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A common way to simulate the transport and spread of pollutants in theatmosphere is via stochastic Lagrangian dispersion models. Mathematically,these models describe turbulent transport processes with stochasticdifferential equations (SDEs). The computational bottleneck is the Monte Carloalgorithm, which simulates the motion of a large number of model particles in aturbulent velocity field; for each particle, a trajectory is calculated with anumerical timestepping method. Choosing an efficient numerical method isparticularly important in operational emergency-response applications, such astracking radioactive clouds from nuclear accidents or predicting the impact ofvolcanic ash clouds on international aviation, where accurate and timelypredictions are essential. In this paper, we investigate the application of theMultilevel Monte Carlo (MLMC) method to simulate the propagation of particlesin a representative one-dimensional dispersion scenario in the atmosphericboundary layer. MLMC can be shown to result in asymptotically superiorcomputational complexity and reduced computational cost when compared to theStandard Monte Carlo (StMC) method, which is currently used in atmosphericdispersion modelling. To reduce the absolute cost of the method also in thenon-asymptotic regime, it is equally important to choose the best possiblenumerical timestepping method on each level. To investigate this, we alsocompare the standard symplectic Euler method, which is used in many operationalmodels, with two improved timestepping algorithms based on SDE splittingmethods.

Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling