The Copernicus Ka-band (35 GHz) radar at the Chilbolton Facility for Atmospheric and Radio Research (CFARR) takes continuous routine observations, including reflectivity, MDV, standard deviation of mean Doppler velocity (σv‾) and spectral width . It also takes observations of Doppler spectra every minute; it is important to note that these are 1 s spectra recorded once per minute, and are not an average over several seconds. Key properties of the radar are summarised in Table  see also. Note that here and throughout this study, negative velocities indicate movement towards the radar, and therefore indicate descending hydrometeors for our vertically pointing radar. Increases or decreases in velocity will be discussed in the absolute sense whilst retaining the negative sign convention.

Using archived data, we identify 23 frontal case studies from a 14-month period in 2017–2018 to examine in closer detail; Table  provides further detail on each of these cases and more information for each case can be found in the Supplement. The cases were chosen by looking for nimbostratus cloud systems in the daily radar quicklook plots, and comparing those events with features marked on the operational Met Office surface pressure analysis charts. The analysed cases were selected to represent typical frontal clouds, and are primarily stratiform with large vertical extents covering a wide range of temperatures, and surface precipitation for part of the observation period. Data from all 24 h of each case study day are included in the analysis that follows. Reflectivity, example spectrograms, and results from the peak finding method (see Sect. ) are shown for each case in the Supplement. Data are received in their raw, uncalibrated form, and therefore noise correction and calibration methods must be applied before further analysis is carried out. Corrections to reduce the impact of signal attenuation by rain and turbulent Doppler spectra broadening are also applied. These processes are explained in the following sections.

Archived NWP model data for Chilbolton for each case was obtained via the ACTRIS Cloudnet portal. ICON model data is available for cases from 6 January to 17 May 2017, which has a lead time of 12–23 h, and ECMWF IFS data is available for cases from 27 June 2017 to 14 February 2018, which has a lead time of 12–35 h. Variables are forecast hourly in both models. Here, we are primarily interested in temperature from the models so that comparisons can be made with the location of different microphysical features. As our cases are associated with extratropical cyclones, they do not have fine scale temperature fluctuations, so hourly forecast temperatures are sufficient. compared the height of the 0 °C isotherm from modelled hourly temperature profiles against the height of the bright band for several frontal cases, and found that models were able to capture of the height of the bright band and the shape of the frontal surface mainly with very good accuracy. Comparison between the height of the bright bands with that of the 0 °C isotherm in our cases showed similarly good agreement, and it is therefore likely that differences between the modelled and true atmospheric temperature are not introducing large uncertainties into our results. Doppler spectra measurements are made every minute; we therefore interpolate the temperature field onto the same grid so that we have a temperature profile for every Doppler spectrogram. The horizontal wind fields are also used as inputs to Eq. ().

In order to quantify the fraction of multimodal spectra in our case studies, we identify the number of peaks in the one dimensional Doppler spectra at each time and height gate (hereafter referred to as “pixels”). It is unrealistic to manually identify the spectral peaks in each of the 15.9 million pixels examined in this study, so we apply a peak finding algorithm to the one dimensional Doppler spectra. We use the SciPy function “find_peaks” to identify peaks in spectral reflectivity. This function was chosen because SciPy is designed to efficiently process large quantities of data. Section  and Table  describes the tuneable parameters in the “find_peaks” functions in more detail and how they were chosen, and Sect.  describes how we validate the accuracy of the peak finding parameters.

On 6 January 2017, an area of relatively deep low pressure, centred between Iceland and Scandinavia, was associated with a complex multi-fronted system. A warm front and two occluded fronts associated with this system passed over the UK before meeting a blocking high pressure centred over Central Europe. An ice cloud associated with these fronts was observed, which was up to 7 km deep above the melting layer (which remained at around 2 km throughout the day). Moment level observations of this cloud made by the Copernicus radar (described in Sect. ) are shown in Fig. . Here we show the reflectivity in Fig. a, MDV in Fig. b, and spectral width in Fig. c. A thin layer of low level cloud is present for several hours during the first half of the day along with some upper level cirrus (see Fig. S1 in the Supplement), before the thick frontal cloud comes into the view of the radar at around 13:00 UTC and persists for the rest of the day. There are hints of microphysically interesting features in this cloud such as discernible regions of increased spectral width that correspond to “streaks” in the reflectivity and changes in MDV, for example between 14:00 and 17:00 UTC and between 21:30 and 23:30 UTC at heights of approximately 2–3 km. There was moderate rainfall associated with this cloud, shown in Fig. d, which started at 14:00 UTC and continued for the rest of the day, reaching peak values of ∼ 4 mm h⁻¹ between 23:00 and 00:00 UTC.

