# Monte Carlo Simulations in Aviation Contrail Study: A Review
## 3 Monte Carlo Simulations for Contrails Formation and Evolution
The result, then, is too heavy for both weather prediction, when employing a limited number of bins, and for detailed studies at cloud-resolving scales, when the number of volume (mass) intervals is increased. Interesting approaches, based on a Lagrangian Monte Carlo simulation of a single or, more often, a bunch of particles at one time, was developed in the last fifteen years by researchers from different backgrounds who proposed similar strategies in different applied contexts [83, 84, 85, 86, 87, 88, 89, 90, 91, 92]. Lagrangian approaches to aerosol/cloud microphysics, conceptually deriving from Direct Simulation Monte Carlo (DSMC, [93]), have the intriguing feature of allowing, at least in principle, single particle tracking, a fundamental step for comprehension of the fluid-dynamical condition for the formation and persistence of contrails and cloudiness in general. In order to limit the demand of computational power, these models usually introduce an ideal object, referred to as a super particle, computational particle, or simulation particle, representing the bunch of particles mentioned above. Lagrangian particles represent a given number (called weighting factor or multiplicity) of real particles characterized by the same volume (mass). Particles belonging to the same collective representation are supposed, within the approximation introduced, to occupy the same position in the grid, and move with the transport equation associated with the fluid motion. Monte Carlo simulations are still a niche in cloud microphysics research and have been applied to the study of aircraft-induced contrails in a relatively small number of papers. In [91], in particular, the technical details of a Lagrangian code dedicated to the microphysical aspects of ice cloudiness, EULAG-LCM, are described. It was pointed out, there, that the number of computational particles to be employed for statistical convergence changes with the microphysical process considered and that the ice nucleation is the most demanding one. The code developed was used in [92] to study the differences in the formation of contrails for different aircrafts and how they are linked with the transformation into cirrus clouds. Six different aircraft, ranging from a small regional airplane to the largest A380, were considered, and the peculiarities of their vortices and engine exhausts were described with large eddy simulations in order to determine the microphysical differences of the forming cloud. Larger vehicles were associated with an enhanced number of ice crystals, that was reduced, however, by the associated stronger vortices in the few seconds after plume emission. Nonetheless, the cirrus associated with the AIC of the largest aircraft were not as persistent as those of the regional one, which lasted from 1.5 to 2.5 times less. Assessments such as the one described above represent the future of the discipline and are crucial to evaluating the non-CO\({}_{2}\) environmental impact of the new configurations and propulsion systems that will be introduced in aviation towards 2050. In this perspective, these kinds of Monte Carlo calculations will become the gold standard for cloud-resolving simulations and, probably, even for larger length scales. The capability of correctly reproducing the role of aircraft-induced cloudiness in the climate equilibrium of the planet is still a challenging task, as described below, and could benefit from the introduction of high-fidelity approaches into models of the atmosphere dynamics.