Our case study comprises a system of towering cumulus clouds observed in 5 June 2021 over the Great Plains in southern Oklahoma (USA) during the Secondary Production of Ice in Cumulus Experiment (SPICULE). Our selection was driven by the existence of a very detailed set of airborne in situ and remote observations of cloud microphysical properties showing evidence of secondary ice production. Airborne measurements were carried out using two coordinated aircrafts, the NSF Gulfstream V, and the Spec Incorporated Learjet model 35 A, referred to from now on as the GV and Learjet. Both airborne platforms were equipped with air motion sensors and in situ microphysical probes covering different size ranges . The GV was monitoring the subcloud and warm cloud section and had additional equipment compared to the Learjet to measure aerosol size distributions , number concentrations of giant cloud condensation nuclei (CCN) , and ice nucleating particles (INP) . The GV was also equipped with a polarimetric millimeter-wavelength radar (HIAPER cloud radar). The Learjet flight was monitoring the uppermost section of the mixed-phase zone and was equipped with a Ka-band up/down radar . Although this case was well documented in , for the sake of completeness, we included a summary of the instruments in Table S1 of the Supplement.

UCLALES–SALSA (University of California Los Angeles Large Eddy Simulation model – Sectional Aerosol module for Large Scale Applications) is a one-of-a-kind LES-model that simulates cloud formation with aerosol-driven microphysical processes . The model employs sectional representation of aerosol and hydrometeor microphysics to get size–resolved growth by condensation and deposition and hydrometeor aggregation rates without employing parametrizations (such as cloud droplet activation, autoconversion, accretion, and riming). Aerosol size-composition effects are accounted for using a microphysical scheme based on aerosol dry particle size and mixing state. Wet sizes are used to evaluate transitions from aerosol particles to cloud droplets, or from cloud droplets to rain droplets in the collision between droplets. Primary ice production pathway includes homogeneous ice nucleation, and heterogeneous ice nucleation includes the immersion, deposition, and contact freezing mechanisms. Ice particles are treated with a microphysical scheme based on maximum particle length using the parameterization of ice–phase microphysics of . The LES modelling framework applicable to liquid clouds can be found in , and to mixed-phase clouds involving only primary ice production in and .

The ice microphysical scheme is similar to the Predicted Particle Properties (P3) scheme of that uses a single ice “free” category to represent time–evolving ice particle properties based on the concept of filling in with rime. Ice particles in each size bin have mass–dimension (i.e. m(D)=αDβ with D equivalent to the maximum particle dimension) and projected area–dimension (i.e. A(D)=γDσ) relationships that vary in time and space determining their effective density and falling speed in accordance with the prognostic value of the bulk rime mass fraction. The maximum particle length D is determined by comparison against critical sizes separating pristine small spherical from dense nonspherical ice, dense nonspherical from graupel and graupel from partially rimed crystals. Parameters of the m-D and A-D relationships of nonspherical pristine ice particles are given as model inputs of simulations . In this study, we implemented the change in the projected area for partially rimed particles using rime fraction–weighted values of the γ and σ parameters varying between those of nonspherical pristine ice crystals and those of spherical graupel. Pristine ice particles are treated as crystals with sectors like branches (P1b).

The immersion freezing mechanism in our simulation is the primary pathway for ice formation. Their rates are calculated using the parametrization of that uses a time–evolving probability density function of the contact angle parameter (i.e. angle formed between liquid water, the INP surface and the ice embryo during nucleation that gives a measure of the composition-dependent INP affinity to the ice embryo; ). The use of a distribution allows to account for heterogeneities in surface properties among a given aerosol population. In our modelling framework, cloud droplets and raindrops can experience heterogeneous freezing via immersion as long as they contain a volume of insoluble species larger than a threshold value (e.g. volume equivalent to a sphere of 10 nm in diameter). The model keeps track of the fraction of nucleated INPs and uses it to increase the lower limit of the contact angle distribution once the most efficient INPs nucleate ice. The contact angle distribution is updated every time mixing and entrainment processes replenish the cloud with fresh INPs .

Production rates of secondary ice particles are modelled as the product between the ice multiplication factor (IMF) and the occurrence of SIP events per unit of time. A collision between two hydrometeors of size Dl and Dm is categorized as a SIP event if the relative size and phase of interacting hydrometeors satisfies triggering conditions that depend on the SIP mechanism. More information about the model treatment given to SIP rates can be found in Sect. S2 of the Supplement. In this study we employed the parameterization of and modified by (see Eqs. S5–S6) to calculate IMF values due to rime splintering (SIP–RS), droplet shattering (SIP–DS) and ice–ice collisional breakup (SIP–IIBR). IMF values related to SIP-DS rates include secondary ice formation during spherical drop freezing or mode 1 and also during collisions of supercooled raindrops with more massive ice or mode 2, whose representations are supported by the laboratory studies of and , respectively. IMF values related to SIP–IIBR also consider the recent experimental findings of . There are other IMF parameterizations available for the SIP–DS and SIP–IIBR mechanisms (e.g. ) that were not considered in this study but have been implemented in UCLALES-SALSA as reported in Table S4.