Microphysical features, such as those mentioned above, can be investigated in greater detail using the results from the peak finding method described in Sect. . From this method we have an estimate of the number of peaks observed in the Doppler spectra for each pixel in a cloud, and the Doppler velocities for both the primary and secondary populations. The results from this analysis are shown in Fig.  and Fig. . Figure a shows the number of identified peaks per pixel and Fig. b shows the skewness of the Doppler spectra. It is useful to compare the location of identified multimodal spectra against the skewness of the one-dimensional Doppler spectra, as multimodal particle populations are thought to cause the shape of the Doppler spectra to deviate from that of a Gaussian distribution. However, two separate identical modes could also cause the skewness to be zero as the distribution would be symmetrical. Fig. a shows the velocity of the primary population, Fig. b shows secondary velocities, Fig. c shows tertiary velocities and Fig. d shows the difference between the primary and secondary velocities. Temperature contours from archived ICON data are shown in blue on all panels.

We find that multimodal spectra are frequent between the temperatures of -5 and 0 °C from around 14:00 UTC until the end of the observed period. It is interesting that the number of peaks also increases with increasing temperature in some parts of this layer; there is a visible shift from bimodal to trimodal spectra with increasing temperature at 14:00–15:00, 17:30–18:30, and 19:00–20:00 UTC. Inspection of spectrograms at different times, for example those shown in Fig. , reveal that there were indeed a mixture of trimodal (Fig. a) and bimodal (Fig. b) spectra observed on this day. At temperatures between -5 and -15 °C, there are a handful of isolated regions with multimodal spectra at approximately 14:00–15:00 and 20:00–21:00 UTC. Multimodal spectra are almost non-existent at temperatures colder than -15 °C. Comparison with the skewness shown in Fig. b reveals that the location of multimodal spectra identified by the peak finding method is largely consistent with regions of positive skewness. Consistent with , skewness appears to increase at temperatures colder than the multimodal spectra identified by the peak finding algorithm; this may suggest that skewness is sensitive to multimodal particle populations where the two populations are too similar to be separated by the peak finding algorithm. An understanding of the microphysical processes that are active in this case may be gained by examining the velocities in Fig. . We find at temperatures lower than -5 °C, primary velocities (Fig. a) remain consistent with height. At temperatures greater than -5 °C, we see that the primary velocity increases as particles fall, with velocities reaching -1.5 to -2 m s⁻¹. These increases in velocity are correlated with the presence of multimodal spectra. This suggests that the process responsible for producing multimodality in the Doppler spectra is connected to the increased primary mode vertical velocities. Riming causes increased particle fall speeds due to increased mass, without causing particles to grow much in size; this is because it acts to “fill in the gaps” of open structured particles such as dendrites and aggregates before adding to the overall size e.g.. Riming necessarily occurs in environments which are saturated with respect to liquid water, and therefore splinters which may be produced by rime splintering can rapidly undergo vapour growth to form needle and column crystals which fall at a distinctly slower speed than the rimed population. If they grow large or fast enough, the needle and column crystals themselves will begin to rime. Secondary and tertiary velocities (Fig. b and c) also appear to increase as temperature increases, suggesting particle growth, but interestingly the difference between the primary and secondary velocities (Fig. d) appears to remain relatively constant. Examination of the velocities shown on the spectrograms in Fig.  suggests that this may result from similar rates of increasing particle population velocities.

Example spectrograms shown in Fig.  support the suggestions outlined above. Figure a shows evidence that both a secondary ice mode and a drizzle mode are present at this time, which corresponds to a region where trimodal spectra were identified (shown in Fig a). The drizzle mode is first visible at 2.75 km, and is identifiable as the vertical velocity of the population does not rapidly increase at the melting layer, and indeed remains separate in the rain below. The one-dimensional Doppler spectra shown in Fig.  shows that the drizzle mode is visible as a tertiary peak in the Doppler spectra above the melting layer, and is also visible as a separate population below the melting layer. The velocity of the primary population increases rapidly at the same height as the drizzle mode is first visible, which suggests the primary population is riming. One explanation for the production of the secondary ice particle mode is therefore rime splintering; cloud droplets are required to form and grow drizzle drops, so the presence of drizzle shows that there is liquid water present at temperatures associated with rime splintering and that liquid water droplets are therefore available for riming. Another explanation is that droplet fragmentation is producing the secondary ice population here, as it is possible that some of the drizzle drops will freeze and produce secondary particles via the mechanisms described by . Figure b shows a secondary particle mode is visible at heights of approximately 2–2.5 km, which corresponds to temperatures of approximately -3 to 0 °C. This secondary mode consists of ice particles as it melts at 0 °C, as seen by the rapid increase in vertical velocity of the population. It seems unlikely that droplet fragmentation is producing the secondary mode here due to the lack of a drizzle mode in the Doppler spectrogram; it follows that rime splintering may be responsible but without knowledge of whether cloud droplets are present, it is not possible to definitively ascertain the mechanisms that may be active. The primary population velocity increases from the top of the profile to around -17 °C, where a slight decrease in velocity is apparent and reaches a minimum at approximately -13 °C. This feature has been observed previously e.g., and the potential mechanisms responsible for producing this feature are discussed in greater detail in Sect. . Particle velocities gradually increase again from around -13 to 0 °C.

On 17 May 2017, low pressure conditions were dominant over the UK resulting in several frontal features which passed over the UK throughout the course of the day. Associated with these frontal features was a long-lived ice cloud which was up to 8 km deep above the melting layer and which persisted for the majority of the day. The melting layer was at about 3 km and dropped slightly in height throughout the day. Moment level observations of this cloud are shown in Fig. , with reflectivity in Fig. a, MDV in Fig. b and spectral width in Fig. c. At a glance, this appears to be a more homogenous cloud than that in the previous case study, with fewer clear microphysical features. There is a region at 5–6 km between 10:00 and 15:00 UTC with MDV that is lower than the surrounding regions, and the values of MDV observed here are less than -0.5 m s⁻¹. Interestingly, Fig. a shows that the velocities of the primary population also decrease in the same region. We see that there are increased values of spectral width at 13:00 UTC which correspond to a disturbance of the melting layer which is visible in Fig. a–b. Figure d shows the rain rate, which remains moderate to heavy throughout the day, with an intense shower at 13:00 UTC. This very heavy shower corresponds with the disturbance in the melting layer visible in Fig. a–c, which suggests that this feature is a cell of embedded convection. Figure  shows that the turbulent contribution to spectral width is high in this region, and is therefore removed when the turbulent filtering method described in Sect.  is applied.

The results from the peak finding method can again be used to infer what processes are influencing the development of this cloud, and are presented in Fig. . Figure a shows the number of identified peaks and Fig. b shows the skewness of the one-dimensional Doppler spectra. As described in Sect. , skewness is an indication of how much the one-dimensional Doppler spectra deviate from a symmetric distribution. We see that the regions of high skewness are largely consistent with regions of multimodality detected by the peak finding algorithm. We see that the distribution of multimodal spectra in this example is different to the that examined in Sect. . Almost all multimodal spectra are bimodal, expect a few isolated regions early in the observation period which are trimodal. From Fig. a, we can see that at temperatures between -5 and 0 °C, multimodal spectra are prevalent throughout much of the cloud. Figure  shows the velocities of the different populations in this cloud; Fig. a shows the velocity of the primary population, Fig. b shows the velocity of the slow mode and Fig.  shows the velocity difference between the two populations. Similarly to the case analysed in Sect. , we suggest that the multimodality observed is associated with riming, as there are increased primary velocities visible in Fig. a that are consistent with particles influenced by riming; particle velocities are approximately -1.5 m s⁻¹ throughout much of the cloud layer at temperatures between -5 and 0 °C. The slow mode velocities in this layer, shown in Fig. b, appear to increase with temperature. The difference in velocity between the two populations (Fig. c) decreases with increasing temperature, indicating growth of the secondary population. The presence of the slow particle mode, together with its increasing velocity with temperature, strengthens the argument that riming is active at these temperatures. Consequently, rime splintering may also be active and responsible for the presence of the slow particle mode. Given the lack of trimodal spectra in this case, it seems unlikely that fragmentation during freezing of drizzle drops is producing the observed multimodal signatures; spectrograms shown in Fig.  support this idea as there is no evidence of a drizzle mode. We also find that between temperatures of -10 and -15 °C there are frequent multimodal regions. The mechanism behind this multimodality is unclear, as this is outside the temperature range which is expected for the rime splintering mechanism. The velocity of the secondary population at these temperatures is very slow at around -0.25 m s⁻¹. As dendritic growth is preferential at these temperatures, it follows that the slow particle mode may consist of small plate-like or dendritic particles which fall slowly due to relatively large surface areas resulting in increased air resistance. It is also possible that small drizzle drops (∼ 100 µm) would produce a similar signature here, but it seems unlikely that they would persist at these temperatures in stratiform cloud.

Figure  shows two examples of spectrograms observed during this case study. In Fig. a, a secondary population is visible that forms at approximately -7 °C and increases in vertical velocity, but remains distinct from the primary population. In Fig. b, it is possible to see a secondary population which forms at -15 °C and grows until the velocity becomes indistinguishable from the primary population at approximately -10 °C. Another secondary population is visible from around -7 °C to the melting layer. It is clear that the secondary populations shown in Fig. a and b are ice as they rapidly increase in velocity at the melting layer, thus suggesting that drizzle is not prevalent in this case; one-dimensional spectrograms shown support this suggestion as there is only population visible below the melting layer.

In Sect.  and , we have qualitatively analysed the distribution of multimodal spectra with temperature, and discussed possible mechanisms influencing the development of the clouds in these case studies. In order to make these findings applicable more generally, it is useful to quantify the distribution of multimodal spectra with temperature across all of the case studies outlined in Table . We therefore calculate an estimate of the fraction of “in-cloud” pixels where multimodal spectra are observed and the results of this analysis are shown in Fig. . The grey lines show the results for individual case studies, and the black line shows the overall statistics. show statistics of multimodal spectra identified using moment-level variables but to the best of our knowledge, the frequency of observed multimodal spectra identified by analysis of spectral reflectivity has not been quantified in this way previously.

The magenta shading in this figure highlights temperatures from -3 to -8 °C, which is the temperature range in which it is thought that the rime splintering mechanism is active and references therein, and indeed previous studies have shown in situ observations of particles which are consistent with rime splintering being observed at these temperatures e.g.. However, as the mechanism behind rime splintering remains uncertain, references to the “rime splintering regime” throughout this section are referring the range of the temperatures between -8 to -3 °C and are not intended to imply that rime splintering is necessarily active. We see that throughout this temperature regime, the percentage of multimodal spectra increases rapidly from approximately 15 % at -8 °C to 40 % at -3 °C. The percentage of multimodal spectra continues to increase at temperatures higher than this ice multiplication regime, which suggests that secondary particle populations continue to grow and evolve throughout this relatively narrow temperature band before reaching the melting layer. Individual cases vary in the magnitude of the percentage of multimodal spectra throughout this regime, but all follow broadly the same pattern.

At temperatures of -10 to -18 °C, we see an increase in the percentage of multimodal spectra from less than 5 % at -18 °C to a maximum of 20 % at -13 °C. This is outside of the temperature range that the rime splintering mechanism is thought to be active in, so we expect that a different mechanism is causing the observed multimodality. It is possible that new particles at these temperatures are formed by primary nucleation and that the newly-formed dendritic particles fall slower than crystals falling from above, leading to two populations of ice crystals with distinctly different fall speeds existing in the same radar volume e.g.. This raises the question of why primary nucleation would consistently occur in this region. There is a lack of evidence in the current literature that ice nucleating particle (INP) concentrations increase at these temperatures, and instead observations support that idea that INP concentrations decrease with increasing temperature e.g.. There have been studies which show that conditions here are potentially favourable for SIP; droplet fragmentation and ice-ice collisional fragmentation have been suggested as potential mechanisms for the production of secondary ice particles at temperatures outside the rime splintering regime . Droplet fragmentation has received some attention in recent years , and occurs when a drizzle drop spontaneously freezes and projects splinters as a result of a shattering ice shell. This process is unlikely to be the primary cause of multimodality observed at these temperatures, as we have not seen signatures consistent with a drizzle mode visible in the Doppler spectra at these temperatures. Trimodal spectra, which are likely to indicate the presence of a drizzle mode (see Fig. a), are only detected at temperatures warmer than -5 °C in Fig. a and there are very few trimodal spectra in Fig. a. Ice-ice collisional breakup has also been proposed as an efficient SIP mechanism (; ; ; ), in which ice fragments are produced during collisions between ice particles. suggest a link between increased aggregation between dendritic particles and potential production of ice fragments formed during collisions. Dendritic growth on particles precipitating from above produces fragile branches which may be susceptible to fragmentation, and the fragments produced may have the potential to grow into a secondary particle mode. Whilst there have been laboratory studies carried out previously to investigate these processes, a lack of observational in situ evidence means uncertainty surrounding the efficiency and feasibility of these mechanisms remains high.

Multimodal spectra are very rare at temperatures lower than -20 °C, with just 0.64 % of all spectra at temperatures less than -20 °C identified as multimodal; this is in agreement with previous studies which support the argument that SIP is very inefficient at low temperatures . However, presented a case study of a precipitating cirrocumulus-nimbostratus cloud system with generating cells of turbulence, and suggested that SIP can be observed at temperatures as low as -27 °C. This demonstrates the continued importance of investigation into SIP processes active outside of the rime splintering regime.

The velocities associated with the peaks identified by the peak finding algorithm can help us gain understanding into how these vary with height; these velocities will be referred to as peak velocities throughout this section, as they are the velocity at which the peak spectral reflectivity is observed. Note that these are not MDVs for each population, but specifically the velocity at which the peak spectral reflectivity occurs. It is possible to separate the peak velocities into the different populations they represent, as described in Sect. , and in Fig.  we therefore show histograms of all peak velocities (a), all primary peak velocities (b), primary peak velocities from monomodal spectra (c), primary peak velocities from multimodal spectra (d) and slow mode velocities (e) against temperature. The medians from Fig. a–e are shown in Fig. f to facilitate simple comparison. This analysis shows some interesting features. We see from Fig. a–c that the vertical profile of all peak velocities, all primary peak velocities and monomodal primary velocities is generally similar, and Fig. f shows that the medians are frequently indistinguishable from each other. This suggests that the influence of secondary peaks on the overall distribution of velocities (Fig. a) is modest, but there are differences which demonstrate that this cannot be neglected. Here, we see that velocities in Fig. a–c increase with temperature from -50 °C, where the median velocity is approximately -0.6 m s⁻¹, to -18 °C, where the median velocity is around -0.9 m s⁻¹. There is a clear decrease in velocity between -18 and -13 °C, where the median velocity falls to around -0.8 m s⁻¹. Whilst this appears to be a small change, this equates to an 11 % reduction between the velocity at -18 and at -13 °C. We attribute this feature to dendritic growth on particles precipitating from above – that is, the growth of dendritic branches on polycrystals and aggregates formed at lower temperatures. These geometrically open dendritic features experience greater drag force than other crystal growth habits, and therefore fall more slowly for a projected area to given mass ratio . From this velocity minimum at -13 °C, the median velocity increases with temperature for the rest of the profile, however the temperature range between -10 and 0 °C is where we see the greatest differences between these profiles. Figure a shows that the median velocity remains approximately constant at -1.1 m s⁻¹ between -8 and -3 °C, before increasing to -1.5 m s⁻¹ at 0 °C. In contrast, the median velocity in Fig. b increases mostly consistently from -1.0 m s⁻¹ at -10 °C to -1.3 m s⁻¹ at 0 °C. In Fig. c, we find that the median velocity increases gradually from -1.0 m s⁻¹ at -10 °C to -1.2 m s⁻¹ at 0 °C.

