The model formulation relies on the usual approach of a bulk model with two (general) moments. Instead of computing the temporal and spatial evolution of a (maybe multivariate) mass distribution with a Boltzmann-type evolution equation, we use the integrated version, i.e., the evolution equations for moments of the underlying mass distribution of the respective class of hydrometeors. The moments are defined in the usual way; i.e., 1Mik=∫0∞xkfi(x)dx with the mass of particles x in kilograms and the mass distribution fi in inverse kilograms for the respective class i of hydrometeors. The mass distribution describes the number and is normalized by the total number concentration of particles ni. For a meaningful closure of the systems of equations, we have to choose a suitable type of mass distribution. We generally assume that the particle mass distributions can be represented by generalized gamma distributions see also of the form 2fi(x)=Aixνiexp⁡-λixμi, where the shape parameters νi and μi are prescribed, and λi and Ai are linked to the zeroth and first distribution moments, the number concentration ni, and the mass content qi: 3ni=Mi0=∫0∞f(x)dx=Aμλν+1μΓν+1μ,4qi=Mi1=∫0∞f(x)xdx=Aμλν+2μΓν+2μ. See Appendix  for details on the properties of the gamma distribution and the analytical solution of the integrals.

For the formulation of single particle processes (e.g., growth or sedimentation), we have to introduce size–mass relations and velocity–mass relations of the form 5Di(x)=aixbi,vi(x)=αixβi with the (generalized) size Di and the terminal velocity vi for a particle of mass x within a class i. These relations represent the different shapes of particles from different classes. The remaining classes of hydrometeors are labeled by indices, i.e., c for cloud droplets, r for raindrops, s for snow, g for graupel, and h for hail. The old class cloud ice is now split into five classes. For details of the formulation and the determination of the shapes for the hydrometeor classes used, we refer to .

For our newly introduced ice modes we use the same parameters of the distribution (Eq. ) and the relations (Eq. ) for all classes. While the formation pathway of an ice crystal might have an impact on its shape, the morphology of the particle is mainly determined by the environmental conditions encountered during its growth, e.g., temperature and humidity see, e.g.,, which are not accounted for in the SB scheme. Using the same coefficients and parameterizations for each ice mode, apart from its source, also has the advantage that it allows for a more concise interpretation of the impact of the individual ice formation pathways on the cloud evolution.

The time evolution of the kth-moment Mik of an ice mode i (or another class of hydrometeors) is governed by 6∂Mik∂t+∇⋅vMik+∂v‾i,kMik∂z-∇⋅Kh∇Mik=source/sink. The terms on the left-hand side describe the effects of advection with the mean wind velocity v, sedimentation with the weighted mean fall speed v‾i,k, and turbulent mixing with the mean turbulent diffusivity of heat Kh. On the right-hand side are the source and sink terms for the particle formation, which is unique for each ice mode; deposition of water vapor and evaporation; and a number of collision processes, most importantly aggregation and riming. These equations must be coupled with a model for atmospheric flows, such as, e.g., suitable approximations of the Navier–Stokes equations within the ICON model.

In the following we focus on the description of ice-related physics and refer to for an in-depth description of warm- and mixed-phase microphysics.

For the treatment of ice particles, we introduce new classes of ice particles, discriminated by their formation mechanisms. The ice mode scheme features five independent ice classes instead of a single one (former class cloud ice), called ice modes in this work, each with their own unique formation pathway. For each new ice mode, we introduce number concentrations and mass content. The other classes (graupel, hail, and snow) remain unchanged; however, we have to reformulate the processes of interactions between the former class cloud ice and other variables (e.g., see below for collision processes). The new classes are as follows:

