Satellite imagery can detect temporary cloud trails or ship tracks formed from aerosols emitted from large ships traversing our oceans, a phenomenon that global climate models cannot directly reproduce. Ship tracks are observ- able examples of marine cloud brightening, a potential solar climate intervention that shows promise in helping combat climate change. In this paper, we demonstrate a simulation-based approach in learning the behavior of ship tracks based upon a novel stochastic emulation mechanism. Our method uses wind fields to determine the move- ment of aerosol-cloud tracks, and uses a stochastic partial differential equation (SPDE) to model their persistence behavior. This SPDE incorporates both a drift and diffusion term which describes the movement of aerosol par- ticles via wind and their diffusivity through the atmosphere, respectively. We first present our proposed approach with examples using simulated wind fields and ship paths. We then successfully demonstrate our tool by applying Approximate Bayesian Computation method - Sequential Monte Carlo (ABC-SMC) for data assimilation.