This study exploits the data collected during the “TRIple-frequency and Polarimetric radar Experiment for improving process observation of winter precipitation” (TRIPEx-pol). The campaign was conducted at the Jülich Observatory for Cloud Evolution Core Facility, Germany (JOYCE-CF 50∘54′31′′ N, 6∘24′49′′ E, 111 m above mean sea level; see ) from November 2018 until February 2019. JOYCE-CF is a triple-frequency radar site including permanent installations of X-, Ka- and W-band vertically pointing Doppler radars. The quality of the remote measurements is continuously monitored with a number of auxiliary sensors, including a Pluvio rain gauge, Parsivel optical disdrometer , microwave radiometers and a Doppler wind lidar installed close to the radars. In order to maximize radar volume matching, all three radars are installed on the same roof platform within 10 m (see Table  for the technical specifications of the radars). Due to differences in the integration time of the radars and differences in the antenna beam widths, the data were averaged over 6 s in order to at least partially compensate for these factors. Because differences in the range resolution do not exceed 20 % and are difficult to correct for, the data at the W- and X-bands are simply interpolated at the Ka-band range bin resolution.

The absolute pointing accuracy of the scanning Ka-band radar has been estimated to be better than ±0.1∘ in elevation and azimuth using a sun-tracking method. Following the methodology of , the mean Doppler velocity of the X- and W-band radars has been compared to the Ka-band system for several cases with different horizontal wind velocities and directions. This analysis showed that the relative misalignment of the three radars is in the range of 0.1∘, which is expected to ensure a very high quality of the multi-frequency measurements.

The focus of our analysis is on a short time period (06:00–12:00 UTC) during a rain event on 24 November 2018. Selected radar measurements for this event are depicted in Fig. . The top and bottom of the melting layer have been derived with the linear depolarization ratio (LDR) from the Ka-band radar following the method described in . This approach is based on a very strong bright band signature in the LDR data in correspondence to the melting regardless of the rainfall intensity. In this study, the inflection points around the LDR peak are used as the top and the bottom of the melting zone. Over the presented time period, the altitude of the 0 ∘C isotherm was very stable and decreased by only 300 m from 1.1 km at 06:00 UTC to 0.8 km at 12:00 UTC. Radar reflectivity data below the bright band indicate two intervals of intensified rainfall: the first period is from 06:45 to 07:45 UTC with the peak at 07:30 UTC and a shorter interval that occurs around 09:00 UTC. Although for both periods similar X-band reflectivities are measured close to the ground (approximately 27 dBZ), the reflectivity and the dual-frequency ratio (DFR) data suggest completely different ice microphysics aloft. The first period is characterized by larger X-band echoes in the ice part coinciding with extremely large DFRX-Ka values reaching 16 dB, which is a signature of strong aggregation and presence of very large snowflakes . Almost no DFR is measured after 07:45 UTC, which indicates relatively small ice particles. Note that the DFR data in ice were corrected for attenuation prior to the analysis. The attenuation due to the rain was derived from the Rayleigh part of the dual-frequency spectral ratio see e.g., assuming negligible attenuation at the X-band. The extinction due to melting particles was estimated from the rainfall rates retrieved below the melting layer with the methodology of . This technique has been shown to be in agreement with multi-frequency Doppler spectra estimates . These two components were added together and were used as a path-integrated attenuation correction factor that is applied to the column. This methodology does not account for any attenuation within snow but this should be minimal at the X- and Ka-bands, which seems to be confirmed by the fact that the DFR at the cloud top (Fig. ), where Rayleigh targets are expected, is close to 0 dB.

The mean Doppler velocity (MDV) is depicted in Fig. c. Despite high temporal variability of the Doppler data (the result of vertical air motion and turbulence), a difference in dynamical properties of ice for the two periods is evident. MDVs of approximately 1–1.5 m s-1 in the first period are in agreement with simulations of large aggregates. Much larger velocities, especially after 08:00 UTC, suggest the presence of rimed ice crystals .

Figure d shows the measured lidar backscattering cross section from the ceilometer that is located less than 5 m away from the radars. Thanks to these measurements, periods where the environmental conditions are favorable for riming can by identified. Liquid clouds, which are essential for riming, appear as optically thick layers that strongly attenuate the light signal . The presented measurements exclude their presence before 08:00 UTC for altitudes below 2 km. Afterwards, liquid clouds are detected in the vicinity or within the melting region. Unfortunately, due to strong attenuation no information about the presence of mixed-phase clouds aloft is available.

Vertically pointing Doppler radars usually provide the full Doppler spectrum, i.e., the spectral distribution of the return power over the range of the line-of-sight velocities. Because the raindrop terminal velocity is an increasing and well-constrained function of the raindrop size , these measurements can be used to resolve the drop size distribution (DSD), once the vertical wind and turbulence are known e.g.,.

Our DSD retrieval in the range bins below the melting zone closely follows the steps described in . The only modification introduced here is the extension of the observation vector from two to three frequency bands in order to fully exploit the measurement capabilities of the radar site. The retrieval is based on Bayes' theorem : it minimizes the cost function that is composed of two equally weighted components. The first component computes the weighted distance to the triple-frequency spectra measurements, with the inverse variance of the measurement error used as a weight. The other term calculates the deviation from the prior knowledge of the DSD. For this retrieval, a widely adopted gamma-shaped DSD that fits the spectral measurements the best is used as the a priori estimate for more detail see. The backscattering cross sections of raindrops are computed with a T‐matrix method using the Python code of . The refractive index of water is computed at 10 ∘C using a model of . Terminal velocities of raindrops are interpolated from a dataset of whereas the aspect ratio is calculated with a formula of . The orientation of raindrops is assumed to follow a normal distribution of about 0∘ with a standard deviation of 8∘ . Doppler spectra are simulated according to the methodology described in accounting for turbulence, vertical wind and radar noise level.

The algorithm retrieves binned DSD along with two dynamical parameters: turbulence and vertical wind.

An example of the measurements and the corresponding retrieval is presented in Fig. . As expected, the spectral power for velocities below 4 m s-1 is nearly identical for the different frequencies, which is a result of Rayleigh (∝D6) scattering at all bands for drops smaller than approximately 1 mm. This Rayleigh part of the spectrum can be used to determine differential path-integrated attenuation for different radar bands . The spectrally derived differential attenuation has been accounted for, prior to the retrieval. A significant reduction in the measured power at the W-band compared to the other frequency measurements can be found for velocities exceeding 4 m s-1. This fall velocity regime corresponds to particle sizes for which non-Rayleigh scattering effects increase and culminate at the first resonant minimum, expected at 5.95 m s-1 according to data. The difference between the measured and the anticipated position of the peak in the spectrum corresponds to the vertical air velocity .

The blue line in Fig. b shows the retrieved DSD that minimizes the cost function. This solution fits the measured radar reflectivity with an accuracy of 0.25 dB at all frequency bands (not shown). As it can be seen, the widely used gamma model (orange line) represents the bulk shape of the binned DSD for drops up to 3 mm in size well. Nevertheless, some subtle features of the Doppler spectra, such as an increase in the X- and Ka-band spectra around 6 m s-1 that corresponds to a local DSD maximum around 2 mm, cannot be modeled with the gamma function. It should be noted that although we assume a gamma-shaped PSD as a prior, no explicit functional shape is assumed for the retrieved DSD. This is an important advantage of the spectral retrieval as it allows the retrieval of complex DSDs, such as multi-modal distributions.

In order to connect properties of ice with the properties of rain, several assumptions are made. Firstly, processes across the melting layer are assumed to be in steady state. Secondly, effects of condensation or evaporation are neglected. The radiosonde launched at 09:00 UTC showed RH values exceeding 90 % in the proximity to the freezing level, which effectively excludes the possibility of evaporation. However, the possibility of condensation on melting ice particles and collision–coalescence with cloud droplets cannot be ruled out. Due to the saturation problem of the GRAW humidity sensor the RH measurements are likely to be underestimated, which is confirmed by lidar measurements where signatures of liquid clouds are present within the melting zone after 08:15 UTC (Fig. d), which indicates water vapor supersaturation conditions. Despite the potential inconsistencies of our assumptions with the actual state of the atmosphere, neglecting condensation and evaporation is used as a simplifying hypothesis that implies the flux of mass through the melting zone is conserved. Furthermore, following , , and , no breakup and no interaction between melting particles are assumed. Consequently, we might assume that one ice particle is converted into one raindrop and the mass of each particle is preserved through the melting layer (ms(Ds)=mr(Dr)); thus the particle number flux is conserved at any size. Mathematically, 1NsDsVsDs+wsdDs=NrDrVrDr+wrdDr, where Ns and Nr denote the concentrations, and Vs and Vr are the still-air terminal velocities of snowflakes above the freezing level (subscript s) and raindrops below the melting zone (subscript r), respectively. Vertical air motions ws and wr in snow and rain are assumed to be negative when upwards. Vertical air motions in stratiform precipitation can be assumed to be small compared to sedimentation velocities and hence they are neglected in the following. We will refer to this set of assumptions as the “melting-only steady-state” hypothesis. It is convenient to formulate Eq. () in terms of the equivalent melted diameter Deq, which is a quantity preserved through the melting process:

2NsDeqVsDeqdDeq=NrDeqVrDeqdDeq⇒NsDeq=NrDeqVrDeqVsDeq. Equation () expresses a link between the PSD of ice and the DSD of rain resulting from melting of snow. It shows how the V-D relationship for ice particles influences the shape of the underlying distribution of rain. This relation should be understood as a first-order approximation that can be applied only when (1) the process is steady state, (2) collision, coalescence and breakup are negligible, and (3) the relative humidity is close to the saturation level.

To verify whether or where the MOSS assumption holds, the procedure shown in Fig.  as the black arrows is applied. First, the triple-frequency measurements are extracted from the ranges just below the melting zone. Then, the full Doppler spectra are used to retrieve a binned rain PSD (step A). By applying the MOSS assumption through the melting zone, the rain DSD is mapped into the PSD of ice (step B, Eq. ()). The procedure is applied to 18 different snow models, described in detail hereafter in Sect. . For ease of display, only two models (needles and graupel) representative of two extremes are illustrated in the insets of Fig. . The number concentration predicted for the ice particles just above the melting layer depends on the snow model due to differences between their aerodynamical properties; e.g. the aggregate models are characterized by higher particle concentration than rimed particles (compare the dashed–dotted with the dashed line in Fig. , panel “PSD of ice”). Doppler spectra corresponding to each snow model are derived with scattering and aerodynamical models (step C). The resulting simulated spectra at the three bands are compared with the actual measurements (step D). As a first closure attempt, simulated radar reflectivities for ice (corrected for attenuation using the methodology described in Sect. ) and Doppler velocities are compared with the measurements.

The Doppler spectrum measured by a vertically pointing radar transmitting at the wavelength λ is given by 3Sλ(V)=Aλ×Sλ,w,target∗Tair(V), where Aλ is the two-way attenuation, Sλ,w,target is the reflectivity spectrum due to scattering from radar targets affected by the vertical wind w, Tair is the air broadening kernel and ∗ denotes the convolution operator for more detail see. Note that the vertical wind only shifts the spectrum, i.e., 4Sλ,w,target(V)=Sλ,target(V-w). The reflectivity spectrum, Sλ,target, can be expressed in terms of the particle size distribution and the backscattering cross section as 5Sλ,target(V)=λ4π5|K|2NDeqσλDeqdDeqdV, where σλ gives the backscattering cross section of a target of a given size and |K|2 denotes its radar dielectric factor, and V is its terminal velocity that is assumed to be dependent on the particle size. In this study a wide gamut of “snow models” are considered to account for the large variability of scattering and aerodynamical properties of ice crystals. Each snow model entails a mass–size and an area–size relationship and provides size-dependent backscattering and extinction cross sections and fall speeds.

Broadly speaking two snow classes are analyzed in this study. The first class consists of unrimed aggregates of different ice habits, i.e., needles, plates, columns and dendrites. These aggregates were created using the aggregation code described in detail in . In total, approximately 30 500 aggregates were generated. The total number of monomers, as well as their size distribution have been varied, in order to produce a large variety of shapes and densities. The monomers are distributed according to an inverse exponential size distribution, with the characteristic size ranging from 0.2 to 1 mm with a minimum and maximum monomer size of 0.1 and 3 mm, respectively. The final aggregates consist of up to 1000 monomers and reach sizes of 2 cm. The scattering properties were obtained with the self-similar Rayleigh–Gans approximation (SSRGA; ). The SSRGA allows the approximation of the scattering properties of an ensemble of self-similar, low-density particles (such as aggregates) with an analytical expression and a set of corresponding fitting parameters which characterize the structural properties of the simulated snowflakes. For more detail on the SSRGA model used in this study see .

The second considered class contains snow particles generated by and comprised of aggregates of dendrites with different degrees of riming. Three riming scenarios are included in this dataset: particles, which grew by riming only (model C, LS15C), aggregation and riming occurring simultaneously (model A, LS15A), or aggregation and riming occurring subsequently (model B, LS15B). The degree of riming is expressed in terms of the equivalent liquid water path ranging from 0 kg m-2 for dry aggregates to 2 kg m-2 for graupel-like particles. For instance, “LS15A1.0” denotes the model of aggregates grown by simultaneous riming and aggregation, where particles passed through a layer of 1 kg m-2 of cloud droplets.