homogeneous freezing of cloud droplets nfrz, qfrz

Deposition of water vapor onto a cloud particle in a supersaturated environment is the most fundamental growth process for all cloud particles. The SB scheme uses saturation adjustment for the water phase; hence whenever the environment is supersaturated with respect to water (Sw>1) at the beginning of a microphysical time step, Sw is relaxed to water saturation (i.e., Sw≡1), and the change in water vapor qv is converted to cloud water qc, considering latent heat release (using a Newton–Raphson scheme). However, supersaturation with respect to ice (i.e., Si>1) is explicitly resolved. The mass growth of an ice particle by deposition of water vapor can be described by formulating the flux of vapor and heat between the particle and the environment considering mass and energy conservation and then integrating these fluxes over the particle surface and evaluating the effect of latent heat of sublimation on the particle surface temperature. Assuming that the temperature difference between the particle surface and the environment is small, we can derive the general growth equation of a single ice particle with mass x using the Clausius–Clapeyron relation : 31∂x∂t|dep=4πC(x)(Si-1)Fv(x)TRvDvesi+LsLsRvT-1KaT, with the saturation ratio with respect to ice Si=eesi(T) and the ventilation coefficient Fv and capacitance C accounting for the enhancement of the depositional growth by the flow field and the non-spherical shape, respectively. The left term in the denominator represents the mass flux relation with the diffusion coefficient Dv and water vapor saturation pressure with respect to ice esi; the right term describes the heat flux with the thermal conductivity of air Ka and the latent heat of sublimation Ls. The capacitance can be related to the maximum diameter C(x)=D(x)/c, with ck depending on the class of the particle k.

Integrating (Eq. ) over the entire particle distribution for an ice mode k, we obtain 32gdep,k=∂qk∂t|dep=∫0∞∂xk∂t|depdxk=4πSi-1ck-1TRvDvesi+LsLsRvT-1KaT∫0∞DxkFv(xk)f(xk)dxk=4πSi-1ck-1TRvDvesi+LsLsRvT-1KaTDxk‾Fv‾, with the mean particle mass xk‾ and averaged ventilation coefficient Fv‾; for details, see calculations in the appendix of SB.

However, we must consider that all ice particle classes compete for water vapor. Thus we follow the semi-analytic approach of to estimate the depositional growth rate with an exponential relaxation towards equilibrium. The change in the mass content of ice particle class k within a physical time step is 33ΔqkΔt|dep=δiXτk1-exp⁡-ΔtX, with δi=qv-qsi expressing the supersaturation with respect to ice and the microphysical time step Δt. τk is defined as the depositional timescale 34τk-1=gdep,kδi. X is the conjoined relaxation time needed to describe the competition between the ice particle classes as a sum of the individual relaxation timescales: 35X=∑jNτj-1-1, where we consider graupel, hail, and snow, as well as all five ice modes. For a derivation and application of this method to resolve supersaturation, see, e.g., , , and .

For the sedimentation of ice particles, we use the mass–velocity relation (Eq. ) for ice crystals; these relations were used for all new ice modes. For use in the evolution equation of moments (Eq. ), an averaged sedimentation velocity must be calculated via a weighted integration; i.e., 36v‾i,k=1Mik∫0∞xkfi(x)vi(x)dx. Using the analytical results for generalized gamma distributions, this results in the following expression: 37v‾i,k=αiΓk+νi+βi+1μiΓk+νi+1μiΓνi+1μiΓνi+2μiβix‾iβi. See also Sect. 3.7 in SB.

Collision is an important process for producing large cloud particles. For the formation of large raindrops, collision is essential. However, considering the formation of rain via the ice phase, collisions between water and ice particles again play an important role. In the presented scheme, the rates for collisions between liquid particles (cloud droplets and raindrops) remain unchanged. However, the collision rates for ice particles must be reconsidered.

As formulated in the SB scheme, we have the following conceptual treatment for sorting new particles stemming from the collision of ice particles with others:

Collision between a cloud ice particle and a cloud droplet leads to a larger ice particle or to a graupel particle, depending on the size of the ice particle (riming).

The setup of the ICON model largely follows the setup described in . ICON is run in limited-area mode with constant boundary conditions derived from the initial conditions. The initial conditions are provided by the Weisman–Klemp setup described in Sect. . The domain extends over 2° in longitude and latitude without topography.

The model grid is an unstructured triangular grid, R02B11, with 2 initial divisions and 11 bisecting iterations . The effective horizontal resolution of the grid is ∼1.23km. The vertical grid contains 128 levels. The physical time step is 2s. The simulation time for each experiment is 240min. Output is written every 10min and interpolated on a regular longitude–latitude grid with a spacing of 0.005°×0.005°.

