controlled and corrected for surface clutter, mounting of the instrument, and aircraft attitude . This results in georeferenced, regularly gridded data with a vertical resolution of 5 m (with reliable measurements starting 150 m above ground level due to ground clutter effects and 200 m distance from the aircraft for full overlap). estimate the accuracy of the radar reflectivity Ze calibration to be 0.5 dBZ (neglecting attenuation). Because Doppler velocity measurements are biased by the aircraft motion, only Ze measurements are used in this study.

The MiRAC-A radar is also equipped with a horizontally polarized 89 GHz passive channel using the same antenna as the radar. The brightness temperature (TB) is also measured under a tilted angle of 25° backward to nadir. From this observation, the liquid water path (LWP) is estimated over open ocean only with a temporal resolution of 1 s, as described in . The retrieval takes profiles of nearby dropsondes to calculate TB as a function of LWP measurements from simulations with the Passive and Active Microwave radiative TRAnsfer tool PAMTRA;. TB (LWP) is approximated by a third-order regression. The regression is then applied in an inverse scheme to the 89 GHz TB measurements to derive LWP. To eliminate biases in the observations, the differences between clear-sky and cloudy observations were used. Due to the variable microwave emissivity of sea ice, the LWP product is only available above open ocean.

Cloud top height (CTH) is obtained from the Airborne Mobile Aerosol Lidar for Arctic research AMALi;, which was also operated on Polar 5. AMALi measures backscatter intensity profiles at 532 nm (polarized) and 355 nm (not polarized), from which the attenuated backscatter coefficient is calculated . CTH is determined by searching for gradients in the backscatter coefficient.

For the present study, Ze has been corrected for attenuation due to atmospheric gases and liquid hydrometeors. The two-way attenuation profile was calculated with PAMTRA. We used measurements from the closest dropsonde and the water vapor absorption model by Rosenkranz (1998) to calculate the attenuation due to water vapor for each time step. To estimate attenuation due to liquid water, we took LWC measurements from the Nevzorov probe operated on board Polar 6 during the temporally closest vertical cloud profile. To obtain information on the vertical structure of clouds, Polar 6 flew vertical profiles in so-called “saw-tooth patterns”. These patterns were flown in addition to straight legs at constant altitudes. Saw-tooth patterns are not well suited to making good-quality collocated measurements with Polar 5, where straight legs are preferred. Therefore, a limited number of vertical profiles are available for each flight with collocation. During each flight analyzed in this study, at least three such saw-tooth patterns were collected. Whenever Nevzorov probe measurements were not available, LWC was calculated by integrating the PSD of liquid particles (< 50 µm) measured with the cloud probes on board Polar 6. In both cases, LWC measurements were averaged to be on a regular vertical grid with a resolution of 10 m. Here, we neglect the distance traveled by Polar 6 during the profile, assuming LWC to be constant at each height bin. This assumption likely does not hold in reality; however, no measurements with more precise information on horizontal and vertical LWC distributions are available. Attenuation due to snowfall is assumed to be negligible compared to liquid droplets. During HALO-(AC)3, we obtain a mean two-way attenuation of 0.41 dB. By comparing integrated LWC measured with the Nevzorov probe and LWC calculated from PSD during cloud profiles (if both are available) to the temporally higher-resolved LWP from MiRAC-A, we estimate uncertainties of the attenuation correction to be 1 dB, leading to a total uncertainty of Ze of 1.5 dB.

In order to combine radar and in situ measurements, it is critical to have a temporally and spatially collocated data set. Following and , the nearest radar data point to the in situ measurements is selected. We matched each 1 Hz Polar 5 data point with the spatially closest Polar 6 data point with a maximum horizontal distance of 5 km within a 5 min time window. Further, the radar range gate closest to the flight altitude of Polar 6 was chosen. Averaging radar reflectivity over certain height ranges close to Polar 6 did not lead to improvements. A rolling average of 30 s was applied to in situ data to obtain more robust statistics and to the radar data to make results comparable. Also, this is done to compensate for the different sampling volumes to a certain extent. While the radar footprint of a cloud in 2500 m distance is approximately 45.15 m in diameter, the cloud probes have measurement volumes in the range of a few cubic centimeters. We are aware that the assumption that the in situ measurement is representative of the entire matched radar volume is not always met and discuss possible implications of the assumption for our results in Sect. .

