A two-dimensional Lagrangian stochastic dispersion model for daytime conditions

Abstract

A two-dimensional (x, z) Lagrangian stochastic dispersion model is presented that is correct (i.e. fulfils the well-mixed condition) for neutral to convective conditions. The probability density function (pdf) of the particle velocities is constructed as a weighted sum of a neutral pdf (u and w jointly Gaussian) and a convective pdf (w skewed, u and w uncorrelated). The transition function ℱ varies continuously with stability and therefore ensures that the model results are not confined to a finite number of stability classes. The model is described in full detail and some sensitivity tests are presented. In particular, the role of Co, the universal constant in the Lagrangian structure function for the inertial subrange, in determining average plume characteristics is discussed. Furthermore, the evolution of average plume-height and -width is investigated for different boundary-layer stabilities ranging from ideally neutral to fully convective. Finally, the model is applied to the situation of a tracer experiment in Copenhagen, and it is shown that the measured surface-concentrations can be well simulated.