Multi Level Monte Carlo Methods for Atmospheric Dispersion Modelling

Abstract

The Met Office uses the NAME dispersion model to solve stochastic differential equations (SDEs) for predicting the transport and spread of atmospheric pollutants. Time stepping methods for this SDE dominate the computation time. In particular the slow convergence of the Monte Carlo Method imposes limitations on the accuracy with which predictions can be made on operational timescales. We review the theory of both the Standard and Multi Level Monte Carlo Methods, and in particular the complexity theorems discussed in [Giles, 2008] in a more general context. We then argue how it can potentially give rise to significant gains for this problem in atmospheric dispersion modelling. To verify these theoretical arguments numerically, we consider two model problems; a simplified problem which corresponds to homogeneous turbulence and is used by the Met Office for long term predictions, as well as a full non-linear model problem close to that used by the Met Office for atmospheric dispersion modelling. For both model problems we performed numerical tests in which we observed significant speed-up as a result of the implementation of the Multi Level Monte Carlo Method. The numerically observed convergence rates are alsoconfirmed by a full theoretical analysis for the simplified model problem. Several open questions, such as the correct treatment of reflective boundary conditions and the Multi Level coarsening factor, are also addressed. We present interesting preliminary numerical results which will be useful for extending the method to more realistic scenarios and hopefully allow it to be used in an operational setting in the future.

Date of Award	22 Nov 2013
Original language	English
Awarding Institution	University of Bath
Sponsors	The Met Office
Supervisor	Robert Scheichl (Supervisor) & Eike Mueller (Supervisor)