In addition to the observations, we use a data set of simulated rimed aggregates to relate particle properties and riming as discussed in . The aggregation and riming model described in , , and is used in the setting “B” (aggregation followed by riming) to generate aggregates built from a predefined number of monomer crystals. The monomer crystal sizes are taken from an exponential size distribution, and the crystals themselves are composed of cubic-volume elements with an edge length of 20 µm. The aggregate sizes range from slightly below 100 µm to 12 mm. In this study, we only use dendrite monomer crystals, which is motivated by manual inspection of the in situ images for the collocated flight segments. After aggregation, the particles are exposed to a predefined amount of liquid water so that riming occurs. The frozen droplets that have rimed onto the ice particles are also represented by cubic-volume elements of 20 µm.

We take advantage of collocated Polar 5 and Polar 6 flights and retrieve the average M of the observed cloud particle population value for each time step from the combination of radar and in situ measurements (Fig. ).

First, Ze is corrected for attenuation (see Sect. ), all cloud edges are removed to avoid non-uniform beam filling, and Polar 5 and Polar 6 data are combined (see Sect. ). PAMTRA is used to simulate Ze from the in situ PSD and an initial guess for M. In principle, Ze is a function of the mass, PSD, and scattering properties of the observed particle population. If the PSD is known and particle mass and backscattering are parameterized as a function of riming, M can be derived from a closure of Ze and PSD. In the retrieval radar forward operator, we use Mie scattering for liquid droplets. For ice particles, we use the self-similar Rayleigh–Gans approximation SSRGA; and calculate the required SSRGA parameters from M with the empirical relations presented in . In addition, we consider the mass–size relation to follow a power law m=am⋅Dmaxbm, and we take the mass–size parameters am and bm for dendrites from the same study. There, am and bm are given for discrete M, so we interpolate am and bm to obtain parameters for a continuous M. We discuss the assumption with regard to particle shape in Appendix .

By parameterizing scattering, as well as mass–size relations, only by M and assuming that the measured PSDs are representative of radar measurements, we can tweak M until measured and forward-simulated radar reflectivities match within a given uncertainty range. This is done by optimal estimation (OE), a retrieval technique based on Bayes' theorem implemented in pyOptimalEstimation . OE uses a priori information xa and a Gaussian statistical model to estimate the state vector x from the observation vector y in an iterative scheme. Starting with xa as a first guess for x, the forward model F(x) (i.e., PAMTRA) is used to convert state to observation space. Then, the difference between y and F(xa) is used to make a next guess for the state vector x1, which requires inverting F(x) with the help of the Jacobian matrix K=∂F(x)/∂x. This scheme is repeated until the a posteriori probability distribution P(x|y)=P(y|x)/P(y) reaches a maximum, resulting in the optimal x. This is achieved by minimizing the cost function J: 3J=y-F(x)TSy-1y-F(x)+x-xaTSa-1x-xa, where Sy is the uncertainty of y (observation covariance matrix), and Sa is the a priori uncertainty (covariance matrix of xa). Given that our problem is unambiguous (one measurement parameter y(Ze) and one state parameter x(M)), using OE is not strictly necessary but has the advantage of providing uncertainties.

We choose x to represent M in common logarithmic scale (x=[log⁡10(M)]) to avoid negative values. We use xa=-1 (corresponding to M=0.1) as a priori information and Sa=1 as a priori uncertainty. We also evaluated different a priori guesses xa and uncertainties Sa, but they lead to almost identical results and are therefore not shown; y refers to the attenuation-corrected Ze measurements at Polar 6 flight altitude (in dBZ), and Sy represents the corresponding measurement uncertainty of 1.5 dB. Uncertainties due to non-exact collocation between Polar 5 and Polar 6 are neglected here. The average standard deviation of Ze is 0.7 dB over distances of 555 m, which corresponds to the mean horizontal distance between the aircraft and is therefore smaller than the assumed uncertainty of 1.5 dB. In Sect. , we discuss implications of the non-exact collocation for the presented results. In Appendix , we show that the OE output captures uncertainties of the combined method with synthetic data.

