Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling

TL;DR

This paper explores the use of Multilevel Monte Carlo methods combined with improved timestepping algorithms to enhance the efficiency and accuracy of atmospheric dispersion simulations, crucial for emergency response scenarios.

Contribution

It demonstrates that MLMC significantly reduces computational costs in atmospheric dispersion modeling and compares advanced timestepping methods for optimal performance.

Findings

MLMC outperforms standard Monte Carlo in computational efficiency

Improved timestepping algorithms enhance simulation accuracy

Operational models benefit from optimized numerical methods

Abstract

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.