Turbulence as a Key Driver of Ice Aggregation and Riming in Arctic Low‐Level Mixed‐Phase Clouds, Revealed by Long‐Term Cloud Radar Observations

Turbulence in clouds is known to enhance particle collision rates, as widely demonstrated for warm rain formation. A similar impact on ice growth processes is expected but a solid observational basis is missing. A statistical analysis of a 15‐month data set of cloud radar observations allows for the first time to quantify the impact of turbulence on ice aggregation and riming in Arctic low‐level mixed‐phase clouds. Increasing eddy dissipation rate (EDR), from below 10−4 to above 10−3 m2 s−3, yields larger ice aggregates, and higher particle concentration, likely caused by increasing fragmentation. In conditions more favorable to riming, higher EDR is associated with dramatically higher particle fall velocities (by up to 125%), under similar liquid water paths, indicative of markedly higher degrees of riming. Our findings thus reveal the key role of turbulence for cold precipitation formation, and highlight the need for an improved understanding of turbulence‐hydrometeor interactions in cold clouds.


Introduction
Precipitation formation is for the most part determined by hydrometeor collisional processes: in warm clouds, hydrometeors transition from cloud droplets into drizzle and raindrops via the collision-coalescence process, while in cold clouds precipitation mainly forms by aggregation, that is, ice-ice collisions, and riming, that is, collisions between ice particles and supercooled droplets (Pruppacher & Klett, 2012).The role of turbulence in the initiation of warm precipitation has been widely debated in the past century (e.g., Arenberg, 1939;East & Marshall, 1954), and a consensus has been reached in recent decades on the key role it plays (e.g., Pumir & Wilkinson, 2016;Seifert & Onishi, 2016;Shaw, 2003).Conversely, the role of turbulence in collisional icegrowth processes has received little attention.A limited number of authors have suggested, based on case studies, that turbulence might induce enhancements in ice collisional growth (e.g., Aikins et al., 2016;Houze & Medina, 2005), and that increases in ice-ice collision rates might further affect precipitation by substantially enhancing secondary ice processes, especially collisional fragmentation (Billault-Roux et al., 2023;Ramelli et al., 2021).Consequently, turbulence represents a poorly understood pathway for the interaction between cloud dynamics and microphysics.Since most precipitation world-wide originates from the ice phase (Heymsfield et al., 2020;Mülmenstädt et al., 2015), a deeper understanding and quantitative estimate of the impact of turbulence on ice microphysical processes is likely to improve precipitation forecasts.
Theoretical fluid dynamics studies have shown dramatic increases in collision rates between particles suspended in a fluid with increasing turbulence.This effect is attributed to increasing modifications of particles trajectories by eddies on the smallest scales of the flow as the eddy dissipation rate (EDR) increases (e.g., Pumir & Wilkinson, 2016).When particle inertia is negligible with respect to the fluid's inertia, particles act as tracers for the fluid motion, and turbulence-induced velocity gradients in the fluid increase collisions (Saffman & Turner, 1956).As particles grow, their inertia becomes comparable to that of eddies on the smallest scales of the flow and particles are subject to so-called inertial effects.Particles tend to cluster in regions of the flow with lower vorticity, and centrifugal forces generated by the eddies enhance relative velocities between particles, leading to large relative velocities even between particles of similar sizes (Shaw et al., 1998;Squires & Eaton, 1991;Voßkuhle et al., 2014).The relevance of these effects for increasing collisions between ice particles, as well as ice particles and supercooled droplets has been suggested by Naso et al. (2018) and Sheikh et al. (2022), among others.
To our knowledge, these theoretical considerations have been poorly supported by observations in atmospheric clouds.Based on case studies, a handful of authors have identified shear layers as regions of precipitation enhancement in orographic precipitation (Aikins et al., 2016;Gehring et al., 2022;Grazioli et al., 2015;Houze & Medina, 2005;Medina & Houze, 2015;Ramelli et al., 2021) and in warm conveyor belts (Gehring et al., 2020).Out of the mentioned studies, Houze and Medina (2005) first suggested that shear leads to the formation of overturning cells, and that subcellular motions might favor increasing differential settling velocities between hydrometeors, leading to enhanced aggregation and riming.Recently, Fitch and Garrett (2022b) reported that in Arctic low-level mixed-phase clouds graupel settling velocity and density increase with increasing turbulence.