The second method exploits the fact that riming impacts ice particle shape and typically leads to more spherical particles that can be derived from in situ image properties obtained by the CIP and PIP. This method can, in principle, be applied to all Polar 6 cloud particle measurements. From the captured images, hydrometeor properties described in the following were estimated. Dmax, particle cross-sectional area A, and the perimeter area P are derived in the unit of pixel numbers. For the calculation of A and P, only particles that do not touch the edges of the OAP are used . From A and P in the unit of pixel numbers, we calculate the complexity parameter χ, which we define as follows: 4χ=P2πA, similarly to so that χ of a sphere is 1. χ was originally proposed by , who included the inter-pixel variability (the variability in the brightness of one pixel compared to its neighbors) in their definition, which is not available for PIP measurements. quantify riming based on χ, where rimed particles (graupel) are defined as χ≤1.35, moderately rimed particles are defined as 1.35<χ≤1.75, and aggregates with negligible riming are defined as χ>1.75.

A disadvantage of using χ to quantify riming is that it is a purely optical measure and not a physical quantity. Also, it should be taken into account that χ depends not only on a particle's shape (closely linked to its riming degree) but also on its size in a pixel. Depending on the resolution of the imager, as well as the exact definition of a perimeter pixel (continuous line vs. only touching outside), χ values of a circle with a diameter larger than 10 pixels can range from slightly below 0.9 to 1.3. Particle features finer than the resolution of the imager are not captured. This leads to smaller ratios of perimeter to area than for the same particle observed with a higher-resolution imager. For better visualization, the reader may imagine a fractal-shaped snowflake: the higher the resolution of the snowflake image, the larger the perimeter not only in pixel numbers but also when converting to a physical length. For any fractal shape, the length of the shape increases with increasing resolution, resulting in an infinitely large perimeter for an infinitely high resolution. In turn, larger particles have larger χ than smaller particles of the exact same shape captured by the same imager. Therefore, we take Dmax, A, and P in the unit of pixel numbers to account for the different resolutions of CIP and PIP.

We use the same data set of simulated rimed aggregates from to relate particle complexity χ and size to M. Only taking simulated aggregates of dendrites, we calculate χ from the average perimeter and area pixel counts over projections in the xy, yz, and zx planes, where one pixel corresponds to a square with 20 µm side lengths. We then derive an empirical relation with R2 = 0.94 of χ depending on M and Dmax in pixels, resulting in the following: 5χ=1.33-0.00243⋅log⁡10(M)⋅Dmax+0.000171⋅Dmax-0.0854⋅log⁡10(M),6log⁡10(M)=1.33-χ+0.000171⋅Dmax0.00243⋅Dmax+0.0854.

χ is calculated from CIP- and PIP-measured P and A for each detected particle. M is then calculated from Dmax and χ for each particle. To avoid unrealistic values, we set all log⁡10(M)>0 to 0 and all log⁡10(M)<-3.5 to -3.5. The latter threshold is chosen based on the minimum M of the results of the combined method.

By applying the relation derived for synthetic particles with a 20 µm resolution to CIP and PIP measurements with 15 µm and 103 µm resolution, respectively, we assume the ice particle shape to be fractal – i.e., χ only depends on Dmax in pixels (and M) and not on Dmax in a physical length unit. To check this assumption, we decreased the “resolution” of the synthetic ice particles to 60 µm by grouping together 3×3 pixels and applied Eq. (). The resulting M bias is 27 % and is in the same range as using the original 20 µm particles (21 %).