Figure d–e show velocities associated with multimodal spectra. It is clear from Fig. f that the primary velocity from multimodal spectra is consistently higher than from monomodal spectra, remaining higher than -1 m s⁻¹ between temperatures of -20 and -10 °C, and increasing to approximately -1.3 m s⁻¹ throughout the rime splintering regime. This may suggest that riming is influencing the velocity of particles in this temperature regime, although the median velocity remains lower than -1.5 m s⁻¹; this is the threshold at which suggest high vertical velocities can be reliably assigned to riming. Figure e shows the velocities of the slow particle mode, and demonstrates clearly the temperatures at which the slow mode is first detectable. The median velocity clearly shows the formation and growth of an appreciable slow falling population from -15 °C, where the median velocity is -0.5 m s⁻¹, to -10 °C, where the median velocity has increased to -0.7 m s⁻¹. Another growth regime is then visible from -5 °C, where the median velocity is -0.6 m s⁻¹, to 0 °C, where the velocity has increased to -0.8 m s⁻¹. This supports our argument for the existence of multiple populations at these temperatures, with the slow particle mode increasing in velocity as temperature increases suggesting growing particle size.

It is also possible to calculate the distribution with temperature of MDV; Fig.  shows this distribution for all spectra (a), monomodal spectra (b) and multimodal spectra (c). Figure d shows the medians from Fig. a–c for simpler comparison. We see from Fig. a–b that the profile of MDV with temperature is very similar in shape, but the median MDV from monomodal spectra is consistently slightly slower than from all spectra at temperatures higher than -15 °C. This is particularly visible in the lowest section of the profile between -5 and 0 °C (see Fig. d). Comparison with Fig. a and c shows that these profiles are consistent with the profiles of primary velocities from all spectra and monomodal spectra respectively. Interestingly, we see in Fig. c–d that the median MDV from multimodal spectra is consistently faster than from monomodal spectra throughout the whole profile, which is in agreement with the increased primary population velocities seen in Fig. d. This further supports the suggestion that the mechanism responsible for producing multimodal spectra acts to increase the velocity of the primary population, and that this has a greater influence on the MDV in both of the identified temperature regimes than the presence of the slow particle mode. However, monomodal spectra have a greater influence on the overall MDV at this temperature, as seen by the decreased MDV at -13 °C visible in Fig. a. Figure  shows that around 20 % of spectra are multimodal at this temperature, and therefore the majority of spectra are monomodal.

Previous remote sensing studies have aimed to characterise the vertical profile of MDV, and have suggested that on average it increases monotonically with increasing temperature. For example, calculate vertical profiles of MDV from Doppler radar for separate coexisting particle populations, and demonstrate that this variable generally follows a monotonically increasing profile for the primary particle mode, with small variations at temperatures close to 0 °C. The vertical MDV profile of the secondary modes show greater variation between cases, both in magnitude and profile shape. However, these results were shown for relatively short time periods (in the order of 20 to 30 min), where short lived but high-frequency random air motions such as turbulence or gravity waves may influence results . Another example is the statistics of MDV from Doppler radar data presented by . The data were collected over a 7-year period in Antarctica and the statistics show that the observed MDV in these cases follows a monotonically increasing profile. However, the profile of MDV is calculated against height, meaning smaller scale features in the this profile may be smoothed by varying vertical temperature profiles in different atmospheric conditions. show findings from a continuous sample of stratiform ice clouds over 17 months that the vertical velocities of ice crystals relative to a 1.5 µm Doppler lidar have a strong temperature dependence; particles fall faster at higher temperatures which indicates the influence of particle growth and aggregation. However, close inspection of Fig. 3 in shows that it is possible to see a fractional decrease (∼ 0.05 m s⁻¹) in the average lidar Doppler velocity at around -16 °C. Using the same dataset, investigate the fall speeds of specularly reflecting ice crystals in layer clouds; these are assumed to be planar crystal types, such as plate-like and dendritic crystals. The distribution of fall speeds of specularly reflecting particles demonstrates that instead of systematically increasing with temperature, there is a reduction in particle velocity at approximately -13 °C see Fig. 13 in. As these statistics are shown for specularly reflecting crystals, and this temperature is within the DGL, it is reasonable to suggest that the dominant crystal type at this temperature is dendritic. This feature is not discussed by , but rather is treated as evidence of the velocity distribution of specularly reflecting crystals being slower and having a weaker variation with temperature compared to the statistics shown for “normal” (i.e. non-specularly reflecting) ice cloud in . However, comparisons with results shown in Figs.  and  suggest that the results shown by are in fact in agreement with the idea that dendritic crystals, whether pristine dendrites or precipitating particles with dendritic growth, consistently fall more slowly than different crystal types in other temperature regimes.

