# Monte Carlo Simulations in Aviation Contrail Study: A Review
## 5 Challenges and Perspectives  
The study of aircraft-induced cloudiness still suffers of some fundamental knowledge gaps, particularly as they relate to microphysical aspects of the formation process. The understanding of contrail formation and persistence, that in last decades has been partly elucidated through laboratory experimentation, field observations, and theoretical and simulation developments, continues to be affected by large uncertainties related to the ice-phase microphysics, including nucleation, aggregation, and direct growth from vapor phase, which are represented in Equation (5) by the interaction kernels \(K(v,v^{\prime})\). The source of the poor understanding of these processes largely lays in the complication related to particle size distribution and shape, resulting in a low capability of modeling persistency, which is linked to the transformation of the contrail into an ice cirrus. Nucleation, or the growth of ice crystals upon solid/liquid particles acting as condensation nuclei, is extremely sensitive to onset conditions, including particle surface shape and size, and their morphological, mechanical, and chemical characteristics that represent a source of uncertainty. Ice growth from vapor, on the other hand, is a relatively homogeneous process through which ice crystals of considerable dimensions can be formed in a relatively short amount of time. The model's sensitivity to parameters, which generates large fluctuations in the possible outcome, must found here, in the vapor diffusion and frost processes, which determine the crystal's shape and dimension. In particular, modeling is limited by the unknown, microscopical distribution of vapor upon a growing crystal surface. Heterogeneity of this distribution determines the evolution of crystals with irregular shapes, which is difficult to predict. This uncertainty about the crystal shape, apart from that regarding their size distribution, induces doubts about the role and dynamics of ice-ice collision break-up, whose rate should depend also on partial water vapor pressure and temperature. Even if Lagrangian particle-tracking schemes have represented a breakthrough in cloud modeling, then, the lack of a clear understanding of the underlying physics represents the first challenge for future developments in this field. Monte Carlo approaches are crucial for quantitatively estimating the impact of a multi-scale, complex process as contrails form in aviation, but much more effort will be devoted to modeling and computation, as well as to airborne and laboratory experiments, for validating and feeding simulations. From this viewpoint, large facilities are a valuable tool that can be used for the experimental measurements of the contrail microphysics, in particular for evaluating the impact of new propulsion systems. Experimental data can then be compared with in-flight observations and simulations, for study of the microphysics of forming contrails. Beyond the physics, however, particle-tracking schemes are computationally expensive because the number of considered computational particles increases in order to deal with larger, more complex systems and obtain a significant statistic. This is the case when the transport of computational particles between two grids is considered, for instance, in the modeling of the exchange of ice and water vapor between clouds and surrounding atmosphere. In [112], it was shown that the computational effort can be reduced by introducing condensation nuclei, which circumvents the need to consider advection outside the cloud. In the same article, it was roughly estimated that between 50 and 200 computational particles per grid are needed for properly simulation of a cloud; the range is due to the number of variables considered. However, Lagrangian approaches show a dependence on computational particle initialization that does not always correctly represent the triggeringof real atmospheric processes [113], as is the case with contrails that transition to ice cirrus.