Parametrizations for IMF and triggering conditions reported in literature vary widely for a single mechanism. Because these differences affect SIP rates, we have set up a common set of modeling constraints reported in Tables S1 and S2 in the Supplement. After a secondary ice production event, secondary ice particles follow a number size distribution of the power-law type D-3 with D equal to the hydrometeor size (i.e. diameter or maximum length). Secondary ice particles are located in ice bins smaller than the hydrometeor that generates them. In all cases, collision kernels are calculated using settling velocities that depend on air properties and diameter in the case of droplets , and also on the crystal habit whose mass-diameter and area-diameter relationships vary according to the rime fraction in the case of ice particles .

A key point for the successful modelling of SIP processes is to accurately simulate the mass distribution of secondary ice particles. There is a single laboratory study providing size distributions for secondary ice particles generated after graupel-graupel and graupel-snowflake collisions. Although these distributions described the general trends in fragment sizes, they are applicable for a very specific subset of hydrometeor collisions, and are limited by the low number of experiments and in the detection of ice fragments with sizes below 25 to 30 µm .

In this study, we assumed that the rime splintering mechanism generates single-size ice crystals in the shape of hexagonal columns with a maximum length of 10 µm and mass of 3.1227 × 10⁻¹³ kg. We used the mass-diameter relationship in to calculate the mass of a splinter. We assumed that the mechanisms of droplet shattering and ice–ice collisional breakup generate ice crystals that can range in size from 2 µm to nearly as large as the fragmenting hydrometeor (i.e. supercooled droplet or ice crystal). We distribute the total number of secondary ice particles NSIP(T,Dl,Dm) produced by a collision between two hydrometeors of size Dl and Dm between size bins smaller than the fragmenting hydrometeor in such a way that each bin gains the same amount of mass. This means that secondary ice particle size distribution follows a D-3-power law distribution with a minimum fragment size D of 2 µm. This relationship aligns with the model of fractal crushing used to describe the scale-invariant low energy fragmentation of brittle materials .

This initial size distribution guarantees that secondary ice particles cover the wide size range observed by airborne in situ optical and imaging system going from small faceted ice crystals and single dendrite branches up to fragments of frozen drops or broken stellar crystals e.g.. It is also particularly useful to mimic the variety of fragmentation pathways observed in laboratory experiments during the freezing of drizzle-size droplets. Droplets of the same size, freezing in moving air under controlled conditions, can undergo bubble bursting or jetting, cracking, and breakup, sometimes occurring in combination in the same droplet . It is expected then that a hypothetical monodisperse population of freezing droplets generates spicules or small ice crystals due to bubble bursting or jetting, but also large spherical fragments after breakup.

Simulations were performed in a model domain of 28.8 km by 28.8 km by 12 km with horizontal and vertical resolution of 300 and 60 m respectively, and a maximum time step of 1 s. The model domain size was selected based on the surface area covered simultaneously by the GV and Learjet flights on 5 June 2021 (see Fig. S1). This time interval coincides with the early stage of the cloud system in which ice multiplication was observed in the rising cloud tower. Model outputs were taken every 30 s to follow closely changes in cloud microphysics. Aerosol and cloud droplet size distributions were modeled with a sectional representation based on dry diameter ranging from 0.003 to 10 µm across 10 size bins. Cloud droplets correspond to activated aerosols in the last 7 aerosol size bins. Rain droplets were represented using 22 size bins based on wet diameter distributed with a constant volume ratio of 2 with the minimum droplet diameter equal to 20 µm. Ice particles were represented using 23 size bins based on maximum length distributed with a constant volume ratio of 3 with the minimum size equal to 2 µm.

Aerosol properties were derived from size distributions measured below cloud base altitude with the Passive Cavity Aerosol Spectrometer Probe (PCASP-100X) . Since these observations corresponded to wet aerosols, we had to use the relative humidity, temperature and aerosol hygroscopicity to obtain the size distribution based on dry size. To do so, we used the kappa factor to account for aerosol hygroscopicity and resolved the kappa-Köhler equation for each particle size using the temperature and relative humidity of observations. We assumed that dry aerosol particles were spherical and composed of sulphate species and mineral dust in volumetric fractions of 0.901 and 0.099, respectively. This chemical composition corresponds to a species-based kappa value of 0.5496 that is numerically equivalent to the average hygroscopicity parameter kappa derived from Cloud Condensation Nuclei Counter and Scanning-Mobility Particle Sizer measurements at the ARM station in the Southern Great Plains, USA performed on 5 June 2021 .

