  A common way to simulate the transport and spread of pollutants in the
atmosphere is via stochastic Lagrangian dispersion models. Mathematically,
these models describe turbulent transport processes with stochastic
differential equations (SDEs). The computational bottleneck is the Monte Carlo
algorithm, which simulates the motion of a large number of model particles in a
turbulent velocity field; for each particle, a trajectory is calculated with a
numerical timestepping method. Choosing an efficient numerical method is
particularly important in operational emergency-response applications, such as
tracking radioactive clouds from nuclear accidents or predicting the impact of
volcanic ash clouds on international aviation, where accurate and timely
predictions are essential. In this paper, we investigate the application of the
Multilevel Monte Carlo (MLMC) method to simulate the propagation of particles
in a representative one-dimensional dispersion scenario in the atmospheric
boundary layer. MLMC can be shown to result in asymptotically superior
computational complexity and reduced computational cost when compared to the
Standard Monte Carlo (StMC) method, which is currently used in atmospheric
dispersion modelling. To reduce the absolute cost of the method also in the
non-asymptotic regime, it is equally important to choose the best possible
numerical timestepping method on each level. To investigate this, we also
compare the standard symplectic Euler method, which is used in many operational
models, with two improved timestepping algorithms based on SDE splitting
methods.