The terminal velocities of individual particles in the two snow classes are simulated for a standard atmosphere using the methodology of . Then the expected velocity–size formula for each snow model is generated by a least-square difference fit of the generated data to the Atlas-like formula (suggested by , as also applicable): 6VDeq=α-βexp⁡-γDeq, where α, β and γ are the optimal fitting parameters. The shape of this fitting function is more realistic than the frequently used power-law fits since it can reproduce velocity saturation at larger sizes. Moreover, this parametrization is characterized by considerably smaller root-mean-square error of the fit than the traditional power-law approach. A complete list of the fitting parameters corresponding to the different snow models is given in Table .

While the bottom-up approach (comparing measured and simulated ice Doppler spectra based on rain DSD) only provides a qualitative evaluation of the MOSS assumption, we aim to directly derive the ice PSD from the measured multi-frequency Doppler spectra just above the freezing level. The principal of this OE retrieval is very similar to the OE retrieval used for rain. Of course, the more complex scattering and terminal velocity behavior of snow must be accounted for and will also likely increase the retrieval uncertainties.

In rain, we used the gamma model DSD that best fits the spectra ; in ice, the exponential PSD that best fits the spectral ratios and the radar reflectivity at the X-band is used as a prior estimate. An uncertainty of a factor of 2 is assumed for the prior binned PSD concentration. A prior for turbulence is derived using the method proposed by . The velocity of the slowest detectable radar targets in ice is used as the prior for the vertical velocity (step E). The uncertainties of these estimates are set to 175 % for the turbulence and 0.16 m s-1 for the vertical wind. These uncertainty values are derived from the corresponding root-mean-square differences between the first guesses and the final estimates in rain over the analysis period. The retrieval is performed for all the selected models independently; the distance between the simulated and the measured spectra, δmodel, is used as a measure of quality of the retrievals at each time step. The final estimate of the posterior PSD is derived as a weighted mean of all the solutions. The weights of each model, Wmodel, are computed as the softmax function of the distances to the spectral measurements, i.e., 7Wmodel=e-δmodel2∑modelse-δmodel2-1. The snow retrievals that do not fit the measurements well do not contribute much to the final estimate due to the exponential decay, and the models that resemble the spectral measurements well contribute the most. The uncertainty estimate of the final retrieval is derived from the weighted standard deviation of the solutions. Uncertainties of individual retrievals are neglected in the final estimate because they are much smaller than the variability corresponding to different snow models. For the final solution, parameters like mass flux and equivalent mass-weighted size can be computed and directly compared with the same parameters in the rain (step F). This allows us to achieve the “closure” and, for instance, to assess the validity of the flux continuity assumption.

The goal of this study is to link the properties of rain with the characteristics of the overlying ice in stratiform precipitation. As the rain DSD is the basis for this closure analysis, we first compare the spectra-retrieved DSD with the Parsivel2 measurements at the ground (Fig. ). Despite the vertical distance of approximately 700–800 m between the disdrometer and the radar-retrieved DSD just below the melting zone, the two methodologies provide comparable results. The comparison reveals several advantages of the radar-derived DSDs. First, it is able to retrieve smaller drop sizes (Deq<0.5 mm) that are not detected by the disdrometer . Second, it has much higher temporal resolution (6 versus 60 s). Third, it provides more reliable estimate of the number of large drops that are very infrequent and may not be captured by the limited sampling volume of the disdrometer. Note that the spectral method also has its limitations; e.g. the retrieval for Deq<0.2 mm must be interpreted with caution due to increasing uncertainties see.

Throughout the rest of the paper, the period of large DFRX-Ka values (aggregation) is marked by the light blue color, whereas the domain of enhanced Doppler velocity (riming) is shaded in red. The DSDs during the two periods are quite distinct: the aggregation-dominated period (almost 1 h) is associated with a larger number of big drops and almost exponential DSDs. During the following riming period, a much larger concentration of small droplets and multi-modalities of the DSD are found. There are two potential sources of this high concentration of small droplets: super-cooled drizzle that forms aloft by coalescence of supercooled cloud droplets or secondary ice crystals, e.g. generated by the Hallett–Mossop process . In the first scenario, the slowly falling mode does not significantly change its intensity and position in the Doppler spectrum while passing through the melting zone because there is no phase change of the particles. In the second scenario, the melting process changes the velocities and backscattering properties of the hydrometeors, thus resulting in a shift and a change in amplitude of the spectral power of the mode. The following analysis of the evolution of the Doppler spectra from the ice to the rain part is therefore expected to better explain the source of the small droplet mode.

