Stochastic trajectory modelling of atmospheric dispersion

The stochastic trajectory-based (Lagrangian) approach has gained increasing importance and sophistication in atmospheric transport and dispersion modelling over the last few decades. State-of-the-art Lagrangian particle dispersion model (LPDMs) are used to compute trajectories of a large number of 'marked' particles and numerically simulate the dispersion of a pollutant (passive tracer) in the turbulent atmosphere. In this thesis, we mainly investigate the stochastic formulation and behaviour of LPDMs in the context of the turbulent atmospheric boundary layer (ABL). A random flight model (RFM) is a type of LPDM that describes the paths of particles of an air pollutant in a turbulent flow, given a statistical knowledge of the random velocity field. Operational RFMs such as FLEXPART have not taken advantage of modern developments of numerical methods for stochastic differential equations. Chapter 2 of this thesis aims to determine whether current numerical schemes used in operational atmospheric dispersion modelling can be improved. Several commonly used numerical schemes are investigated in a simple one-dimensional dispersion model describing the vertical turbulence in the ABL. Eulerian Fokker-Planck equation (FPE) solutions with the required level of accuracy are used to validate the performance of the RFM numerical schemes. The results allow for optimal time-step selection and recommendations to be made for use in operational models. RFMs are known to have a finite Lagrangian decorrelation time. Another class of LPDMs are the random displacement models (RDMs), which are essentially the zero decorrelation time limit of the RFMs. In Chapter 3, the problem of shear dispersion in the ABL is revisited, with the aim to improve understanding of how and why the behaviour of RFMs can differ to the RDMs. First, the effective horizontal diffusivity is examined for a tracer in the long-time dispersion in the RFM. Second, with `poison gas release' problems in mind, a large-deviation approach is used to understand in greater detail the behaviour of the concentration in the tails of the distribution. Results are verified by solving the LPDM equations numerically for a large ensemble of particles. Chapter 4 discusses methods of kernel density estimation for the optimal construction of particle concentration fields from the trajectory distributions. We demonstrate these methods on a two-dimensional advection-diffusion model (equivalent to the RDM) in a chaotic advection flow. Some well-known techniques of bandwidth selection are briefly discussed and a new approach in constructing a kernel density estimator is developed