The detection efficiency of particles that do not touch the edges of the OAPs is size dependent: larger particles are more likely to touch the edge and are therefore less likely to be detected than smaller particles. To account for this, we derive weighting factors for CIP and PIP by comparing the count of total particles detected (including particles that touch edges) to the count of particles that do not touch edges. The weighing factors are derived for particle size bins from 10 to 65 pixels in five pixel bins (see Table  in Appendix ). From the calculated M, we obtain the weighted average for 1 s time steps. Then, a rolling average of 30 s (corresponding to 1.8–2.4 km for the typical Polar 6 flight speed of 60–80 m s-1) is applied to make the results comparable with the M retrieval described in the previous section. We only consider particles with diameters larger than 14 pixels, which corresponds to 210 µm for the CIP and 1400 µm for the PIP. The threshold of 14 pixels was chosen such that 99 % of Polar 6 CIP- and PIP-measured particles with χ smaller than 1 lie below the threshold and are therefore sorted out for the analysis. χ values smaller than 1 are due to the low pixel resolution. This leaves us with a gap in the size range from about 1.0 to 1.4 mm. Evidently, only a subset of particles detected by CIP and PIP can be used to calculate M. Therefore, the in situ method can only be applied to a subset of the in situ data that are used for the combined method. This raises the question of how many particles per second is enough to achieve reasonable results assuming that high enough particle counts minimize the effects of the data gap. By comparison to the combined method, in addition to manual inspection of CIP and PIP images, we find that, in sum, at least seven particles per second need to be observed for reliably calculating M; thus, we discard data with lower counts.

We classify particles with M≥1.0 as heavily rimed (graupel; Fig. b). M values larger 1.0 are physically possible and indicate rime densities larger than assumed in the aggregation and riming model (ρrime=700 kg m-3). Particles with M<0.01 are classified as unrimed or having negligible riming due to their similar behavior to unrimed particles in . In between, we call particles with 0.01≤M<0.1 lightly rimed and with 0.1≤M<1.0 moderately rimed (Fig. b). In most cases, unrimed particles (Fig. a, left) have much more complex shapes and therefore larger χ than more heavily rimed ones (Fig. a, right), which are almost spherical (χ close to 1). Figure b shows the size dependency of χ. χ for the most heavily rimed particles, which reach M of about 0.87, is close to 1.33. Not shown are χ values of in-situ-measured cloud particles, which span values from about 0.7 to 5.0, with the majority of data (95 %) in the range of 1.0 to 3.0 for the CIP and 0.8 to 2.0 for the PIP.

Figure  shows a 2D histogram of combined and in situ method results of M for all collocated flight segments, as well as their respective M distributions. A high density of data points lies close to the 1 : 1 line, but data-point-per-data-point perfect agreement could not be achieved. However, the latter cannot be expected: although we match remote sensing and in situ data points as best as possible, there still remain offsets in time (less than 5 min) and space (less than 5 km). Additionally, radar and in situ probes have different measurements volumes.

The respective distributions look very similar in shape, but combined method results are shifted to slightly larger values than with the in situ method. The mean of M is 0.035 and 0.033, the median is 0.021 and 0.024, and the 25 % to 75 % quantile ranges are 0.016 to 0.042 and 0.014 to 0.035 for the combined and in situ methods, respectively. The similarity, in addition to the close agreement of means, medians, and quantile ranges, gives us confidence that we achieve agreement with both methods and that both can be used to quantify riming. Mean error (ME) and root mean square error (RMSE) are 0.0026 and 0.031 for the point-by-point comparison. While we do not achieve good point-by-point agreement (large RMSE), both methods agree in a statistical sense (small ME).

Assuming particles with M<0.01 have negligible riming, we derive average rimed fractions of 88 % and 87 % over all collocated flight segments with the combined and the in situ methods, respectively. These numbers appear to be quite high. However, they depend heavily on the rimed vs. unrimed threshold that is chosen; if we assume M<0.05 to be unrimed instead of M<0.01, we get 11 % and 9 % rimed particles, respectively. We note that 12 % and 13 % of particles have M<0.01 for the combined and in situ method, respectively; 83 % and 83 % fall in the range 0.01≤M<0.1; and only 5 % and 3 % have M≥0.1.

