Multilevel Monte Carlo Methods in Atmospheric Dispersion Modelling
23rd March 2018, 2:00 pm – 3:00 pm
Main Maths Building, SM3
To predict the spread and transport of atmospheric pollutants such as volcanic ash, a stochastic differential equation (SDE) has to be solved. Fast solvers are particularly important in emergency response scenarios considered by the Met Office. A prominent example is the Eyjafjallajoekull eruption in 2010 and its impact on international aviation.
Accurate predictions are achieved by reducing both the deterministic (bias) error from a finite time step size and the statistical error from Monte Carlo sampling. By using hierarchical sampling, Multilevel Monte Carlo methods achieve a significant reduction of the computational complexity of the method at a given total error tolerance.
We demonstrate the effectiveness of the method for different realistic atmospheric dispersion scenarios, which require careful treatment for boundary conditions in the lower atmosphere. We show how advanced numerical integrators based on splitting methods further reduce the computational cost by correct and stable treatment of divergent background turbulence profiles. This superior behaviour can be explained using the theory of modified equations as an alternative to proofs based on strong convergence.