Partitioning the primary ice formation modes in large eddy simulations of mixed–phase clouds

. State of the art aerosol dependent parameterisations describing each heterogeneous ice nucleation mode, as well as homogeneous nucleation, were incorporated into a large eddy simulation model. Several cases representing commonly occurring cloud types were simulated in an effort to understand which ice nucleation modes contribute the most to total concentrations of ice crystals. The cases include a completely idealised warm bubble, semi–idealised deep convection, an orographic cloud, and 5 a stratiform case. Despite clear differences in thermodynamical conditions in each case, the results are remarkably consistent between the different cloud types. In all the investigated cloud types and under normal aerosol conditions, immersion freezing dominates and contact freezing also contributes signiﬁcantly. At colder temperatures, deposition nucleation plays little role, and homogeneous freezing is important. To some extent, the temporal evolution of the cloud determines the dominant freezing mechanism, and hence the subsequent microphysical processes. Precipitation is not correlated with any one ice nucleation 10 mode, instead occurs simultaneously when several nucleation modes are active. Furthermore, large variations in the aerosol concentration have only a minor inﬂuence on the precipitation amount.

show that the 5 th and 95 th percentiles of dust number concentrations are representative of low and high dust concentrations. These concentrations are often more than an order of magnitude smaller and larger than the median, depending on the season. The dust aerosol properties used in this study correspond roughly to the properties during summer from Hande et al. (2015), during which concentrations and aerosol sizes are the lowest throughout the year. In order to investigate the sensitivity of ice nucleation to the aerosol size distribution, two additional aerosol size distributions are defined in Figure   5 1, shown as the dashed lines. Here, the total number concentration of both modes was modified by a factor of ±10, which simulates high and low dust aerosol number concentrations.
The aerosol and droplet distributions were divided into 10 bins, over which the integration for the parameterisations was performed. The immersion and contact freezing parameterisations are only applied to cloud droplets. Contact freezing of rain droplets is not considered, since rain drops collect many particles through collision-coalesence and are therefore efficient in 10 the immersion mode (Paukert et al., 2017).
Immersion freezing acts only on the immersed dust aerosols, and contact freezing acts on the interstitial aerosols. The segregation of immersed and interstitial aerosols is treated simplistically in this work, where the ratio of these quantities is pre-defined. In these simulations, 50% of the dust aerosol is defined to be interstitial and hence available for contact freezing, and the remaining 50% is defined to be immersed and available for immersion freezing. This is not necessarily a realistic 15 assumption, however it allows the relative concentrations of immersion and contact INPs to be compared independent of this assumption. Finally, depletion of immersed aerosols is not taken into account in these simulations.

Case study description
Ice nucleation is influenced by ambient environmental conditions, so in order to systematically study the relative contribution of each mode, a distinction between cloud types must be made. In this section, the model configurations for two cases of 20 convection, an idealised orographic cloud, and finally a stratiform cloud, are described.
Since deep convective clouds span temperature ranges relevant for warm and cold cloud microphysics, including into the homogeneous nucleation regime, two cases will be investigated here: an fully idealised warm bubble case, and a semi-idealised cloud. Starting with the former, the thermodynamic profile described in Weisman and Klemp (1982) was used to initialise the simulation, shown in the left panel of Figure 2 as the black lines. A 3D temperature disturbance of 1.5 K, with radius of 10 km, 25 was placed in the centre of the domain at a height of 1.4 km. 100 vertical levels, with 600 × 600 grid cells horizontally, were used, and the time step was 1 second for the duration of the 4 hour simulation.
The semi-idealised deep convective cloud represents a more realistic simulation of convection, and provides an interesting comparison with the previous idealised heat bubble. A detailed description of the model configuration for this case appears in Hande et al. (2017), and is summarised here. A real sounding with CAPE of 2801 J kg −1 was used to initialise the simulation, 30 and realistic topography was specified at each grid point, as shown in Figure 6 of Hande et al. (2017). The topography represents the region near Jülich, in western Germany, with mountains reaching up to 560 m in the south west of the domain. 100 vertical levels were used, and 600 × 600 grid cells horizontally, with a time step of 2 seconds for the duration of the 9 hour simulation.
To initialise the orographic cloud case, an idealised bell-shaped hill was used along with a real sounding, shown in the right panel of Figure 2 as the black lines. The hill has a maximum height of 800 m and a half-width of 15 km. In the longitudinal direction, 1441 grid points were used, and 271 in the latitudinal direction, with 100 vertical levels. A time step of 1 second was used for the duration of the 4 hour simulation.
The final case to be investigated is a stratiform cloud, which was initialised from a real sounding from central Germany 5 during winter, shown in the right panel of Figure 2 as the blue lines. A smaller domain with 400 × 400 horizontal grid points were used, again with 100 vertical levels. In this case, the horizontal wind speed was artificially increased by a factor of 1.5 in the lowest 5.5 km, in oder to increase the dynamical forcing enough to activate cloud droplets through shear driven turbulence in the boundary layer. Due to the higher wind speeds in this simulation, a shorter time step of 0.5 seconds was used for the x hour simulation. All investigated cases employed fully periodic boundary conditions. 10