Here, we present a new view on the subject of ice growth enhancement by turbulence, investigating the topic in low-level mixed-phase clouds (LLMPCs) at the Arctic site of Ny-Ålesund.Arctic LLMPCs are inherently turbulent, as the liquid layer, typically located close to cloud top, drives radiative cooling, which in turn produces buoyant overturning and turbulence throughout the cloud layer (e.g., Morrison et al., 2012).Ice is nucleated and grows in the liquid layer, first by vapor deposition, then via collisional processes, both by riming (Fitch & Garrett, 2022a;Maherndl et al., 2024), and by aggregation (Chellini et al., 2022).It is in the liquid layer that subcellular turbulent motions could potentially increase the collision rates between cloud particles, leading to an enhancement in aggregation and riming.Due to the limited depth of LLMPCs, information on cloud top temperature (CTT) allows us to constrain the ice habits that are nucleated (Bühl et al., 2016;Myagkov et al., 2016).Furthermore, the wide range of liquid water path (LWP) values typically observed, from a few tens up to 400 g m 2 (Chellini et al., 2022;Gierens et al., 2020), allows us to discriminate between scenarios with varying likelihood of riming.Hence, the wide spectrum of conditions provided by Arctic LLMPCs makes them ideal natural laboratories to test the dependence of the turbulence-ice-growth interaction on ice habits and varying supercooled liquid availability conditions.
The data set was recorded at the AWIPEV observatory in Ny-Ålesund, located on the western coast of Svalbard at 79°N.It spans a 15-month period from 10 October 2021 until 31 December 2022, and only includes LLMPC events.The events were selected by requiring that ice and liquid phases, identified with the Cloudnet target classification (Illingworth et al., 2007), coexist for at least 1 hour, and cloud top remains below 2,500 m.The Geophysical Research Letters 10.1029/2023GL106599 two cornerstones of the data set are a 94-GHz zenith-pointing single-polarization Doppler radar (hereafter referred to as W-band; Küchler et al., 2017), and a 35-GHz scanning dual-polarization Doppler radar (hereafter Ka-band; Chellini et al., 2023b).The radar data have undergone quality control and post-processing, including attenuation corrections.Temperature profiles and LWP from a co-located microwave radiometer have been retrieved following the approaches by Crewell and Löhnert (2007) and Nomokonova et al. (2020).For further technical details on the data set and the processing methods applied we refer the reader to Chellini et al. (2023b).
We use equivalent radar reflectivity factor (hereafter reflectivity) Z e and mean Doppler velocity (MDV) observed by the W-band in zenith, while polarimetric variables are taken from Ka-band observations at 30-40°elevation.Zenith reflectivities from the two systems are combined into the dual-wavelength ratio (DWR).The DWR is the ratio (in linear scale) between reflectivities observed at two separate frequencies, and is sensitive to the characteristic size of the ice particle population in the size range where hydrometeor backscattering is in the Rayleigh regime at the lower frequency, and non-Rayleigh at the higher frequency (Battaglia et al., 2020).For the used frequency combination (35-94 GHz), DWR is sensitive to mean particle sizes ranging from 0.5 to 5 mm approximately, and takes on increasing values up to approximately 10 dB, where it saturates and is no longer sensitive to further increases in size (e.g., Ori et al., 2020).As for polarimetric variables, we focus on differential reflectivity Z DR , mostly sensitive to the aspect ratio, density, and size of asymmetrical particles (Griffin et al., 2018;Schrom & Kumjian, 2016), correlation coefficient ρ HV , which decreases with increasing diversity in shape and orientation of particles (Andrić et al., 2013), and specific differential phase K DP , related to the number concentration of small asymmetric ice particles (Bechini et al., 2013;Schrom et al., 2015).The EDR is retrieved via the variance of velocity time series, using a modified version of the approach by Borque et al. (2016).Further details are given in the Supplement.

