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 [9] 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 also confirmed by a full theoretical analysis for the simplified model problem.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:616582 |
| Date | January 2013 |
| Creators | Cook, Sarah Elizabeth |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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