Spatial distribution of INPs
In this section the spatial distribution of INPs in each mode will be analysed, along with the cloud droplet properties. Contact freezing INPs are parameterised in terms of a rate, so multiplying by the time step of the simulation the number concentrations are obtained. All diagrams in this section are domain mean horizontal cross sections taken at a particular time step indicated in the figure captions, where the mean is taken over all latitudes. As described in the Section 2, cloud droplet size was calculated 15 from cloud liquid water content and number concentration, assuming a gamma distribution at each grid point. The mode in the cloud droplet radius distribution which is shown in the following diagrams is simply the radius at which the maximum in the cloud droplet size distribution occurred, and the variance and skewness of the distributions are not represented.
Starting with the idealised heat bubble, Figure 3 shows the concentrations of INPs (left panels), along with the cloud droplet properties (right panels) at 0.5 hrs into the simulation. Immersion and contact freezing both contribute significantly at warmer 20 temperatures, and homogeneous nucleation is a major contributor at colder temperatures. Deposition nucleation, however, is limited to low concentrations occurring over a narrow temperature range.
Looking closer at immersion freezing, there is a trend of higher INP concentrations at colder temperatures. This should be expected since, according to this parameterisation, there is an inverse exponential relationship between INAS density and temperature.  The results for the semi-idealised deep convective case, shown in Figure 4, are remarkably consistent with the previous case: immersion and contact freezing both dominate, and homogeneous nucleation contributes the most at cold temperatures.
Furthermore, the trend in immersion and contact INPs is the same as the idealised heat bubble.
The added complexity in this case highlights an interesting feature of the contact parameterisation employed in this study.
Looking at the relative humidity, between about 16-26 km in the horizontal direction, the relative humidity is less than ap-  The sounding used to initialise this case, shown in Figure 2, has a strong decrease in moisture at 5.5 km (T = 248 K, p = 475 hPa), which inhibits INP formation at colder temperatures. The maximum in the cloud droplet number concentration and size is between 1-2 km, which is outside the temperature range of the contact parameterisation. Therefore, the concentration of contact INPs is reduced due to the lower concentration of smaller cloud droplets in the region of contact freezing.

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The temporal development of the ice phase influences a host of cloud properties, including cloud lifetime, radiative properties, and precipitation amount. conditions in these cases. Notice that the droplet properties of both convective cases, shown in Figures 1, 3, and 4, are very similar. Fan et al. (2017), however, show that thermodynamics contributes significantly to cloud microphysical processes for an orographic mixed-phase case. This suggests the sensitivity for non-convectively forced clouds could be larger.
The stratiform case study represents the only cloud type in this study which is weakly forced. Despite high levels of moisture above the main inversion, the conditions for homogeneous freezing or deposition nucleation were not met in this simulation.

5
There is a fundamental difference between cirrus produced in different dynamical environments. In the convective cases, liquid water is lifted from the mixed-phase regime to colder temperatures, where it freezes. Since the stratiform case is weakly forced, the origin of the moisture is from higher altitudes. These two categories are known as either 'liquid origin cirrus' or 'in-situ cirrus' (Krämer et al., 2016;Luebke et al., 2016). Since the stratiform cloud investigated here has no cirrus, the dominant ice forming mechanism for this so-called 'in-situ cirrus' remains an open question. has a large influence on nucleation ability in different temperature and super saturation regimes. Whether this has a significant impact on the dominant ice nucleation mode remains to be investigated.

Conclusions
A number of high resolution modelling case studies are presented in order to systematically investigate which ice nucleation modes dominate for a number of typical cloud types. The results indicate that immersion freezing dominates in all cases. Con-20 tact nucleation plays a significant role in most simulations, accounting for between about 2-33 % of total INP concentrations under the reference aerosol conditions. Deposition nucleation only contributes a fraction of a percent in the convective cases, and homogeneous freezing accounts for up to 6 % of total INP concentrations. However in the non-convective cases, no INPs were produced in the cirrus regime.
In the later stages of the convective clouds, homogeneous freezing became more important, and contact freezing dominated 25 at warm temperatures. The orographic and stratiform case reached a steady state soon after the formation of the cloud. The occurrence of precipitation is not correlated with any one ice nucleation mode, instead occurs at the same time as multiple ice nucleation modes, including homogeneous nucleation.
Since the results from the two convective cases were quite similar, this suggests ice nucleation could be insensitive to thermodynamical conditions in these cases. The main consequence of the much higher CAPE in the heat bubble case, compared 30 to the semi-idealised deep convective case, was faster cloud development.
For the convective cases, perturbation in aerosol concentrations produced proportional changes in the relative contribution of immersion freezing INPs. The relative contribution of the other modes decreased. The opposite occurred for the orographic shown in Figure 1. The relative contribution (%) of each mode to the total INP concentrations is shown in parenthesis.