This article provides a review of the role of stochastic approaches, in particular Monte Carlo calculations, in the study of aviation-induced contrails at different characteristic lengths, ranging from micrometers to the planetary scale. Pioneered in the 1960s by Bird, Direct Simulation Monte Carlo has for long time been considered unfeasible in extended dispersed-phase systems as clouds. Due to the impressive increase in computational power, Lagrangian Monte Carlo approaches are currently available, even for studying cloud formation and evolution. Some aspects of these new approaches are reviewed after a detailed introduction to the topic of aircraft-induced cloudiness. The role of Monte Carlo approaches in reducing the different source of uncertainty about the contribution of aviation contrails to climate change is introduced. Perspectives on their role in future experimental and theoretical studies are discussed throughout the paper.
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