Case Study
Before we present and discuss the statistical analysis based on the long-term LLMPC data set (Section 4), we shortly illustrate the typical structure of LLMPCs occurring over Ny-Ålesund and introduce the most relevant observables in a case study (Figure 1).We can identify three main periods based on turbulence characteristics: a first period from 3:00 until 5:00 UTC, when EDR is below 10 4 m 2 s 3 throughout the cloud layer, a second period between 5:00 and 11:00 UTC when EDR increases at cloud top, reaching values between 10 4 and 10 3 m 2 s 3 , and a third period after 11:00 UTC when EDR at cloud top is close to or higher than 10 3 m 2 s 3 , and high EDR values are found also below liquid base.The three periods are accompanied by varying microphysical fingerprints in the radar data.
The first two periods are characterized by similar CTTs close to 13°C and LWP values mostly below 50 g m 2 .During the first period of low turbulence at cloud top, we find Z DR values reaching up to 4 dB, consistent with the expected growth of dendritic particles within this temperature regime (e.g., Takahashi, 2014).As soon as turbulence at cloud top increases (ca. 5 UTC), Z DR drops, and DWR below the liquid layer increases to values between 4 and 7 dB.The increase in DWR together with the overall small change in MDV strongly suggests that the increasing turbulence fosters the formation of larger aggregates.
The third period with most intense turbulence seems to favor riming, likely alongside aggregation: DWR increases further up to 8-10 dB, accompanied by MDV exceeding, in some regions, values of 1.5 m s 1 , and much higher LWP values ranging between 100 and 350 g m 2 .The high MDV values are indicative of higher-density rimed particles (Kneifel & Moisseev, 2020;Mosimann, 1995), whose more spherical shape is consistent with Z DR values being close to 0 dB.
While the case study presented already establishes a potential connection between turbulence and collisional icegrowth processes in LLMPCs, the presence of such interaction can only be demonstrated via robust statistics based on a high number of events.Such analysis is presented in the next section.

Results and Discussion
In this section we test the sensitivity of ice growth processes to varying turbulence conditions, discriminating the cases into various classes, based on ice habit (via CTT) and availability of liquid (via LWP).We build upon the results by Chellini et al. (2022), who observed that ice aggregation predominantly occurs in LLMPCs at Ny-Ålesund if the liquid layer of the cloud is at temperatures compatible with growth of plate-like particles, that is, between 20 and 10°C.They attributed this to the rapid growth of dendritic particles, favored by saturation with respect to liquid; dendrites then aggregate efficiently due to their large cross sectional area and sticking efficiency (Pruppacher & Klett, 2012).Chellini et al. (2022) then reported a dramatic decrease in occurrence of ice aggregates when CTT is warmer than 10°C, hence the production of large, fast-falling particles in this temperature regime can be predominantly explained by riming.Therefore, we here classify all available profiles into either a dendritic-growth regime (CTT between 20 and 10°C), where both aggregation and riming can occur, or a columnar regime (CTT between 10 and 2°C), where predominantly riming can take place.In order to determine connections between microphysics and turbulence we classify profiles based on the mean EDR calculated across the layer between cloud top and 500 m below cloud top (or subsets thereof in case of thinner clouds).The mean is computed in log-scale, as EDR is typically thought to be log-normally distributed (e.g., Siebert et al., 2006).The reasoning behind this approach is given in the Supplement, together with distributions of uppermost-500-m averaged EDR.All available profiles are classified into three EDR classes: EDR < 10 4 m 2 s 3 , EDR between 10 4 and 10 3 m 2 s 3 , and EDR > 10 3 m 2 s 3 .They were determined based on the quartiles of the distribution of uppermost-500-m averaged EDR throughout all events, which are: 10 4.2 , 10 3.5 , 10 2.9 m 2 s 3 .The number of samples available in each CTT and EDR class is given in the Supplement.