PCASP-derived dry aerosol distributions measured below cloud altitude were fitted to a multimodal lognormal distribution and then fed into UCLALES–SALSA. Since the limit for the smallest particle detected with the PCASP-100X is 125 nm ± 5 % , we added an aerosol mode to account for sub-micron particles missed during observations. This particle mode had a geometric mean diameter of 0.0055 µm in agreement with summer average values reported for the ARM station Southern Great Plains (SGP) and consistent with frequent events of new particle formation . The aerosol size distribution used for model initialization has four particle modes centered at [0.0055, 0.090, 0.440, 1.05]µm, geometric standard deviation of [2.8, 1.44, 1.44, 1.42] and total number concentration of [1085.0, 810.0, 2.48, 4.96] mg-1 at altitudes below 1.2 km. Based on PCASP observations, we accounted for the vertical variability in total aerosol loading assuming an exponential decay function (Eq. ) between 1.2 and 3.5 km to scale down the total aerosol number concentration (see Fig. S2). 1N(z>1200m)=N(z<1200m)exp⁡(-0.05log⁡(z[m])2-1.1234log⁡(z[m])+16.7735)

We used a contact angle distribution centered at 132° with variance of 20° to account for ice nucleating abilities for mineral dust as in . This set of parameters allowed us to match observed ice nucleating particle concentrations with ice number concentrations simulated in a scenario that did not consider secondary ice production. Details about this are presented in Sect. S4 of the Supplement.

Atmospheric properties used for model initialization were derived from hourly ECMWF–ERA5 reanalyzed data for 05 June 2021 for a horizontal domain of 1° by 1° that encloses flight trajectories for our selected case . Temperature and humidity profiles were adjusted to reproduce the observed cloud base conditions (e.g., altitude, pressure, and temperature). Atmospheric conditions at higher altitudes were modified to test different values of convective available potential energy (CAPE) and equilibrium level (EL) or level of neutral buoyancy in order to reach the observed cloud top altitude. The optimal sounding is shown in Fig. . Information about the model sensitivity analysis can be found in Sect. S5, simulation scenarios tested are described in Table S3 and atmospheric soundings are presented in Fig. S4.

Convective buoyancy was emulated adding additional sensible and latent heat to the surface fluxes by means of a Gaussian distribution with a maximum of 600 Wm-2 and a linear variance of 2000 m around the domain center. Surface fluxes were increased 1 h after the beginning of the simulation to initiate convection.

The comparison focuses on observations taken between 19:55 and 20:15 UTC during cloud penetrations into updraft cores with the presence of liquid water. During this time interval, both flights examined the same system of ascending cumulus congestus towers as shown in Fig. S1 of the Supplement. Cloud penetration in the GV flight covered conditions from below cloud base altitude up to 3.5 km. Cloud penetrations in the Learjet flight went as deep as 300 m below the cloud top altitude where the temperature reached a minimum of 255.6 K. While ice number concentrations (INC) were as high as 2351 L-1, number concentrations of ice nucleating particles (INP) only reached a maximum of 1 L-1 at 255.1 K indicating that secondary ice production was active and responsible for the ice concentration in updraft cores. Images taken with the Cloud Particle Imager (CPI) and the Optical Array Probe (OAP) during the Learjet cloud penetrations showed pieces of fragmented frozen drops coexisting with 100–300 µm stellar dendrites and hexagonal plates ice crystals likely formed from monocrystalline ice particles . The profuse amount of small columnar particles and the presence of fragmented frozen drops in measurements from the CPI and OAP imaging systems, combined with the occurrence of high reflectivity regions in Ka-band Doppler radar profiles characteristic of large water drops, support the hypothesis that the droplet shattering was mainly responsible for the observed ice multiplication . The coexistence of fragmented frozen droplets and small ice crystals of around 100 µm in maximum length was also observed at 256.25 K in young convective updrafts of cumulus congestus during the RF06 flight of the SPICULE campaign .

It is extremely challenging to determine the exact size and shape of freshly generated secondary ice particles by laboratory experiments or airborne in situ observations. It is expected that secondary ice particles vary across a wide range of sizes and shapes reflecting not only the nature of the ice fracturing mechanism but also the changes induced by their growth after water vapor deposition. Using airborne in situ observations, found that small faceted ice crystals with sizes smaller than 100 µm can be used as tracers of SIP events. A small secondary ice particle is likely to be monocrystalline (e.g. as fragments of frozen drops or dendrite branches) that can regrow by water vapor deposition to acquire the crystal habits of pristine ice particles. Small secondary ice particles can have shapes that go from plates to long columns depending on the residence time, temperature and ice supersaturation conditions in the environment where they were originated.