The model uses parameterizations for subgrid-scale orographic drag and non-orographic gravity wave drag , and the turbulence and vertical diffusion scheme is from . The setup does not use a surface scheme. Radiation transfer physics are disabled. Convection is treated explicitly; i.e., all convection parameterizations (shallow and deep) are switched off.

The Weisman–Klemp setup WK82 hereafter is a suitable test environment for evaluating the ice mode scheme microphysics, as all microphysics classes and associated model routines are active, and both mixed-phase and pure ice clouds – the latter mostly located in the anvil – are observed. The WK82 setup is frequently used to achieve confidence in newly developed models . It has also been utilized in many studies to investigate convection or cloud microphysics (see, e.g., ). The WK82 setup is available in ICON version 2.6 as one of the standard test cases.

The vertical profiles of temperature and relative humidity are chosen following WK82 to represent a typical sounding of a deep convection event with a maximum water vapor mixing ratio near the surface of 0.014kgkg-1 and a surface temperature of 300K. The horizontal wind uz varies with altitude from 0 to Us=5ms-1. Convection was initiated with a symmetric thermal perturbation of 1400m vertical extent and 10000m diameter with a temperature amplitude of 2K at the center, which decays to 0K at the edge of the bubble. Temperature, wind, and moisture profiles of the setup can be found in WK82.

Experiments with the ice mode scheme in several configurations were performed to evaluate the impact of different heterogeneous nucleation schemes on the distribution of the ice modes and the liquid origin vs. in situ formation pathway. Table  lists all experiments. HA, UL, and PH label experiments using the heterogeneous ice nucleation schemes of , , and , respectively. The choice of parameters for the dust aerosol profiles is explained in Sect. . PH3 refers to a simulation with the parameterization including the soot and biological aerosol modes. The HA experiment denotes the default setup for the ice mode scheme, as the scheme is the most widely used heterogeneous ice nucleation scheme for ICON simulations with the SB microphysics scheme.

The reference simulation (REF) uses the standard SB scheme with only a single class for cloud ice. However, the same microphysical parameterizations and assumptions as the ice mode microphysics scheme are employed. In particular, REF uses the same setup for the heterogeneous ice nucleation as the HA experiment. Thus we can assess the ramifications of using multiple ice classes instead of a single one for the overall cloud evolution.

We investigate the origin of cloud ice by introducing the ice mode mass fractions fx for ice mode x: 51fx=qxqtot. Thus, fx describes the relative contribution of ice mode x to the total cloud ice at each grid point. Insignificant trace amounts of cloud ice can distort the statistics of ice mode mass fractions. Hence, we only calculate mass fractions for grid points where the (total) cloud ice mass content exceeds 0.1mgkg-1. This threshold value was used by previous studies that investigated ice cloud origins to identify regions where ice clouds of significant thickness are present .

fliq is the liquid origin mass fraction describing the ratio of cloud ice stemming from liquid origin formation processes: 52fliq=qfrz+qimm+qsecqfrz+qimm+qhom+qdep+qsec, where HOM and DEP contribute to in-situ-formed cirrus and FRZ and IMM to liquid origin cirrus.

Figure  shows the temporal evolution of the different hydrometeor classes as the domain-averaged (ice) water path, (I)WP (a, b), and vertically integrated number concentrations, (I)WPN (c, d), beneath the cloud system. Ice is displayed as the sum of all ice modes (TOT). Note that the output interval of the model is 10min, and we only display domain-averaged water path values above 10-6kgm-2. Hence, the plots only show the time where hydrometeor classes appear in a “significant” number.