Differences between riming and aggregation regimes are reflected in the Doppler spectra that are shown in Fig. . During aggregation, the spectra in the ice phase are unimodal and the position of the peak is relatively constant at different heights, which indicates weak vertical air motion (Fig. a). The transition from ice to rain, corresponding to a strong broadening of the spectra, happens very rapidly within less than 200 m. The “aggregates” have a consistent spectral peak to 4 km, while the “rimed” particles also show a vertically coherent peak, but only up to 1.75 km in altitude. The spectra from the riming period (Fig. b) are characterized by a much thicker melting layer (approximately 400 m) and by bimodal distributions both in rain and in ice. The secondary ice mode appears approximately 1–1.5 km above the melting level, which corresponds to temperatures ranging between -4 and -6.5 ∘C according to the radiosonde launched at 09:00 UTC. There is high vertical variability in the position of the main peak, which indicates more dynamical conditions. The secondary mode increases its intensity while approaching the melting level but remains clearly separated from the main peak (see Fig. b). In the melting zone this separation disappears, and the fall speed of the secondary mode increases so that the secondary peak stretches out in the velocity domain and merges with the primary mode. This behavior excludes the scenario of super-cooled drizzle above the freezing level as it was discussed before. The LDR measurements at the Ka-band (Fig. d) are in agreement with this theory. The slowly falling mode corresponds to LDR reaching -15 dB; such values are much larger than those expected for nearly spherical drizzle droplets. This spectral feature is similar to the enhanced LDR signatures found in and . They related the high-LDR region to columnar ice crystals grown in liquid-cloud layers through secondary ice production. Interestingly, the high-LDR signature of the small ice mode can also be detected during the melting of these particles, which might imply that the columnar crystals are of considerable size as they seem to maintain their asymmetric shape for quite some time until they are completely melted into drops (Fig. d). During aggregation, the opposite is true, i.e., the Ka-band LDR of large snowflakes is clearly larger than that of small ice crystals. This increase in LDR for large aggregates is principally consistent with scattering simulations of realistic snowflakes in their Fig. 7 where LDR values are predicted to increase for maximum sizes exceeding 5 mm.

Note that the secondary mode in rain (Fig. b) appears to be disconnected from the secondary mode in ice during riming. At an altitude of approximately 800 m there is a clear gap between them, which is shown by the black box in Fig. b. This separation is present over several minutes, which suggests that the small rain droplets do not originate from the melting of ice crystals; thus the assumption of one-to-one correspondence between ice particles and raindrops may not hold for this profile. Lidar measurements (Fig. d) indicate the presence of a small droplets within the melting zone; therefore the secondary mode in rain is likely to be drizzle generated by this liquid layer or melting ice crystals (too little to be detected by the radar) that underwent rapid growth through collision–coalescence processes while passing through the cloud.

In a first step, we derive the DSD of ice from the PSD of rain via the MOSS assumption (Eq. ). Figure a shows the DSD mass-weighted mean diameter (Dm) and the water content (WC), as it is retrieved from the Doppler spectra in the rain below the melting region. The aggregation period is characterized by smaller water content but larger characteristic size of raindrops compared to the riming period. With the MOSS assumption, the ice WC and the melted Dm of snow depend on the V-D relationship of ice and on the rain DSD. Because the velocities of raindrops are larger than those of the same-mass snowflakes of any density, it follows that Ns(Deq)>Nr(Deq). Consequently, the assumptions made in Sect.  imply that the ice WCs at the freezing level are always larger than the rain WCs just below the melting zone (Fig. b). In the most extreme scenario, i.e., in the case of slow dendrite aggregates, ice WC can be 7 times larger than rain WC. For rimed snowflakes, this difference is much smaller, but still a factor of 2 is expected for graupel-like particles. Because the ratio Vr(Deq)/Vs(Deq) is not constant but rather monotonically increases with size, the ice PSD is not simply a scaled version of the underlying DSD of rain; i.e., the number concentration of large particles is increased compared to the small ones. This causes a reduction of the mean mass-weighted diameter (Dm) during melting; i.e., the expected characteristic size of the DSD below the melting zone is up to 30 % smaller than the corresponding size in the ice aloft (Fig. c), and this change is purely ascribed to aerodynamic effects combined with the mass flux conservation constraint. Note that for the majority of the particle models, the associated difference in Dm usually does not exceed 10 %; for rimed particles this change is even less pronounced and the characteristic melted-equivalent size is practically preserved.