We see similar results when comparing the individual flights, except for 10 April (Fig. ). Manual inspection of CIP and PIP images shows a high proportion of rimed particles during the collocated segment on 10 April (not shown), which is in agreement with the combined method. These particles appear to predominately have sizes around 1 mm – large enough to often touch edges in CIP images but too small to be able to calculate χ from PIP images. In all further analysis steps, we exclude the 10 April data, which correspond to 6 min of collocated data.

The good statistical agreement between both methods in combination with a rather large RMSE raises the question of why agreement in terms of temporal confluctuations could not be achieved for all flight segments. In the following, we use a case study to demonstrate under which conditions combined and in situ methods agree on a data-point-per-data-point basis and discuss possible biases of both methods.

A high-pressure system north of Greenland and a strong low-pressure complex north of Siberia lead to northerly and northeasterly winds almost parallel to the ice edge in the Fram Strait, where the measurements were performed. The movement of cold air from the colder sea ice north of the Fram Strait to the warmer ocean resulted in the formation of cloud streets, which can be seen in Fig. a. identified this cold-air advection as a strong marine cold-air outbreak (MCAO) that lasted from 1 to 2 April. On 1 April, Polar 5 and Polar 6 conducted collocated flights, crossing the Fram Strait perpendicular to the cloud streets from 7.6 to 1.5 ° E, traveling back and forth three times. Clouds were thicker, more pronounced, and extended higher over the open ocean on the eastern side of these segments than close to the MIZ and were absent over sea ice. Polar 5 stayed at a constant altitude of 3 km, while Polar 6 performed predominately staircase patterns, measuring in and above clouds. Here, we show a short segment where Polar 6 flew inside clouds from west to east on the eastern side of the measurement area close to 7.6 ° E, while Polar 5 flew above. Then, both aircraft turned and flew the same way back westward. Excluding the turn, the horizontal distance between both airplanes ranged from 48 m to 2.7 km and was, on average, 1.2 km.

A detailed view of collocated in situ and radar measurements during this segment is presented in Fig. . The first column shows measurements before the turn (aircraft flying from west to east, about 11:08 to 11:18 UTC), while the second column shows measurements after the turn (east to west, about 11:25 to 11:35 UTC). We cut out the turn due to unreliable measurements and/or collocation matching when the radar is tilted due to the aircraft roll. In-cloud temperatures decreased with height, ranging from -22 to -15 °C in the measured area (Fig. e and f). The cloud's roll structure is clearly visible in the radar measurements: Ze shows periodic streaks of high and low values (Fig. c and d), which can also be seen in the averaged (moving over 30 s), corrected Ze at the altitude of Polar 6 (Fig. a and b). D32 is the proxy for the mean mass-weighted diameter e.g., and is defined as the ratio of the third to the second measured PSD moments M3/M2 assuming a typical value of 2 for the exponent b of the mass–size relation e.g.,. D32 calculated from the 30 s running average of the combined in situ PSD (Fig. g and h) and the PSD (Fig. i and j) shows gaps when Polar 6 was flying close to cloud top (before the turn), and streaks of high Ze appear to correlate with increases in D32. Nevzorov probe measurements (Fig. k and l) show that the sampled cloud was mixed-phase, with LWC being, in general, slightly higher close to the cloud top.

We see good agreement when looking at mean, median, and quantile ranges of M derived with combined and in situ methods before and after the turn. The combined method results in a median (mean) M of 0.031 (0.040) before and 0.032 (0.037) after the turn, while the in situ method gives a median (mean) M of 0.031 (0.033) before and 0.022 (0.031) after the turn. The 25 % to 75 % quantile ranges are 0.022 to 0.044 and 0.024 to 0.042 for the combined method before and after the turn, respectively. Quantiles range from 0.021 to 0.043 and 0.018 to 0.036 for the in situ method.