First, we focus on the experiment with the default setup for the ice mode scheme (HA) in Fig. a and c. Panels (b) and (d) are discussed in Sect. . In panel (a) we note that cloud droplets condense within the first 10min of the simulation, followed by the initiation of the warm-rain process. Ice and graupel appear at the same time around 18min and quickly become, within 5min, the two major contributors to the water path. Snow becomes relevant with a short delay of up to 5min after the occurrence of graupel. Strong riming is the last microphysical process to become active, with hail first occurring at 30min. At a 60min simulation time the cell matures. Hence, all hydrometeor classes are present, and their avg water path increases only slightly after that. Note that the cell shows no signs of dissipation within the simulation time. The ratio of the avg water path between the classes also remains constant. Graupel, followed by cloud ice, is the dominate class with regard to IWP, while hail, rain, and cloud droplets show mostly the same avg IWP values. Snow is distinctly the weakest hydrometeor class with regard to avg IWP. The mass content of cloud particles in general is primarily governed by the availability of water vapor and thus thermodynamics. The number concentrations of the classes, on the other hand, are more varied since they directly depend on the formation pathways. Panel (c) in Fig.  shows the avg integrated number concentrations (IWPNs) of all hydrometeor classes. We observe a large gap in avg IWPNs between cloud droplets and ice compared to the other classes, with an increase of 3.2 and 4 orders of magnitude for simulation times after 130min, respectively. Cloud droplet number concentrations are tied to the cloud condensation nuclei (CCN) activation scheme of , which depends mainly on upward vertical velocity and thus produces a large droplet number concentration in a strong convective case like the WK82 setup. However, the scheme is still limited by the number of available CCN. We discuss the connection between high cloud ice and cloud droplet number concentrations in the following paragraphs.

Figure  provides insight into the development of each ice mode as domain-averaged IWP and IWPN. We focus on the results of the default setup of the ice mode schemes (HA) first (panels a and e). At the beginning, ice consists of frozen cloud droplets with both immersion and homogeneous freezing, represented by the IMM and FRZ modes with avg IWP values of 2×10-4 and 5×10-1kgm-2, respectively. FRZ is the most dominant ice mode by several orders of magnitude, especially with regard to avg IWPN. Secondary (SEC) ice from rime splintering occurs with a 20min offset to the first occurrence of graupel and becomes almost as important as immersion freezing in regard to avg IWP with values up to 2×10-3kgm-2 at the end of the simulation. This is consistent with the findings of , who also performed simulations with the ice mode schemes for the same test case but utilized Lagrangian trajectory analysis to investigate rime splintering and spread of secondary ice through the cloud system. The first occurrence of secondary ice of significant number concentrations (nsec>0.1l-1) was observed after 30min, even for simulations of higher wind shear. They found riming with graupel that sedimented from higher levels into the Hallett–Mossop temperature zone (265<T<270K) to be the dominant source of secondary ice.

Ice from homogeneous (HOM) and deposition (DEP) nucleation occurs first from nucleation events in the overshoot starting at 30 and 40min for DEP and HOM, respectively. Both types of nucleation events occur multiple times during the simulation, and the avg IWP of both modes increases over time. Initially, DEP is overall stronger in terms of avg IWP, although with significant IWP (≥10-6kgm-2) occurring at 95min. However, at the end of the simulation, HOM shows almost the same avg IWP and IWPN values as DEP, with 2×10-5kgm-2 and 2×106m-2, respectively.

In summary, FRZ dominates with regard to avg IWP with up to 2.5 orders of magnitude and with regards to avg IWPN with up to 4 orders of magnitude. These results are strongly tied to the CCN activation scheme. Droplets freeze preferably heterogeneously (here by immersion freezing) and then homogeneously once the active INPs for immersion freezing are depleted. Thus, if more CCN than INPs are available, the FRZ mode becomes more dominant than the IMM mode as more (activated) droplets will freeze homogeneously once the INPs are depleted. The integrated total ice number concentration (as the sum of all ice modes) is overall dictated by FRZ in this case and thus tied to the high number concentrations of droplets that the CCN scheme activates.

We now investigate the vertical distribution of cloud particles. Figure  shows a vertical slice of the cloud through the domain center after 200min simulation time and the mass content of all hydrometeor classes, where ice is represented as the sum of all ice modes. The red and blue contours show the critical LWC and IWC value of 0.1mgm-3, respectively. The matured convective cell has a vertical extent of 15km and developed an anvil between 9 and 12km. The cell produces strong precipitation beneath the cell, as can be seen from panel (e) for rain. Most of the cloud is glaciated, with rimed particles, mainly graupel, being the most prevalent in terms of mass, with mass contents of up to 10-3kgm-3. Hail is mostly found in the narrow updraft core at 130km, where riming rates and resident times are the highest. Ice is present in most parts of the cloud above the melting temperature and forms an anvil of (pure) ice with an overshooting top above 12km. Snow is a product of aggregation and thus depends on the mass content and number concentrations of ice. Cloud regions with high cloud ice number concentrations and mass content have high aggregation rates. However, snow has a lower mean size than cloud ice and thus higher sedimentation rates. Thus, snow is mostly located below the maximum cloud ice mass content.