Observations were grouped by altitude and temperature to simplify their graphical representation in comparison plots. Model outputs were conditionally sampled selecting only grid points with a liquid water content (LWC) greater than the threshold value of 0.01 g m⁻³ and vertical wind (w-wind) stronger than 0.02 ms-1 to be consistent with the analysis of observational data during cloud penetrations. When observations indicated mixed phase conditions, we considered an additional constraint on the ice water content (IWC) above a threshold value of 0.001 g m⁻³. To compare hydrometeor size distributions, we selected cloudy grid points of the model layer with the closest agreement between the modeled and observed temperature.

During the simulation time, SIP processes caused small changes in the cloud base conditions. The average cloud base altitude in our simulations was 1498 and 1326 m with temperatures of 288.1 and 289.1 K, in the SIP-ON and SIP-OFF scenarios respectively. Both agree reasonably well with the observed altitude and temperature of 1180 m and 290.65 K . The variability in modeled cloud base conditions should not be interpreted as model uncertainty. Differences in the cloud base altitude and temperature reflected the cloud dynamical response along the simulation, in particular the changes related to surface precipitation with stronger rates in the SIP-ON scenario.

The extent of the deep convective core was calculated adding up those grid cells with total water path (TWP) above a threshold value of of 1500 g m⁻². In both simulation scenarios, time series of the convective system area evolved similarly with minimal differences. At the beginning, just 10 min after we increased surface turbulent fluxes to induce convection, our simulations showed the development of individual convective cells of approximately 1000 m of diameter covering an area of 1.7 km2. 30 min later, when the total water path has reached a global maximum of 20 000 g m⁻², the convective area has grown to be 9.45 and 10.17 km2 in the SIP-OFF and SIP-ON scenarios, respectively. This continued to reach maximum values of 16.7 and 17.3 km2 at 60 min.

Despite these commonalities between simulation scenarios, once the deep convective core had risen above freezing level, SIP processes caused noticeable changes in cloud geometry, phase structure and microphysics, particularly at the mixed-phase cloud section. Figure  depicts the total water path (TWP), cloud top altitude and ice water path (IWP) in the deep convective core (i.e. model columns with the highest TWP values) and reflect the pulsating growth habit that is characteristic of cumulus clouds. During the convective initiation stage, cloud tower conditions in the SIP-ON scenario corresponded to higher total water contents (Fig. a) and higher altitudes (Fig. b) with the cloud phase shifted towards ice due to higher ice water content values (Fig.c). Peaks in TWP are indicative of convection intensity and can be characterized by its occurrence time and duration. The SIP-ON scenario showed taller and wider peaks suggesting a slower weakening of the convection intensity along the simulation compared to the SIP-OFF scenario. 50 min after convection initiation, there was a reduction in TWP values due to surface precipitation. It was noticeable that the SIP-OFF scenario did not produce as much ice as the SIP-ON scenario after 60 min.

Secondary ice processes in the SIP-ON scenario not only affected the cloud geometrical thickness and cloud top conditions, they also affected the liquid and ice water content profiles. For example, Fig.  compares the variability in modeled and observed vertical profiles of liquid water content in updraft cores. Modeled mean values are represented together with the main percentiles of the variable distribution, while observations are represented with mean and standard deviations. The spatial heterogeneity of mixed-phase conditions along the model domain agreed with the variability observed during different cloud penetrations. The distribution of liquid water in updraft cores in the mixed-phase region (i.e. between freezing level and cloud top) was better represented in the SIP-ON scenario. Although, the differences in the LWC vertical profiles of the SIP-OFF and the SIP-ON scenarios were minimal in the warm section between cloud base and 2.5 km of altitude, they increased at higher altitudes and became particularly important above 3.5 km in the proximity of the freezing level located approximately at an altitude of 4 km. Differences in the mean LWC values of the SIP-ON scenario compared to the SIP-OFF scenario can be grouped in three trends, slightly lower liquid water contents in the warm cloud section (i.e. between 3 and 4 km), higher liquid water content at the beginning of the mixed phase part of cloud tower (i.e. between 4 and 6 km) and lower liquid water content at the tower top (i.e from 6 up to 8.5 km).

Modeled droplet size distributions in cloudy updrafts agreed with in-cloud observations from several instruments as shown in Fig. . Modeled and observed droplet size distributions were conditionally sampled to represent cloudy conditions in convective updrafts (i.e. LWC > 0.01 g m⁻³ and updraft velocity > 0.02 m s⁻¹). Each modelled size distribution in Fig.  is from the layer where the temperature was closest to observed values. Figure  displays the variability in droplet size distributions in the warm cloud section. Observed and modeled binned droplet number concentrations for droplet sizes above 20 µm in diameter are in agreement. This suggested that the model captured well the liquid droplet growth processes. In both scenarios, the model showed a systematic negative deviation in droplet number concentrations for droplets with diameter below 10 µm that was more relevant at 3.5 km as shown in Fig. c. It is difficult to point out if the cause of this deviation is related to our modelling treatment for droplet activation or limited resolution to capture possible activation in the entrainment process at cloud edges, or if the FCDP was falsely registering droplets in the smallest channels as indicated by .