However, when comparing the time series of M, we see a much better agreement in terms of temporal confluctuations after the turn compared to before. We assume that the discrepancy before the turn is due to the Polar 6 measurements being close to the upper edge of the cloud. As discussed in Appendix , agreement between both methods is worse close to the highest radar range gates with cloud signals. This is likely due to the higher spatial variability and larger spatial gradients of cloud properties. Even slight horizontal offsets of Polar 5 and Polar 6 in addition to the different measurement volumes of radar and cloud probes can result in disagreements between radar and in situ probes. Close to the upper edge of the cloud, this can result in the radar detecting a gap in clouds while the in situ probes measure a particle concentration larger than zero or vice versa. Apparently, the running averages of 30 s in both data sets cannot completely resolve this problem. In addition, median particle count increases from 17 before the turn to 22 after the turn, resulting in the in situ method being less reliable before the turn as well. Therefore, near the cloud top, both methods are less reliable in a spatio-temporal sense. They do, however, both produce reliable estimations of M in a statistical sense.

After the turn, combined and in situ results for M show better agreement as Polar 6 was flying deeper in-cloud under more homogeneous conditions. Both methods show an almost periodic increase and decrease in M, with (almost) matching maxima and minima in terms of extent and location. Compared to Ze (Fig. b and d), high M values correlate with high Ze, indicating that riming plays a dominant role in MPC variability, as observed by radar.

CIP and PIP images taken at 7.0 ° E after the turn are presented in Fig. o and p and show a mixture of small liquid drops, pristine plates, and a high proportion of rimed (aggregated) dendritic ice particles, explaining the peak in M for both methods.

Figure  gives an overview of the occurrence of riming depending on (a–d) Polar 6 noseboom measurements of air temperature T; (e–h) Nevzorov probe LWC; (i–l) Nevzorov probe TWC; (m–p) MiRAC-A-retrieved LWP; and (q–t) the normalized position of Polar 6 in cloud, which we define as the fraction of Polar 6 flight altitude minus cloud bottom height (CBH) and CTH minus CBH (therefore, cloud bottom = 0 and cloud top = 1). CTH is determined from AMALi, while CBH is determined from radar measurements, where cloud bottom is the lowest Ze measurement not affected by ground clutter. If there is a continuous signal from 150 m to the flight altitude of Polar 6 then cloud bottom is set to 150 m. Note that the liquid cloud base, which is commonly used when using ground-based remote sensing, is not available for airborne measurements. Our cloud definition includes precipitation falling out of the cloud liquid layer so that multi-layer clouds connected by precipitation would be treated as a single cloud. During the collocated flight segments used in this study, no separate cloud layers were observed by the radar above Polar 6. The average rimed fractions derived with both methods show a similar behavior for all parameters and lie, on average, within 6 percentage points of each other. Linear medians match within a factor of 0.3.

When analyzing the relation of riming to temperature, moderate riming also occurs at low temperatures below -15 °C. Between -10 and -15 °C, (local) minima of rimed fractions and M are evident with both methods. This coincides with the so-called dendritic growth zone, where aggregation is favored . Complex aggregated forms can appear to be round when viewed from certain angles and imaged with a limited resolution. This might lead to an overestimation of riming with the in situ method. Note that the temperature is available only at the point of observation, not where – at potentially colder temperatures – the riming process itself took place. The disagreement above -10 °C stems from a 10 min flight segment on 4 April, where M results from the in situ method go slightly below 0.01, while M results from the combined method stay slightly above 0.01. Median (25 %–75 % quantile range) M values are 0.019 (0.016–0.020) and 0.012 (0.006–0.016) for the combined and in situ methods, respectively.

There is no clear dependence of riming on LWC. The rimed particles could easily have undergone riming in an SLW layer above and fallen out to a place in the cloud with little to no SLW. Rimed fraction only increases slightly with TWC. This is likely because M results are low for the whole campaign, and large, unrimed aggregates can also result in large TWC.

For LWP, median M and rimed fractions increase with increasing LWP up until 50 g m-2 and decrease in the two highest LWP bins. This decrease could be due to limited sampling as the bins contain less than 500 data points. Overall, the agreement between both methods is very good, with rimed fractions agreeing, on average, within 3 percentage points below and 11 percentage points above 100 g m-2.