Figure  shows the same vertical slice as in Fig.  but for the mass content of each ice mode after 200min simulation time. The lower part of the cloud from 3 to 9km around the updraft core is dominated by secondary ice from rime splintering (SEC) with mass contents of up to 10-5kgm-3. This coincides with the region where riming is active, which is evident from the high mass content of graupel and hail in this region, as observed in Fig. . The prevalence of secondary ice from rime splintering in this region was also observed by .

Ice between 6 and 10km partially stems from heterogeneously frozen droplets (IMM), while in the upper part of the cloud, homogeneously frozen droplets (FRZ) are prevalent. The latter shows the highest mass contents for cloud ice with 10-4kgm-3 within a wide region extending from altitudes of 8 to 12km and the length of the convective cloud (150km). When cloud droplets are transported upwards into colder regions, they freeze first through immersion freezing due to the lower temperature threshold. Once all the INPs are activated, there is still a significant number of cloud droplets left or provided by the constant supply of humidity (and then saturation adjustment) from convection. At this point homogeneous freezing begins to dominate over immersion freezing. Moreover, the ice mode scheme only shows the ice formation pathway of the ice observed at this time; it does not track sources and sinks individually. This means that ice from IMM could have been converted to snow by aggregation or lost in collisions with graupel and is for this reason not as prevalent as FRZ.

The part of the cloud consisting of ice from FRZ stays structurally mostly the same during the simulation run time, only widening as the anvil expands. However, the cloud parts where IMM and SEC are present fluctuate with the evolution of the cell. SEC follows the liquid core where riming occurs. IMM is at the beginning located above the liquid core between the sections where SEC and FRZ are prevalent and is later mostly present in the flanks.

Ice from homogeneous (HOM) nucleation is limited to the overshoot, and deposition (DEP) nucleation also occurs in small amounts outside the liquid core in the glaciated parts of the cloud between 6 and 9km.

Overall, we notice a mostly clear spatial separation of the ice modes with some overlapping areas where ice of a different origin is found. Ice in the upper part of the cloud above 9km is mostly of liquid origin, hence consisting of frozen droplets and stemming from rime splintering below them. This general spatial distribution of the ice modes is also true for the other sensitivity experiments.

In this section we compare the reference simulation (REF) performed with the (unmodified) SB scheme to the ice mode simulation (HA). As elaborated on in Sect. , both experiments use the same setup for heterogeneous nucleation (HA17). Thus the only difference between them is the split of the cloud ice class into the five ice modes.

The overall cloud evolution of the reference (REF) simulation is very close to the ice mode scheme (HA). As can be seen in Fig. b, the evolution of microphysics classes directly related to the liquid phase, which is cloud droplets, rain, graupel, and hail, shows the same temporal evolution. Even the onset times for cloud ice, where the governing parameterizations of both schemes differ, are mostly the same. We observe, however, a large difference in the average water path of snow, which shows an increase of an order of magnitude for the simulation with the ice mode scheme (HA), although the difference decreases with time to a factor of ∼2.5.

This is also evident in the vertical slice of the convective cloud. Figure  shows the vertical slice of the convective cloud at 200min through the domain center for snow with (a) the ice mode simulation and (b) the reference simulation. There is significantly more snow present in the ice mode simulation than in the reference simulation. While the maximum snow mass content is still at 104kgm-3, snow is distributed over a wider area of the cloud, especially towards the flanks and higher altitudes (up to 11km). However, comparing the sum of ice and snow for both simulations in panels (c) and (d) shows that there is in general no increase in combined ice particle mass content. Rather, we notice there is a tendency for the ice mode scheme (represented by the HA experiment) to shift mass from the ice to the snow class(es); hence the aggregation rates have to be higher. This is linked to the conceptional differences between both schemes: the SB standard scheme only produces snow by self-collection of a single cloud ice class, where in the ice mode schemes, there are five independent cloud ice classes. They aggregate snow not only by self-collection, but also by collisions with each other. While the physics of self-collection and ice mode–ice mode collision are the same, the increased number of collision processes leads to higher aggregation rates (see also Sect. ).

