Monte Carlo methods are commonly used to simulate the transport and spread of atmospheric pollutants via the solution of Stochastic Differential Equations. Although the Standard Monte Carlo (StMC) which is currently used can be fast enough when low accuracy is required, the method becomes expensive when the accuracy increases and therefore a more efficient method is required. In this talk, we demonstrate the asymptotic efficiency and reduced computational cost of the Multilevel Monte Carlo (MLMC) method when compared to StMC which becomes very important in emergency-response applications such as tracking radioactive clouds from nuclear accidents or predicting the impact of volcanic ash clouds on international aviation. Also, we present how the choice of the numerical timestepping method can reduce the absolute cost in the non-asymptotic regime which is also very important and finally we present a reflective boundary conditions treatment which doesn’t reduce the efficiency of the MLMC method.