Rimed fractions agree within 2.7 percentage points for in-cloud positions above 0.2 (meaning Polar 6 is flying higher than the lowest 20 % of the cloud). Below 0.2, rimed fractions derived by the in situ method are, on average, 19.5 percentage points lower than those derived by the combined method. However, median M values agree within a factor 0.29 above and 0.17 below 0.2. Because our definition of a cloud includes precipitation below, low cloud positions might be below the liquid cloud base. If this is indeed the case, we expect the falling particles to be larger and heavier than the particles in the cloud above. The detection efficiency of cloud probes is worse for particles close to the upper end of their size range, even if we count particles that touch edges (as is done in the PSD calculation). Therefore the higher rimed fractions obtained by the combined method could be due to missing large particles in the PSD that the radar can see. The optimal estimation retrieval would then overcompensate by increasing M, resulting in a higher number of rimed particle populations for the combined method. Averaging the in situ data for longer time spans should ensure the capture of more large particles. Using running averages of 60 instead of 30 s shifts the rimed fractions below 0.2 only slightly closer together (agreement within 18.8 percent points; not shown). However, average particle sizes increase at small normalized positions in-cloud. Median values of D32 increase by about 150 % from 1.52 mm at 0.15–0.2 to 3.71 mm at 0.05–0.1. Disagreement between both methods is higher when Polar 6 is flying near the top of the radar signal (Fig. ) due to the higher variability of measurements, as we show in Appendix .

Here, we extend the analysis to periods only covered by the in situ aircraft to analyze how representative of the complete Polar 6 data the collocated measurements are. Even though a large, unique data set of collocated, airborne measurements was collected in the Arctic during HALO-(AC)3, the total amount of in situ cloud measurement time exceeds the collocated measurement time by a factor of 5. Figure  shows the dependence of M on temperature and LWC as in Fig.  but for the extended in situ data set. The position of Polar 6 in-cloud and MiRAC-A-retrieved LWP must be omitted due to the missing Polar 5 remote sensing information. TWC is not shown due to not adding further information, as discussed in Sect. . The average rimed fraction, assuming M<0.01 (M<0.05) to be unrimed, is 69 % (13 %), with a mean M=0.030, median M=0.016, and a 25 % to 75 % quantile range of 0.009 to 0.031. These values are slightly lower and indicate a slight shift towards more riming during the collocated segments.

When focusing on temperature bins with a sufficiently high number of observations, we observed decreasing riming with decreasing temperature from -10 and -16 °C (Fig. b). The rimed fraction for all in situ flights follows a similar shape to the collocated sub-sample in that temperature range, albeit with a lower local maximum at -11 °C (0.72 vs. 1.0). There is a slight local minimum of median M and rimed fraction at about -14 °C. Lower rimed fractions and median M result for lower temperatures when including all Polar 6 data. Similarly, rimed fraction and median M are lower for LWC below 0.05 g m-3.

Differences between the in situ method results for only collocated vs. for all segments are smaller when excluding Polar 6 data below 150 m, as can be seen in Fig. : the rimed fraction curve is shifted towards larger values. Also, both rimed fraction vs. LWC curves are very close, deviating by a maximum of 5.4 percentage points. The better agreement above 150 m could be simply due to the higher proportion of common data points because the collocated M of the in situ method is a subset of the M of the in situ method derived for all Polar 6 flight segments. Another explanation could be the influence of cloudless ice crystal precipitation (diamond dust). This phenomenon describes the formation of ice crystals under clear or nearly clear skies. Diamond dust typically occurs between November and mid-May at heights below 250 m over the Arctic Ocean . This could shift the curve towards less riming for cold temperatures, resulting in a (near-) disappearance of the -15 °C local minimum.

We can conclude that the collocated flight segments are, in part, representative of all Polar 6 flight segments where Polar 6 flew above 150 m: they show similar behavior in terms of M dependence on LWC. However the collocated segments are biased towards higher amounts of rimed particles at low temperatures below -17 °C.