While the shift of ice to snow should affect overall sedimentation rates of ice particles, there seems to be little impact on the cloud evolution and dynamics of the convective cell since the IWC and LWC outlines as well as the general evolution of the cloud observed in Fig.  remain the same. It is also important to note that pure ice and especially cirrus clouds will be mostly unaffected by this effect since collision efficiencies are small at low temperatures (see Sect. ). Generally, ice number concentrations are also insufficient to produce significant amounts of snow for pure ice clouds.

A change in assumptions regarding the distribution of INPs or a switch to a different INP activation scheme entirely can have a large impact on the evolution of the ice phase. We compare the experiments HA, PH, PH3, and UL here. For the general evolution of an average cloud water path and ice water path, we do not observe major differences (not shown here). Hence, we discuss the general evolution of the convective cloud only briefly here. Since the same CCN activation scheme is used for all experiments, we do not observe significant change in the evolution of the liquid phase. The rainwater path is slightly lower for PH after the initial warm-rain formation but catches up later. Hail formation starts sooner for PH but also reaches the same average value as for the other experiments. Further, we observe a shift towards more snow and slightly less (total) cloud ice for the PH simulation. Thus, the overall evolution of the convective clouds is similar for all heterogeneous ice nucleation schemes tested here.

We now investigate the spatial and temporal distribution of the ice modes more closely for HA, PH, PH3, and UL. When studying the evolution of the ice mode average IWP in Fig. a to d, we observe that FRZ and SEC stay mostly the same for all runs at an avg IWP of 10-3 and 10-1kgm-2, respectively. SEC stems from rime splintering and thus depends on the evolution of the graupel and hail class, which again is mostly sensitive to CCN activation and the resulting number of supercooled droplets. We observe in Sect.  that SEC occupies a distinct part of the lower cloud around the updraft core. A change in the heterogeneous nucleation scheme seems not to significantly affect the dominance of ice from rime splintering in this region or change the avg IWP from secondary ice.

FRZ is also strongly sensitive to the CCN activation scheme, which remains unchanged between the simulations. A weaker IMM mode should affect FRZ since droplets that do not freeze heterogeneously freeze homogeneously instead, unless they are removed by evaporation or collision. Hence, both modes are in direct competition for unfrozen cloud droplets. However, FRZ is overall so dominant in this case study that this effect is not noticeable with regard to avg mass content and number concentrations.

Compared to HA, IMM is weaker in the simulation with the PH scheme for both avg IWP and IWPN (Fig. b, f), with values of 5×10-4kgm-2 and 106m-2, respectively. However, for UL (panel d, f), the avg IWP and IWPN of IMM stays the same as for HA. The latter is not surprising since the assumptions about immersion freezing and the number concentrations of INPs are almost the same. In Sect.  we choose the dust concentration parameters for the PH parameterization such that the maximum number of INPs activated for immersion freezing was the same as for the UL and HA schemes. The important difference between the PH scheme and the HA and UL schemes is that immersion freezing occurs at higher temperatures (close to 263 instead of 258K), thus, in lower and warmer parts of the cloud, where hydrometeor classes other than cloud ice are abundant, e.g., graupel. Collisions with those classes are an efficient sink for the IMM mode. Hence, the average IWP and IWPN of IMM are smaller for PH compared to HA and UL.

For PH3 (Fig. c, h) we observe a higher avg IWP of IMM than for all other simulations, with values of up to 5×10-2kgm-2. Even though we stated in Sect.  that the maximum number of active INPs is lower with this scheme than for the others, the inclusion of soot and biological aerosols triggers immersion freezing at higher temperatures even close to the melting temperature level Tm=273K. While the shift to higher activation temperatures lowered the IMM content for the PH scheme with the dust-only mode, for PH3, with the inclusion of the soot and biological aerosol mode, IMM content increased. This even “earlier” activation of INPs likely changes the cloud evolution such that the IMM mode becomes more important. Indeed, we note that the cloud shape is different for PH3 when we later present a vertical slice of the cloud.