In terms of the secondary ice production effects at cloud base altitude, the average droplet size distribution in updrafts for droplets with diameter below 100 µm did not change between the SIP-OFF and the SIP-ON scenarios as seen in Fig. a. At higher altitudes, average droplet size distributions changed progressively with increasing altitude indicating a reduction in binned number concentrations of droplets with diameter above 50 µm or below 10–15 µm as seen in Fig. b and c. These claims were also valid for other altitudes as shown in Figs. S6–S8. UCLALES-SALSA has also showed good performance reproducing observed droplet size distributions in stratocumulus clouds .

Figure compares modeled and observed hydrometeor size distributions at high altitudes inside cloud turrets. Since the only source of ice particles in the SIP-OFF scenario was the immersion freezing mechanism, we considered that modeled ice number concentrations were directly proportional to primary ice production rates and reflected background ice concentrations given by INPs. The differences in binned ice number concentrations between the SIP-ON and the SIP-OFF scenarios indicated ice multiplication effects of up to three orders of magnitude. Beyond, the modelled ice size distributions in the SIP-ON scenario overlapped very well with the ones observed at different altitudes. This indicated that the model was able to capture both the changes in number and also size of ice particles giving support to the modelling treatment used to describe the size distribution of freshly generated secondary ice particles. Ice particle number concentrations per size bin varied by more than an order of magnitude suggesting that the variability in convective intensity was an important factor driving the occurrence of SIP events via hydrometeor collisions.

Besides the reproduction of the ice multiplication effects, the model gave also a close description of the droplet size distribution in the drizzle–rain droplet size range. SIP processes reduced number concentrations of droplets larger than 50 µm in diameter due to their participation in SIP events via collisions with ice particles during droplet shattering (i.e. a limit of 50 µm was selected for effective droplet fragmentation following experiments; ). This reduction increased at higher altitudes where the temperature was favorable for ice multiplication via droplet shattering . Droplets above 50 µm in diameter can also participate in SIP events by rime splintering but IMF values are minimal outside the optimal temperature range of 265–270 K of SIP–RS.

SIP processes affected cloud dynamics in such an impactful way that it is impossible to convey temporal and spatial differences between the SIP-OFF and SIP-ON scenarios in two-dimensional graphical representations. First, we focus on the time interval before the cloud reached the strongest peak in convection intensity developing a distinctive cloud tower or turret, until the time instance at which simulations scenarios started to deviate substantially from each other in terms of thermodynamic cloud phase and cloud extent (i.e. between 40 and 50 min after convection initiation). Second, although these changes affected the entire three-dimensional cloud structure, for the sake of simplicity, we focus on the two-dimensional space enclosing the model column with the highest TWP value, which in turn shows the conditions that are representative of the deep convective core.

We have chosen the time instances of 40, 43 and 46 min to follow the changes in the vertical profiles of LWC and IWC in correlation with changes in the vertical wind and SIP rates. Figure a, c compares liquid water contents at 40 min after convection initiation indicating larger values above freezing level for the SIP-ON scenario (i.e. wider area with TWC > 3.5 g m⁻³). It was at this time instance when IWC values overpass the threshold (i.e. IWC > 0.001 g m⁻³) even the cloud top had reached freezing conditions 5 min earlier. Areas containing ice are depicted in Fig. b, d. Rates of secondary ice production were observed at the top of the cloud turret with effects over larger areas and higher rates for the mechanism of droplet shattering compared to the rime splintering as shown in Fig. .

These findings are consistent with those from in-cloud observations in two different ways. First, the temperature at which ice formation started in the SIP-OFF scenario is consistent with the ice nucleating abilities observed for aerosol particles collected during our case study (i.e. INP concentrations were measurable below 259.15 K, see Fig. S3) . Second, the mechanism of droplet shattering was active at the tallest and coldest point of the cloud turret indicating that there were collisions between ice particles and supercooled droplets with diameter above 50 µm at 258.15 K (i.e. these are limiting conditions of SIP events by this mechanism in our modelling framework). This agrees with the first detected presence of large frozen droplets at 259.15 K during cloud penetrations .

With the formation of secondary ice particles, the number of droplet–ice collisions rapidly increased leading to substantially higher SIP rates along the entire mixed-phase zone and not only at the cloud top as shown in Fig. d–f. There is an enhancement in turbulent mixing driven by latent heat released during ice-related processes (i.e. droplet freezing, riming, vapor deposition through the Weneger–Bergeron–Findeisen process). As ice number concentrations increased, the rates of riming and ice–ice aggregation processes increased leading to larger ice particles, which in turn triggered the ice–ice collisional breakup (i.e. as early as 41 min). At the time instance of 43 min, SIP–IIBR rates were higher than SIP–RS and SIP–DS rates, suggesting the presence of large rimed ice particles that have the highest ice multiplication factors in the parametrization of –. The combined effects of all SIP mechanisms shifted the phase structure from a liquid–dominated mixed-phase zone in the SIP-OFF scenario to a ice–dominated one in the SIP-ON scenario as shown in Fig. . The corresponding changes in LWC and IWC profiles are included in Fig. S9.