Dependence of Radar Observables on EDR
The signatures obtained in the dendritic-growth regime in Figures 2a-2f confirm that the main ice-growth process in this temperature regime is aggregation.All median curves display values close to 0.6-0.7 m s 1 , compatible with low-density aggregates (Karrer et al., 2020;Locatelli & Hobbs, 1974).Increasing DWR with increasing EDR in Figure 2b suggests that aggregation might be indeed enhanced by higher EDR.The three median DWR curves especially diverge in the top 500 m, with median values at 500 m below cloud top of 1.0, 1.8, and 2.4 dB.Z DR in the low EDR class displays a vastly different behavior compared to the intermediate and high EDR classes: it increases from cloud top until 300-400 m below cloud top, then decreases.This could be a signature of depositional growth.The absence of such signature in the two remaining EDR classes likely originates from onsetting aggregation already close to cloud top.Similar features were already observed when comparing the first and second period in the case study in Figure 1.Hence, we argue that the combined decrease in Z DR and increase in DWR with EDR and height are a clear indication of increasing aggregation with turbulence.
In the classical theory of aggregation, the process is considered one-dimensional, taking place along the vertical axis, and driven by sedimentation velocity differences (e.g., Field & Heymsfield, 2003;Westbrook et al., 2004).Turbulence can strongly enhance relative velocities both in the vertical and horizontal components and also lead to locally enhanced particle concentrations.Direct numerical simulations by Sheikh et al. (2022) with 300-μm plate particles revealed that collision kernels display an approximate power law dependence on EDR with exponent 0.5.In the case of inertial particles, they attributed the collision rate increases to enhanced relative velocities generated by centrifugal forces.The lack of a clear peak in Z DR in the intermediate and high EDR cases in Figure 2d, compared to the low EDR, suggests that such an enhancement in collision rate might already be relevant close to cloud top.The enhanced K DP between 100 and 300 m below cloud top might also be a consequence of an increase in collision rates, as it signals a higher number concentration of small particles.One possible explanation for this signature might be fragmentation of dendritic and stellar structures during particle collisions, which has been frequently suggested in literature (e.g., Rangno & Hobbs, 2001;Schwarzenboeck et al., 2009;von Terzi et al., 2022).
In the columnar regime, when CTT is higher than 10°C, aggregation is not dominant in our data set, as evident from DWR for the most part being below 1 dB in Figure 2h.Hence, the main relevant ice-growth process is riming: MDV values in panel c are in fact compatible with small high-density ice particles (Barthazy & Schefold, 2006;Locatelli & Hobbs, 1974), and Z DR is close to 0 dB, indicative of the presence of spherical particles.Reflectivity and MDV both display increasing median and quartile values with increasing EDR, while ρ HV displays values reaching closer to unity as particles sediment, and moving from the lower EDR to the higher EDR class.All these signatures are compatible with increasing riming with EDR, however, it cannot be clearly inferred from Figures 2g-2l whether these fingerprints are generated by increased ice-liquid collision rates associated with increasing EDR, or by increased liquid production associated with conditions that favor high EDR.In the next section we disentangle the effects of increased liquid production and turbulence on the ice microphysics.
In Figure 2l K DP displays a similar behavior in all EDR classes, with a maximum at cloud top close to 0.1°km 1 , then decreasing with height as particles sediment.Luke et al. (2021) reported the occurrence of secondary ice production in less than 10% of cases of MPCs in this temperature regime at the Arctic site of Utqiaġvik.Assuming a similar frequency of occurrence of secondary ice production at Ny-Ålesund, we can attribute most of the K DP signal in Figure 2l to primary ice production.The maximum at cloud top is likely associated with higher liquid water content (LWC) at cloud top (Mioche et al., 2017), as in Arctic MPCs ice nucleation is thought to originate from the liquid phase (De Boer et al., 2011;Prenni et al., 2009).Assuming that similar primary ice nucleation pathways are present above and below 10°C, the K DP maxima between 100 and 300 m below cloud top in the dendritic regime in Figure 2f can be indeed interpreted as generated by turbulence-induced secondary ice production.Therefore, increasing collision rates with turbulence might lead to higher number of fragments produced by collisions between plate-like particles.However, we do not have an explanation for the higher values of K DP found in the intermediate EDR class compared to those in the high EDR class.

