Modos de Integración

More than 50% of the earth's precipitation originates in the ice phase. Ice nucleation, therefore, is the starting mechanism leading to precipitation. The poorly understood processes of ice initiation and secondary ice multiplication in clouds result in large uncertainties in the ability to model precipitation production and to predict climate changes (Heymseld et al., 2010). San- tachiara et al. (2014) point out that ice formation can take place by two phase changes: water vapor deposition or freezing of small water drops. Both these processes are possible, in principle, through homogeneous or heterogeneous nucleation, i.e. triggered by aerosol particles called ice nuclei (IN). These processes can also be called as Primary processes (namely nucleation of ice

from the liquid or water vapour phases) whereas Secondary processes (i.e. a single ice crystal may act as IN, favoring, in some circumstances, the gener- ation and the nucleation of new ice particles) could happen in a subsequent stage.

Homogeneous freezing of small water droplets initiates within the inte- rior volume of a cloud droplet and may occur when enough water molecules stick together within the droplet to form an embryo of ice. In other words, random uctuations of water molecules produce a structure acting as IN, carrying on the ice particle formation. As in homogeneous nucleation of wa- ter drops from vapor, the dimensions of stable nuclei and the probability of embryo formation behave as key factors. Considering that these quantities derive from solid-liquid interfacial free energy, a temperature of -40◦_{C has}

been calculated as needed for freezing of liquid supercooled drops smaller than 5µm and, in addition, the temperature at which water droplets rst freeze increases with the droplet size. In the atmosphere, even though super- cooled liquid drops are frequent, very occasionally at such low temperature conditions, a water drop exits because heterogeneous nucleation has yielded to ice particle at higher temperatures. Although freezing does not take place immediately below 0◦_{C, the ice phase is frequently observed in the atmo-}

sphere as cloud temperature approaches -20◦_{C (Pruppacher and Klett, 1997)}

thanks to heterogeneous nucleation.

Homogeneous deposition, in turn, comes from water vapor molecules ran- dom collisions forming a stable ice embryo. In order for this process to be ecient very high values of supersaturation would be required (10-70 % re- spect to the ice). In the atmosphere rarely supersaturation exceeds a value of 1-2% with respect to water, because the heterogeneous nucleation of liquid droplets starts at lower values of vapor density excess implicating a decrease

of supersaturation. Hence homogeneous deposition it is not possible in the atmosphere.

Ice crystals thus appear below -20◦_{C /-15}◦_{C indicating heterogeneous nu-}

cleation, and this temperature is assumed as a cut-o threshold for that process. The probability of nucleation mostly depends on the properties of the substrate material. The more tightly-bound the water molecules are to the substrate, the greater will be the probability of ice nucleation. In ad- dition, if the crystal structure of the substrate closely resembles that of an ice crystal, it will increase the chances of ice nucleation (Liou and Yang, 2016), along with supercooling and supersaturation conditions. Moreover, when the binding and the matching of the crystal lattice are good, heteroge- neous freezing occurs at lower supersaturation and higher temperatures than homogeneous freezing (Santachiara et al., 2014).

Therefore supercooled clouds (also known as "mixed phase" clouds, mean- ing consisting of supercooled liquid droplets and ice particles) exist thanks to a huge concentration of aerosol particles in the atmosphere, of which a small amount acts as ice nuclei. Indeed these IN are rare in comparison to cloud condensation nuclei which form liquid droplets.

Heterogeneous ice nucleation has been hypothesized to occur in four dif- ferent modes: deposition, condensation, immersion and contact (Vali, 1985). These can be briey described as follows by referring to descriptions made by Murray et al. (2011) and by Broadley et al. (2012):

• deposition mode nucleation involves deposition of ice onto the solid surface directly from the vapor phase and can occur when conditions are supersaturated with respect to ice. It seems to be less important than the other mechanisms in mixed phase clouds, but it is probably important in upper-tropospheric ice clouds;

• immersion freezing occurs when ice nucleates on a solid particle im- mersed in a supercooled liquid droplet;

• condensation freezing involves ice formation during the condensation of liquid water onto a solid particle. The distinction between immer- sion and condensation modes is subtle, since the most likely route for immersing a particle inside a droplet is through condensation on that particle;

• contact freezing occurs when a solid particle comes into contact or collides with the water-air interface.

Immersion mode and contact freezing are thought to be most important in many mixed phase clouds. Generally, contact nucleation has been observed to occur at higher temperatures than immersion freezing for the same IN. Because of the subtle dierences among these mechanisms, we usually speak of nucleation by freezing, thus avoiding to specify the process. Furthermore, the relative importance of these freezing modes in the atmosphere is not yet well understood.