There have been different explanations in literature for observations of decreased MDV in the DGL. One suggestion is that the presence of a slow-falling secondary ice mode acts to decrease the observed MDV . An alternative interpretation suggests that these changes at -15 °C are driven by ascending air motion at that level. However, our observation of multimodal spectra at this temperature over many events seems inconsistent with this idea as it is not obvious why ascent would be concentrated at that particular temperature. Our data is dominated by frontal clouds formed by large-scale ascent, which occurs over a wide range of temperatures. Another explanation suggests that enhanced depositional growth in the DGL causes latent heat release that is sufficient to increase buoyancy and consequently cause upward air motion . test these interpretations by analysing spectral edge velocities and conclude that the reduction in MDV is the result of new particle formation with low vertical velocities combined with the presence of a weak updraft likely caused by latent heat release from enhanced depositional growth. Our results instead demonstrate that changes in the primary population typically govern this decrease in MDV.

In Fig. , we show that there are two temperature regimes in which multimodal spectra are frequently detected. These temperature regimes are located between approximately -8 and -3 °C, where up to 40 % of spectra are multimodal, and between approximately -18 and -10 °C, where up to 20 % of spectra are multimodal. Whilst relatively little research into ice multiplication has focussed on frontal clouds, show findings from aircraft observations of a frontal case study that multimodal particle size distributions (PSDs) at -5 °C were likely to be caused by rime splintering in the case analysed. Two flight segments were analysed at -5 °C, one with significant liquid water content (LWC) but infrequent observations of drizzle-sized drops, and one without significant LWC. Analysis of particle shape in the segment with liquid water showed results consistent with the presence of two distinct particle populations coexisting in the same cloud volume, along with observations of needle crystals which were significantly higher in concentration than the expected ice nuclei concentration . Ice particle concentrations in the segment where liquid water was absent were consistent with primary nucleation. Based on these observations, it is reasonable to suggest that neither ice-ice collisional fragmentation nor droplet fragmentation was the dominant source of small particles in this case. Given that the case studies described in Table  were selected to represent similar cloud types (i.e. stratiform frontal clouds), it may be reasonable to suggest that rime splintering is also active at similar temperatures in many or all of the cases analysed here. However, some care is needed in this interpretation as small particles produced by any mechanism, whether primary or secondary ice production, within this temperature range of around -8 to -3 °C would be likely to grow rapidly by vapour diffusion into a distinct population of needle-like and columnar crystals; it is therefore nearly impossible to definitively state which ice production mechanism is dominant based on observations alone.

The frequent detection of multimodal spectra between -18 and -10 °C is more puzzling. In Figs.  and , we show that there is a local minimum in the velocity of the primary population in the DGL; we suggest is caused by growth of dendritic branches on particles falling from higher altitudes, which acts to increase their drag and reduce the fall speeds of those particles. One possible explanation for the formation of the secondary mode in this temperature regime is that secondary particles are created by collisions between ice particles. Dendritic branches are thin and one could imagine that they could therefore break away from the rest of the ice particle or shatter into smaller fragments on impact and references therein. Once detached, these fragments will grow from vapour into new ice particles, producing a new population of slow-falling secondary particles which grow and sediment faster as they evolve and settle through the DGL. These will appear as a slow mode in the Doppler spectra with the velocity of this secondary peak increasing in magnitude as they fall to lower altitudes, consistent with our observations. The breaking off of these dendritic branches would reduce the surface area of the particle, and collisions between particles could lead to aggregation; both of these processes may cause an increase in the vertical velocity of the primary population as a result.