At the peak of convection intensity in the SIP-ON scenario (46 min after convection initiation), the SIP-IIBR mechanism was active across the mixed-phase zone, while other SIP mechanisms are constrained to smaller areas as shown in Fig. g–i. The mixed-phase zone in the SIP-ON scenario was almost completely glaciated with only a few areas indicating the existence of liquid water as seen in Fig. c–d. At this time instance, the SIP-OFF and SIP-ON scenario showed contrasting clouds not only in terms of total water content and thermodynamic cloud phase but also in cloud geometrical thickness and cloud top conditions. In the SIP-ON scenario, the warm section of the deep convective core (i.e. area with TWC > 3.5 g m⁻³ at lower altitudes) was smaller but more densely loaded with liquid water in the proximity of the freezing level, suggesting an important role of the ice melting process. The mixed-phase zone in the SIP-ON scenario not only had higher total water content but also was stretched vertically, reaching higher altitudes and lower cloud top temperatures. With more water displaced towards upper levels, we expect to see changes in the development of precipitation via ice particles (see Figs. S10 and S11).

The SIP-ON scenario showed a distinctive signal of stronger convective uplift that increased the supercooled water content of the mixed-phase cloud section expanding the mixed-phase zone and triggering glaciation of the mixed-phase zone. This set of cloud dynamic responses aligns with the concept of invigoration, which is defined as an increase in the vertical wind speed of convective updrafts due to a net buoyancy gain due to changes in temperature, water vapor and water condensate mass or changes in vertical pressure gradients . The concept of invigoration was formulated to explain aerosols effects in deep convective clouds exposed to higher CCN concentrations that end up with higher droplet number concentrations and smaller droplet sizes. The mechanisms leading to stronger updrafts are not firmly established but have been linked to enhancements in thermal buoyancy due to latent heat release. Depending on which process is responsible for more latent heating, deep convection can be intensified by warm–phase invigoration when higher cloud droplet number concentrations lead to faster condensation at the lower part of the DCC, or by mixed-phase invigoration when smaller droplet sizes suppress drizzle formation allowing more cloud liquid water to be lifted higher in the mixed-phase region where droplets freeze. In both cases, the invigoration of convective updrafts requires an increase in positive buoyancy from latent heat that can surpass the negative buoyancy caused by a greater condensate loading . More recently, it has been hypothesized that these CCN–induced changes on droplet size distributions can also trigger additional changes in rates of riming, primary and secondary ice production .

Our findings support this hypothesis because SIP also worked as a driving force for convective invigoration increasing the updraft strength in the mixed-phase region as shown in Fig. . While the modeled and observed distributions of updrafts varied similarly in the warm cloud section with minimal differences between the SIP-OFF and the SIP-ON scenario, SIP increased modeled mean values and percentiles above the freezing level, in particular at altitudes between 4 and 6 km where temperatures were optimal for the occurrence of SIP by droplet shattering and rime splintering. With this increase in vertical wind velocity in the mixed-phase region, the SIP-ON scenario provided better agreement with the observed updrafts than the SIP-OFF simulation.

To explore thoroughly the nature of the SIP-induced invigoration, it is necessary to quantify possible shifts in the distributions of vertical wind velocity given by the two simulation scenarios. However, all conclusions derived from a time instance comparison must be carefully interpreted since invigoration effects may not impact instantaneously the cloud properties. Instead, the time delay of the dynamic cloud responses depends on which process dominates the buoyancy balance. Also, SIP effects related to invigoration may not be sustained because as the cloud experiences glaciation, the negative buoyancy related to condensate loading may become high enough to cancel or overpass the positive buoyancy due to enhanced phase transitions. It is also relevant that once the cloud dynamics of the two simulation scenarios (SIP-ON and SIP-OFF) has departed from each other, it is meaningless to make a one-to-one comparison in time and space since the cloud extent changes drastically due to precipitation, for example. A definite bifurcation in cloud dynamics from simulation scenarios occurred at the time instance of 50 min when the SIP-OFF scenario indicated surface precipitation and a noticeable reduction in cloud extent. Before that, the divergence between cloud fields was localized and clouds had very similar boundaries as seen in Figs. S9–S11 of the Supplement.