Combined Impact of LWP and EDR on Riming
In this section we aim at disentangling the contributions from turbulence and LWP, as in LLMPCs higher LWC has been reported in updrafts (Khain et al., 2022;Shupe et al., 2008), and stronger updrafts might in turn be associated with higher EDR.In Figure 3 we display distributions of Z e and MDV, taken at 500 m below cloud top, classified based on LWP and uppermost-500-m averaged EDR, in the columnar regime.A similar figure for the dendritic regime can be found in the Supplement.
As already mentioned, in this temperature regime we can assume that riming is the dominant ice growth process.Z e and MDV display an increase with EDR in all LWP classes with LWP > 100 g m 2 .The increase in MDV being accompanied by an increase in reflectivity indicates an enhancement in riming.Looking only at the lowest EDR class, median Z e and MDV remain approximately constant at any LWP value higher than 50 g m 2 .Even in the higher LWP classes (LWP > 200 g m 2 ), the values of Z e and MDV shown in Figure 3 suggest low degrees of riming when EDR < 10 4 m 2 s 3 .We argue that this is a strong indication that turbulence is an essential component needed to obtain riming, at least in the shallow liquid layers subject of this study.Furthermore, the increase in interquartile range of the MDV distributions as EDR increases might be attributable, in addition to the intrinsic increase in variance of air velocity associated with higher EDR, to the inhomogeneity of the riming process, which leads to a larger spread in the fall velocity distribution (e.g., Vogl et al., 2022).In the two lowest LWP classes (i.e., LWP < 100 g m 2 ), reflectivities are similar across all EDR classes, while MDV increases with EDR.This might in part be attributable to settling velocity enhancement by turbulence, via a process known as preferential sweeping (Aliseda et al., 2002;Li et al., 2021;Maxey, 1987).
The riming intensification here reported might be attributed to higher EDR favoring the formation of larger droplets, via collision-coalescence enhancement; riming has been in fact shown to be sensitive to droplet size (Erfani & Mitchell, 2017;Jensen & Harrington, 2015).Erfani and Mitchell (2017) reported that for LWC of 0.05 g m 3 a doubling of the mass-median diameter of droplets from 8 to 16 μm quadruples the riming rate.In warm rain formation, the role of turbulence in favoring the formation of collision-coalescence initiators has been suggested.These are droplets sufficiently large to initiate precipitation formation, and are thought to be generated by cloud top turbulence, which locally enhances collision-coalescence (Small & Chuang, 2008).Similarly, in MPCs turbulence might favor the initial formation of rimed crystals, which then collect droplets more and more efficiently as they rime, due to the dramatic dependence of collection efficiency on the particle's Reynolds number Re, which in turn increases with size (Wang & Ji, 2000).
In addition to a collision-coalescence enhancement, inertial effects have also been suggested to play a role in the enhancement of ice-liquid collision rates (Pinsky & Khain, 1998).Furthermore, we speculate that turbulence might favor collisions between ice crystals and droplets on the smaller side of the size distribution.Due to the small sizes and relatively low inertia of droplets, modifications of the flow field by the ice particle play a large role in riming.Direct numerical simulation studies have shown that if modifications of the flow by the collector are neglected, collision rates between ice crystals and droplets are only marginally increased under increasing EDR (Naso et al., 2018).In contrast, if the two-way interaction between the collector and the flow is taken into account, an increase in collision efficiency for small particles with EDR at constant collector Re has been suggested by Homann et al. (2016), although they did not investigate cloud microphysics applications specifically.

Conclusions
In this study, we use state-of-the-art dual-frequency and polarimetric Doppler cloud radar observations of Arctic low-level mixed-phase clouds to evaluate the role of turbulence in the growth of precipitating ice particles.We perform a statistical analysis based on a large number of events (for a total duration of 3,426 hr), which highlights the key role that turbulence plays in cold precipitation formation.In particular, following previous studies, categorizing the events based on CTT allows us to discriminate between cases where both aggregation and riming are relevant growth processes (at CTT between 20 and 10°C, i.e., at dendritic-growth temperatures), and cases where mainly riming is relevant (at CTT warmer than 10°C, i.e., at columnar-growth temperatures).The main findings of this study are as follows: • At dendritic-growth temperatures, higher EDR is associated with increasing size of ice particles.We argue that such an increase is attributable to increasing collision rates between ice particles, leading to larger aggregates.We suggest that, in this temperature regime, increasing collision rates with EDR might lead to increasing secondary ice production via fragmentation of dendritic structures, in addition to an enhancement in aggregation.