Weighing against this interpretation is the observation that the local minimum in Doppler velocity in the DGL is observed systematically in monomodal spectra as well as multimodal spectra. In fact, Fig.  shows that this minimum is more pronounced in monomodal cases than in multimodal ones. If dendritic arms are growing on particles precipitating from above in these monomodal cases, why do collisions between them not form secondary particles?

One possible explanation could be that particle concentrations are systematically lower in monomodal spectra compared to multimodal spectra. This would mean that the number of collisions between particles is also lower, preventing sufficient break off of dendritic branches to form a clear secondary mode. Particles then slow down more in monomodal spectra compared to in multimodal spectra because the dendritic branches causing greater air resistance are less likely to break off.

An alternative hypothesis is that the secondary production process involves riming, and our data provides some evidence to suggest this is the case. When we examine the velocity of the primary population in multimodal spectra, it is systematically higher than the primary velocity in monomodal spectra, which suggests that the processes involved in the formation of the multimodal population are also conducive to increasing the vertical velocity of the primary population. Riming is an effective mechanism to increase the fall speed of snowflakes . The existing literature on rime splintering is focussed on the temperature window near -5 °C, where report hundreds of secondary ice particles produced per milligram of rime. However, close examination of their Fig. 2 reveals a slower (but non-zero) production rate of a few tens of splinters per milligram of rime at -13.5 and -15.5 °C. If those findings are accurate, then our measurements could potentially be explained by a (relatively slow) rime splintering process in the DGL.

The uncertainty surrounding both the mechanism producing multimodal spectra and mechanism causing the observed decrease in primary population velocity in the DGL demonstrates the importance of further research into the microphysical processes active at these temperatures. In particular, ice multiplication and aggregation processes involving dendritic particles remain poorly understood. For example, if increased drag force against pristine dendritic crystals causes a decrease in velocity, what happens when dendritic crystals aggregate – does the velocity increase due to the increased mass, or does the velocity remain similar or continue to decrease due to increased air resistance? Despite recent efforts to improve parameterisation of the terminal velocities of aggregated snowflakes, including aggregates comprised of dendrites e.g., the answer to this question remains unclear. Are the rime splintering or ice-ice fragmentation mechanisms efficient enough at low temperatures in non-turbulent clouds to cause one fifth of all spectra at these temperatures to be multimodal? One way to approach this further research is to use detailed super-particle models such as that developed by , combined with extensive scattering databases and radar forward operators such as that detailed by , which link microphysics with radar observables.

If the analysis presented here were to be repeated on a different dataset, it could be developed further by utilising polarimetric radar data; polarimetric data were not available for the cases analysed here. Polarimetric data can provide insights into the properties of the particles in the observed cloud volume. For example, the linear depolarisation ratio (LDR) can be used to infer the shape of particles; high values of LDR imply the presence of needle or column crystals, whereas planar crystals correspond to low values of LDR e.g.. Likewise, values of differential reflectivity (ZDR) and specific differential phase (KDP) close to zero can be used to infer an active riming process . Another avenues of future work which arise from this work may include using lidar based techniques or machine learning based methods to identify liquid water. It would also be interesting to investigate whether cloud top height or temperature has an impact on the number of modes identified or location of multimodality, or whether multimodal signatures are different between clouds associated with cold and warm fronts.

The implications of the findings presented in this study are apparent for NWP, where ice microphysical processes are crudely represented. For example, some models have no parameterisation in place to represent SIP , and those that do are usually focussed on rime splintering . Ice microphysical processes such as SIP have significant influences on cloud development and inaccurate representation can cause large errors in forecast process rates , thus demonstrating the importance of continued efforts to better understand these fundamental processes.