As an example of the spatial variability in vertical wind velocities, we compare in Fig.  the wind fields corresponding to the thicker cloud column at the selected time instances. We used a divergent colormap to visualize better areas of positive and negative buoyancy in connection with water uplift or condensate loading dominant–effects. At 40 min we can see in Fig. a–b how there were minimal differences in the updraft/downdraft distribution, but once SIP rates increased at 43 min, the mixed-phase region showed stronger updrafts in areas affected by SIP that correlate well with the profiles of SIP rates shown in Fig. d–f particularly in the cloud top section where the ice–ice collisional breakup was the dominant SIP mechanism. At 46 min, the SIP-OFF and SIP-ON scenarios had very different structures of vertical velocity as it can be seen in Fig. e–f. Unlike before, areas with with active SIP mechanisms showed weaker updrafts at temperatures below 265.15 where the cloud phase was more glaciated with higher total water contents as seen in Fig. d. This suggested that the updraft strengthening requires that the thermal buoyancy can oppose and surpass the condensate loading buoyancy, something that is feasible just at the beginning of the glaciation when the condensate mass is low and there is latent heating from both, liquid water freezing and depositional growth of fresh secondary ice particles. When such conditions are fulfilled, secondary ice formation leads to mixed-phase invigoration which in turn enhances the cloud vertical development causing differences of up to 600 m in the cloud top height as seen in Fig. e–f.

The SIP-ON scenario depicted the rapid glaciation of the mixed-phase cloud section in a short time period of about 5 min. The phase transition followed the chain-reaction type mechanism driven by ice multiplication that has been known since the 1960s, when proposed it to explain the rapid metamorphosis of the phase structure in young cumulus congestus clouds. Based on an insightful analysis of observed cloud microphysics, the mechanism explains how clouds having a scarce presence of ice nucleating particles and supercooled liquid tops with rain-sized droplets (i.e. 1 mm in diameter at concentrations of 50 m-3) are able to develop high ice number concentrations because of the autocatalytic role played by small ice particles generated during the freezing of drops. Since then, there have been numerous field campaigns collecting evidence of this glaciation mechanism e.g..

This research provides a detailed process-level description of the glaciating mechanism validated by a good model closure of observed cloud microphysics in both, the warm and mixed-phase cloud sections. The stages of SIP-induced glaciating mechanism is shown in Fig.  using horizontal average cloud properties along the time interval where secondary ice production occurred. As show already in Fig. , there was appreciable horizontal variability in the phase mixing.

Keeping the analogy between a chemical reaction and a secondary ice production event as collision-driven processes, we included the rates of secondary ice production per mechanism to quantify the process velocity and duration in Fig. a–c. In Fig. d–e, we included the integral diameter or first moment of the size distributions for rain droplets (i.e. D‾N(D) for droplets with sizes between 150 µm and 2 cm) and ice particles to quantify the effective presence of reagents and products. The progress of glaciation was followed using the cloud phase partitioning factor αiw (i.e. ratio between IWC and TWC) in Fig. f. We included a contour plot to account for temperature effects included in the parameterization of ice multiplication factors (IMF).

The glaciation started at 40 min after convection initiation with minimal presence of ice particles in the average cloud field due to INP-limited primary ice formation. At this time instance, secondary ice production by droplet shattering (SIP–DS) was the only one active with rates above 5 m-3s-1 at altitudes between 5.6 and 6.1 km with temperatures varying between 262 and 265 K as shown in Fig. b. Higher rates of SIP–DS were reached when the integral diameter of rain droplets was above 3.5 mmL-1.

For the next 2 min (i.e. 40–42 min), the secondary ice particles increased the number of droplet–ice collisions working catalytically to boost the rates of the droplet shattering mechanism up to a maximum of 774 m-3s-1. They also triggered SIP events by the rime-splintering and ice–ice collisional breakup but at much lower rates. The integral diameter of ice particles increased along the vertical cloud domain expanding the mixed-phase zone and increasing the IWC to TWC to a maximum ratio of 0.18.

With an increasing number of secondary ice particles, supercooled droplets were rapidly depleted. This is when the size distribution of freshly generated secondary ice particles played an important role on the cloud glaciation. After a series of droplet shattering events, the droplet population would have generated a number of of small ice crystals but also a fraction of large ice fragments. Since these secondary ice particles spread over a wide range of sizes, they have an impact over a larger number of microphysical processes. Small ice particles will trigger more droplet–ice collisions that will lead to droplet shattering and rime splintering events. Large ice particles will increase not only the riming rates due to collisions with smaller droplets, but also the occurrence of droplet shattering via mode 2 (i.e. accretion of rain drop by a more massive ice particle) .

After 43 min, these processes had modified both the droplet and ice size distributions. While the integral diameter of rain droplets decreased, the integral diameter of ice particles increased rapidly in correlation with SIP rates of the ice–ice collisional mechanism (SIP–IIBR) that reached a maximum of 5300 m-3s-1. The thermodynamic phase in the mixed-phase cloud section became dominated by ice.

