Monte Carlo simulation of plume dispersion in the convective boundary layer

Abstract

Measurements of vertical wind velocities in the convective boundary layer (CBL) reveal that the corresponding probability density function (PDF) is positively skewed, but has a negative mode. This is a consequence of the organized motion in the CBL, characterized by updrafts and downdrafts. A Monte Carlo model for plume dispersion under these circumstances is presented. The vertical velocity PDF is expressed as the sum of two Gaussian distributions with different statistics, one for each phase of vertical motion. To characterize the variability with height of the PDF, empirical expressions for σ 2 w , the vertical velocity variance, and S 3 w , the skewness of the PDF, are constructed from measurements found in the literature. The resulting PDF is in good agreement with existing measurements. A new Monte Carlo scheme, which fulfils the requirements of the PDF, is developed. Different statistics are used when particles are in updrafts and downdrafts, respectively. The particles are reflected perfectly at the top and bottom of the CBL, and are furthermore allowed to change phase between the boundaries with a certain height dependent probability. Model predictions of crosswind integrated concentration, ground level concentration, mean particle height, and overall particle displacement for three release heights are compared with similar measurements from the water tank experiments of Willis and Deardorff (1976, 1978, 1981), and agreement between model and experiment is very good.