DEP is in general weak in this convective case since deposition nucleation events usually only trigger outside mixed-phase clouds (see Sect. ). In Fig.  we observe different triggering times and strengths of deposition nucleation events. However, these differences are mostly caused by non-linear realizations of the model dynamics and are not sensitive to the choice of nucleation scheme.

While DEP is not continuously persistent in the overshoot, there are smaller nucleation events being triggered in the anvil and the flanks of the convective cloud. Also note that output is written only every 10min; hence not all nucleation events are sampled in the output data, and ice from DEP and HOM could be removed by aggregation or evaporation before it is sampled. When using the PH or PH3 scheme DEP is almost not present at all. This is consistent with our description of the scheme in Sect. , where even weak nucleation events are only triggered at high Si compared to UL and HA. Consequently, the HOM mode is strengthened for PH since homogeneous nucleation events are not suppressed by pre-existing ice from DEP.

Figure  shows vertical slices of the cloud at 200min through the domain center. Plotted are the mass contents of ice from immersion freezing (IMM) and homogeneously frozen droplets (FRZ) as well as snow for HA, PH, PH3, and UL (first, second, third, and fourth columns, respectively). As already discussed, FRZ dominates the upper part of the convective cloud with values of up to 10-4kgm-3 for all heterogeneous nucleation schemes. The structure of vertically layered ice modes described in Sect.  holds true for all simulations. As immersion freezing is mostly the same for HA and UL, the distribution of ice modes and snow shows only marginal differences between both experiments (first and fourth columns).

For PH, however, we found that IMM is much weaker in terms of mass content (and number densities). This also limits its horizontal distribution, which is confined more towards the core of the cloud compared to HA and UL. This directly affects the snow class, which shows lower number densities and less spreading throughout the cloud. This underlines again that IMM is important for aggregation because it produces ice crystals large enough for efficient collection kernels (see Sect. ).

Using PH3 affects not only the IMM mode but also the overall structure of the cloud. As discussed above, PH3 favors immersion freezing, and its biological and soot INP modes show an onset of higher temperatures compared to other heterogeneous ice schemes. We observe the result of INP activation at higher temperatures with a shift of ice mass towards the lower model levels. This can also be observed in the shape of the convective cloud. For example, the PH3 cloud shows a less developed left flank. Additionally, there is a pocket of IMM ice above the melting temperature line which is not present for HA and UL, for which immersion freezing is not possible in this temperature region. While the general structure and layering of ice modes are the same, the shape and location of liquid water zones change (as can be seen from the red LWC outlines), which has a direct effect on the SEC mode that in general follows the liquid core (where riming occurs) closely. The PH3 simulation also shows an increase in snow, underlining the importance of aggregation as a sink for the IMM mode (stronger in PH3).

Figure  shows the average mass fraction for all ice modes at 200min simulation time. The mass fraction describes the ratio of ice from a particular mode x to the total cloud ice qtot (see Sect. ).

The majority of the fully glaciated parts of the cloud above the secondary ice region between 6 and 12km is dominated by IMM (for HA, PH, and UL) or FRZ (for PH3) classifying the parts of (pure) ice cloud as liquid origin (hence, LIQ is close to 1). This includes the anvil of the deep convective cloud. The overshoot is located above 12km, and the liquid origin fraction is determined by the amount of FRZ ice being mixed into this region and the strength of DEP nucleation events. PH and PH3 show a weak DEP mode with incursions from HOM, resulting in liquid origin fractions between 0.3 and 0.7. For HA and UL the liquid origin fraction is below 0.4. This makes the overshoot a region where ice stemming from different formation pathways mixes. The dynamic forcing transporting FRZ and IMM ice into the overshoot, the occurrence and strength of HOM and DEP nucleation events, and the sedimentation of newly formed ice from the overshoot into the cloud below all affect and change the liquid origin fraction. That the majority of the fully glaciated parts of the deep convection cloud is of liquid origin is in accordance with previous studies .