At 50 min, SIP rates of all three mechanisms decreased below 5 m-3s-1. Once the ice size distribution had shifted towards larger sizes, rapidly falling large ice particles collected slowly settling supercooled drizzle droplets limiting droplet growth in ascending updrafts . This is an essential step in the precipitation formation via ice-phase.

Due to the pulsating growth habit of cumulus clouds, another short time rounds of SIP events started at 53 and 60 min but with lower rates for all mechanisms due to smaller values of the integral diameter of rain droplets. The weakening of SIP rates suggested that once precipitation was initiated via ice-phase, cloud dynamics were dominated by it and the initial conditions that trigger the positive-feedback of ice multiplication became impossible to reach.

The timeline of events related to secondary ice production indicated the rapid transformation of supercooled large droplets into large ice particles of graupel–type, an essential process for the enhancement of rainfall rates and accumulated precipitation as found in cloud hygroscopic seeding experiments . We can identify SIP-induced changes in the size of precipitating droplets below cloud base comparing the SIP-OFF and SIP-ON scenarios as shown in Fig. . Below cloud base, secondary ice production caused differences in droplet number concentrations for droplets with diameter above 100 µm. These differences indicated that SIP had an important influence on the collision–coalescence processes that progressively lead to a narrower droplet size distribution with higher number concentrations. These changes cannot be studied using the average size distribution, they must be analyzed in correlation with the simulation time. We have divided the simulation time in two hourly periods to account for different SIP effects in number concentrations of drizzle-sized droplets at an altitude of 1.17 km in the proximity of the cloud base. The first one comprises the SIP-active period that ended at 60 min after convection initiation (i.e. rates above 5 m-3s-1) are shown in Fig. a–b, while the second period corresponded to the next simulation hour as shown in Fig. c–d. To understand how changes in the droplet spectrum affected the formation of precipitation, we have included contour plots of cumulative precipitation in Fig. S14 corresponding to the same time periods.

Changes in the early phase of precipitation development depicted in Fig. a–b indicated that both simulation scenarios began with a very similar droplet size distribution (DSD) that was narrow with a peak at a droplet diameter of 1 mm. Around the 50 min time instance, just 10 min after SIP started in the SIP-ON scenario, there was an increase in number concentrations for all droplet sizes below 4 mm in diameter, but a noticeable reduction in number concentrations for droplets above this value. By 48 min, the SIP-IIBR mechanism had already established itself as the dominant secondary ice production pathway. Consequently, the positive feedback associated with the SIP-DS and SIP-IIBR mechanisms is expected to have substantially reduced the number concentration of raindrops, compared with the higher concentrations maintained in the SIP-OFF scenario. The droplet size distribution in the SIP-ON scenario became narrower with higher concentrations of millimeter-sized droplets compared to that of the SIP-OFF scenario. Since these differences balanced out, there were indistinguishable changes in the domain-average cumulative precipitation shown in Fig. S12a–b. The droplet size distribution in the SIP-ON scenario was closer to observations, but the degree of agreement is strongly affected by differences in the time resolution and spatial coverage of observations and model outputs. While DSD observations in the rain droplet size range correspond to a time period of 15 s, model outputs were taken every 30 s and averaged around the horizontal model domain. The total area in the model domain enclosing cumulative precipitation values larger than 1 mm increased slightly due to the time delay in the sedimentation and melting of large ice particles generated in the mixed-phase zone (e.g. a 1 mm droplet falling 4.5 ms-1 undisturbed in a line trajectory will take 11 min to descend from the 4 km melting altitude to cloud base at 1 km).

Changes in DSD occurring in the later stage depicted in Fig. c–d were more drastic compared to those detected earlier. In the SIP-ON scenario there was a noticeable reduction in number concentration of droplets smaller than 500 µm that correlated positively with increasing number of millimeter-size droplets. With copious amounts of larger droplets, the distribution of surface precipitation rates moved up to higher probabilities for modest precipitation rates below 20 mmh-1 as shown in Fig. a. This caused a relative increase of 26 % in the domain-mean cumulative precipitation as shown in Fig. b as well as a relative increase of 15.6 % in the area with cumulative precipitation values larger than 1 mm (see Fig. S12c–d). Once ice multiplication ended leaving the mixed-phase section almost depleted from liquid, it takes more time for small secondary ice particles to grow, fall and melt and therefore, their influence on precipitation rates comes with a time delay. This explained the stretching of the higher cumulative precipitation area along the trajectory followed by the moving deep convective core. Liquid and solid precipitation rates in the deep convective core are described in Figs. S13 ans S14.

With the exception of our study and the one by , the majority of cloud modelling studies about SIP-induced effects on precipitation have found significant reduction of instantaneous and cumulative rates at surface level e.g..