Modeling Contrail Formation Via an SIR-Framework

Abstract

Condensation trails, or contrails, are streaks of condensed water released behind jet aircraft at high altitudes that can extend to become artificial cirrus clouds. They have become increasingly prevalent in the discussion of aviation climate impact due to their ability to trap heat within the atmosphere, accounting for 35% of all aviation emissions. However, the behavior of contrails during and after production is still poorly understood. We introduce a system of one-dimensional compartmental models motivated by the Susceptible-Infected-Recovered (SIR) framework to model and simulate contrail formation and dissipation. The susceptible compartment consists of air parcels where contrail formation is likely due to a cold and humid atmosphere. Secondly, air parcels become “infected” into contrails once hot aircraft exhaust passes through them. Finally, after a period of time the area “recovers” into the final compartment. Modeling begins with a baseline advection-diffusion equation including a constant wind velocity term (u) that accounts for contrail movement post-production. Using the method of manufactured solutions (MMS), the partial differential equation is solved for each compartment to generate a solution for each parameter β (rate of contrail formation) and ɣ (rate of contrail dissipation). Using a forward time-centered space (FTCS) algorithm and adhering to stability conditions, preliminary results show that predicting contrail rates of formation and dissipation is accurate within 1% using controlled timesteps on both the time and space axes. Future research aims to analyze models with a fluctuating wind velocity and including multi-dimensional frameworks. Doing so will continue supporting United Nations Sustainable Development Goal #13: Climate Action.