Geophysical Research Letters
10.1029/2023GL106599 • At temperatures warmer than 10°C, turbulence appears to increase riming rates.Dramatic increases in MDV and reflectivity (up to 120% in MDV and 8 dB in Z e ) with increasing EDR and constant LWP are observed, suggesting that riming in shallow liquid layers, such as those observed in the LLMPCs here studied, is a fundamentally turbulent process.We discuss a number of possible processes that could lead to the observed increased riming rates, however the remote sensing observations here used do not allow us either to pinpoint or exclude specific processes.We deem that further work combining model experiments with remote-sensing observations is highly needed in this regard to explain the riming rate enhancement here reported.
We argue that turbulence is potentially a key component determining the characteristics of precipitation.The current study only highlighted this key role in shallow clouds characterized by low to intermediate EDR values, between 10 5 and 10 2 m 2 s 3 .Mid-latitude frontal systems display similar values (Chapman & Browning, 2001), while deep convective systems have been reported to produce EDR up to 10 0.5 m 2 s 3 (Feist et al., 2019).Therefore interactions between turbulence and ice growth might be at play in many cloud systems that produce precipitation at mid-latitudes.The inclusion of turbulence-dependent collision kernels for collisioncoalescence has been shown to produce large improvements in warm rain formation in models (e.g., Seifert et al., 2010).We thus argue that fully quantifying and parametrizing the impact of turbulence on snow and graupel growth is crucial to improve model performance.The development of such parametrizations will need to rely on coincident remote-sensing and in-situ observations (either air-or balloon-borne), as the latter would allow for an accurate quantification of aggregate characteristics and rime mass fraction.Furthermore, large efforts are needed to reach a theoretical understanding of particle inertial effects in snow, as well as the processes leading to riming enhancement in turbulence.

Figure 1 .
Figure 1.Case study of low-level mixed-phase cloud, detected on 5 May 2022.Panels respectively display: reflectivity from W-band radar with temperature contours overlayed (a), Ka-W dual-wavelength ratio (b), mean Doppler velocity from W-band radar, smoothed with a 2-min rolling average (c; negative values indicate targets moving toward the radar), differential reflectivity from Ka-band observations at 30°elevation (d), eddy dissipation rate (e), liquid water path (f).The dotted magenta line on panels a through e indicates liquid base height from a ceilometer, while the contours in panel a indicate temperature in °C retrieved from microwave radiometer data.Vertical dash-dotted lines indicate the three periods identified in the text.

Figure 2 .
Figure 2. Contoured frequency by altitude diagram of several radar variables in eddy dissipation rate (EDR) classes, for profiles with cloud top temperature between 20 and 10°C (a-f) and between 10 and 2°C (g-l).Solid lines indicate median values, dashed lines indicate lower and upper quartiles.Panels respectively display: reflectivity from W-band radar (a, g), Ka-W dual-wavelength ratio (b, h), mean Doppler velocity from W-band radar (c, i), differential reflectivity (d, j), correlation coefficient (e, k), specific differential phase (f, l).The y-axis indicates the distance from cloud top along the vertical direction.Profiles are classified based on the mean EDR across the topmost 500 m of the cloud layer.EDR values in the legend are reported in m 2 s 3 , height bins are 25 m wide.

Figure 3 .
Figure 3. Quartiles of W-band reflectivity (a), and W-band mean Doppler velocity (b), measured at 500 m below cloud top, classified into liquid water path (LWP) and eddy dissipation rate (EDR) classes, for profiles with cloud top temperature between 10 and 2°C.The edges of the LWP classes are indicated on the x-axis.Distributions belonging to the same LWP class, but different EDR classes are shifted with respect to each other to facilitate the interpretation of the plot.Profiles are classified based on the mean EDR across the topmost 500 m of the cloud layer.EDR values in the legend are reported in m 2 s 3 .