Dispersion by time-varying atmospheric boundary layers

The periods of time-varying turbulence in the atmospheric boundary layer, i.e.\ the morning and evening transitions, are often overlooked or highly idealised by dispersion models. These transitions make up a significant portion of the diurnal cycle and are known to affect the spread of pollution due to the properties of turbulence in the residual and stable layers, resulting in phenomena such as lofting, trapping, and fumigation.\\ Two main simulation techniques are presented for the purpose of modelling the dispersion of passive tracers in both convective and evening transitional boundary layers: Lagrangian stochastic (LS) modelling for 1D, inhomogeneous, non-stationary turbulence; and large-eddy simulation (LES) with a particle model tracing pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent sub-grid scale motions.\\ In the convective boundary layer, LS models more accurately representing the state of turbulence, and including the effect of skewness, are shown to produce dispersion results in closer agreement with LES. By considering individual particle trajectories, a reflective top boundary in LS models is shown to produce un-physical, sharp changes in velocity and position. By applying a correction to the vertical velocity variance based on representing the stable potential temperature gradient above the boundary layer, particles are contained within the boundary layer in a physically accurate way. \\ An LS model for predicting dispersion in time-varying, skewed turbulence is developed and tested for various particle releases in transitional boundary layers with different rates of decay, showing an improvement in accuracy compared with previous LS models. Further improvement is made by applying a correction to the vertical velocity variance to represent the effect of a positive potential temperature gradient developing over the course of the transition. Finally, a developing stable boundary layer is shown to have a significant trapping effect on particles released near the surface. \