Instead of only a qualitative comparison of the MOSS assumption (step D in the schematic Fig. ), we are now able to directly analyze the differences in mass flux and PSD above and below the melting layer by using the associated retrieval results for rain and ice. In this way, we can quantify the differences according to the dominating processes, which is expected to also be relevant for future modeling studies.

The PSD multi-spectral retrieval described in Sect.  (step E in Fig. ) is applied to the whole period, and the results are presented in Fig. . The mass flux and Dm above the melting level (continuous lines in Figs. a–b) are derived as an ensemble mean of the multi-frequency spectral OE ice retrievals where each solution is weighted by its distance to the observed spectra as is shown in Fig. . The most probable snow model for the “aggregate” period is aggregates of dendrites (LS15A0.1 represents aggregates of dendrites with very light riming). During the period of enhanced Doppler velocities, the retrieval suggests snow models of rimed particles. Rimed snow models also fit the measurements the best at later times, but because the characteristic size of particles is relatively low (Fig. ), the mean Doppler velocity cannot be used to unequivocally confirm the presence of rimed particles. The agreement between the snow model selection discussed in Sect.  and the models suggested by the OE technique is quite remarkable, which confirms a potential of using the MOSS hypothesis to at least reduce the number of plausible snow models in the analysis of the spectra just above the melting layer.

As a consistency check, the reflectivities for the derived PSD and snow model are compared in Fig. c, illustrating a very good match with the observations. The comparison of the derived mass fluxes in rain and ice (Fig. a) suggests that for most of the time the mass flux across the melting zone is well preserved. The rain rate below the melting zone is within the uncertainty estimates of the precipitation rate above for the whole case study except a 30 min period around 09:00 UTC where strong riming occurs. The estimated total accumulations of rain (2.30 mm) and the melted equivalent accumulation of snow (1.93 mm) during the 6 h time period show only a 19 % difference. Interestingly, the mass flux during the aggregation period tends to be higher than the precipitation rate below while the opposite is true during the riming period. As expected, there is a strong correlation of 0.67 between the mass fluxes above and below the melting layer (CC = 0.82 if the 30 min period around 09:00 UTC is removed).

During the aggregation period, the snowfall rate is on average 34 % larger than the precipitation rate below the melting zone, which corresponds to a mean decrease from 0.43 to 0.32 mm h-1. The characteristic size is found to be 84 % larger in ice than in rain and 67 % larger than one would expect, based on the MOSS assumption. Because aggregates are often composed of loosely connected crystals , this change in size could be caused by the breakup of the melting snowflakes as already conjectured in Sect. . The breakup hypothesis is also supported by a recent simulation study , where it was shown that the melting of the fragile ice connections within unrimed aggregates causes the particles to break into multiple droplets. Laboratory measurements of melting of snow aggregates, recorded under controlled temperature, relative humidity and air velocity , are also in agreement with this interpretation. However, the decrease in precipitation rate during the aggregation period cannot be explained by breakup that does not affect the mass flux. Other processes, such as evaporation and sublimation during melting would be needed to explain this reduction in the precipitation rate. If present, those processes would also contribute to a reduction of the characteristic size.

During the riming period the rain rate is approximately 44 % larger than the snowfall rate, with the largest difference reported between 08:45 and 09:15 UTC (approximately 58 % difference). This increase in precipitation rate could be explained by continuous riming within the melting layer. The ceilometer data (see Fig. d) seem to indicate a layer of small liquid drops within the melting layer which might contribute to the enhanced rain rate by either riming or later also collision–coalescence of the small cloud droplets with raindrops from already melted snowflakes. However, the characteristic size appears not to change during this period, which is inconsistent with this hypothesis. Therefore, we speculate that additional processes, such as shattering of large drops, might compensate for the raindrop size growth.

Considering the case study except the extreme aggregation period, we find the characteristic size of snow to be only 2 % larger than that of the rain underneath. The root-mean-square difference between them is equal to 0.18 mm only, whereas the correlation coefficient is 0.81. Recently published DWR statistics reveal that the very large DWR signals found in this case study due to aggregation are relatively infrequent, which suggests that the relationship between snow and underlying rain is quite robust. If this can be confirmed for different locations and a larger dataset, it would provide a very strong constraint for micro-physical retrievals .